{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,9]],"date-time":"2025-12-09T08:22:20Z","timestamp":1765268540406,"version":"build-2065373602"},"reference-count":32,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2019,3,29]],"date-time":"2019-03-29T00:00:00Z","timestamp":1553817600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Key Technology Program of Shenzhen Science and Technology Innovation Commission (SZSTI)","award":["Z20170201"],"award-info":[{"award-number":["Z20170201"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>This paper focuses on passive emitter localization using moving sensors. The increase in observation time is beneficial to improve the localization accuracy, but it could cause deterioration of the relative motion between the emitter and the sensors, especially the nonlinear motion. The common localization algorithms typically have two steps: (1) parameter estimation and (2) position determination, where the parameters are assumed to be constant, and it is not applicable for long observation times. We proposed the time-varying delay-based direct position determination (DPD-TVD) method, regarding the variation in the propagation time delay during the observation time. Using one step, the proposed algorithm can obtain the emitter\u2019s position directly from the received signals by calculating the cost function corresponding to the map grid. By better adapting to highly dynamic scenarios, the proposed algorithm can achieve better localization accuracy than that of constant parameters using one-step or two-step procedures, which is demonstrated by the simulation results.<\/jats:p>","DOI":"10.3390\/s19071541","type":"journal-article","created":{"date-parts":[[2019,3,29]],"date-time":"2019-03-29T13:09:58Z","timestamp":1553864998000},"page":"1541","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Multi-Sensor Passive Localization Using Direct Position Determination with Time-Varying Delay"],"prefix":"10.3390","volume":"19","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-0523-6875","authenticated-orcid":false,"given":"Shangyu","family":"Zhang","sequence":"first","affiliation":[{"name":"School of Aerospace Engineering, Tsinghua University, Beijing 100084, China"},{"name":"Beijing National Research Center for Information Science and Technology, Tsinghua University, Beijing 100084, China"}]},{"given":"Zhen","family":"Huang","sequence":"additional","affiliation":[{"name":"Beijing National Research Center for Information Science and Technology, Tsinghua University, Beijing 100084, China"},{"name":"Space Center, Tsinghua University, Beijing 100084, China"}]},{"given":"Xuefeng","family":"Feng","sequence":"additional","affiliation":[{"name":"School of Aerospace Engineering, Tsinghua University, Beijing 100084, China"},{"name":"Beijing National Research Center for Information Science and Technology, Tsinghua University, Beijing 100084, China"}]},{"given":"Jiazhi","family":"He","sequence":"additional","affiliation":[{"name":"School of Aerospace Engineering, Tsinghua University, Beijing 100084, China"},{"name":"Beijing National Research Center for Information Science and Technology, Tsinghua University, Beijing 100084, China"}]},{"given":"Lei","family":"Shi","sequence":"additional","affiliation":[{"name":"School of Aerospace Engineering, Tsinghua University, Beijing 100084, China"},{"name":"Beijing National Research Center for Information Science and Technology, Tsinghua University, Beijing 100084, China"}]}],"member":"1968","published-online":{"date-parts":[[2019,3,29]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1695","DOI":"10.1016\/j.sigpro.2005.03.007","article-title":"Bearings-only target localization using total least squares","volume":"85","author":"Dogancay","year":"2005","journal-title":"Signal Process."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"2542","DOI":"10.1109\/TASL.2007.903312","article-title":"An Accurate Algebraic Closed-Form Solution for Energy-Based Source Localization","volume":"15","author":"Ho","year":"2007","journal-title":"IEEE Trans. Audio Speech Lang. Process."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"2887","DOI":"10.1109\/TSP.2011.2116012","article-title":"Source Localization in Wireless Sensor Networks From Signal Time-of-Arrival Measurements","volume":"59","author":"Xu","year":"2011","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"1938","DOI":"10.1109\/TSP.2014.2304433","article-title":"Multiple Source Localization in Wireless Sensor Networks Based on Time of Arrival Measurement","volume":"62","author":"Shen","year":"2014","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"1558","DOI":"10.1109\/TVT.2009.2037509","article-title":"Constrained Total Least-Squares Location Algorithm Using Time-Difference- of-Arrival Measurements","volume":"59","author":"Yang","year":"2010","journal-title":"IEEE Trans Veh. Technol."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"684","DOI":"10.1109\/TSP.2006.885744","article-title":"Source localization using TDOA and FDOA measurements in the presence of receiver location errors: Analysis and solution","volume":"55","author":"Ho","year":"2007","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"44","DOI":"10.1109\/TWC.2011.102611.110728","article-title":"An Efficient Constrained Weighted Least Squares Algorithm for Moving Source Location Using TDOA and FDOA Measurements","volume":"11","author":"Yu","year":"2012","journal-title":"IEEE Trans. Wirel. Commun."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"758","DOI":"10.1587\/transcom.2015EBP3355","article-title":"A Moving Source Localization Method Using TDOA, FDOA and Doppler Rate Measurements","volume":"99","author":"Hu","year":"2016","journal-title":"IEICE Trans. Commun."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"513","DOI":"10.1109\/LSP.2004.826501","article-title":"Direct position determination of narrowband radio frequency transmitters","volume":"11","author":"Weiss","year":"2004","journal-title":"IEEE Signal Process. Lett."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"5500","DOI":"10.1109\/TSP.2008.929655","article-title":"Localization of Narrowband Radio Emitters Based on Doppler Frequency Shifts","volume":"56","author":"Amar","year":"2008","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"2513","DOI":"10.1109\/TSP.2011.2128311","article-title":"Direct Geolocation of Wideband Emitters Based on Delay and Doppler","volume":"59","author":"Weiss","year":"2011","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Weiss, A.J., and Amar, A. (September, January 31). Direct geolocation of stationary wideband radio signal based on time delays and Doppler shifts. Proceedings of the 2009 IEEE\/SP 15th Workshop on Statistical Signal Processing, Cardiff, UK.","DOI":"10.1109\/SSP.2009.5278630"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"58","DOI":"10.1016\/j.dsp.2015.09.008","article-title":"Coherent summation of multiple short-time signals for direct positioning of a wideband source based on delay and Doppler","volume":"48","author":"Li","year":"2016","journal-title":"Digit. Signal Process."},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Pourhomayoun, M., and Fowler, M.L. (2012, January 17\u201320). Sensor network distributed computation for Direct Position Determination. Proceedings of the 2012 IEEE 7th Sensor Array and Multichannel Signal Processing Workshop (SAM), Hoboken, NJ, USA.","DOI":"10.1109\/SAM.2012.6250445"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"2878","DOI":"10.1109\/TAES.2014.130005","article-title":"Distributed computation for direct position determination emitter location","volume":"50","author":"Pourhomayoun","year":"2014","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"1616","DOI":"10.1109\/TAES.2013.110499","article-title":"TDOA based direct positioning maximum likelihood estimator and the cramer-rao bound","volume":"50","author":"Vankayalapati","year":"2014","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_17","unstructured":"Steffes, C., and Oispuu, M. (2015, January 6\u20139). Direct single sensor TDOA localization using signal structure information. Proceedings of the 2015 18th International Conference on Information Fusion (Fusion), Washington, DC, USA."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"32","DOI":"10.1016\/j.sigpro.2016.10.015","article-title":"Expectation-maximization algorithm for direct position determination","volume":"133","author":"Tzoreff","year":"2017","journal-title":"Signal Process."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"161","DOI":"10.1016\/j.cja.2017.11.007","article-title":"A direct position determination method with combined TDOA and FDOA based on particle filter","volume":"31","author":"Lu","year":"2018","journal-title":"Chin. J. Aeronaut."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"192","DOI":"10.1109\/LSP.2015.2503921","article-title":"High Resolution Direct Position Determination of Radio Frequency Sources","volume":"23","author":"Tirer","year":"2016","journal-title":"IEEE Signal Process. Lett."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"6449","DOI":"10.1109\/TWC.2016.2585116","article-title":"High-Resolution Direct Position Determination Using MVDR","volume":"15","author":"Tzafri","year":"2016","journal-title":"IEEE Trans. Wirel. Commun."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"2448","DOI":"10.1016\/j.sigpro.2009.04.009","article-title":"Direct position determination of cyclostationary signals","volume":"89","author":"Reuven","year":"2009","journal-title":"Signal Process."},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Yin, J., Wang, D., and Wu, Y. (2018). An Efficient Direct Position Determination Method for Multiple Strictly Noncircular Sources. Sensors, 18.","DOI":"10.3390\/s18020324"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"52","DOI":"10.1016\/j.dsp.2005.03.003","article-title":"Direct position determination in the presence of model errors\u2014Known waveforms","volume":"16","author":"Amar","year":"2006","journal-title":"Digit. Signal Process."},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Wang, D., Yu, H., Wu, Z., and Wang, C. (2017). Performance Analysis of the Direct Position Determination Method in the Presence of Array Model Errors. Sensors, 17.","DOI":"10.3390\/s17071550"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"653549","DOI":"10.1155\/ASP.2005.37","article-title":"Direct Position Determination of Multiple Radio Signals","volume":"2005","author":"Weiss","year":"2005","journal-title":"EURASIP J. Adv. Signal Process."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"2348","DOI":"10.1016\/j.sigpro.2007.03.008","article-title":"A decoupled algorithm for geolocation of multiple emitters","volume":"87","author":"Amar","year":"2007","journal-title":"Signal Process."},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Zhang, Y., Ba, B., Wang, D., Geng, W., and Xu, H. (2018). Direct Position Determination of Multiple Non-Circular Sources with a Moving Coprime Array. Sensors, 18.","DOI":"10.3390\/s18051479"},{"key":"ref_29","doi-asserted-by":"crossref","unstructured":"Chen, X., Wang, D., Yin, J., and Wu, Y. (2018). A Direct Position-Determination Approach for Multiple Sources Based on Neural Network Computation. Sensors, 18.","DOI":"10.3390\/s18061925"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"137","DOI":"10.1016\/j.cja.2017.11.005","article-title":"Joint TDOA, FDOA and differential Doppler rate estimation: Method and its performance analysis","volume":"31","author":"Hu","year":"2018","journal-title":"Chin. J. Aeronaut."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"588","DOI":"10.1109\/TASSP.1981.1163621","article-title":"Algorithms for ambiguity function processing","volume":"29","author":"Stein","year":"1981","journal-title":"IEEE Trans. Acoust. Speech Signal Process."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"893","DOI":"10.1587\/transcom.2016EBP3383","article-title":"A Method for FDOA Estimation with Expansion of RMS Integration Time","volume":"100","author":"Zhang","year":"2017","journal-title":"IEICE Trans. Commun."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/19\/7\/1541\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T12:41:36Z","timestamp":1760186496000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/19\/7\/1541"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,3,29]]},"references-count":32,"journal-issue":{"issue":"7","published-online":{"date-parts":[[2019,4]]}},"alternative-id":["s19071541"],"URL":"https:\/\/doi.org\/10.3390\/s19071541","relation":{},"ISSN":["1424-8220"],"issn-type":[{"type":"electronic","value":"1424-8220"}],"subject":[],"published":{"date-parts":[[2019,3,29]]}}}