Huber-based divided difference filter with application to relative navigation

Abstract

In this article, a simplified divided difference filter based on the model structure with linear output equations and the assumption of additive Gaussian noise is introduced. By making use of the Huber technique to modify the measurement update equations of the simplified divided difference filter, the new filter exhibits robustness with respect to deviations from the common assumption of Gaussian distributed random measurement errors, for which the simplified divided difference filter exhibits mild degradation in estimation accuracy. In addition, in contrast to standard extended Kalman filter, more accurate estimation and fast convergence are achieved from the poor initial conditions. The proposed Huber-based simplified divided difference filter algorithm has been tested in relative navigation using global position system for spacecraft formation flying in low Earth orbits with real orbit perturbations and non-Gaussian random measurement errors in flight simulations. Simulations results indicate that the proposed filter provides better performance in relative navigation accuracy and robustness when compared to extended Kalman filter and simplified divided difference filter in the presence of non-Gaussian measurement noise.