Knowledge Bank

The steadily increasing stream of geodetic data primarily provided by automatized measurement techniques calls for a data processing method which is both simple and fast. The simplicity of least-squares collocation can hardly be surpassed, however, the processing speed, which depends on covariance calculation procedure and matrix inversion algorithms used, can be improved considerably by the faster covariance computation procedure presented in this report. The method is basically a differentiation - interpolation procedure applied to a smooth function interpolating on a regular rectangular grid of exact covariances. Once this covariance network has been generated, the covariance approximation procedure, called COVAPP, is able to provide covariance expressions of second and lower order derivatives of the disturbing potential about ten times faster than existing methods. The approximation error can be kept as small as we please by choosing an appropriately small grid spacing. A FORTRAN IV program listing together with sample inputs and outputs are included in the report. The reader only interested in application may bypass the technical chapters 3 and 4.