Current Output Observer for Stochastic-Parameter Models and Application to Sensor Failure

In this paper, linear discrete-time systems with white stochastic parameters are considered. Most results on the optimal state estimation of linear discrete time systems with stochastic parameters rely strongly on the generalization of the one step prediction type Kalman filter to this type of systems. But it has been shown that the current output observer results in less estimation error as compared to the one step prediction Kalman Filter for the case of systems with deterministic parameters. In this work, the current output observer is generalized to stochastic-parameter systems and the estimation error performance improvement is mathematically shown. We have particularly directed our attention to the application to the sensor failure problem, which involves a stochastic model with non-Gaussian parameter distribution. Experimental results confirm our prediction and shows that the current output observer has a substantial benefit for the sensor failure problem over the one step prediction generalized Kalman filter solution.