Simultaneous Detection and Estimation for Diffusion Process Signals

We consider the problem of simultaneous detection and estimation when the signals corresponding to the M different hypotheses can be modelled as outputs of M distinct stochastic dynamical systems of the Ito type. Under very mild assumptions on the models and on the cost structure we show that there exist a set of sufficient statistics for the simultaneous detection-estimation problem that can be computed recursively by linear equations. Furthermore we show that the structure of the detector and estimator is completely determined by the cost structure. The methodology used employes recent advances in nonlinear filtering and stochastic control of partially observed stochastic systems of the Ito type. Specific examples and applications in radar tracking and discrimination problems are discussed.