Multi-model information fusion Kalman filtering and white noise deconvolution

For the linear discrete time-varying stochastic control systems with multi-model and multisensor, using the Kalman filtering method, based on the Riccati equations and Lyapunov equations, according to three optimal fusion rules weighted by matrices, diagonal matrices, and scalars, three optimal weighted fusion Kalman estimators and white noise deconvolution estimators are presented in a unified framework, respectively. The corresponding steady-state local and fused estimators also are presented. The accuracy of the fuser with the matrix weights is higher than that of the fuser with scalar weights, and the accuracy of the fuser with diagonal matrix weights is between both of them. The accuracy of the fusers is higher than that of each local estimator. They can handle the fused filtering, smoothing and prediction problems. They can be applied to the information fusion filtering of the state and input white noises for the multisensor systems with the colored measurement noises. In order to compute the optimal weights, the formulas of computing the cross-covariances among local estimation errors are proposed. Two Monte Carlo simulation examples for an infrared target tracking system and a Bernoulli–Gaussian white noise deconvolution system show their effectiveness.