{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,2]],"date-time":"2026-06-02T23:50:22Z","timestamp":1780444222729,"version":"3.54.1"},"reference-count":21,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2014,6,11]],"date-time":"2014-06-11T00:00:00Z","timestamp":1402444800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>It is well known that reflected signals from Global Navigation Satellite Systems (GNSS) can be used for altimetry applications, such as monitoring of water levels and determining snow height. Due to the interference of these reflected signals and the motion of satellites in space, the signal-to-noise ratio (SNR) measured at the receiver slowly oscillates. The oscillation rate is proportional to the change in the propagation path difference between the direct and reflected signals, which depends on the satellite elevation angle. Assuming a known receiver position, it is possible to compute the distance between the antenna and the surface of reflection from the measured oscillation rate. This technique is usually known as the interference pattern technique (IPT). In this paper, we propose to normalize the measurements in order to derive an alternative model of the SNR variations. From this model, we define a maximum likelihood estimate of the antenna height that reduces the estimation time to a fraction of one period of the SNR variation. We also derive the Cram\u00e9r\u2013Rao lower bound for the IPT and use it to assess the sensitivity of different parameters to the estimation of the antenna height. Finally, we propose an experimental framework, and we use it to assess our approach with real GPS L1 C\/A signals.<\/jats:p>","DOI":"10.3390\/s140610234","type":"journal-article","created":{"date-parts":[[2014,6,11]],"date-time":"2014-06-11T11:59:22Z","timestamp":1402487962000},"page":"10234-10257","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":18,"title":["Normalized GNSS Interference Pattern Technique for Altimetry"],"prefix":"10.3390","volume":"14","author":[{"given":"Miguel","family":"Ribot","sequence":"first","affiliation":[{"name":"Electronics and Signal Processing Laboratory (ESPLAB), \u00c9cole Polytechnique F\u00e9d\u00e9ralede Lausanne (EPFL), Maladi\u00e8re 71B (Microcity), CH-2002 Neuch\u00e2tel, Switzerland"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jean-Christophe","family":"Kucwaj","sequence":"additional","affiliation":[{"name":"Laboratoire d'Informatique, Signal et Image de la C\u00f4te d'Opale (LISIC), Univ Lille Nord de France, F-59000 Lille, France. Universit\u00e9 du Littoral C\u00f4te d'Opale (ULCO), 50, rue Ferdinand Buisson,BP719-62228 Calais cedex, France"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Cyril","family":"Botteron","sequence":"additional","affiliation":[{"name":"Electronics and Signal Processing Laboratory (ESPLAB), \u00c9cole Polytechnique F\u00e9d\u00e9ralede Lausanne (EPFL), Maladi\u00e8re 71B (Microcity), CH-2002 Neuch\u00e2tel, Switzerland"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Serge","family":"Reboul","sequence":"additional","affiliation":[{"name":"Laboratoire d'Informatique, Signal et Image de la C\u00f4te d'Opale (LISIC), Univ Lille Nord de France, F-59000 Lille, France. Universit\u00e9 du Littoral C\u00f4te d'Opale (ULCO), 50, rue Ferdinand Buisson,BP719-62228 Calais cedex, France"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Georges","family":"Stienne","sequence":"additional","affiliation":[{"name":"Laboratoire d'Informatique, Signal et Image de la C\u00f4te d'Opale (LISIC), Univ Lille Nord de France, F-59000 Lille, France. Universit\u00e9 du Littoral C\u00f4te d'Opale (ULCO), 50, rue Ferdinand Buisson,BP719-62228 Calais cedex, France"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"J\u00e9r\u00f4me","family":"Lecl\u00e8re","sequence":"additional","affiliation":[{"name":"Electronics and Signal Processing Laboratory (ESPLAB), \u00c9cole Polytechnique F\u00e9d\u00e9ralede Lausanne (EPFL), Maladi\u00e8re 71B (Microcity), CH-2002 Neuch\u00e2tel, Switzerland"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2759-4799","authenticated-orcid":false,"given":"Jean-Bernard","family":"Choquel","sequence":"additional","affiliation":[{"name":"Laboratoire d'Informatique, Signal et Image de la C\u00f4te d'Opale (LISIC), Univ Lille Nord de France, F-59000 Lille, France. Universit\u00e9 du Littoral C\u00f4te d'Opale (ULCO), 50, rue Ferdinand Buisson,BP719-62228 Calais cedex, France"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Pierre-Andr\u00e9","family":"Farine","sequence":"additional","affiliation":[{"name":"Electronics and Signal Processing Laboratory (ESPLAB), \u00c9cole Polytechnique F\u00e9d\u00e9ralede Lausanne (EPFL), Maladi\u00e8re 71B (Microcity), CH-2002 Neuch\u00e2tel, Switzerland"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Mohammed","family":"Benjelloun","sequence":"additional","affiliation":[{"name":"Laboratoire d'Informatique, Signal et Image de la C\u00f4te d'Opale (LISIC), Univ Lille Nord de France, F-59000 Lille, France. Universit\u00e9 du Littoral C\u00f4te d'Opale (ULCO), 50, rue Ferdinand Buisson,BP719-62228 Calais cedex, France"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2014,6,11]]},"reference":[{"key":"ref_1","first-page":"331","article-title":"A passive reflectometry and interferometry system (PARIS): Application to ocean altimetry","volume":"17","year":"1993","journal-title":"ESA J."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"173","DOI":"10.1007\/s10291-007-0076-6","article-title":"Using GPS multipath to measure soil moisture fluctuations: Initial results","volume":"12","author":"Larson","year":"2007","journal-title":"GPS Solut."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"1109","DOI":"10.1109\/LGRS.2012.2190379","article-title":"Snow Thickness Monitoring Using GNSS Measurements","volume":"9","author":"Aguasca","year":"2012","journal-title":"IEEE Geosci. Remote Sens. 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