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.
scientific article; zbMATH DE number 1340512