Guaranteed Cost Robust Weighted Measurement Fusion Kalman Estimators With Uncertain Noise Variances and Missing Measurements

Abstract

This paper is concerned with guaranteed cost robust weighted measurement fusion (WMF) estimation problem for multisensor system with both uncertain noise variances and missing measurements. By introducing the fictitious measurement white noises, the original multisensor system is converted into one only with uncertain noise variances. Two classes of guaranteed cost robust WMF Kalman estimators (predictor, filter and smoother) are presented by the Lyapunov equation approach, based on the minimax robust estimation principle and the parameterization representation of uncertain noise variance perturbations. The maximal lower bound and minimal upper bound of actual accuracy deviations are given. A unified approach of designing the robust WMF Kalman estimators is presented based on the robust WMF Kalman predictor. A simulation example shows the correctness and effectiveness of the proposed results.

Reliable fusion estimation over sensor networks with outliers and energy constraints

“…For the issues of fusion estimation (FE), the main challenge focuses on how to design an engineering‐oriented algorithm to obtain optimal or suboptimal fusion weights. At the beginning of this century, some classical fusion algorithms have been reported by utilizing the decentralized or distributed fusion structures, under which local sensors firstly perform well‐known local filtering algorithms based on its own measurement (see related works and the references therein). For instance, the distributed mixed H 2 / H ∞ FE problem has been transformed into a convex optimization problem by using Lyapunov theory and matrix analysis method so as to obtain the optimal weighted fusion criterion .…”

“…Finally, a numerical example is used to illustrate the effectiveness of the proposed method. XIE ET AL.well-known local filtering algorithms based on its own measurement (see related works [13][14][15][16][17][18] and the references therein). For instance, the distributed mixed H 2 ∕H ∞ FE problem has been transformed into a convex optimization problem by using Lyapunov theory and matrix analysis method so as to obtain the optimal weighted fusion criterion.…”

WMF reduced‐order robust estimators for multisensor descriptor systems

“…Substituting the estimates of unknown parameters or unknown variances based on the system identification into the optimal estimators yields the self‐tuning estimators [6]. The robust estimators [13, 18–21] for the non‐descriptor systems with uncertain noise variances are presented based on the mini‐max robust estimation principle. These uncertain noise variances exists the upper bound variances matrices.…”

“…The robust weighted fusion Kalman estimators for multi‐model multisensor systems with uncertain‐variance multiplicative and linearly correlated additive white noises were obtained in [19]. The information fusion method of the literatures [13, 21, 22] is the WMF method. The robust Kalman estimators for the multisensor systems with uncertain noise variances and missing measurements were solved in [21].…”

“…The information fusion method of the literatures [13, 21, 22] is the WMF method. The robust Kalman estimators for the multisensor systems with uncertain noise variances and missing measurements were solved in [21]. The literature [13] gave the robust Kalman estimators for the uncertain system with linearly correlated white noise.…”