Filtering with discrete state observations
Filtering with discrete state observations
In this paper, a finite state signal Markov chain is meant to model the possible orientations (for example, forward, up, down, right turn, left turn) of a target. The states of the Markov chain are observed indirectly through a process with ``information'' that has two sources, an independent counting source (noise), and a source that contains information about the Markov chain in one of two possible forms, the first in terms of \(\sigma\)-fields (this yields the weak formulation of the problem) and the second in terms of counting related to the state (this yields the strong formulation). In both cases a finite dimensional filtering formula is provided. A suboptimal filter is shown to converge to the signal Markov chain when the intensity of the independent counting component goes to zero.
- CentraleSupélec France
- French National Centre for Scientific Research France
- Supélec France
- University of Alberta Canada
- Laboratoire des Signaux & Systèmes France
suboptimal filtering, tracking finite Markov chains, Inference from stochastic processes and prediction, Filtering in stochastic control theory, Continuous-time Markov processes on discrete state spaces, filtering formula
suboptimal filtering, tracking finite Markov chains, Inference from stochastic processes and prediction, Filtering in stochastic control theory, Continuous-time Markov processes on discrete state spaces, filtering formula
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