Self-Tuning Weighted Measurement Fusion Kalman Filter for ARMA Signals with Colored Noise

Based on the modern time series analysis method, for single channel autoregressive moving average (ARMA) signals with colored noise, a self-tuning weighted measurement fusion Kalman filter is presented when the model parameters and noise statistics are unknown. By applying the recursive instrumental variable (RIV) algorithm and the Gevers-Wouters (G-W) iterative algorithm with dead band, the local and fused estimates for the unknown model parameters and noise variances can be obtained. Then a self-tuning weighted measurement fusion Kalman filter is obtained by substituting the fused estimates into the corresponding optimal fusion Kalman filter. Further, applying the dynamic error system analysis (DESA) method, it is rigorously proved that the self-tuning weighted measurement fusion Kalman filter has globally asymptotic optimality. A simulation example shows its effectiveness.