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Practical implementation of joint multitarget probabilities
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Paper Abstract

A Joint Multitarget Probability (JMP) is a posterior probability density pT(x1,...,xTZ) that there are T targets (T an unknown number) with unknown locations specified by the multitarget state X equals (x1,...,xT)T conditioned on a set of observations Z. This paper presents a numerical approximation for implementing JMP in detection, tracking and sensor management applications. A problem with direct implementation of JMP is that, if each xt, t equals 1,...,T, is discretized on a grid of N elements, NT variables are required to represent JMP on the T-target sector. This produces a large computational requirement even for small values of N and T. However, when the sensor easily separates targets, the resulting JMP factorizes and can be approximated by a product representation requiring only O(T2N) variables. Implementation of JMP for multitarget tracking requires a Bayes' rule step for measurement update and a Markov transition step for time update. If the measuring sensor is only influenced by the cell it observes, the JMP product representation is preserved under measurement update. However, the product form is not quite preserved by the Markov time update, but can be restored using a minimum discrimination approach. All steps for the approximation can be performed with O(N) effort. This notion is developed and demonstrated in numerical examples with at most two targets in a 1-dimensional surveillance region. In this case, numerical results for detection and tracking for the product approximation and the full JMP are very similar.

Paper Details

Date Published: 17 July 1998
PDF: 12 pages
Proc. SPIE 3374, Signal Processing, Sensor Fusion, and Target Recognition VII, (17 July 1998); doi: 10.1117/12.327111
Show Author Affiliations
Stanton Musick, Air Force Research Lab. (United States)
Keith D. Kastella, Lockheed Martin Tactical Defense Systems (United States)
Ronald P. S. Mahler, Lockheed Martin Tactical Defense Systems (United States)

Published in SPIE Proceedings Vol. 3374:
Signal Processing, Sensor Fusion, and Target Recognition VII
Ivan Kadar, Editor(s)

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