TY - JOUR

T1 - Filtering, smoothing and M-ary detection with discrete time Poisson observations

AU - Elliott, R. J.

AU - Malcolm, W. P.

AU - Aggoun, Lakhdar

PY - 2005

Y1 - 2005

N2 - 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.

AB - 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.

KW - Backwards dynamics

KW - Detection

KW - Discrete parameter martingales

KW - Jump markov systems

KW - Poisson random variables

KW - Reference probability

UR - http://www.scopus.com/inward/record.url?scp=24344439880&partnerID=8YFLogxK

U2 - 10.1080/07362990500184808

DO - 10.1080/07362990500184808

M3 - Article

SN - 0736-2994

VL - 23

SP - 939

EP - 952

JO - Stochastic Analysis and Applications

JF - Stochastic Analysis and Applications

IS - 5

ER -