Estimation and control of systems with unknown covariance and multiplicative noise

The problem of estimation and control for systems with multiplicative noise and unkown second order statistics is considered. Conditions are found for the existence of a solution based on game theoretic ideas. The conditions for existence of a saddle point for the time-invariant filtering problem are necessary and sufficient, whereas for all other cases only necessary. The central idea of the solution is to convert the stochastic problem to a deterministic optimal control problem whose minimax point is sought with respect to the control, filter, and unknown statistics parameters.