A Study of the Effects of Stochastic Inertial Sensor Errors in Dead-Reckoning Navigation

Abstract

The research presented in this thesis seeks to quantify the error growth of navigation frame attitude, velocity, and position as solely derived from acceleration and rotation- rate measurements from a strapdown Inertial Measurement Unit (IMU). The wide-spread availability of the Global Positioning System (GPS) and increased technological advances in Inertial Navigation Systems (INS) technology has made possible the use of increasingly affordable and compact GPS/INS navigation systems. While the fusion of GPS and inertial sensing technology offers exceptional performance under nominal conditions, the accuracy of the provided solution degrades rapidly when traveling under bridges, dense foliage, or in urban canyons due to loss of communication with GPS satellites. The degradation of the navigation solution in this inertial dead-reckoning mode is a direct result of the numerical integration of stochastic errors exhibited by the inertial sensors themselves. As the accuracy of the GPS/INS combined system depends heavily on the standalone performance of the INS, firm quantification of the performance of inertial dead-reckoning is imperative for system selection and design.

To provide quantification of the accuracy of inertial dead-reckoning, stochastic mod- els are selected which approximate the noise and bias drift present on a wide variety of both accelerometers and rate-gyroscopes. The stochastic identification techniques of Al- lan variance and experimental autocorrelation are presented to illustrate the extraction of process parameters from experimental data using the assumed model forms. The selected models are then used to develop analytical expressions for the variance of subse- quent integrations of the stochastic error processes. The resulting analytical expressions are validated using Monte Carlo simulations. The analytical analysis is extended to a simple navigation scenario in which a vehicle is constrained to travel on a planar surface with no lateral velocity. Monte Carlo simulation techniques are employed to exemplify and compare the expected results of inertial navigation in higher dynamic scenarios.