Self-tuning measurement fusion Kalman filter with correlated measurement noises and its convergence

For the multisensor system with unknown noise statistics and correlated measurement noises, based on the solution of the matrix equations for correlation function, the on-line estimators of the noise variances and cross-covariances are obtained. Further, a self-tuning weighted measurement fusion Kalman filter is presented. Based on the stability of the dynamic error system and the concept of the convergence in a realization, it is strictly proved that the proposed self-tuning filter convergencies to the steady-state optimal Kalman filter in a realization or with probability one, so that it has asymptotic global optimality. Compared with the centralized self-tuning Kalman filter, it can reduce the computational burden, and is suitable for real time applications. A simulation example for a target tracking system with 3-sensor shows its effectiveness.