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Filtering of Poorly Known Systems: Estimation Variations as Source of Uncertainty

This paper presents a mathematical framework for state estimation of dynamic systems for which only a simplified and rough model is available, using an approach that considers estimation variation itself as a possible source of uncertainty. The discrete-time case is studied and the filtering problem is solved, using a modified version of the Regularized Least Squares (RLS) and tools from the nonsmooth analysis. The solution points to a region in the innovation space in which no variation of estimation is optimal. An algorithm for real-time applications is presented and a numeric example is included to illustrate the benefits of this approach.