Optimal and self-tuning weighted measurement fusion Wiener filter for the multisensor multichannel ARMA signals

For the multisensor multichannel autoregressive moving average (ARMA) signals with white measurement noises, using the modern time series analysis method, based on the ARMA innovation models, white noise estimators, and measurement predictors, an optimal weighted measurement fusion Wiener filter is presented by the weighted least squares (WLS) method. It can handle the fused filtering, smoothing and prediction problems in a unified framework. When the noise variances and model parameters are unknown, based on the on-line identification of the local and fused ARMA innovation models, a self-tuning weighted measurement fusion Wiener filter is presented. By the dynamic error system analysis (DESA) method, it is rigorously proved that the self-tuning fuser converges to the optimal fuser in a realization, so that it has the asymptotic optimality. Compared with the globally optimal centralized fusion time-varying Kalman filter, the proposed optimal and self-tuning Wiener fusers have the asymptotic global optimality, whose accuracies are higher than these of the optimal and self-tuning distributed Wiener fusers and local Wiener filters, respectively. A simulation example shows their effectiveness.