Uniform Observability of Hidden Markov Models and Filter Stability for Unstable Signals

@inproceedings{Handel2009UniformOO,
title={Uniform Observability of Hidden Markov Models and Filter Stability for Unstable Signals},
author={Ramon van Handel},
year={2009}
}

A hidden Markov model is called observable if distinct initi al laws give rise to distinct laws of the observation process. Observabi lity implies stability of the nonlinear filter when the signal process is tight, but t his need not be the case when the signal process is unstable. This paper introdu ces a stronger notion of uniform observability which guarantees stability o f the nonlinear filter in the absence of stability assumptions on the signal. By dev eloping certain uniform… CONTINUE READING