Exponential parameter estimation In the presence of known components and noise

Abstract

In the determination of the natural modes of an electromagnetic scatterer, the measured time series will contain desired information, noise, and quite often known transient components introduced by the excitation source or measuring equipment. This paper describes a linearly constrained total least squares (LCTLS)-Prony method for extracting the exponential model parameters from observed transient data. For such problems, the TLS criterion yields better parameter estimates than LS. Moreover, the incorporation of known signal information via constraints leads to even greater improvements in performance. Mathematical connections between LCTLS-Prony and a TLS variation of time series deflation (TSD) are used to derive constraints for higher order excitation poles. Also, we use TSD concepts to derive numerically superior data transformations For LCTLS. Simulation studies involving idealized test data and synthetic scattering response data of a perfectly conducting sphere demonstrate the advantages of the method.