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Type: Journal article
Title: Filtering, smoothing and M-ary detection with discrete time poisson observations
Author: Elliott, R.
Malcolm, W.
Aggoun, L.
Citation: Stochastic Analysis and Applications, 2005; 23(5):939-952
Publisher: Marcel Dekker Inc
Issue Date: 2005
ISSN: 0736-2994
Statement of
R. J. Elliott; W. P. Malcolm; Lakhdar Aggoun
Abstract: In this article, we solve a class of estimation problems, namely, filtering smoothing and detection for a discrete time dynamical system with integer-valued observations. The observation processes we consider are Poisson random variables observed at discrete times. Here, the distribution parameter for each Poisson observation is determined by the state of a Markov chain. By appealing to a duality between forward (in time) filter and its corresponding backward processes, we compute dynamics satisfied by the unnormalized form of the smoother probability. These dynamics can be applied to construct algorithms typically referred to as fixed point smoothers, fixed lag smoothers, and fixed interval smoothers. M-ary detection filters are computed for two scenarios: one for the standard model parameter detection problem and the other for a jump Markov system.
Keywords: Backwards dynamics
Discrete parameter martingales
Jump Markov systems
Poisson random variables
Reference probability.
Rights: Copyright © Taylor & Francis, Inc.
DOI: 10.1080/07362990500184808
Appears in Collections:Aurora harvest
Mathematical Sciences publications

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