Filtering,Smoothing and M-ary Detection with Discrete Time Poisson Observations |
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| Authors: | R J Elliott W P Malcolm Lakhdar Aggoun |
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| Institution: | 1. RBC Financial Group Professor of Finance , Haskayne School of Business, Scurfield Hall, University of Calgary , Calgary, Alberta, Canada relliott@ucalgary.ca;3. National ICT Australia (NICTA) , Systems Engineering and Complex Systems (SEACS) Program, Research School of Information Sciences and Engineering (RSISE), The Australian National University , Canberra, Australia;4. Department of Mathematics and Statistics , College of Science, Sultan Qaboos University , Oman |
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| Abstract: | 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. |
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| Keywords: | Backwards dynamics Discrete parameter martingales Detection Jump Markov systems Poisson random variables Reference probability |
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