Guaranteed cost LQG filtering for stochastic discrete time uncertain systems via risk-sensitive control

The paper considers a robust filtering problem for stochastic discrete time uncertain systems. The uncertainty in the system is represented in terms of an uncertain probability distribution for the noise input. This uncertainty is assumed to satisfy a certain relative entropy constraint. The solution to a specially parametrized stochastic risk-sensitive filtering problem is used to construct a filter for the uncertain system which guarantees a certain upper bound on the filter error for all admissible uncertainties. The results of the paper are applied to a problem of equalization for an ISI channel arising in telecommunications.