Practical implementation of joint multitarget probabilities

Stanton Musick; Keith D. Kastella; Ronald P. S. Mahler

doi:10.1117/12.327111

17 July 1998 Practical implementation of joint multitarget probabilities

Stanton Musick, Keith D. Kastella, Ronald P. S. Mahler

Proceedings Volume 3374, Signal Processing, Sensor Fusion, and Target Recognition VII; (1998) https://doi.org/10.1117/12.327111
Event: Aerospace/Defense Sensing and Controls, 1998, Orlando, FL, United States

Abstract

A Joint Multitarget Probability (JMP) is a posterior probability density p_T(x₁,...,x_TZ) that there are T targets (T an unknown number) with unknown locations specified by the multitarget state X equals (x₁,...,x_T)^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 x_t, t equals 1,...,T, is discretized on a grid of N elements, N^T 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.

Citation Download Citation

Stanton Musick, Keith D. Kastella, and Ronald P. S. Mahler "Practical implementation of joint multitarget probabilities", Proc. SPIE 3374, Signal Processing, Sensor Fusion, and Target Recognition VII, (17 July 1998); https://doi.org/10.1117/12.327111

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