Spatial outlier detection on discrete GNSS velocity fields using robust Mahalanobis-distance-based unsupervised classification

Abstract

GNSS velocity field filtering can be identified as a multidimensional unsupervised spatial outlier detection problem. To detect and classify the spatial outliers, we jointly interpret the horizontal and vertical velocity fields with the related standard deviations. We also describe the applied feature engineering process, which represents the underlying problem better than the initial attributes. According to this, we discuss the utilized algorithms and techniques, like the spatial- and non-spatial mapping functions, the k-nearest neighborhood (kNN) technique to retrieve the local environment of each GNSS station, as well as the principal component analysis (PCA) as a dimensionality reduction technique. We also assume that regular velocity field samples containing no outliers come from an approximate multivariate normal distribution (MVN) at the local scale. Regarding this, we evaluate the corresponding sample-wise distance related to model distribution, namely the Mahalanobis distance, with the estimation of the robust covariance matrix derived by the minimum covariant determinant (MCD) algorithm. Subsequently, we introduce the applied binary classification on the values of the derived robust Mahalanobis distances (RMD) which follows the χ2distribution. We also present three cases of artificially generated, pre-labeled synthetic velocity field datasets to perform cross-validation and comparison of the proposed RMD approach to other classification techniques. According to this, we found that k = 12 yields > 95% classification accuracy. While the compared methods have a mean classification accuracy of 96.2–99.8%, the advantage of the RMD approach is that it does not require pre-defined labels to indicate regular and outlier samples. We also demonstrate the proposed RMD based filtering process on a real dataset of the EUREF Permanent Network Densification velocity products. The RMD-based approach has been integrated into the EPN Densification as a quality checking algorithm. According to this, we also introduce a co-developed and regularly updated interactive webpage to disseminate the corresponding results.