Self-tuning information fusion Wiener filter for ARMA signals and its convergence

For the multisensor autoregressive moving average (ARMA) signals with unknown model parameters and noise variances, using recursive extended least squares (RELS) algorithm, the correlation method and the Gevers-Wouters algorithm with dead band, the fused estimators of model parameters and noise variances are presented. They have strong consistence. Then substituting them into the optimal fusion signal filter weighted by scalars, a self-tuning information fusion Wiener filter for the ARMA signals is presented. Further, applying the dynamic error system analysis (DESA) method, it is rigorously proved that the self-tuning fused Wiener signal filter converges to the optimal fused Wiener signal filter in a realization, i.e. it has asymptotic optimality. A simulation example shows its effectiveness.