فیلترذره مبتنی برMCMC به منظور ردگیری چندهدفه در میان مشاهدات خام و آشکارنشده

نویسنده

پردازش

چکیده

در این مقاله به مسئله پرچالش ردگیری چندهدفه در میان داده­های آشکارنشده پرداخته می­شود. برای انجام این کار، ابتدا با تقسیم فضای حالت به دو زیر فضای خطی و غیرخطی و با به­کارگیری اصل Rao–Blackwellization، چگالی اهمیتی بهینه را برای نوع خاصی از مدل سنسور، که مشاهدات منشعب و در هم ادغام­شده را برای ناحیه مشاهده مشبک­شده تولید می­نماید، به­دست آمد. در ادامه، برای کاهش پیچیدگی محاسباتی نمونه برداری از چگالی اهمیتی بهینه، از معروف­ترین نمونه­بردار خانواده MCMC یعنی نمونه­بردار Gibbs برای نمونه­برداری از چگالی اهمیتی بهینه استفاده شد و سپس با مقایسه عملکرد این دو در یک محیط ردگیری چندهدفه و در میان مشاهدات خام و آشکارنشده، نشان داده شد که نمونه­بردار Gibbs به مبادله­ای بین کاهش حجم محاسبات و میزان دقت در ردگیری دست می­یابد. ایده مطرح­شده را می­توان به­عنوان جایگزین برای مواقعی که نمونه­برداری از چگالی اهمیتی بهینه عملا غیرممکن است، استفاده نمود.

کلیدواژه‌ها


عنوان مقاله [English]

An MCMC-baesd Particle Filter for Multitarget Tracking within Raw Measurements

نویسنده [English]

  • M. R. Danaee
چکیده [English]

This paper examines multitarget tracking within raw measurements which has always been considered to be a hassle. This was achieved by separating the state space model of each target into linear and nonlinear subspaces. Then, the Rao–Blackwellization principle was utilized to derive the optimum importance density for special kind of sensor which generates both split and merged measurements within a pixelized observation area. To relieve the complexity associated with the achieved optimum importance, the Gibbs sampler, the well-known sampler from MCMC family, is used to sample from the optimal importance density. The synthetic multitarget tracking scenario using raw data will then be used to show that our new Gibbs sampling method could reach a compromise between accuracy of tracking and computational expense. The proposed idea is motivating to be used in applications where sampling from the optimum proposal density is practically impossible. 

کلیدواژه‌ها [English]

  • Multitarget tracking
  • Gibbs Sampler
  • Rao–Blackwellization
  • Optimal Importance Density
  • Particle Filter

[1]     Doucet, A.; De Fiestas, N.; Gordon, N.; Eds, J. “Sequential Monte Carlo Methods in Practice”; New York: Springer-Verlag, 2001.##

[2]     Orton, M.;  Fitzgerald, W. “A Bayesian Approach to Tracking Multiple Targets Using Sensor Arrays and Particle Filters”; Signal Processing, IEEE Transactions on; 2005, 50 (2), 216-223.##

[3]     Hue, C.; Le Cadre, J.-P.; Perez, P. “Sequential Monte Carlo Methods for Multiple Target Tracking and Data Fusion”; Signal Processing, IEEE Transactions on; 2002, 50 (2), 309-325.##

[4]     Rezatofighi, S. H.; Gould, S.; Ba Truong, Vo.; Ba-Ngu, Vo.; Mele, K.; Hartley, R. “Multi-Target Tracking With Time-Varying Clutter Rate and Detection Profile: Application to Time-Lapse Cell Microscopy Sequences”; Medical Imaging, IEEE Transactions on. 2015, 34 (6), 1336-1348.##

[5]     Kreucher, C.; Kastella, K.; Hero, A. O. “Multitarget Tracking Using the Joint Multitarget Probability Density”; Aerospace and Electronic Systems, IEEE Transactions on; 2005, 41 (4), 1396- 1414.##

[6]     Vo, B. T.; Vo, B. N. “Labeled Random Finite Sets and Multi-Object Conjugate Priors”; IEEE Transactions on Signal Processing. 2013, 61(13), 3460-3475.##

[7]     Vo, B. N.; Singh, S.; Doucet, A. “Sequential Monte Carlo Methods for Multi-Target Filtering with Random Finite Sets”; IEEE Transactions Aerospace & Electronic Sys-tems. 2005,  41 (4), 1224–1245.##

[8]     Whitley, N.; Singh, S.; Goodwill, S. “Auxiliary Particle Implementation of Probability Hypothesis Density Filter”; in IEEE Trans. Aerospace and Electronic Systems. 2010, 46 (3), 1437–1454.##

[9]     Rustic, B.; Clark,  D.; Vo, B.-N. "Improved SMC Implementation of the PHD Filter."; in Proc. 13th Annual Conf. Information Fusion, Edinburgh, UK, 2010.##

[10]  Vermaak, J.; Goodwill, S. J.; Pérez, P. “Monte Carlo Filtering for Multi Target Tracking and Data Association”; Aerospace and Electronic Systems, IEEE Transactions on. 2005, 41 (1), 309-332.##

[11]  Hue, C.; Le Cadre, J.-P.; Pérez, P. “Tracking Multiple Objects with Particle Filtering”; Aerospace and Electronic Systems, IEEE Transactions on. 2002, 38 (3), 791- 812.##

[12]  Khan, Z.; Bach, T.; Dellaert, F. “Multitarget Tracking with Split and Merged Measurements”; Computer Vision and Pattern Recognition, IEEE Computer Society Conference on. 2005, 1, 605- 610.##

[13]  Jianru, Xue; Nanning, Zhang; Xiaopin, Zhang. “An Integrated Monte Carlo Data Association Framework for Multi-Object Tracking”; Pattern Recognition, 18th International Conference on. 2006, 1, 703-706.##

[14]  Hwang, R. R.; Huber, M. “A Particle Filter Approach for Multi-Target Tracking”; Intelligent Robots and Systems, IEEE/RSJ International Conference on. 2007, 2753-2760.##

[15]  Scepter, F.; Pang Sze Kim; Carmi, A.; Goodwill, S. “On MCMC-Based Particle Methods for Bayesian Filtering: Application to Multitarget Tracking”; Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP), 3rd IEEE International Workshop on. 2009, 360-363.##

[16]  Cox, I. J. “A Review of Statistical Data Association Techniques for Motion Correspondence”; International Journal of Computer Vision. 1993, 10, 53–66.##

[17]  Gauvrit, H.; Cadre, J.P.; Jauffret C. “A formulation of Multitarget Tracking As an Incomplete Data Problem”; Aerospace and Electronic Systems, IEEE Transactions on; 1997, 33 (4), 1242-1257.##

[18]  Boers, Y.; Dresden, J. N. “Multitarget Particle Filter Track Before Detect Application”; Radar, Sonar and Navigation, IEE Proceedings. 2004, 151 (6), 351- 357.##

[19]  Moreland, M. R.; Kreucher, C. M.; Kastella, K. “A Bayesian Approach to Multiple Target Detection and Tracking”; Signal Processing, IEEE Transactions on; 2007, 55 (5), 1589-1604.##

[20]  Doucet, A.; Goodwill, S.; Angrier, C. “On sequential Monte Carlo Sampling Methods for Bayesian Filtering”; Stat. Comput. 2000, 10, 197–208.##

[21]  Gilks, W. R.; Richardson, S.; Spiegelhalter,  D. J. “Markov Chain Monte Carlo in Practice”; Chapman and Hall. 1996.##

[22]  Blackman, S.; Popoli, R. “Design and Analysis of Modern Tracking Systems”; Artech House. 1999.##

[23]  Danaee, M. R.; Behnia, F. “Extension of Particle Filters for Time-Varying Target Presence Through Split and Raw Measurements”; Radar, Sonar & Navigation. IET, 2013, 7 (5), 517-526.##

[24]  Genovesio, A.; Olivo-Marin, J.-C. “Split and Merge Data Association Filter for Dense Multi-Target Tracking”; Pattern Recognition, Proceedings of the 17th International Conference on. 2004, 4, 677- 680.##

[25]  Koch, W.; Van Keuk, G. “Multiple Hypothesis Track Maintenance with Possibly Unresolved Measurements”; Aerospace and Electronic Systems, IEEE Transactions on. 1997, 33 (3), 883-892.##

[26]  Chang, Kuo-Chu.; Bar-Shalom, Y. “Joint Probabilistic Data Association for Multitarget Tracking with Possibly Unresolved Measurements and Maneuvers”; Automatic Control, IEEE Transactions on. 1984, 29 (7), 585- 594.##

[27]  Rotten, M. G.; Gordon, N. J.; Maskell, S. “Recursive Track-Before-Detect with Target Amplitude Fluctuations”; Radar, Sonar and Navigation, IEE Proceedings. 2005, 152 (5), 345- 352.##

[28]  Pitt, M. K.; Shepard, N. “Filtering via Simulation: Auxiliary Particle Filters”; Technical Report, Nuffield College, Oxford University. September 1997.##

[29]  Särkkä, S.; Vehtari, A.; Lampinen, J. “Rao-Blackwellized Oarticle Filter for Multiple Target Tracking”; Information Fusion. 2007, 8 (1), 2-15.##

[30]  Anderson, B. D. O.; Moore, J. B. “Optimal Filtering”; Englewood Cliffs: Prentice-Hall. 1979.##

[31]  Doucet, A.; Vo, B.-N.; Angrier, C.;  Davy, M. “Particle Filtering for Multi-Target Tracking and Sensor Management”; Information Fusion, Proceedings of the Fifth International Conference on. 2002, 1, 474- 481.##

[32]  Bar-Shalom Y. “Tracking and Data Association”; San Diego, CA, USA: Academic Press Professional, Inc. 1987.##

[33]  Khan, Zia; Balch, T.; Dellaert, F. “MCMC-Based Particle Filtering for Tracking a Variable Number of Interacting Targets”; Pattern Analysis and Machine Intelligence, IEEE Transactions on. 2005, 27(11), 1805-1819.

Gilks, W. R.; Berzuini, C. “Following a Moving Target—Monte Carlo Inference for Dynamic Bayesian Models”; J. R. Statist. Soc. 2001, 63, 127–146.##