Filtering for fast mean-reverting processes

Article type: Research Article

Authors: Papanicolaou, Andrew

Affiliations: Sherrerd Hall, Charlton Street, Princeton, NJ 08544, USA. E-mail: apapanic@princeton.edu

Abstract: 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 nonlinear filtering algorithms for multi-scale models with FMR states can be simplified significantly 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 efficiency and robustness.

Keywords: nonlinear filtering, tracking, fast mean reversion, Kramers–Smoluchowski

DOI: 10.3233/ASY-2010-1011

Journal: Asymptotic Analysis, vol. 70, no. 3-4, pp. 155-176, 2010