Self-tuning measurement fusion Kalman filter for multisensor systems with companion form

For multisensor discrete time-invariant systems with the companion form, and unknown model parameters and noise variances, based on the recursive extended least square (RELS) and the correlation method, the strong consistent information fusion estimators of model parameters and noise variances are presented, and then by substituting them into the optimal weighted measurement fusion Kalman filter based on the autoregressive moving average (ARMA) innovation model, a self-tuning weighted measurement fusion Kalman filter is presented. Furthermore, applying the dynamic error system analysis (DESA) method, it is rigorously proved that the self-tuning fused Kalman filter converges to the optimal fused Kalman filter in a realization, so that it has asymptotically global optimality. A simulation example applied to signal processing shows its effectiveness.