A half-century of Baarda’s concept of reliability: a review, new perspectives, and applications

Over the 50 years of its existence, Baarda’s concept of reliability has been used as a standard practice for the quality control in geodesy and surveying. In this study, we analysed the pioneering work of Baarda (Publ Geod New Ser 2(4) 1967; Publ Geod New Ser 2(5) 1968) and recent studies on the subject. We highlighted that the advent of personal computers with powerful processors has rendered Monte Carlo method as an attractive and cost-effective approach for quality control purposes. We also provided an overview of the latest advances in the reliability theory for geodesy, with particular emphasis on Monte Carlo method.

[1]  Tayfur Altiok,et al.  Simulation Modeling and Analysis with ARENA , 2007 .

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

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

[4]  Witold Prószyński,et al.  Another approach to reliability measures for systems with correlated observations , 2010 .

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

[6]  S. Sinha Introduction to Bayesian Statistics (2nd ed.) , 2008 .

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

[8]  Maurício Roberto Veronez,et al.  Least trimmed squares estimator with redundancy constraint for outlier detection in GNSS networks , 2017, Expert Syst. Appl..

[9]  P. Vaníček,et al.  Robustness analysis of geodetic horizontal networks , 2001 .

[10]  Xiaoli Ding,et al.  Multiple outlier detection by evaluating redundancy contributions of observations , 1996 .

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

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

[13]  Ivandro Klein,et al.  An Attempt to Analyse Baarda’s Iterative Data Snooping Procedure based on Monte Carlo Simulation , 2017 .

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

[15]  A. Voss-Böhme,et al.  On the statistical power of Baarda’s outlier test and some alternative , 2017 .

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

[17]  K. Koch Introduction to Bayesian Statistics , 2007 .

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

[19]  Xrin –Xe,et al.  DEPARTMENT OF COMMERCE National Oceanic and Atmospheric Administration , 2017 .

[20]  Y. Hsu,et al.  A first modeling of dynamic and static crustal strain field from near-field dilatation measurements: example of the 2013 $$M_w$$Mw 6.2 Ruisui earthquake, Taiwan , 2017 .

[21]  Christian Marx,et al.  Outlier Detection by means of Monte Carlo Estimation including resistant Scale Estimation , 2015 .

[22]  Witold Prószyński Criteria for internal reliability of linear least squares models , 1994 .

[23]  Hisashi Tanizaki,et al.  Computational methods in statistics and econometrics , 2004 .

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

[25]  Gerhard Navratil,et al.  Adjustment computations: spatial data analysis , 2011, Int. J. Geogr. Inf. Sci..

[26]  Hoon Kim,et al.  Monte Carlo Statistical Methods , 2000, Technometrics.

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

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

[29]  P.J.G. Teunissen Quality control in integrated navigation systems , 1990, IEEE Symposium on Position Location and Navigation. A Decade of Excellence in the Navigation Sciences.

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

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

[32]  Karl-Rudolf Koch,et al.  Minimal detectable outliers as measures of reliability , 2015, Journal of Geodesy.

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

[34]  Mohamed A. Ismail,et al.  Fuzzy outlier analysis a combined clustering - outlier detection approach , 2007, 2007 IEEE International Conference on Systems, Man and Cybernetics.

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

[36]  S. E. Ahmed,et al.  Markov Chain Monte Carlo: Stochastic Simulation for Bayesian Inference , 2008, Technometrics.

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

[38]  Anthony C. Atkinson,et al.  Simulated Annealing for the detection of Multiple Outliers using least squares and least median of squares fittin , 1991 .

[39]  P.J.G. Teunissen,et al.  Quality control in integrated navigation systems , 1990, IEEE Aerospace and Electronic Systems Magazine.

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

[41]  Burkhard Schaffrin,et al.  Reliability Measures for Correlated Observations , 1997 .

[42]  Arjun K. Gupta The Theory of Linear Models and Multivariate Analysis , 1981 .

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

[44]  Peter Teunissen,et al.  Minimal detectable biases of GPS data , 1998 .

[45]  Dongyi Ye,et al.  A New Algorithm for High-Dimensional Outlier Detection Based on Constrained Particle Swarm Intelligence , 2008, RSKT.

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

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

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

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

[50]  Sergio Baselga Nonexistence of Rigorous Tests for Multiple Outlier Detection in Least-Squares Adjustment , 2011 .

[51]  Chris Rizos,et al.  Extension of Internal Reliability Analysis Regarding Separability Analysis , 2017 .

[52]  Serdar Kurt,et al.  Genetic algorithms for outlier detection in multiple regression with different information criteria , 2011 .

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