Optimization-based iterative and robust strategy for spacecraft relative navigation in elliptical orbit

Abstract

The nonlinear relative dynamics in elliptical orbits and heavy-tailed observation noise can induce a noticeable degradation in navigation accuracy. Although the extensively applied Huber-based M-estimation can cope with non-Gaussian noise, the iterative strategy employed fails to re-linearize the observation model using posterior estimate, and this can induce degradation in filtering efficiency. Considering the inadequate research on iterative and robust strategies, we combine iterated unscented Kalman filter (IUKF) with generalized M-estimation, thereby uniformly and strictly deriving an optimization-based iterative and robust strategy. To approximate the nonlinear observation model more exactly, statistical linearization regression is introduced in the Gauss-newton method, by which the uncertainty induced by approximation errors is compensated in observation noise covariance. Further, we improve the IUKF-based iterative and robust strategy by presenting a novel cost function, where the modified covariance matrix from the previous iteration is incorporated again in the next iteration loop. Comparative studies under non-Gaussian noise show that the novel strategy can facilitate the estimator to achieve higher filtering accuracy, stronger robustness and better consistency. Therefore, the proposed strategy is more suitable for the robust filtering framework.