Practical Stability of Approximating Discrete-Time Filters with Respect to Model Mismatch Using Relative Entropy Concepts

Abstract

This paper establishes practical stability results for an important range of approximate discrete-time filtering problems involving mismatch between the true system and the approximating filter model. Using local consistency assumption, the practical stability established is in the sense of an asymptotic bound on the amount of bias introduced by the model approximation. Significantly, these practical stability results do not require the approximating model to be of the same model type as the true system. Our analysis applies to a wide of range of estimation problems and justifies the common practice of approximating intractable infinite dimensional nonlinear filters by simpler computationall..