{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,12]],"date-time":"2026-02-12T07:48:49Z","timestamp":1770882529526,"version":"3.50.1"},"reference-count":35,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2018,10,15]],"date-time":"2018-10-15T00:00:00Z","timestamp":1539561600000},"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>In this paper, we study the problem of the joint detection and direction-of-arrival (DOA) tracking of a single moving source which can randomly appear or disappear from the surveillance volume. Firstly, the Bernoulli random finite set (RFS) is employed to characterize the randomness of the state process, i.e., the dynamics of the source motion and the source appearance. To increase the performance of the detection and DOA tracking in low signal-to-noise ratio (SNR) scenarios, the measurements are obtained directly from an array of sensors and allow multiple snapshots. A track-before-detect (TBD) Bernoulli filter is proposed for tracking a randomly on\/off switching single dynamic system. Secondly, since the variances of the stochastic signal and measurement noise are unknown in practical applications, these nuisance parameters are marginalized by defining an uninformative prior, and the likelihood function is compensated by using the information theoretic criteria. The simulation results demonstrate the performance of the filter.<\/jats:p>","DOI":"10.3390\/s18103473","type":"journal-article","created":{"date-parts":[[2018,10,16]],"date-time":"2018-10-16T02:52:53Z","timestamp":1539658373000},"page":"3473","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Joint Detection and DOA Tracking with a Bernoulli Filter Based on Information Theoretic Criteria"],"prefix":"10.3390","volume":"18","author":[{"given":"Guangpu","family":"Zhang","sequence":"first","affiliation":[{"name":"Acoustic Science and Technology Laboratory, Harbin Engineering University, Harbin 150001, China"},{"name":"Key Laboratory of Marine Information Acquisition and Security (Harbin Engineering University), Ministry of Industry and Information Technology, Harbin 150001, China"},{"name":"College of Underwater Acoustic Engineering, Harbin Engineering University, Harbin 150001, China"},{"name":"Qindao Haina Underwater Information Technology Co., Ltd., Qindao 266500, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3569-2700","authenticated-orcid":false,"given":"Ce","family":"Zheng","sequence":"additional","affiliation":[{"name":"Acoustic Science and Technology Laboratory, Harbin Engineering University, Harbin 150001, China"},{"name":"Key Laboratory of Marine Information Acquisition and Security (Harbin Engineering University), Ministry of Industry and Information Technology, Harbin 150001, China"},{"name":"College of Underwater Acoustic Engineering, Harbin Engineering University, Harbin 150001, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2728-4934","authenticated-orcid":false,"given":"Sibo","family":"Sun","sequence":"additional","affiliation":[{"name":"Acoustic Science and Technology Laboratory, Harbin Engineering University, Harbin 150001, China"},{"name":"Key Laboratory of Marine Information Acquisition and Security (Harbin Engineering University), Ministry of Industry and Information Technology, Harbin 150001, China"},{"name":"College of Underwater Acoustic Engineering, Harbin Engineering University, Harbin 150001, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Guolong","family":"Liang","sequence":"additional","affiliation":[{"name":"Acoustic Science and Technology Laboratory, Harbin Engineering University, Harbin 150001, China"},{"name":"Key Laboratory of Marine Information Acquisition and Security (Harbin Engineering University), Ministry of Industry and Information Technology, Harbin 150001, China"},{"name":"College of Underwater Acoustic Engineering, Harbin Engineering University, Harbin 150001, China"},{"name":"Qindao Haina Underwater Information Technology Co., Ltd., Qindao 266500, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yifeng","family":"Zhang","sequence":"additional","affiliation":[{"name":"Acoustic Science and Technology Laboratory, Harbin Engineering University, Harbin 150001, China"},{"name":"Key Laboratory of Marine Information Acquisition and Security (Harbin Engineering University), Ministry of Industry and Information Technology, Harbin 150001, China"},{"name":"College of Underwater Acoustic Engineering, Harbin Engineering University, Harbin 150001, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2018,10,15]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Liang, G., Hao, Y., and Fan, Z. (2017). Spatial rotation technique with application to unmanned underwater vehicle (UUV) sonar arrays. Electron. Lett., 53.","DOI":"10.1049\/el.2017.3502"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"34306","DOI":"10.7498\/aps.63.034306","article-title":"Characteristics of mapping domain of the acoustic field interference structures radiated by a moving target","volume":"63","author":"Lin","year":"2014","journal-title":"Acta Phys. Sin."},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Zhao, A., Lin, M., Ma, X., and Hui, J. (2017). An Improved Azimuth Angle Estimation Method with a Single Acoustic Vector Sensor Based on an Active Sonar Detection System. Sensors, 17.","DOI":"10.3390\/s17020412"},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Zhang, Y., Liang, J., Jiang, S., and Chen, W. (2016). A Localization Method for Underwater Wireless Sensor Networks Based on Mobility Prediction and Particle Swarm Optimization Algorithms. Sensors, 16.","DOI":"10.3390\/s16020212"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"5225","DOI":"10.1109\/TSP.2017.2721904","article-title":"Transmit Array Interpolation for DOA Estimation via Tensor Decomposition in 2D MIMO Radar","volume":"65","author":"Cao","year":"2017","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Zhang, Z.Y., Zhang, J.Y., Zhou, Q.S., and Li, X.B. (2018). Multi-Target Angle Tracking Algorithm for Bistatic MIMO Radar Based on the Elements of the Covariance Matrix. Sensors, 18.","DOI":"10.3390\/s18030805"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"363","DOI":"10.1109\/JSEN.2011.2168204","article-title":"Particle Filtering and Posterior Cram\u00e9r-Rao Bound for 2-D Direction of Arrival Tracking Using an Acoustic Vector Sensor","volume":"12","author":"Zhong","year":"2012","journal-title":"IEEE Sens. J."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"2655","DOI":"10.1109\/78.790648","article-title":"Tracking the direction-of-arrival of multiple moving targets by passive arrays: Algorithm","volume":"47","author":"Zhou","year":"1999","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"216","DOI":"10.1109\/78.978377","article-title":"A Bayesian approach to tracking multiple targets using sensor arrays and particle filters","volume":"50","author":"Orton","year":"2002","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"2926","DOI":"10.1109\/TSP.2002.805251","article-title":"Particle filters for tracking an unknown number of sources","volume":"50","author":"Larocque","year":"2002","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1155\/2008\/428036","article-title":"A comparison of detection performance for several Track-Before-Detect algorithms","volume":"2008","author":"Davey","year":"2007","journal-title":"EURASIP J. Adv. Signal Process."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"1408","DOI":"10.1109\/PROC.1969.7278","article-title":"High-resolution frequency-wavenumber spectrum analysis","volume":"57","author":"Capon","year":"1969","journal-title":"Proc. IEEE"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"2450","DOI":"10.1109\/78.98000","article-title":"Detection and localization of multiple sources via the stochastic signals model","volume":"39","author":"Wax","year":"1991","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"3051","DOI":"10.1109\/78.330365","article-title":"Detection and estimation of DOA\u2019s of signals via Bayesian predictive densities","volume":"42","author":"Cho","year":"1994","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"1668","DOI":"10.1109\/TSP.2009.2037074","article-title":"MUSIC-Like DOA Estimation without Estimating the Number of Sources","volume":"58","author":"Zhang","year":"2010","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"772","DOI":"10.1109\/LSP.2014.2368987","article-title":"Reduced-Complexity Super-Resolution DOA Estimation with Unknown Number of Sources","volume":"22","author":"Reddy","year":"2015","journal-title":"IEEE Signal Process. Lett."},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Balakwmar, B., Sinha, A., Kirubarajan, T., and Reilly, J.P. (2005, January 17\u201320). PHD filtering for tracking an unknown number of sources using an array of sensors. Proceedings of the IEEE Workshop Stat. Signal Process, Bordeaux, France.","DOI":"10.1109\/SSP.2005.1628561"},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Mahler, R. (2007). Statistical Multisource-Multitarget Information Fusion, Artech House.","DOI":"10.1201\/9781420053098.ch16"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"1147","DOI":"10.1109\/TSP.2015.2504349","article-title":"CPHD-DOA Tracking of Multiple Extended Sonar Targets in Impulsive Environments","volume":"64","author":"Saucan","year":"2016","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_20","unstructured":"Choppala, P.B., Teal, P.D., and Frean, M.R. (2014, January 7\u201310). Adapting the multi-Bernoulli filter to phased array observations using MUSIC as pseudo-likelihood. Proceedings of the 17th International Conference on Information Fusion (FUSION), Salamanca, Spain."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"1385","DOI":"10.1109\/TAES.2012.6178069","article-title":"Multi-Sensor Joint Detection and Tracking with the Bernoulli Filter","volume":"48","author":"Vo","year":"2012","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"3406","DOI":"10.1109\/TSP.2013.2257765","article-title":"A Tutorial on Bernoulli Filters: Theory, Implementation and Applications","volume":"61","author":"Ristic","year":"2013","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"1145","DOI":"10.1109\/LSP.2014.2325566","article-title":"Bernoulli Filter for Trakc-Before-Detect using MIMO Radar","volume":"21","author":"Papi","year":"2014","journal-title":"IEEE Signal Process. Lett."},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Lin, S. (2018, January 15\u201320). Jointly Tracking and Separating Speech Sources Using Multiple Features and the generalized labeled multi Bernoulli Framework. Proceedings of the 2018 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), Calgary, AB, Canada.","DOI":"10.1109\/ICASSP.2018.8461605"},{"key":"ref_25","first-page":"1228","article-title":"Acoustic Source Localization and Tracking Using Track Before Detect","volume":"18","author":"Fallon","year":"2010","journal-title":"IEEE Trans. Acoust. Speech Signal Process."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"2809","DOI":"10.1121\/1.420337","article-title":"Space-time array processing: The model-based approach","volume":"102","author":"Sullivan","year":"1997","journal-title":"J. Acoust. Soc. Am."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"1133","DOI":"10.1109\/78.295205","article-title":"Tracking the direction of arrival of multiple moving targets","volume":"42","author":"Rao","year":"1994","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"1190","DOI":"10.1109\/29.31267","article-title":"Detection of the number of coherent signals by the MDL principle","volume":"37","author":"Wax","year":"1989","journal-title":"IEEE Trans. Acoust. Speech Signal Process."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"15","DOI":"10.1214\/aos\/1176344136","article-title":"Estimating the Dimension of a Model","volume":"6","author":"Schwarz","year":"1978","journal-title":"Ann. Stat."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"716","DOI":"10.1109\/TAC.1974.1100705","article-title":"A new look at the statistical model identification","volume":"19","author":"Akaike","year":"1974","journal-title":"IEEE Trans. Autom. Control"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"416","DOI":"10.1214\/aos\/1176346150","article-title":"A Universal Prior for Integers and Estimation by Minimum Description Length","volume":"11","author":"Rissanen","year":"1983","journal-title":"Ann. Stat."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"2405","DOI":"10.1109\/TAES.2012.6237599","article-title":"Bernoulli Particle Filter with Observer Control for Bearing-Only Tracking in Clutter","volume":"48","author":"Ristic","year":"2012","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_33","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."},{"key":"ref_34","doi-asserted-by":"crossref","unstructured":"Doucet, A., De, F.N., and Gordon, N. (2001). Sequential Monte Carlo Methods in Practice, Springer.","DOI":"10.1007\/978-1-4757-3437-9"},{"key":"ref_35","doi-asserted-by":"crossref","unstructured":"Ristic, B., Arulampalam, S., and Gordon, N. (2004). Beyond the Kalman Filter: Particle Filters for Tracking Applications, Artech House.","DOI":"10.1155\/S1110865704405095"}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/18\/10\/3473\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T15:25:47Z","timestamp":1760196347000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/18\/10\/3473"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,10,15]]},"references-count":35,"journal-issue":{"issue":"10","published-online":{"date-parts":[[2018,10]]}},"alternative-id":["s18103473"],"URL":"https:\/\/doi.org\/10.3390\/s18103473","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,10,15]]}}}