Measure-valued processes and interacting particle systems. Application to nonlinear filtering problems

1998/05/01 by Pierre Del Moral · 4 citations
Computer Science · Mathematics · #Bayesian Methods and Mixture Models #Target Tracking and Data Fusion in Sensor Networks #Statistical Methods and Inference #Measure (data warehouse) #Nonlinear system #Mathematics #Dynamical systems theory #Particle system #Statistical physics #Particle filter #Applied mathematics #Dynamical system (definition) #Class (philosophy) #Nonlinear dynamical systems #Computer science #Artificial intelligence #Kalman filter #Physics #Data mining #Statistics

paper · doi:10.1214/aoap/1028903535

openalex publication_date 1998/05/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/04/04

Abstract

In the paper we study interacting particle approximations of discrete time and measure-valued dynamical systems. These systems have arisen in such diverse scientific disciplines as physics and signal processing. We give conditions for the so-called particle density profiles to converge to the desired distribution when the number of particles is growing. The strength of our approach is that is applicable to a large class of measure-valued dynamical systems arising in engineering and particularly in nonlinear filtering problems. Our second objective is to use these results to solve numerically the nonlinear filtering equation. Examples arising in fluid mechanics are also given.

Citations

• A propagation of chaos result for a system of particles with moderate interaction
• Nonlinear filtering and measure-valued processes
• Conditional Markov Processes
• Convergence of a Branching Particle Method to the Solution of the Zakai Equation
• Novel approach to nonlinear/non-Gaussian Bayesian state estimation
• Optimal nonlinear filtering in GPS/INS integration

Cited by

• An example of Ensemble Kalman Filter with resampling
• On the stability of interacting processes with applications to filtering and genetic algorithms
• Branching and interacting particle systems approximations of feynman-kac formulae with applications to non-linear filtering
• Monte Carlo method [wikipedia]