In this paper, we present a generic method to solve the subspace-oriented estimation problem. We have optimized our approach by taking account of the a priori and a posteriori covariances of both the data and the model parameters in general linear inverse notations. In our work, singular value decomposition (SVD) was employed to provide a robust optimal solution. In computation of the generalized matrix inverse, a very simple truncation criterion on the singular value (SV) spectrum was set up which guarantees the minimal variance of the estimate. This algorithm based on SVD produces an optimal estimate independent of computing resources. Specifically, we applied this method to studies of ionospheric tomography by inverting total electron content (TEC), which may be measured by means of satellite beacons. We processed two simulated cases. The residual variances of the a posteriori covariances of the model parameters were used as the measure to evaluate the uncertainties of the estimates. Our examples indicate that this algorithm can resolve about 60% of the a priori variance while achieving a significant decrease of the computation time by truncation of the SV spectrum.
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