Simultaneous Mean and Covariance Correction Filter for Orbit Estimation

Abstract

This paper proposes a novel filtering design, from a viewpoint of identification instead of the conventional nonlinear estimation schemes (NESs), to improve the performance of orbit state estimation for a space target. First, a nonlinear perturbation is viewed or modeled as an unknown input (UI) coupled with the orbit state, to avoid the intractable nonlinear perturbation integral (INPI) required by NESs. Then, a simultaneous mean and covariance correction filter (SMCCF), based on a two-stage expectation maximization (EM) framework, is proposed to simply and analytically fit or identify the first two moments (FTM) of the perturbation (viewed as UI), instead of directly computing such the INPI in NESs. Orbit estimation performance is greatly improved by utilizing the fit UI-FTM to simultaneously correct the state estimation and its covariance. Third, depending on whether enough information is mined, SMCCF should outperform existing NESs or the standard identification algorithms (which view the UI as a constant independent of the state and only utilize the identified UI-mean to correct the state estimation, regardless of its covariance), since it further incorporates the useful covariance information in addition to the mean of the UI. Finally, our simulations demonstrate the superior performance of SMCCF via an orbit estimation example.

A New Adaptive Robust Unscented Kalman Filter for Improving the Accuracy of Target Tracking

“…However, under strong nonlinearity, the first-order linearization truncation and neglecting the higher-order term, bring the large error and lead to the filter divergence [23], [24]. EKF is not a good choice for dealing with strong nonlinear systems to replace traditional nonlinear estimation from the perspective of identification [25]. Recently, a very effective alternative to EKF is UKF, which has received wide attention [26].…”