Robust optimal filtering for linear time-varying systems with stochastic uncertainties

In this study, the robust optimal filtering problem is investigated for a class of linear time-varying systems with stochastic uncertainties. A new model is presented that accounts for both stochastic parameter uncertainties and noise. On the basis of the new model, a robust optimal filter is proposed. It takes stochastic uncertainties into full consideration, but does not depend on any specific structure of uncertainties. By resorting to linear system theory and utilising stochastic analysis methods, the filter gain is designed such that the estimation error covariance is minimised at each time step. The authors' developed filtering algorithm is recursive, and therefore suitable for real-time online applications. In the end, two simulation studies are performed to illustrate the effectiveness and applicability of their proposed strategy.