State estimation for singularly perturbed systems with uncertain perturbation parameter

The problem of state estimation for a singularly perturbed system with unknown perturbation parameter is considered. A combined detection-estimation structure with a finite number of estimators is found to be optimal in a minimax incremental MSE sense, even in the presence of a convex uncertainty set. The resulting estimator is much less pessimistic than the standard MSE minimax filter. It is recursive and easily implemented with standard MMSE filters, all of which can be designed off line. Its performance is also shown to be superior to that of the reduced filter.