Self-tuning WMF Kalman predictors for the multisensor descriptor systems and their convergence analysis

For the multisensor linear stochastic descriptor systems with uncorrelated noises, the self-tuning WMF prediction problem is solved, when the noise variances of the process noise and measurement noise are unknown. The consistent estimates of these unknown noise variances are obtained by applying the correlation method, and the weighted measurement fusion equation. Applying the singular value decomposition method and the classical Kalman filtering theory, substituting these consistent estimates of unknown noise variances into the optimal WMF reduced-order Kalman predictors yields the self-tuning reduced-order Kalman predictors. The convergence of these presented self-tunning WMF Kalman predictors is proven. An example of three-sensor descriptor systems verifies the effectiveness.