Assignment Algorithms For The Passive Sensor Data Association Problem

Abstract

This paper is concerned with the problem of associating measurements from multiple passive line-of-sight only sensors in the presence of clutter, missed detections and unknown number of targets. The measurement-target association problem is formulated as one of maximizing the joint likelihood function of the measurement partition. Mathematically, this formulation of the data association problem leads to a generalization of the multi-dimensional matching problem, which is known to be NP-complete ( of non polynomial complexity ) when the number of sensors S ≥ 3. Suboptimal algorithms are therefore of considerable importance. In this paper we present two suboptimal algorithms - a backtracking algorithm with a complexity of order 0(M in M), where M is the number of possible measurement-target associations, and a relaxation algorithm that successively solves a series of generalized two-dimensional assignment problems, with the worst case complexity of 0(3k n3 ), where n is the number of reports from each sensor, and k is the number of relaxation iterations. The performance of the backtracking algorithm is guaranteed to be much better than the "row-column" heuristic, which has complexity of 0(M). A nice feature of the relaxation approach is that the resulting primal and dual solutions provide a measure of how close the solution is to the (perhaps unknowable) optimal solution in terms of the duality gap. For the passive sensor data association problem, the duality gaps are typically less than 1%. We present comparisons between the two algorithms in terms of performance and time complexity in the context of passive sensor data-association problem involving three sensors. Both of the algorithms are tested on a wide variety of scenarios involving a wide range of target densities, measurement accuracy, and false alarm and missed-detection probabilities.