Particle Flow Solutions Avoiding Stiff Integration

Abstract

Particle flow filters are a promising approach to nonlinear Bayesian estimation. However, the only flow with an analytic solution is the so-called exact flow. Other flows, including the geodesic and Gromov flows, are often represented by stiff deterministic or stochastic differential equations that must be numerically integrated. In this paper, we derive an analytic solution for the geodesic flow and we reduce the Gromov flow to an explicit term plus simple integrals involving a single Wiener process. Given the analytic solutions, good asymptotic performance as a function of the measurement variance is demonstrated.

Open PDF

Document Details

Document Type
Technical Report
Publication Date
May 25, 2021
Accession Number
AD1134516

Entities

People

  • David F. Crouse

Organizations

  • United States Naval Research Laboratory

Tags

Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Algorithms
  • Cartesian Coordinates
  • Coordinate Systems
  • Covariance
  • Data Analysis
  • Data Mining
  • Data Processing
  • Data Science
  • Differential Equations
  • Equations
  • Filters
  • Gaussian Distributions
  • Geometry
  • Information Processing
  • Information Science
  • Integrals
  • Military Research
  • Multitarget Tracking
  • Random Variables
  • Sequential Monte Carlo Methods
  • Simulations
  • Standards
  • Statistical Algorithms

Fields of Study

  • Mathematics

Readers

  • Computational Fluid Dynamics (CFD)
  • Positioning, Navigation, and Timing (PNT) Technology.
  • Statistical inference.

Technology Areas

  • AI & ML
  • AI & ML - Bayesian Inference
  • AI & ML - Machine Learning Algorithms