Consistent covariance estimation for PMHT

Wayne R. Blanding; Peter Willett; Roy L. Streit; Darin T. Dunham

doi:10.1117/12.738495

21 September 2007 Consistent covariance estimation for PMHT

Wayne R. Blanding, Peter Willett, Roy L. Streit, Darin T. Dunham

Proceedings Volume 6699, Signal and Data Processing of Small Targets 2007; 66990I (2007) https://doi.org/10.1117/12.738495
Event: Optical Engineering + Applications, 2007, San Diego, California, United States

Abstract

The Probabilistic Multi-Hypothesis Tracker (PMHT) has been demonstrated to be an effective multi-target tracker while retaining linear computational complexity in the number of measurements and targets. However PMHT only provides a point estimate for target tracks. The "covariance" returned by the PMHT is a byproduct of applying the Expectation-Maximization algorithm to maximize the PMHT likelihood function and is not intended to be the track estimate covariance. In this paper we derive a consistent covariance estimator for PMHT. By re-introducing the constraint that the sum of the PMHT weights (posterior probabilities that a measurement is target-originated) across measurements sum to unity, a covariance based on Probabilistic Data Association (PDA) principles is derived. We show through simulations that the resulting covariance provides a consistent covariance for the PMHT track estimates. There has been some work both in the statistics and engineering literature that gives the posterior covariance for ML Gaussian-mixture estimation, and the PMHT can be viewed as a tracker whose genesis is of MAP Gaussian-mixture estimation with a Gaussian prior. The expressions and calculations are, unfortunately, complicated. Consequently we also report on a novel and intuitive way to derive these via calculus.

Citation Download Citation

Wayne R. Blanding, Peter Willett, Roy L. Streit, and Darin T. Dunham "Consistent covariance estimation for PMHT", Proc. SPIE 6699, Signal and Data Processing of Small Targets 2007, 66990I (21 September 2007); https://doi.org/10.1117/12.738495

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