Continuous-Discrete Filtering for Systems with Markovian Switching Coefficients

摘要

The classical continuous-time linear system with Markovian switching coefficients is extended, to incorporate jumps in R to the nth power which occur simultaneously with coefficient switching. The system is defined by a stochastic differential equation in a hybrid space, which is driven by a Brownian motion and a Poisson random measure with a randomly time-changed mean measure. The exact continuous-discrete filter for such a system is approximated by a numerical algorithm, which is in its most simple form the Interacting Multiple Model algorithm. For application to the problem of tracking a maneuvering aircraft, given measurements of uncertain origin, the obtained methods can easily be combined with Probabilistic Data Association.