{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,14]],"date-time":"2025-10-14T00:51:48Z","timestamp":1760403108950,"version":"build-2065373602"},"reference-count":41,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2022,1,6]],"date-time":"2022-01-06T00:00:00Z","timestamp":1641427200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"The Scientific Instrument Developing Project of the Chinese Academy of Sciences","award":["YJKYYQ20190063"],"award-info":[{"award-number":["YJKYYQ20190063"]}]},{"name":"The Key Research and Development Plan of Hubei Province","award":["2020BHB014"],"award-info":[{"award-number":["2020BHB014"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Remote Sensing"],"abstract":"<jats:p>Stochastic models play a crucial role in global navigation satellite systems (GNSS) data processing. Many studies contribute to the stochastic modeling of GNSS observation noise, whereas few studies focus on the stochastic modeling of process noise. This paper proposes a method that is able to jointly estimate the variances of observation noise and process noise. The method is flexible since it is based on the least-squares variance component estimation (LS-VCE), enabling users to estimate the variance components that they are specifically interested in. We apply the proposed method to estimate the variances for the dual-frequency GNSS observation noise and for the process noise of the receiver code bias (RCB). We also investigate the impact of the stochastic model upon parameter estimation, ambiguity resolution, and positioning. The results show that the precision of GNSS observations differs in systems and frequencies. Among the dual-frequency GPS, Galileo, and BDS code observations, the precision of the BDS B3 observations is highest (better than 0.2 m). The precision of the BDS phase observations is better than two millimeters, which is also higher than that of the GPS and Galileo observations. For all three systems, the RCB process noise ranges from 0.5 millimeters to 1 millimeter, with a data sampling rate of 30 s. An improper stochastic model of the observation noise results in an unreliable ambiguity dilution of precision (ADOP) and position dilution of precision (PDOP), thus adversely affecting the assessment of the ambiguity resolution and positioning performance. An inappropriate stochastic model of RCB process noise disturbs the estimation of the receiver clock and the ionosphere delays and is thus harmful for timing and ionosphere retrieval applications.<\/jats:p>","DOI":"10.3390\/rs14020258","type":"journal-article","created":{"date-parts":[[2022,1,9]],"date-time":"2022-01-09T23:08:26Z","timestamp":1641769706000},"page":"258","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["LS-VCE Applied to Stochastic Modeling of GNSS Observation Noise and Process Noise"],"prefix":"10.3390","volume":"14","author":[{"given":"Pengyu","family":"Hou","sequence":"first","affiliation":[{"name":"State Key Laboratory of Geodesy and Earth\u2019s Dynamics, Innovation Academy for Precision Measurement Science and Technology, Chinese Academy of Sciences, Wuhan 430071, China"},{"name":"College of Earth and Planetary Sciences, University of Chinese Academy of Sciences, Beijing 100049, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jiuping","family":"Zha","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Geodesy and Earth\u2019s Dynamics, Innovation Academy for Precision Measurement Science and Technology, Chinese Academy of Sciences, Wuhan 430071, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Teng","family":"Liu","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Geodesy and Earth\u2019s Dynamics, Innovation Academy for Precision Measurement Science and Technology, Chinese Academy of Sciences, Wuhan 430071, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Baocheng","family":"Zhang","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Geodesy and Earth\u2019s Dynamics, Innovation Academy for Precision Measurement Science and Technology, Chinese Academy of Sciences, Wuhan 430071, China"},{"name":"State Key Laboratory of Satellite Navigation System and Equipment Technology, The 54th Research Institute of China Electronics Technology Group Corporation, Shijiazhuang 050081, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,1,6]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Leick, A., Rapoport, L., and Tatarnikov, D. 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