Schmidt-Kalman Filter for Navigation Biases Mitigation during Mars Entry

Abstract

Advanced navigation systems for pinpoint landing are required in the Mars entry, descent, and landing (EDL) phases. Some new high-precision EDL navigation technologies based on beacons have been presented; however, the measurement bias errors of the beacons—range, position, and velocity errors—have not been considered in the past, which may lead to severe degradation in filtering process. The lack of navigation accuracy may result in a large growth of spurious navigations. In this paper, the Schmidt-Kalman filter is formulated for mitigating the effects of the systematic bias errors. This filter incorporates statistics of measurement errors into the system formulation; instead of only estimating them, it considers the cross correlation between the states and the measurement bias errors, leading to a realistic covariance estimate. Additionally, the UD decomposition is implemented in the Schmidt-Kalman filter to avoid the matrix inversion operation and ensure the numerical stability of the filtering. Monte Carlo simulation results are presented to demonstrate good performance of the Schmidt-Kalman filter with UD decomposition for navigation during the Mars entry. The Schmidt-Kalman filter not only refrains from the divergence of the filtering but also significantly improves the state accuracy.