{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:00:28Z","timestamp":1760144428097,"version":"build-2065373602"},"reference-count":27,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2024,4,12]],"date-time":"2024-04-12T00:00:00Z","timestamp":1712880000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Defense Science and Technology Foundation Strengthening Plan 173","award":["2022-JCJQ-ZD-010-12","62301119"],"award-info":[{"award-number":["2022-JCJQ-ZD-010-12","62301119"]}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["2022-JCJQ-ZD-010-12","62301119"],"award-info":[{"award-number":["2022-JCJQ-ZD-010-12","62301119"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Remote Sensing"],"abstract":"<jats:p>This paper presents a simple and fast closed-form solution approach for two-dimensional (2D) target localization using range difference (RD) measurements. The formulation of the localization problem is derived using a pentagram array. The target position is determined using passive radar measurements (RDs) between the target and the (N+1=10) receivers\u2019 locations. The method facilitates the problem of target position and can be used as a counter-parallel method for spherical interpolation (SI) and spherical intersection (SX) methods in time difference of arrival (TDOA) and radar systems. The performance of the method is examined in 2D target localization using numerical analysis under the distribution of receivers in the pentagram array. The simulations are conducted using four different far-distance targets and comparatively large-area distributed receivers. The RD measurements were distorted by two different values of Gaussian errors based on ionosphedriec time delays of 20 and 50 nsec owing to the different receivers\u2019 positions. The findings highly verified the validity of the method for addressing the problem of target localization. Additionally, a theoretical accuracy study of the method is given, which solely relies on the RD measurements.<\/jats:p>","DOI":"10.3390\/rs16081370","type":"journal-article","created":{"date-parts":[[2024,4,15]],"date-time":"2024-04-15T03:56:13Z","timestamp":1713153373000},"page":"1370","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Two-Dimensional Target Localization Approach via a Closed-Form Solution Using Range Difference Measurements Based on Pentagram Array"],"prefix":"10.3390","volume":"16","author":[{"ORCID":"https:\/\/orcid.org\/0009-0009-9043-3734","authenticated-orcid":false,"given":"Mohammed","family":"Khalafalla","sequence":"first","affiliation":[{"name":"School of Information and Communication Engineering, University of Electronic Science and Technology of China, Chengdu 611731, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3478-7916","authenticated-orcid":false,"given":"Kaili","family":"Jiang","sequence":"additional","affiliation":[{"name":"School of Information and Communication Engineering, University of Electronic Science and Technology of China, Chengdu 611731, China"}]},{"given":"Kailun","family":"Tian","sequence":"additional","affiliation":[{"name":"School of Information and Communication Engineering, University of Electronic Science and Technology of China, Chengdu 611731, China"}]},{"given":"Hancong","family":"Feng","sequence":"additional","affiliation":[{"name":"School of Information and Communication Engineering, University of Electronic Science and Technology of China, Chengdu 611731, China"}]},{"given":"Ying","family":"Xiong","sequence":"additional","affiliation":[{"name":"School of Information and Communication Engineering, University of Electronic Science and Technology of China, Chengdu 611731, China"}]},{"given":"Bin","family":"Tang","sequence":"additional","affiliation":[{"name":"School of Information and Communication Engineering, University of Electronic Science and Technology of China, Chengdu 611731, China"}]}],"member":"1968","published-online":{"date-parts":[[2024,4,12]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"234","DOI":"10.1109\/JOE.1987.1145216","article-title":"A passive localization algorithm and its accuracy analysis","volume":"12","author":"Friedlander","year":"1987","journal-title":"IEEE J. Ocean. Eng."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"107","DOI":"10.1049\/ip-rsn:20045077","article-title":"FM radio based bistatic radar","volume":"152","author":"Howland","year":"2005","journal-title":"Inst. Elect. Eng. Proc. Radar Sonar Navig."},{"key":"ref_3","first-page":"192","article-title":"Navigation systems: Fundamentals of low and very low frequency hyperbolic techniques","volume":"45","year":"1970","journal-title":"Electric. Commun."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"572","DOI":"10.1109\/TAES.2012.6129656","article-title":"Two methods for target localization in multistatic passive radar","volume":"48","author":"Malanowski","year":"2012","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Noroozi, A., and Sebt, M.A. (2015, January 24\u201326). Comparison between range-difference-based and bistatic-range-based localization in multistatic passive radar. Proceedings of the 16th International Radar Symposium (IRS), Dresden, Germany.","DOI":"10.1109\/IRS.2015.7226218"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"1660","DOI":"10.1109\/TAES.2017.2669558","article-title":"Target localization in multistatic passive radar using SVD approach for eliminating the nuisance parameters","volume":"53","author":"Noroozi","year":"2017","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"144","DOI":"10.1016\/j.sigpro.2015.04.004","article-title":"Weighted least squares algorithm for target localization in distributed MIMO radar","volume":"115","author":"Einemo","year":"2015","journal-title":"Signal Process."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"1056","DOI":"10.1109\/TAES.2003.1238756","article-title":"Closed-form solution for determining emitter location using time difference of arrival measurements","volume":"39","author":"Mellen","year":"2003","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"1223","DOI":"10.1109\/TASSP.1987.1165266","article-title":"Passive source localization employing intersecting spherical surfaces from time-of-arrival differences","volume":"35","author":"Schau","year":"1987","journal-title":"IEEE Trans. Acoust. Speech Signal Process."},{"key":"ref_10","unstructured":"Malanowski, M., Kulpa, K., and Suchozebrski, R. (2009, January 6\u20139). Two-stage tracking algorithm for passive radar. Proceedings of the 12th International Conference on Information Fusion, Seattle, WA, USA."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"50","DOI":"10.1109\/MAES.2014.130165","article-title":"Planning and design phases of a commensal radar system in the FM broadcast band","volume":"29","author":"Inggs","year":"2014","journal-title":"IEEE Aerosp. Electron. Syst. Mag."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"1654","DOI":"10.1109\/TAES.2010.5595585","article-title":"Observability and performance analysis of bi\/multi-static Doppler-only radar","volume":"46","author":"Xiao","year":"2010","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Langellotti, D., Colone, F., Lombardo, P., Sedehi, M., and Tilli, E. (2014, January 19\u201323). DVB-T based passive bistatic radar for maritime surveillance. Proceedings of the IEEE Radar Conference, Cincinnati, OH, USA.","DOI":"10.1109\/RADAR.2014.6875779"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"36","DOI":"10.1109\/MAES.2012.6380824","article-title":"Passive 3D tracking of low altitude targets using DVB (SFN broadcasters)","volume":"27","author":"Poullin","year":"2012","journal-title":"IEEE Aerosp. Electron. Syst. Mag."},{"key":"ref_15","unstructured":"Schroeder, A., and Edrich, M. (2011, January 7\u20139). CASSIDIAN multiband mobile passive radar system. Proceedings of the 12th International Radar Symposium (IRS), Leipzig, Germany."},{"key":"ref_16","unstructured":"Del, R.M.N., Mata, M.D., Jarabo, A.M.P., Rosado, S.J., and Gomez, D.H.P. (2017, January 20\u201322). Doa estimation based on a ULA of commercial antennas in semi-urban passive radar scenario. Proceedings of the International Conference on Control, Artificial Intelligence, Robotics & Optimization (ICCAIRO), Prague, Czech Republic."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"123","DOI":"10.1049\/iet-rsn.2013.0207","article-title":"Two-dimensional location of moving targets within local areas using WiFi-based multistatic passive radar","volume":"8","author":"Falcone","year":"2014","journal-title":"IET Radar Sonar Navig."},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Filippini, F., Martelli, T., Colone, F., and Cardinali, R. (2018, January 23\u201327). Target DoA estimation in passive radar using non-uniform linear arrays and multiple frequency channels. Proceedings of the IEEE Radar Conference (RadarConf18), Oklahoma City, OK, USA.","DOI":"10.1109\/RADAR.2018.8378749"},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Bournaka, G., Heckenbach, J., Baruzzi, A., Cristallini, D., and Kuschel, H. (2016, January 2\u20136). A two stage beamforming approach for low complexity CFAR detection and localization for passive radar. Proceedings of the IEEE Radar Conference, Philadelphia, PA, USA.","DOI":"10.1109\/RADAR.2016.7485291"},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Huang, J.H., Garry, J.L., Smith, G.E., and Baker, C.J. (2016, January 2\u20136). Array based passive radar target localization. Proceedings of the IEEE Radar Conference (RadarConf), Philadelphia, PA, USA.","DOI":"10.1109\/RADAR.2016.7485106"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"1905","DOI":"10.1109\/78.301830","article-title":"A simple and efficient estimator for hyperbolic location","volume":"42","author":"Chan","year":"1994","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"821","DOI":"10.1109\/TAES.1972.309614","article-title":"A new approach to geometry of range difference location","volume":"8","author":"Schmidt","year":"1972","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"234","DOI":"10.1109\/7.481265","article-title":"Least squares range difference location","volume":"32","author":"Schmidt","year":"1996","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"246","DOI":"10.1109\/JOE.1987.1145217","article-title":"The spherical interpolation method of source localization","volume":"12","author":"Smith","year":"1987","journal-title":"IEEE J. Ocean. Eng."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"1661","DOI":"10.1109\/TASSP.1987.1165089","article-title":"Closed-form least-squares source location estimation from range-difference measurements","volume":"35","author":"Smith","year":"1987","journal-title":"IEEE Trans. Acoust. Speech Signal Process."},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Khalafalla, M., Jiang, K., Tian, K., Feng, H., Xiong, Y., and Tang, B. (2024). Pentagram Arrays: A New Paradigm for DOA Estimation of Wideband Sources Based on Triangular Geometry. Remote Sens., 16.","DOI":"10.3390\/rs16030535"},{"key":"ref_27","unstructured":"Powers, E.D., Miranian, M., White, J.D., and Brad, J. (1997, January 2\u20134). Absolute Time Error Calibration of GPS Receivers Using Advanced GPS Simulators. Proceedings of the 29th Annual Precise Time and Time Interval (PTTI) Systems and Applications Meeting, Long Beach, CA, USA."}],"container-title":["Remote Sensing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2072-4292\/16\/8\/1370\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T14:27:22Z","timestamp":1760106442000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2072-4292\/16\/8\/1370"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,4,12]]},"references-count":27,"journal-issue":{"issue":"8","published-online":{"date-parts":[[2024,4]]}},"alternative-id":["rs16081370"],"URL":"https:\/\/doi.org\/10.3390\/rs16081370","relation":{},"ISSN":["2072-4292"],"issn-type":[{"type":"electronic","value":"2072-4292"}],"subject":[],"published":{"date-parts":[[2024,4,12]]}}}