Skip to main content
Disciplines
Automotive Business IT + Informatics Construction + Real Estate Electrical Engineering + Electronics Energy + Sustainability Insurance + Risk Finance + Banking Management + Leadership Marketing + Sales Mechanical Engineering + Materials
Events
DE
EN
Books
Journals
Topic Page
Marketing
Start single access now
Access for companies
EXTENDED SEARCH
Log in
Top
Measurement Techniques
Published in: Measurement Techniques 6/2018

18-10-2018

Decomposition and Regularization of the Solution of Ill-Posed Inverse Problems in the Processing of Measurement Information. Part 2. Application of Theory to a Practical Problem

Author: Yu. V. Surnin

Published in: Measurement Techniques | Issue 6/2018

Log in

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

Abstract

Application of the theory of double decomposition (physical and canonical) and two-sided regularization (of the left and right sides of a system of linear equations) to the solution of one of the ill-posed inverse problems of space geodesy is considered. The problem is related to transformation of the coordinates of the ground points of local satellite geodetic networks to the state reference frame. A variant of the Helmert decomposed model along with an adaptive algorithm for regularization of the solution of an ill-posed inverse problem are proposed.
previous article Distribution Function for Estimates of Allan Variance: Theory and Practice
next article Application of Optical Microresonators for Measuring the Concentration of Nanoparticles in Liquids

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

inform now
Literature
1.
Yu. V. Surnin, “Decomposition and regularization of the solution of ill-posed inverse problems in the processing of measurement information. Part 1.Theoretical evaluation of the method,” Metrologiya, No. 1, 17–35 (2018).
2.
V. V. Glushkov, K. K. Nasretdinov, and A. A. Sharavin, Space Geodesy: Methods and Future Development, Institute for Political and Military Analysis, Moscow (2002).
3.
V. N. Baranov, E. G. Boiko, I. I. Krasnorylov, et al., Space Geodesy, Nedra, Moscow (1986).
4.
A. P. Gerasimov, Compensation of the State Geodetic Network, Kartgeotsentr-Geodezisdat, Moscow (1996).
5.
A. P. Gerasimov, Satellite Geodetic Networks, Izd. Progress, Moscow (2012).
6.
V. D. Bol’shakov, Yu. I. Markuze, and V. V. Golubev, Compensation of Geodetic Structures: Textbook, Nedra, Moscow (1989).
7.
Yu. V. Surnin, “On the correct applications of the international terminology, Reference Systems and Reference Frames, to the concepts, ‘coordinate system’ and ‘reference frame’ in geodetic use in Russia,” Geodez. Kartograf., No. 8, 2–9 (2015).
8.
T. Soler and J. Marshall, “A note on frame transformation with applications to geodeteic datums,” GPS Solutions, 7, No. 1, 23–32 (2003).CrossRef
9.
A Leick, GPS Satellite Surveying, Wiley-Interscience, New York (1995).
10.
P. E. El’yasberg, Determination of Motion from the Results of Measurements, Nauka, Moscow (1976).
11.
M. S. Molodenskii, V. F. Eremeev, and M. I. Yurkina, “Methods for the study of the external gravitational field and the figure of the Earth,” Tr. TsNIIGAiK, Geodezizdat, Moscow (1961), Iss. 131.
12.
V. S. Pugachev, Probability Theory and Mathematical Statistics, Nauka, Moscow (1979).MATH
13.
Yu. V. Surnin, “Field astrogravitational geodetic standard for metrological tests of geodetic equipment,” Izmer. Tekhn., No. 9, 3–7 (2004).
14.
E. G. Gienko, V. I. Kuz’min, and Yu. V. Surnin, “Certain results of a determination of the gravitational field from a local segment of the Earth’s surface from satellite, astronomical-geodetic, and gravimetric data,” in: GEO-Sibir-2005. Vol. 1. Geodesy, Cartography, Surveying: Proc. Sci. Congress of GEO-Sibir-2005, April 25–29, 2005, SGGA, Novosibirsk (2005), pp. 132–136.
15.
G. Veis, “Geodetic uses of artificial satellites,” Smiths. Contrib. Astrophys., No. 3 (9), 95–161 (1960).ADSCrossRef
16.
S. K. Godunov, A. G. Antonov, O. P. Kirilyuk, and V. I. Kostin, Guaranteed Precision of the Solution of Systems of Linear Equations in Euclidean Spaces., Nauka, Novosibirsk (1992), 2nd ed.MATH
17.
G. E. Forsythe, M. A. Malcolm, and C. R. Moler, Computational Methods for Mathematical Computations, Prentice Hall, Englewood Cliffs, N.Y. (1977).MATH
18.
V. V. Voevodin, Computational Foundations of Linear Algebra, Nauka, Moscow (1977).MATH
19.
Yu. V. Surnin and E. G. Gienko, “A technique for regular estimation of the parameters of mutual transformation of geodetic networks constructed by satellite and traditional methods,” in: Geo-Sibir-2008: Proc. 4th Int. Sci. Congress, SGGA, Novosibirsk (2008), Vol.1, Pt. 1, pp. 262–266.
20.
Yu. V. Surnin, V. A. Ashcheulov, S. V. Kuzhelev, et al., Improvement and Practical Implementation of Dynamic Method of Space Geodesy: Monograph, SGGA, Novosibirsk (2015).
Metadata
Title
Decomposition and Regularization of the Solution of Ill-Posed Inverse Problems in the Processing of Measurement Information. Part 2. Application of Theory to a Practical Problem
Author
Yu. V. Surnin
Publication date
18-10-2018
Publisher
Springer US
Published in
Measurement Techniques / Issue 6/2018
Print ISSN: 0543-1972
Electronic ISSN: 1573-8906
DOI
https://doi.org/10.1007/s11018-018-1465-7

Other articles of this Issue 6/2018

Measurement Techniques 6/2018 Go to the issue

OriginalPaper

Methods for Increasing the Accuracy of Reproducing Specified Values of the Attenuation of Optical Radiation in Fiber-Optic Attenuators

RADIO MEASUREMENTS

Comparative Analysis of the Methods Aimed at the Determination of the Complex Transfer Coefficients of Superhigh-Frequency Mixers

ELECTROMAGNETIC MEASUREMENTS

Microwave Photonic Detector for Measuring Pulsed Electric Field Strengths in the Sub-Nanosecond Region

OriginalPaper

Radar Reflectors for Precision Measurements

OPTOPHYSICAL MEASUREMENTS

A Refraction Method of Measurement of the Rate of Evaporation of a Liquid Droplet Under Conditions of Pinning of a Contact Line

MEDICAL AND BIOLOGICAL MEASUREMENTS

Measuring Transducers Based on Systems with Variable Parameters for Medical and Biological Research