2002/10/02 by Anastasia Papavasiliou, Papavasiliou, Anastasia
Computer Science · Engineering · Mathematics · #60G35 #93D20 #93E11 #Bayesian Methods and Mixture Models #Control Systems and Identification #FOS: Mathematics #Optimization and Control (math.OC) #Probability (math.PR) #Target Tracking and Data Fusion in Sensor Networks #math.OC #math.PR #msc:60G35 #msc:93D20 #msc:93E11
paper · pdf · doi:10.48550/arxiv.math/0210031
16 pages, second draft (October 14, 2004)
openalex publication_date 2002/10/02 · arxiv created 2005/02/21 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we study the problem of estimating a Markov chain X(signal) from its noisy partial information Y, when the transition probability kernel depends on some unknown parameters. Our goal is to compute the conditional distribution process \mathbb P\Xn|Yn,...,Y1\, referred to hereafter as the \it optimal filter. Following a standard Bayesian technique, we treat the parameters as a non-dynamic component of the Markov chain. As a result, the new Markov chain is not going to be mixing, even if the original one is. We show that, under certain conditions, the optimal filters are still going to be asymptotically stable with respect to the initial conditions. Thus, by computing the optimal filter of the new system, we can estimate the signal adaptively.