Robust Kalman filtering for discrete time-varying uncertain systems with multiplicative noises

In this note, a robust finite-horizon Kalman filter is designed for discrete time-varying uncertain systems with both additive and multiplicative noises. The system under consideration is subject to both deterministic and stochastic uncertainties. Sufficient conditions for the filter to guarantee an optimized upper bound on the state estimation error variance for admissible uncertainties are established in terms of two discrete Riccati difference equations. A numerical example is given to show the applicability of the presented method.