A review of non-stationary spatial methods for geodetic least-squares collocation

This paper reviews a field that is herein termed spatial 'non-stationarity', which is specifically concerned with non-stationarity in the geodetic theory of least-squares collocation (LSC). In practice, many geodesists rely on stationary assumptions in LSC, i.e. using a constant mean and isotropic and spatially invariant covariance for estimation and prediction of geodetic quantities. However, new theories in spatial statistics and geostatistics allow for better statistical methodologies to be used in geodesy. The aim of this paper is to introduce these methodologies and adapt them for dealing with non-stationarity in LSC.