Filtering for Fast Mean-Reverting Processes
Asymptotic Analysis, Vol. 70, Nos. 3-4, 2010, pp. 155-176
28 Pages Posted: 20 Oct 2012 Last revised: 2 Dec 2013
Date Written: April 15, 2010
We consider nonlinear filtering applications to target tracking based on a vector of multi-scaled models where some of the processes are rapidly mean reverting to their local equilibria. We focus attention on target tracking problems because multiple scaled models with fast mean-reversion (FMR) are a simple way to model latency in the response of tracking systems. The main results of this paper show that nonlinearfiltering algorithms for multi-scale models with FMR states can be simplied signicantly by exploiting the FMR structures, which leads to a simplified Baum-Welch recursion that is of reduced dimension. We implement the simplified algorithms with numerical simulations and discuss their eciency and robustness.
Keywords: hidden Markov model, multiscale, filtering
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