An LP-based algorithm for the data association problem in multitarget tracking

Abstract

In this work we present a linear programming (LP) based approach for solving the data association problem (DAP) in multiple target tracking. It is well-known that the DAP can be formulated as an integer program. We present a compact formulation of the DAP. To solve practical instances of the DAP we propose an algorithm that uses an iterated K-scan sliding window technique. In each iteration we solve the LP relaxation of an integer program and next apply a greedy rounding procedure. Computational experiments indicate that the quality of the solutions found is quite satisfactory. Scope and purpose The purpose of this article is to present an alternative approach to solving data association problems that arise from multitarget tracking. As a starting point we use the work reported by Poore et al. (Comput. Optim. Appl. 3 (1994) 27; SPIE 1954 (1993) 552) in which the data association problem is viewed as a multidimensional assignment problem. Instead of using Lagrangian relaxation techniques (SIAM J. Optim. 3 (1993) 554; SPIE 1955 (1993) 172; SPIE 1954 (1993) 564; SPIE 2561 (1995) 448), we apply linear programming (LP) relaxation. A feasible solution is constructed from the relaxed solution by a new heuristic greedy rounding procedure called GRP. The choice for a heuristic approach is justified by the hard real-time requirements that are inherent to multitarget tracking. The application of the GRP lies mainly within the field of (air) surveillance systems for both the military and the civilian domain. Although the focus of this paper is on single sensor systems (i.e. a surveillance radar), the scope can be extended to sensor data fusion systems in which multiple (dissimilar) sensors are involved. More generally, real-time algorithms that provide good-quality solutions for multidimensional assignment problems have a broad scope of applications in the field of robotics (e.g. planning of robot arm movement), communications and the military domain (e.g. weapon assignment, sensor resource allocation, etc.).