Electronic Journal of Statistics

Statistical consistency of the data association problem in multiple target tracking

Curtis B. Storlie, Jan Hannig, and Thomas C.M. Lee

Full-text: Open access

Abstract

Simultaneous tracking of multiple moving objects extracted from an image sequence is an important problem which finds numerous applications in science and engineering. In this article we conduct an investigation of the theoretical properties a statistical model for tracking such moving objects, or targets. This tracking model allows for birth, death, splitting and merging of targets, and uses a Markov model to decide the times at which such events occur. This model also assumes that the track traveled by each target behaves like a Gaussian process. The estimated tracking solution is obtained via maximum likelihood. One of the contributions of this article is to establish the almost sure consistency to the data association problem by using these maximum likelihood tracking estimates. A major technical challenge for proving this consistency result is to identify the correct track (data association) amongst a group of similar (but incorrect) track proposals that are results of various combinations of target birth, death, splitting and/or merging. This consistency property of the tracking estimates is empirically verified by numerical experiments. To the best of our knowledge, this is the first time that a comprehensive study is performed for the large sample properties of a multiple target tracking method. In addition, the issue of how to quantify the confidence of a tracking estimate is also addressed.

Article information

Source
Electron. J. Statist., Volume 5 (2011), 1227-1275.

Dates
First available in Project Euclid: 19 October 2011

Permanent link to this document
https://projecteuclid.org/euclid.ejs/1319028568

Digital Object Identifier
doi:10.1214/11-EJS639

Mathematical Reviews number (MathSciNet)
MR2842905

Zentralblatt MATH identifier
1329.60108

Subjects
Primary: 60G35: Signal detection and filtering [See also 62M20, 93E10, 93E11, 94Axx]
Secondary: 60G17: Sample path properties 60G15: Gaussian processes 62M20: Prediction [See also 60G25]; filtering [See also 60G35, 93E10, 93E11]

Keywords
Data association in-fill asymptotics multiple hypothesis tracking multiple target tracking merging splitting Brownian motion

Citation

Storlie, Curtis B.; Hannig, Jan; Lee, Thomas C.M. Statistical consistency of the data association problem in multiple target tracking. Electron. J. Statist. 5 (2011), 1227--1275. doi:10.1214/11-EJS639. https://projecteuclid.org/euclid.ejs/1319028568


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