Filtering for fast mean-reverting processes

Andrew Papanicolaou

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish (US)
Pages (from-to)155-176
Number of pages22
JournalAsymptotic Analysis
Issue number3-4
StatePublished - 2010


  • Kramers-Smoluchowski
  • fast mean reversion
  • nonlinear filtering
  • tracking

ASJC Scopus subject areas

  • General Mathematics


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