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

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.