Self-Tuning Decoupled Fusion Kalman Predictor and Its Convergence Analysis

Abstract

For the multisensor systems with unknown noise variances, by the correlation method, the information fusion noise variance estimators are presented by taking the average of the local noise variance estimators under the least squares fusion rule. They have the average accuracy and have consistency. A self-tuning Riccati equation with the fused noise variance estimators is presented, and then a self-tuning decoupled fusion Kalman predictor is presented based on the optimal fusion rule weighted by scalars for state component predictors. In order to prove their convergence, the dynamic variance error system analysis (DVESA) method is presented, which transforms the convergence problem of the selftuning Riccati equation into a stability problem of a dynamic variance error system described by the Lyapunov equation. A stability decision criterion of the Lyapunov equation is presented. By the DVESA method, the convergence of the self-tuning Riccati equation is proved, and then it is proved that the self-tuning decoupled fusion Kalman predictor converges to the optimal decoupled fusion Kalman predictor in a realization, so it has asymptotic optimality. A simulation example for a tracking system with 3-sensor shows the effectiveness, and verifies the convergence.Index Terms-Convergence, dynamic variance error system analysis (DVESA) method, information fusion noise variance estimation, multisensor information fusion, self-tuning Riccati equation, self-tuning weighted fusion Kalman predictor.

A Kalman Filter with Noise Covariances Estimation and Its Stability Analysis

“…On the other hand, the matrix A is invertible if the system (1) can be transformed from a continuous-time LTI system. And in [17], the state transfer matrix…”

Distributed Kalman filtering

“…Some of the recent work in this area is as follows. Self-tuning decoupled fusion Kalman predictor is proposed in [160] and self-tuning weighted measurement Kalman filter is included in [161]. Self-tuning measurement system using the correlation method, can be viewed as the least-squares (LS) fused estimator and found in [285].…”

Convergence of self-tuning Riccati equation with correlated noises

“…The convergence problem of the selftuning Riccati equation can be converted into the stability problem of a dynamic variance error system described by a time-varying Lyapunov equation, which is solved by the DVESA method [5,6]. The results proposed in [5] are extended to the general case with correlated noises, and with unknown model parameters in the state transition matrix, input noise matrix and measurement matrix, and in [5], only the convergence of the self-tuning Riccati equation to the steady-state Riccati equation was proved.…”