Kalman filtering with multiplicative and additive noises

This paper issues the problem of performing Kalman filtering for both discrete-time stochastic linear (DTSL) systems and discrete-time stochastic nonlinear (DTSN) systems. Multiplicative and additive noise is considered in the system model. An optimal Kalman filter for the DTSL system and a suboptimal Kalman filter for the DTSN are designed based on the standard Kalman filter. For Optimal Kalman filter, we also study the statiscal convergence properties of the estimation error covariance. The results are illustrated with examples.