On the analysis of repeated geodetic experiments

In the linear estimation problem associated with an experiment that is exactly repeated a number of times, the estimation parameters may naturally be partitioned into two groups, those that are common to all repetitions, and those that are particular to each repeat experiment. We derive least-squares solutions that minimise in norm either group of parameters, as also the trace of the corresponding covariance matrix. These solutions are applied to the station adjustment of triangulation surveying, and to the estimation problem of satellite radar altimetry: to estimate simultaneously mean sea surface heights and residual radial orbit errors, while minimising the norm of either group of parameters. This altimetry problem is considered in the cases of collinear, local crossover and global crossover data. Received: 6 January 1997 / Accepted: 21 December 1998