Self-tuning multisensor measurement fusion Kalman estimator and its convergence analysis

For the multisensor system with unknown noise variances, by the weighted least squares (WLS) method, a weighted fused measurement equation is obtained. Together with the state equation, it thus constitutes an equivalent measurement fusion system. Using the modern time series analysis method, based on on-line identification of the moving average (MA) innovation model parameters for the measurement fusion system, the online estimators of noise variances can be obtained, and a self-tuning weighted measurement fusion Kalman estimator is presented, which can handle the self-tuning fused filtering, prediction, and smoothing problems in a unified framework. Its convergence is also proved by using the dynamic error system analysis method, i.e. if the parameter estimation of the MA innovation model is consistent, then it will converge to a globally optimally weighted measurement Kalman estimator, in a realization or with probability one. Consequently it has asymptotic global optimality. A simulation example for a tracking system with 3 sensors shows its effectiveness.