{"id":"https://openalex.org/W7225396705","doi":"https://doi.org/10.21203/rs.3.rs-11637033/v1","title":"Over-injection of time-correlated tropospheric constraints induces PPP height shifts: a Gauss\u2013Markov remedy","display_name":"Over-injection of time-correlated tropospheric constraints induces PPP height shifts: a Gauss\u2013Markov remedy","publication_year":2026,"publication_date":"2026-11-06","ids":{"openalex":"https://openalex.org/W7225396705","doi":"https://doi.org/10.21203/rs.3.rs-11637033/v1"},"language":"en","primary_location":{"id":"doi:10.21203/rs.3.rs-11637033/v1","doi":"https://doi.org/10.21203/rs.3.rs-11637033/v1","is_oa":true,"landing_page_url":"https://doi.org/10.21203/rs.3.rs-11637033/v1","pdf_url":"https://www.researchsquare.com/article/rs-11637033/latest.pdf","source":{"id":"https://openalex.org/S4306525896","display_name":"Research Square","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Research Square","raw_type":"posted-content"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://www.researchsquare.com/article/rs-11637033/latest.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5161039699","display_name":"Jing WU","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I14243506","display_name":"Hong Kong Polytechnic University","ror":"https://ror.org/0030zas98","country_code":"HK","type":"education","lineage":["https://openalex.org/I14243506"]}],"countries":["HK"],"is_corresponding":false,"raw_author_name":"Jing WU","raw_affiliation_strings":["Hong Kong Polytechnic University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Hong Kong Polytechnic University","institution_ids":["https://openalex.org/I14243506"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5042517863","display_name":"Zhizhao Liu","orcid":"https://orcid.org/0000-0001-6822-9248","observed_orcids":["https://orcid.org/0000-0001-6822-9248"]},"institutions":[{"id":"https://openalex.org/I14243506","display_name":"Hong Kong Polytechnic University","ror":"https://ror.org/0030zas98","country_code":"HK","type":"education","lineage":["https://openalex.org/I14243506"]}],"countries":["HK"],"is_corresponding":false,"raw_author_name":"Zhizhao Liu","raw_affiliation_strings":["Hong Kong Polytechnic University"],"raw_orcid":"https://orcid.org/0000-0001-6822-9248","affiliations":[{"raw_affiliation_string":"Hong Kong Polytechnic University","institution_ids":["https://openalex.org/I14243506"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I14243506"],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10655","display_name":"GNSS positioning and interference","score":0.9990000128746033,"subfield":{"id":"https://openalex.org/subfields/2202","display_name":"Aerospace Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10655","display_name":"GNSS positioning and interference","score":0.9990000128746033,"subfield":{"id":"https://openalex.org/subfields/2202","display_name":"Aerospace Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T13487","display_name":"Statistical and numerical algorithms","score":0.0006000000284984708,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T13511","display_name":"Geodetic Measurements and Engineering Structures","score":0.0,"subfield":{"id":"https://openalex.org/subfields/2205","display_name":"Civil and Structural Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/precise-point-positioning","display_name":"precise point positioning","score":0.9940000176429749},{"id":"https://openalex.org/keywords/gauss-markov-process","display_name":"Gauss-Markov process","score":0.7829999923706055},{"id":"https://openalex.org/keywords/kinematic-ppp","display_name":"kinematic PPP","score":0.5730000138282776},{"id":"https://openalex.org/keywords/static-ppp","display_name":"static PPP","score":0.9240000247955322}],"concepts":[{"id":"https://openalex.org/C9075549","wikidata":"https://www.wikidata.org/wiki/Q40631","display_name":"Troposphere","level":2,"score":0.5465999841690063},{"id":"https://openalex.org/C155512373","wikidata":"https://www.wikidata.org/wiki/Q287450","display_name":"Residual","level":2,"score":0.5327000021934509},{"id":"https://openalex.org/C175291020","wikidata":"https://www.wikidata.org/wiki/Q1156822","display_name":"Offset (computer science)","level":2,"score":0.5224000215530396},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5189999938011169},{"id":"https://openalex.org/C48677424","wikidata":"https://www.wikidata.org/wiki/Q6888088","display_name":"Mode (computer interface)","level":2,"score":0.4779999852180481},{"id":"https://openalex.org/C53970728","wikidata":"https://www.wikidata.org/wiki/Q82806","display_name":"Zenith","level":2,"score":0.4593000113964081},{"id":"https://openalex.org/C202511199","wikidata":"https://www.wikidata.org/wiki/Q7239503","display_name":"Precise Point Positioning","level":4,"score":0.44279998540878296},{"id":"https://openalex.org/C126691448","wikidata":"https://www.wikidata.org/wiki/Q2028919","display_name":"Magnitude (astronomy)","level":2,"score":0.41609999537467957},{"id":"https://openalex.org/C39432304","wikidata":"https://www.wikidata.org/wiki/Q188847","display_name":"Environmental science","level":0,"score":0.3815000057220459},{"id":"https://openalex.org/C2776036281","wikidata":"https://www.wikidata.org/wiki/Q48769818","display_name":"Constraint (computer-aided design)","level":2,"score":0.3806000053882599},{"id":"https://openalex.org/C25570617","wikidata":"https://www.wikidata.org/wiki/Q1006462","display_name":"Hilbert\u2013Huang transform","level":3,"score":0.3637999892234802},{"id":"https://openalex.org/C39920418","wikidata":"https://www.wikidata.org/wiki/Q11476","display_name":"Kinematics","level":2,"score":0.34689998626708984},{"id":"https://openalex.org/C153294291","wikidata":"https://www.wikidata.org/wiki/Q25261","display_name":"Meteorology","level":1,"score":0.3422999978065491},{"id":"https://openalex.org/C2780092901","wikidata":"https://www.wikidata.org/wiki/Q3433612","display_name":"Correlation coefficient","level":2,"score":0.3386000096797943},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.3230000138282776},{"id":"https://openalex.org/C93038891","wikidata":"https://www.wikidata.org/wiki/Q1061524","display_name":"Intensity (physics)","level":2,"score":0.31949999928474426},{"id":"https://openalex.org/C99498987","wikidata":"https://www.wikidata.org/wiki/Q2210247","display_name":"Noise (video)","level":3,"score":0.31709998846054077},{"id":"https://openalex.org/C13280743","wikidata":"https://www.wikidata.org/wiki/Q131089","display_name":"Geodesy","level":1,"score":0.3095000088214874},{"id":"https://openalex.org/C204323151","wikidata":"https://www.wikidata.org/wiki/Q905424","display_name":"Range (aeronautics)","level":2,"score":0.3075999915599823},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.305400013923645},{"id":"https://openalex.org/C2777042071","wikidata":"https://www.wikidata.org/wiki/Q6509304","display_name":"Leakage (economics)","level":2,"score":0.30149999260902405},{"id":"https://openalex.org/C75778745","wikidata":"https://www.wikidata.org/wiki/Q342626","display_name":"Lag","level":2,"score":0.3012999892234802},{"id":"https://openalex.org/C48921125","wikidata":"https://www.wikidata.org/wiki/Q10861030","display_name":"Linear regression","level":2,"score":0.2987000048160553},{"id":"https://openalex.org/C19619285","wikidata":"https://www.wikidata.org/wiki/Q196372","display_name":"Observational error","level":2,"score":0.2896000146865845},{"id":"https://openalex.org/C112633086","wikidata":"https://www.wikidata.org/wiki/Q381287","display_name":"White noise","level":2,"score":0.2802000045776367},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.26350000500679016},{"id":"https://openalex.org/C44648626","wikidata":"https://www.wikidata.org/wiki/Q1049848","display_name":"Percentage point","level":2,"score":0.2547999918460846},{"id":"https://openalex.org/C71134354","wikidata":"https://www.wikidata.org/wiki/Q458825","display_name":"Kernel density estimation","level":3,"score":0.2547000050544739},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.2533000111579895}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.21203/rs.3.rs-11637033/v1","doi":"https://doi.org/10.21203/rs.3.rs-11637033/v1","is_oa":true,"landing_page_url":"https://doi.org/10.21203/rs.3.rs-11637033/v1","pdf_url":"https://www.researchsquare.com/article/rs-11637033/latest.pdf","source":{"id":"https://openalex.org/S4306525896","display_name":"Research Square","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Research Square","raw_type":"posted-content"}],"best_oa_location":{"id":"doi:10.21203/rs.3.rs-11637033/v1","doi":"https://doi.org/10.21203/rs.3.rs-11637033/v1","is_oa":true,"landing_page_url":"https://doi.org/10.21203/rs.3.rs-11637033/v1","pdf_url":"https://www.researchsquare.com/article/rs-11637033/latest.pdf","source":{"id":"https://openalex.org/S4306525896","display_name":"Research Square","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Research Square","raw_type":"posted-content"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320331771","display_name":"European Centre for Medium-Range Weather Forecasts","ror":"https://ror.org/014w0fd65"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7225396705.pdf","grobid_xml":"https://content.openalex.org/works/W7225396705.grobid-xml"},"referenced_works_count":22,"referenced_works":["https://openalex.org/W90689849","https://openalex.org/W1984123740","https://openalex.org/W2079986986","https://openalex.org/W2084389047","https://openalex.org/W2095142679","https://openalex.org/W2105934661","https://openalex.org/W2150680604","https://openalex.org/W2154396746","https://openalex.org/W2441682984","https://openalex.org/W2558686734","https://openalex.org/W2598484049","https://openalex.org/W2790374560","https://openalex.org/W2796331854","https://openalex.org/W2911498096","https://openalex.org/W2914475297","https://openalex.org/W3151181560","https://openalex.org/W4313259660","https://openalex.org/W4327606235","https://openalex.org/W4391281443","https://openalex.org/W4408305262","https://openalex.org/W4411236868","https://openalex.org/W4412734520"],"related_works":["https://openalex.org/W2558686734","https://openalex.org/W4410494347","https://openalex.org/W3067427516","https://openalex.org/W2007298276","https://openalex.org/W2054454775","https://openalex.org/W2085061793","https://openalex.org/W2778099803","https://openalex.org/W2351517847","https://openalex.org/W3034775998","https://openalex.org/W2804358047"],"abstract_inverted_index":{"Abstract":[0],"External":[1],"zenith":[2],"total":[3],"delay":[4],"(ZTD)":[5],"constraints":[6],"improve":[7],"precise":[8],"point":[9],"positioning":[10],"(PPP)":[11],"but":[12,171],"are":[13,119],"commonly":[14],"treated":[15],"as":[16,71,121,151],"temporally":[17],"independent":[18],"epoch-wise":[19],"pseudo-observations.":[20],"Their":[21],"errors":[22,70],"exhibit":[23],"substantial":[24],"temporal":[25,114],"correlation.":[26],"Neglecting":[27],"this":[28,113],"correlation":[29],"can":[30],"over-inject":[31],"constraint":[32,69,117],"information":[33,77],"and":[34,106,132,146,192,215,224],"distort":[35],"PPP":[36],"height":[37,64,177,200,222,227],"through":[38],"its":[39],"strong":[40],"coupling":[41],"with":[42,142],"ZTD.":[43],"This":[44],"study":[45],"uses":[46],"ZTD":[47,68],"derived":[48],"from":[49,202,210],"the":[50,62,67,90,94,97,116,143,147,158,164,168,175,182,197,203,216,219,225],"fifth-generation":[51],"European":[52],"Centre":[53],"for":[54],"Medium-Range":[55],"Weather":[56],"Forecasts":[57],"reanalysis":[58],"(ERA5)":[59],"to":[60,86,187,212],"quantify":[61],"resulting":[63],"effects.":[65],"Treating":[66],"white":[72],"noise":[73],"overestimates":[74],"their":[75],"effective":[76],"content":[78],"by":[79,89,137],"a":[80,122,125,128,133,138],"factor":[81],"of":[82,96,124,181],"about":[83],"65":[84],"relative":[85],"that":[87,157],"implied":[88],"residual":[91],"autocorrelation,":[92],"while":[93],"magnitude":[95,180],"ZTD-to-height":[98,183],"leakage":[99,184],"coefficient":[100,185],"reaches":[101],"1.74":[102],"in":[103,108,189,194,206],"static":[104,190,207],"mode":[105,191,208],"1.93":[107],"kinematic":[109,195],"mode.":[110],"To":[111],"handle":[112],"correlation,":[115],"residuals":[118],"modeled":[120],"combination":[123],"diurnal":[126],"cycle,":[127],"daily":[129],"constant":[130,144],"offset,":[131],"time-correlated":[134],"component":[135],"described":[136],"first-order":[139],"Gauss\u2013Markov":[140,148],"process,":[141],"offset":[145],"process":[149],"introduced":[150],"additional":[152],"filter":[153],"states.":[154],"Results":[155],"show":[156],"proposed":[159],"approach":[160],"not":[161],"only":[162],"retains":[163],"convergence":[165],"gain":[166],"over":[167],"unconstrained":[169,204],"solution":[170,205],"also":[172],"substantially":[173,230],"mitigates":[174],"constraint-induced":[176],"shifts.":[178],"The":[179],"decreases":[186,209],"0.08":[188],"0.11":[193],"mode,":[196],"median":[198],"absolute":[199],"difference":[201],"9.4":[211],"0.4":[213],"mm,":[214],"discrepancy":[217],"between":[218],"filter-reported":[220],"formal":[221],"uncertainty":[223],"empirical":[226],"error":[228],"is":[229],"reduced.":[231]},"counts_by_year":[],"updated_date":"2026-11-09T13:22:03.289127","created_date":"2026-11-07T00:00:00"}