{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,3]],"date-time":"2026-06-03T18:37:14Z","timestamp":1780511834359,"version":"3.54.1"},"reference-count":59,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2021,12,23]],"date-time":"2021-12-23T00:00:00Z","timestamp":1640217600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Remote Sensing"],"abstract":"<jats:p>With the advancement of multi-constellation and multi-frequency global navigation satellite systems (GNSSs), more observations are available for high precision positioning applications. Although there is a lot of progress in the GNSS world, achieving realistic precision of the solution (neither too optimistic nor too pessimistic) is still an open problem. Weighting among different GNSS systems requires a realistic stochastic model for all observations to achieve the best linear unbiased estimation (BLUE) of unknown parameters in multi-GNSS data processing mode. In addition, the correct integer ambiguity resolution (IAR) becomes crucial in shortening the Time-To-Fix (TTF) in RTK, especially in challenging environmental conditions. In general, it is required to estimate various variances for observation types, consider the correlation between different observables, and compensate for the satellite elevation dependence of the observable precision. Quality control of GNSS signals, such as GPS, GLONASS, Galileo, and BeiDou can be performed by processing a zero or short baseline double difference pseudorange and carrier phase observations using the least-squares variance component estimation (LS-VCE). The efficacy of this method is investigated using real multi-GNSS data sets collected by the Trimble NETR9, SEPT POLARX5, and LEICA GR30 receivers. The results show that the standard deviation of observations depends on the system and the observable type in which a particular receiver could have the best performance. We also note that the estimated variances and correlations among different observations are also dependent on the receiver type. It is because the approaches utilized for the recovery techniques differ from one type of receiver to another kind. The reliability of IAR will improve if a realistic stochastic model is applied in single or multi-GNSS data processing. According to the results, for the data sets considered, a realistic stochastic model can increase the computed empirical success rate to 100% in multi-GNSS as well as a single system. As mentioned previously, the realistic precision of the solution can be achieved with a realistic stochastic model. However, using the estimated stochastic model, in fact, leads to better precision and accuracy for the estimated baseline components, up to 39% in multi-GNSS.<\/jats:p>","DOI":"10.3390\/rs14010060","type":"journal-article","created":{"date-parts":[[2021,12,23]],"date-time":"2021-12-23T21:40:21Z","timestamp":1640295621000},"page":"60","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["Improvement of Multi-GNSS Precision and Success Rate Using Realistic Stochastic Model of Observations"],"prefix":"10.3390","volume":"14","author":[{"given":"Farinaz","family":"Mirmohammadian","sequence":"first","affiliation":[{"name":"Department of Geomatics Engineering, Faculty of Civil Engineering and Transportation, University of Isfahan, Isfahan 81746-73441, Iran"},{"name":"Department of Geoscience and Remote Sensing, Delft University of Technology, 2600 AA Delft, The Netherlands"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jamal","family":"Asgari","sequence":"additional","affiliation":[{"name":"Department of Geomatics Engineering, Faculty of Civil Engineering and Transportation, University of Isfahan, Isfahan 81746-73441, Iran"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Sandra","family":"Verhagen","sequence":"additional","affiliation":[{"name":"Department of Geoscience and Remote Sensing, Delft University of Technology, 2600 AA Delft, The Netherlands"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Alireza","family":"Amiri-Simkooei","sequence":"additional","affiliation":[{"name":"Department of Geomatics Engineering, Faculty of Civil Engineering and Transportation, University of Isfahan, Isfahan 81746-73441, Iran"},{"name":"Department of Geoscience and Remote Sensing, Delft University of Technology, 2600 AA Delft, The Netherlands"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2021,12,23]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Wang, L., Li, Z., Zhao, J., Zhou, K., Wang, Z., and Yuan, H. 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