Multitarget Moments and their Application to Multitarget Tracking

Abstract

The concept of a "statistical moment" has played a fundamental role in practical single-target tracking. The optimal tracking approach, the recursive Bayes filter, propagates the entire posterior density through time. Because this filter is computationally daunting, most practical single-target tracking approaches assume that signal-to-noise ratio is large enough that the posterior is approximately characterized by its low-order moments. For example, the alpha-beta-gamma filter propagates the first-order moment (the posterior expectation) whereas the extended Kalman filter (EKF) additionally propagates a second-order moment (the posterior covariance). Until recently, the possibility of an analogous multitarget approach seems to have been ignored---apparently for lack of a systematic statistical foundation for multitarget problems. In two recent papers, I introduced multitarget moment statistics of arbitrary order and developed a Bayes filtering theory for the first-order multitarget moment, the "probability hypothesis density (PHD)." In this paper I continue this line of investigation. I will describe a preliminary implementation of the first-order filter. I will introduce the concept of multitarget posterior covariances of arbitrary order. Using them, I will show how a suitable extension of the finite-set statistics (FISST) multisensor-multitarget differential calculus can be used to construct multitarget statistical analogs of the EKF.

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Document Details

Document Type
Technical Report
Publication Date
Jan 01, 2001
Accession Number
ADA414365

Entities

People

  • Ronald Mahler

Organizations

  • Lockheed Martin

Tags

DTIC Thesaurus Topics

  • Air Force
  • Algorithms
  • Bayes Filters
  • Computational Science
  • Detectors
  • Estimators
  • Filtration
  • Information Science
  • Kalman Filters
  • Mathematical Filters
  • Mathematics
  • Military Research
  • Multitarget Tracking
  • Probability
  • Probability Hypothesis Density Filters
  • Statistics
  • Target Tracking

Fields of Study

  • Engineering

Readers

  • Adaptive Control and Estimation with Uncertainty in Dynamic Systems.
  • Statistical inference.