Self-tuning centralized fusion Kalman filter for multisensor systems with companion form and its convergence

For the multisensor systems with companion form and unknown model parameters and noise variances, using recursive instrumental variable(RIV) algorithm, the local and fused model parameter estimators are obtained. Based on the fused model parameter estimators, the information fusion noise variance estimators are presented by using correlation method. They have strong consistence. Further, a self-tuning centralized fusion Kalman filter based on a self-tuning information matrix equation is presented, which can reduce the computational burden. By the dynamic variance error system analysis(DVSEA) method, it is proved that the self-tuning information matrix equation convergence to the optimal information matrix equation. Based on this, by the dynamic error system analysis (DESA) method, it is rigorously proved that the self-tuning centralized fusion Kalman filter converges to the optimal centralized fusion Kalman filter with probability one, so that it has asymptotic global optimality. A simulation example shows its effectiveness.