{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,20]],"date-time":"2026-03-20T15:41:19Z","timestamp":1774021279838,"version":"3.50.1"},"reference-count":35,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2019,2,1]],"date-time":"2019-02-01T00:00:00Z","timestamp":1548979200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001659","name":"Deutsche Forschungsgemeinschaft","doi-asserted-by":"publisher","award":["'CITEC'(EXC 277)"],"award-info":[{"award-number":["'CITEC'(EXC 277)"]}],"id":[{"id":"10.13039\/501100001659","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>The Two-Way Ranging (TWR) method is commonly used for measuring the distance between two wireless transceiver nodes, especially when clock synchronization between the two nodes is not available. For modeling the time-of-flight (TOF) error between two wireless transceiver nodes in TWR, the existing error model, described in the IEEE 802.15.4-2011 standard, is solely based on clock drift. However, it is inadequate for in-depth comparative analysis between different TWR methods. In this paper, we propose a novel TOF Error Estimation Model (TEEM) for TWR methods. Using the proposed model, we evaluate the comparative analysis between different TWR methods. The analytical results were validated with both numerical simulation and experimental results. Moreover, we demonstrate the pitfalls of the symmetric double-sided TWR (SDS-TWR) method, which is the most highlighted TWR method in the literature because of its highly accurate performance on clock-drift error reduction when reply times are symmetric. We argue that alternative double-sided TWR (AltDS-TWR) outperforms SDS-TWR. The argument was verified with both numerical simulation and experimental evaluation results.<\/jats:p>","DOI":"10.3390\/s19030616","type":"journal-article","created":{"date-parts":[[2019,2,1]],"date-time":"2019-02-01T11:19:58Z","timestamp":1549019998000},"page":"616","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":54,"title":["Numerical and Experimental Evaluation of Error Estimation for Two-Way Ranging Methods"],"prefix":"10.3390","volume":"19","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-6144-9544","authenticated-orcid":false,"given":"Cung","family":"Lian Sang","sequence":"first","affiliation":[{"name":"Cognitronics and Sensor Systems Group (CITEC), Bielefeld University, 33619 Bielefeld, Germany"}]},{"given":"Michael","family":"Adams","sequence":"additional","affiliation":[{"name":"Cognitronics and Sensor Systems Group (CITEC), Bielefeld University, 33619 Bielefeld, Germany"}]},{"given":"Timm","family":"H\u00f6rmann","sequence":"additional","affiliation":[{"name":"Cognitronics and Sensor Systems Group (CITEC), Bielefeld University, 33619 Bielefeld, Germany"}]},{"given":"Marc","family":"Hesse","sequence":"additional","affiliation":[{"name":"Cognitronics and Sensor Systems Group (CITEC), Bielefeld University, 33619 Bielefeld, Germany"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1005-5753","authenticated-orcid":false,"given":"Mario","family":"Porrmann","sequence":"additional","affiliation":[{"name":"Cognitronics and Sensor Systems Group (CITEC), Bielefeld University, 33619 Bielefeld, Germany"}]},{"given":"Ulrich","family":"R\u00fcckert","sequence":"additional","affiliation":[{"name":"Cognitronics and Sensor Systems Group (CITEC), Bielefeld University, 33619 Bielefeld, Germany"}]}],"member":"1968","published-online":{"date-parts":[[2019,2,1]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"115","DOI":"10.1109\/JSYST.2013.2260638","article-title":"Experimental Characterization of Diversity Navigation","volume":"8","author":"Conti","year":"2014","journal-title":"IEEE Syst. J."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"124","DOI":"10.1109\/MSP.2010.938757","article-title":"Clock synchronization of wireless sensor networks","volume":"28","author":"Wu","year":"2011","journal-title":"IEEE Signal Process. Mag."},{"key":"ref_3","unstructured":"IEEE 802.15.4 (2011). IEEE Standard for Local and Metropolitan Area Networks\u2013Part 15.4: Low-Rate Wireless Personal Area Networks (LR-WPANs). IEEE Std 802.15.4-2011 (Revision of IEEE Std 802.15.4-2006), IEEE Computer Society. LAN\/MAN Standard Committee."},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Neirynck, D., Luk, E., and McLaughlin, M. (2016, January 19\u201320). An alternative double-sided two-way ranging method. Proceedings of the 13th Workshop on Positioning, Navigation and Communications (WPNC), Bremen, Germany.","DOI":"10.1109\/WPNC.2016.7822844"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"404","DOI":"10.1109\/JPROC.2008.2008846","article-title":"Ranging with ultrawide bandwidth signals in multipath environments","volume":"97","author":"Dardari","year":"2009","journal-title":"Proc. IEEE"},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Sang, C.L., Adams, M., H\u00f6rmann, T., Hesse, M., Porrmann, M., and R\u00fcckert, U. (Ocotober, January 30). An Analytical Study of Time of Flight Error Estimation in Two-Way Ranging Methods. Proceedings of the 2018 International Conference on Indoor Positioning and Indoor Navigation (IPIN) Nantes, Nantes, France.","DOI":"10.1109\/IPIN.2018.8533697"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"486","DOI":"10.1109\/LCOMM.2009.090093","article-title":"Double-sided two-way ranging algorithm to reduce ranging time","volume":"13","author":"Kim","year":"2009","journal-title":"IEEE Commun. Lett."},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Kwak, M., and Chong, J. (2010, January 24\u201326). A new double two-way ranging algorithm for ranging system. Proceedings of the 2nd IEEE International Conference on Network Infrastructure and Digital Content, Beijing, China.","DOI":"10.1109\/ICNIDC.2010.5657814"},{"key":"ref_9","unstructured":"Baba, A.I., and Atia, M.M. (, January 10\u201312). Burst mode symmetric double sided two way ranging. Proceedings of the IFIP Wireless Days (WD), Niagara Falls, ON, Canada."},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Lee, J.X., Lin, Z., and Francois, C.P.S. (2007, January 15). Symmetric double side two way ranging with unequal reply time. Proceedings of the IEEE 66th Vehicular Technology Conference, Baltimore, MD, USA.","DOI":"10.1109\/VETECF.2007.416"},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Nam, Y., Lee, H., Kim, J., and Park, K. (2008, January 11\u201313). Two-way ranging algorithms using estimated frequency offsets in WPAN and WBAN. Proceedings of the 3rd International Conference on Convergence and Hybrid Information Technology, Busan, Korea.","DOI":"10.1109\/ICCIT.2008.296"},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Dalce, R., van den Bossche, A., and Val, T. (2016, January 18\u201321). A study of the ranging error for parallel double sided-two way ranging protocol. Proceedings of the IEEE 84th Vehicular Technology Conference (VTC-Fall), Montreal, QC, Canada.","DOI":"10.1109\/VTCFall.2016.7880884"},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Horv\u00e1th, K.A., Ill, G., and Mil\u00e1nkovich, \u00c1. (2017, January 4\u20137). Passive extended double-sided two-way ranging algorithm for UWB positioning. Proceedings of the 9th International Conference on Ubiquitous and Future Networks (ICUFN), Milan, Italy.","DOI":"10.1109\/ICUFN.2017.7993831"},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Ganeriwal, S., Kumar, R., and Srivastava, M.B. (2003, January 5\u20137). Timing-sync protocol for sensor networks. Proceedings of the 1st International Conference on Embedded Networked Sensor Systems (SenSys \u201903), Los Angeles, CA, USA.","DOI":"10.1145\/958507.958508"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"1685","DOI":"10.1109\/TSP.2007.910536","article-title":"On Maximum Likelihood Estimation of Clock Offset and Skew in Networks with Exponential Delays","volume":"56","author":"Chaudhari","year":"2008","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"182","DOI":"10.1109\/TVT.2009.2028147","article-title":"On Clock Synchronization Algorithms for Wireless Sensor Networks Under Unknown Delay","volume":"59","author":"Leng","year":"2010","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"2379","DOI":"10.1109\/JSAC.2015.2430521","article-title":"Joint Ranging and Clock Parameter Estimation by Wireless Round Trip Time Measurements","volume":"33","author":"Dwivedi","year":"2015","journal-title":"IEEE J. Sel. Areas Commun."},{"key":"ref_18","unstructured":"Hach, R. (2005). Symmetric double side two way ranging. Contribution to IEEE 802.15.4A, IEEE P802.15 Working Group for Wireless Personal Area Networks (WPAN), Doc. IEEE P.802.15-05-0334-00-004a, IEEE Computer Society."},{"key":"ref_19","unstructured":"Jiang, Y., and Leung, V.C.M. (August, January 30). An asymmetric double sided two-way ranging for crystal offset. Proceedings of the International Symposium on Signals, Systems and Electronics, Montreal, QC, Canada."},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Baba, A.I. (2011, January 16\u201318). Calibrating time of flight in Two Way ranging. Proceedings of the 7th International Conference on Mobile Ad-Hoc and Sensor Networks, Beijing, China.","DOI":"10.1109\/MSN.2011.23"},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Lim, J.M., Yoo, S.H., Park, J.K., Sung, T.K., Oh, J.H., Jeong, S., and Lee, K.E. (2014, January 15\u201317). Error analysis of cooperative positioning system using two-way ranging measurements. Proceedings of the 8th International Conference on Signal Processing and Communication Systems (ICSPCS), Gold Coast, QLD, Australia.","DOI":"10.1109\/ICSPCS.2014.7021104"},{"key":"ref_22","unstructured":"(2017). DW1000 User Manual: How to Use, Configure and Program the DW1000 UWB Transceiver, Decawave. Revision 2.15."},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"McElroy, C., Neirynck, D., and McLaughlin, M. (2014, January 10\u201314). Comparison of wireless clock synchronization algorithms for indoor location systems. Proceedings of the IEEE International Conference on Communications Workshops (ICC), Sydney, NSW, Australia.","DOI":"10.1109\/ICCW.2014.6881189"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"38","DOI":"10.1109\/35.667411","article-title":"Overview of radiolocation in CDMA cellular systems","volume":"36","author":"Caffery","year":"1998","journal-title":"IEEE Commun. Mag."},{"key":"ref_25","unstructured":"Hoffman, J.D. (2001). Numerical Methods for Engineers and Scientists, Marcel Dekker Press. [2nd ed.]. Revised and Expended."},{"key":"ref_26","unstructured":"Sang, C.L., Adams, M., H\u00f6rmann, T., Hesse, M., Porrman, M., and R\u00fcckert, U. (2018). Supplementary Data for the Paper entitled \u201cAn Analytical Study of Time of Flight Error Estimation in Two-Way Ranging Methods\u201d. Bielef. Univ., Available online: https:\/\/pub.uni-bielefeld.de\/data\/2919795."},{"key":"ref_27","unstructured":"(2018). DW1000 Datasheet\u2014DW1000 IEEE802.15.4-2011 UWB Transceiver (Datasheet for DW1000), Decawave. Revision 2.17."},{"key":"ref_28","unstructured":"(2018). STM32L476XX Datasheet\u2014Ultra-Low-Power Arm Cortex-M4 32-Bit MCU+FPU, 100DMIPS, up to 1MB Flash, 128 KB SRAM, USB OTG FS, LCD, Ext. SMPS, STMicroelectronics. DS10198, Rev. 7."},{"key":"ref_29","unstructured":"(2018). APS014 Application Note\u2014Antenna Delay Calibration of DW1000-Based Products and Systems, DecaWave. [1st ed.]."},{"key":"ref_30","unstructured":"(2015). APS012 Application Note\u2014Production Tests for DW1000-Based Products (Typical Production Tests That Should Be Applied to DW1000-Based Products), Decawave. [1st ed.]."},{"key":"ref_31","doi-asserted-by":"crossref","unstructured":"Fofana, N.I., van den Bossche, A., Dalc\u00e9, R., and Val, T. (2016). An Original Correction Method for Indoor Ultra Wide Band Ranging-Based Localisation System. Lecture Notes in Computer Science, Proceedings of the International Conference on Ad-Hoc Networks and Wireless, Lille, France, 4\u20136 July 2016, Springer.","DOI":"10.1007\/978-3-319-40509-4_6"},{"key":"ref_32","unstructured":"Ledergerber, A., Hamer, M., and D\u2019Andrea, R. (October, January 28). A robot self-localization system using one-way ultra-wideband communication. Proceedings of the IEEE\/RSJ International Conference on Intelligent Robots and Systems (IROS), Hamburg, Germany."},{"key":"ref_33","doi-asserted-by":"crossref","unstructured":"Zandian, R., and Witkowski, U. (2017, January 25\u201326). Robot self-localization in ultra-wideband large scale multi-node setups. Proceedings of the 14th Workshop on Positioning, Navigation and Communications (WPNC), Bremen, Germany.","DOI":"10.1109\/WPNC.2017.8250062"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"22292","DOI":"10.1109\/ACCESS.2018.2829020","article-title":"Self-Calibrating Ultra-Wideband Network Supporting Multi-Robot Localization","volume":"6","author":"Hamer","year":"2018","journal-title":"IEEE Access"},{"key":"ref_35","doi-asserted-by":"crossref","unstructured":"Tiemann, J., Eckermann, F., and Wietfeld, C. (2016, January 4\u20137). Multi-user interference and wireless clock synchronization in TDOA-based UWB localization. Proceedings of the International Conference on Indoor Positioning and Indoor Navigation (IPIN), Alcala de Henares, Spain.","DOI":"10.1109\/IPIN.2016.7743696"}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/19\/3\/616\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T12:30:17Z","timestamp":1760185817000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/19\/3\/616"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,2,1]]},"references-count":35,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2019,2]]}},"alternative-id":["s19030616"],"URL":"https:\/\/doi.org\/10.3390\/s19030616","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,2,1]]}}}