Self-tuning Weighted Measurement Fusion Kalman Filter and its Convergence Analysis

For the multisensor systems with unknown noise variances, using correlation method and least squares fusion criterion, information fusion noise variance estimators are presented by the average of local noise variance estimators, which have the consistence. Substituting the fused noise variance online estimators into the optimal Riccati equation and the optimal weighted measurement fusion Kalman filter, a self-tuning Riccati equation and a new self-tuning weighted measurement fusion Kalman filter are presented. In order to prove the convergence of the self-tuning Riccati equation, a dynamic variance error system analysis (DVSEA) method is presented, which converts the convergence problem to the stability problem of a time-varying Lyapunov equation. A stability decision criterion is presented for the Lyapunov equation. By the dynamic error system analysis (DESA) method and DVSEA method, it proves that the self-tuning weighted measurement fusion Kalman filter converges to the globally optimal weighted measurement fusion Kalman filter in a realization, so that it has asymptotic global optimality. A simulation example for target tracking system with 3-sensor shows its effectiveness.