Collocation with integer trend

Abstract

Collocation is a popular method in geodesy for combining heterogeneous data of different kind. It comprises adjustment, interpolation and extrapolation as special cases. Current methods of collocation apply however only if the trend parameters are real valued. In the present contribution we generalize the theory of collocation by permitting the trend parameters to be integer valued. It will be shown how the collocation formulae change when the integerness of the trend parameters is taken into account. We will also address the problem of evaluating the quality of the collocation results. The quality of the collocation results is usually described by the so-called error covariances. We will show how the error covariances change due to the integerness of the trend. But we also show that the approach based on error covariances does not give an adequate quality description of the collocation results in case of an integer trend. How this approach needs to be generalized is also presented.