{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,8]],"date-time":"2026-02-08T08:35:23Z","timestamp":1770539723952,"version":"3.49.0"},"reference-count":27,"publisher":"MDPI AG","issue":"13","license":[{"start":{"date-parts":[[2019,7,9]],"date-time":"2019-07-09T00:00:00Z","timestamp":1562630400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/2.zoppoz.workers.dev:443\/https\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100010198","name":"Ministerio de Econom\u00eda, Industria y Competitividad, Gobierno de Espa\u00f1a","doi-asserted-by":"publisher","award":["DPI2016-79960-C3-2-P"],"award-info":[{"award-number":["DPI2016-79960-C3-2-P"]}],"id":[{"id":"10.13039\/501100010198","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>The accuracy requirements for sensor network positioning have grown over the last few years due to the high precision demanded in activities related with vehicles and robots. Such systems involve a wide range of specifications which must be met through positioning devices based on time measurement. These systems have been traditionally designed with the synchronization of their sensors in order to compute the position estimation. However, this synchronization introduces an error in the time determination which can be avoided through the centralization of the measurements in a single clock in a coordinate sensor. This can be found in typical architectures such as Asynchronous Time Difference of Arrival (A-TDOA) and Difference-Time Difference of Arrival (D-TDOA) systems. In this paper, a study of the suitability of these new systems based on a Cram\u00e9r-Rao Lower Bound (CRLB) evaluation was performed for the first time under different 3D real environments for multiple sensor locations. The analysis was carried out through a new heteroscedastic noise variance modelling with a distance-dependent Log-normal path loss propagation model. Results showed that A-TDOA provided less uncertainty in the root mean square error (RMSE) in the positioning, while D-TDOA reduced the standard deviation and increased stability all over the domain.<\/jats:p>","DOI":"10.3390\/s19133024","type":"journal-article","created":{"date-parts":[[2019,7,10]],"date-time":"2019-07-10T03:05:26Z","timestamp":1562727926000},"page":"3024","update-policy":"https:\/\/2.zoppoz.workers.dev:443\/https\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":40,"title":["Accuracy Analysis in Sensor Networks for Asynchronous Positioning Methods"],"prefix":"10.3390","volume":"19","author":[{"ORCID":"https:\/\/2.zoppoz.workers.dev:443\/https\/orcid.org\/0000-0001-7734-4539","authenticated-orcid":false,"given":"Rub\u00e9n","family":"\u00c1lvarez","sequence":"first","affiliation":[{"name":"Positioning Department, Drotium, Universidad de Le\u00f3n, 24071 Le\u00f3n, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/2.zoppoz.workers.dev:443\/https\/orcid.org\/0000-0002-6566-1630","authenticated-orcid":false,"given":"Javier","family":"D\u00edez-Gonz\u00e1lez","sequence":"additional","affiliation":[{"name":"Department of Mechanical, Computer and Aerospace Engineering, Universidad de Le\u00f3n, 24071 Le\u00f3n, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Efr\u00e9n","family":"Alonso","sequence":"additional","affiliation":[{"name":"Positioning Department, Drotium, Universidad de Le\u00f3n, 24071 Le\u00f3n, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/2.zoppoz.workers.dev:443\/https\/orcid.org\/0000-0001-6573-8477","authenticated-orcid":false,"given":"Laura","family":"Fern\u00e1ndez-Robles","sequence":"additional","affiliation":[{"name":"Department of Mechanical, Computer and Aerospace Engineering, Universidad de Le\u00f3n, 24071 Le\u00f3n, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/2.zoppoz.workers.dev:443\/https\/orcid.org\/0000-0002-5152-4555","authenticated-orcid":false,"given":"Manuel","family":"Castej\u00f3n-Limas","sequence":"additional","affiliation":[{"name":"Department of Mechanical, Computer and Aerospace Engineering, Universidad de Le\u00f3n, 24071 Le\u00f3n, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hilde","family":"Perez","sequence":"additional","affiliation":[{"name":"Department of Mechanical, Computer and Aerospace Engineering, Universidad de Le\u00f3n, 24071 Le\u00f3n, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2019,7,9]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"2238","DOI":"10.1109\/TWC.2010.07.090465","article-title":"TOA Estimation with the IEEE 802.15.4a Standard","volume":"9","author":"Mengali","year":"2010","journal-title":"IEEE Trans. Wirel. Commun."},{"key":"ref_2","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_3","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_4","doi-asserted-by":"crossref","unstructured":"Xu, J., Ma, M., and Law, C.L. (2006, January 24\u201327). Position Estimation Using UWB TDOA Measurements. Proceedings of the 2006 IEEE International Conference on Ultra-Wideband, Waltham, MA, USA.","DOI":"10.1109\/ICU.2006.281617"},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Xu, J., Ma, M., and Law, C.L. (2008, January 30). AOA Cooperative Position Localization. Proceedings of the IEEE Globecom 2008-2008 IEEE Global Telecommunications Conference, New Orleans, LA, USA.","DOI":"10.1109\/GLOCOM.2008.ECP.720"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"527","DOI":"10.1109\/TWC.2012.121412.111346","article-title":"Distributed Angle Estimation for Localization in Wireless Sensor Networks","volume":"12","author":"Zhang","year":"2013","journal-title":"IEEE Trans. Wirel. Commun."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"1389","DOI":"10.1109\/TWC.2011.031611.101585","article-title":"A New Approach to Sensor Node Localization Using RSS Measurements in Wireless Sensor Networks","volume":"10","author":"Wang","year":"2011","journal-title":"IEEE Trans. Wirel. Commun."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"1508","DOI":"10.1109\/TVT.2003.819613","article-title":"On the Accuracy of a Cellular Location System Based on RSS Measurements","volume":"52","author":"Weiss","year":"2003","journal-title":"IEEE Trans. Vehicular Technol."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"54","DOI":"10.1109\/MSP.2005.1458287","article-title":"Locating the Nodes","volume":"22","author":"Patwari","year":"2005","journal-title":"IEEE Signal Process. Mag."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"2207","DOI":"10.1109\/TWC.2011.042211.100966","article-title":"Joint TOA and AOA Estimation for UWB Localization Applications","volume":"10","author":"Mengali","year":"2011","journal-title":"IEEE Trans. Wirel. Commun."},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Zou, Z., Deng, T., Zou, Q., Sarmiento, D., Jonsson, F., and Zheng, L.-R. (2010, January 20\u201323). Energy detection receiver with TOA estimation enabling positioning in passive UWB-RFID system. Proceedings of the 2010 IEEE International Conference on Ultra-Wideband, Nanjing, China.","DOI":"10.1109\/ICUWB.2010.5615993"},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Badorrey, R., Hernandez, A., Choliz, J., Valdovinos, A., and Alastruey, I. (2008, January 22\u201325). Evaluation of TOA estimation algorithms in UWB receivers. Proceedings of the 14th European Wireless Conference, Prague, Czech Republic.","DOI":"10.1109\/EW.2008.4623872"},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Ye, R., Redfield, S., and Liu, H. (2010, January 20\u201323). High-precision indoor UWB localization: Technical challenges and method. Proceedings of the 2010 IEEE International Conference on Ultra-Wideband, Nanjing, China.","DOI":"10.1109\/ICUWB.2010.5616888"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"281","DOI":"10.1016\/j.adhoc.2005.01.002","article-title":"Clock synchronization for wireless sensor networks: A survey","volume":"3","author":"Sundararaman","year":"2005","journal-title":"Ad Hoc Netw."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"45","DOI":"10.1109\/MNET.2004.1316761","article-title":"Time synchronization in sensor networks: A survey","volume":"18","author":"Sivrikaya","year":"2004","journal-title":"IEEE Netw."},{"key":"ref_16","unstructured":"Elson, J., and Estrin, D. (2000, January 1\u20135). Time Synchronization for Wireless Sensor Networks. Proceedings of the 15th International Parallel and Distributed Processing Symposium, San Francisco, CA, USA."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"1728","DOI":"10.1109\/TIM.2017.2666278","article-title":"High-Accuracy Localization Platform Using Asynchronous Time Difference of Arrival Technology","volume":"66","author":"He","year":"2017","journal-title":"IEEE Trans. Instrum. Meas."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"03018","DOI":"10.1051\/matecconf\/201820703018","article-title":"A New Method of D-TDOA Time Measurement Based on RTT","volume":"207","author":"Zhou","year":"2018","journal-title":"MATEC Web Conf."},{"key":"ref_19","unstructured":"Kaune, R., H\u00f6rst, J., and Koch, W. (2011, January 5). Accuracy Analysis for TDOA Localization in Sensor Networks. Proceedings of the 14th International Conference on Information Fusion, Chicago, IL, USA."},{"key":"ref_20","unstructured":"Jia, T., and Buehrer, R.M. (2008, January 16\u201319). A New Cramer-Rao Lower Bound for TOA-based Localization. Proceedings of the MILCOM 2008-2008 IEEE Military Communications Conference, San Diego, CA, USA."},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Qi, Y., and Kobayashi, H. (2002, January 13\u201317). Cram\u00e9r-Rao Lower bound for geolocation in non-line-of-sight environment. Proceedings of the 2002 IEEE International Conference on Acoustics, Speech, and Signal Processing, Orlando, FL, USA.","DOI":"10.1109\/ICASSP.2002.5745148"},{"key":"ref_22","unstructured":"Chang, C., and Shai, A. (2004, January 4\u20137). Estimation Bounds for Localization. Proceedings of the 2004 First Annual IEEE Communications Society Conference on Sensor and Ad Hoc Communications and Networks, Santa Clara, CA, USA."},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Huang, B., Xie, L., and Yang, Z. (2014, January 28\u201330). Analysis of TOA Localization with Heteroscedastic Noises. Proceedings of the 33rd Chinese Control Conference, Nanjing, China.","DOI":"10.1109\/ChiCC.2014.6896643"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"468","DOI":"10.1109\/TWC.2014.2351798","article-title":"TDOA-Based Source Localization with Distance-Dependent Noises","volume":"14","author":"Huang","year":"2015","journal-title":"IEEE Trans. Wirel. Commun."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"837","DOI":"10.1109\/JSEN.2010.2072496","article-title":"Radio Frequency Time-of-Flight Distance Measurement for Low-Cost Wireless Sensor Localization","volume":"11","author":"Lanzisera","year":"2011","journal-title":"IEEE Sens. J."},{"key":"ref_26","first-page":"35","article-title":"Effect of Path Loss Propagation Model on the Position Estimation Accuracy of a 3-Dimensional Minimum Configuration Multilateration System","volume":"10","author":"Yaro","year":"2018","journal-title":"Int. J. Integr. Eng."},{"key":"ref_27","unstructured":"Rappaport, T.S. (2002). Wireless Communications-Principles and Practice, Prentice Hall."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/2.zoppoz.workers.dev:443\/https\/www.mdpi.com\/1424-8220\/19\/13\/3024\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T13:03:58Z","timestamp":1760187838000},"score":1,"resource":{"primary":{"URL":"https:\/\/2.zoppoz.workers.dev:443\/https\/www.mdpi.com\/1424-8220\/19\/13\/3024"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,7,9]]},"references-count":27,"journal-issue":{"issue":"13","published-online":{"date-parts":[[2019,7]]}},"alternative-id":["s19133024"],"URL":"https:\/\/2.zoppoz.workers.dev:443\/https\/doi.org\/10.3390\/s19133024","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,7,9]]}}}