Multivariate outlier detection based on robust computation of Mahalanobis distances. Application to positioning assisted by RTK GNSS Networks

Abstract RTK GNSS Networks for real time and post-processing positioning services are becoming more and more numerous throughout the world. In order to study the quality of the real time positioning services offered by these facilities with particular respect to outlier identification and rejection and accuracy assessment, classical statistical methods do not appear adequate. In fact, they are mainly based on Least Squares adjustment results and on the hypothesis of normally distributed samples; in addition, most outlier detection tests are set up for univariate samples. This paper presents a method based on the robust computation of Mahalanobis distances able to detect outliers in multivariate samples, and its evaluation by comparing the results obtained from randomly generated data with those stemming from other classical methods. The application of this method in the processing of RTK positions, recorded in real time with a GNSS receiver assisted by a RTK Network for positioning services is shown. In the various tests performed using both simulated samples and those from real GPS observations, the proposed method has been found effective for the outlier detection.

[1]  Clemens Reimann,et al.  Multivariate outlier detection in exploration geochemistry , 2005, Comput. Geosci..

[2]  Douglas M. Hawkins.  Identification of Outliers , 1980, Monographs on Applied Probability and Statistics.

[3]  M. Healy,et al.  Multivariate Normal Plotting , 1968 .

[4]  V. Yohai,et al.  Robust Statistics: Theory and Methods , 2006 .

[5]  D. Massart,et al.  The Mahalanobis distance , 2000 .

[6]  A. Afifi,et al.  On Tests for Multivariate Normality , 1973 .

[7]  T. Moore,et al.  Quality assessment of a network-based RTK GPS service in the UK , 2009 .

[8]  K. Mardia,et al.  Omnibus tests of multinormality based on skewness and kurtosis , 1983 .

[9]  Peter J. Rousseeuw,et al.  Robust regression and outlier detection , 1987 .

[10]  Vic Barnett,et al.  Outliers in Statistical Data , 1980 .

[11]  A. Atkinson.  Fast Very Robust Methods for the Detection of Multiple Outliers , 1994 .

[12]  P. Rousseeuw,et al.  Breakdown Points of Affine Equivariant Estimators of Multivariate Location and Covariance Matrices , 1991 .

[13]  H. Thode.  Testing For Normality , 2002 .

[14]  Bernhard Hofmann-Wellenhof,et al.  GNSS - Global Navigation Satellite Systems: GPS, GLONASS, Galileo, and more , 2007 .

[15]  D. G. Simpson,et al.  Unmasking Multivariate Outliers and Leverage Points: Comment , 1990 .

[16]  P. Rousseeuw,et al.  Unmasking Multivariate Outliers and Leverage Points , 1990 .

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

[18]  R. Garrett.  The chi-square plot: a tool for multivariate outlier recognition , 1989 .

[19]  R. Zamar,et al.  A multivariate Kolmogorov-Smirnov test of goodness of fit , 1997 .

[20]  P. Rousseeuw,et al.  A fast algorithm for the minimum covariance determinant estimator , 1999 .

[21]  Gerhard Wübbena,et al.  Study of a Simplified Approach in Utilizing Information from Permanent Reference Station Arrays , 2001 .

[22]  G. Seeber.  Satellite Geodesy: Foundations, Methods, and Applications , 1993 .