<abstract xmlns="http://www.w3.org/1999/xhtml">

Alignment of an engineering object project in the field is always conducted at the points of the geodetic control network, the coordinates of which are determined on the basis of the results of its elements survey and with connection to the national spatial reference system. The points of the national spatial reference system determined on the basis of previous surveys have specified coordinates with adequate accuracy, which is included in their covariance matrix. The coordinates of the geodetic control network points are determined more accurately than the points of the national spatial reference system and this means that the results of surveys of the geodetic control network have to be adequately incorporated into the coordinates of the reference points. In order to perform this incorporation, it may be assumed that the coordinates of the reference points are random, that is, they have a covariance matrix, which should be used in the process of adjusting the results of the geodetic control network observation. This research paper presents the principles for the estimation of the Gauss-Markov model parameters applied in case of those geodetic control networks in which the coordinates of the reference points have random character. On the basis of the observation equations δ + <bold>AX</bold> = <bold>L</bold> for the geodetic control network and using the weighting matrix <bold>P</bold> and the matrix of conditional covariances (<bold>P</bold>−1 + <bold>AC</bold><italic>X</italic><bold>A</bold><italic>T</italic>) for the observation vector <bold>L</bold>, the parameter vector <bold>X</bold> is estimated in the form of the derived formula 
<inline-formula>
<alternatives>
<inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/j_rgg-2021-0001_ieq_001.png"></inline-graphic>
<math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mover accent="true"><mtext mathvariant="bold">X</mtext><mo>^</mo></mover><mo>=</mo><msup><mrow><mrow><mo>(</mo><mrow><msubsup><mtext mathvariant="bold">C</mtext><mi>X</mi><mrow><mo>−</mo><mn>1</mn></mrow></msubsup><mo>+</mo><msup><mtext mathvariant="bold">A</mtext><mi>T</mi></msup><mtext mathvariant="bold">PA</mtext></mrow><mo>)</mo></mrow></mrow><mrow><mo>−</mo><mn>1</mn></mrow></msup><msup><mtext mathvariant="bold">A</mtext><mi>T</mi></msup><mtext mathvariant="bold">P</mtext><mo>⋅</mo><mtext mathvariant="bold">L</mtext></mrow></math>
<tex-math>{\bf{\hat X}} = {\left( {{\bf{C}}_X^{ - 1} + {{\bf{A}}^T}{\bf{PA}}} \right)^{ - 1}}{{\bf{A}}^T}{\bf{P}} \cdot {\bf{L}}</tex-math>
</alternatives>
</inline-formula>
. The verification of these estimation principles has been illustrated by the example of a fragment of a levelling geodetic control network consisting of three geodetic control points and two reference points of the national spatial reference system.
The novel feature of the proposed solution is the application of covariance matrices of the reference point coordinates to adjust the results of the survey of geodetic control networks and to determine limit standard deviations for the estimated coordinates of geodetic control network points.
</abstract>

Gauss-Markov model with random parameters to adjust results of surveys of geodetic control networks

AHEAD OF PRINT

Volume 117 (2024): Issue 1 (June 2024)

Volume 116 (2023): Issue 1 (December 2023)

Volume 115 (2023): Issue 1 (June 2023)

Volume 114 (2022): Issue 1 (December 2022)

Volume 113 (2022): Issue 1 (June 2022)

Volume 112 (2021): Issue 1 (December 2021)

Volume 111 (2021): Issue 1 (June 2021)

Volume 110 (2020): Issue 1 (December 2020)

Volume 109 (2020): Issue 1 (June 2020)

Volume 108 (2019): Issue 1 (December 2019)

Volume 107 (2019): Issue 1 (June 2019)

Volume 106 (2018): Issue 1 (December 2018)

Volume 105 (2018): Issue 1 (June 2018)

Volume 104 (2017): Issue 1 (December 2017)

Volume 103 (2017): Issue 1 (June 2017)

Volume 102 (2016): Issue 1 (December 2016)

Volume 101 (2016): Issue 1 (June 2016)

Volume 100 (2016): Issue 1 (May 2016)

Volume 99 (2015): Issue 1 (December 2015)

Volume 98 (2015): Issue 1 (July 2015)

Volume 97 (2014): Issue 1 (December 2014)

Volume 96 (2014): Issue 1 (June 2014)

Volume 95 (2013): Issue 1 (December 2013)

Volume 94 (2013): Issue 1 (October 2013)

Reports on Geodesy and Geoinformatics

 Reports on Geodesy and Geoinformatics (formerly Reports on Geodesy) is recognized as a semi-annual scientific journal that has appeared since 1991. The volumes of this journal had been prepared and edited by the staff of the Institute of Geodesy and Geodetic Astronomy until 2008 and then during the reorganization of the Faculty of Geodesy and Cartography between years 2008-2011 the volumes were edited and printed by the scientists of the Department of Geodesy and Geodetic Astronomy of Warsaw University of Technology (WUT). Since 2012 the journal has been edited by the scientific staff of the Faculty of Geodesy and Cartography of WUT.  Each paper submitted for publishing in Reports on Geodesy and Geoinformatics is peer-reviewed. The list of our revisers contains more than 200 scientists both from Poland as well as from other countries. Our revisers are recognized specialists from different branches of geodesy and cartography. In some issues of Reports on Geodesy and Geoinformatics there are presented contents of papers announced at international conferences and such volumes may be recognized as the proceedings from these scientific meetings.  All papers published in Reports on Geodesy and Geoinformatics are available in an open access formula. All of them have been also distributed among over 110 libraries in Poland as well as foreign institutions and are considered to be very well acknowledged by the international geodetic community.  Peer-review. The journal uses single-blind peer review (the authors do not know the reviewers) to avoid bias. See more information &lt;Peer Review&gt;.  Journal policies. The journal provides its’ policies, which include detailed information about submission, editorial and publishing processes and guidelines for authors and reviewers. All parties are being introduced to their rights and responsibilities to ensure smooth and ethical publishing process. See more information &lt;Journal Policies&gt;  Fees and Charges. The journal operates as open access journal, the process is completely free of charges to both authors and readers. All publication fees are covered by Warsaw University of Technology.　  Publication schedule. The journal is semi-annual (2 Issues per year in June and December). All articles are published online under CC BY-NC-ND licence 4.0 within four weeks after acceptance as a continuous publication (Online first) to avoid any delays.　  Copyright. Individual articles are published Open Access under the Creative Commons Licence: CC BY-NC-ND 4.0, which permits non-commercial use, distribute, display and perform only original copies of the work in any medium, provided the original author and source are credited. Authors retain copyright in their articles, but grant RGG the right of the first publication. The journal is copyright RGG © Warsaw University of Technology (WUT), all rights reserved.   Aims and ScopeReports on Geodesy and Geoinformatics in keeping with tradition, is intent on presenting the whole of technological and scientific progress taking place in modern geodesy and cartography, where research and implementation of geoinformatic character play an exceptionally important role in accelerating the development of our discipline. It is for this reason that we have decided to expand the journal’s formula so as to encourage a broader group of scientists and specialists in the realms of geodesy, computer science, cartography, photogrammetry, remote sensing, geography, geology, and related sciences who are developing new methods and technologies of geovisualization and are involved in the modeling of space applying GIS technology to collaborate with us. At the same time, the journal’s profile shall maintain the importance of other theoretical, industrial, and development research in the areas of theoretical geodesy, geodetic astronomy, navigation, and studies on displacements and the classic problems facing geodesic surveying.  Journal PoliciesThe journal provides its’ policies, which include detailed information about submission, editorial and publishing processes and guidelines for authors and reviewers. All parties are being introduced with their rights and responsibilities to ensure smooth and ethical publishing process. Visit following subsections for more details on each policy:    Publication Ethics and Publication Malpractice Statement  Open Access  Privacy Statement   Reports on Geodesy and Geoinformatics (formerly Reports on Geodesy) in keeping with tradition, is intent on presenting the whole of technological and scientific progress taking place in modern geodesy and cartography, where research and implementation of geoinformatic character play an exceptionally important role in accelerating the development of our discipline. It is for this reason that we have decided to expand the journal's formula so as to encourage a broader group of scientists and specialists in the realms of geodesy, computer science, cartography, photogrammetry, remote sensing, geography, geology, and related sciences who are developing new methods and technologies of geovisualization and are involved in the modeling of space applying GIS technology to collaborate with us. At the same time, the journal's profile shall maintain the importance of other theoretical, industrial, and development research in the areas of theoretical geodesy, geodetic astronomy, navigation, and studies on displacements and the classic problems facing geodesic surveying.Internet access to complete articles in an "open access" formula will significantly facilitate use by those who are interested as well as expand the circle of readers.  Archiving  Sciendo archives the contents of this journal in Portico - digital long-term preservation service of scholarly books, journals and collections.  Plagiarism Policy  The editorial board is participating in a growing community of Similarity Check System's users in order to ensure that the content published is original and trustworthy. Similarity Check is a medium that allows for comprehensive manuscripts screening, aimed to eliminate plagiarism and provide a high standard and quality peer-review process. 

Reports on Geodesy and Geoinformatics

Volume 111 (2021): Issue 1 (June 2021)

Original Article

Gauss-Markov model with random parameters to adjust results of surveys of geodetic control networks

Chercher

Tous les volumes et éditions dans cette revue