Comparison of kriging and least-squares collocation – Revisited

Abstract The well-known to physical geodesists method of least-squares collocation and the geostatistical method of kriging probably known to the broader audience are compared. Both methods are rooted in Wiener–Kolmogorov’s (W–K) prediction theory; but, since necessity is the mother of invention, the W–K foundations have been extended to satisfy the needs of particular applications. The paper presents a link or rather an equivalence of the two methods as far as their basic forms are considered (specialization to geodetic boundary-value problems, covariance propagation between functionals and nonlinear geostatistical methods are excluded from this comparison). Only scalar random fields (univariate case) and the assumption of a second-order structure of a random function are considered. Due to the equivalence of their basic formulas, both techniques share the same advantages and disadvantages. The paper also shows the difference as to the predicted values and prediction variances in case of exact and filtered (noise reduction) prediction models. This theoretical comparison of the methods has practical implications because of readily available geostatistical software that, in local as well as global applications, can be used for predictive problems occurring in geodesy and surveying.