Robust approaches for the data association problem

Hassene Aissi
LAMSADE at Paris-Dauphine University

*Daniel Vanderpooten
LAMSADE at Paris-Dauphine University

*Jean-Michel Vanpeperstraete

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     Last modified: June 14, 2005

Abstract
The data association problem is central in multi-target tracking. This problem has been extensively studied in the literature where typical applications arise in air traffic control and space surveillance. The challenge is to partition the observations into tracks. Mathematically, the problem can be stated as a multidimensional assignment problem. The cost coefficient of each association in the assignment problem is usually defined as the negative log-likelihood
of the corresponding track of targets. However, due to various sources of imprecision (low precision of sensors, imprecise knowledge of probabilities of detection and false alarms), it seems more appropriate to evaluate the cost coefficients by intervals instead of point values. This way, we obtain an interval programming problem where each association can have any cost value in its interval independently of the other associations.

One possible approach when dealing with interval data is to consider a min-max regret criterion in order to construct solutions hedging against objective coefficients variations. Min-max regret criterion aims at obtaining a solution minimizing, over all possible cost scenarios, the maximum deviation of the value of the solution from the optimal value. Alternative robust approaches, based on the construction of a set of good candidate solutions and a new reliability measure, are also presented. The focus of this work is to generate and evaluate a diversity of hypotheses of associations in order to detect the most robust ones. Numerical experiments for demonstrating the effectiveness of our approach are presented.

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