{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,18]],"date-time":"2026-09-18T17:26:30Z","timestamp":1789752390593,"version":"4.0.1"},"reference-count":49,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2020,3,26]],"date-time":"2020-03-26T00:00:00Z","timestamp":1585180800000},"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 the last few years, the number of applications relying on position of vessels at sea has grown significantly. Usually, these applications exploit information provided by the Automatic Identification System (AIS). Unfortunately, the cooperative nature of AIS makes it vulnerable to different types of attack. Therefore, especially for critical applications, the veracity of the position information reported in the AIS message needs to be verified. Several techniques can be adopted to this end. This paper presents a mathematical extension of the traditional Time Difference Of Arrival (TDOA) localisation technique allowing merging TDOA measurement from synchronous and non-synchronous receivers. This technique was tested in a simulated scenario, where the position of a moving target was estimated using different configurations of the receivers network. The robustness of the proposed algorithm with respect to the traditional one is demonstrated. The proposed approach, which is derived form satellite applications, is not limited to the AIS signals or to the maritime domain, and it can be adopted to estimate the position of any radiofrequency transmitter, by employing a suitable number of non-synchronous receivers.<\/jats:p>","DOI":"10.3390\/s20071842","type":"journal-article","created":{"date-parts":[[2020,4,1]],"date-time":"2020-04-01T03:44:13Z","timestamp":1585712653000},"page":"1842","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Multi-Network Asynchronous TDOA Algorithm Test in a Simulated Maritime Scenario"],"prefix":"10.3390","volume":"20","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-6510-9240","authenticated-orcid":false,"given":"Ciro","family":"Gioia","sequence":"first","affiliation":[{"name":"Joint Research Centre (JRC), European Commission, Via E. Fermi 2749, I-21027 Ispra, Italy"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Francesco","family":"Sermi","sequence":"additional","affiliation":[{"name":"Joint Research Centre (JRC), European Commission, Via E. Fermi 2749, I-21027 Ispra, Italy"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Dario","family":"Tarchi","sequence":"additional","affiliation":[{"name":"Joint Research Centre (JRC), European Commission, Via E. Fermi 2749, I-21027 Ispra, Italy"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2020,3,26]]},"reference":[{"key":"ref_1","unstructured":"International Maritime Organization (2016). International Convention for the Safety of Life at Sea (SOLAS), Technical Report."},{"key":"ref_2","unstructured":"Jones, M. (2020, March 25). Spoofing in the Black Sea: What Really Happened?. Available online: https:\/\/www.gpsworld.com\/spoofing-in-the-black-sea-what-really-happened\/."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"1756","DOI":"10.1109\/TAES.2016.150148","article-title":"A Sum-of-Squares Approach to GNSS Spoofing Detection","volume":"52","author":"Borio","year":"2016","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_4","unstructured":"Parsons, M.W., Reckley, A.R., and Castro, A.H. (2020, March 25). Encrypted Automatic Identification System (EAIS) Interface Design Description (IDD). Available online: https:\/\/epic.org\/foia\/dhs\/uscg\/nais\/EPIC-15-05-29-USCG-FOIA-20151030-Production-2.pdf."},{"key":"ref_5","first-page":"97","article-title":"S3 (Secure Ship-to-Ship) Information Sharing Scheme using Ship Authentication in the e-Navigation","volume":"9","author":"Oh","year":"2015","journal-title":"Int. J. Secur. Its Appl."},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Gioia, C., Sermi, F., Tarchi, D., Vespe, M., and Kyovtorov, V. (2017, January 9\u201312). Multi-Network TDOA: An opportunity for vessels radiolocation. Proceedings of the European Navigation Conference (ENC), Lausanne, Switzerland.","DOI":"10.1109\/EURONAV.2017.7954215"},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Xu, B., Yu, R., Sun, G., and Yang, Z. (2011, January 20\u201324). Whistle: Synchronization-Free TDOA for Localization. Proceedings of the 31st International Conference on Distributed Computing Systems, Minneapolis, MN, USA.","DOI":"10.1109\/ICDCS.2011.30"},{"key":"ref_8","unstructured":"Gioia, C., and Borio, D. (2015, January 14\u201318). GGTO: Stability and Impact on Multi-constellation Positioning. Proceedings of the 28th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS+ 2015), Tampa, FL, USA."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"1279","DOI":"10.1007\/s00190-016-0925-6","article-title":"A statistical characterization of the Galileo-to-GPS inter-system bias","volume":"90","author":"Gioia","year":"2016","journal-title":"J. Geodesy"},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Gioia, C., Pisoni, F., and Fortuny, J. (2014, January 3\u20135). Estimation of the GPS to Galileo Time Offset and its Validation on a Mass Market Receiver. Proceedings of the 2014 7th ESA Workshop on Satellite Navigation Technologies and European Workshop on GNSS Signals and Signal Processing (NAVITEC), Noordwijk, The Netherlands.","DOI":"10.1109\/NAVITEC.2014.7045145"},{"key":"ref_11","unstructured":"Kuang, Y., Ask, E., Burgess, S., and Astrom, K. (2012, January 6\u20138). Undestanding TOA and TDOA network calibration using far field approximation as initial estimate. Proceedings of the 1st International Conference on Pattern Recognition Applications and Methods, Algarve, Portugal."},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Wang, T., Xiong, H., Ding, H., and Zheng, L. (2020). TDOA Based Joint Synchronization and Localization Algorithm for Asynchronous Wireless Sensor Networks. IEEE Trans. Commun.","DOI":"10.1109\/TCOMM.2020.2973961"},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Stefanski, J., and Sadowski, J. (2018). TDOA versus ATDOA for wide area multilateration system. EURASIP J. Wirel. Commun. Netw., 179.","DOI":"10.1186\/s13638-018-1191-5"},{"key":"ref_14","unstructured":"Kim, R., Ha, T., Lim, H., and Jung, D. (2014, January 10\u201312). TDoA Localization for Wireless Networks with Imperfect Clock Synchronization. Proceedings of the IEEE International Conference on Information Networking, Phuket, Thailand."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"832351","DOI":"10.1155\/2015\/832351","article-title":"An Efficient TDOA-Based Localization Algorithm without Synchronization between Base Stations","volume":"11","author":"Kim","year":"2015","journal-title":"Int. J. Distrib. Sens. Netw."},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Gioia, C., Sermi, F., Tarchi, D., Vepe, M., and Kyovtorov, V. (2017, January 21\u201323). Inter-Network Bias: Impact on Multi-Network TDOA. Proceedings of the IEEE International Workshop on Metrology for AeroSpace (MetroAeroSpace), Padova, Italy.","DOI":"10.1109\/MetroAeroSpace.2017.7999609"},{"key":"ref_17","first-page":"67","article-title":"3G Mobile phones positioning systems","volume":"57","author":"Jayant","year":"2007","journal-title":"Telecommunications"},{"key":"ref_18","unstructured":"Sammartino, P.F., Vespe, M., Oliveri, F., and Tarchi, D. (2015). A New Method to Verify Vessel Positions (AIS Message). Pre-Operational Validation and Future Perspectives, Joint Research Centre. Technical Report."},{"key":"ref_19","unstructured":"Curtice, W.R. (1978, January 27\u201329). A Logic Module Using Transferred-Electron Logic Devices for Time-of-Arrival Determination of GHz Signals. Proceedings of the IEEE-MTT-S International Microwave Symposium Digest, Ottawa, ON, Canada."},{"key":"ref_20","unstructured":"Aronson, E.A. (2020, March 25). Location Errors in Time of Arrival (TOA) and Time Difference of Arrival (TDOA) Systems, Available online: https:\/\/www.osti.gov\/biblio\/7284650."},{"key":"ref_21","unstructured":"Silventoinen, M., and Rantalainen, T. (1996, January 21). Mobile station emergency locating in GSM. Proceedings of the IEEE International Conference on Personal Wireless Communications, New Delhi, India."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"3399","DOI":"10.1109\/TVT.2020.2968118","article-title":"Localization in 3GPP LTE based on one RTT and one TDOA observation","volume":"69","author":"Radnosrati","year":"2020","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"674","DOI":"10.1109\/25.933304","article-title":"On the accuracy of cellular mobile station location estimation","volume":"50","author":"Spirito","year":"2001","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"108","DOI":"10.1109\/MCOM.2002.1018015","article-title":"Standardization of mobile phone positioning for 3G systems","volume":"40","author":"Zhao","year":"2002","journal-title":"IEEE Commun. Mag."},{"key":"ref_25","first-page":"35","article-title":"Tracking and positioning of mobile phones in telecommunications","volume":"2","author":"Panimalar","year":"2015","journal-title":"Int. J. Sci. Res. Eng. Technol."},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Zou, Y., and Liu, H. (2020). TDOA Localization with Unknown Signal Propagation Speed and Sensor Position Errors. IEEE Commun. Lett.","DOI":"10.1109\/LCOMM.2020.2968434"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"75","DOI":"10.1109\/TPWRS.2019.2927613","article-title":"Adaptive Event Location Technique via Time Difference of Event Arrival","volume":"35","author":"Kim","year":"2020","journal-title":"IEEE Trans. Power Syst."},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Cao, H., Chan., Y.T., and So, H.C. (2020). Compressive TDOA Estimation: Cramer-Rao Bound and Incoherent Processing. IEEE Trans. Aerosp. Electron. Syst.","DOI":"10.1109\/TAES.2020.2966095"},{"key":"ref_29","doi-asserted-by":"crossref","unstructured":"Piccinni, G., Avitabile, G., and Coviello, G. (2017, January 9\u201311). Narrowband distance evaluation technique for indoor positioning systems based on Zadoff-Chu sequences. Proceedings of the 13th IEEE International Conference on Wireless and Mobile Computing, Networking and Communications (WiMob), Rome, Italy.","DOI":"10.1109\/WiMOB.2017.8115766"},{"key":"ref_30","doi-asserted-by":"crossref","unstructured":"Piccinni, G., Avitabile, G., and Coviello, G. (2017, January 25\u201328). A novel distance measurement technique for indoor positioning systems based on Zadoff-Chu Sequences. Proceedings of the 15th IEEE International New Circuits and Systems Conference (NEWCAS), Strasbourg, France.","DOI":"10.1109\/NEWCAS.2017.8010174"},{"key":"ref_31","unstructured":"Kaplan, E.D., and Hegarty, C.J. (2017). Understanding GPS\/GNSS: Principles and Applications, Artech House. [3rd ed.]."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"3615","DOI":"10.1109\/TSP.2015.2430842","article-title":"Cooperative Joint Synchronization and Localization in Wireless Sensor Networks","volume":"63","author":"Vaghefi","year":"2015","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"2166","DOI":"10.1109\/TMC.2018.2792443","article-title":"Position and Velocity Estimation of a Non-cooperative Source From Asynchronous Packet Arrival Time Measurements","volume":"17","author":"Ricciato","year":"2018","journal-title":"IEEE Trans. Mob. Comput."},{"key":"ref_34","first-page":"2166","article-title":"A survey on TOA based wireless localization and NLOS mitigation techniques","volume":"17","author":"Guvenc","year":"2009","journal-title":"IEEE Commun. Surv. Tutor."},{"key":"ref_35","unstructured":"Panwar, A., Kumar, A., and Kumar, S.A. (2011, January 4\u20136). Least Squares Algorithms for Time of Arrival Based Mobile Source Localization and Time Synchronization in Wireless Sensor Networks. Proceedings of the International Conference on Computer Communication and Networks (COMNET-2011), Udaipur, India."},{"key":"ref_36","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_37","doi-asserted-by":"crossref","first-page":"4874","DOI":"10.1109\/TSP.2013.2272288","article-title":"Sparsity-Aware Multi-Source TDOA Localization","volume":"61","year":"2013","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_38","doi-asserted-by":"crossref","unstructured":"Luo, M., Chen, X., Cao, S., and Zhang, X. (2018). Two New Shrinking-Circle Methods for Source Localization Based on TDoA Measurements. Sensors, 18.","DOI":"10.3390\/s18041274"},{"key":"ref_39","doi-asserted-by":"crossref","unstructured":"Parkinson, B., Axelrad, P., Parkinson, B.W., and Enge, P. (1996). Global Positioning System: Theory And Applications, American Institute of Aeronautics and Astronautics.","DOI":"10.2514\/4.866395"},{"key":"ref_40","unstructured":"Gioia, C. (2014). GNSS Navigation in Difficult Environments: Hybridization and Reliability. [Ph.D. Thesis, University Parthenope of Naples]."},{"key":"ref_41","doi-asserted-by":"crossref","unstructured":"Borio, D., and Gioia, C. (2016). Galileo: The Added Value for Integrity in Harsh Environments. Sensors, 16.","DOI":"10.3390\/s16010111"},{"key":"ref_42","unstructured":"Kaune, R. (2012, January 9\u201312). Accuracy Studies for TDOA and TOA Localization. Proceedings of the 15th International Conference on Information Fusion, Singapore."},{"key":"ref_43","doi-asserted-by":"crossref","unstructured":"Sun, X., Li, J., Huang, P., and Pang, J. (2008, January 25\u201328). Total Least-Squares Solution of Active Target Localization Using TDOA and FDOA Measurements in WSN. Proceedings of the 22nd International Conference on Advanced Information Networking and Applications\u2014Workshops (AINA Workshops 2008), Okinawa, Japan.","DOI":"10.1109\/WAINA.2008.150"},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"592","DOI":"10.1109\/LCOMM.2014.021214.132662","article-title":"TOA-based passive localization in quasi-synchronous network","volume":"18","author":"Wang","year":"2014","journal-title":"IEEE Commun. Lett."},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"187","DOI":"10.1109\/TAES.1976.308294","article-title":"Position-location solutions by Taylor-series estimation","volume":"2","author":"Foy","year":"1976","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_46","doi-asserted-by":"crossref","unstructured":"Hoffmann-Wellenhof, B., Lichtenegger, H., and Collins, J. (1992). Global Positioning System: Theory and Practice, Springer. [2nd ed.].","DOI":"10.1007\/978-3-7091-5126-6"},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"568","DOI":"10.1049\/iet-rsn.2014.0292","article-title":"Radiolocation and Tracking of Automatic Identification System Signals for Maritime Situational Awareness","volume":"9","author":"Papi","year":"2015","journal-title":"IET Radar Sonar Navig."},{"key":"ref_48","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_49","doi-asserted-by":"crossref","first-page":"259","DOI":"10.1049\/ip-rsn:20000554","article-title":"GPS GDOP metric","volume":"147","author":"Yarlagadda","year":"2000","journal-title":"IEEE Proc. Radar Sonar Navig."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/20\/7\/1842\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T09:11:53Z","timestamp":1760173913000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/20\/7\/1842"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,3,26]]},"references-count":49,"journal-issue":{"issue":"7","published-online":{"date-parts":[[2020,4]]}},"alternative-id":["s20071842"],"URL":"https:\/\/doi.org\/10.3390\/s20071842","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,3,26]]}}}