Detection-Estimation Schemes for Uncertain Signals.

The three primary aspects of the research are summarized. The first involves the use of combined detection-estimation schemes for state estimation in dynamical stochastic systems with uncertainties. Several different performance criteria such asd minimax mean-squared error (MSE) and incremental MSE are applied to the problems of state estimation of systems with uncertainties modeled by parametric bounds or by Markovian jump parameters. The second aspect of this research considers the problem of state estimation for the slow modes of hierarchical singularly perturbed linear stochastic systems. The solution to this problem involves a reduced-order detection-estimation approach for near-optimal estimation when the perturbation parameter is small and an alternate superior scheme for the case in which the perturbation parameter is not small. The third aspect of this research considers the problem of state estimation in linear stochastic systems driven simultaneously by Wiener and low-intensity Poisson processes. A suboptimal sequential smoothing (SSS) scheme is developed which exhibits superior performance to both optimal causal (minimum MSE) and linear noncausal filters.