EFFORTS TOWARD DESIGN, DEVELOPMENT AND IMPLEMENTATION OF AN 
INTEGRATED AND FLEXIBLE SUPPORT SYSTEM FOR CALIBRATION OF  
AIR DATA ATTITUDE HEADING REFERENCE SYSTEMS  
 
 
Except where reference is made to the work of others, the work described in this thesis is 
my own or was done in collaboration with my advisory committee. This thesis does not 
include proprietary or classified information. 
 
 
______________________________________ 
Arvind Raghuraman 
 
 
 
 
Certificate of Approval: 
 
 
 
 
 
 
  
 
____________________________________ 
Thomas S. Denney Jr. 
Professor 
Electrical and Computer Engineering 
__________________________________ 
Michael E. Greene, Chair 
Professor 
Electrical and Computer Engineering 
 
___________________________________
Victor P. Nelson 
Professor 
Electrical and Computer Engineering 
 
__________________________________ 
Joe F. Pittman 
Interim Dean 
Graduate School 
EFFORTS TOWARD DESIGN, DEVELOPMENT AND IMPLEMENTATION OF AN 
INTEGRATED AND FLEXIBLE SUPPORT SYSTEM FOR CALIBRATION OF  
AIR DATA ATTITUDE HEADING REFERENCE SYSTEMS  
 
 
Arvind Raghuraman 
 
 
 
 
 
A Thesis 
Submitted to 
the Graduate Faculty of 
Auburn University 
in Partial Fulfillment of the  
Requirements for the  
Degree of  
Master of Science 
 
 
Auburn, Alabama 
May 10, 2007 
 iii 
EFFORTS TOWARD DESIGN, DEVELOPMENT AND IMPLEMENTATION OF AN 
INTEGRATED AND FLEXIBLE SUPPORT SYSTEM FOR CALIBRATION OF  
AIR DATA ATTITUDE HEADING REFERENCE SYSTEMS 
 
 
 
Arvind Raghuraman 
 
 
 
 
Permission is granted to Auburn University to make copies of this thesis at its discretion, 
upon request of individuals or institutions and at their expense. The author reserves all 
publication rights. 
 
 
 
 
 
 ___________________________ 
           Signature of Author 
 
 
 
 
___________________________ 
           Date of Graduation 
 
 
 
     
 
 
 
 
 
 
 
 iv 
VITA 
 
 
  Arvind Raghuraman was born on December 19, 1980 in Chennai, India. After 
graduating from Boston Matriculation Higher Secondary School in 1998 he attended 
Madras University, India where he received his bachelor?s degree in engineering 
specializing in instrumentation and control. On completion of his undergraduate degree, 
He worked on design, development and deployment of industrial automation solutions for 
Apna Technologies and Solutions, an alliance member of National Instruments, India, till 
July 2003. He entered graduate school at Auburn University in the fall of 2003. His 
research interests include industrial automation and control and embedded systems. 
 
 
 
 
 
 
 
 
 
 
 
 v 
THESIS ABSTRACT 
 
EFFORTS TOWARD DESIGN, DEVELOPMENT AND IMPLEMENTATION OF AN 
INTEGRATED AND FLEXIBLE SUPPORT SYSTEM FOR CALIBRATION OF  
AIR DATA ATTITUDE HEADING REFERENCE SYSTEMS 
 
 
Arvind Raghuraman 
 
Master of Science, May 10, 2007 
(Bachelor of Engineering, Madras University, Chennai, India, 2002) 
 
152 Typed Pages 
 
Directed by Michael E. Greene 
      
      An Air Data Attitude Heading Reference System is a device that provides a 
modern day Aircraft with altitude, air-speed, attitude, and magnetic parameters. A typical 
ADAHRS contains a number of tightly integrated sensors to sense the various operating 
variables required to compute these parameters.  The operation of ADAHRS greatly 
depends on the accuracy of measurements made by its sensor systems. When deployed 
for use, the accuracy of sensors is affected due to various error sources. These errors may 
be induced due to the inherent characteristics of sensors themselves or due to the ambient 
conditions the sensors operate in. It is important that the characteristics of these error 
sources are well understood and their effects mitigated using suitable correction and
 vi 
compensation schemes. In a typical ADAHRS production environment each ADAHRS 
unit has to be individually calibrated and tested to ensure its accuracy within its rated 
operating limits. The work presented in this thesis provides a commercially deployable 
calibration support system that provides an enabling framework for production line 
calibration, and acceptance testing of Air Data Attitude Heading Reference Systems.
 vii 
ACKNOWLEDGMENTS 
 
 
I take this opportunity to thank my academic advisor Dr. Edward Michael Greene 
for the guidance, motivation, inspiration and support he provided for my research and my 
master?s degree program in Auburn University. I am grateful to my research associates 
Jay, Sangram, Stephen, Victor and Karthick for the cooperation and help they extended 
for my work. I am thankful to my manager Christopher Sholler for his understanding and 
support. I wish to dedicate this degree and work to my family who made this possible. 
 
  
 
 
 
 
 
 
 
 
 
 
 
 viii 
Style manual or journal used:  IEEE 
Computer software used:  Microsoft Office System 2003 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 ix 
TABLE OF CONTENTS 
 
LIST OF FIGURES .......................................................................................................... xii 
 
LIST OF TABLES........................................................................................................... xvi 
 
1 INTRODUCTION ...................................................................................................... 1 
1.1 Introduction......................................................................................................... 1 
1.2 What is ADAHRS?............................................................................................. 2 
1.3 Background on ADAHRS: Case Study ? The AHR150A.................................. 4 
1.4 Need for Calibration in ADAHRS...................................................................... 8 
1.5 Existing IMU and ADS Sensor Calibration Methods......................................... 9 
1.6 Need for a Comprehensive Calibration Support System for ADAHRS ........... 13 
1.7 Proposed system - ADAHRS Calibration Support System .............................. 17 
1.8 Goals and Contributions ................................................................................... 19 
1.9 Thesis Organization .......................................................................................... 20 
 
2 ADAHRS CALIBRATION METHOD AND PROCESS........................................ 21 
2.1 Overview........................................................................................................... 21 
2.2 Inertial Measurement Unit  (IM3) ..................................................................... 22 
2.3 ADXL210E MEMS Accelerometer Sensor...................................................... 24 
2.4 ADXRS150 MEMS Gyro Sensor ..................................................................... 25 
2.5 Air Data System................................................................................................ 26 
2.5.1 Model 1230 Piezo-Resistive Pressure Sensor........................................... 27 
2.6 IMU ? Error Sources......................................................................................... 28 
2.6.1 Accelerometer Temperature Drift............................................................. 28 
2.6.2 Accelerometer Offset and Scale factor ..................................................... 29 
2.6.3 Cross-Axis Error ....................................................................................... 29 
2.6.4 Gyroscope Errors ...................................................................................... 29 
2.6.5 Gyroscope Temperature Drift................................................................... 30 
2.6.6 Gyroscope Scale Factor and Offsets......................................................... 31 
2.6.7 Gyroscope Scale-Factor Non-Linearity .................................................... 32 
2.6.8 Gyroscope Scale Factor Dependency on Temperature............................. 33 
2.7 Air Data System (ADS) ? Error Sources .......................................................... 34 
2.7.1 Pressure Sensor Temperature Drift........................................................... 34 
2.7.2 Offset and Scale Factor............................................................................. 35 
2.7.3 Scale Factor Non-Linearity....................................................................... 36
 x 
2.7.4 Offset and Scale-Factor Dependency on Temperature ............................. 37 
2.8 IMU calibration - Method and Process............................................................. 38 
2.8.1 IMU Thermal Calibration ......................................................................... 38 
2.8.2 Accelerometer Offset and Scale Factor Calibration ................................. 41 
2.8.3 Gyroscope Scale Factor Calibration ......................................................... 48 
2.8.4 Accelerometer and Gyroscope Cross-Axis Calibration............................ 51 
2.9 ADS Calibration Method - Method and Process .............................................. 54 
2.9.1 Ps and Pt Pressure Sensor Calibration Method......................................... 54 
 
3 ADAHRS CALIBRATION SYSTEM DESIGN AND IMPLEMENTATION ....... 57 
3.1 Chapter Overview ............................................................................................. 57 
3.2 IMU Calibration System - Layout and Description.......................................... 58 
3.2.1 Rate Table ................................................................................................. 59 
3.2.2 Environmental Chamber ........................................................................... 60 
3.2.3 Four Port RS232 to USB Converter.......................................................... 60 
3.2.4 Calibration Computer................................................................................ 61 
3.3 ADS Calibration System - Layout and Description.......................................... 61 
3.3.1 Environmental Chamber ........................................................................... 62 
3.3.2 DRUCK 403 Air Data Test System.......................................................... 62 
3.4 LabVIEW Application Development Platform ................................................ 63 
3.5 IMU Calibration System Application Software................................................ 64 
3.6 IMU Calibration System Requirements............................................................ 69 
3.7 IMU Calibration System ? Application Software Implementation .................. 71 
3.7.1 Main Module............................................................................................. 71 
3.7.2 IMU Calibration Communications Setup Module.................................... 72 
3.7.3 Thermal Calibration Module..................................................................... 74 
3.7.4 IMU Sensor Calibration Module .............................................................. 83 
3.8 ADS Calibration System ? Application Software ............................................ 93 
3.9 ADS Calibration System Application Software Requirements ........................ 97 
3.10 ADS Calibration System ? Application Software Implementation .................. 99 
3.10.1 ADS Calibration Communications Setup ................................................. 99 
3.10.2 ADS Burn-in Module.............................................................................. 102 
3.10.3 ADS Calibration Module ........................................................................ 109 
 
4 ADAHRS CALIBRATION SUPPORT SYSTEM TESTING AND RESULTS... 118 
4.1 Chapter Overview ........................................................................................... 118 
4.2 IMU Calibration System Results .................................................................... 118 
4.2.1 IMU Thermal Calibration ....................................................................... 118 
4.2.2 IMU Accelerometer Offset and Scale Factor Calibration....................... 120 
4.2.3 IMU Gyroscope Scale Factor Calibration............................................... 122 
4.2.4 IMU Cross-Axis Calibration................................................................... 122 
4.2.5 IMU Sensor Calibration Acceptance Test .............................................. 124 
4.3 ADS Calibration System Results.................................................................... 128 
 xi 
4.3.1 ADS Sensor Calibration.......................................................................... 128 
4.3.2 ADS Sensor Calibration Acceptance Test .............................................. 129 
 
5 CONCLUSION....................................................................................................... 131 
REFERENCES????????????????????????????133  
 xii 
LIST OF FIGURES 
 
 
Figure 1: Role of ADAHRS in an aircraft .......................................................................... 3 
Figure 2: AHR150A, a product of Archangel Systems Inc ................................................ 4 
Figure 3: AHR150A architecture........................................................................................ 5 
Figure 4: Optical tracking system..................................................................................... 11 
Figure 5: ADAHRS calibration support instruments........................................................ 18 
Figure 6: IM3 hardware layout ......................................................................................... 22 
Figure 7: Inertial Measurement Cube - IM3. (a) Accelerometer triad mounting, (b) IM3. 
(c) Gyroscope triad mounting ........................................................................................... 23 
 
Figure 8: ADXL210E PWM output.................................................................................. 25 
Figure 9: ADS hardware layout ........................................................................................ 26 
Figure 10: Accelerometer temperature drift.. ................................................................... 28 
 
Figure 11: Gyroscope temperature drift............................................................................ 31 
 
Figure 12: Gyroscope scale factor non-linearity............................................................... 32 
 
Figure 13: Gyro scale factor dependency on temperature.. .............................................. 33 
 
Figure 14: Pressure sensor temperature drift.. .................................................................. 35 
 
Figure 15: Pressure sensor scale factor non-linearity.. ..................................................... 36
 xiii 
Figure 16: Pressure sensor scale factor dependency on temperature................................ 37 
 
Figure 17: Thermal profile used for IMU calibration....................................................... 39 
Figure 18: The six orientations used for IMU calibration. ............................................... 45 
Figure 19: Z- Axis accelerometer calibration data. .......................................................... 46 
Figure 20: X-Axis accelerometer calibration data............................................................ 47 
Figure 21: Y-Axis accelerometer calibration data............................................................ 48 
Figure 22: Gyro scale factor non-linearity calibration data.............................................. 50 
 
Figure 23: Gyro scale factor non-linearity curve-fit,........................................................ 51 
 
Figure 24: Altitude sensor calibration data....................................................................... 56 
 
Figure 25: IMU calibration system layout........................................................................ 58 
Figure 26: IDEAL-Aerosmith rate table/ rate table with environmental chamber ........... 59 
Figure 27: ADS calibration system layout........................................................................ 61 
Figure 28: DRUCK 403 ADTS......................................................................................... 63 
Figure 29: Software modules involved in IMU calibration process................................. 66 
Figure 30: Main GUI ........................................................................................................ 72 
Figure 31: IMU communications setup GUI .................................................................... 73 
Figure 32: Communications setup module flowchart....................................................... 74 
Figure 33: Download thermal profiles GUI...................................................................... 76 
Figure 34: Download thermal profiles flowchart-I........................................................... 77 
Figure 35: Download thermal profiles flowchart-II.......................................................... 78 
Figure 36: Profile download process flowchart................................................................ 79 
Figure 37: IMU thermal calibration GUI.......................................................................... 80 
Figure 38: IMU thermal calibration.................................................................................. 81 
 xiv 
Figure 39: IMU thermal calibration result generation GUI.............................................. 82 
Figure 40: Thermal calibration flowchart......................................................................... 83 
Figure 41: IMU sensor calibration setup GUI .................................................................. 84 
Figure 42: IMU sensor calibration setup flowchart .......................................................... 85 
Figure 43: IMU sensor calibration GUI............................................................................ 87 
Figure 44: IMU sensor calibration flowchart - I............................................................... 88 
Figure 45: IMU sensor calibration flowchart - II.............................................................. 89 
Figure 46: IMU sensor calibration flowchart ?III............................................................. 90 
Figure 47: IMU sensor calibration flowchart - IV............................................................ 91 
Figure 48: IMU sensor calibration result generation GUI................................................ 92 
Figure 49: IMU sensor calibration result generation flowchart........................................ 93 
Figure 50: ADS calibration process.................................................................................. 95 
Figure 51: ADS communications setup GUI.................................................................. 100 
Figure 52: ADS communications setup flowchart.......................................................... 101 
Figure 53: WATLOW series 942 programmer GUI....................................................... 103 
Figure 54: WATLOW programmer flowchart................................................................ 104 
Figure 55: ADS burn-in GUI .......................................................................................... 106 
Figure 56: ADS burn-in flowchart.................................................................................. 107 
Figure 57: ADS burn-in validation GUI ......................................................................... 108 
Figure 58: ADS burn-in flowchart.................................................................................. 109 
Figure 59: ADS calibration setup GUI ........................................................................... 110 
Figure 60: ADS calibration setup flowchart ................................................................... 111 
Figure 61: ADS calibration GUI..................................................................................... 113 
 xv 
Figure 62: ADS calibration flowchart............................................................................. 114 
Figure 63: ADS calibration components flowchart ........................................................ 115 
Figure 64: ADS result generation ................................................................................... 117 
Figure 65: IMU thermal calibration data, temperature cycle used was from -20 ?C to +65 
?C. Plots 1, 2, and 3, show the gyro measurements (gx, gy and gy) in counts scaled by a 
division factor 20972 [9] on Y-axis. Plots 4, 5, 6, 7, 8 and 9, show the accelerometer 
measurements (az1, ax1, ay1, az2, ax2, and ay2) in pulse width scaled by a multiplication 
factor of 25 [8]. X-axis represents time (not to scale). ................................................... 119 
 
Figure 66: Accelerometer calibration acceptance test, delta velocities acquired in 
orientations 11, 21 and 31 are shown. Delta velocity unit in m/s. X-axis represents time 
(not to scale).................................................................................................................... 124 
 
Figure 67: Gyroscope calibration acceptance test, delta angles acquired at rates -150 ?/s, -
100 ?/s, -50 ?/s, 0 ?/s, 50 ?/s, 100 ?/s, and 150?/s,  in orientations 11, 21 and 31 are shown. 
Delta angle unit in degrees. X-axis represents time (not to scale).................................. 126 
 
Figure 68: IMU thermal calibration acceptance test, conducted between -20 ?C and +65 
?C, in orientation 31. Plots 1,2, and 3 shows delta roll angle, pitch angle and yaw angle 
on Y-axis in degrees. Plots 3,4, and 5 show delta velocities along X, Y and Z axis along 
Y-axis in m/s. X-axis represents time (no to scale). ....................................................... 128 
 
Figure 69: ADS altitude error observed at reference altitudes between 0 feet to 12000 feet 
at 1000 feet increments. At temperatures 25 ?C, 45 ?C, and 65 ?C................................ 130 
 xvi 
LIST OF TABLES 
 
 
Table 1: IMU inertial measurement accuracy table.......................................................... 14 
Table 2: ADS altitude accuracy table ............................................................................... 14 
Table 3: ADS air-speed accuracy table............................................................................. 15 
Table 4: ADAHRS operating limits table......................................................................... 15 
Table 5: ADAHRS temperature specifications................................................................. 15 
Table 6: ADXL210E specifications, from Analog Devices data sheet [8]....................... 25 
Table 7: ADXRS150 specifications, from Analog Devices data sheet [9]....................... 26 
Table 8: IMU calibration application modules and sub-modules..................................... 65 
Table 9: Steps supported in IMU calibration sequence .................................................... 67 
Table 10: IMU calibration application software system requirements............................. 69 
Table 11: ADS calibration application software module and sub-modules ..................... 96 
Table 12: ADS calibration application software requirements......................................... 97 
Table 13: Computed thermal calibration constants for data shown in Figure 65, a          
2nd-order polynomial fit was used................................................................................... 120 
 
Table 14: Mean of accelerometer measurements acquired under orientations 11, 12, 21, 
22, 31, and 32 are shown. Temperature compensated accelerometer measurement unit in 
pulse width...................................................................................................................... 121 
 
Table 15: Computed accelerometer offsets for data shown in Table 14. Eq. (12) was used 
to compute the offsets. .................................................................................................... 121 
 
Table 16: Computed accelerometer scale factors for data shown in Table 14. Eq. (12) was 
used to compute the scale factors.................................................................................... 121
 xvii 
Table 17: Mean of gyro measurements taken at the chosen rates; -150 ?/s, -100 ?/s,     -50 
?/s, 0 ?/s, 50 ?/s, 100 ?/s, and 150 ?/s in orientations 11, 21 and 31. Temperature 
compensated gyro measurement unit in counts. ............................................................. 122 
 
Table 18: Computed gyro scale factor constants for data shown in Table 17 a 3rd-order 
polynomial fit was used to compute the scale factor constants. ..................................... 122 
 
Table 19: IMU cross-axis calibration, mean of delta velocities obtained in orientations 11, 
21 and 31 are shown. Delta velocity unit in m/s............................................................. 123 
 
Table 20: IMU cross-axis calibration, mean of delta angles obtained in orientations 11, 21 
and 31 are shown. Delta angle unit in degrees................................................................ 123 
 
Table 21: Mean of delta velocities in orientations 11, 21 and 31. Delta velocity unit in 
m/s................................................................................................................................... 125 
 
Table 22: Mean of delta angles in orientation 11 acquired at rates -150 ?/s, -100 ?/s, -50 
?/s, 0 ?/s, 50 ?/s, 100 ?/s, and 150 ?/s. Delta angle unit in degrees.................................. 126 
 
Table 23: Mean of delta angles in orientation 21 acquired at rates -150 ?/s, -100 ?/s, -50 
?/s, 0 ?/s, 50 ?/s, 100 ?/s, and 150 ?/s. Delta angle unit in degrees.................................. 126 
 
Table 24: Mean of delta angles in orientation 31 acquired at rates -150 ?/s, -100 ?/s, -50 
?/s, 0 ?/s, 50 ?/s, 100 ?/s, and 150 ?/s. Delta angle unit in degrees.................................. 127 
 
Table 25: Computed surface fit constants....................................................................... 129 
 
 
 1 
1 INTRODUCTION 
 
1.1 Introduction  
This thesis provides a detailed description of efforts toward design, development 
and implementation of an integrated and flexible calibration support system for Air Data 
Attitude Heading Reference Systems (ADAHRS). A number of published sensor 
calibration methods have been reviewed, and a tool has been developed and implemented 
to realize a comprehensive method and process for ADAHRS calibration. An ADAHRS 
is a distributed multi-processor embedded system composed of independent sub-systems, 
such as, an Inertial Measurement Unit (IMU), an Air Data System (ADS), and a 
Magnetic Sensing Unit (MSU). The sensor systems employed by these sub-systems are 
composed of a number of uniquely different sensors: the inertial measurement unit 
employs tri-axial accelerometers and tri-axial gyroscopes, the air data system employs 
static and differential piezo-resistive pressure sensors, and the magnetic sensing unit 
employs tri-axial magnetometers and bi-axial accelerometers. The operation of each of 
the stand-alone sub-systems and the ADAHRS as a whole greatly depend on the accuracy 
of measurements made by these sensors. The accuracy of ADAHRS sensors is affected 
by a number of error sources. These errors may be induced due to the inherent 
characteristics of sensors themselves or due to the ambient conditions in which the 
sensors operate. Since these errors are unique to a given sensor, in a typical production 
 2 
environment, each ADAHRS unit has to be individually calibrated and tested for its 
accurate operation within its rated operating limits. The calibration support system 
presented in this thesis provides a flexible framework that will enable the developer to 
study and characterize the sensor error sources, experiment with different sensor 
calibration strategies for error correction and compensation, and evaluate the 
effectiveness of calibrations performed with relevant acceptance tests. Once satisfactory 
results are obtained with a chosen calibration strategy the user can freeze the system 
configuration and deploy it for production line calibration and testing of each individual 
ADAHRS unit. The organization of this chapter is given as follows: Section 1.1 gives a 
brief introduction to ADAHRS and its commercial applications. Section 1.2 gives an 
overview of the ADAHRS, its components and their functionality. Section 1.3 discusses 
the need for calibration in ADAHRS. Section 1.4 presents a literature review of existing 
calibration methods. Section 1.5 discusses the need for a comprehensive calibration 
support system for ADAHRS. Section 1.6 presents the proposed calibration support 
system. Section 1.7 presents the goals and contributions achieved. Section 1.8 presents 
the organization of this thesis. 
1.2 What is ADAHRS?  
An Air Data Attitude Heading Reference System (ADAHRS) is an integral part of 
a modern aircraft?s flight control and navigation systems as well as pilot instrumentation 
such as an Electronic Flight Information System (EFIS). It provides vital flight 
parameters like body lateral acceleration, body longitudinal acceleration, body normal 
acceleration, body pitch rate, body roll rate, body yaw rate, magnetic heading, pitch 
 3 
angle, roll angle, inertial pitch rate, inertial roll rate, along heading acceleration, cross 
heading acceleration, altitude, altitude rate, computed air-speed, mach, true air-speed, 
total air temperature and baro-corrected altitude [2]. The ADAHRS provides the 
combined functionality of three traditional flight systems: an air data system that provides 
an aircraft?s altitude and air speed parameters, an inertial measurement unit that measures 
linear accelerations and rotation rates which are used to calculate an aircraft?s pitch, roll 
and yaw parameters, and a magnetic sensing unit that measures the magnetic field along 
the three axes and provides the magnetic heading for an aircraft. A typical ADAHRS is 
an a integral part of an aircrafts fly-by wire system, driving vital aircraft components like 
primary flight displays (PFD), navigation displays and autopilots, making it the heart of 
an aircraft?s electronic flight instrumentation system, as shown in Figure 1. ADAHRS 
finds its applications throughout aviation from single engine to multi engine propeller 
general aviation aircraft, turbine business aircraft, helicopters, air transport craft and in 
military aircraft worldwide [1].  
 
Primary Flight Display
PFD
Navigation Display
Flight Auto-Pilot
Inertial Measurement Unit
IMU
Air Data System
ADS
Magnetic Sensing Unit
MSU
ADAHRS
 
Figure 1: Role of ADAHRS in an aircraft. 
 
 4 
1.3 Background on ADAHRS: Case Study ? The AHR150A 
The ADAHRS system considered in this thesis for development of the ADAHRS 
support system is the AHR150A air data and attitude heading reference system, a product 
of Archangel Systems Inc, USA [2]. In modern ADAHRS systems, a combination of 
attitude heading with air data is used to obtain robust inertial solutions. The AHR150-A 
is one such system [1]. The AHR150A is a complete avionics attitude and air data sensor 
system composed of hardware and software. The system is composed of two boxes: an 
AHR150A-1 Inertial Sensing Unit (ISU) and an AHR150A-2 Magnetic Sensing Unit 
(MSU) [2], which are shown in Figure 2(a) and 2(b), respectively. The architecture of the 
AHR150A system is shown in Figure 3. The AHR150A communicates to the external 
world via a dedicated bi-directional ARINC bus through which the inertial solutions are 
transmitted to the flight computers. ARINC is a communication standard for instrument 
communication in aircrafts [11]. An RS 232 compliant maintenance port is provided for 
diagnostics and calibration. The AHR150A also provides sensor interface ports for static 
pressure sensor, pitot pressure sensors and the outside air temperature (OAT) sensor.  
       
(a) (b) 
Figure 2: AHR150A, a product of Archangel Systems Inc. 
 5 
Inertial Measurement Unit
dsPIC 6012
IMU
3 Accelerometers, 3 Gyros
Computes FLASP solution from
sensor data.
Air Data System
dsPIC 6012
ADS
Pitot & Static pressure sensors
Computes Air Data Solution from
sensor data.
Core Processing Element
TI TMS320C6713
DSP
Computes FLASP solution from
IMU data and validates it.
Computes Air Data solution from
ADS data and validates it
I/O Processor
dsPIC 6012
IOP
ARINC Xceivers, RS 232 Xceivers
Transmits ARINC data
AHR150A-2
MSU
3-axis Magnetometers, 2-axis
accelerometers
Provides Magnetic heading
Pt Ps OAT
Calibration and
Maintenance port
Discrete's
ARINC bus
AHR150A-1 (ISU)
 
 
Figure 3: AHR150A architecture. 
 6 
The ISU contains multiple embedded subcomponents: Inertial Measurement Cube 
(IM3), Air Data System (ADS), Digital Signal Processor (DSP), and Input Output 
Processor (IOP).The components of the ISU are explained as follows. 
The IM3 measures tri-axial accelerations and tri-axial angular rotation rates.  It 
consists of solid state strap down MEMS gyros, MEMS accelerometers, temperature 
sensors, power/signal conditioning circuitry and a digital signal programmable interface 
controller (dsPIC) for computing the accelerations and angular rotation rates along the 
X,Y and Z axes. The IMU acquires data from the sensors and executes an advanced 
Fuzzy Logic Adaptive Signal Processing (FLASP) corrective algorithm to ensure the 
correctness of the inertial attitude solution. It outputs the sampled accelerometer, gyro 
and sensor temperature data along with the computed inertial solution to the main DSP 
where the solution is recomputed and validated with dissimilar software.  
The ADS measures and transmits air pressure data, which is used to derive the 
altitude and airspeed of an airborne system. It consists of pitot and static pressure sensors, 
power and signal conditioning circuitry, and a dsPIC for computing the air data solutions. 
The ADS transmits solution parameters like: mach number, altitude, true air speed, total 
air temperature, and the sampled sensor data to the DSP. The DSP recomputes and 
validates the solution parameters with dissimilar software. Non-conforming solutions by 
either or both of the subsystems generate a fault which is used to ensure measurement 
integrity.  
The Input Output Processor (IOP) serves as the bridge between the AHR150A 
and the other flight systems. It obtains various solution parameters from the DSP 
processor and transmits it over several ARINC 429 busses [2].  The IOP contains ARINC 
 7 
interface drivers and a dsPIC for synchronizing and coordinating the communication 
between the AHR150A system and the flight computer. The IOP also monitors the fault 
lines from the various subcomponents to assert the ARINC fault line.  
The DSP is the core processing element. It is responsible for acquisition, 
verification, and validation of inertial, altitude and air speed solutions computed by the 
system sub-components. It consists of an external flash memory, program memory, 
communication peripherals and a TI TMS320C6713 DSP for performing the above 
mentioned functions. The DSP contains an RS232 maintenance port, which serves as a 
communication window between the AHR150A system and external support systems for 
testing, and calibration. 
The AHR150A-2 consists of a three-axis magnetic sensor to measure the tri-axial 
magnetic flux, a two-axis accelerometer to measure the acceleration along the X and Y 
axis, associated analog interface circuitry, power conditioning, and a PIC16C773 micro-
controller for computing the magnetic heading [5]. The MSU remotely transmits the 
magnetic heading data for the computation of inertial solutions. The AHR150A-2 outputs 
magnetic field strength on an RS422 bus at 100 Hz [5]. 
The IMU and ADS sub-components described above are dealt with in detail in the 
following chapters. The IOP and the IMU communicate with the DSP through a 
dedicated Serial Peripheral Interface (SPI) bus and the ADS communicate with the DSP 
through an UART interface. The ADS unit is calibrated after system integration of the 
AHR150A through the maintenance port, while the IMU and MSU are calibrated 
independently before integration. 
 8 
1.4 Need for Calibration in ADAHRS 
In the inertial measurement unit, the tri-axial linear acceleration and rotation rate 
measurements made by the MEMS accelerometers and gyroscopes are integrated with 
respect to time to determine the inertial parameters such as pitch, roll and yaw. As a 
consequence of this time integration even small errors induced by the inertial sensors can 
propagate with an unbounded growth leading to serious system inaccuracies [6].  The 
accelerometers and gyroscope sensors used in the IMU are plagued by sensor offset and 
scale factor errors caused by inherent sensor design inconsistencies and cross-axis errors 
caused by device-mounting imperfections. They are also susceptible to thermal drift 
errors induced by operating ambient temperature conditions [8, 9]. In addition to these 
errors, the gyroscope scale factor exhibits non-linearity over the measurement span and a 
dependency on operating ambient temperature [16]. The nature of these sensor errors has 
to be studied and error models have to be developed for the prominent error sources. 
Suitable calibration strategies have to be devised for correction and compensation of 
modeled errors and the measurement accuracy using the devised strategy has to be 
verified with suitable acceptance tests in order to evaluate the effectiveness of calibration. 
In the air data system, the PC board mountable piezo-resistive silicon pressure 
sensors used for measurement of static and pitot pressures are affected by sensor thermal 
drift errors, offsets and scale factor errors, scale factor non-linearity errors, errors caused 
by scale factor dependency on temperature, errors caused by measurement hysteresis, and 
errors caused by temperature hysteresis. These error sources need to be thoroughly 
investigated and suitable calibration techniques should be adopted to get the ADS system 
to perform within the error budget specified by the relevant ARINC706-4 standard [11].  
 9 
The magnetic sensing unit present in the ADAHRS employs MEMS 
accelerometers and magnetometers for measurement of X and Y axis accelerations and 
the tri-axial magnetic flux, respectively.  The accelerometers suffer from errors due to 
sensor scale factor and thermal drifts, while the magnetometers need to be calibrated for 
sensor scale factor. The ADAHRS support system presented in this thesis does not 
provide calibration support for the MSU calibration. [10] presents a comprehensive 
calibration system for calibration of the MSU. 
1.5 Existing IMU and ADS Sensor Calibration Methods  
Various methods and algorithms have been proposed for calibration of 
accelerometer triads. Lukowicz et al [12] proposed an automatic accelerometer 
calibration method that uses earth?s acceleration due to gravity g as a known acceleration 
reference. In this method, the IMU accelerometer triad measurements are taken in six 
random, significantly different positions under a precondition that the accelerometers are 
perfectly orthogonal to each other. Under this premise, when measurements are taken in 
six orientations with no dynamic acceleration effects, Eq.(1) stands true. 
 1)( 222 =++=? zyxX  
 
)1(  
 
Where x , y  and z  are acceleration components measured along the X, Y and Z axes 
respectively. The general equation for acceleration measured along an axis, say X-axis is 
given by Eq.(2). 
 xxx aSOx ?+=  )2(  
 
 10 
Where xO  is the offset, xS  is the scale factor, x  is the calibrated measurement and xa  is 
the un-calibrated measurement for the X-axis accelerometer. Substituting Eq.(2) in (1) we 
get, 
 1)/)(()/)(()/)(( 222 =?+?+?
zxzyyyxxx SOasOaSOa
 
 
)3(  
 
From Eq.(3), we have six unknowns zyxzyx SSSOOO ,,,,, . With measurements taken in 
six random orientations we will have a system of six equations which can be solved to 
obtain the unknowns. In this method, care should be taken to make sure that the six 
orientations are significantly different to ensure convergence while solving the equation 
system. Axes orthogonality is a mandatory precondition for this method. Since sensor 
mounting in an IMU triad can never be truly orthogonal, this method will fail for 
ADAHRS IMU calibration. 
Hung et al [13] presented a calibration algorithm similar to [12] that uses earth?s 
acceleration due to gravity g as a known acceleration reference. In this method, IMU 
accelerometer triad measurements are taken in 12 predefined positions [13]. The 
measured quantity is the earth?s gravity and the triad measurement is the vector sum of 
outputs of the x, y, and z axes accelerometers. The accelerometer error model considered 
in this paper consists of three bias uncertainties ),,( zyx BBB , three scale factor 
constants ),,( zyx KKK , three dis-symmetry constants ),,( zyx DSDSDS  and three non-
orthogonality constants ),,( zyzxyx NONONO , where x, y and z are the respective 
coordinate axes. The 12 unknowns of the triad?s error model can be obtained by solving 
the system of 12 equations obtained from the 12 position test. In order for the 12 position 
test to be effective, the IMU should be accurately and precisely placed in the 12 
 11 
predetermined positions mentioned in [13]. This method is not very well suited for a 
production line calibration, since mechanical automation will require an elaborate test jig 
design, making the system complicated and expensive. 
Golnaraghi et al [15] proposed an accelerometer triad calibration method that is 
relatively more expensive to implement, but highly efficient in terms of calibration time. 
A standard calibration run takes about half a minute. This method requires an optical 
tracking system, shown in Figure 4, which will measure the true translational and 
rotational kinematics of the IMU. Three tracking LED?s are attached to the corners of the 
IMU to enable the cameras present in the optical tracking system to track the motion of 
the IMU, as shown in Figure 4. A typical calibration run involves accelerating the IMU in 
six degrees of freedom and acquiring the IMU output simultaneously. The optical 
tracking system tracks and records the position of the IMU throughout the duration of this 
process. In order to calibrate the gyros the IMU is rotated in all six degrees of freedom at 
an angular rate of 90 ?/s while the IMU output is acquired. 
 
Figure 4: Optical tracking system. 
 12 
On completion of the calibration process a non-linear least squares algorithm, 
presented in this paper, is used to determine the accelerometer and gyro offsets and scale 
factors. The infrastructure required to implement this method for mass IMU calibration is 
quite complicated and expensive. Automation of this method drives the costs even higher.  
Krohn et al [14] proposed a simple six-position rotational calibration method for 
calibration of accelerometer triads. This is the chosen method for IMU accelerometer 
calibration in this thesis. The method and process are clearly explained under Section 2.6. 
Although axis orthogonality is a precondition for this method, cross-axis calibration 
explained under Section 2.6 compensates for any axis misalignments. 
Ojeda et al [16] presented a gyro calibration method that employs a rate table to 
provide known reference angular rates to the IMU. The gyroscopes present in the IMU 
are calibrated with respect to this known reference. This is the chosen method for IMU 
gyroscope calibration in this thesis. This method, published for calibrating fiber-optic 
gyros, will be employed to calibrate MEMS gyros used in the IMU. The algorithms used 
and implementation of this method are explained in detail in Section 2.6.   
 In order to calibrate the pressure sensors used in the air data system, one of the 
commonly practiced methods to compensate for scale factor nonlinearity and temperature 
dependency is implemented using a look-up table approach. The behavior of a pressure 
sensor under various temperatures at different regions of the measurement span is 
captured and implemented as a look-up table. During operation, the altitude and air-speed 
measurement is obtained from the look-up table based on the current temperature and 
pressure measurements. 
 13 
Reynolds et al [21] presented a methodology to calibrate pressure sensors to 
compensate for their scale factor non-linearity and scale-factor dependency on 
temperature. The method proposed involves subjecting the pressure sensors to known 
altitude and airspeed inputs over the operating measurement range to capture scale factor 
non-linearity. This procedure is repeated at a number of equidistant points on the 
operating temperature span to capture the scale factor dependency on temperature. Data 
is continuously acquired and logged during this procedure. A 3-D polynomial least-
squares curve fit was used to fit the measured pressure data and temperature data to the 
true altitude reference and air-speed reference used during calibration. The ADS 
calibration system implemented in this thesis provides a modular framework to 
implement this procedure. 
1.6 Need for a Comprehensive Calibration Support System for ADAHRS  
A typical ADAHRS that can be deployed for commercial avionic applications 
should comply with a number of rigorous specifications. Typical technical specifications 
required for an ADAHRS unit will include data accuracy, operating limits and 
environmental specifications. Tables 1, 2, 3, 4 and 5 show the technical specifications for 
a typical ADAHRS unit in compliance with FAA TSO standards. From the previous 
discussion in Section 1.4, it is seen that the scale factors for some of the sensors are non-
linear over the measurement span and dependent on the operating temperature conditions. 
A comprehensive calibration system for ADAHRS should provide a mechanism to ensure 
data accuracy over the operating temperature range and measurement span. All 
calibration methods presented in Section 1.5, except [15], might satisfy the calibration 
 14 
requirements for a particular ADAHRS sensor, but are not comprehensive enough to 
calibrate all ADAHRS sensors to operate within their rated measurement span and 
operating temperature range. The method proposed in [15] is complicated to implement 
for mass production of ADAHRS and relatively more expensive. In addition this method 
does not account for any environmental effects.  Currently, there are no calibration tools 
that are commercially available that provide a comprehensive and integrated framework 
for calibration of ADAHRS.  
 
Table 1: IMU inertial measurement accuracy table 
 
Parameter Specification 
Inertial angles Magnetic heading < 0.1?, pitch and roll < 0.01? 
Inertial rates Pitch, roll, yaw and turn rate < 0.015?/s 
Body rates Pitch, roll and yaw < 0.015?/s 
Accelerations Along X, Y, and Z axes is 1.0 mg 
 
 
Table 2: ADS altitude accuracy table 
 
Altitude (feet) Accuracy (feet) 
-1000 feet to Sea level ? 15 
At 10,000 ? 15 
At 30,000 ? 20 
At 50,000 ? 80 
 
 
 
 
 15 
Table 3: ADS air-speed accuracy table 
 
Air-speed (knots) Accuracy (knots) 
At 60  ? 5  
At 100 ? 2 
At 300 ? 1 
At 450 ? 1 
 
Table 4: ADAHRS operating limits table 
 
Parameter Specification 
Rates ?150?/s (-A), ?300?/s (-B) 
Accelerations ?10 g (-A), ?18 g (-B) 
Altitude -1000 feet to 50000 feet 
Airspeed 30 knots to 450 knots 
 
Table 5: ADAHRS temperature specifications 
 
Parameter Specification 
Temperature -40 ?C to +85 ?C 
 
 
In a complex measurement system like the ADAHRS, the sensor error models 
considered for each of the sensors employed model only some of the more prominent 
error sources. There are always error sources that are not considered which are typically 
deemed negligible. In a typical industrial product development environment, the 
ADAHRS development process might involve many design iterations that investigate 
these error sources and their effects on measurement accuracy. Various error correction 
 16 
and compensation strategies may have to be evaluated in order to reach an error 
compensation scheme that provides a perfect balance between computational overhead 
and measurement accuracy. Considering these factors, an ideal ADAHRS calibration 
support system should possess the following characteristics. 
 
? It should provide the developer a flexible framework that will enable him or her to 
perform sensor error modeling by studying various aspects of sensor behavior in its 
operating environment.  
? It should provide an infrastructure to execute preliminary burn-in tests in order to 
reduce ADAHRS infant-mortality rate. 
? It should provide a flexible framework to investigate various calibration, error 
correction and compensation strategies to account for the modeled errors.  
? It should provide a test infrastructure to evaluate the effectiveness of calibration 
performed with suitable acceptance tests. 
? It should implement a calibration method that is simple and effective. 
? It should provide an integrated platform that would optimize the production 
economics and time to market.  
 
The absence of published calibration methods that are comprehensive in nature, or 
commercially available tools that satisfy the characteristics required by an ideal 
ADAHRS calibration support system, provides the motivation for the work presented in 
this thesis. 
 17 
1.7 Proposed system - ADAHRS Calibration Support System 
The calibration and support framework proposed in this thesis provides a simple 
and cost effective platform for sensor characterization, sensor calibration, and acceptance 
testing of various sensors used in the IMU and ADS. The proposed system will be 
commissioned for use in a real ADAHRS research, development and production 
environment. In order to develop an ADAHRS calibration system characterized by the 
features presented in Section 1.6, the calibration application has been implemented as a 
robust state-machine that executes a calibration sequence of the user?s choice. The 
proposed system provides the user a powerful and intuitive Graphical User Interface 
(GUI) which enables him to create a customized calibration sequence composed of a 
number of configurable steps. Each of these steps performs a particular calibration 
function. By sequencing these steps in different combinations, sensor characterization, 
sensor calibration and calibration acceptance testing sequences can be realized and 
implemented. A single generic framework able to perform the functions necessary to 
satisfy the system characteristics presented in Section 1.6 results in a highly productive 
ADAHRS calibration support system. The ADAHRS calibration and support system is 
composed of both hardware and software. The software component, referred to as the 
ADAHRS calibration support software, enables a user to implement the desired 
procedure through a flexible, powerful and intuitive graphical user interface. The 
hardware component is composed of a number of support instruments that provide 
various calibration services required by the ADAHRS calibration support software, as 
illustrated in Figure 5. The ADAHRS calibration support software runs on a dedicated 
calibration computer. It essentially controls and sequences the operations of the support 
 18 
instruments in order to implement the ADAHRS calibration procedure that will be 
discussed in Chapter 2.  
 
Ideal Aerosmith thermal chamber
and Rate table assembly
-for IMU Thermal calibration
and sensor calibration
Tenney Junior thermal chamber
-for ADS Thermal calibration
DRUCK 403 Air Data Test System
-for ADS sensor calibration
Calibration computer
- running the ADAHRS calibration
system application software
 
 
Figure 5: ADAHRS calibration support instruments. 
 
The ADAHRS calibration support software consists of two components, the IMU 
calibration support system, and the ADS calibration support system. The IMU calibration 
support system supports burn-in, sensor calibration, thermal calibration and acceptance 
 19 
testing for the MEMS accelerometers and gyros used in the inertial measurement unit. 
The ADS calibration and support system provides burn-in, sensor calibration, thermal 
calibration, and acceptance testing for pressure sensors used in the air data system. In 
addition to their calibration functions, these systems also provide a solid framework for 
sensor characterization and study. 
1.8 Goals and Contributions 
The goal of this thesis is to develop a commercially deployable calibration 
support system that can be used for sensor characterization, calibration, and acceptance 
testing of Air Data Attitude Heading Reference Systems. The implemented system 
provides the user the framework to implement calibration strategies that would ensure 
ADAHRS data accuracy over its operating measurement and temperature range. Various 
sensor error sources that affect the performance of ADAHRS sensors have been reviewed 
and the more prominent ones were identified. Various published methods for the 
correction and compensation of these sensor errors have been reviewed and an integrated 
tool has been developed to implement a comprehensive method and process for IMU and 
ADS sensor calibration. The calibration support software tool design has been structured 
and optimized for: cost, modularity, scalability, portability, testability, and most 
importantly re-configurability of the system. Since the calibration strategy is always 
under continuous research and development, the calibration tool has been designed and 
developed to adapt to new calibration requirements, sequences and routines with minimal 
modifications to the tool environment, consequently reducing the ADAHRS unit?s time 
to market. The proposed support system is suited for batch calibration of IMU and can be 
 20 
easily extended to support batch calibration of ADS, as well enabling mass production. 
The integrated nature of the system optimizes production time and economics of 
calibration.  
1.9  Thesis Organization 
This thesis document is organized as follows:  Chapter 2 presents the IMU and 
ADS error sources, and describes the implementation of the chosen method and process 
for IMU and ADS calibration. Chapter 3 describes the system design and software 
implementation details of the IMU and ADS calibration system. Chapter 4 presents the 
results obtained from trial calibration runs verifying the calibration system?s functionality 
and usefulness. Chapter 5 concludes this thesis by discussing the goals achieved and 
scope for future development. 
 21 
2 ADAHRS CALIBRATION METHOD AND PROCESS 
 
 
2.1 Overview 
The IMU considered for this thesis is the Inertial Measurement Cube (IM3), a 
product of Archangel Systems Inc, USA, shown in Figure 7(b) [4]. An inertial 
measurement unit is the heart of any ADAHRS system. It provides linear acceleration 
and angular rotation rate parameters to the ADAHRS unit for computation of inertial 
solutions. The air data system considered for this thesis is the ADS, a product of 
Archangel Systems Inc, USA [2]. The air data system measures static pressure, pitot 
pressure and outside air temperature. Based on these measurements it computes and 
transmits altitude, altitude rate, computed air-speed, MACH, true air-speed, total air 
temperature and baro-corrected altitude as final outputs on the ARINC bus. Section 2.2 of 
this chapter covers the basic hardware layout of the IM3 with a brief discussion on its 
manufacturing process. Section 2.3 covers the basic hardware layout of the ADS. Section 
2.4 describes the error sources present in the sensors employed by the IMU. Section 2.5 
describes the error sources present in the sensors employed by the ADS. Section 2.6 
presents the implemented IMU calibration method and process. Section 2.7 presents the 
implemented ADS calibration method and process. 
 22 
2.2 Inertial Measurement Unit ? IM3 
Figure 6 shows the hardware layout of the IM3. The digital signal Programmable 
Interface Controller (dsPIC) serves as the main processing element. It is responsible for 
sensor data acquisition and computation of the inertial solutions.  
Microchip dsPICA/Dconverters
X-axes temp
sensor
Y-axes temp
sensor
Z-axes temp
sensor
X-axes accel
aX1
X-axes accel
aX2
Y-axes accel
aY1
Y-axes accel
aY2
Z-axes accel
aZ1
Z-axes accel
aZ2
X-axes gyro
gX
Y-axes gyro
gY
Z-axes gyro
gZ
Internal A/D converters
PWM capture ports
UART
SPI
 
Figure 6: IM3 hardware layout. 
 
The sensor system consists of strap-down solid state accelerometers, gyros, and 
temperature sensors. The main processing element, along with the sensor systems, forms 
the IM3, shown in Figure 7(b). The manufacturing process of the IM3 involves populating 
the sensors, microcontroller (dsPIC), power regulation and signal conditioning 
components on six, ? inch square PCB?s (printed circuit boards), which form the faces of 
the IM3. The printed circuit boards are interconnected using a rigid-flex card to form the 
IM3 flats. The IM3 flats are then subjected to burn-in tests to assess their infant-mortality. 
 23 
On completion of the burn-in process the IM3 flats are folded in the form of a cube and 
epoxy-glued to form the IM3 shown in Figure 7(b). Three dual-axes accelerometers 
212121 ,, zzyyxx aaandaaaa    mounted   on   orthogonal   faces of the cube measure the 
+ve/-ve linear accelerations along the X, Y and Z axes, as illustrated in Figure 7(a).  
 
 
 
 
Figure 7: Inertial Measurement Cube. (a) Accelerometer triad mounting, (b) IM3. (c) 
Gyroscope triad mounting. 
 
  
 24 
The accelerometers provided for each axis are interfaced to the internal capture 
ports of the dsPIC. Three MEMS gyros, ,, yx gg and zg  mounted on the orthogonal faces 
of the IM3, measure the angular rates along the X, Y and Z-axes, respectively, as shown 
in Figure 7(c). The Gyros are interfaced to external 19-bit A/D converters that 
communicate with the dsPIC via a dedicated Serial Peripheral Interface (SPI) channel. 
The Gyros have inbuilt temperature sensors that are interfaced to the dsPIC?s internal 
A/D converters. These sensors provide the temperature data that is required for thermal 
compensation of sensor data during run-time. The IM3 outputs data via SPI/UART ports 
present in the dsPIC. 
2.3 ADXL210E MEMS Accelerometer Sensor 
The ADXL210E is a low-cost, low-power, dual-axis, monolithic MEMS 
accelerometer from Analog Devices [8]. It provides a digital duty cycle output that can be 
readily interfaced with PWM peripherals of modern day microcontrollers. These 
accelerometers can be employed for both dynamic (vibration) and static acceleration 
measurements. Table 6 shows the relevant specifications of the ADXL210E. The sensor 
output is an analog output proportional to the acceleration measured. After being low-
pass filtered, this analog signal is converted to a Duty Cycle Modulated (Pulse Width 
Modulated PWM) signal by a DCM modulator present in the sensor. At 0g a 50% duty 
cycle signal is produced. Accelerations below/above 0g are determined from pulse widths 
T1 and T2, as shown in Figure 8. 
 
 
 25 
Table 6: ADXL210E specifications, from Analog Devices data sheet [8] 
 
Specification Value 
Full-scale measurement range ? 10 g 
Non-Linearity  2% of Full-Scale 
Alignment-Error ?1 ? 
Alignment-Error X-sensor to Y-sensor ? 1 ? 
Temperature Drift  ? 0.5 % 
Operating Temperature Range -40 ?C to +85 ?C 
 
T1
T2
 
Figure 8: ADXL210E PWM output 
2.4 ADXRS150 MEMS Gyro Sensor 
 
The ADXRS150 is a complete single-axis angular rate sensing gyroscope 
manufactured by Analog Devices [9]. The output signal produced by the sensor is an 
analog signal that can be calibrated to measure the angular rate in ?/s. The MEMS gyro 
has an inbuilt temperature sensor which produces an analog signal that is proportional to 
the operating absolute temperature. During operation, this temperature output is used by 
 26 
the IM3 for thermal compensation of accelerometers and gyros in the IMU. The relevant 
specifications of the ADXRS150 are given in Table 7. 
 
Table 7: ADXRS150 specifications, from Analog Devices data sheet [9] 
 
Specification Value 
Full-scale measurement range ? 150 ?/s (clockwise + ve) 
Non-Linearity   0.1% of Full-Scale 
Sensitivity over temperature  11.25-13.75 mV/ ?/s 
Operating Temperature Range  -40 ?C to +85 ?C 
 
2.5 Air Data System  
Figure 9 shows the hardware layout of the ADS unit. The digital signal 
Programmable Interface Controller (dsPIC) serves as the main processing element. It is 
responsible for sensor data acquisition and computation of the altitude/air-data solution.  
Microship dsPIC
A/D
converters
ADS1254
OAT sensor
Pressure
sensor Ps
Pressure
sensor Pt
Internal A/D converters
Power supply
UART
to DSP
 
Figure 9: ADS hardware layout 
 27 
The sensor system consists of two piezo-resistive pressure sensors, Ps and Pt, that 
measure the absolute static pressure and the differential pitot pressure, respectively. The 
main processing element along with the sensor system forms the ADS unit, shown in 
Figure 9.  The pressure sensors are interfaced to the dsPIC controller through an 
ADS1254 24-bit analog to digital converter. The A/D converter transmits the sampled 
pressure sensor output to the dsPIC through a dedicated Serial Peripheral Interface 
channel. The pressure sensors used are temperature compensated over a range of -20 oC 
to +85 oC. The sensor bridge provides an analog voltage output proportional to the 
sensor?s operating ambient temperature which is used for thermal compensation of ADS 
sensors during run time. The Outside Air Temperature (OAT) sensor is interfaced to the 
dsPIC through one of the on-chip A/D converters. The ADS transmits the computed air 
data to the main processing DSP via a dedicated UART interface. 
2.5.1 Model 1230 Piezo-Resistive Pressure Sensor 
The model 1230 piezo-resistive pressure sensor is a low cost, high performance, 
temperature compensated piezo-resistive silicon pressure sensor package manufactured 
by IC Sensors [20]. The model 1230 pressure sensor employed for the ADS is capable of 
measuring absolute pressure between 0 PSI to 15 PSI and differential pressure between 0 
PSI to 15 PSI. The sensors have a rated +/- 0.1% non-linearity, +/- 0.5% temperature 
error, 0.05 % temperature hysteresis and a 0.1% pressure hysteresis over the 
measurement span. The sensors have an operating temperature range of -40 oC to 125 oC. 
 
 28 
2.6 IMU ? Error Sources  
2.6.1 Accelerometer Temperature Drift 
The ADXL210E accelerometers used in the IM3 are susceptible to sensor thermal 
drift error. Thermal drift is a characteristic error source that is inherent to the sensor 
design and unique to every sensor. It causes a constant, measured acceleration value to 
drift with respect to ambient temperature. If the accelerometers are not suitably calibrated 
and compensated for thermal drift, the sensors can introduce severe measurement errors 
while operating under changing ambient temperature conditions.  Figure 10 shows the 
variation in a constant measured acceleration with respect to the operating ambient 
temperature. 
 
Figure 10: Accelerometer temperature drift. 
 29 
2.6.2 Accelerometer Offset and Scale factor 
In general, MEMS accelerometers are generally not calibrated post-production. 
They are shipped with a scale factor S  and offset O  on each of their measurement axes 
[8]. The ADXL210E has a wide range of tolerance for initial offset. Hence, the 
accelerometers need to be calibrated individually in order to determine their offset and 
scale factor.  
2.6.3 Cross-Axis Error  
As shown in Figure 7(a), the IM3 contains three dual-axis accelerometers 
orthogonally mounted to form a 3-dimensional acceleration measurement system. In this 
type of application, a source of error called sensor non-orthogonality error creeps in. 
Since the dual-axis sensors are manually or machine mounted on the orthogonal surfaces, 
the axes of the sensors are often misaligned from perfect orthogonality. This 
misalignment introduces erroneous sensor measurements along the three measurement 
axes. The Gyro triad also suffers from this error source. 
2.6.4 Gyroscope Errors  
Traditionally, gyroscopes suffer from static bias drift errors, i.e, a stationary gyro 
that is supposed to read an angular rate sec/00.0 ?? = , reads a bias which drifts over 
time. The AHR150A uses a proprietary Fuzzy Logic Adaptive Signal Processing 
(FLASP) algorithm to propagate the gyro bias drift errors for correction and 
compensation. This keeps the gyro drift rate per hour within the relevant error budget 
specifications.  With reduction in the prominent bias drift errors, other gyro errors like 
 30 
scale factor nonlinearity, and scale factor dependency on temperature gain significance, 
and need to be compensated for. 
2.6.5 Gyroscope Temperature Drift 
  The ADXRS150 MEMS gyroscopes used in the IM3 are susceptible to sensor 
thermal drift error. Thermal drift is a characteristic error source that is inherent to the 
sensor design and unique to every sensor. It causes a constant, measured angular rate 
value to drift with respect to ambient temperature. If the gyroscopes are not suitably 
calibrated and compensated for thermal drift, the sensors can introduce severe 
measurement errors while operating under changing ambient temperature conditions. 
Figure 11 shows the variation in a stationary gyro output with respect to the operating 
ambient temperature. 
 31 
 
Figure 11: Gyroscope temperature drift. 
 
2.6.6 Gyroscope Scale Factor and Offsets  
Although the X, Y and Z axis gyroscopes are similar in construction and design, 
when subjected to a given angular rate, they produce different outputs. This is because of 
the fact that sensor sensitivity about an axis is unique to a sensor. This quantity is 
captured as a multiplication factor and referred to as sensor scale factor. The offset of a 
gyro is given by the gyro output under stationary conditions (0 angular rate input). This 
parameter is also unique to every gyroscope. Scale factors and offsets for the X, Y and Z 
axis gyroscopes have to be determined. 
 32 
2.6.7 Gyroscope Scale-Factor Non-Linearity  
In MEMS gyroscopes, it is observed that the scale factor is non-linear over the 
measurement span. Figure12 shows the relationship between gyro measurement and 
angular rate input. As shown, the relationship is not a linear one. Considering the scale 
factor as a constant linear quantity will lead to measurement errors during operation over 
the full measurement span. Hence the scale factor non-linearity over the rated 
measurement span should be captured and compensated for. 
 
 
Figure 12: Gyroscope scale factor non-linearity. 
 
 33 
2.6.8 Gyroscope Scale Factor Dependency on Temperature  
In addition to the scale factor non-linearity presented above, the gyro scale factor 
exhibits a dependency on operating ambient temperature. Figure 13 shows the surface of 
gyro measurement at fixed rates, acquired under different ambient temperatures. Since 
the surface observed is not flat, the nature of this surface should be studied and any scale 
factor dependency on operating ambient temperature has to be captured during gyro scale 
factor calibration.    
 
 
Figure 13: Gyro scale factor dependency on temperature. 
 
 34 
2.7 Air Data System (ADS) ? Error Sources 
The Ps and Pt pressure sensors employed are affected by a number of error 
sources. In order to calibrate the ADS to provide the accuracy level required by the 
ARINC706-4 standard [11], the effects of these error sources have to be studied and a 
suitable calibration strategy must be adopted. According to the 706-4 Mark 5 Subsonic 
Air data system requirements [11], the ADS unit must capable of operating between an 
altitude range of -1000 feet to 50000 feet and an airspeed range between 30 knots and 
450 knots. It should comply with the accuracy specifications shown in Table 2 and Table 
3 over the rated temperature range shown in Table 5. 
2.7.1 Pressure Sensor Temperature Drift  
The model 1230 IC pressure sensors used in the ADS are susceptible to sensor 
thermal drift error. Thermal drift is a characteristic error source that is inherent to the 
sensor design and unique to each individual sensor. It causes a constant, measured 
pressure value to drift with respect to ambient temperature. If the pressure sensors are not 
suitably calibrated and compensated for thermal drift, the sensors can introduce severe 
measurement errors while operating under changing ambient temperature conditions. 
Figure 14 shows the drift in static pressure counts Ps and pitot pressure counts Pt with 
respect to operating ambient temperature. 
 35 
 
Figure 14: Pressure sensor temperature drift. 
 
2.7.2 Offset and Scale Factor  
IC pressure sensors are not calibrated post-production. They are shipped with a 
scale factor and an offset. Under a zero pressure input the pressure sensors have a +/- 2 
mV output voltage tolerance, this voltage output is constant and unique to every sensor. 
This output is accounted for by identifying and adding an offset. The pressure sensor 
output acquired by the dsPIC is in counts, and has to be scaled to attitude units in feet. 
This scaling is accomplished using a scale factor. When two identical pressure sensors 
are subjected to the same constant pressure input they tend to output measurements of 
 36 
different magnitude. Due to difference in sensitivities exhibited by the sensor, the sensor 
scale factor is unique to every sensor. 
2.7.3 Scale Factor Non-Linearity  
In ADS pressure sensors, it is observed that the scale factor is non-linear over the 
measurement span. Figure 15 shows the relationship between measured altitude (counts) 
and true altitude (feet). As observed, the scale factor is clearly non-linear. Considering 
the scale factor as a constant linear quantity will lead to measurement errors over the full 
measurement span. Therefore, it is important that the scale factor non-linearity over the 
measurement span is captured and compensated. 
 
Figure 15: Pressure sensor scale factor non-linearity. 
 37 
2.7.4 Offset and Scale-Factor Dependency on Temperature  
In using piezo-resistive pressure sensors, it is observed that the scale factor has a 
dependency on operating ambient temperature. Figure 16 shows the results of an 
investigation conducted on the scale factor dependency on temperature. As can be seen in 
the figure, with decrease in ambient temperature the curves shift higher. Hence scale 
factor dependency on temperature should be captured and compensated. The plots shown 
look linear since it has been zoomed in to show the shifts in detail, the scale factor non-
linearity shown in Figure 15 still exists. 
 
Figure 16: Pressure sensor scale factor dependency on temperature. 
 38 
2.8 IMU calibration - Method and Process 
The IMU calibration process is a multi-stage process. The various calibration 
stages are the IMU burn-in stage, IMU thermal calibration, accelerometer sensor 
calibration, gyroscope sensor calibration, and accelerometer and gyroscope cross-axis 
calibration. 
  The calibration process begins with a burn-in stage, where the IMU flats are 
subjected to a known temperature cycle. The chosen temperature cycle typically covers 
the rated operating temperature range of the IMU, which is shown in Figure 17. 
Subjecting the IMU flats to these temperature extremes helps to reduce the infant 
mortality rate of the manufactured units. 
2.8.1 IMU Thermal Calibration  
The IMU thermal calibration process calibrates the IMU sensors for operation 
under varying ambient temperature conditions. This stage compensates for the 
accelerometer and gyroscope temperature drift error sources explained in Section 2.4. 
Thermal calibration of the IMU is performed by subjecting the IMU to a known 
temperature cycle and acquiring the IMU output data throughout the duration of thermal 
cycling. A thermal chamber, explained in Section 3.2, was employed to provide the 
necessary ambient temperature conditions. The temperature profile used is shown in 
Figure 17. The flat regions on the profile were provided to ensure ample time for the 
IMU units under calibration to reach the peak temperatures. On completion of the thermal 
profile, the data acquired is processed and fitted to a 2nd-order polynomial equation.  The 
curve fit constants obtained are downloaded to the IMU units. At the end of the thermal 
 39 
calibration stage the IMU batch is reprogrammed to transmit thermally calibrated 
accelerometer 
?
Ta  and gyro 
?
Tg  data. 
 
 
Figure 17: Thermal profile used for IMU calibration. 
  
If TDa?  is the accelerometer thermal drift correction factor, TDg?  is the gyroscope thermal 
drift correction factor, 
?
Ta is the thermal drift compensated accelerometer output vector 
and 
?
Tg is the thermal drift compensated gyroscope output vector. Then, 
?
Ta and 
?
Tg  are 
given by Eq.(4) and Eq.(5). 
 ??? ?=
TDaUTa ?  
 
and 
???
?= TDgVTg ?  
)4(  
 
 
)5(  
 40 
Where, 
?
U  is the raw un-calibrated accelerometer output vector, 
?
TDa?  is the accelerometer 
thermal drift correction vector for accelerometers 222111 ,,,,, yxzyxz aaaaaa  given by vectors 
)6(  and )7( , respectively. 
 
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
=
?
2
2
2
1
1
1
y
x
z
y
x
z
ua
ua
ua
ua
ua
ua
U  
 
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
=
?
2
2
2
1
1
1
TDay
TDax
TDaz
TDay
TDax
TDaz
TDa
?
?
?
?
?
?
?  
 
)6(  
 
 
 
 
 
 
 
)7(  
?
V  is the raw un-calibrated gyroscope output vector, 
?
TDg?  is the gyroscope thermal drift 
correction vector for gyroscopes zyx ggg ,,  given by vectors )8(  and )9( , respectively. 
 
?
?
?
?
?
?
?
?
?
?
=
?
z
y
x
Vg
Vg
Vg
V  
 
?
?
?
?
?
?
?
?
?
?
=
?
3
2
1
TDg
TDg
TDg
TDg
?
?
?
?  
 
)8(  
 
 
 
 
)9(  
 
 41 
The thermal drift correction factors for accelerometers and gyroscopes are obtained using 
a second order polynomial fit given by Eq. )10( and Eq. )11( , respectively.  
 2210 tktkkTDa ++=?  
 
2
210 tktkkTDg ++=?  
 
)10(  
 
)11(  
 
 
 
210 ,, kkk  are the polynomial fit constants and t  is the measured temperature. 
2.8.2 Accelerometer Offset and Scale Factor Calibration  
In order to be used as a linear acceleration measurement sensor in the IMU, the 
ADSL210E has to be calibrated for offset and scale factor, as discussed in Section 2.4. 
The rotational calibration method [14] was employed for accelerometer offset and scale 
factor calibration. The rotational calibration method is a six-position calibration process 
that determines the offset and scale factor parameters for each of the accelerometers 
independently. This method uses earth?s acceleration due to gravity g as a known 
acceleration reference. In this method, the accelerometer triad is placed in six pre-defined 
orientations which subject each of the six accelerometers to +1g and -1 g acceleration, as 
shown in Figure 18. For example, if the Z-axis accelerometer is being calibrated, the 
IMU is placed in a position subjecting the Z-axis accelerometer 1za  to +1g and 
accelerometer 2za  to -1g gravity vector, as shown in orientation 31 in Figure 18. The 
IMU is locked in this orientation and the stationary IMU output data is acquired and 
logged. Next, the IMU is rotated 1800, subjecting Z-axis accelerometer 1za  to -1g and 
accelerometer 2za  to +1g gravity vector, as shown in orientation 32 in Figure 18. The 
 42 
IMU is locked in this orientation and IMU output is acquired and logged. Data acquired 
during Z-axis accelerometer calibration is shown in Figure 19. The same exercise is 
repeated for X axis accelerometers 1xa  2xa , and Y axis accelerometers 1ya 2ya . Figure 20 
and 21 show the data acquired during X and Y axes accelerometer calibration. Care 
should be taken to ensure that the IM3 is positioned perfectly horizontal in a known and 
repeatable fashion in all orientations. The rotation of the cube while changing 
orientations should be performed slowly to minimize the effects of dynamic acceleration.  
In order to obtain the scale factor and offset calibrated acceleration vector aC
?
, the 
temperature compensated accelerometer output vector 
?
Ta  is used in Eq. )12( . 
 ???? += TaSOC
a  
 
)12(  
 
To obtain the accelerometer offsets 
?
O  and scale factor 
?
S  for the Z-axis, let 
gzUa 11+ and gzUa 12?  represent the mean of the sample set acquired under orientation 31 
for accelerometers 1za  and 2za . Similarly let gzUa 11?  and gzUa 12+  represent the mean of 
the sample set acquired under orientation 32 for accelerometers 1za  and 2za . Based on 
Eq. )12( , under orientation 31, the accelerometers 1za  and 2za  experience an acceleration 
of +1g and -1g, given by Eq. )13( , and Eq. )14( . 
 1
1
111 +=?+
z
zgz
S
OUa  
 
1
2
212 ?=??
z
zgz
S
OUa  
)13(  
 
 
 
)14(  
 
 
 43 
Similarly, based on Eq. )12( , under orientation 32, the accelerometers 1za  and 2za  
experience an acceleration of -1g and +1g, respectively, given by Eq. )15(  and Eq. )16( . 
 
    1
1
111 ?=??
z
zgz
S
OUa  
 
 1
2
212 +=?+
z
zgz
S
OUa  
 
 
)15(  
 
 
 
)16(  
 
From Eq. )13(  and Eq. )15( , we get the offset and scale factor for 
accelerometer 1za  using Eq. )17(  and Eq. )18( . 
  
2
1111
1
gzgz
z
UaUaO ?+ +=  
 
2
1111
1
gzgz
z
UaUaS ?+ ?=   
 
 
)17(  
 
 
 
)18(  
 
Similarly, from Eq. )14(  and Eq. )16( , we get offset and scale factor for 
accelerometer 2za  using Eq. )19(  and Eq. )20( . 
  
2
1212
2
gzgz
z
UaUaO ?+ +=  
 
2
1212
2
gzgz
z
UaUaS ?+ ?=   
 
 
)19(  
 
 
 
)20(  
 
The same algorithm can be applied for X and Y axes accelerometer calibration to 
obtain the offset vector 
?
O  and scale factor vector 
?
S  given by Eq. )21(  and Eq. )22( . 
 
 
 44 
  
[ ]222111 yxzyxz ooooooO =?  
 
[ ]222111 yxzyxz ssssssS =?   
 
 
)21(  
 
)22(  
 
 
?
O , 
?
S  and temperature compensated accelerometer output 
?
Ta  can be used in Eq. )12(  to 
obtain the scale factor and offset calibrated accelerometer output 
?
aC . 
 
 45 
X
Z
Y
G
G
X
Y
Z
Orientation 31 Orientation 32
Y
X
Z
G
G
Y
Z
X
Orientation 11 Orientation 12
z
Y
x
G
G
z
x
y
Orientation 21 Orientation 22  
Figure 18: The six orientations used for IMU calibration. 
 46 
 
Figure 19: Z- Axis accelerometer calibration data. 
 47 
 
Figure 20: X-Axis accelerometer calibration data. 
 48 
 
Figure 21: Y-Axis accelerometer calibration data. 
 
2.8.3 Gyroscope Scale Factor Calibration  
The gyroscope calibration method implemented is similar the method proposed in 
[16]. This method involves determining the scale-factor non-linearity using a rate table to 
provide known angular rate inputs. In order to capture the scale factor non-linearity, the 
IMU units are subjected to known rotation rates at different points on the rated 
measurement span. The ADXRS150 has a measurement span of +/- 150 ?/s. For any 
given axis, the gyroscope is subjected to seven equidistant angular rate inputs: -150 ?/s, -
100 ?/s, -50 ?/s, 0 ?/s, 50 ?/s, 100 ?/s, 150 ?/s. These rates were chosen in order to cover 
the entire gyro measurement span. A rate table, which is explained in Section 3.2, was 
used to provide known reference rotational rates. The IMU data output is acquired and 
 49 
logged at each reference rate input used. This procedure is repeated for all three axes in 
order to capture scale factor non-linearity components for the gyros mounted on X, Y and 
Z axes. The calibration data acquired from a trial calibration run is shown in Figure 22. 
As shown, under orientations 11, 21 and 31 gyros xg , yg  and zg  are calibrated, 
respectively. Care must be taken to make sure that the gyroscope under calibration is 
mounted in a manner to ensure the alignment of the axis of measurement to the axis of 
rotation. 
In order to calibrate the X-axis gyroscope, let 150?xTg , 100?xTg , 50?xTg , 0xTg , 
50+xTg , 100+xTg , 150+xTg  represent the mean of sample set acquired under orientation 11 
under angular rate inputs -150 ?/s, -100 ?/s, -50 ?/s, 0 ?/s, 50 ?/s, 100 ?/s, 150 ?/s, 
respectively. The means obtained are normalized for each of the rates. The normalized 
means )( 0150 xx TgTg ?? , )( 0100 xx TgTg ?? , )( 050 xx TgTg ?? , )( 050 xx TgTg ?+ , 
)( 0100 xx TgTg ?+ , and )( 0150 xx TgTg ?+ are plotted against reference angular rate inputs 
used, as shown in Figure 23. A third order curve is fitted to the plotted data and the curve 
fit constants 0xl , 1xl , 2xl , and 3xl obtained provide the gyro non-linearity scale factors for 
gyro xg . Similarly, scale factor non-linearity constants are obtained for gyros yg  and zg . 
The calibrated gyroscope output vector 
?
gC  is given by Eq. )23( . 
 
 
 
 
 50 
  
?
?
?
?
?
?
?
?
?
?
?
?
+++
+++
+++
=
?
?
?
?
?
?
?
?
?
?
=
?
?
?
?
?
?
?
?
?
?
=
?
3
3
2
210
3
3
2
210
3
3
2
210
)(
)(
)(
zzzzzzz
yyyyyyy
xxxxxxx
z
y
x
z
y
x
g
TglTglTgll
TglTglTgll
TglTglTgll
Tgf
Tgf
Tgf
cg
cg
cg
C  
 
 
 
)23(  
 
 
 
?
gT is the temperature compensated gyroscope output. 
 
Figure 22: Gyro scale factor non-linearity calibration data. 
 
On completion of calibration for all three axes, the gyroscope non-linearity scale 
factors and the accelerometer scale factors and offsets are downloaded to the IMU unit by 
the user. At the end of the gyro sensor calibration stage, the IMU transmits partially 
calibrated accelerometer and gyro data. The IMU still needs to be calibrated for 
accelerometer and gyro cross-axis errors discussed in Section 2.4. 
 51 
 
Figure 23: Gyro scale factor non-linearity curve-fit. 
 
2.8.4 Accelerometer and Gyroscope Cross-Axis Calibration  
By the beginning of this stage the accelerometers and gyroscopes have been 
calibrated for their respective scale factors and offsets. The IMU now transmits calibrated 
linear velocity rates aC
?
 and angular rotational rates gC
?
. The cross-axis calibration is 
performed to offset the effects of any axis misalignments that might have occurred during 
the accelerometer and gyro mounting on the orthogonal measurement triad. The cross-
axis calibration methodology and algorithm presented below was developed by 
Archangel Systems, Inc [2]. Cross-axis calibration is accomplished by first subjecting the 
IMU to constant known reference acceleration along each of the axes of the 3-D 
acceleration measurement system and then subjecting the IMU to a known reference 
 52 
angular rate about each axis of the 3-D angular rate measurement system. During the 
cross-axis calibration process, care should be taken to ensure that the IMU acceleration 
measurement axis is perfectly aligned with the reference acceleration vector and the 
angular rate measurement axis is perfectly aligned with the axis of reference angular rate 
input in all orientations.  
In order to perform cross-axis calibration for the X-axis accelerometers, the IMU 
is placed in orientation 11, as shown in Figure 18. This subjects the IMU to an 
acceleration of +1g along the X-axis. The IMU output, which contains the linear velocity 
rates 
?
aC , is acquired and logged. The same exercise is repeated for orientations 21 and 
31, subjecting the IMU to 1g acceleration along the Y-axis and Z-axis, respectively. The 
IMU output is acquired and logged in all three orientations. Now the cross-axis 
calibration constants for the accelerometers are calculated in the following method.  
Let, I represent the matrix containing the mean of the linear velocity rates 
acquired from the IMU under orientations 11, 21 and 31, as shown in Eq. )24( . 
  
?
?
?
?
?
?
?
?
?
?
=
313131
212121
111111
)()()(
)()()(
)()()(
zyx
zyx
zyx
CaCaCa
CaCaCa
CaCaCa
I  
 
 
 
)24(  
 
 
11)( xCa , 11)( yCa , and 11)( zCa  are the mean of the linear velocity rates obtained under 
orientation 11. 21)( xCa , 21)( yCa , and 21)( zCa  are the mean of the linear velocity rates 
obtained under orientation 21. 31)( xCa , 31)( yCa , and 31)( zCa  are the mean of the linear 
velocity rates obtained under orientation 31. Now, the cross-axis correction matrix can be 
obtained using Eq. )25( . 
 53 
 
  
?
?
?
?
?
?
?
?
?
?
?= ?
81.900
081.90
0081.9
][ 1ICA  
 
 
 
)25(  
 
 
The cross-axis calibrated acceleration vector 
?
A  is given by Eq. )26( . 
  
??
???
??
???=?
z
y
x
Ca
Ca
Ca
CAA  
 
 
)26(  
 
 
 
In order to perform X-axis gyroscope cross-axis calibration, the IMU is mounted 
on the rate table and locked in orientation 11, as shown in Figure 18. Under this setup, the 
IMU is subjected to an angular rotation rate of 150 ?/s and its output data which contains 
the calibrated angular rotation rate gC
?
,  is acquired and logged. The same exercise is 
repeated for orientations 21 and 31, subjecting the IMU gyro triad to an angular rotation 
rate of 150 ?/s about the Y-axis and Z-axis, respectively. The IMU output is acquired and 
logged in all three orientations. The cross-axis calibration constants for the gyroscopes 
are calculated in the following manner.  
Let, J represent the matrix containing the mean of the angular rotation rates 
acquired from the IMU under orientations 11, 21 and 31, as shown in Eq. )27( . 
  
?
?
?
?
?
?
?
?
?
?
=
313131
212121
111111
)()()(
)()()(
)()()(
zyx
zyx
zyx
CgCgCg
CgCgCg
CgCgCg
J  
 
 
 
)27(  
 
 
 54 
11)( xCg , 11)( yCg , and 11)( zCg  are the mean of the linear velocity rates obtained under 
orientation 11; 21)( xCg , 21)( yCg , and 21)( zCg  are the mean of the linear velocity rates 
obtained under orientation 21; 31)( xCg , 31)( yCg , and 31)( zCg  are the mean of the linear 
velocity rates obtained under orientation 31. Now, the cross-axis correction matrix can be 
obtained using Eq. )28( . 
  
?
?
?
?
?
?
?
?
?
?
?= ?
15000
01500
00150
][ 1JCG  
 
 
 
)28(  
 
 
The cross-axis calibrate angular rotation rate vector 
?
G is given by Eq. )29( . 
  
??
???
??
???=?
z
y
x
Cg
Cg
Cg
CGG  
 
 
 
)29(  
 
 
 
2.9 ADS Calibration Method - Method and Process 
2.9.1 Ps and Pt Pressure Sensor Calibration Method  
The implemented ADS sensor calibration method is an integrated process in 
which the static and pitot pressure sensors are calibrated to compensate for all the error 
sources presented in Section 2.5. In order to capture the scale factor non-linearity over the 
measurement span, the calibration process essentially subjects the ADS pressure sensors 
to reference altitude/air-speed inputs at various points on their measurement span. The 
ADS output and the reference inputs are acquired and logged throughout this process. 
 55 
Since the altitude accuracy levels required at lower altitudes are more stringent than 
accuracy levels acquired at higher altitudes, as given in Table 2, the reference calibration 
altitudes employed must be more closely placed at lower altitudes then at higher altitudes. 
Similarly, air-speed accuracy levels required at higher air-speeds are more stringent 
compared to lower air-speeds, as given in Table 3, hence the reference air-speeds 
employed must be more closely spaced at higher air-speeds then at lower air-speeds. This 
will ensure an optimal fit that will provide the necessary accuracy levels. A DRUCK 403 
air data test system, discussed in Section 3.3, was used to provide known static and 
differential pressure inputs. In order to capture the scale factor dependency on 
temperature, the scale factor calibration process explained above is repeated at various 
temperatures over the operating temperature span. The ADS output, the reference inputs, 
and ambient temperatures are acquired and logged throughout this process. Equidistant 
temperatures covering the operating temperature range can be used to capture the scale-
factor temperature dependency. The environmental chamber explained in Section 3.3 was 
used to provide known operating temperatures. The ADS calibration system presented in 
Chapter 3 provides the user a flexible and modular framework to execute the above 
explained calibration procedure described above. Figure 24 shows the results obtained 
from a sample altitude sensor calibration run. On completion of the calibration run, a 3-D 
polynomial fit is used to fit the acquired pressure sensor data and temperature data to the 
true reference inputs used during calibration. The surface fit constants obtained are 
downloaded to the ADS units by the user. The final ADS output will have altitude 
expressed as a function of measured static pressure (counts) and temperature (counts) and 
 56 
airspeed expressed as a function of measured pitot pressure (counts) and temperature 
(counts). 
 
Figure 24: Altitude sensor calibration. 
 57 
3 ADAHRS CALIBRATION SYSTEM DESIGN AND 
IMPLEMENTATION 
3.1 Chapter Overview 
 
The IMU calibration support system and ADS calibration support system provide 
an integrated support environment for sensor characterization, calibration and acceptance 
testing of IMU and ADS, respectively. The system provides the user with a software tool 
that can be used to implement the IMU and ADS calibration procedure presented under 
Chapter 2. This software tool henceforth will be referred to as the IMU calibration 
application and ADS calibration application. The IMU calibration application employs 
the services of a number of support instruments in order to perform the various functions 
involved in the IMU calibration process. The instruments used include a rate table for 
gyroscope calibration and an environmental chamber for thermal calibration of the IMU. 
In addition to other functions, the IMU calibration application essentially controls and 
sequences the operations of these support instruments to implement the IMU calibration 
procedure. Similarly, ADS calibration application controls and sequences the operation of 
support instruments like DRUCK 403 air data test system for altitude/airspeed calibration 
and an environmental chamber for thermal calibration of ADS.  Sections 3.2 and 3.3 
describe the IMU calibration system and ADS calibration system layout. Section 3.4 
describes the labVIEW application development platform which was employed for 
development of the ADAHRS calibration support system. Section 3.5 presents 
 58 
the IMU calibration application software and explains the role played by the various 
modules and sub-modules present in it. Section 3.6 lists the system requirements for 
implementation of the IMU calibration application. Section 3.7 presents the software 
design flowcharts and details the functionality of each of the individual modules present 
in the IMU calibration application. Section 3.8 presents the ADS calibration application 
software and explains the role played by the various modules and sub-modules present in 
it. Section 3.9 lists the system requirements for implementation of the ADS calibration 
application. Section 3.10 presents the software design flowcharts and details the 
functionality of each of the individual modules present in the ADS calibration 
application. 
3.2 IMU Calibration System - Layout and Description 
The IMU calibration system comprises a calibrating computer and other support 
instruments like the rate table, thermal chamber, and communication hardware. 
 
Calibration
computer Aero812 Rate table
controller Rate table
WATLOW series F4
tamperature controller Environmental chamber
IMU
1
IMU
2
IMU
3
IMU
4
Quad UART to USB
RS 232
MODBUS
UART
USB
 
Figure 25: IMU calibration system layout 
 59 
The rate table provides known precision angular rates for gyro calibration and the thermal 
chamber provides controlled ambient temperature conditions for thermal calibration of 
accelerometers and gyros. Figure 25 shows the architecture of the IMU calibration 
system. Brief descriptions of the various components are given as follows. 
3.2.1 Rate Table 
The rate table chosen for this application is the Ideal Aerosmith, 1621-200 series 
single-axis precision positioning and rate table system [17]. The rate table system can be 
used to provide precision position, rate and acceleration motion for development, 
calibration and production testing of inertial navigational systems. The rate table is driven 
by a servo motor controlled by a servo motor driver/table controller. The rotating disc on 
the table contains a slip ring assembly which enables the IMU communication with the 
calibration computer.  
                                         
Figure 26: IDEAL-Aerosmith rate table/ rate table with environmental chamber 
 
 60 
The Aero812 rate table controller supports IEE 488.1 and RS232 communication 
capability to communicate with external systems. The rate table operation is controlled 
by the calibrating computer by issuing Aerosmith Table Language (ATL) commands 
over a dedicated RS232 link. 
3.2.2 Environmental Chamber  
The Ideal Aerosmith rate table comes with an integrated environmental chamber 
which is mounted on top of the table, housing the rotating plate [17]. The operating 
temperature of the IMU units can be controlled using the environmental chamber 
mounting. The environmental chamber supports a MODBUS compatible serial 
communication interface to enable communication with external systems. The calibrating 
computer issues temperature commands in compliance with MODBUS protocol to the 
WATLOW series F4 temperature controller in order to control and monitor the 
operations of the environmental chamber.  
3.2.3 Four Port RS232 to USB Converter  
The four-port RS232 to USB converter [12] was chosen to provide additional 
serial communication channels for the calibration computer to communicate with the 
IMU units under calibration. This device enables calibration of 4 IMU units at a time. 
The serial data from the four ports are transmitted to the calibrating computer through a 
single USB stream.  
 61 
3.2.4 Calibration Computer  
The calibration computer is a personal computer running the IMU calibration 
application. It is responsible for supervisory control of the rate table, and thermal 
chamber and data acquisition from the IMU units.  
3.3 ADS Calibration System - Layout and Description 
Figure 27 shows the ADS calibration system layout. The calibration computer runs 
the ADS calibration application. It is responsible for data acquisition from the ADS units 
and supervisory control of the DRUCK 403 air data test system and the environmental 
chamber. The application is also responsible for data analysis, data post-processing, result 
generation and acceptance-testing. The air data test system is a closed-loop pressure 
control system which provides known precision static/pitot pressure inputs for calibration 
of the Ps and Pt pressure sensors present in the ADS unit. The environmental chamber 
provides controlled ambient temperature conditions for thermal calibration of Ps and Pt 
pressure sensors. 
 
Calibration
computer WATLOW series 940
temperature controller
Tenney Junior
Environmental chamber
DRUCK 403
 Air Data Test system
Air compressor
Vacuum pump
ADS unit
Ps
Pt
RS232
GPIB
RS232
pressure
supply
vacuum
supply  
Figure 27: ADS calibration system layout 
 62 
3.3.1 Environmental Chamber 
The environmental chamber employed is a bench-top Tenney Junior 
environmental chamber unit housing a WATLOW series 942 temperature controller [18]. 
The environmental chamber supports a temperature range between -75 oC to +200 oC and 
is capable of controlling the internal chamber temperature at a 0.3 oC tolerance. The ADS 
units are placed in the environmental chamber and their ambient temperature is cycled for 
thermal calibration of the Ps and Pt pressure sensors. The temperature controller supports 
RS232/422 communication interface to enable communication with external systems. 
The calibration computer issues WATLOW series 942 controller commands over the 
RS232 link to control and monitor the operations of the environmental chamber.  
3.3.2 DRUCK 403 Air Data Test System  
The DRUCK 403 air data test system is a twin-channel Ps and Pt pressure control 
system for precision calibration and verification of aircraft pitot/statics [19]. The DRUCK 
403 air data test system is capable of altitude calibration between -3000 feet to +80000 
feet, and air-speed calibration between 10 knots to 1000 knots. The air data test system 
requires a pressure/vacuum supply for generation of precision static/differential 
pressures. An air compressor and vacuum pump with an output capacity of at least 25% 
more than the operating pressure were employed to provide supply pressures. The 
DRUCK 403 system provides an IEEE 488 GPIB interface for communication with 
external systems. It supports an elaborate command set which enables the user to 
effectively control the operations of the ADTS.   
 63 
 
Figure 28: DRUCK 403 ADTS 
3.4 LabVIEW Application Development Platform  
LabVIEW, a product of National Instruments Inc is a highly productive graphical 
programming language for development of industrial automation and control, data 
acquisition, and instrumentation solutions. LabVIEW provides an object-oriented data 
flow paradigm for application development. Traditional text based programming relies on 
the sequence of instructions for program execution, but labVIEW provides a data flow 
programming paradigm which relies on flow of data for program execution. LabVIEW 
provides a highly intuitive and powerful graphical user interface which provides a solid 
man machine interface for the ADAHRS calibration system. It also provides a very 
comprehensive set of functions for data management, data processing and report 
generation. Application development in LabVIEW is highly scalable and portable 
providing a single powerful integrated platform to accomplish all the needs of the 
ADAHRS calibration system. The LabVIEW application development platform 
comprises a front panel and a block diagram. The front panel provides a feature rich suite 
of GUI objects like buttons, text boxes, graphs, plots, etc. Instances of these objects are 
accessible from the block diagram and they can be used with a rich suite of arithmetic, 
 64 
logical, string, array manipulation, data acquisition, and data processing functions to 
implement the data flow logic of the application being developed. The various functional 
components of the ADAHRS calibration system application software have been 
implemented as virtual instruments (VI?s). A VI in LabVIEW is analogous to a function 
in C.   
3.5 IMU Calibration System Application Software 
The IMU calibration application has been developed in a highly modular 
architecture with each module implemented to perform a particular functional component 
of the IMU calibration process presented under Chapter 2. Each of these modules 
comprises a number of sub-modules. The basic modules and their sub modules are shown 
in Table 8. Figure 29 shows the role played by each of the modules in the IMU 
calibration process. The Communications setup module is responsible for setting up the 
serial communication parameters for the IMU batch under calibration and the other 
calibration support systems. The Thermal calibration module is responsible for burn-in 
test and thermal calibration of the IMU batch. It consists of a number of sub-modules. 
The Download thermal profile sub-module enables the user to create and download 
customized thermal profiles to the WATLOW series F4 temperature controller present in 
the thermal chamber. The Thermal calibration sub-module prompts the user to mount the 
IMU batch inside the thermal chamber and executes the downloaded thermal profile 
which subjects the IMU batch to desired thermal loading. This module also continuously 
acquires and logs the output data from the IMU batch during this process. On completion 
of the thermal profile it prompts the user. The Thermal calibration result generation sub-
 65 
module retrieves the logged thermal calibration data and presents graphical plots of 
acquired data to the user. It also passes a file handle of the acquired calibration data file 
to a MATLAB engine invoked in LabVIEW. The user has the flexibility to implement a 
MATLAB script of his choice, which will be executed by the MATLAB engine to post-
process the acquired thermal calibration data.  
 
Table 8: IMU calibration application modules and sub-modules 
 
 MODULES SUB-MODULES 
1 Communications setup module Communication setup 
2 Thermal calibration module Download thermal profile 
  Thermal calibration 
  Thermal calibration result generation 
3 IMU sensor calibration module IMU sensor calibration setup 
  IMU sensor calibration 
  IMU sensor calibration result generation 
 
 66 
IMU Calibration start
IMU communications set-up
Download thermal profile
IMU burn-in process
Burn-in
complete ?
IMU burn-in validation
Co
mm
un
ica
tio
n
 se
t-u
p m
od
ule
IM
U 
Th
erm
al 
cal
ibr
ati
on
 m
od
ule
IMU sensor calibration set-up
IMU accelerometer calibration
Accel Cal
complete ?
IMU gyroscope calibration
IMU cross-axis calibration
Cross-axis cal
complete ?
IMU Calibration end
IM
U 
sen
so
r c
ali
bra
tio
n m
od
ule
Download thermal profile
IMU Thermal calibration
Thermal cal
complete ?
Thermal calibration result
generation
IM
U 
Th
erm
al 
cal
ibr
ati
on
 m
od
ule
Gyro Cal
complete ?
User re-programs the IMU batch
with thermal calibration constants
User re-programs the IMU batch with
Accel and Gyro calibration constants
User re-programs IMU batch with
cross-axis calibration constants
no
no
no
no no
yes
yes
yes
yes
 
Figure 29: Software modules involved in IMU calibration process 
 
The IMU sensor calibration module provides a flexible framework for 
accelerometer and gyroscope calibration. It consists of the following sub-modules. The 
IMU sensor calibration setup sub-module provides the user the flexibility to implement a 
calibration sequence of his choice. The calibration sequence is composed of a list of 
configurable steps which will be sequentially executed to implement the sensor 
 67 
calibration process. The calibration steps supported and their functions are listed in Table 
9.  
Table 9: Steps supported in IMU calibration sequence 
 
Tag Step Step configuration 
parameters 
Functions 
OA Accelerometer 
calibration   
1. Enter accelerometer  
3-D orientation tag OA. 
2. Number of IMU data 
packets to acquire ?N 
1. Prompts user to mount IMU 
batch for orientation OA 
2. On user confirmation, acquires 
N data packets. 
OG Gyroscope 
calibration  
1. Enter gyroscope 
3-D orientation tag OG. 
2. Number of IMU data 
packets to acquire ?N. 
3. Minimum rate - Rmin. 
4. Maximum rate - 
Rmax. 
5. Rate increment - Rinc 
1. Generates equidistant rate 
command sequence Rseq based on 
Rmin, Rmax and Rinc. 
2. Prompts user to mount IMU 
batch for orientation OG. 
3. Waits for user confirmation. 
4. Issues the rate command in the 
rate command sequence Rseq. 
5. Waits till target rate is reached. 
6. Acquires N data packets 
7. Repeats steps 4-6 till all rate 
commands in Rseq are exhausted. 
 
 68 
TT  Target 
Temperature 
1.Target Temperature -  
Tt 
2. Soak time - Ts in 
HRS, MIN, SEC 
1. Issues target temperature Tt 
command to the environmental 
chamber 
2. Waits, till the target temperature 
Tt is reached. 
3. Soaks at target temperature Tt 
for soak time Ts. 
CA Cross-axis 
calibration 
None 1. Performs accelerometer cross-
axis calibration procedure 
presented in Chapter 2. 
2. Performs gyroscope cross-axis 
calibration procedure presented in 
Chapter 2. 
 
The IMU sensor calibration setup module enables the user to create a calibration 
sequence of his choice from the calibration steps listed in Table 9. The created sequence 
can be stored and retrieved at the user?s will. The TAG fields OA, OG, and TT are user 
configurable one byte values that will be appended to every data packet acquired in a 
particular calibration step. This TAG will be used at the time of data post-processing to 
sort and manipulate calibration data. The IMU sensor calibration sub-module executes 
the calibration sequence created by the IMU sensor calibration setup sub-module, 
collects calibration data and alerts the user on completion of the calibration sequence. 
The IMU sensor calibration result generation sub-module retrieves the calibration data 
 69 
file and passes a handle of the file to a MATLAB engine invoked in LabVIEW. The user 
can implement the calibration algorithm presented under Chapter 2 as a MATLAB script 
to be executed by the MATLAB engine for data post-processing and result generation. 
3.6 IMU Calibration System Requirements 
In order to implement the calibration procedure discussed under Chapter 2, the 
calibration application running in the calibrating computer must comply with the 
following high level functional requirements. The requirements are categorized under the 
various modules of the IMU calibration system presented in Table 10. 
 
Table 10: IMU calibration application software system requirements 
 
IMU Thermal Calibration Module 
IMU_thermal_cal_req1 1. The application shall be capable of establishing serial 
communication and be able to log data from at least 4 IMU. 
IMU_thermal_cal_req2 1. The application shall be capable of communicating with 
the environmental chamber?s WATLOW series F4 ramping 
temperature controller via a dedicated serial channel using 
MODBUS communication protocol.  
2. The application shall be capable of controlling the 
operations of the WATLOW F4 temperature controller by 
issuing MODBUS command messages [11].  
 
3. The application shall enable the user to create, edit and 
 70 
download custom thermal profiles to the WATLOW F4 
ramping temperature controller using MODBUS command 
messages. 
IMU_thermal_cal_req3 The application shall be capable of parsing the logged data 
and present the user with graphical plots of logged data. 
IMU Sensor Calibration Module 
IMU_sensor_cal_req1 1. The application shall be capable of establishing serial 
communication and be able to log data from at least 4 IMU.  
IMU_sensor_cal_req2 1. The application shall be capable of communicating with 
the environmental chamber?s WATLOW F4 ramping 
temperature controller via a dedicated serial channel using 
MODBUS communication protocol.  
2. The application shall be capable of controlling the 
operations of the WATLOW F4 temperature controller by 
issuing MODBUS command messages [11].  
IMU_sensor_cal_req3 1. The application shall be capable of communicating with 
the Ideal Aerosmith rate table controller [17] via a dedicated 
serial RS232 channel.  
2. The application shall be capable of controlling the 
operations of the rate table using Aerosmith Table Language 
(ATL) [17].  
IMU_sensor_cal_req4 The calibration application shall enable the user to configure 
 71 
a calibration sequence of his choice composed of steps 
presented in Table 9. 
IMU_sensor_cal_req5 In order to ensure the orientation of the IMU mounting, 
necessary software  interlocks shall be provided in the 
calibration application for both accelerometer and gyro 
calibration.  
 
 
3.7 IMU Calibration System ? Application Software Implementation 
The IMU application software modules have been implemented as LabVIEW 
virtual instruments (VI). The implementation of IMU calibration application software is 
presented as follows. 
3.7.1 Main Module 
Sub-module: Main 
Virtual instrument: main.vi 
Called by: none 
Calls: imu_cal_comm_setup.vi, watlow_f4_programmer.vi, imu_thermal_cal.vi, 
imu_thermal_cal_result_gen.vi, imu_cal_setup.vi, imu_sensor_cal.vi, 
imu_cal_result_gen.vi, ads_cal_comm_setup.vi, watlow_programmer.vi, ads_burn_in.vi,  
ads_burn_in_val.vi, ads_cal_ setup.vi, ads_sensor_cal.vi, ads_cal_result_gen.vi 
 
The Main module provides the central user interface from which all other system 
modules and sub-modules can be called. The GUI for main.vi is shown in Figure 30. 
 72 
 
 
Figure 30: Main GUI 
3.7.2 IMU Calibration Communications Setup Module 
Sub-module: Communication setup 
Virtual instrument: imu_cal_comm_setup.vi 
Called by: main .vi  
Calls: none 
The imu_cal_comm_setup.vi enables the user to allocate serial communication resources 
and setup the communication parameters for each of the system components present in 
the IMU calibration system. Figure 31 shows the GUI for this sub-module. Figure 32(a), 
Figure 32(b) and Figure 32(c) present the flow chart for communication settings required 
for the IMU batch, Aero812 rate table controller, and the WATLOW F4 temperature 
 73 
controller, respectively. As shown, the communication settings are obtained from the user 
and saved to the imu_comm_setup.dat file. Depending on the IMU batch size being 
calibrated, the user can enable or disable data logging for individual IMU units. 
 
 
Figure 31: IMU communications setup GUI 
 74 
IMU calibration batch setup
start
Aero812 rate table controller setup
start
WATLOW F4 temperature controller
setup start
Obtain & load serial port
configuration from file
Obtain serial port
configuration from file
Obtain & load serial port
configuration from file
Select IMU n to configure
n = 0,1,2 ....15
1. Enable/Disable  data logging for
the selected IMU
2. Allocate serial resource for the
selected IMU.
3. Enter Baud Rate
All IMU
configured ?
Save revised configuration to
imu_comm_setup.dat file
IMU calibration batch configuration
done
yes
no
1. Allocate serial resource for the
Aero812 rate table controller.
2. Enter Baud Rate
Save revised configuration to
imu_comm_setup.dat file
Aero812 rate table controller
configuration done
1. Allocate serial resource for
communication with WATLOW
F4 temperature controller.
Save revised configuration to
imu_comm_setup.dat file
WATLOW F4 temperature
controller configuration done
(a) IMU batch communication setup (b) Aero812 rate table controller setup (c) WATLOW F4 controller setup  
Figure 32: Communications setup module flowchart 
 
3.7.3 Thermal Calibration Module  
Sub-module: Download thermal profiles 
Virtual instrument: watlow_f4_programmer.vi 
Called by: main .vi  
Calls: download__f4_profile.vi 
The watlow_f4_programmer.vi enables the user to create and download custom 
temperature profiles to the series F4 WATLOW ramping temperature controller. Figure 
 75 
33 shows the GUI for this sub-module. Figure 34 and Figure 35 present the flowchart of 
the Download thermal profiles sub-module. This sub-module enables a user to implement 
a thermal profile of his choice using a combination of ramp time, ramp rate, soak and 
jump commands. A command_list array is built from the user commands and encoded in 
a format in compliance with the MODBUS protocol [18]. This encoded thermal profile is 
serially transmitted to the WATLOW F4 temperature controller. The download_profile.vi 
shown in Figure 36 presents the flowchart of the profile download process. The 
download_profile.vi obtains the environmental chambers serial communication settings 
from the imu_comm_setup.dat file. The encoded command_list array is downloaded to 
the temperature controller with necessary error checking and message 
acknowledgements. The command list contains the temperature commands, encoded as a 
list of WATLOW F4 controller registers and their values [18].  
 
 76 
 
Figure 33: Download thermal profiles GUI 
 77 
watlow_f4_programmer.vi start
CREATE / EDIT
/ DOWNLOAD ?
Select step
AUTO
START
RAMP
TIME
RAMP
RATE
SOAK
JUMP
A
B
C
D
E
select file & load saved  profile
"command_list" from file
ensure a new profile is created /
saved profile is loaded
download_f4_profile.virevise / edit loaded "command_list"
Save edited "command_list" to file F
DownloadCreate
Edit
G
F
 
 
 
Figure 34: Download thermal profiles flowchart-I 
 78 
A B C D E
Enter "AUTO START"
parameters module
Enter "RAMP_TIME"
parameters module
Enter "RAMP_RATE"
parameters module
Enter "SOAK"
parameters module
Enter"JUMP"
parameters module
Enter "wait_for"
parameters
Enter RAMP_TIME in
Hours,Minutes,Seconds
Enter Temperature set
point
Enter "wait_for"
parameters
Enter RAMP_RATE in
"units per minute"
Enter "wait_for"
parameters
Enter SOAK_TIME
in Hours, Minutes,
Seconds
Enter Temperature set
point
enter "step" to jump to
enter "number of
repeats"
Enter Date
Enter Time
Enter "END" parameters
module
Enter "END"mode
Profile
complete?
Add step to "command_
list"
Save "command_list" to file watlow_f4_programmer.vi end
F
F
User "Exit
Module"
yes
G
no
 
 
Figure 35: Download thermal profiles flowchart-II 
 
 79 
download_profile.vi start
open serial resource (COM port) for
communication with environmental chamber
flush UART RX buffer
write cmmand_list[i] to UART TX buffer
close COM port
error status ?
download_profile.vi end
error
no error
n= bytes in UART RX buffer
read n bytes from UART RX buffer
i=0
i = i+1
i >=
size(command_list
)
true
false
 
 
Figure 36: Profile download process flowchart 
 
Sub-module: Thermal calibration  
Virtual instrument: imu_thermal_cal.vi 
Called by: main .vi  
Calls: none 
The imu_thermal_cal.vi enables the user to execute the IMU batch thermal calibration 
process. Figure 37 shows the GUI for this sub-module. The flowchart of 
imu_thermal_cal.vi is shown in Figure 38. As shown, the communication settings are 
 80 
obtained from the imu_comm_setup.dat file and serial COM port handles are opened for 
communication with the enabled IMU units and the WATLOW F4 temperature controller 
in the thermal chamber. This module initiates the thermal profile loaded to the 
temperature controller by the Download thermal profiles sub-module and logs the output 
data from the IMU batch continuously.  
 
Figure 37: IMU thermal calibration GUI 
 
 81 
Thermal calibration start
retrieve IMU communications
set-up from
imu_comm_setup.dat file
Handle Ai = Open serial COM port
handles to communicate with
enabled IMU units i= 0,1,2,3...n.
Handle B = Open serial COM port
handle to communicate with
environmental chamber
Start thermal profile by initiating the
thermal profile execution via
Handle B
flush UART RX buffer (Handle Ai)
N = bytes in RX buffer (Handle Ai)
imu_data_msg = Read N bytes from UART
RX buffer (Handle A)
Parse (imu_data_msg)
check CRC
pass
fail
save imu_data_msg to imu_log.dat file
i < n
true
A
false
B
i=i+1
i = 0
"User input"
stop acquisition
false
thermal calibration end
A
B
Close open serial port handles.
 
 
Figure 38: IMU thermal calibration 
 
 82 
Sub-module: Thermal calibration result generation 
Virtual instrument: imu_thermal_cal_result_gen.vi 
Called by: main .vi  
Calls: none 
The imu_cal_result_gen.vi enables the user to view and analyze the acquired thermal 
calibration data. Figure 39 shows the GUI for this sub-module. Figure 40 shows the 
flowchart of this VI. This module provides the user with provisions to select a data 
component to view and displays the selected plots. It also passes the IMU thermal 
calibration data retrieved to a MATLAB engine. The MATLAB engine executes the 
thermal calibration data processing procedure presented in Chapter 2, implemented as a 
MAT script to generate the thermal calibration results.  
 
Figure 39: IMU thermal calibration result generation GUI 
 83 
Thermal calibration result
generation start
retrieve logged IMU data
from imu_log.dat file
poll "user input" for the
IMU parameter to view
"user input"
update plot
Display selected parameter on
plot
Thermal calibration result
generation end
false
true
"User input"
Exit and return
false
true
Pass retrieved IMU data to the
MATLAB Engine
Thermal
calibration
Result
 
Figure 40: Thermal calibration flowchart 
3.7.4 IMU Sensor Calibration Module  
Sub-module: IMU sensor calibration setup 
Virtual instrument: imu_cal_setup.vi 
Called by: main .vi  
Calls: none 
The imu_cal_setup.vi provides the user the flexibility of creating a calibration sequence 
of his choice.  Figure 41 shows the GUI for this sub-module. The flowchart for the 
imu_cal_setup.vi is shown in Figure 42. The user creates the calibration sequence by 
 84 
sequencing the accelerometer calibration, gyroscope calibration and target temperature 
steps. Table 9 presents the functions provided by each of the steps. The imu_cal_setup.vi 
essentially obtains the input parameters required to implement the functions performed 
by each of the steps and creates a calibration sequence array main_cmd_list. 
 
Figure 41: IMU sensor calibration setup GUI 
 85 
IMU Sensor Calibration
Setup imu_cal_setup.vi Start
Enter 3-D orientation tag for
accelerometer calibration OA
Enter number of data
packets to acquire N
Enter limits for orientation
sanity checks
Enter rates Rmin,Rmax and
Rinc
Enter number of data
packets to acquire N
Enter target temperature tag
TT
Enter target temperature Tt
Add step
"user input"
Add step
"user input"
Add step
"user input
append accelerometer calibration
specifications "accel_cal" to command list
cmd_list [i]
R = Rmin
i=0
create Aero812 rate table command word
for rate R, rate_cmd[i]
R = Rmin+ Rinc
i=i+1
R > Rmax
set-up done
"user input" IMU sensor calibration done
imu_cal_setup.vi end
main_cmd_list [k] = concatenate incoming cmd_list[i]
arrays
k = k+size(i)
yes
yes yes
yes
A
A A
A
no no
no
no
no
yes
B
B
save main_cmd_list[] to file
"imu_cal_setup.dat"
Enter Soak time
Ts - HRS, MIN, SEC
accelerometer calibration step
gyroscope calibration step
Temperature step
Enter 3-D orientation tag for
gyroscope calibration OG
"user
selection"
append accelerometer temperature
command  specifications "target_temp" to
command list
cmd_list [i]
append gyroscope calibration "gyro_cal"
specifications to command list
cmd_list [i]
append cross-axis calibration
specifications "cross_axis" to
command list
cmd_list [i]
C
C
 
Figure 42: IMU sensor calibration setup flowchart 
 
 
 86 
Sub-module: IMU sensor calibration 
Virtual instrument: imu_sensor_cal.vi 
Called by: main .vi  
Calls: none 
The imu_sensor_cal.vi executes the calibration sequence created by imu_cal_setup.vi. 
Figure 43 shows the GUI for this sub-module. Figures 44, 45, 46 and 47 present the 
relevant flow charts for IMU sensor calibration sub-module. The sensor calibration 
module has been implemented as a robust state machine that transits between the various 
calibration steps in order to implement the IMU calibration process, as shown in Figure 
44. Figure 45(a) shows the accel_cal.vi. The accel_cal.vi step checks for the mounting 
orientation and prompts the user for any improper orientation based on the limit checks 
configured by the user. Under proper mounting orientation, a sample set of size N is 
acquired and logged. Figure 45(b) shows the gyro_cal.vi. The gyro_cal.vi jogs the IMU 
batch at 100 ?/s to check for gyro triad mounting orientation. It prompts the user in case 
an improper orientation is detected based on the gyro triad measurement made. Under 
proper mounting orientation, the rate table is jogged at the configured rotation rates and 
IMU batch output is acquired and logged once the rate table stabilizes at each configured 
rate. On completion of all configured rates program control exits the gyroscope 
calibration step. Figure 45(c) shows the target_temp.vi. The target temperature step 
creates a two-step thermal profile targeting the configured temperature followed by a 
soak. The target temperature and soak time is configured by the user using the 
imu_cal_setup.vi. The created profile is downloaded to the WATLOW F4 temperature 
controller and executed. The environmental chamber temperature is polled to let the 
 87 
chamber temperature to stabilize at set temperature. On stabilization, IMU batch output 
data of size N is acquired and logged. Figure 46 shows the flowchart for cross_axis.vi. As 
shown in the flowchart, the accel_cal.vi and gyro_cal.vi are called for orientations 11, 21, 
and 31 to calibrate the IMU for cross-axis errors. 
 
Figure 43: IMU sensor calibration GUI 
 
 88 
IMU calibration
imu_sensor_cal.vi start
read and load
"imu_comm_setup.dat" file
read and load "imu
_cal_setup.dat" file
retrieve serial COM port settings
retrieve main_cmd_list []
i=0
user input
"Calibration_start"
current_command =
main_cmd_list [i]
cal_status = if(
i>=size(main_cmd_list))
Execute accel_cal.vi
i=i+1
Execute gyro_cal.vi
i=i+1
Execute
target_temperature.vi
i=i+1
"C
ali
bra
tio
n_
sta
rt"
 = 
0
"Calibration_start" = 1 current_c
omm
and =
acce
l_cal
current_c
ommand
 = gyro_
cal
current_c
ommand
  = target
_temp
acce
l_cal
 don
e
gyro_cal
 done
target_te
mp done
IMU calibration
imu_sensor_cal.vi end
cal_status = 1
Execute cross_axis.vi
i=i+1
cro
ss_
axi
s d
one
cur
ren
t_c
om
ma
nd
 =
cro
ss_
axi
s
 
Figure 44: IMU sensor calibration flowchart - I 
 
 89 
accel_cal.vi start
Prompt user to mount the IMU batch
in orientation OA.
wait for user
confirmation
orientation
check
pass
Prompt user
for improper
orientation fail
Log N data packets
call - log_n_data_packets.vi
accel_cal.vi end
gyro_cal.vi start
Prompt user to mount the IMU batch
in orientation OG.
wait for user
confirmation
Log N data packets (N=1)
call - log_n_data_packets.vi
orientation
check
pass
Prompt user
for improper
orientation fail
Log N data packets (N=1)
call - log_n_data_packets.vi
Jog rate table at 100 deg/sec
call - dispatch_rate.vi
Jog rate table at Rseq[i]
call - dispatch_rate.vi
Log N data packets
call - log_n_data_packets.vi
i = i + 1
i > size (Rseq)
gyro_cal.vi end
true
false
true
false
true
false
(b) Gyroscope calibration step
target_temp.vi start
Create 2 step thermal profile
download thermal profile
call  - download_profile.vi
Chamber
temperature
stabilized  ?
target_temp.vi end
(c) Target temperature step
(a) Accelerometer calibration step
 
Figure 45: IMU sensor calibration flowchart - II 
 90 
cross_axis.vi start
orientation OA = 11.
orientation OG = 11.
Rseq[0] = 150 deg/sec.
Call accel_cal.vi
orientation OA = 21.
orientation OG = 21.
Rseq[0] = 150 deg/sec.
Call gyro_cal.vi
Call accel_cal.vi
Call gyro_cal.vi
orientation OA = 31.
orientation OG = 31.
Rseq[0] = 150 deg/sec.
Call accel_cal.vi
Call gyro_cal.vi
cross_axis.vi end
 
 
 
Figure 46: IMU sensor calibration flowchart ?III 
 
 91 
 
dispatch_rate.vi start log_n_data_packets.vi start
read and load
"imu_comm_setup.dat" file
flush UART RX buffer (Handle Ai)
N = bytes in RX buffer (Handle Ai)
imu_data_msg = Read N bytes from UART
RX buffer (Handle A)
Parse (imu_data_msg)
check CRC
pass
fail
save imu_data_msg to imu_log.dat file
i < n
true
A
false
i=i+1
Handle Ai = Open serial COM port
handles to communicate with
enabled IMU units i= 0,1,2,3...n.
read and load
"imu_comm_setup.dat" file
Load data tag to append
example: OA, OG, TT etc
Load number of data packets
to log N
append data tag to imu_data_msg
Load rate sequence array
Rseq[]
i = 0
Issue rate command
for rate Rseq[i]
Read current table rate R
R >= Rseq[i]
dispatch_rate.vi end
i = i + 1
true
false
 
 
Figure 47: IMU sensor calibration flowchart - IV 
 
 92 
Sub-module: IMU sensor calibration result generation 
Virtual instrument: imu_cal_result_gen.vi 
Called by: main .vi  
Calls: none 
The imu_cal_result_gen.vi enables the user to implement and evaluate various calibration 
algorithms.  Figure 48 shows the GUI for this sub-module. This module provides an 
interface to MATLAB from the labVIEW environment. Figure 49 presents the flow chart 
of the IMU result generation module. As shown, the logged IMU calibration data is 
retrieved and fed to the MATLAB engine. The calibration algorithm presented under 
Chapter 2, implemented as a MAT script, processes the IMU calibration data and 
presents the results to the user.  
  
Figure 48: IMU sensor calibration result generation GUI 
 
 93 
imu_cal_result_gen.vi start
retrieve logged IMU
calibration data from
ads_log.dat file
parse retrieved data and input
the calibration data to the
MATLAB script
Execute the calibration algorithm
implemented in MATLAB
Display results
imu_cal_result_gen.vi end
"User input"
Exit and return
"User input"
process data
true
false
true
false
 
 
Figure 49: IMU sensor calibration result generation flowchart 
 
3.8 ADS Calibration System ? Application Software 
The ADS calibration application is characterized by a highly modular architecture, with 
each module implemented to perform a particular function of the ADS calibration 
process. Each of these component modules comprises a number of sub-modules. Table 11 
lists the various modules and sub-modules involved in the ADS calibration process. 
 94 
Figure 50 presents the operational sequence in which the various modules   and sub-
modules will be employed by the user. The ADS communications setup module is 
responsible for allocating serial communication resources for each of the calibration 
system components and setting up their communication settings. The ADS burn-in 
module is responsible for conducting burn-in tests on an ADS unit. It consists of a 
number of sub-modules: The Download thermal profile sub-module allows a user to 
create and download customized thermal profiles to the environmental chamber. The 
ADS burn-in sub-module begins the execution of the downloaded thermal profile and 
subjects the ADS unit in the environmental chamber to desired thermal loading. During 
thermal loading, ADS output data is acquired and logged. On completion of thermal 
cycling, the ADS burn-in validation sub-module presents the user with graphical plots of 
logged ADS data based on which the user validates the assembled ADS board. The ADS 
calibration module is responsible for sensor calibration of the ADS unit. The ADS 
calibration setup sub-module provides the user the versatility to create any custom 
calibration or acceptance test sequence. 
 95 
ADS Calibration start
ADS communications set-up module
Download thermal profile
ADS burn-in
burn-in
complete ?
ADS burn-in validation
ADS calibration set-up
ADS calibration
Calibration
complete ?
ADS calibration result generation
ADS acceptance tests
Acceptance
complete ?
ADS Calibration end
Communication set-up
ADS sensor calibration
process
ADS burn-in process
yes
yes
yes
no
no
no
 
Figure 50: ADS calibration process 
 
 
 
 
 96 
Table 11: ADS calibration application software module and sub-modules 
 
 MODULES SUB-MODULES 
1 ADS communications  
setup module 
ADS calibration communication setup 
2 ADS Burn-in module Download thermal profile 
  ADS burn-in 
  ADS burn-in validation 
3 ADS calibration module ADS sensor calibration setup 
  ADS calibration 
  ADS calibration result generation 
 
A calibration sequence/acceptance test sequence comprises a number of steps, 
each of which performs a specific function of the ADS sensor calibration/acceptance 
process. For example: go to temperature 25 oC, wait for 10 minutes, go to altitude -1000 
ft, log 100 ADS data packets, go to altitude 0 ft, log 100 ADS data packets, go to altitude 
1000 ft, log 100 ADS data packets, and so on, is a calibration sequence that calibrates the 
altitude sensor over an altitude span between -1000 ft and 1000 ft at a temperature of 25 
oC. The ADS calibration sub-module executes the calibration sequence created by the 
ADS sensor calibration setup sub-module, collects calibration data and alerts the user on 
completion of the calibration sequence. The ADS calibration result generation sub-
module retrieves the calibration data collected by the ADS calibration sub-module and 
uses a MATLAB script to post process the data. It generates the ADS calibration surface 
plots and presents the user with the surface fit constants, which are re-programmed into 
 97 
the ADS unit by the user. The ADS acceptance process involves evaluating a calibrated 
ADS unit?s output at various temperatures, altitudes and air-speeds specified by the 
acceptance test criteria. The ADS acceptance tests enable the user to evaluate the quality 
of calibration. The user using the test sequences created by the ADS calibration setup 
module can create suitable acceptance test. The ADS calibration module can be used to 
execute these acceptance tests. Suitable scripts can be implemented for evaluating 
conformance with acceptance criteria. 
3.9 ADS Calibration System Application Software Requirements 
In order to implement the calibration procedure discussed under Chapter 2, the 
ADS calibration application must comply with the functional requirements given in Table 
12. The requirements are categorized under the various modules of the ADS calibration 
application. 
 
Table 12: ADS calibration application software requirements 
 
ADS burn-in module 
ADS_burn_in_req1 The application shall be capable of establishing serial 
communication and be able to log data from at least one 
ADS unit. 
ADS_burn_in_req2 The application shall be capable of communicating with the 
environmental chamber?s series 942 temperature controller 
via a dedicated serial channel. It shall be capable of 
monitoring and controlling the operations of the series 942 
 98 
temperature controller. It shall enable the user to create, edit 
and download thermal profiles to the series 942 controller.  
ADS_burn_in_req3 The application shall be capable of parsing the logged data 
and present the user with graphical plots of logged data for 
identification of shifts, dropouts, or any abnormal noise that 
might have occurred due to thermal loading. 
ADS sensor calibration module 
ADS_sensor_cal_req1 The application shall be capable of establishing serial 
communication and be able to log data from at least one 
ADS unit. 
ADS_sensor_cal_req2 The application shall be capable of communicating with the 
environmental chamber?s series 942 temperature controller 
via a dedicated serial link. It must be capable of monitoring 
and controlling the operations of the series 942 temperature 
controller. 
ADS_sensor_cal_req3 The application shall be capable of communicating with the 
DRUCK 403 air data test system via a dedicated GPIB 
interface. The operations of the air data test system will be 
controlled through DRUCK 403 ADTS commands over the 
GPIB bus.  
ADS_sensor_cal_req4 The application shall be capable of parsing the logged data 
and present the user with graphical plots of logged data. 
 99 
ADS calibration acceptance test module 
ADS_cal_acceptance_r
eq1 
The module must me capable of retrieving, parsing and 
processing logged ADS calibration data to generate the 
surface fit equation and its constants.  
ADS_cal_acceptance_r
eq2 
The module must be capable of applying the obtained 
surface fit equation on raw calibration data and present the 
user with calibrated ADS data. 
 
3.10 ADS Calibration System ? Application Software Implementation 
The ADS application software modules have been implemented as labVIEW virtual 
instruments (VI?s). The implementation of the ADS calibration application software is 
presented as follows. 
3.10.1 ADS Calibration Communications Setup  
Sub-module: ADS calibration communication setup 
Virtual instrument: ads_cal_comm_setup.vi 
Called by: main .vi  
Calls: none 
The ads_cal_comm_setup.vi enables the user to allocate serial communication resources 
and setup the communication parameters for each of the system components present in 
the ADS calibration system.  Figure 51 shows the GUI for this sub-module. Figure 52 
presents the flow chart of the ADS communications setup module. As shown, the 
 100 
communication settings are obtained from the user and saved to ads_comm_setup.dat 
file.  
 
Figure 51: ADS communications setup GUI 
 101 
ads_cal_comm_setup.vi start
Select serial "COM" port for
WATLOW series 942 controller
Select port number for GPIB
communication with DRUCK
Enter WATLOW series 942
baud rate
Select serial "COM" port for
ADS unit
Enter ADS serial baud rate
Enter number of ADS data
packets to log
Save set-up data
"user input"
ads_cal_comm_setup.vi end
Save communication settings to
ads_comm_setup.dat
no
yes
 
Figure 52: ADS communications setup flowchart 
 
 
 
 
 
 102 
3.10.2 ADS Burn-in Module 
Sub-module: Download thermal profiles 
Virtual instrument: watlow_programmer.vi 
Called by: main .vi  
Calls: download_profile.vi 
The watlow_programmer.vi enables the user to create and download custom temperature 
profiles to the series 942 WATLOW temperature controller. Figure 53 shows the GUI for 
this sub-module. Figure 54(a) presents the flowchart of the Download thermal profiles 
sub-module. This sub-module obtains the temperature profile data from the user and 
encodes it in series 942 temperature controller?s command message format [18]. The 
encoded temperature command input from user is appended to a temp_cmd_list array and 
downloaded to the series 942 controller by the download_profile.vi. Figure 54(b) presents 
the flowchart of the download_profile.vi. The download_profile.vi obtains the serial 
communication settings for communication with the environmental chamber from the 
ads_comm_setup.dat file. The temp_cmd_list array is downloaded to the temperature 
controller with necessary error checking and message acknowledgements, as shown in 
Figure 54(b).  
 103 
 
Figure 53: WATLOW series 942 programmer GUI 
 104 
watlow_programmer.vi start
select step type :
stp_typ = StPt or SoAh  or
Jmp or End
configure step
"user input"
stp_typ
Enter set point = set_pt
ramp rate = rmp_rt
Enter Soah time
hours = hrs, minutes = min,
seconds = sec
Enter Jmp step_number Enter End state
stp_cmd = "STP i 1 set_pt rmp_rt 1 1 0"
 step number i = 0
array temp_cmd_list[]
i = i+1
stp_cmd = "STP i 2 hrs_min sec 1 1 0"
i = i+1
temp_cmd_list [i] = stp_cmd
temp_cmd_list [i] = stp_cmd
download_profile.vi start
retrieve ADS communications set-up
from ads_comm_setup.dat file
open serial resource (COM port) for
communication with environmental chamber
flush UART RX buffer
Write temp_cmd_list[i] to UART TX buffer
close COM port
Error status ?
download_profile.vi end
error
no error
n= bytes in UART RX buffer
Read n bytes from UART RX buffer
i=0
i = i+1
i >=
size(temp_cmd_lis
t)
true
false
A
stp_cmd = "STP i 1 set_pt rmp_rt 1 1 0"
i = i+1
temp_cmd_list [i] = stp_cmd
stp_cmd = "STP i 1 set_pt rmp_rt 1 1 0"
i = i+1
temp_cmd_list [i] = stp_cmd
A A
B
Execute download_profile.vi
StPt
SoAh
Jmp End
Download profile
"user input"
A
button press
no button press
button press
A
B
no button press
(a) WATLOW series 942 programmer
(b) Download thermal profiles
 
 
Figure 54: WATLOW programmer flowchart 
 105 
 
Sub-module: ADS burn-in 
Virtual instrument: ads_burn_in.vi 
Called by: main .vi  
Calls: none 
The ads_burn_in.vi enables the user to execute the ADS burn-in process. Figure 55 
shows the GUI for this sub-module. Figure 56 presents the flowchart of the ADS burn-in 
sub-module. This sub-module obtains the communications settings from the 
ads_comm_setup.dat file and opens serial resource handles for communication with the 
ADS unit and the environmental chamber. It commences the thermal profile programmed 
into the WATLOW series 942 temperature controller by the Download thermal profiles 
sub-module and continually acquires and logs the ADS output data.   
 
 106 
 
Figure 55: ADS burn-in GUI 
 107 
ads_burn_in.vi start
retrieve ADS communications
set-up from
ads_comm_setup.dat file
K = ADS data message size
Handle A = Open serial COM port
handle to communicate with ADS
unit
Handle B = Open serial COM port
handle to communicate with
environmental chamber
Start thermal profile by issuing
START command via Handle B
flush UART RX buffer (Handle A)
N = bytes in RX buffer (Handle A)
N >= K ?
ads_data_msg = Read N bytes from UART
RX buffer (Handle A)
Parse (ads_data_msg)
check CRC
false
true
pass
fail
save ads_data_msg to ads_log.dat file
"User input"
stop acquisition
false
ads_burn_in.vi start
 
 
Figure 56: ADS burn-in flowchart 
 
 
 108 
Sub-module: ADS burn-in validation 
Virtual instrument: ads_burn_in_val.vi 
Called by: main .vi  
Calls: none 
The ads_burn_in_val.vi enables the user to view and validate the results of the thermal 
burn-in process. Figure 57 shows the GUI for this sub-module. Figure 58 presents the 
flowchart of the ADS burn-in validation sub-module. This sub-module retrieves the 
logged ADS data from the ads_log.dat file and displays plots of various ADS output 
parameters. The GUI provides various zoom features to thoroughly analyze and validate 
the ADS output. 
 
Figure 57: ADS burn-in validation GUI 
 109 
ads_burn_in_val.vi start
retrieve logged ADS data from
ads_log.dat file
poll "user input" for the ADS
parameter to view
"user input"
update plot
Display parameter on plot
ads_burn_in.vi start
false
true
"User input"
Exit and return
false
 
Figure 58: ADS burn-in flowchart 
 
3.10.3 ADS Calibration Module 
Sub-module: ADS calibration setup 
Virtual instrument: ads_cal_ setup.vi 
Called by: main .vi  
Calls: none 
The ads_cal_cal_setup.vi gives the user the modularity to execute a calibration sequence 
of his choice. Figure 59 shows the GUI for this sub-module. Figure 60 presents the 
flowchart for the ads_cal_setup.vi. This module obtains the inputs required for a 
 110 
particular calibration step and encodes it in an appropriate communication message 
format. The supported calibration steps enable a user to target and soak at a temperature, 
target an altitude, or target an airspeed. Using a combination of these steps the user has 
the flexibility to implement and execute any calibration sequence of his choice. A master 
command array is built out of these individually encoded calibration steps, which can be 
edited at the user?s will. After creating a sequence of his/her choice the user can save the 
calibration setup to a file which will be retrieved by the ADS calibration sub-module at 
the time of ADS sensor calibration.  
 
Figure 59: ADS calibration setup GUI 
 111 
ADS Sensor Calibration Setup
ads_cal_setup.vi Start
Enter Minimum Altitude Altmin
Enter Maximum Altitude Altmax
Enter Altitude step-size Altstp
Enter Minimum Airspeed
Airmin
Enter Maximum Airspeed
Airmax
Enter Air-speed step-size Airstp
Enter Target temperature Ts
Enter ramp rate Tr
Enter Soah time
Shr , Smin , Ssec ,
Add step
"user input"
Add step
"user input"
Add step
"user input
Alt = Altmin
i=0
create Altitude DRUCK command word
cmd_list [i] = "SOURce:PRESsure alt, Alt"
Alt = Altmin+ Altstp
i=i+1
Alt >= Altmax
Air = Airmin
i=0
create Air-speed DRUCK command word
cmd_list [i] = "SOURce:PRESsure cas, Air"
Air = Airmin+ Airstp
i=i+1
Air >= Airmax
Create target temperature series 942 word
cmd_list [i] = STP 1 1 Ts Tr 1 1 0
create tempetarure soah series word
cmd_list[i+1] = "STP 2 2 Shr Smin Ssec 1 1 0"
main_cmd_list [k] = concatenate
incoming cmd_list[i] arrays
set-up done
"user input"
ADS Sensor Calibration Setup
ads_cal_setup.vi end
k = k+size(i)
yes yes yes
yes yes
A
A A
A
no no
no
no no
no
yes
B
B
save main_cmd_list[] to file
"cal_setup.dat"
 
 
Figure 60: ADS calibration setup flowchart 
 
 112 
Sub-module: ADS calibration 
Virtual instrument: ads_sensor_cal.vi 
Called by: main .vi  
Calls: dispatch_temp_cmd.vi, dispatch_cmd.vi, dispatch_air_cmd.vi, ads_log_n_packets 
The ads_sensor_cal.vi enables the user to execute the ADS sensor calibration process. 
Figure 61 shows the GUI for this sub-module. Figure 62 and Figure 63 present the flow 
charts for ads_sensor_cal.vi. The communication settings are retrieved from the 
ads_comm_setp.dat file and the calibration sequence is retrieved from the 
ads_cal_setup.dat file.  The execution of the calibration sequence has been implemented 
as a state-machine as shown in Figure 62. Based on the action requested by the current 
command in the calibration sequence one of the two execution modules, 
dispatch_temp_cmd.vi or dispatch_adts_cmd.vi, is executed. Figure 63(a) shows the 
dispatch_temp_cmd.vi. As shown, the VI opens the appropriate serial communication 
resource and writes the current temperature command to the series 942 WATLOW 
temperature controller with suitable error checking. Figure 63(b) shows the 
dispatch_adts_cmd.vi. As shown, this VI opens the appropriate serial GPIB resource and 
issues the current ADTS command. The command can be either an altitude command or 
an air-speed command. Figure 63(c) shows the flowchart for ads_log_n_packets.vi. As 
shown the VI opens the appropriate serial resource, logs J data packets with suitable CRC 
checks and saves it to the ads_log.dat file. On completion of the ADS sensor calibration 
sequence, the user is prompted with the calibration status.  
 113 
 
Figure 61: ADS calibration GUI 
 
 
 
 114 
ADS calibration
ads_cal_module.vi start
read and load
"ads_comm_setup.dat" file
read and load "cal_setup.dat"
file
retrieve COM port/GPIB settings
retrieve main_cmd_list []
i=0
user input
"Calibration_start"
current_command =
main_cmd_list [i]
cal_status = if(
i>=size(main_cmd_list))
Execute
dispatch_temp_cmd.vi
i=i+1
Execute
dispatch_alt_cmd.vi
i=i+1
Execute
dispatch_air_cmd.vi
i=i+1
log n ADS data packets
ads_log_n_packets.vi
"C
ali
bra
tio
n_
sta
rt"
 = 
0
"Calibration_start" = 1
cur
ren
t_co
mm
and
 = t
emp
 com
man
d
current_command
 = Alt command
current_c
ommand=Air_spee
d comma
nd
set_
tem
p_r
eac
hed
alti
tud
e_r
eac
hed
air
_sp
eed
_re
ach
ed
n d
ata 
pac
kets
 log
ged
ADS calibration
ads_cal_module.vi end
cal_status = 1
 
 
Figure 62: ADS calibration flowchart 
 
 115 
dispatch_tmp_cmd.vi start
open serial resource (COM port) for
communication with environmental chamber
flush UART RX buffer
Write "current_command" to UART TX
buffer
close COM port
Error status ?
dispatch_tmp_cmd.vi end
true
false
n= bytes in UART RX buffer
Read n bytes from UART RX buffer
dispatch_adts_cmd.vi start
open serial resource (GPIB port) for
communication with DRUCK ADTS
Write "current_command" to GPIB device
GPIB Error ?
write_status = GPIB controller status
wait 200 ms
operation_status = Read GPIB device
operation status
?
dispatch_adts_cmd.vi end
"prompt
user"
true
false
done
in progress
ads_log_n_packets.vi start
open serial resource (COM port) for
communication with ADS unit
flush UART RX buffer
N = bytes in (RX buffer)
K = ADS data message size
J = Number of ads packets to log
i=0
N >= K ?
ads_data_msg = Read N bytes from UART
RX buffer
Parse (ads_data_msg)
check CRC
close COM port
i >= J ?
ads_log_n_packets.vi end
save ads_data_msg to ads_log.dat file
i=i+1
close COM port
false
true
pass
fail
true
(a) Dispatch temperature command
(b) Dispatch Druck ADTS command
(c) ADS log N data packets
 
Figure 63: ADS calibration components flowchart 
 116 
Sub-module: ADS calibration result generation 
Virtual instrument: ads_cal_ result_gen.vi 
Called by: main .vi  
Calls: none 
The ads_cal_result_gen.vi enables the user to implement and evaluate various calibration 
algorithms.  This module provides an interface to MATLAB from the labVIEW 
environment. Figure 64 presents the flow chart of the ADS result generation module. As 
shown, the logged ADS calibration data is retrieved and fed to the MATLAB engine. The 
calibration algorithm presented under Chapter 2, implemented in MATLAB, processes 
the ADS calibration data and presents the results to the user. 
 
 117 
ads_cal_result_gen.vi start
retrieve logged ADS
calibration data from
ads_log.dat file
parse retrieved data and input
the calibration data to the
MATLAB script
Execute the calibration algorithm
implemented in MATLAB
Display results
ads_cal_result_gen.vi end
"User input"
Exit and return
"User input"
process data
true
false
true
false
 
 
Figure 64: ADS result generation
 118 
4 ADAHRS CALIBRATION SUPPORT SYSTEM  
TESTING AND RESULTS 
 
4.1 Chapter Overview 
The ADAHRS calibration system presented in this thesis was tested and its 
functionality was verified at system level. Trial calibration runs were executed using the 
IMU calibration application software and ADS calibration application software presented 
under Chapter 3. The calibration method presented under Chapter 2 was used. Trial 
acceptance test runs were executed to verify and validate the functionality and usefulness 
of calibration performed by the ADAHRS calibration support system. This chapter 
presents the results obtained from the trial calibration runs and acceptance test runs 
conducted.  
4.2 IMU Calibration System Results 
4.2.1 IMU Thermal Calibration 
IMU thermal calibration was done using the Thermal calibration module. A 
temperature cycle between -20 ?C and +65 ?C was used and the data acquired during the 
trial thermal calibration run is shown in Figure 65. Table 13 gives the thermal calibration 
constants generated by the Thermal calibration result generation sub-module. 
 119 
 
Figure 65: IMU thermal calibration data, temperature cycle used was from -20 ?C to +65 
?C. Plots 1, 2, and 3, show the gyro measurements (gx, gy and gy) in counts scaled by a 
division factor 20972 [9] on Y-axis. Plots 4, 5, 6, 7, 8 and 9, show the accelerometer 
measurements (az1, ax1, ay1, az2, ax2, and ay2) in pulse width scaled by a multiplication 
factor of 25 [8]. X-axis represents time (not to scale). 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 120 
 
Table 13: Computed thermal calibration constants for data shown in Figure 65, a          
2nd-order polynomial fit was used. 
 
Accelerometer Thermal constant  
k2 
Thermal constant  
k1 
Thermal constant 
k0 
xg  -8.8615 e-002  7.6793 e+002 -1.1758 e+006 
yg  -2.0937 e-001  1.1421 e+003 -1.4166 e+006 
zg  -9.6758 e-002  4.9812 e+002 -7.1191 e+005 
1za  -2.1004 e-008  7.6304 e-005  4.4814 e-001 
1xa   5.5724 e-009 -2.2270 e-005  4.9489 e-001 
1ya   3.8915 e-008 -1.4233 e-004  5.7257 e-001 
2za   1.8567 e-008 -7.3550 e-005  4.8380 e-001 
2xa  -1.3784 e-008  4.5704 e-005  4.3152 e-001 
2ya  -1.0779 e-009  5.2205 e-006  4.5086 e-001 
 
4.2.2 IMU Accelerometer Offset and Scale Factor Calibration 
The IMU accelerometer offset and scale factor calibration was done using the 
IMU sensor calibration module. The mean of accelerometer data acquired under each of 
the six orientations is shown in Table 14. Tables 15 shows the accelerometer offsets and 
Table 16 shows the accelerometer scale factors computed by the IMU sensor calibration 
result generation module.  
 
 
 
 
 
 
 
 
 
 
 121 
Table 14: Mean of accelerometer measurements acquired under orientations 11, 12, 21, 
22, 31, and 32 are shown. Temperature compensated accelerometer measurement unit in 
pulse width. 
 
 1za   
(mean) 
1xa  
(mean) 
1ya  
(mean) 
2za  
(mean) 
2xa  
(mean) 
2ya  
(mean) 
Orientation 11 -0.03 0.03 5.69 e-5 0.03 -0.03 0.00 
Orientation 12 -0.03 -0.04 0.00 0.00 0.04 0.00 
Orientation 21 0.00 0.00 -0.03 -8.00 e-5 0.00 0.03 
Orientation 22 0.00 0.00 0.03 0.00 0.00 -0.04 
Orientation 31 0.03 0.00 0.00 -0.03 0.00 -0.00 
Orientation 32 -0.04 0.00 0.00 0.03 0.00 0.00 
 
Table 15: Computed accelerometer offsets for data shown in Table 14. Eq. (12) was used 
to compute the offsets. 
 
Accelerometer Offset 
Offset for 1za  -0.0395 
Offset for 1xa  -0.0002 
Offset for 1ya   0.0001 
Offset for 2za   0.0385 
Offset for 2xa   0.0009 
Offset for 2ya   0.0001 
 
Table 16: Computed accelerometer scale factors for data shown in Table 14. Eq. (12) was 
used to compute the scale factors. 
 
Accelerometer Scale factor 
Scale factor for 1za  -25.3533 
Scale factor for 1xa  -25.0795 
Scale factor for 1ya   25.2551 
Scale factor for 2za   25.9297 
Scale factor for 2xa   25.5728 
Scale factor for 2ya  -25.7141 
 122 
4.2.3 IMU Gyroscope Scale Factor Calibration 
Gyro scale factor calibration was done using the IMU sensor calibration module. 
The gyroscope data was acquired at the chosen angular rates in each of the three 
orientations 11, 21 and 31 subjecting gyros xg , yg , zg  to the reference rates. The mean 
of data collected is shown in Table 17. Table 18 shows the gyro scale factor constants 
computed by the IMU sensor calibration result generation sub-module. 
 
Table 17: Mean of gyro measurements taken at the chosen rates; -150 ?/s, -100 ?/s,  -50 
?/s, 0 ?/s, 50 ?/s, 100 ?/s, and 150 ?/s in orientations 11, 21 and 31. Temperature 
compensated gyro measurement unit in counts. 
 
 s0150?  s0100?  s050?  s00  s050  s0100  s0150  
xg  -3.21 e6 -2.14 e6 -1.07 e6 -8203.8  1.05 e6  2.11 e6  3.16 e6 
yg  -3.10 e6 -2.06 e6 -1.02 e6  4905.2  1.03 e6  2.06 e6  3.09 e6 
zg   3.11 e6  2.07 e6  1.05 e6  3388.3 -1.03 e6 -2.08 e6 -3.12 e6 
 
Table 18: Computed gyro scale factor constants for data shown in Table 17 a 3rd-order 
polynomial fit was used to compute the scale factor constants. 
 
Gyroscope Scale factor 
constant 3l  
Scale factor 
constant 2l  
Scale factor 
constant 1l  
Scale factor 
constant 0l  
xg   2.4852 e-20  6.6801 e-14  4.6782 e-5  3.2071 e-2 
yg   8.2173 e-21  4.3668 e-14  4.8363 e-5 -5.8402 e-3 
zg  -1.0998 e-20 -7.4890 e-14 -4.7983 e-5 -8.9218 e-2 
 
 
4.2.4 IMU Cross-Axis Calibration  
IMU cross-axis calibration was done using the IMU sensor calibration module. 
The mean of delta velocities obtained under a reference acceleration input of 1g is shown 
in Table 19 for all three orientations. The mean of delta angles acquired under a reference 
 123 
rate input of +150 ?/s is shown in Tables 20 for all three orientations. The linear velocity 
rates and angular rotation rates measured by the IMU are multiplied by 0.01 internally, to 
obtain the delta velocities and delta angles at 100 Hz. Eq. (30) and Eq. (31), shown the 
computed accelerometer cross-axis matrix CA and computed gyroscope cross-axis matrix 
GA. 
Table 19: IMU cross-axis calibration, mean of delta velocities obtained in orientations 11, 
21 and 31 are shown. Delta velocity unit in m/s. 
 
 Mean of delta 
velocity along 
X-axis (m/s) 
Mean of delta 
velocity along  
Y-axis (m/s) 
Mean of delta 
velocity along  
Z-axis (m/s) 
Orientation 11 -0.0988  0.0015  0.0009 
Orientation 21 -0.0014 -0.0974  0.0014 
Orientation 31 -0.0021  0.0010 -0.0974 
 
Table 20: IMU cross-axis calibration, mean of delta angles obtained in orientations 11, 21 
and 31 are shown. Delta angle unit in degrees. 
 
 Mean of delta  
angle along  
X-axis (deg) 
Mean of delta  
angle along  
Y-axis (deg) 
Mean of delta 
angle along  
Z-axis (deg) 
Orientation 11 1.5051 -0.0168 -0.0129 
Orientation 21 0.0120  1.4977 -0.0034 
Orientation 31 0.0041 -0.0085  1.5105 
 
  
?
?
?
?
?
?
?
?
?
?
??
?=
0054.10102.00221.0
0149.00056.10147.0
0097.00158.09905.0
CA  
 
 
 
)30(  
 
 
 
  
?
?
?
?
?
?
?
?
?
?
?
?=
9993.00056.00027.0
0022.00014.10080.0
0085.00112.09965.0
GA  
 
 
 
)31(  
 
 
 124 
4.2.5 IMU Sensor Calibration Acceptance Test  
The IMU calibration performed was evaluated using acceptance test sequences 
executed by the IMU sensor calibration module. For accelerometer acceptance testing, 
IMU output data was collected in orientations 11, 21 and 31. Figure 66 shows the 
acquired delta velocities in orientations 11, 21 and 31. Table 21 shows the mean of delta 
velocities acquired in the three orientations. In the data presented it can be observed that 
the maximum error caused by cross-axis misalignment is 30 mg?s.  
 
 
Figure 66: Accelerometer calibration acceptance test, delta velocities acquired in 
orientations 11, 21 and 31 are shown. Delta velocity unit in m/s. X-axis represents time 
(not to scale). 
 
 
 
 125 
Table 21: Mean of delta velocities in orientations 11, 21 and 31. Delta velocity unit in 
m/s. 
 
 Mean of  
delta velocity 
along X-axis 
(m/s) 
Mean of 
delta velocity 
along Y-axis (m/s) 
Mean of 
delta velocity 
along Z-axis 
(m/s) 
Orientation 11 -0.0980  0.0020  0.0030 
Orientation 21 -0.0020 -0.0980  0.0004 
Orientation 31 -0.0020 -0.0005 -0.0980 
 
 
For gyroscope acceptance testing, IMU output data was collected at seven chosen 
rates; -150 ?/s, -100 ?/s, -50 ?/s, 0 ?/s, 50 ?/s, 100 ?/s, and 150 ?/s. This acceptance test 
was performed in orientations 11, 21 and 31 to test X, Y and Z axes gyroscopes. Figure 
68 shows the delta angles acquired in orientations 11, 21 and 31. Table 22, 23 and 24, 
show the mean of delta angles acquired in orientations 11, 21 and 31 respectively. In the 
data presented, it can be observed that the maximum error along the major axes is 0.3 ?/s 
in orientation 11 and 31. Maximum error caused by cross-axis misalignment along the 
minor axis is 2.3 ?/s in orientation 21. 
 126 
 
Figure 67: Gyroscope calibration acceptance test, delta angles acquired at rates -150 ?/s, -
100 ?/s, -50 ?/s, 0 ?/s, 50 ?/s, 100 ?/s, and 150?/s,  in orientations 11, 21 and 31 are shown. 
Delta angle unit in degrees. X-axis represents time (not to scale). 
 
 
 
Table 22: Mean of delta angles in orientation 11 acquired at rates -150 ?/s, -100 ?/s, -50 
?/s, 0 ?/s, 50 ?/s, 100 ?/s, and 150 ?/s. Delta angle unit in degrees. 
 
 Mean at 
sec1500?
 
Mean at 
sec1000?
 
Mean at 
sec500?
 
Mean at 
sec00  
Mean at 
sec500  
Mean at 
sec1000
 
Mean at 
sec1500
 
xg  
(deg) 
-1.5023 -1.0035 -0.4994  0.0006  0.4987  0.9991  1.5005 
yg  
(deg) 
 0.0182  0.0115  0.0045  0.0053 -0.0068 -0.0139 -0.0225 
zg  
(deg) 
 0.0207  0.0129  0.0079  0.0011 -0.0080 -0.0153 -0.0212 
 
Table 23: Mean of delta angles in orientation 21 acquired at rates -150 ?/s, -100 ?/s, -50 
?/s, 0 ?/s, 50 ?/s, 100 ?/s, and 150 ?/s. Delta angle unit in degrees. 
 127 
 
 Mean at 
sec1500?
 
Mean at 
sec1000?
 
Mean at 
sec500?
 
Mean at 
sec00  
Mean at 
sec500  
Mean at 
sec1000
 
Mean at 
sec1500
 
xg  
(deg) 
-0.0235 -0.0166 -0.0088 -0.0018 0.0063 0.0136 0.0215 
yg  
(deg) 
-1.5006 -1.0008 -0.5005 -0.0007 0.4999 1.0001 1.5000 
zg  
(deg) 
 -0.0055 -0.0025  0.0002  0.0005 0.0042 0.0067 0.0091 
 
 
Table 24: Mean of delta angles in orientation 31 acquired at rates -150 ?/s, -100 ?/s, -50 
?/s, 0 ?/s, 50 ?/s, 100 ?/s, and 150 ?/s. Delta angle unit in degrees. 
 
 Mean at 
sec1500?
 
Mean at 
sec1000?
 
Mean at 
sec500?
 
Mean at 
sec00  
Mean at 
sec500  
Mean at 
sec1000
 
Mean at 
sec1500
 
xg  
(deg) 
-0.0180 -0.0120 -0.0059 -0.0009   0.0054   0.0120   0.0185 
yg  
(deg) 
 0.0031  0.0037  0.0010 -0.0002  -0.0035  -0.0052  -0.0079 
zg  
(deg) 
-1.5018 -1.0011 -0.4986  0.0000   0.4967   0.9972   1.500 
 
 For IMU thermal calibration acceptance testing, the IMU unit was subjected to 
the same temperature profile that was used for thermal calibration. IMU output data was 
acquired and logged during thermal loading. Figure 69 shows plots of data collected 
during the thermal calibration acceptance test in orientation 31. The maximum standard 
deviation observed is 0.20 ?/s for gyros and 4 mg?s for accelerometers. The IMU thermal 
calibration module can be used to further investigate and improve the quality of IMU 
thermal calibration by evaluating higher order curve fits for temperature compensation.  
 128 
 
Figure 68: IMU thermal calibration acceptance test, conducted between -200C and +650C, 
in orientation 31. Plots 1,2, and 3 shows delta roll angle, pitch angle and yaw angle on Y-
axis in degrees. Plots 3,4, and 5 show delta velocities along X, Y and Z axis along Y-axis 
in m/s. X-axis represents time (no to scale).  
 
4.3 ADS Calibration System Results 
4.3.1 ADS Sensor Calibration 
A trial ADS sensor calibration was done using the ADS sensor calibration 
module. The calibration was performed for an altitude range between -2000 feet to 10000 
feet, at temperatures 250C, 350C, 450C, 550C, and 650C.  A surface fit to the acquired data 
was done using a software tool named Table curve 3-D [22] to model the surface. A 
cubic equation of form y jxixyhygxfxyeydxcybxaz 223322 +++++++++= was 
 129 
chosen to model the surface. Where, z represents the computed altitude in feet, x 
represents the measured altitude in counts and y represents the measured temperature in 
counts. Table 25 shows the surface fit constants computed.  
 
Table 25: Computed surface fit constants 
 
Surface fit 
constants 
Values 
A  1004224.8 
B -0.0731 
C -1376.8546 
D  1.8239 e-08 
E  0.6633 
F  1.7150 e-05 
G -1.2018 e-15 
H -0.0001 
I -3.5173 e-10 
J -4.0258 e-12 
 
 
4.3.2 ADS Sensor Calibration Acceptance Test  
 
The computed counts were downloaded to the ADS unit and an acceptance test 
was conducted at temperatures 250C, 450C, and 650C, at altitudes from -2000 feet to 
10,000 feet at 1000 feet increments. Figure 69 shows the altitude errors observed at 
various altitudes and temperatures. 
 130 
 
Figure 69: ADS altitude error observed at reference altitudes between 0 feet to 12000 feet 
at 1000 feet increments. At temperatures 250C, 450C, and 650C. 
 
 
 The altitude errors observed at lower temperatures are clearly out of the ADS 
error budget specifications shown in Table 2. The ADS calibration support system can be 
used to further refine the ADS calibration by using more closely spaced altitude points 
and temperatures during calibration. Other surface fit equations can be evaluated to bring 
the ADS to function within its rated accuracy specifications. 
 131 
5 CONCLUSION 
 
 
The various sensor error sources relevant to the sensors used in the ADAHRS were 
considered and a comprehensive calibration support system has been developed and 
tested. Unlike the existing calibration methods that cater to the calibration requirements 
of an individual sensor, a simple, comprehensive and integrated calibration framework 
has been developed to calibrate all ADAHRS sensors within the rated temperature and 
measurement range. In addition to its basic calibration function, the flexible nature of the 
calibration support system provides an enabling framework to study and characterize the 
sensors, perform initial burn-in to reduce ADAHRS infant mortality rate, and evaluate the 
effectiveness of calibration using suitable calibration acceptance tests. A highly 
productive LabVIEW application development environment has been used to develop the 
calibration software application. It provides the user a powerful and intuitive GUI in the 
front-end and performs instrument control, calibration data acquisition and data logging 
in the back-end. Post-processing of acquired calibration data is implemented as a MAT 
script, which is executed by a MATLAB engine invoked from LabVIEW. This provides 
the user an open framework to investigate and study various correction and compensation 
algorithms without having to worry about software implementation in LabVIEW. The 
developed calibration system has been tested and verified using trial calibration runs. The
 132 
developed framework can be used in future work to refine the existing calibration process 
and to investigate and develop algorithms to compensate for other sources of errors like 
gyro scale factor dependency on temperature, pressure sensor temperature hysteresis, 
pressure sensor measurement hysteresis, etc. 
 133 
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