{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,20]],"date-time":"2026-01-20T02:50:03Z","timestamp":1768877403265,"version":"3.49.0"},"reference-count":25,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2015,12,4]],"date-time":"2015-12-04T00:00:00Z","timestamp":1449187200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Knowledge of the clutter rate is of critical importance in multi-target Bayesian tracking. However, estimating the clutter rate is a difficult problem in practice. In this paper, an improved multi-Bernoulli filter based on random finite sets for multi-target Bayesian tracking accommodating non-linear dynamic and measurement models, as well as unknown clutter rate, is proposed for radar sensors. The proposed filter incorporates the amplitude information into the state and measurement spaces to improve discrimination between actual targets and clutters, while adaptively generating the new-born object random finite sets using the measurements to eliminate reliance on prior random finite sets. A sequential Monte-Carlo implementation of the proposed filter is presented, and simulations are used to demonstrate the proposed filter\u2019s improvements in estimation accuracy of the target number and corresponding multi-target states, as well as the clutter rate.<\/jats:p>","DOI":"10.3390\/s151229804","type":"journal-article","created":{"date-parts":[[2015,12,9]],"date-time":"2015-12-09T07:06:30Z","timestamp":1449644790000},"page":"30385-30402","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["Multi-Target Tracking Based on Multi-Bernoulli Filter with Amplitude for Unknown Clutter Rate"],"prefix":"10.3390","volume":"15","author":[{"given":"Changshun","family":"Yuan","sequence":"first","affiliation":[{"name":"School of Electronic and Information Engineering, Beihang University, Beijing 100191, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jun","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Electronic and Information Engineering, Beihang University, Beijing 100191, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Peng","family":"Lei","sequence":"additional","affiliation":[{"name":"School of Electronic and Information Engineering, Beihang University, Beijing 100191, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yanxian","family":"Bi","sequence":"additional","affiliation":[{"name":"School of Electronic and Information Engineering, Beihang University, Beijing 100191, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zhongsheng","family":"Sun","sequence":"additional","affiliation":[{"name":"School of Electronic and Information Engineering, Beihang University, Beijing 100191, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2015,12,4]]},"reference":[{"key":"ref_1","unstructured":"Skolnik, M.I. (2007). Introduction to Radar Systems, Publishing House of Electronics Industry. [3rd ed.]."},{"key":"ref_2","unstructured":"Blackrnan, S., and House, A. (1999). Design and Analysis of Modern Tracking Systems, Artech House."},{"key":"ref_3","unstructured":"Bar-Shalom, Y., and Blair, W.D. (2000). Multitarget-Multisensor Tracking: Advanced Applications, Artech House."},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Mahler, R. (2007). Statistical Multisource-Multitarget Information Fusion, Artech House.","DOI":"10.1201\/9781420053098.ch16"},{"key":"ref_5","unstructured":"Bar-Shalom, Y., and Li, X.R. (1995). Multitarget-Multisensor Tracking: Principles and Techniques, Yaakov Bar-Shalom."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"1093","DOI":"10.1109\/TAES.2004.1337482","article-title":"Joint integrated probabilistic data association: JIPDA","volume":"40","author":"Evans","year":"2004","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"1152","DOI":"10.1109\/TAES.2003.1261119","article-title":"Multitarget Bayes filtering via first-order multitarget moments","volume":"39","author":"Mahler","year":"2003","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_8","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_9","doi-asserted-by":"crossref","first-page":"1224","DOI":"10.1109\/TAES.2005.1561884","article-title":"Sequential Monte Carlo methods for multitarget filtering with random finite sets","volume":"41","author":"Vo","year":"2005","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"4091","DOI":"10.1109\/TSP.2006.881190","article-title":"The Gaussian mixture probability hypothesis density filter","volume":"54","author":"Vo","year":"2006","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"3553","DOI":"10.1109\/TSP.2007.894241","article-title":"Analytic implementations of the cardinalized probability hypothesis density filter","volume":"55","author":"Vo","year":"2007","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"2652","DOI":"10.1109\/TSP.2006.874845","article-title":"Convergence results for the particle PHD filter","volume":"54","author":"Clark","year":"2006","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"1204","DOI":"10.1109\/TSP.2006.888886","article-title":"Convergence analysis of the Gaussian mixture PHD filter","volume":"55","author":"Clark","year":"2007","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"2920","DOI":"10.3390\/s120302920","article-title":"FISST based method for multi-target tracking in the image plane of optical sensors","volume":"12","author":"Xu","year":"2012","journal-title":"Sensors"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"3497","DOI":"10.1109\/TSP.2011.2128316","article-title":"CPHD filtering with unknown clutter rate and detection profile","volume":"59","author":"Mahler","year":"2011","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"409","DOI":"10.1109\/TSP.2008.2007924","article-title":"The cardinality balanced multi-target multi-Bernoulli filter and its implementations","volume":"57","author":"Vo","year":"2009","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Hoseinnezhad, R., Vo, B.N., and Vo, B.T. (2011, January 22\u201327). Bayesian integration of audio and visual information for multi-target tracking using a CB-MeMBer filter. Proceedings of the IEEE International Conference on Acoustics, Speech and Signal Processing, Prague, Czech.","DOI":"10.1109\/ICASSP.2011.5946942"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"3625","DOI":"10.1016\/j.patcog.2012.04.004","article-title":"Visual tracking of numerous targets via multi-Bernoulli filtering of image data","volume":"45","author":"Hoseinnezhad","year":"2012","journal-title":"Pattern Recognit."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"5129","DOI":"10.1109\/TSP.2010.2050482","article-title":"Joint detection and estimation of multiple objects from image observations","volume":"58","author":"Vo","year":"2010","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"2429","DOI":"10.1109\/TAC.2011.2163862","article-title":"Adaptive control and reconfiguration of mobile wireless sensor networks for dynamic multi-target tracking","volume":"56","author":"Zhang","year":"2011","journal-title":"IEEE Trans. Autom. Control."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"392","DOI":"10.1109\/TSP.2012.2222389","article-title":"Visual tracking in background subtracted image sequences via multi-Bernoulli filtering","volume":"61","author":"Hoseinnezhad","year":"2013","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"399","DOI":"10.1109\/JSTSP.2013.2252325","article-title":"Robust multi-Bernoulli filtering","volume":"7","author":"Vo","year":"2013","journal-title":"IEEE J. Sel. Top. Signal Process."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"1656","DOI":"10.1109\/TAES.2012.6178085","article-title":"Adaptive target birth intensity for PHD and CPHD filters","volume":"48","author":"Ristic","year":"2012","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1155\/2012\/584140","article-title":"Convergence analysis for the SMC-MeMBer and SMC-CBMeMBer filters","volume":"2012","author":"Lian","year":"2012","journal-title":"J. Appl. Math."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"3447","DOI":"10.1109\/TSP.2008.920469","article-title":"A consistent metric for performance evaluation of multi-object filters","volume":"56","author":"Schuhmacher","year":"2008","journal-title":"IEEE Trans. Signal Process."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/15\/12\/29804\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T20:53:26Z","timestamp":1760216006000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/15\/12\/29804"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,12,4]]},"references-count":25,"journal-issue":{"issue":"12","published-online":{"date-parts":[[2015,12]]}},"alternative-id":["s151229804"],"URL":"https:\/\/doi.org\/10.3390\/s151229804","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2015,12,4]]}}}