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.
Highlights
The orbit estimation problem is to obtain an accurate estimation of a space target’s position and velocity from noisy observations
That the original orbit estimation is transferred into JESI, we design a novel two-stage expectation maximization (EM) algorithm (Figures 3 and 4) to deal with the key difficulty of how to simultaneously fit or identify the first two moments (FTM) of unknown input (UI) associated with the state
This paper mainly aims to demonstrate the superiority of the novel JESI to the standard nonlinear estimation schemes (NESs), and simultaneous mean and covariance correction filter (SMCCF) to the standard nonlinear filters, including extended Kalman filter (EKF), and UKF, among others
Summary
The orbit estimation problem is to obtain an accurate estimation of a space target’s (e.g., satellite) position and velocity from noisy observations. In order to avoid the nonlinear perturbation integral computation, a joint estimation and identification scheme (JEIS) views Fp as an additional unknown input (UI) and analytically identifies Fp to accurately correct the orbit state estimation [6]. The existing EM is incapable of dealing with the case when the UI is associated with the state Following this idea, that the original orbit estimation is transferred into JESI, we design a novel two-stage EM algorithm (Figures 3 and 4) to deal with the key difficulty of how to simultaneously fit or identify the FTM of UI associated with the state. (2) The second EM is designed for fitting the UI-FTM by UI-PMs from different sensors, and used to simultaneously correct the orbit state estimation and its covariance in the first EM.
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