Rank defect analysis and the realization of proper singularity in normal equations of geodetic networks

Kotsakis, C.; Chatzinikos, Miltiadis

doi:10.1007/s00190-016-0989-3

Cited by 11 publications

(11 citation statements)

References 20 publications

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“…The matrix condition number is about 10 4 , which indicates that the NEQ matrix is invertible, and there is no rank deficiency in the original NEQ. There is an apparent gap between the 3rd and 4th eigenvalues, and according to Kotsakis and Chatzinikos (2017) [13], the smallest three eigenvalues largely reflect the weak frame origin information in the NEQ, which can also be revealed in the geometrical assessment.…”

Section: Diagnosing Rank-deficient Problems Of the Original Neqmentioning

confidence: 99%

“…Kotsakis and Chatzinikos (2017) employed several indices and patterns to infer the datum contents of the NEQ, including the eigenvalues, the reference system effects, the geometrical assessment, the spectral assessment, and the "network distortions" [13]. To diagnose the rank-deficient problems of the original NEQ from the CMONOC network, we choose to test three items-the eigenvalue analysis, the geometrical assessment, and the network distortion-for one general NEQ on 2014101.…”

Section: Diagnosing Rank-deficient Problems and Cdr Filtering Of The mentioning

confidence: 99%

“…The geometrical assessment is implemented by multiplying the NEQ matrix N with the so-called similarity transformation matrix G T (see Equation (2) in Kotsakis and Chatzinikos (2017) [13]), which represents the orthogonality level between those two matrices, and further reflects the strength of the contained datum-related contents in the NEQ [35]. For more elaborate descriptions and details of the geometrical assessment, refer to Kotsakis and Chatzinikos (2017) [13].…”

Section: Diagnosing Rank-deficient Problems Of the Original Neqmentioning

confidence: 99%

“…For more elaborate descriptions and details of the geometrical assessment, refer to Kotsakis and Chatzinikos (2017) [13]. In Figure 2b, we present the cosine angles between the NEQ and the seven datum-related parameters, namely, three origin-related, three orientation-related, and one scale-related factors.…”

Section: Diagnosing Rank-deficient Problems Of the Original Neqmentioning

confidence: 99%

“…The closer the cosine angles are to zero, the less information is contained in the NEQ for the corresponding datum parameters. As shown in Figure 2b, the frame-origin-related parts show smaller values at (−0.005, 0.005) than do the orientation-and As regards the influence of the redundant datum contents contained in the original NEQ on the obtained solution of station positions, Kotsakis and Chatzinikos (2017) [13] have proposed the so-called "network distortion" to quantitatively assess the effects. The network distortion is defined by the differences between the "free network" solution (note that here the free network solution is the direct inversion of the free NEQ matrix N in Equation (2)) and the "minimally constrained solution" (the solution with MC conditions imposed to the free NEQ matrix N in Equation (3)).…”

Section: Diagnosing Rank-deficient Problems Of the Original Neqmentioning

confidence: 99%

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A Study of Rank Defect and Network Effect in Processing the CMONOC Network on Bernese

Meng

2018

Remote Sensing

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High-precision GPS data processing on Bernese has been employed to routinely resolve daily position solutions of GPS stations in the Crustal Movement Observation Network of China (CMONOC). The rank-deficient problems of the normal equation (NEQ) system and the network effect on the frame alignment of NEQs in the processing of CMONOC data on Bernese still present difficulties. In this study, we diagnose the rank-deficient problems of the original NEQ, review the efficiency of the controlled datum removal (CDR) method in filtering out the three frame-origin-related datum contents, investigate the reliabilities of the inherited frame orientation and scale information from the fixation of the GPS satellite orbits and the Earth rotation parameters in establishing the NEQ of the CMONOC network on Bernese, and analyze the impact of the network effect on the position time series of GPS stations. Our results confirm the nonsingularity of the original NEQ and the efficiency of the CDR filtering in resolving the rank-deficient problems; show that the frame origin parameters are weakly defined and should be stripped off, while the frame orientation and scale parameters should be retained due to their insufficient redefinition from the minimal constraint (MC) implementation through inhomogeneous and asymmetrical fiducial networks; and reveal the superiority of a globally distributed fiducial network for frame alignment of the reconstructed NEQs via No-Net-Translation (NNT) MC conditions. Finally, we attribute the two apparent discontinuities in the position time series to the terrestrial reference frame (TRF) conversions of the GPS satellite orbits, and identify it as the orbit TRF effect.

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Section: Diagnosing Rank-deficient Problems Of the Original Neqmentioning

confidence: 99%

Section: Diagnosing Rank-deficient Problems and Cdr Filtering Of The mentioning

confidence: 99%

Section: Diagnosing Rank-deficient Problems Of the Original Neqmentioning

confidence: 99%

Section: Diagnosing Rank-deficient Problems Of the Original Neqmentioning

confidence: 99%

Section: Diagnosing Rank-deficient Problems Of the Original Neqmentioning

confidence: 99%

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A Study of Rank Defect and Network Effect in Processing the CMONOC Network on Bernese

Meng

2018

Remote Sensing

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Alternative Strategies for the Optimal Combination of GNSS and Classical Geodetic Networks: A Case-Study in Greece

Ampatzidis,

Tzanou,

Demirtzoglou

et al. 2023

International Association of Geodesy Symposia

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The present study discusses two alternative strategies for the optimal combination of different geodetic reference frames in a rigorous way. The methodological variations stem from the (un)availability and types of the 3D network observables. The alternative strategies are tested in Drama region, Northern Greece, where two local networks were established; a 3D one expressed in ITRF2008 (a modern GNSS network established for precise surveying) and a classical one which refers to the official Greek Geodetic Reference System, the Hellenic Geodetic Reference System of 1987. The concept of the proposed strategy is based on the rigorous combination of the different networks at the Normal Equation (NEQ) level. The zenith angles play crucial role for the implementation of the alternative strategies, especially for the correct use of the vertical information. The results of the case study show that the combined solutions provide generally a good level of consistency with the individual networks (GNSS and conventional land surveying).

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Terrestrial Datum Definition Methods in VLBI Global Solutions

Kern,

Krásná,

Nothnagel

et al. 2024

International Association of Geodesy Symposia

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A geodetic datum describes the origin, orientation and scale of a station network, typically with respect to a reference frame. In the analysis process of Very Long Baseline Interferometry (VLBI) observations, the introduction of a geodetic datum is inevitable for the determination of precise reference frames and Earth orientation parameters (EOP). In general, several methods of datum definition exist within the VLBI community, including Helmert rendering and the no-net-translation/no-net-rotation (NNT/NNR) approach. While the first introduces conditions with quasi-infinite weight, the NNT/NNR method can be controlled by the selection of formal errors. Evaluations of the CONT17 legacy-1 campaign and a longer time series of IVS 24-hour sessions show that the variance information (formal errors) of the estimated terrestrial reference frames based on the different methods can differ in the mm to almost cm range. Neglecting this issue could lead to potential issues when combining or comparing solutions from different analysis centers.

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Rank defect analysis and the realization of proper singularity in normal equations of geodetic networks

Cited by 11 publications

References 20 publications

A Study of Rank Defect and Network Effect in Processing the CMONOC Network on Bernese

A Study of Rank Defect and Network Effect in Processing the CMONOC Network on Bernese

Alternative Strategies for the Optimal Combination of GNSS and Classical Geodetic Networks: A Case-Study in Greece

Terrestrial Datum Definition Methods in VLBI Global Solutions

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