LSC – Least Squares Collocation

Least Squares Collocation is an advanced mathematical method which his employed geodesy to estimate a continuous signal from discrete, noisy observations utilizing their spatial correlation. In contrast to standard deterministic least squares adjustment, which solves for fixed parameters, LSC treats the underlying physical process, such as variations in the Earth’s gravity field or crustal deformation, as a stochastic one with a specific spatial structure defined by a covariance function. The technique effectively decomposes measurements into three parts: a deterministic trend, a spatially correlated “signal” (the collocation component), and random measurement noise. It utilizes the known statistical relationships between points and allows to interpolate values at unobserved locations and filter out noise, and/or predict signals which are related through a cross-covariance function with the input signal.