A new relationship between the quality criteria for geodetic networks

Klein, Ivandro; Matsuoka, Marcelo Tomio; Guzatto, Matheus Pereira; Geremia‐Nievinski, Felipe; Veronez, Maurício Roberto; Rofatto, Vinicius Francisco

doi:10.1007/s00190-018-1181-8

Cited by 24 publications

(22 citation statements)

References 46 publications

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“…This hypothesis test-based approach is called the mean-shift model [20]. The mean-shift model has been widely employed in a variety of applications, such as structural deformation analyses, sensor data processing, the integrity monitoring of GNSS (Global Navigation Satellite System) models and the design and quality control of geodetic networks (see, e.g., [1,3,6,8,12,[19][20][21][22]45,51,[57][58][59][60][61]). The alternative to the mean-shift model is variance inflation.…”

Section: Note That the Alternative Hypothesis H (I)mentioning

confidence: 99%

“…The Monte Carlo method provides insights into these cases, in which analytical solutions are too complex to fully understand, are doubted for one reason or another or are not available [12]. The Monte Carlo method for quality control purposes has already been applied in geodesy (see, e.g., [2,10,22,23,33,46,[48][49][50][51]). For in-depth coverage of Monte Carlo methods, consult, for instance, [52][53][54].…”

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A Monte Carlo-Based Outlier Diagnosis Method for Sensitivity Analysis

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An iterative outlier elimination procedure based on hypothesis testing, commonly known as Iterative Data Snooping (IDS) among geodesists, is often used for the quality control of modern measurement systems in geodesy and surveying. The test statistic associated with IDS is the extreme normalised least-squares residual. It is well-known in the literature that critical values (quantile values) of such a test statistic cannot be derived from well-known test distributions but must be computed numerically by means of Monte Carlo. This paper provides the first results on the Monte Carlo-based critical value inserted into different scenarios of correlation between outlier statistics. From the Monte Carlo evaluation, we compute the probabilities of correct identification, missed detection, wrong exclusion, over-identifications and statistical overlap associated with IDS in the presence of a single outlier. On the basis of such probability levels, we obtain the Minimal Detectable Bias (MDB) and Minimal Identifiable Bias (MIB) for cases in which IDS is in play. The MDB and MIB are sensitivity indicators for outlier detection and identification, respectively. The results show that there are circumstances in which the larger the Type I decision error (smaller critical value), the higher the rates of outlier detection but the lower the rates of outlier identification. In such a case, the larger the Type I Error, the larger the ratio between the MIB and MDB. We also highlight that an outlier becomes identifiable when the contributions of the measures to the wrong exclusion rate decline simultaneously. In this case, we verify that the effect of the correlation between outlier statistics on the wrong exclusion rate becomes insignificant for a certain outlier magnitude, which increases the probability of identification.

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confidence: 99%

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A Monte Carlo-Based Outlier Diagnosis Method for Sensitivity Analysis

et al. 2020

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“…Mean-shift model has been widely employed in a variety of applications, such as structural deformation analyses, sensor data processing, the integrity monitoring of GNSS (Global Navigation Satellite System) models and the design and quality control of geodetic networks (see e.g. [1,3,6,8,12,[19][20][21][22]36,43,[49][50][51][52][53]).…”

Section: Note That the Alternative Hypothesis H (I)mentioning

confidence: 99%

“…Monte Carlo method for quality control proposals has already been applied in geodesy (see e.g. [2,10,22,23,37,[39][40][41][42][43]). For an in-depth coverage of Monte Carlo methods consult, for instance, [44][45][46].…”

Section: Introductionmentioning

confidence: 99%

A Monte Carlo-Based Outlier Diagnosis Method for Sensitivity Analysis

Rofatto¹,

Matsuoka²,

Klein³

et al. 2020

Preprint

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An iterative outlier elimination procedure based on hypothesis testing, commonly known as Iterative Data Snooping (IDS) among geodesists, is often used for the quality control of the modern measurement systems in geodesy and surveying. The test statistic associated with IDS is the extreme normalised least-squares residual. It is well-known in the literature that critical values (quantile values) of such a test statistic cannot be derived from well-known test distributions, but must be computed numerically by means of Monte Carlo. This paper provides the first results about Monte Carlo-based critical value inserted to different scenarios of correlation between the outlier statistics. From the Monte Carlo evaluation, we compute the probabilities of correct identification, missed detection, wrong exclusion, overidentifications and statistical overlap associated with IDS in the presence of a single outlier. Based on such probability levels we obtain the Minimal Detectable Bias (MDB) and Minimal Identifiable Bias (MIB) for the case where IDS is in play. MDB and MIB are sensitivity indicators for outlier detection and identification, respectively. The results show that there are circumstances that the larger the Type I decision error (smaller critical value), the higher the rates of outlier detection, but the lower the rates of outlier identification. For that case, the larger the Type I Error, the larger the ratio between MIB and MDB. We also highlight that an outlier becomes identifiable when the contribution of the measures to the wrong exclusion rate decline simultaneously. In that case, we verify that the effect of the correlation between the outlier statistics on the wrong exclusion rates becomes insignificant from a certain outlier magnitude, which increases the probability of identification.

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“…Therefore, hypothesis testing is often employed to check whether the possible shifting of the random error distribution under H 0 by an outlier is, in fact, a systematic effect (bias) or merely a random effect. This hypothesis test-based approach is called the mean-shift model (see, e.g., [18,23,29,46,47,52,54,[57][58][59][60][61][62][63][64][65].…”

Section: Note That the Alternative Hypothesis H (I)mentioning

confidence: 99%

Which Are the Effects of Hard and Soft Equality Constraints on the Iterative Outlier Elimination Procedure?

Rofatto¹,

Matsuoka²,

Klein³

et al. 2020

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In this paper we evaluate the effects of hard and soft constraints on the Iterative Data Snooping (IDS), an iterative outlier elimination procedure. Here, the measurements of a levelling geodetic network were classified according to the local redundancy and maximum absolute correlation between the outlier test statistics, referred to as clusters. We highlight that the larger the relaxation of the constraints, the higher the sensitivity indicators MDB (Minimal Detectable Bias) and MIB (Minimal Identifiable Bias) for both the clustering of measurements and the clustering of constraints. There are circumstances that increase the family-wise error rate (FWE) of the test statistics, increase the performance of the IDS. Under a scenario of soft constraints, one should set out at least three soft constraints in order to identify an outlier in the constraints. In general, hard constraints should be used in the stage of pre-processing data for the purpose of identifying and removing possible outlying measurements. In that process, one should opt to set out the redundant hard constraints. After identifying and removing possible outliers, the soft constraints should be employed to propagate their uncertainties to the model parameters during the process of least-squares estimation.

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A new relationship between the quality criteria for geodetic networks

Cited by 24 publications

References 46 publications

A Monte Carlo-Based Outlier Diagnosis Method for Sensitivity Analysis

A Monte Carlo-Based Outlier Diagnosis Method for Sensitivity Analysis

A Monte Carlo-Based Outlier Diagnosis Method for Sensitivity Analysis

Which Are the Effects of Hard and Soft Equality Constraints on the Iterative Outlier Elimination Procedure?

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