Effects of Hard and Soft Equality Constraints on Reliability Analysis

The reliability analysis allows to estimate the system’s probability of detecting and identifying outlier. Failure to identify an outlier can jeopardise the reliability level of a system. Due to its importance, outliers must be appropriately treated to ensure the normal operation of a system. The system models are usually developed from certain constraints. Constraints play a central role in model precision and validity. In this work, we present a detailed optical investigation of the effects of the hard and soft constraints on the reliability of a measurement system model. Hard constraints represent a case in which there exist known functional relations between the unknown model parameters, whereas the soft constraints are employed for the case where such functional relations can slightly be violated depending on their uncertainty. The results highlighted that the success rate of identifying an outlier for the case of hard constraints is larger than soft constraints. This suggested that hard constraints should be used in the stage of pre-processing data for the purpose of identifying and removing possible outlying measurements. After identifying and removing possible outliers, one should set up the soft constraints to propagate the uncertainties of the constraints during the data processing. This recommendation is valid for outlier detection and identification purpose.

[1]  A. Madansky.  Identification of Outliers , 1988 .

[2]  Peter Teunissen,et al.  Minimal Detectable and Identifiable Biases for quality control , 2019 .

[3]  Xiaomin Luo,et al.  A new parameterized approach for ionospheric tomography , 2019, GPS Solutions.

[4]  W. Baarda,et al.  Statistical concepts in geodesy. , 1967 .

[5]  Jinling Wang,et al.  New Outlier Separability Test and Its Application in GNSS Positioning , 2012 .

[6]  M. E. Muller,et al.  A Note on the Generation of Random Normal Deviates , 1958 .

[7]  A. Dermanis,et al.  The Choice of Reference System in ITRF Formulation , 2012 .

[8]  R. Lehmann.  On the formulation of the alternative hypothesis for geodetic outlier detection , 2013, Journal of Geodesy.

[9]  Karl-Rudolf Koch,et al.  Parameter estimation and hypothesis testing in linear models , 1988 .

[10]  Cüneyt Aydın,et al.  Power of Global Test in Deformation Analysis , 2012 .

[11]  Mengyue Han,et al.  The Application of Robust Least Squares Method in Frequency Lock Loop Fusion for Global Navigation Satellite System Receivers , 2020, Sensors.

[12]  W. Baarda,et al.  A testing procedure for use in geodetic networks. , 1968 .

[13]  Christopher Kotsakis.  Datum Definition and Minimal Constraints , 2018 .

[14]  Ivandro Klein,et al.  A new relationship between the quality criteria for geodetic networks , 2018, Journal of Geodesy.

[15]  Boris Kargoll,et al.  On the theory and application of model misspecification tests in geodesy , 2008 .

[16]  P. Teunissen.  Zero Order Design: Generalized Inverses, Adjustment, the Datum Problem and S-Transformations , 1985 .

[17]  C. Rao.  Markoff's theorem with linear restrictions on parameters , 1945 .

[18]  Comparing Parameter Estimation of Random Coefficient Autoregressive Model by Frequentist Method , 2020 .

[19]  Extending the Application of Grubbs-Type Tests in Rejecting Anomalous Measurements , 2005 .

[20]  G. Livadiotis.  General Fitting Methods Based on Lq Norms and their Optimization , 2020 .

[21]  A. Dermanis.  Free network solutions with the DLT method , 1994 .

[22]  P. J. G. Teunissen,et al.  DIA-datasnooping and identifiability , 2018, Journal of Geodesy.

[23]  Peter Teunissen,et al.  Distributional theory for the DIA method , 2017, Journal of Geodesy.

[24]  Felipe G. Nievinski,et al.  An approach to identify multiple outliers based on sequential likelihood ratio tests , 2017 .

[25]  Hiddo Velsink,et al.  Testing Methods for Adjustment Models with Constraints , 2018, Journal of Surveying Engineering.

[26]  Chris Rizos,et al.  Generalised measures of reliability for multiple outliers , 2010 .

[27]  F. Sansò,et al.  Optimization and design of geodetic networks , 1985 .

[28]  Rüdiger Lehmann,et al.  Improved critical values for extreme normalized and studentized residuals in Gauss–Markov models , 2012, Journal of Geodesy.

[29]  Peter Teunissen,et al.  First and second moments of non-linear least-squares estimators , 1989 .

[30]  P. Xu.  A general solution in geodetic nonlinear rank-defect models , 1997 .

[31]  Thomas Gruber,et al.  Definition and Proposed Realization of the International Height Reference System (IHRS) , 2017, Surveys in Geophysics.

[32]  L. G. D. Silveira,et al.  A Monte Carlo-Based Outlier Diagnosis Method for Sensitivity Analysis , 2020, Remote. Sens..

[33]  Takuji Nishimura,et al.  Mersenne twister: a 623-dimensionally equidistributed uniform pseudo-random number generator , 1998, TOMC.

[34]  Ivandro Klein,et al.  Control Points Selection Based on Maximum External Reliability for Designing Geodetic Networks , 2019, Applied Sciences.

[35]  J. Van Mierlo,et al.  Statistical Analysis of Geodetic Measurements for the Investigation of Crustal Movements , 1979 .

[36]  G. Schmitt,et al.  Optimization of geodetic networks , 1982 .

[37]  F. Neitzel,et al.  Testing the compatibility of constraints for parameters of a geodetic adjustment model , 2013, Journal of Geodesy.

[38]  R. Lehmann,et al.  Congruence analysis of geodetic networks – hypothesis tests versus model selection by information criteria , 2017 .

[39]  Rüdiger Lehmann,et al.  Observation error model selection by information criteria vs. normality testing , 2015, Studia Geophysica et Geodaetica.

[40]  D. U. Sanli,et al.  Detecting Configuration Weaknesses in Geodetic Networks , 2011 .

[41]  A. Sedeek,et al.  Vertical ionospheric delay estimation for single-receiver operation , 2019, Journal of Applied Geodesy.

[42]  Xing Fang,et al.  Weighted total least-squares with constraints: a universal formula for geodetic symmetrical transformations , 2015, Journal of Geodesy.

[43]  Michael Lösler,et al.  Multiple Outlier Detection: Hypothesis Tests versus Model Selection by Information Criteria , 2016 .

[44]  Lingdong Meng,et al.  Performance of Selected Ionospheric Models in Multi-Global Navigation Satellite System Single-Frequency Positioning over China , 2019, Remote. Sens..

[45]  Andreas Wagner,et al.  Using IATS to Read and Analyze Digital Levelling Staffs , 2016 .

[46]  H. van der Marel,et al.  Statistical Testing and Quality Analysis in 3-D Networks (part II) Application to GPS , 1990 .

[47]  Peter Teunissen,et al.  An Integrity and Quality Control Procedure for Use in Multi Sensor Integration , 1990 .

[48]  Alyne Raminelli Siguel Gemin,et al.  APPLICATION OF CALIBRATION CERTIFICATE OF DIGITAL LEVELING SYSTEMS IN THE MONITORING OF STRUCTURES: A CASE STUDY AT THE GOVERNADOR JOSÉ RICHA HYDROELECTRIC POWER PLANT - PR , 2018, Boletim de Ciências Geodésicas.

[49]  João Francisco Galera Monico,et al.  Modeling tropospheric wet delays with dense and sparse network configurations for PPP-RTK , 2016, GPS Solutions.

[50]  Hiddo Velsink,et al.  On the deformation analysis of point fields , 2015, Journal of Geodesy.

[51]  Ling Yang,et al.  Outlier separability analysis with a multiple alternative hypotheses test , 2013, Journal of Geodesy.

[52]  H. Velsink,et al.  Extendable linearised adjustment model for deformation analysis , 2015 .

[53]  H. Velsink.  Testing deformation hypotheses by constraints on a time series of geodetic observations , 2018 .

[54]  Calyampudi R. Rao,et al.  Generalized inverse of a matrix and its applications , 1972 .

[55]  Yidong Lou,et al.  Precise Orbit Determination for GNSS Maneuvering Satellite with the Constraint of a Predicted Clock , 2019, Remote. Sens..

[56]  A. el-Mowafy,et al.  Comparison of advanced troposphere models for aiding reduction of PPP convergence time in Australia , 2019 .

[57]  P. Teunissen.  Testing Theory: an introduction , 2009 .

[58]  Jia He,et al.  Output-Only Parameters Identification of Earthquake-Excited Building Structures with Least Squares and Input Modification Process , 2019, Applied Sciences.

[59]  Pierre Sakic,et al.  A Multi-Observation Least-Squares Inversion for GNSS-Acoustic Seafloor Positioning , 2020, Remote. Sens..

[60]  Q. Gui,et al.  A Bayesian unmasking method for locating multiple gross errors based on posterior probabilities of classification variables , 2011 .

[61]  Xiaodong Yang,et al.  Estimation of Crop Growth Parameters Using UAV-Based Hyperspectral Remote Sensing Data , 2020, Sensors.

[62]  Zhou,et al.  An Improved Autoencoder and Partial Least Squares Regression-Based Extreme Learning Machine Model for Pump Turbine Characteristics , 2019 .

[63]  Ivandro Klein,et al.  A half-century of Baarda’s concept of reliability: a review, new perspectives, and applications , 2018, Survey Review.

[64]  Rdiger Lehmann,et al.  Monte Carlo-based data snooping with application to a geodetic network , 2011 .

[65]  AliReza Amiri-Simkooei,et al.  Weighted Total Least Squares with Singular Covariance Matrices Subject to Weighted and Hard Constraints , 2017 .

[66]  AliReza Amiri-Simkooei,et al.  Least-squares variance component estimation: theory and GPS applications , 2007 .

[67]  Christoforos Kotsakis,et al.  Reference frame stability and nonlinear distortion in minimum-constrained network adjustment , 2012, Journal of Geodesy.

[68]  Dongkai Yang,et al.  A Cycle Slip Detection Framework for Reliable Single Frequency RTK Positioning , 2020, Sensors.

[69]  Witold Prószyński,et al.  Revisiting Baarda’s concept of minimal detectable bias with regard to outlier identifiability , 2015, Journal of Geodesy.

[70]  Ivandro Klein,et al.  DESIGN OF GEODETIC NETWORKS BASED ON OUTLIER IDENTIFICATIONCRITERIA: AN EXAMPLE APPLIED TO THE LEVELING NETWORK , 2018, Boletim de Ciências Geodésicas.

[71]  C. Aydin,et al.  Computation of Baarda’s lower bound of the non-centrality parameter , 2004 .

[72]  Peter J. G. Teunissen,et al.  Does RAIM with Correct Exclusion Produce Unbiased Positions? , 2017, Sensors.

[73]  Yufeng Nie,et al.  Specific Direction-Based Outlier Detection Approach for GNSS Vector Networks , 2019, Sensors.

[74]  Van Khang Nguyen,et al.  Environment Monitoring for Anomaly Detection System Using Smartphones † , 2019, Sensors.

[75]  Paavo Rouhiainen,et al.  Development of a System Calibration Comparator for Digital Levels in Finland , 2004 .

[76]  Chao Wei.  Estimation for the Discretely Observed Cox-Ingersoll-Ross Model Driven by Small Symmetrical Stable Noises , 2020, Symmetry.

[77]  Michael Wolf,et al.  Multiple Testing of One-Sided Hypotheses: Combining Bonferroni and the Bootstrap , 2017, Predictive Econometrics and Big Data.

[78]  P. Teunissen.  The geometry of geodetic inverse linear mapping and non-linear adjustment , 1985 .

[79]  Dennis Odijk,et al.  Stochastic modelling of the ionosphere for fast GPS ambiguity resolution , 2000 .

[80]  Coast Groundfish,et al.  OF COMMERCE National Oceanic and Atmospheric , 2022 .