Robust Mahalanobis-distance based spatial outlier detection on discrete GNSS velocity fields

The GNSS velocity field filtering topic can be identified as a multi-dimensional unsupervised spatial outlier detection problem. In the discussed case, we jointly interpreted the horizontal and vertical velocity fields and its uncertainties as a six dimensional space. To detect and classify the spatial outliers, we performed an orthogonal linear transformation technique called Principal Component Analysis (PCA) to dynamically project the data to a lower dimensional subspace, while redacting the most (~99%) of the explained variance of the input data.

Therefore, the resulting component space can be seen as an attribute function, which describes the investigated deformation patterns. Then we constructed two subspace mapping functions, respectively the k-nearest neighbor (k-NN) and median based neighbor function with Haversine metric, and the samplewise comparison function which compares the samples with the properties of its k-NN environment. Consequently, the resulting comparison function scores highlights the significantly different observations as outliers. Assuming that the data comes from Multivariate Gaussian Distribution (MVD), we evaluated the corresponding Mahalanobis-distance with the estimation of the robust covariance matrix of the investigated area. Then, as the main result of the Robust Mahalanobis-distance (RMD) based approach, we implemented the binary classification via the p-value and critical Mahalanobis-distance thresholding.

Compared to the formerly investigated and applied One-Class Support Vector machine (OCSVM) approach, the RMD based solution gives ~ 17% more accurate results of the European scaled velocity field filtering (like EPN D1933), as well as it corrects the ambiguities and non-desired features (like overfitting) of the former OCSVM approach.

The results will be also presented as an interactive web page of the velocity fields of the latest version of EPN D2050 filtered with the introduced RMD approach.