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.

This article considers the filtering problem with nonlinear measurements. We propose a new enabling variational inference model for approximating measurement likelihood, which is constructed by a linear Gaussian regression process.The resulting filter is referred to as the new enabling variational inference filter (NEVIF). In variational inference framework, the NEVIF obtains the variational posterior of state by minimizing the Kullback-Leibler divergence between the variational distribution and the true posterior. Then, the accuracy improvement and robustness of the NEVIF compared with the traditional methods are analyzed. Furthermore, an evaluation rule called the filtering evidence lower bound is developed to analyze the estimation accuracy performance of filters.Finally, the efficiency and superiority of the proposed filters compared with some existing filters are shown in numerical simulations.

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