{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,27]],"date-time":"2026-03-27T17:12:02Z","timestamp":1774631522243,"version":"3.50.1"},"reference-count":36,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2022,1,5]],"date-time":"2022-01-05T00:00:00Z","timestamp":1641340800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/100000181","name":"AFOSR","doi-asserted-by":"publisher","award":["FA9550-201-0132"],"award-info":[{"award-number":["FA9550-201-0132"]}],"id":[{"id":"10.13039\/100000181","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000181","name":"AFOSR","doi-asserted-by":"publisher","award":["FA9550-17-1-0100"],"award-info":[{"award-number":["FA9550-17-1-0100"]}],"id":[{"id":"10.13039\/100000181","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>The paper considers the problem of tracking an unknown and time-varying number of unlabeled moving objects using multiple unordered measurements with unknown association to the objects. The proposed tracking approach integrates Bayesian nonparametric modeling with Markov chain Monte Carlo methods to estimate the parameters of each object when present in the tracking scene. In particular, we adopt the dependent Dirichlet process (DDP) to learn the multiple object state prior by exploiting inherent dynamic dependencies in the state transition using the dynamic clustering property of the DDP. Using the DDP to draw the mixing measures, Dirichlet process mixtures are used to learn and assign each measurement to its associated object identity. The Bayesian posterior to estimate the target trajectories is efficiently implemented using a Gibbs sampler inference scheme. A second tracking approach is proposed that replaces the DDP with the dependent Pitman\u2013Yor process in order to allow for a higher flexibility in clustering. The improved tracking performance of the new approaches is demonstrated by comparison to the generalized labeled multi-Bernoulli filter.<\/jats:p>","DOI":"10.3390\/s22010388","type":"journal-article","created":{"date-parts":[[2022,1,9]],"date-time":"2022-01-09T23:08:26Z","timestamp":1641769706000},"page":"388","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Bayesian Nonparametric Modeling for Predicting Dynamic Dependencies in Multiple Object Tracking"],"prefix":"10.3390","volume":"22","author":[{"given":"Bahman","family":"Moraffah","sequence":"first","affiliation":[{"name":"School of Electrical, Computer, and Energy Engineering, Arizona State University, Tempe, AZ 85281, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Antonia","family":"Papandreou-Suppappola","sequence":"additional","affiliation":[{"name":"School of Electrical, Computer, and Energy Engineering, Arizona State University, Tempe, AZ 85281, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,1,5]]},"reference":[{"key":"ref_1","unstructured":"Bar-Shalom, Y., and Li, X.R. (1995). Multitarget-Multisensor Tracking: Principles and Techniques, YBs."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Mahler, R.P.S. (2007). Statistical Multisource-Multitarget Information Fusion, Artech House.","DOI":"10.1201\/9781420053098.ch16"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"1523","DOI":"10.1109\/TAES.2007.4441756","article-title":"PHD filters of higher order in target number","volume":"43","author":"Mahler","year":"2007","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Mahler, R. (2001). Random Set Theory for Target Tracking and Identification, CRC Press.","DOI":"10.1201\/9781420038545.ch14"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"6554","DOI":"10.1109\/TSP.2014.2364014","article-title":"Labeled random finite sets and the Bayes multi-target tracking filter","volume":"62","author":"Vo","year":"2014","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"3246","DOI":"10.1109\/TSP.2014.2323064","article-title":"The labeled multi-Bernoulli filter","volume":"62","author":"Reuter","year":"2014","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"1975","DOI":"10.1109\/TSP.2016.2641392","article-title":"An efficient implementation of the generalized labeled multi-Bernoulli filter","volume":"65","author":"Vo","year":"2017","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"3040","DOI":"10.1109\/TSP.2018.2821650","article-title":"Multiple object tracking in unknown backgrounds with labeled random finite sets","volume":"66","author":"Punchihewa","year":"2018","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Buonviri, A., York, M., LeGrand, K., and Meub, J. (2019, January 2\u20139). Survey of challenges in labeled random finite set distributed multi-sensor multi-object tracking. Proceedings of the IEEE Aerospace Conference, Sky, MT, USA.","DOI":"10.1109\/AERO.2019.8742216"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"209","DOI":"10.1214\/aos\/1176342360","article-title":"A Bayesian analysis of some nonparametric problems","volume":"1","author":"Ferguson","year":"1973","journal-title":"Ann. Stat."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.jmp.2011.08.004","article-title":"A tutorial on Bayesian nonparametric models","volume":"56","author":"Gershman","year":"2012","journal-title":"J. Math. Psychol."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"1152","DOI":"10.1214\/aos\/1176342871","article-title":"Mixtures of Dirichlet processes with applications to Bayesian nonparametric problems","volume":"2","author":"Antoniak","year":"1974","journal-title":"Ann. Stat."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"855","DOI":"10.1214\/aop\/1024404422","article-title":"The two-parameter Poisson-Dirichlet distribution derived from a stable subordinator","volume":"25","author":"Pitman","year":"1997","journal-title":"Ann. Probab."},{"key":"ref_14","unstructured":"Teh, Y.W. (2021, December 01). Dirichlet Process. Encyclopedia of Machine Learning, Available online: https:\/\/www.stats.ox.ac.uk\/teh\/research\/npbayes\/Teh2010a.pdf."},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Topkaya, I.S., Erdogan, H., and Porikli, F. (2013, January 29\u201331). Detecting and tracking unknown number of objects with Dirichlet process mixture models and Markov random fields. Proceedings of the International Symposium on Visual Computing, Rethymnon, Greece.","DOI":"10.1007\/978-3-642-41939-3_18"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"1569","DOI":"10.1109\/TSP.2010.2102756","article-title":"Bayesian nonparametric inference of switching dynamic linear models","volume":"59","author":"Fox","year":"2011","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_17","unstructured":"Caron, F., Davy, M., and Doucet, A. (2007, January 19\u201322). Generalized P\u00f3lya urn for time-varying Dirichlet process mixtures. Proceedings of the Conference on Uncertainty in Artificial Intelligence, Vancouver, BC, Canada."},{"key":"ref_18","first-page":"1","article-title":"Generalized P\u00f3lya urn for time-varying Pitman-Yor processes","volume":"18","author":"Caron","year":"2017","journal-title":"J. Mach. Learn. Res."},{"key":"ref_19","unstructured":"MacEachern, S.N. (1999). Dependent nonparametric processes. Proceedings of the Bayesian Statistical Science Section, American Statistical Association."},{"key":"ref_20","unstructured":"MacEachern, S.N. (2000). Dependent Dirichlet Processes, Department of Statistics, Ohio State University. Technical Report."},{"key":"ref_21","unstructured":"Campbell, T., Liu, M., Kulis, B., How, J.P., and Carin, L. (2013). Dynamic clustering via asymptotics of the dependent Dirichlet process mixture. arXiv."},{"key":"ref_22","first-page":"2461","article-title":"Distance dependent Chinese restaurant processes","volume":"12","author":"Blei","year":"2011","journal-title":"J. Mach. Learn. Res."},{"key":"ref_23","unstructured":"Neiswanger, W., Wood, F., and Xing, E. (2014, January 22\u201325). The dependent Dirichlet process mixture of objects for detection-free tracking and object modeling. Proceedings of the International Conference on Artificial Intelligence and Statistics, Reykjavik, Iceland."},{"key":"ref_24","first-page":"639","article-title":"A constructive definition of Dirichlet priors","volume":"4","author":"Sethuraman","year":"1994","journal-title":"Stat. Sin."},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Aldous, D.J. (1985). Exchangeability and related topics. Lecture Notes in Mathematics, Springer.","DOI":"10.1007\/BFb0099421"},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Moraffah, B., and Papandreou-Suppappola, A. (2018, January 28\u201331). Dependent Dirichlet process modeling and identity learning for multiple object tracking. Proceedings of the Asilomar Conference on Signals, Systems, and Computers, Pacific Grove, CA, USA.","DOI":"10.1109\/ACSSC.2018.8645084"},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"MacEarchern, S.N. (1998). Computational methods for mixture of Dirichlet process models. Practical Nonparametric and Semiparametric Bayesian Statistics, Springer.","DOI":"10.1007\/978-1-4612-1732-9_2"},{"key":"ref_28","unstructured":"Moraffah, B. (2019). Bayesian Nonparametric Modeling and Inference for Multiple Object Tracking. [Ph.D. Thesis, Arizona State University]."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"577","DOI":"10.1080\/01621459.1995.10476550","article-title":"Bayesian density estimation and inference using mixtures","volume":"90","author":"Escobar","year":"1995","journal-title":"J. Am. Stat. Assoc."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"268","DOI":"10.1080\/01621459.1994.10476468","article-title":"Estimating normal means with a Dirichlet process prior","volume":"89","author":"Escobar","year":"1994","journal-title":"J. Am. Stat. Assoc."},{"key":"ref_31","first-page":"170","article-title":"Remarks on consistency of posterior distributions","volume":"3","author":"Choi","year":"2008","journal-title":"IMS Collect."},{"key":"ref_32","doi-asserted-by":"crossref","unstructured":"Teh, Y.W. (2006, January 17\u201321). A hierarchical Bayesian language model based on Pitman-Yor processes. Proceedings of the 21st International Conference on Computational Linguistics and 44th Annual Meeting of the Association for Computational Linguistics, Sydney, Australia.","DOI":"10.3115\/1220175.1220299"},{"key":"ref_33","doi-asserted-by":"crossref","unstructured":"Moraffah, B., Papandreou-Suppappola, A., and Rangaswamy, M. (2019, January 2\u20135). Nonparametric Bayesian methods and the dependent Pitman-Yor process for modeling evolution in multiple object tracking. Proceedings of the International Conference on Information Fusion, Ottawa, ON, Canada.","DOI":"10.23919\/FUSION43075.2019.9011340"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"3452","DOI":"10.1109\/TSP.2011.2140111","article-title":"A metric for performance evaluation of multi-target tracking algorithms","volume":"59","author":"Ristic","year":"2011","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_35","unstructured":"Bar-Shalom, Y., and Fortmann, T.E. (1988). Tracking and Data Association, Academic Press."},{"key":"ref_36","doi-asserted-by":"crossref","unstructured":"Mahler, R. (2018, January 16\u201319). A clutter-agnostic generalized labeled multi-Bernoulli filter. Proceedings of the SPIE Signal Processing, Sensor\/Information Fusion, and Target Recognition XXVII, Orlando, FL, USA.","DOI":"10.1117\/12.2305464"}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/22\/1\/388\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,13]],"date-time":"2025-10-13T14:00:25Z","timestamp":1760364025000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/22\/1\/388"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,1,5]]},"references-count":36,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2022,1]]}},"alternative-id":["s22010388"],"URL":"https:\/\/doi.org\/10.3390\/s22010388","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,1,5]]}}}