Relative entropy rate based model selection for linear hybrid system filters of uncertain nonlinear systems

Hybrid system representations have been exploited in a number of challenging modelling situations, including situations where the original nonlinear dynamics are too complex (or too imprecisely known) to be directly filtered. Unfortunately, the question of how to best design suitable hybrid system models has not yet been fully addressed, particularly in the situations involving model uncertainty. This paper proposes a novel joint state-measurement relative entropy rate based approach for design of hybrid system filters in the presence of (parameterised) model uncertainty. We also present a design approach suitable for suboptimal hybrid system filters. The benefits of our proposed approaches are illustrated through design examples and simulation studies.

► We investigate hybrid system model approximations of uncertain nonlinear systems.
► We present a relative entropy rate based approach for the design of hybrid model.
► We present a design approach for suboptimal hybrid filter e.g. the IMM algorithm.
► We characterise the estimation error introduced by hybrid filtering approximations.
► We establish a new relationship between relative entropy rate and estimation error.