Abstract
The central problem in multitarget/multisensor tracking is the data association problem of partitioning the observations into tracks and false alarms so that an accurate estimate of the true tracks can be recovered. This data association problem is formulated in this work as a multidimensional assignment problem. These NP-hard data association problems are large scale, have noisy objective functions, and must be solved in real-time. A class of Lagrangian relaxation algorithms has been developed to construct near-optimal solutions in real-time, and thus the purpose of this work is to demonstrate many of the salient features of tracking problems by using these algorithms to numerically investigate constant acceleration models observed by a radar in two dimensional space. This formulation includes gating, clustering, and optimization problems associated with filtering. Extensive numerical simulations are used to demonstrate the effectiveness and robustness of a class of Lagrangian relaxation algorithms for the solution of these problems to the noise level in the problems.
This work was partially supported by the Federal Systems Corporation of the IBM Corporation in Boulder, CO and Owego, NY and by the Air Force Office of Scientific Research through AFOSR Grant Numbers AFOSR-91-0138 and AFOSR F49620-93-1-0133.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Aho, A. V., Hopcroft, J. E. and Ullman, J. D. (1974), The Design and Analysis of Computer Algorithms, Addison-Westley Publishing Company, Reading, Massachusets.
Bar-Shalom, Y. and Fortmann, T. E. (1988), Tracking and Data Association, Academic Press, Boston, Massachusets.
Bar-Shalom, Y., ed. (1990), Multitarget-Multisensor Tracking: Advanced Applications, Artech House, Dedham, Massachusets.
Bar-Shalom, Y., ed. (1992), Multitarget-Multisensor Tracking: Applications and Advances, Artech House, Dedham, Massachusets.
Bertsekas, D. P. (1992), “Auction Algorithms for Network Flow Problems: A Tutorial Introduction,” Computational Optimization and Applications 1, 7–66.
Bertsekas, D. P. (1991), Linear Network Optimization: Algorithms and Codes, The MIT Press, Cambridge, Massachusets.
Bertsekas, D. P., Castanon, D. A. and Tsaknakis, H., “Reverse Auction and the Solution of Inequality Constrained Assignment Problems,” to appear in the SIAM Journal on Optimization.
Blackman, S. S. (1992), “Association and Fusion of Multiple Sensor Data,” in Multitarget-Multisensor Tracking: Applications and Advances, Y. Bar-Shalom, ed., Artech House, Dedham, Massachusets.
Blackman, S. S. (1986), Multiple Target Tracking with Radar Applications, Artech House, Dedham, Massachusets.
Deb, S., Pattipati, K. R. and Bar-Shalom, Y. (1992), “A Multisensor-multitarget Data Association Algorithm for Heterogeneous Systems,” preprint.
Fisher, M. L. (1981), “The Lagrangian Relaxation Method for Solving Integer Programming Problem,” Management Science, Vol. 27, No. 1, 1–18.
Frieze, A. M. and Yadegar, J. (1981), “An Algorithm for Solving 3-Dimensional Assignment Problems with Application to Scheduling a Teaching Practice,” Journal of the Operational Research Society, Vol. 32, 989–995.
Garvey, M. R. and Johnson, D. S. (1979), Computers and Intractability: A Guide to the Theory of NP-Completeness, W. H. Freeman & Co., California.
Geoffrion, A. M. (1974), “Lagrangean Relaxation for Integer Programming,” Mathematical Programming Study 2, 82–114.
Held, M. and Karp, R. M. (1970), “The Traveling Salesman Problem and Minimal Spanning Trees,” Operations Research 18, 1138–1162.
Held, M. and Karp, R. M. (1971), “The Traveling-Salesman Problem and Minimum Spanning Trees: Part II,” Mathematical Programming 1, 6–25.
Jonker, R. and Volgenant, A. (1987), “A Shortest Augmenting Path Algorithm for Dense and Sparse Linear Assignment Problems,” Computing 38, 325–340.
Lemarechal, C. (1978), “Bundle Methods in Nonsmooth Optimization,” Lemarechal C. and Mifflin, R., Eds, Nonsmooth Optimization, IIASA Proceedings 3, Pergamon, Oxford, 79–102.
Morefield, C. L. (1977), “Application of 0-1 Integer Programming to Multitarget Tracking Problems,” IEEE Transactions on Automatic Control, Vol. AC-22, No. 3, 302–312.
Murty, K., Pardalos, P. M. and Li, Y. (1992), “Local Search Algorithms for the Quadratic Assignment Problem,” Informatica, Vol. 3, No. 4, 524–538.
Nemhauser, G. L. and Wolsey, L. A. (1988), Integer and Combinatorial Optimization, John Wiley and Sons, New York.
Pardalos, P. M. and Rosen, J. B. (1987), Constrained Global Optimization, Algorithms and Applications, Springer Verlag, Lecture Notes in Computer Science 268.
Pardalos, P. M., Phillips, A. T. and Rosen, J. B. (1992), Topics in Parallel Computing in Mathematical Programming, Science Press.
Poore, A. B. and Rijavec, N. (1993), “Partitioning Multiple Data Sets via Mul-tidimensional Assignments and Lagrangian Relaxation,” submitted to DIMACS Series in Discrete Mathematics and Theoretical Computer Science.
Poore, A. B. and Rijavec, N. (1993), “A Lagrangian Relaxation Algorithm for Multi-dimensional Assignment Problems Arising from Multi-target Tracking,” SIAM Journal on Optimization, Vol. 3, No. 3, 545–563.
Poore, A. B. and Rijavec, N. (1993), “Multidimensional Assignment Formulation of Data Association Problems Arising From Multitarget Tracking and Multisen- sor Data Fusion,” to appear in Computational Optimization and Applications.
Reid, D. B. (1979), An Algorithm for Tracking Multiple Targets,” IEEE Transactions on Automatic Control, Vol. AC-24, No. 6, 843–854.
Rijavec, N. (1992), A Lagrangian Relaxation Algorithm for Some Multidimensional Assignment Problems, Ph.D. Thesis, Colorado State University, Fort Collins, Colorado.
Shor, N. Z. (1985), Minimization Methods for Non-Differentiate Functions, Springer-Verlag, New York.
Schramm, H. and Zowe, J. (1992), “A Version of the Bundle Idea for Minimizing a Nonsmooth Function: Conceptual Idea, Convergence Analysis, Numerical Results” SIAM Journal on Optimization, Vol 2, 121–152.
Waltz, E. and Llinas, J. (1990), Multisensor Data Fusion, Artech House, Boston, Massachusets.
Wolfe, P. (1975), “A Method of Conjugate Subgradients for Minimizing Nondif- ferentiable Functions,” Mathematical Programming Study 3., 147–173.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1994 Kluwer Academic Publishers
About this chapter
Cite this chapter
Poore, A.B., Rijavec, N. (1994). A Numerical Study of Some Data Association Problems Arising in Multitarget Tracking. In: Hager, W.W., Hearn, D.W., Pardalos, P.M. (eds) Large Scale Optimization. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-3632-7_17
Download citation
DOI: https://doi.org/10.1007/978-1-4613-3632-7_17
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4613-3634-1
Online ISBN: 978-1-4613-3632-7
eBook Packages: Springer Book Archive