Non-parametric Estimation of Geometric Anisotropy from Environmental Sensor Network Measurements

This paper addresses the estimation of geometric anisotropy parameters from scattered data in two dimensional spaces. The parameters involve the orientation angle of the principal anisotropy axes and the anisotropy ratio (i.e., the ratio of the principal correlation lengths). The mathematical background is based on the covariance Hessian identity (CHI) method developed in [3, 1]. CHI links the expectation of the first-order sample derivatives tensor with the Hessian matrix of the covariance function [6]. The paper focuses on the application of CHI to samples that require segmentation into clusters, either due to sampling density variations or due to systematic changes in the process values. A non-parametric isotropy test is also presented. Finally, a composite (real and synthetic) data set is used to investigate the impact of CHI anisotropy estimation on spatial interpolation with ordinary kriging.