Probabilistic Adaptive Extended Kalman Filter for Satellite Localization in the Presence of Measurement Faults

In this study, a probabilistic adaptive filtering technique is described for the extended Kalman filter (EKF) algorithm, which is used to estimate low Earth orbit (LEO) satellite position, velocity, and clock bias using global navigation satellite system (GNSS) distance measurements. The proposed probabilistic adaptive extended Kalman filter (pAEKF) algorithm is based on tracking normalized innovation sequences in the filter and calculating the probability of normal operation of the estimation system. The filter gain is adjusted based on this probability to maintain the filter's tracking performance despite inaccurate measurements. The developed pAEKF algorithm is used in the LEO satellite navigation system, which includes four global positioning system (GPS) receivers, to estimate orbital motion parameters from distance measurements. The orbital motion of the LEO satellite is simulated using the Kepler and Newton equations, taking into account the effect of the J₂ perturbation caused by the oblateness of the Earth. In order to evaluate the performance of the proposed method, several simulations are performed where measurement bias type faults (additive measurement faults) are introduced to the GPS distance measurements. The estimation accuracies of the proposed pAEKF, multiple measurement noise scale factors (MMNSFs)-based adaptive extended Kalman filter (AEKF) and conventional EKF were investigated and compared.