{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,18]],"date-time":"2026-09-18T17:26:26Z","timestamp":1789752386905,"version":"4.0.1"},"reference-count":31,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2018,5,8]],"date-time":"2018-05-08T00:00:00Z","timestamp":1525737600000},"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>This paper focuses on underwater target tracking based on a multi-static sonar network composed of passive sonobuoys and an active ping. In the multi-static sonar network, the location of the target can be estimated using TDOA (Time Difference of Arrival) measurements. However, since the sensor network may obtain insufficient and inaccurate TDOA measurements due to ambient noise and other harsh underwater conditions, target tracking performance can be significantly degraded. We propose a robust target tracking algorithm designed to operate in such a scenario. First, track management with track splitting is applied to reduce performance degradation caused by insufficient measurements. Second, a target location is estimated by a fusion of multiple TDOA measurements using a Gaussian Mixture Model (GMM). In addition, the target trajectory is refined by conducting a stack-based data association method based on multiple-frames measurements in order to more accurately estimate target trajectory. The effectiveness of the proposed method is verified through simulations.<\/jats:p>","DOI":"10.3390\/s18051481","type":"journal-article","created":{"date-parts":[[2018,5,8]],"date-time":"2018-05-08T12:15:03Z","timestamp":1525781703000},"page":"1481","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":11,"title":["Robust Target Tracking with Multi-Static Sensors under Insufficient TDOA Information"],"prefix":"10.3390","volume":"18","author":[{"given":"Hyunhak","family":"Shin","sequence":"first","affiliation":[{"name":"Department of Electrical Engineering, Korea University, Seoul 02841, Korea"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Bonhwa","family":"Ku","sequence":"additional","affiliation":[{"name":"Department of Electrical Engineering, Korea University, Seoul 02841, Korea"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jill","family":"Nelson","sequence":"additional","affiliation":[{"name":"Department of Electrical and Computer Engineering, George Mason University, Fairfax, VA 22030, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Hanseok","family":"Ko","sequence":"additional","affiliation":[{"name":"Department of Electrical Engineering, Korea University, Seoul 02841, Korea"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2018,5,8]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1216","DOI":"10.1109\/78.134483","article-title":"Maximum likelihood estimation for long-range target tracking using passive sonar measurements","volume":"40","author":"Meyling","year":"1992","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"614","DOI":"10.1109\/TASSP.1981.1163609","article-title":"Passive source tracking using sonar time delay data","volume":"29","author":"McCabe","year":"1981","journal-title":"IEEE Trans. Acoust. Speech Signal Process."},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Prosperi, S. (1991, January 14\u201317). New passive tracking algorithms using power information with application to passive sonar. Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing, Toronto, ON, Canada.","DOI":"10.1109\/ICASSP.1991.150709"},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Hempel, C.G. (2006, January 10\u201313). Probabilistic multi-hypothesis tracking for distributed multi-static active sonar. Proceedings of the IEEE International Conference Information Fusion, Florence, Italy.","DOI":"10.1109\/ICIF.2006.301760"},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Tokekar, P., Vander Hook, J., and Isler, V. (2011, January 25\u201330). Active target localization for bearing based robotic telemetry. Proceedings of the IEEE\/RSJ International Conference on Intelligent Robots and Systems, San Francisco, CA, USA.","DOI":"10.1109\/IROS.2011.6048778"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"1371","DOI":"10.1109\/TAES.2008.4667715","article-title":"Performance Comparison of Target Localization for Active Sonar Systems","volume":"44","author":"Kim","year":"2008","journal-title":"IEEE Trans. Aerosp."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"1005","DOI":"10.1109\/TSP.2007.909052","article-title":"Relationship between Geometric Translations and TLS Estimation Bias in Bearings-only Target Localization","volume":"56","author":"Dogancay","year":"2008","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"2453","DOI":"10.1109\/TSP.2004.831921","article-title":"An accurate algebraic solution for moving source location using TDOA and FDOA measurements","volume":"52","author":"Ho","year":"2004","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_9","unstructured":"Zhou, Y., and Lamont, L. Constrained linear least squares approach for TDOA localization: A global optimum solution, In Proceedings of the IEEE International Conference on Acoustics, Speech and Signal Processing, Las Vegas, NV, USA, 31 March\u20134 April 2008; pp."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"172902","DOI":"10.1155\/2011\/172902","article-title":"Total Least Squares Method for Robust Source Localization in Sensor Networks Using TDOA Measurements","volume":"7","author":"Weng","year":"2011","journal-title":"Int. J. Distrib. Sens. Netw."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"1676","DOI":"10.1109\/TMC.2009.75","article-title":"Wireless Location Tracking Algorithms for Environments with Insufficient Signal Sources","volume":"8","author":"Tseng","year":"2009","journal-title":"IEEE Trans. Mob. Comput."},{"key":"ref_12","unstructured":"Song, T.L., and Mu\u0161icki, D. (2010, January 26\u201329). Range only multi-static tracking. Proceedings of the IEEE International Conference Information Fusion, Edinburgh, UK."},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Musicki, D., and Evans, R.J. (2006, January 10\u201313). Measurement Gaussian sum mixture target tracking. Proceedings of the IEEE International Conference on Information Fusion, Florence, Italy.","DOI":"10.1109\/ICIF.2006.301646"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"2445","DOI":"10.1109\/LSP.2015.2491961","article-title":"Target localization from bistatic range measurements in multi-transmitter multi-receiver passive radar","volume":"22","author":"Noroozi","year":"2015","journal-title":"IEEE Signal Process. Lett."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"207","DOI":"10.1016\/j.sigpro.2014.02.023","article-title":"Target localization in a multi-static passive radar system through convex optimization","volume":"102","author":"Chalise","year":"2014","journal-title":"Signal Process."},{"key":"ref_16","first-page":"3","article-title":"Bistatic and multistatic radar systems","volume":"17","author":"Bezousek","year":"2008","journal-title":"Radioengineering"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"4673","DOI":"10.1109\/TSP.2014.2338835","article-title":"Elliptic Localization: Performance Study and Optimum Receiver Placement","volume":"62","author":"Rui","year":"2014","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"4180","DOI":"10.1109\/TSP.2016.2566611","article-title":"Optimal Geometry Analysis for Multistatic TOA Localization","volume":"64","author":"Nguyen","year":"2016","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"2182","DOI":"10.1109\/TWC.2012.040412.110697","article-title":"Accurate Passive Location Estimation Using TOA Measurements","volume":"11","author":"Shen","year":"2012","journal-title":"IEEE Trans. Wirel. Commun."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"82","DOI":"10.1109\/MCS.2009.934469","article-title":"The probabilistic data association filter","volume":"29","author":"Daum","year":"2009","journal-title":"IEEE Control Syst."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"642","DOI":"10.1109\/TAES.2014.130571","article-title":"Iterative joint integrated probabilistic data association for multitarget tracking","volume":"51","author":"Song","year":"2015","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"232","DOI":"10.1016\/j.dsp.2017.10.020","article-title":"Iterative joint integrated probabilistic data association filter for multiple-detection multiple-target tracking","volume":"72","author":"Xie","year":"2018","journal-title":"Dig. Signal Process."},{"key":"ref_23","unstructured":"Ren, X., Huang, Z., Sun, S., Liu, D., and Wu, J. (2012, January 9\u201312). Multiple objects video tracking using GRASP-MHT. Proceedings of the IEEE Conference on Information Fusion, Singapore."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"86","DOI":"10.1109\/TAES.2013.120041","article-title":"An efficient MHT implementation using GRASP","volume":"50","author":"Ren","year":"2014","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Kim, C., Li, F., Ciptadi, A., and Rehg, J.M. (2015, January 7\u201313). Multiple hypothesis tracking revisited. Proceedings of the IEEE International Conference on Computer Vision, Santiago, Chile.","DOI":"10.1109\/ICCV.2015.533"},{"key":"ref_26","unstructured":"Bar-Shalom, Y. (1990). Multitarget Multisensor Tracking, Artech House."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"1605","DOI":"10.1109\/TAES.2011.5937253","article-title":"Suppressing Ghost Targets Via Gating and Tracking History in Y-shaped Passive Linear Array Sonars","volume":"47","author":"Ku","year":"2011","journal-title":"IEEE Trans. Aerosp."},{"key":"ref_28","unstructured":"Bar-Shalom, Y., and Fortmann, T.E. (1988). Tracking and Data Association, Academic Press."},{"key":"ref_29","doi-asserted-by":"crossref","unstructured":"Zhou, W., and Nelson, J.K. (2013, January 26\u201331). Sequential detection for sparse channels via a multiple tree algorithm. Proceedings of the IEEE International Conference on Acoustics, Speech and Signal Processing, Vancouver, BC, Canada.","DOI":"10.1109\/ICASSP.2013.6638546"},{"key":"ref_30","unstructured":"Nelson, J.K., and Roufarshbaf, H. (2009, January 6\u20139). A tree search approach to target tracking in clutter. Proceedings of the IEEE International Conference on Information Fusion, Seattle, WA, USA."},{"key":"ref_31","unstructured":"Robert, J.U. (2013). Principles of Underwater Sound-3\/E, Peninsula Pub."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/18\/5\/1481\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T15:03:50Z","timestamp":1760195030000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/18\/5\/1481"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,5,8]]},"references-count":31,"journal-issue":{"issue":"5","published-online":{"date-parts":[[2018,5]]}},"alternative-id":["s18051481"],"URL":"https:\/\/doi.org\/10.3390\/s18051481","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,5,8]]}}}