Optimal truncation criterion for application of singular value decomposition to ionospheric tomography

In this paper, we present a generic method to solve the subspace-oriented e stimation problem. We have optimized our approach by taking account of the a priori and a posteriori covariances of both the data and the model parame ters in general linear inverse notations. In our work, singular value decom position (SVD) was employed to provide a robust optimal solution. In comput ation of the generalized matrix inverse, a very simple truncation criterion on the singular value (SV) spectrum was set up which guarantees the minima l 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 co ntent (TEC), which may be measured by means of satellite beacons. We proces sed two simulated cases. The residual variances of the a posteriori covaria nces of the model parameters were used as the measure to evaluate the uncer tainties of the estimates. Our examples indicate that this algorithm can re solve about 60% of the a priori variance while achieving a significant decr ease of the computation time by truncation of the SV spectrum.