Self-tuning full-order WMF Kalman filter for multisensor descriptor systems

For the multisensor descriptor systems with correlated measurement noises and unknown noise variances, a self-tuning full-order weighted measurement fusion (WMF) Kalman filter is presented. First, based on the controlled autoregressive moving average innovation model of the multisensor descriptor systems, the consistent estimates of the unknown noise variances are obtained applying correlation function method. A compressed measurement equation for the multisensor descriptor systems is obtained by the WMF method, and an optimal full-order WMF descriptor Kalman filter is given. Based on the optimal full-order WMF Kalman filter and the estimates of noise variances, a self-tuning full-order WMF Kalman filter with the self-tuning descriptor Riccati equation is presented. By the dynamic variance error system analysis method, it is proven that the solution of the self-tuning descriptor Riccati equation converges to the solution of the optimal descriptor Riccati equation. Then, the convergence of the presented self-tuning full-order WMF Kalman filter is proven. A simulation example of a six-sensor descriptor system verifies the effectiveness and convergence of the presented algorithms.