{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,3]],"date-time":"2026-06-03T18:37:08Z","timestamp":1780511828718,"version":"3.54.1"},"reference-count":57,"publisher":"MDPI AG","issue":"24","license":[{"start":{"date-parts":[[2019,12,7]],"date-time":"2019-12-07T00:00:00Z","timestamp":1575676800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["CNS-1815349"],"award-info":[{"award-number":["CNS-1815349"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["ECCS-1845833"],"award-info":[{"award-number":["ECCS-1845833"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Navigation problems are generally solved applying least-squares (LS) adjustments. Techniques based on LS can be shown to perform optimally when the system noise is Gaussian distributed and the parametric model is accurately known. Unfortunately, real world problems usually contain unexpectedly large errors, so-called outliers, that violate the noise model assumption, leading to a spoiled solution estimation. In this work, the framework of robust statistics is explored to provide robust solutions to the global navigation satellite systems (GNSS) single point positioning (SPP) problem. Considering that GNSS observables may be contaminated by erroneous measurements, we survey the most popular approaches for robust regression (M-, S-, and MM-estimators) and how they can be adapted into a general methodology for robust GNSS positioning. We provide both theoretical insights and validation over experimental datasets, which serves in discussing the robust methods in detail.<\/jats:p>","DOI":"10.3390\/s19245402","type":"journal-article","created":{"date-parts":[[2019,12,9]],"date-time":"2019-12-09T05:54:51Z","timestamp":1575870891000},"page":"5402","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":34,"title":["Robust Statistics for GNSS Positioning under Harsh Conditions: A Useful Tool?"],"prefix":"10.3390","volume":"19","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1586-3269","authenticated-orcid":false,"given":"Daniel","family":"Medina","sequence":"first","affiliation":[{"name":"Institute of Communications and Navigation, German Aerospace Center (DLR), 17235 Neustrelitz, Germany"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6953-755X","authenticated-orcid":false,"given":"Haoqing","family":"Li","sequence":"additional","affiliation":[{"name":"Electrical and Computer Engineering Dept., Northeastern University, Boston, MA 02115, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7858-4171","authenticated-orcid":false,"given":"Jordi","family":"Vil\u00e0-Valls","sequence":"additional","affiliation":[{"name":"Institut Sup\u00e9rieur de l\u2019A\u00e9ronautique et de l\u2019Espace (ISAE-SUPAERO), University of Toulouse, 31055 Toulouse, France"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5960-6600","authenticated-orcid":false,"given":"Pau","family":"Closas","sequence":"additional","affiliation":[{"name":"Electrical and Computer Engineering Dept., Northeastern University, Boston, MA 02115, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2019,12,7]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Williams, N., Wu, G., and Closas, P. 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