Transient analysis with the linearly constrained TLS Prony method

The authors present an LCTLS (linearly constrained total least squares) based Prony method for use in scattering analysis problems where additive white noise and known signal components hamper the exponential parameter estimation process. The LCTLS-Prony and TLS-TSD (time series deflation) methods were derived in a common framework for comparison. It was shown that the LCTLS constraint transformations could be expressed as the compact Q-factor of the QR decomposition of the TSD transformation. Hence, while the TSD transformation may lead to ill-conditioning, the LCTLS constraint transformation is perfectly conditioned with a unit condition number. It was also shown how to derive constraint transformations for problems with known higher-order exponential components. Simulation studies showed that the LCTLS-Prony method extends the range of SNR where useful results can be obtained