Self-Tuning Weighted Measurement Fusion Kalman Filter for Multi-Channel AR Signals and Its Convergence

Abstract

For the multisensor multi-channel autoregressive (AR) signals with colored measurement noises, when the model parameters and noise variances are partially unknown, the consistent estimators of unknown AR model parameters and noise variance are obtained by the bias compensated recursive least-squares (BCRLS) algorithm. Then, substituting these estimators into the optimal weighted measurement fusion signal Kalman filter, a self-tuning weighted measurement fusion signal Kalman filter is presented. Further, applying the dynamic error system analysis (DESA) method, it is rigorously proved that the proposed self-tuning fusion signal Kalman filter converges to the optimal fuser in a realization, so that it has asymptotic global optimality. A simulation example shows their effectiveness.