An optimal data association method based on the minimum weighted bipartite perfect matching

Data association is an important problem in simultaneous localization and mapping, however, many single frame based methods only provide suboptimal solutions. In this paper an optimal graph theoretic approach is proposed. We formulate the data association as an integer programming (IP) and then prove that it is equivalent to a minimum weight bipartite perfect matching problem. Therefore, optimally solving the bipartite matching problem implies optimally resolving the IP, i.e. the data association problem. We compare the proposed approach with other widely used data association methods. Experimental results validate the effectiveness and accuracy of the proposed approach, and manifest that this graph based data association method can be used for online application.

[1]  Samuel J. Davey.  Simultaneous Localization and Map Building Using the Probabilistic Multi-Hypothesis Tracker , 2007, IEEE Transactions on Robotics.

[2]  Donald Reid.  An algorithm for tracking multiple targets , 1978 .

[3]  Ingemar J. Cox,et al.  An Efficient Implementation of Reid's Multiple Hypothesis Tracking Algorithm and Its Evaluation for the Purpose of Visual Tracking , 1996, IEEE Trans. Pattern Anal. Mach. Intell..

[4]  Andreas Birk,et al.  On behalf of: Multimedia Archives , 2012 .

[5]  Robert E. Tarjan,et al.  Fibonacci heaps and their uses in improved network optimization algorithms , 1987, JACM.

[6]  D. West.  Introduction to Graph Theory , 1995 .

[7]  Eduardo Mario Nebot,et al.  Real time data association for FastSLAM , 2003, 2003 IEEE International Conference on Robotics and Automation (Cat. No.03CH37422).

[8]  Gamini Dissanayake,et al.  Sparse Local Submap Joining Filter for Building Large-Scale Maps , 2008, IEEE Transactions on Robotics.

[9]  M. Kam,et al.  Applying the Hungarian method to stereo matching , 1997, Proceedings of the 36th IEEE Conference on Decision and Control.

[10]  Hugh F. Durrant-Whyte,et al.  Data association for mobile robot navigation: a graph theoretic approach , 2000, Proceedings 2000 ICRA. Millennium Conference. IEEE International Conference on Robotics and Automation. Symposia Proceedings (Cat. No.00CH37065).

[11]  Sen Zhang,et al.  An Efficient Data Association Approach to Simultaneous Localization and Map Building , 2005, Int. J. Robotics Res..

[12]  Yaakov Bar-Shalom,et al.  Sonar tracking of multiple targets using joint probabilistic data association , 1983 .

[13]  Ingemar J. Cox,et al.  Dynamic Map Building for an Autonomous Mobile Robot , 1992 .

[14]  N. K. Bose,et al.  Multitarget tracking in clutter: fast algorithms for data association , 1993 .

[15]  Juan D. Tardós,et al.  Data association in stochastic mapping using the joint compatibility test , 2001, IEEE Trans. Robotics Autom..

[16]  Chee-Yee Chong,et al.  Graph approaches for data association , 2012, 2012 15th International Conference on Information Fusion.

[17]  L. Hong,et al.  Computational complexity analysis for multiple hypothesis tracking , 1997, Proceedings of the 36th IEEE Conference on Decision and Control.

[18]  Hugh F. Durrant-Whyte,et al.  A Bayesian Algorithm for Simultaneous Localisation and Map Building , 2001, ISRR.

[19]  I. R. Goodman,et al.  Mathematics of Data Fusion , 1997 .

[20]  Zhi-Quan Luo,et al.  An interior point linear programming approach to two-scan data association , 1999 .

[21]  Martin David Adams,et al.  Toward multidimensional assignment data association in robot localization and mapping , 2006, IEEE Transactions on Robotics.

[22]  Wang Jianguo,et al.  Study on the Hungarian algorithm for the maximum likelihood data association problem * * This projec , 2007 .

[23]  Favio R. Masson,et al.  Simultaneous localization and map building using natural features and absolute information , 2002, Robotics Auton. Syst..

[24]  Y. Bar-Shalom,et al.  Joint probabilistic data association for autonomous navigation , 1993 .

[25]  Y. Wong,et al.  An optimal graph theoretic approach to data association in SLAM , 2008 .