Knowledge Bank

This investigation studies the possibility of improving the accuracy of geodetic results by use of simultaneously observed ranges to Lageos, in a differencing mode, from pairs of stations. Despite their complexity and expensive computational requirements, orbital models are still not accurate enough to achieve geodetic parameter accuracies comparable to those of laser measurements. Parameters of interest here are the baseline lengths and the coordinates of the pole. Simulation tests show that model errors can be effectively minimized by simultaneous range-differencing (SRO) for a rather broad class of network-satellite pass configurations. To generate the required quasi-simultaneous range events, we compare the methods of least squares approximation with monomials and Chebyshev polynomials and the cubic spline interpolation. The latter seems preferable in the case of uniform and dense sets of data. Analysis of three types of orbital biases (radial, along- and across-track) shows that radial biases are the ones most efficiently minimized in the SRC mode. The degree to which the other two can be minimized depends on the type of parameters under estimation and the geometry of the problem. Sensitivity analyses of the SRO observation show that for baseline length estimations the most useful data are those collected in a direction parallel to the baseline and at a low elevation. Estimating individual baseline lengths with respect to an assumed but fixed orbit not only decreases the cost, but it further reduces the effects of model biases on the results as opposed to a network solution. Enforcing the simultaneity constraint ensures that the results are also free of possible biases introduced by inconsistent coordinate systems in which independent station determinations refer. Analogous results and conclusions are obtained for the estimates of the coordinates of the pole.