Observability and nonlinear filtering
By Ramon van Handel. 2007
56 citations recorded by the source corpus.
This paper develops a connection between the asymptotic stability of nonlinear filters and a notion of observability. We consider a general class of hidden Markov models in continuous time with compact signal state space, and call such a model observable if no two initial measures of the signal process give rise to the same law of the observation process. We demonstrate that observability implies stability of the filter, i.e., the filtered estimates become insensitive to the initial measure at large times. For the special case where the signal is a finite-state Markov process and the observations are of the white noise type, a complete (necessary and sufficient) characterization of filter stability is obtained in terms of a slightly weaker detectability condition. In addition to observability, the role of controllability is explored. Finally, the results are partially extended to non-compact signal state spaces.
Subfields: Artificial Intelligence, Control and Systems Engineering
View Paper: https://www.semanticscholar.org/paper/1e5cd5161ee458c832f8a1a5e0ae79ef34b4fb2f
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In Artificial Intelligence
In Control and Systems Engineering
Citations in the corpus
- The stability of conditional Markov processes and Markov chains in random environments (2008, background): “In the general setting, however, little is known about the asymptotic properties of nonlinear filters beyond the work of Kunita [23] and subsequent papers, such as [25], which rely directly on the approach of [23] (but see [36]).”