Performance Comparison of an Extended Kalman Filter and an Iterated Extended Kalman Filter for Orbit Determination of Space Debris with Poor Apriori Information and Intermittent Observations

Abstract

The growing space debris population threatens active and future missions bound for low earth orbit. The purpose of this study is to determine if an iterated extended Kalman filter (IEKF) can be used to yield better performance than the extended Kalman filter (EKF) in the orbit determination of space debris in low earth orbit with poor apriori data and intermittent observations. A simulation using two-body and J2 effects was constructed using actual Space Surveillance Network sensor locations to generate experimental observational data, which contains multiple data outages. This data was then used to compare the performance of the EKF and IEKF. The filters are compared using the difference in the filter estimate and the true state and the difference in the estimated observation and true observation. An increase in estimate accuracy will allow for better predictions concerning the interaction of space debris with missions in low earth orbit.

The IEKF was chosen for this study due to the low number of observations provided and the large apriori covariance matrix. The state update step in the IEKF includes a local iteration that processes each observation until convergence of the state update is reached, which becomes the new best estimate of the state. Following the local convergence, the covariance matrix is updated using this new estimate, which prevents the covariance matrix from growing small as quickly as that of the EKF.