Propagation of error analysis in a total least squares estimator in absolute gravimetry

High-precision measurements often resort to least-squares estimation via observation models in which the quantity of interest is one of the unknowns. The case when both the dependent and independent variables of the model are stochastic is of particular interest. An example is absolute gravimetry, where the orbit of a test mass is tracked by a laser interferometer and is reconstructed by the least-squares method. In orbit reconstruction, space and time enter symmetrically and both time and position are stochastic. We present orbit reconstruction as a total least-squares problem to establish an error model for the propagation of tracking errors. We also give an asymptotic formula expressing the relevant contribution to the uncertainty of gravity determination.