What should be the observation-calculation residuals in modern astrometric experiments?

Dzhun, I. V.

doi:10.3103/s0884591312010096

Cited by 2 publications

(5 citation statements)

References 5 publications

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“…If the systematic errors are carefully eliminated, then the skewness usually achieves the small values. For example, in the case of the astrometric observations within the project MERIT, β 1 = 0.0048 (Dzhun', 2012); for the phase measurements from the SAPOS ® , GNSS observations, β 1 = 0.0121 (Luo et al, 2011). Similar values for GPS observations were also obtained by Tiberius and Borre (2000).…”

Section: Introductionsupporting

confidence: 63%

“…Pearson, 1920;Friori and Zenga, 2009). Kukuča (1967) and Dzhun' (2012) indicated such a reason of asymmetry of the error distributions in the case of geodetic or astronomical observations. If the systematic errors are carefully eliminated, then the skewness usually achieves the small values.…”

Section: Introductionmentioning

confidence: 99%

“…Except for small asymmetry, such a note is consistent with other empirical analyses. For example, Dzhun' (1992Dzhun' ( , 2012 showed that the errors of the astronomic observations have usually the kurtosis β 2 = 3.8 (however, β 2 = 4.858 was obtained during the project MERIT). Similar values of the kurtosis were obtained by Wassef (1959) and (Kukuča 1967) in the precise leveling.…”

Section: Introductionmentioning

confidence: 99%

“…The general properties of the Pearson distributions are discussed by Elderton (1953) or Friori and Zenga (2009). The several selected distributions of that system were applied in astronomy (Dzhun', 1992(Dzhun', , 2012 and in geodesy (Wiśniewski, 1987(Wiśniewski, , 2014.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

MP estimation applied to platykurtic sets of geodetic observations

Wiśniewski¹

2017

Geodesy and Cartography

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M P estimation is a method which concerns estimating of the location parameters when the probabilistic models of observations differ from the normal distributions in the kurtosis or asymmetry. The system of Pearson's distributions is the probabilistic basis for the method. So far, such a method was applied and analyzed mostly for leptokurtic or mesokurtic distributions (Pearson's distributions of types IV or VII), which predominate practical cases. The analyses of geodetic or astronomical observations show that we may also deal with sets which have moderate asymmetry or small negative excess kurtosis. Asymmetry might result from the infl uence of many small systematic errors, which were not eliminated during preprocessing of data. The excess kurtosis can be related with bigger or smaller (in relations to the Hagen hypothesis) frequency of occurrence of the elementary errors which are close to zero. Considering that fact, this paper focuses on the estimation with application of the Pearson platykurtic distributions of types I or II. The paper presents the solution of the corresponding optimization problem and its basic properties. Although platykurtic distributions are rare in practice, it was an interesting issue to fi nd out what results can be provided by M P estimation in the case of such observation distributions. The numerical tests which are presented in the paper are rather limited; however, they allow us to draw some general conclusions.

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Section: Introductionsupporting

confidence: 63%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

MP estimation applied to platykurtic sets of geodetic observations

Wiśniewski¹

2017

Geodesy and Cartography

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“…For example, Dzhun' (1992) showed that every astronomical instrument gives measurement errors with a certain kurtosis, which is mostly close to β 2 = 3.8. In contemporary astrometric experiments the kurtosis is even bigger, for example, within the project MERIT β 2 = 4.858 (Dzhun' 2012). Here, the asymmetry coefficient is equal to β 1 = 0.0048.…”

Section: Introductionmentioning

confidence: 99%

M-estimation with probabilistic models of geodetic observations

Wiśniewski

2014

J Geod

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The paper concerns M-estimation with probabilistic models of geodetic observations that is called M P estimation. The special attention is paid to M P estimation that includes the asymmetry and the excess kurtosis, which are basic anomalies of empiric distributions of errors of geodetic or astrometric observations (in comparison to the Gaussian errors). It is assumed that the influence function of M P estimation is equal to the differential equation that defines the system of the Pearson distributions. The central moments μ k , k = 2, 3, 4, are the parameters of that system and thus, they are also the parameters of the chosen influence function. The M P estimation that includes the Pearson type IV and VII distributions (M PD(l) method) is analyzed in great detail from a theoretical point of view as well as by applying numerical tests. The chosen distributions are leptokurtic with asymmetry which refers to the general characteristic of empirical distributions. Considering M-estimation with probabilistic models, the Gram-Charlier series are also applied to approximate the models in question (M G−C method). The paper shows that M P estimation with the application of probabilistic models belongs to the class of robust estimations; M PD(l) method is especially effective in that case. It is suggested that even in the absence of significant anomalies the method in question should be regarded as robust against gross errors while its robustness is controlled by the pseudo-kurtosis.

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What should be the observation-calculation residuals in modern astrometric experiments?

Cited by 2 publications

References 5 publications

MP estimation applied to platykurtic sets of geodetic observations

MP estimation applied to platykurtic sets of geodetic observations

M-estimation with probabilistic models of geodetic observations

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