Exact IMM estimation of Markov switching diffusios with hybrid jumps

Abstract

Stochastic hybrid processes with hybrid jumps have discontinuities that occur simultaneously with mode switching. A typical example is a rapid change in an aircraft’s bank angle that happens simultaneously with a mode switching from straight flight to a maneuver. The common approach in handling hybrid jumps is to combine a Variable Structure (VS) approach with Interacting Multiple Model (IMM) estimation. Chapter 4 improves this situation through deriving an exact characterization of the nonlinear filter for a Markov switching diffusion with hybrid jumps, and through showing how this characterization leads to exact Hybrid Jump extensions of the IMM estimator and the IMM particle filter.