Application of expectation–maximization algorithm to estimate random walk process noise for GNSS tropospheric delay
GNSS (Global Navigation Satellite Systems) tropospheric delay, specifically zenith wet delay (ZWD), shows clear spatial–temporal variations and is usually modeled as RWPN (random walk process noise). However, because RWPN does not take the geographical position of GNSS stations and local weather con...
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| Veröffentlicht in: | GPS solutions 2024-10, Vol.28 (4), p.204, Article 204 |
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| creator | Zhang, Xinggang Li, Pan Wang, Miaomiao Ge, Maorong Schuh, Harald |
| description | GNSS (Global Navigation Satellite Systems) tropospheric delay, specifically zenith wet delay (ZWD), shows clear spatial–temporal variations and is usually modeled as RWPN (random walk process noise). However, because RWPN does not take the geographical position of GNSS stations and local weather conditions into account for precise point positioning (PPP), it may lead to biased ZWD estimates. To address the scientific problem and improve ZWD estimates, we adopt the Expectation–Maximization algorithm (EM algorithm) to validate the feasibility of estimating RWPN using only GNSS measurements. Numerical experiments reveal that using only GNSS observations is capable of determining the RWPN parameter, although it could take several days to reach a stable solution if the initial guess deviates far away from the truth. It is also shown that estimating RWPN can almost always effectively improve ZWD estimates by several millimeters in contrast with traditional PPP results. If the ambiguities are fixed to their integer values correctly, the accuracy of RWPN estimates for ZWD can be greatly reduced by
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| doi_str_mv | 10.1007/s10291-024-01714-7 |
| format | Article |
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2
mm
/
hour
.</description><identifier>ISSN: 1080-5370</identifier><identifier>EISSN: 1521-1886</identifier><identifier>DOI: 10.1007/s10291-024-01714-7</identifier><language>eng</language><publisher>Berlin/Heidelberg: Springer Berlin Heidelberg</publisher><subject>Algorithms ; Atmospheric Sciences ; Automotive Engineering ; Delay ; Earth and Environmental Science ; Earth Sciences ; Electrical Engineering ; Estimates ; Geophysics/Geodesy ; Global navigation satellite system ; Maximization ; Optimization ; Original Article ; Parameter estimation ; Position measurement ; Random walk ; Satellite observation ; Space Exploration and Astronautics ; Space Sciences (including Extraterrestrial Physics ; Troposphere ; Weather</subject><ispartof>GPS solutions, 2024-10, Vol.28 (4), p.204, Article 204</ispartof><rights>The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2024. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><cites>FETCH-LOGICAL-c200t-407eb6e3c4d3ea1298d64ce43fdd51b501bdea3b5350a809e9b39b218862e93d3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s10291-024-01714-7$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s10291-024-01714-7$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,777,781,27905,27906,41469,42538,51300</link.rule.ids></links><search><creatorcontrib>Zhang, Xinggang</creatorcontrib><creatorcontrib>Li, Pan</creatorcontrib><creatorcontrib>Wang, Miaomiao</creatorcontrib><creatorcontrib>Ge, Maorong</creatorcontrib><creatorcontrib>Schuh, Harald</creatorcontrib><title>Application of expectation–maximization algorithm to estimate random walk process noise for GNSS tropospheric delay</title><title>GPS solutions</title><addtitle>GPS Solut</addtitle><description>GNSS (Global Navigation Satellite Systems) tropospheric delay, specifically zenith wet delay (ZWD), shows clear spatial–temporal variations and is usually modeled as RWPN (random walk process noise). However, because RWPN does not take the geographical position of GNSS stations and local weather conditions into account for precise point positioning (PPP), it may lead to biased ZWD estimates. To address the scientific problem and improve ZWD estimates, we adopt the Expectation–Maximization algorithm (EM algorithm) to validate the feasibility of estimating RWPN using only GNSS measurements. Numerical experiments reveal that using only GNSS observations is capable of determining the RWPN parameter, although it could take several days to reach a stable solution if the initial guess deviates far away from the truth. It is also shown that estimating RWPN can almost always effectively improve ZWD estimates by several millimeters in contrast with traditional PPP results. If the ambiguities are fixed to their integer values correctly, the accuracy of RWPN estimates for ZWD can be greatly reduced by
2
mm
/
hour
.</description><subject>Algorithms</subject><subject>Atmospheric Sciences</subject><subject>Automotive Engineering</subject><subject>Delay</subject><subject>Earth and Environmental Science</subject><subject>Earth Sciences</subject><subject>Electrical Engineering</subject><subject>Estimates</subject><subject>Geophysics/Geodesy</subject><subject>Global navigation satellite system</subject><subject>Maximization</subject><subject>Optimization</subject><subject>Original Article</subject><subject>Parameter estimation</subject><subject>Position measurement</subject><subject>Random walk</subject><subject>Satellite observation</subject><subject>Space Exploration and Astronautics</subject><subject>Space Sciences (including Extraterrestrial Physics</subject><subject>Troposphere</subject><subject>Weather</subject><issn>1080-5370</issn><issn>1521-1886</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2024</creationdate><recordtype>article</recordtype><recordid>eNp9kEtOwzAQhiMEEqVwAVaWWAfGj7yWVQUFqYJFYW05zqRNSeJgp6JlxR24ISfBbZDYsZoZzf_P4wuCSwrXFCC5cRRYRkNgIgSaUBEmR8GIRoyGNE3jY59DCmHEEzgNzpxbAzDIMjEKNpOuqyut-sq0xJQEtx3q_lB-f341als11cfQVfXS2KpfNaQ3BF1fNapHYlVbmIa8q_qVdNZodI60pnJISmPJ7HGxIL01nXHdCm2lSYG12p0HJ6WqHV78xnHwcnf7PL0P50-zh-lkHmoG0IcCEsxj5FoUHBVlWVrEQqPgZVFENI-A5gUqnkc8ApVChlnOs5ztX2aY8YKPg6thrr_sbeNvlmuzsa1fKbknIqKYcu5VbFBpa5yzWMrO-ufsTlKQe7xywCs9XnnAKxNv4oPJeXG7RPs3-h_XD04cgLk</recordid><startdate>20241001</startdate><enddate>20241001</enddate><creator>Zhang, Xinggang</creator><creator>Li, Pan</creator><creator>Wang, Miaomiao</creator><creator>Ge, Maorong</creator><creator>Schuh, Harald</creator><general>Springer Berlin Heidelberg</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope><scope>8FD</scope><scope>H8D</scope><scope>L7M</scope></search><sort><creationdate>20241001</creationdate><title>Application of expectation–maximization algorithm to estimate random walk process noise for GNSS tropospheric delay</title><author>Zhang, Xinggang ; Li, Pan ; Wang, Miaomiao ; Ge, Maorong ; Schuh, Harald</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c200t-407eb6e3c4d3ea1298d64ce43fdd51b501bdea3b5350a809e9b39b218862e93d3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2024</creationdate><topic>Algorithms</topic><topic>Atmospheric Sciences</topic><topic>Automotive Engineering</topic><topic>Delay</topic><topic>Earth and Environmental Science</topic><topic>Earth Sciences</topic><topic>Electrical Engineering</topic><topic>Estimates</topic><topic>Geophysics/Geodesy</topic><topic>Global navigation satellite system</topic><topic>Maximization</topic><topic>Optimization</topic><topic>Original Article</topic><topic>Parameter estimation</topic><topic>Position measurement</topic><topic>Random walk</topic><topic>Satellite observation</topic><topic>Space Exploration and Astronautics</topic><topic>Space Sciences (including Extraterrestrial Physics</topic><topic>Troposphere</topic><topic>Weather</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Zhang, Xinggang</creatorcontrib><creatorcontrib>Li, Pan</creatorcontrib><creatorcontrib>Wang, Miaomiao</creatorcontrib><creatorcontrib>Ge, Maorong</creatorcontrib><creatorcontrib>Schuh, Harald</creatorcontrib><collection>CrossRef</collection><collection>Technology Research Database</collection><collection>Aerospace Database</collection><collection>Advanced Technologies Database with Aerospace</collection><jtitle>GPS solutions</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Zhang, Xinggang</au><au>Li, Pan</au><au>Wang, Miaomiao</au><au>Ge, Maorong</au><au>Schuh, Harald</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Application of expectation–maximization algorithm to estimate random walk process noise for GNSS tropospheric delay</atitle><jtitle>GPS solutions</jtitle><stitle>GPS Solut</stitle><date>2024-10-01</date><risdate>2024</risdate><volume>28</volume><issue>4</issue><spage>204</spage><pages>204-</pages><artnum>204</artnum><issn>1080-5370</issn><eissn>1521-1886</eissn><abstract>GNSS (Global Navigation Satellite Systems) tropospheric delay, specifically zenith wet delay (ZWD), shows clear spatial–temporal variations and is usually modeled as RWPN (random walk process noise). However, because RWPN does not take the geographical position of GNSS stations and local weather conditions into account for precise point positioning (PPP), it may lead to biased ZWD estimates. To address the scientific problem and improve ZWD estimates, we adopt the Expectation–Maximization algorithm (EM algorithm) to validate the feasibility of estimating RWPN using only GNSS measurements. Numerical experiments reveal that using only GNSS observations is capable of determining the RWPN parameter, although it could take several days to reach a stable solution if the initial guess deviates far away from the truth. It is also shown that estimating RWPN can almost always effectively improve ZWD estimates by several millimeters in contrast with traditional PPP results. If the ambiguities are fixed to their integer values correctly, the accuracy of RWPN estimates for ZWD can be greatly reduced by
2
mm
/
hour
.</abstract><cop>Berlin/Heidelberg</cop><pub>Springer Berlin Heidelberg</pub><doi>10.1007/s10291-024-01714-7</doi></addata></record> |
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| subjects | Algorithms Atmospheric Sciences Automotive Engineering Delay Earth and Environmental Science Earth Sciences Electrical Engineering Estimates Geophysics/Geodesy Global navigation satellite system Maximization Optimization Original Article Parameter estimation Position measurement Random walk Satellite observation Space Exploration and Astronautics Space Sciences (including Extraterrestrial Physics Troposphere Weather |
| title | Application of expectation–maximization algorithm to estimate random walk process noise for GNSS tropospheric delay |
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