Detection-filter representations for Markov jump diffusions

Detection-filter representations for Markov jump diffusions

Blom, H.A.P.

National Aerospace Laboratory NLR

1982-03-11

The problem considered is filtering for Gaussian observations of linear differential systems that are driven by both Wiener processes and marked Poisson point processes. Well-known representations of the MMSE-filter for such a Markov jump-diffusion are a differential for the evolution of its conditional density or differentials for all its conditional central moments. For Markov jump-diffusions that embed finite state Markov processes some transformed filter-representations have been derived. They throw a new light on the problem of filtering for Markov jump-diffusions. A resulting finite dimensional approximate MMSE-filter shows promising advantages above previous approximations. Some illustrative examples are given.

Information theory
Tracking filters
Nonlinear filters
Kalman filters
Wiener filtering
Markov chains
Markov processes
Counting
Differential equations
Diffusion theory
Jump detection
Stochastic processes
Poisson density functions
Martingales
Ito differential equation
Fokker-Planck equation

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(c)1982 National Aerospace Laboratory NLR