Self-tuning fusion Kalman smoother for multisensor multi-channel ARMA signals and its convergence

For the multisensor multi-channel autoregressive moving average (ARMA) signals with white measurement noises and an AR colored measurement noise as common disturbance noises, a multi-stage information fusion identification method is presented when model parameters and noise variances are partially unknown. The local estimators of model parameters and noise variances are obtained by the multi-dimensional recursive instrumental variable (MRIV) algorithm, correlation method, and the Gevers-Wouters algorithm, and the fused estimators are obtained by taking the average of the local estimators. They have the consistency. Substituting them into the optimal fusion Kalman smoother, a self-tuning fusion Kalman smoother for multi-channel ARMA signals is presented. Applying the dynamic error system analysis (DESA) method, it is proved that the proposed self-tuning fusion Kalman smoother converges to the optimal fusion Kalman smoother in a realization, so that it has asymptotic optimality. A simulation example shows its effectiveness.