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Volume 3, Issue 6, November 2018, Page: 113-128
Robust Time-Varying Kalman State Estimators with Uncertain Noise Variances
Wenjuan Qi, School of Mechnical and Electronical Engineering, Heilongjiang University, Harbin, China
Zunbing Sheng, School of Mechnical and Electronical Engineering, Heilongjiang University, Harbin, China
Received: Sep. 7, 2018;       Accepted: Sep. 19, 2018;       Published: Jan. 4, 2019
Abstract
This paper addresses the design of robust Kalman estimators (filter, predictor and smoother) for the time-varying system with uncertain noise variances. According to the unbiased linear minimum variance (ULMV) optimal estimation rule, the robust time-varying Kalman estimators are presented. Specially, two robust Kalman smoothing algorithms are presented by the augmented and non-augmented state approaches, respectively. They have the robustness in the sense that their actual estimation error variances are guaranteed to have a minimal upper bound for all admissible uncertainties of noise variances. Their robustness is proved by the Lyapunov equation approach, and their robust accuracy relations are proved. The corresponding steady-state robust Kalman estimators are also presented for the time-invariant system, and the convergence in a realization between the time-varying and steady-state robust Kalman estimators is proved by the dynamic error system analysis (DESA) method and the dynamic variance error system analysis (DVESA) method. A simulation example is given to verify the robustness and robust accuracy relations.
Keywords
Uncertain System, Uncertain Noise Variance, Robust Kalman Filtering, Minimax Estimator, Robust Accuracy, Lyapunov Equation Approach, Convergence
Wenjuan Qi, Zunbing Sheng, Robust Time-Varying Kalman State Estimators with Uncertain Noise Variances, Mathematics and Computer Science. Vol. 3, No. 6, 2018, pp. 113-128. doi: 10.11648/j.mcs.20180306.11
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