Self-tuning reduced-order Kalman smoother for the descriptor system
Chengxiang Liu, Chenjian Ran · 2018
For the linear stochastic descriptor system with uncorrelated noises, the self-tuning reduced-order smoothing 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 optimal Kalman reduced-order smoother is obtained based on the singular value decomposition method and the classical Kalman filtering theory. Then substituting these consistent estimates of unknown noise variances into the optimal reduced-order Kalman smoother yields the self-tuning reduced-order smoother and the smoothing error variance. A example of singular system verifies the effectiveness.