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The method of detection and localization of configuration defects in geodetic networks by means of Tikhonov regularization Cover

The method of detection and localization of configuration defects in geodetic networks by means of Tikhonov regularization

By: Roman Kadaj  
Open Access
|Dec 2021

Figures & Tables

Figure 1

Defects in geodetic network: outliers and geometric (datum or configuration) defects.
Defects in geodetic network: outliers and geometric (datum or configuration) defects.

Figure 2

Structure of the R matrix (0 – elements assumed to be zero, X – other elements of the matrix), r – rank of the normal matrix B, u = n–r = defect of the normal matrix.
Structure of the R matrix (0 – elements assumed to be zero, X – other elements of the matrix), r – rank of the normal matrix B, u = n–r = defect of the normal matrix.

Figure 3

A symbolic sketch of an extensive geodetic network in a district in Poland. In the Polish classification, it is a third-class network related to the network of classes I and II. The sketch shows a place in the network where configuration defects have been artificially introduced.
A symbolic sketch of an extensive geodetic network in a district in Poland. In the Polish classification, it is a third-class network related to the network of classes I and II. The sketch shows a place in the network where configuration defects have been artificially introduced.

Figure 4

Localized configuration defects (numerical results in Table 1).
Localized configuration defects (numerical results in Table 1).

Fragment of the result set (coordinates and accuracy parameters) of the network adjustment containing configuration defects using Tikhonov regularization with the parameter = 1/10,000 (assuming a priori standard deviations of the coordinates μx = μy = 100 m)

Point Nox [m]y [m]s [m]a [m]b [m]θ[m]
113510515734128.73137593963.79170.02290.01650.0159114.89
113510525733836.11227593815.79400.03370.02650.0207125.33
113510315734659.96227593795.21900.03380.02890.017547.35
113510305734794.18187593605.84200.05550.05000.024143.80
113510295734961.87977593605.26040.06910.06330.027757.73
113510285735150.90547593600.77690.08830.08200.032969.19
113510275735344.55307593600.107199.999399.99930.050699.78
113510265735593.18987593599.205790.012390.01230.055899.77
113510255735845.27087593593.379143.595243.59520.0460101.09
113510245736163.62107593598.83950.08480.07920.030274.12
113510235736508.71767593598.48210.05690.05120.024955.53
113510225736792.56647593337.16970.02760.02140.017461.38
113511125737672.61617592856.10530.02730.02070.017856.84
113511025737876.89707592817.78280.03040.02320.019649.43
113511015738021.95207592509.61900.03570.02760.022649.04

Fragment of the result set (corresponding to the data in Table 1) without defects and without Tikhonov regularization

Point Nox [m]y [m]s [m]a [m]b [m]θ[m]
113510515734128.73077593963.79360.02090.01530.014320.80
113510525733836.11137593815.79650.03100.02370.0199126.34
113510315734659.96057593795.21310.02630.02080.016253.54
113510305734794.17607593605.82990.03890.03220.021848.54
113510295734961.87667593605.24000.04450.03790.023458.27
113510285735150.90487593600.74380.05000.04310.025466.20
113510275735344.55537593600.10440.05380.04670.026671.41
113510265735593.19557593599.38100.05580.04880.027074.54
113510255735845.26707593593.03630.05450.04770.026374.50
113510245736163.61397593598.84980.04870.04210.024569.68
113510235736508.71377593598.48770.03920.03240.022157.19
113510225736792.56387593337.17180.02300.01660.016087.27
113511125737672.61617592856.10530.02620.01990.017156.84
113511025737876.89707592817.78280.02920.02230.018949.43
113511015738021.95207592509.61900.03430.02650.021749.04
DOI: https://doi.org/10.2478/rgg-2021-0004 | Journal eISSN: 2391-8152 | Journal ISSN: 0867-3179
Language: English
Page range: 19 - 25
Submitted on: Jul 22, 2021
Accepted on: Nov 8, 2021
Published on: Dec 17, 2021
Published by: Warsaw University of Technology
In partnership with: Paradigm Publishing Services
Publication frequency: 2 issues per year

© 2021 Roman Kadaj, published by Warsaw University of Technology
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.