Title :
A non-Markov finite dimensional filter
Author :
Elliott, Robert J. ; Sworder, David D. ; Taylor, Thomas J.
Author_Institution :
Dept. of Stat. & Appl. Probability, Alberta Univ., Edmonton, Alta., Canada
Abstract :
The state space of a general, not necessarily Markov, finite state space process is identified with the set of unit vectors in an Euclidean space. A filtering problem is considered where the observation process records only jumps between certain subsets of the states. A recursive equation for the filtered estimate of the state is obtained. If the transition rates are measurable with respect to the observations this filter is finite dimensional. The corresponding Zakai equation is also derived
Keywords :
filtering and prediction theory; Euclidean space; Zakai equation; filtered estimate; finite state space process; nonMarkov finite dimensional filter; observation process; recursive equation; transition rates; unit vectors; Equations; Filters; Mathematics; Probability; Recursive estimation; State estimation; State-space methods; Statistics; Time measurement; Writing;
Conference_Titel :
Signals, Systems and Computers, 1991. 1991 Conference Record of the Twenty-Fifth Asilomar Conference on
Conference_Location :
Pacific Grove, CA
Print_ISBN :
0-8186-2470-1
DOI :
10.1109/ACSSC.1991.186437
