Minimax State Estimation for Jump-Parameter Discrete-Time Systems with Multiplicative Noise of Uncertain Covariance

We consider state estimation for jump Markov parameter discrete-time systems with additive and multiplicative independent noises. First, the covariances of additive and multiplicative noises are assumed to be known and the unbiased linear minimum variance filter is derived. Then, the case of unknown covariances is considered and a minimax optimal design is presented. In the steady state, this filter requires the mean square boundedness of system state, so necessary and sufficient conditions for this are derived. Both the existence of a saddle point and its characterization are considered.