M-estimator for the 3D symmetric Helmert coordinate transformation View Full Text


Ontology type: schema:ScholarlyArticle     


Article Info

DATE

2018-01

AUTHORS

Guobin Chang, Tianhe Xu, Qianxin Wang

ABSTRACT

The M-estimator for the 3D symmetric Helmert coordinate transformation problem is developed. Small-angle rotation assumption is abandoned. The direction cosine matrix or the quaternion is used to represent the rotation. The 3×1 multiplicative error vector is defined to represent the rotation estimation error. An analytical solution can be employed to provide the initial approximate for iteration, if the outliers are not large. The iteration is carried out using the iterative reweighted least-squares scheme. In each iteration after the first one, the measurement equation is linearized using the available parameter estimates, the reweighting matrix is constructed using the residuals obtained in the previous iteration, and then the parameter estimates with their variance-covariance matrix are calculated. The influence functions of a single pseudo-measurement on the least-squares estimator and on the M-estimator are derived to theoretically show the robustness. In the solution process, the parameter is rescaled in order to improve the numerical stability. Monte Carlo experiments are conducted to check the developed method. Different cases to investigate whether the assumed stochastic model is correct are considered. The results with the simulated data slightly deviating from the true model are used to show the developed method’s statistical efficacy at the assumed stochastic model, its robustness against the deviations from the assumed stochastic model, and the validity of the estimated variance-covariance matrix no matter whether the assumed stochastic model is correct or not. More... »

PAGES

47-58

References to SciGraph publications

  • 2008-07. On weighted total least-squares adjustment for linear regression in JOURNAL OF GEODESY
  • 2014. Geodesy, Introduction to Geodetic Datum and Geodetic Systems in NONE
  • 2008-06. On the multivariate total least-squares approach to empirical coordinate transformations. Three algorithms in JOURNAL OF GEODESY
  • 2005-06. Sign-constrained robust least squares, subjective breakdown point and the effect of weights of observations on robustness in JOURNAL OF GEODESY
  • 2011-12. Horizontal crustal movement in China fitted by adaptive collocation with embedded Euler vector in SCIENCE CHINA EARTH SCIENCES
  • 2015-05. M-estimator-based robust Kalman filter for systems with process modeling errors and rank deficient measurement models in NONLINEAR DYNAMICS
  • 2017-04. On rotation of frames and physical vectors: an exercise based on plate tectonics theory in GPS SOLUTIONS
  • 2002-07. Robust estimator for correlated observations based on bifactor equivalent weights in JOURNAL OF GEODESY
  • 2010-12. Generalization of total least-squares on example of unweighted and weighted 2D similarity transformation in JOURNAL OF GEODESY
  • 2003-05. Nonlinear analysis of the three-dimensional datum transformation [conformal group ℂ7(3)] in JOURNAL OF GEODESY
  • 2014-12. Transformation model selection by multiple hypotheses testing in JOURNAL OF GEODESY
  • 1989-09. On robust estimation with correlated observations in BULLETIN GÉODÉSIQUE (1946-1975)
  • 1988-03. The non-linear 2D symmetric helmert transformation : An exact non-linear least-squares solution in JOURNAL OF GEODESY
  • 2013-08. Weighted total least squares: necessary and sufficient conditions, fixed and random parameters in JOURNAL OF GEODESY
  • 2015-06. On least-squares solution to 3D similarity transformation problem under Gauss–Helmert model in JOURNAL OF GEODESY
  • 2006-08. A Quaternion-based Geodetic Datum Transformation Algorithm in JOURNAL OF GEODESY
  • 2014-08. Variance components in errors-in-variables models: estimability, stability and bias analysis in JOURNAL OF GEODESY
  • 1999-06. Robust estimation of geodetic datum transformation in JOURNAL OF GEODESY
  • 2009-08. Adaptive filtering for deformation parameter estimation in consideration of geometrical measurements and geophysical models in SCIENCE IN CHINA SERIES D EARTH SCIENCES
  • 2013-07. The effect of incorrect weights on estimating the variance of unit weight in STUDIA GEOPHYSICA ET GEODAETICA
  • 2012-08. Total least squares adjustment in partial errors-in-variables models: algorithm and statistical analysis in JOURNAL OF GEODESY
  • 2013-07. Adjustment of geodetic measurements with mixed multiplicative and additive random errors in JOURNAL OF GEODESY
  • Journal

    TITLE

    Journal of Geodesy

    ISSUE

    1

    VOLUME

    92

    Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/s00190-017-1043-9

    DOI

    http://dx.doi.org/10.1007/s00190-017-1043-9

    DIMENSIONS

    https://app.dimensions.ai/details/publication/pub.1086103727


    Indexing Status Check whether this publication has been indexed by Scopus and Web Of Science using the SN Indexing Status Tool
    Incoming Citations Browse incoming citations for this publication using opencitations.net

    JSON-LD is the canonical representation for SciGraph data.

    TIP: You can open this SciGraph record using an external JSON-LD service: JSON-LD Playground Google SDTT

    [
      {
        "@context": "https://springernature.github.io/scigraph/jsonld/sgcontext.json", 
        "about": [
          {
            "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/0104", 
            "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
            "name": "Statistics", 
            "type": "DefinedTerm"
          }, 
          {
            "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/01", 
            "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
            "name": "Mathematical Sciences", 
            "type": "DefinedTerm"
          }
        ], 
        "author": [
          {
            "affiliation": {
              "alternateName": "Chinese Academy of Surveying and Mapping", 
              "id": "https://www.grid.ac/institutes/grid.464302.7", 
              "name": [
                "School of Environmental Science and Spatial Informatics, China University of Mining and Technology, 221116, Xuzhou, China", 
                "State Key Laboratory of Geo-information Engineering, Xi\u2019an Research Institute of Surveying and Mapping, 710054, Xi\u2019an, China"
              ], 
              "type": "Organization"
            }, 
            "familyName": "Chang", 
            "givenName": "Guobin", 
            "id": "sg:person.013156413714.88", 
            "sameAs": [
              "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.013156413714.88"
            ], 
            "type": "Person"
          }, 
          {
            "affiliation": {
              "alternateName": "Chinese Academy of Surveying and Mapping", 
              "id": "https://www.grid.ac/institutes/grid.464302.7", 
              "name": [
                "Institute of Space Science, Shandong University, 264209, Weihai, China", 
                "State Key Laboratory of Geo-information Engineering, Xi\u2019an Research Institute of Surveying and Mapping, 710054, Xi\u2019an, China"
              ], 
              "type": "Organization"
            }, 
            "familyName": "Xu", 
            "givenName": "Tianhe", 
            "id": "sg:person.015636155053.81", 
            "sameAs": [
              "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.015636155053.81"
            ], 
            "type": "Person"
          }, 
          {
            "affiliation": {
              "alternateName": "Chinese Academy of Surveying and Mapping", 
              "id": "https://www.grid.ac/institutes/grid.464302.7", 
              "name": [
                "School of Environmental Science and Spatial Informatics, China University of Mining and Technology, 221116, Xuzhou, China", 
                "State Key Laboratory of Geo-information Engineering, Xi\u2019an Research Institute of Surveying and Mapping, 710054, Xi\u2019an, China"
              ], 
              "type": "Organization"
            }, 
            "familyName": "Wang", 
            "givenName": "Qianxin", 
            "id": "sg:person.015677045675.89", 
            "sameAs": [
              "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.015677045675.89"
            ], 
            "type": "Person"
          }
        ], 
        "citation": [
          {
            "id": "https://doi.org/10.1016/j.laa.2006.03.044", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1003019371"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/s10291-016-0521-5", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1003024270", 
              "https://doi.org/10.1007/s10291-016-0521-5"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1046/j.1365-246x.1999.00807.x", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1003191976"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/s00190-013-0635-2", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1006083530", 
              "https://doi.org/10.1007/s00190-013-0635-2"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1111/j.1365-246x.1996.tb04053.x", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1007875300"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1111/j.1365-246x.1996.tb04053.x", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1007875300"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/s11200-012-0665-x", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1009027983", 
              "https://doi.org/10.1007/s11200-012-0665-x"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/s11430-011-4286-y", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1009812204", 
              "https://doi.org/10.1007/s11430-011-4286-y"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/s00190-012-0552-9", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1012023773", 
              "https://doi.org/10.1007/s00190-012-0552-9"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/s00190-007-0186-5", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1013910509", 
              "https://doi.org/10.1007/s00190-007-0186-5"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/s00190-007-0186-5", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1013910509", 
              "https://doi.org/10.1007/s00190-007-0186-5"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/s001900050243", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1018914540", 
              "https://doi.org/10.1007/s001900050243"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/s00190-002-0256-7", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1019267106", 
              "https://doi.org/10.1007/s00190-002-0256-7"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/s00190-006-0054-8", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1025657261", 
              "https://doi.org/10.1007/s00190-006-0054-8"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/s00190-006-0054-8", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1025657261", 
              "https://doi.org/10.1007/s00190-006-0054-8"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/j.cam.2015.03.006", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1028573652"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bf02519322", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1034537520", 
              "https://doi.org/10.1007/bf02519322"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/s00190-005-0454-1", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1034554052", 
              "https://doi.org/10.1007/s00190-005-0454-1"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/s11071-015-1953-0", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1036290454", 
              "https://doi.org/10.1007/s11071-015-1953-0"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/s00190-007-0190-9", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1037161997", 
              "https://doi.org/10.1007/s00190-007-0190-9"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/s00190-007-0190-9", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1037161997", 
              "https://doi.org/10.1007/s00190-007-0190-9"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/s00190-002-0299-9", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1039556356", 
              "https://doi.org/10.1007/s00190-002-0299-9"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/s00190-015-0799-z", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1041203560", 
              "https://doi.org/10.1007/s00190-015-0799-z"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/s00190-013-0643-2", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1041532147", 
              "https://doi.org/10.1007/s00190-013-0643-2"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.3390/s140101249", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1042701781"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bf02520474", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1043611342", 
              "https://doi.org/10.1007/bf02520474"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1590/s1982-21702014000300035", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1044086004"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/s00190-014-0747-3", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1044488056", 
              "https://doi.org/10.1007/s00190-014-0747-3"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/s11430-009-0095-y", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1045119830", 
              "https://doi.org/10.1007/s11430-009-0095-y"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/s11430-009-0095-y", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1045119830", 
              "https://doi.org/10.1007/s11430-009-0095-y"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/s00190-014-0717-9", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1048589533", 
              "https://doi.org/10.1007/s00190-014-0717-9"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://app.dimensions.ai/details/publication/pub.1049138916", 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/978-3-642-41245-5", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1049138916", 
              "https://doi.org/10.1007/978-3-642-41245-5"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/978-3-642-41245-5", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1049138916", 
              "https://doi.org/10.1007/978-3-642-41245-5"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/j.laa.2009.09.014", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1050901475"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/s00190-010-0408-0", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1051305984", 
              "https://doi.org/10.1007/s00190-010-0408-0"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/s00190-010-0408-0", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1051305984", 
              "https://doi.org/10.1007/s00190-010-0408-0"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1061/(asce)0733-9453(2005)131:2(43)", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1057602208"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1061/(asce)su.1943-5428.0000112", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1057643478"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1061/(asce)su.1943-5428.0000154", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1057643520"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1080/00396265.2016.1234806", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1058283229"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1080/03610927708827533", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1058331936"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1214/aoms/1177703732", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1064400228"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1214/aos/1176344610", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1064407497"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/j.asr.2017.02.034", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1084060201"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1002/9780470434697", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1098662402"
            ], 
            "type": "CreativeWork"
          }
        ], 
        "datePublished": "2018-01", 
        "datePublishedReg": "2018-01-01", 
        "description": "The M-estimator for the 3D symmetric Helmert coordinate transformation problem is developed. Small-angle rotation assumption is abandoned. The direction cosine matrix or the quaternion is used to represent the rotation. The 3\u00d71 multiplicative error vector is defined to represent the rotation estimation error. An analytical solution can be employed to provide the initial approximate for iteration, if the outliers are not large. The iteration is carried out using the iterative reweighted least-squares scheme. In each iteration after the first one, the measurement equation is linearized using the available parameter estimates, the reweighting matrix is constructed using the residuals obtained in the previous iteration, and then the parameter estimates with their variance-covariance matrix are calculated. The influence functions of a single pseudo-measurement on the least-squares estimator and on the M-estimator are derived to theoretically show the robustness. In the solution process, the parameter is rescaled in order to improve the numerical stability. Monte Carlo experiments are conducted to check the developed method. Different cases to investigate whether the assumed stochastic model is correct are considered. The results with the simulated data slightly deviating from the true model are used to show the developed method\u2019s statistical efficacy at the assumed stochastic model, its robustness against the deviations from the assumed stochastic model, and the validity of the estimated variance-covariance matrix no matter whether the assumed stochastic model is correct or not.", 
        "genre": "research_article", 
        "id": "sg:pub.10.1007/s00190-017-1043-9", 
        "inLanguage": [
          "en"
        ], 
        "isAccessibleForFree": false, 
        "isPartOf": [
          {
            "id": "sg:journal.1052480", 
            "issn": [
              "0949-7714", 
              "1432-1394"
            ], 
            "name": "Journal of Geodesy", 
            "type": "Periodical"
          }, 
          {
            "issueNumber": "1", 
            "type": "PublicationIssue"
          }, 
          {
            "type": "PublicationVolume", 
            "volumeNumber": "92"
          }
        ], 
        "name": "M-estimator for the 3D symmetric Helmert coordinate transformation", 
        "pagination": "47-58", 
        "productId": [
          {
            "name": "readcube_id", 
            "type": "PropertyValue", 
            "value": [
              "7635be2f1754c4aa178cde319d508e5d52e4ae729810f860b9fea4ab1e60c012"
            ]
          }, 
          {
            "name": "doi", 
            "type": "PropertyValue", 
            "value": [
              "10.1007/s00190-017-1043-9"
            ]
          }, 
          {
            "name": "dimensions_id", 
            "type": "PropertyValue", 
            "value": [
              "pub.1086103727"
            ]
          }
        ], 
        "sameAs": [
          "https://doi.org/10.1007/s00190-017-1043-9", 
          "https://app.dimensions.ai/details/publication/pub.1086103727"
        ], 
        "sdDataset": "articles", 
        "sdDatePublished": "2019-04-11T10:01", 
        "sdLicense": "https://scigraph.springernature.com/explorer/license/", 
        "sdPublisher": {
          "name": "Springer Nature - SN SciGraph project", 
          "type": "Organization"
        }, 
        "sdSource": "s3://com-uberresearch-data-dimensions-target-20181106-alternative/cleanup/v134/2549eaecd7973599484d7c17b260dba0a4ecb94b/merge/v9/a6c9fde33151104705d4d7ff012ea9563521a3ce/jats-lookup/v90/0000000347_0000000347/records_89819_00000003.jsonl", 
        "type": "ScholarlyArticle", 
        "url": "https://link.springer.com/10.1007%2Fs00190-017-1043-9"
      }
    ]
     

    Download the RDF metadata as:  json-ld nt turtle xml License info

    HOW TO GET THIS DATA PROGRAMMATICALLY:

    JSON-LD is a popular format for linked data which is fully compatible with JSON.

    curl -H 'Accept: application/ld+json' 'https://scigraph.springernature.com/pub.10.1007/s00190-017-1043-9'

    N-Triples is a line-based linked data format ideal for batch operations.

    curl -H 'Accept: application/n-triples' 'https://scigraph.springernature.com/pub.10.1007/s00190-017-1043-9'

    Turtle is a human-readable linked data format.

    curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1007/s00190-017-1043-9'

    RDF/XML is a standard XML format for linked data.

    curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1007/s00190-017-1043-9'


     

    This table displays all metadata directly associated to this object as RDF triples.

    215 TRIPLES      21 PREDICATES      66 URIs      19 LITERALS      7 BLANK NODES

    Subject Predicate Object
    1 sg:pub.10.1007/s00190-017-1043-9 schema:about anzsrc-for:01
    2 anzsrc-for:0104
    3 schema:author N25f55d83f0df424d926e2f6a2d1b7bfd
    4 schema:citation sg:pub.10.1007/978-3-642-41245-5
    5 sg:pub.10.1007/bf02519322
    6 sg:pub.10.1007/bf02520474
    7 sg:pub.10.1007/s00190-002-0256-7
    8 sg:pub.10.1007/s00190-002-0299-9
    9 sg:pub.10.1007/s00190-005-0454-1
    10 sg:pub.10.1007/s00190-006-0054-8
    11 sg:pub.10.1007/s00190-007-0186-5
    12 sg:pub.10.1007/s00190-007-0190-9
    13 sg:pub.10.1007/s00190-010-0408-0
    14 sg:pub.10.1007/s00190-012-0552-9
    15 sg:pub.10.1007/s00190-013-0635-2
    16 sg:pub.10.1007/s00190-013-0643-2
    17 sg:pub.10.1007/s00190-014-0717-9
    18 sg:pub.10.1007/s00190-014-0747-3
    19 sg:pub.10.1007/s00190-015-0799-z
    20 sg:pub.10.1007/s001900050243
    21 sg:pub.10.1007/s10291-016-0521-5
    22 sg:pub.10.1007/s11071-015-1953-0
    23 sg:pub.10.1007/s11200-012-0665-x
    24 sg:pub.10.1007/s11430-009-0095-y
    25 sg:pub.10.1007/s11430-011-4286-y
    26 https://app.dimensions.ai/details/publication/pub.1049138916
    27 https://doi.org/10.1002/9780470434697
    28 https://doi.org/10.1016/j.asr.2017.02.034
    29 https://doi.org/10.1016/j.cam.2015.03.006
    30 https://doi.org/10.1016/j.laa.2006.03.044
    31 https://doi.org/10.1016/j.laa.2009.09.014
    32 https://doi.org/10.1046/j.1365-246x.1999.00807.x
    33 https://doi.org/10.1061/(asce)0733-9453(2005)131:2(43)
    34 https://doi.org/10.1061/(asce)su.1943-5428.0000112
    35 https://doi.org/10.1061/(asce)su.1943-5428.0000154
    36 https://doi.org/10.1080/00396265.2016.1234806
    37 https://doi.org/10.1080/03610927708827533
    38 https://doi.org/10.1111/j.1365-246x.1996.tb04053.x
    39 https://doi.org/10.1214/aoms/1177703732
    40 https://doi.org/10.1214/aos/1176344610
    41 https://doi.org/10.1590/s1982-21702014000300035
    42 https://doi.org/10.3390/s140101249
    43 schema:datePublished 2018-01
    44 schema:datePublishedReg 2018-01-01
    45 schema:description The M-estimator for the 3D symmetric Helmert coordinate transformation problem is developed. Small-angle rotation assumption is abandoned. The direction cosine matrix or the quaternion is used to represent the rotation. The 3×1 multiplicative error vector is defined to represent the rotation estimation error. An analytical solution can be employed to provide the initial approximate for iteration, if the outliers are not large. The iteration is carried out using the iterative reweighted least-squares scheme. In each iteration after the first one, the measurement equation is linearized using the available parameter estimates, the reweighting matrix is constructed using the residuals obtained in the previous iteration, and then the parameter estimates with their variance-covariance matrix are calculated. The influence functions of a single pseudo-measurement on the least-squares estimator and on the M-estimator are derived to theoretically show the robustness. In the solution process, the parameter is rescaled in order to improve the numerical stability. Monte Carlo experiments are conducted to check the developed method. Different cases to investigate whether the assumed stochastic model is correct are considered. The results with the simulated data slightly deviating from the true model are used to show the developed method’s statistical efficacy at the assumed stochastic model, its robustness against the deviations from the assumed stochastic model, and the validity of the estimated variance-covariance matrix no matter whether the assumed stochastic model is correct or not.
    46 schema:genre research_article
    47 schema:inLanguage en
    48 schema:isAccessibleForFree false
    49 schema:isPartOf N7635edf2641547a19edcef086d015c38
    50 Nfe98c303ba1149ac856649b085070303
    51 sg:journal.1052480
    52 schema:name M-estimator for the 3D symmetric Helmert coordinate transformation
    53 schema:pagination 47-58
    54 schema:productId N29f1ba26a1b3485da9783f45b28f348a
    55 N49c895f48adc4e9e9736bc0d94e0e12b
    56 N7582ed39681348a19c0b37b34f2257e8
    57 schema:sameAs https://app.dimensions.ai/details/publication/pub.1086103727
    58 https://doi.org/10.1007/s00190-017-1043-9
    59 schema:sdDatePublished 2019-04-11T10:01
    60 schema:sdLicense https://scigraph.springernature.com/explorer/license/
    61 schema:sdPublisher Nd2eb5427e2f8471885ec3721dae36760
    62 schema:url https://link.springer.com/10.1007%2Fs00190-017-1043-9
    63 sgo:license sg:explorer/license/
    64 sgo:sdDataset articles
    65 rdf:type schema:ScholarlyArticle
    66 N25f55d83f0df424d926e2f6a2d1b7bfd rdf:first sg:person.013156413714.88
    67 rdf:rest N4aaa8f74c7a64da7a38f40eafb34ee8c
    68 N29f1ba26a1b3485da9783f45b28f348a schema:name readcube_id
    69 schema:value 7635be2f1754c4aa178cde319d508e5d52e4ae729810f860b9fea4ab1e60c012
    70 rdf:type schema:PropertyValue
    71 N2ddcef6e91fa43fcb07edaf9ffdc6784 rdf:first sg:person.015677045675.89
    72 rdf:rest rdf:nil
    73 N49c895f48adc4e9e9736bc0d94e0e12b schema:name doi
    74 schema:value 10.1007/s00190-017-1043-9
    75 rdf:type schema:PropertyValue
    76 N4aaa8f74c7a64da7a38f40eafb34ee8c rdf:first sg:person.015636155053.81
    77 rdf:rest N2ddcef6e91fa43fcb07edaf9ffdc6784
    78 N7582ed39681348a19c0b37b34f2257e8 schema:name dimensions_id
    79 schema:value pub.1086103727
    80 rdf:type schema:PropertyValue
    81 N7635edf2641547a19edcef086d015c38 schema:volumeNumber 92
    82 rdf:type schema:PublicationVolume
    83 Nd2eb5427e2f8471885ec3721dae36760 schema:name Springer Nature - SN SciGraph project
    84 rdf:type schema:Organization
    85 Nfe98c303ba1149ac856649b085070303 schema:issueNumber 1
    86 rdf:type schema:PublicationIssue
    87 anzsrc-for:01 schema:inDefinedTermSet anzsrc-for:
    88 schema:name Mathematical Sciences
    89 rdf:type schema:DefinedTerm
    90 anzsrc-for:0104 schema:inDefinedTermSet anzsrc-for:
    91 schema:name Statistics
    92 rdf:type schema:DefinedTerm
    93 sg:journal.1052480 schema:issn 0949-7714
    94 1432-1394
    95 schema:name Journal of Geodesy
    96 rdf:type schema:Periodical
    97 sg:person.013156413714.88 schema:affiliation https://www.grid.ac/institutes/grid.464302.7
    98 schema:familyName Chang
    99 schema:givenName Guobin
    100 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.013156413714.88
    101 rdf:type schema:Person
    102 sg:person.015636155053.81 schema:affiliation https://www.grid.ac/institutes/grid.464302.7
    103 schema:familyName Xu
    104 schema:givenName Tianhe
    105 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.015636155053.81
    106 rdf:type schema:Person
    107 sg:person.015677045675.89 schema:affiliation https://www.grid.ac/institutes/grid.464302.7
    108 schema:familyName Wang
    109 schema:givenName Qianxin
    110 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.015677045675.89
    111 rdf:type schema:Person
    112 sg:pub.10.1007/978-3-642-41245-5 schema:sameAs https://app.dimensions.ai/details/publication/pub.1049138916
    113 https://doi.org/10.1007/978-3-642-41245-5
    114 rdf:type schema:CreativeWork
    115 sg:pub.10.1007/bf02519322 schema:sameAs https://app.dimensions.ai/details/publication/pub.1034537520
    116 https://doi.org/10.1007/bf02519322
    117 rdf:type schema:CreativeWork
    118 sg:pub.10.1007/bf02520474 schema:sameAs https://app.dimensions.ai/details/publication/pub.1043611342
    119 https://doi.org/10.1007/bf02520474
    120 rdf:type schema:CreativeWork
    121 sg:pub.10.1007/s00190-002-0256-7 schema:sameAs https://app.dimensions.ai/details/publication/pub.1019267106
    122 https://doi.org/10.1007/s00190-002-0256-7
    123 rdf:type schema:CreativeWork
    124 sg:pub.10.1007/s00190-002-0299-9 schema:sameAs https://app.dimensions.ai/details/publication/pub.1039556356
    125 https://doi.org/10.1007/s00190-002-0299-9
    126 rdf:type schema:CreativeWork
    127 sg:pub.10.1007/s00190-005-0454-1 schema:sameAs https://app.dimensions.ai/details/publication/pub.1034554052
    128 https://doi.org/10.1007/s00190-005-0454-1
    129 rdf:type schema:CreativeWork
    130 sg:pub.10.1007/s00190-006-0054-8 schema:sameAs https://app.dimensions.ai/details/publication/pub.1025657261
    131 https://doi.org/10.1007/s00190-006-0054-8
    132 rdf:type schema:CreativeWork
    133 sg:pub.10.1007/s00190-007-0186-5 schema:sameAs https://app.dimensions.ai/details/publication/pub.1013910509
    134 https://doi.org/10.1007/s00190-007-0186-5
    135 rdf:type schema:CreativeWork
    136 sg:pub.10.1007/s00190-007-0190-9 schema:sameAs https://app.dimensions.ai/details/publication/pub.1037161997
    137 https://doi.org/10.1007/s00190-007-0190-9
    138 rdf:type schema:CreativeWork
    139 sg:pub.10.1007/s00190-010-0408-0 schema:sameAs https://app.dimensions.ai/details/publication/pub.1051305984
    140 https://doi.org/10.1007/s00190-010-0408-0
    141 rdf:type schema:CreativeWork
    142 sg:pub.10.1007/s00190-012-0552-9 schema:sameAs https://app.dimensions.ai/details/publication/pub.1012023773
    143 https://doi.org/10.1007/s00190-012-0552-9
    144 rdf:type schema:CreativeWork
    145 sg:pub.10.1007/s00190-013-0635-2 schema:sameAs https://app.dimensions.ai/details/publication/pub.1006083530
    146 https://doi.org/10.1007/s00190-013-0635-2
    147 rdf:type schema:CreativeWork
    148 sg:pub.10.1007/s00190-013-0643-2 schema:sameAs https://app.dimensions.ai/details/publication/pub.1041532147
    149 https://doi.org/10.1007/s00190-013-0643-2
    150 rdf:type schema:CreativeWork
    151 sg:pub.10.1007/s00190-014-0717-9 schema:sameAs https://app.dimensions.ai/details/publication/pub.1048589533
    152 https://doi.org/10.1007/s00190-014-0717-9
    153 rdf:type schema:CreativeWork
    154 sg:pub.10.1007/s00190-014-0747-3 schema:sameAs https://app.dimensions.ai/details/publication/pub.1044488056
    155 https://doi.org/10.1007/s00190-014-0747-3
    156 rdf:type schema:CreativeWork
    157 sg:pub.10.1007/s00190-015-0799-z schema:sameAs https://app.dimensions.ai/details/publication/pub.1041203560
    158 https://doi.org/10.1007/s00190-015-0799-z
    159 rdf:type schema:CreativeWork
    160 sg:pub.10.1007/s001900050243 schema:sameAs https://app.dimensions.ai/details/publication/pub.1018914540
    161 https://doi.org/10.1007/s001900050243
    162 rdf:type schema:CreativeWork
    163 sg:pub.10.1007/s10291-016-0521-5 schema:sameAs https://app.dimensions.ai/details/publication/pub.1003024270
    164 https://doi.org/10.1007/s10291-016-0521-5
    165 rdf:type schema:CreativeWork
    166 sg:pub.10.1007/s11071-015-1953-0 schema:sameAs https://app.dimensions.ai/details/publication/pub.1036290454
    167 https://doi.org/10.1007/s11071-015-1953-0
    168 rdf:type schema:CreativeWork
    169 sg:pub.10.1007/s11200-012-0665-x schema:sameAs https://app.dimensions.ai/details/publication/pub.1009027983
    170 https://doi.org/10.1007/s11200-012-0665-x
    171 rdf:type schema:CreativeWork
    172 sg:pub.10.1007/s11430-009-0095-y schema:sameAs https://app.dimensions.ai/details/publication/pub.1045119830
    173 https://doi.org/10.1007/s11430-009-0095-y
    174 rdf:type schema:CreativeWork
    175 sg:pub.10.1007/s11430-011-4286-y schema:sameAs https://app.dimensions.ai/details/publication/pub.1009812204
    176 https://doi.org/10.1007/s11430-011-4286-y
    177 rdf:type schema:CreativeWork
    178 https://app.dimensions.ai/details/publication/pub.1049138916 schema:CreativeWork
    179 https://doi.org/10.1002/9780470434697 schema:sameAs https://app.dimensions.ai/details/publication/pub.1098662402
    180 rdf:type schema:CreativeWork
    181 https://doi.org/10.1016/j.asr.2017.02.034 schema:sameAs https://app.dimensions.ai/details/publication/pub.1084060201
    182 rdf:type schema:CreativeWork
    183 https://doi.org/10.1016/j.cam.2015.03.006 schema:sameAs https://app.dimensions.ai/details/publication/pub.1028573652
    184 rdf:type schema:CreativeWork
    185 https://doi.org/10.1016/j.laa.2006.03.044 schema:sameAs https://app.dimensions.ai/details/publication/pub.1003019371
    186 rdf:type schema:CreativeWork
    187 https://doi.org/10.1016/j.laa.2009.09.014 schema:sameAs https://app.dimensions.ai/details/publication/pub.1050901475
    188 rdf:type schema:CreativeWork
    189 https://doi.org/10.1046/j.1365-246x.1999.00807.x schema:sameAs https://app.dimensions.ai/details/publication/pub.1003191976
    190 rdf:type schema:CreativeWork
    191 https://doi.org/10.1061/(asce)0733-9453(2005)131:2(43) schema:sameAs https://app.dimensions.ai/details/publication/pub.1057602208
    192 rdf:type schema:CreativeWork
    193 https://doi.org/10.1061/(asce)su.1943-5428.0000112 schema:sameAs https://app.dimensions.ai/details/publication/pub.1057643478
    194 rdf:type schema:CreativeWork
    195 https://doi.org/10.1061/(asce)su.1943-5428.0000154 schema:sameAs https://app.dimensions.ai/details/publication/pub.1057643520
    196 rdf:type schema:CreativeWork
    197 https://doi.org/10.1080/00396265.2016.1234806 schema:sameAs https://app.dimensions.ai/details/publication/pub.1058283229
    198 rdf:type schema:CreativeWork
    199 https://doi.org/10.1080/03610927708827533 schema:sameAs https://app.dimensions.ai/details/publication/pub.1058331936
    200 rdf:type schema:CreativeWork
    201 https://doi.org/10.1111/j.1365-246x.1996.tb04053.x schema:sameAs https://app.dimensions.ai/details/publication/pub.1007875300
    202 rdf:type schema:CreativeWork
    203 https://doi.org/10.1214/aoms/1177703732 schema:sameAs https://app.dimensions.ai/details/publication/pub.1064400228
    204 rdf:type schema:CreativeWork
    205 https://doi.org/10.1214/aos/1176344610 schema:sameAs https://app.dimensions.ai/details/publication/pub.1064407497
    206 rdf:type schema:CreativeWork
    207 https://doi.org/10.1590/s1982-21702014000300035 schema:sameAs https://app.dimensions.ai/details/publication/pub.1044086004
    208 rdf:type schema:CreativeWork
    209 https://doi.org/10.3390/s140101249 schema:sameAs https://app.dimensions.ai/details/publication/pub.1042701781
    210 rdf:type schema:CreativeWork
    211 https://www.grid.ac/institutes/grid.464302.7 schema:alternateName Chinese Academy of Surveying and Mapping
    212 schema:name Institute of Space Science, Shandong University, 264209, Weihai, China
    213 School of Environmental Science and Spatial Informatics, China University of Mining and Technology, 221116, Xuzhou, China
    214 State Key Laboratory of Geo-information Engineering, Xi’an Research Institute of Surveying and Mapping, 710054, Xi’an, China
    215 rdf:type schema:Organization
     




    Preview window. Press ESC to close (or click here)


    ...