Self-tuning weighted measurement fusion Wiener filter for autoregressive moving average signals with coloured noise and its convergence analysis

For the multisensor single-channel autoregressive moving average (ARMA) signal with common coloured measurement noise, applying the modern time-series analysis method, based on the ARMA innovation model, the optimal weighted measurement fusion Wiener filter is presented. When the model parameters of coloured measurement noise and partial noise variances are unknown, by applying the recursive instrumental variable, the correlation method and the Gevers-Wouters iterative algorithm with dead band, their local estimates are obtained, then the fused estimates are obtained by taking the average of all corresponding local estimates. Substituting these fused estimates into the optimal weighted measurement fusion Wiener filter, a self-tuning weighted measurement fusion Wiener filter is obtained. By applying the dynamic error system analysis method, it is rigorously proved that the self-tuning weighted measurement fusion Wiener filter converges to the corresponding optimal weighted measurement fusion Wiener filter in a realisation, so that it has asymptotically global optimality. A simulation example shows its effectiveness.