Signal Identiication Using a Least L 1 Norm Algorithm

errors, and are essentially independent of the 25 larger errors. This is shown clearly by the fact that the SNTLN1 solution is changed only slightly byachange in .I n contrast, the VarPro solution nal error is determined primarily by the largest data errors, and will increase in proportion to ,a s is increased. This will also be true for any approximation method based on L 2 norm minimization. It is also signiicant that SNTLN1 is able to reduce the relative error from an initial value of about 10% to about 3e-7, in an average of 6.1 iterations. This demonstrates the rapid convergence rate of the SNTLN1 algorithm for this class of problems. The robustness of the algorithm is also shown by the relatively small range for nal errors (from min to max) in Table 2, for the 10 diierent problems solved. This robust performance was observed in all test problems solved. Parameter estimation with prior knowledge of known signal poles for the quantiication of NMR spectroscopy data in the time domain. The diierentiation of pseudo-inverses and nonlinear least squares problems whose variables separate. A variable projectionmethod for solving separable nonlinear least squares problems. Total least norm for linear and nonlinearstructured problems, Recentadvances in total least squares techniques and errors-in-variables modeling. Formulation and solution of structured total least norm problems for parameterestimation.