{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,5]],"date-time":"2026-06-05T07:33:25Z","timestamp":1780644805579,"version":"3.54.1"},"reference-count":36,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2021,5,6]],"date-time":"2021-05-06T00:00:00Z","timestamp":1620259200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100003524","name":"Ministry of Business, Innovation and Employment","doi-asserted-by":"publisher","award":["UOOX1208"],"award-info":[{"award-number":["UOOX1208"]}],"id":[{"id":"10.13039\/501100003524","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Trajectory reconstruction is the process of inferring the path of a moving object between successive observations. In this paper, we propose a smoothing spline\u2014which we name the V-spline\u2014that incorporates position and velocity information and a penalty term that controls acceleration. We introduce an adaptive V-spline designed to control the impact of irregularly sampled observations and noisy velocity measurements. A cross-validation scheme for estimating the V-spline parameters is proposed, and, in simulation studies, the V-spline shows superior performance to existing methods. Finally, an application of the V-spline to vehicle trajectory reconstruction in two dimensions is given, in which the penalty term is allowed to further depend on known operational characteristics of the vehicle.<\/jats:p>","DOI":"10.3390\/s21093215","type":"journal-article","created":{"date-parts":[[2021,5,6]],"date-time":"2021-05-06T11:10:27Z","timestamp":1620299427000},"page":"3215","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":14,"title":["V-Spline: An Adaptive Smoothing Spline for Trajectory Reconstruction"],"prefix":"10.3390","volume":"21","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-6667-9392","authenticated-orcid":false,"given":"Zhanglong","family":"Cao","sequence":"first","affiliation":[{"name":"SAGI West, School of Molecular and Life Sciences, Curtin University, Perth 6085, Australia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"David","family":"Bryant","sequence":"additional","affiliation":[{"name":"Department of Mathematics &amp; Statistics, University of Otago, Dunedin 9054, New Zealand"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2022-0380","authenticated-orcid":false,"given":"Timothy C.A.","family":"Molteno","sequence":"additional","affiliation":[{"name":"Department of Physics, University of Otago, Dunedin 9054, New Zealand"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9278-1777","authenticated-orcid":false,"given":"Colin","family":"Fox","sequence":"additional","affiliation":[{"name":"Department of Physics, University of Otago, Dunedin 9054, New Zealand"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6588-0219","authenticated-orcid":false,"given":"Matthew","family":"Parry","sequence":"additional","affiliation":[{"name":"Department of Mathematics &amp; Statistics, University of Otago, Dunedin 9054, New Zealand"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2021,5,6]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"33","DOI":"10.1080\/10630730802401942","article-title":"Using GPS Data to Understand Driving Behavior","volume":"15","author":"Grengs","year":"2008","journal-title":"J. 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