A generalized pencil-of-function (GPOF) method is developed for extracting the poles of an electromagnetic system from its transient response. The GPOF method needs the solution of a generalized eigenvalue problem to find the poles. Subspace decomposition is also used to optimize the performance of the GPOF method. The GPOF method has advantages over the Prony method in both computation and noise sensitivity, and approaches the Cramer-Rao bound when the signal-to-noise ratio (SNR) is above threshold. An application of the GPOF method to a thin-wire target is presented.<>

Several algorithms for estimating generalized eigenvalues (GEs) of singular matrix pencils perturbed by noise are reviewed. The singular value decomposition (SVD) is explored as the common structure in the three basic algorithms: direct matrix pencil algorithm, pro-ESPRIT, and TLS-ESPRIT. It is shown that several SVD-based steps inherent in the algorithms are equivalent to the first-order approximation. In particular, the Pro-ESPRIT and its variant TLS-Pro-ESPRIT are shown to be equivalent, and the TLS-ESPRIT and its earlier version LS-ESPRIT are shown to be asymptotically equivalent to the first-order approximation. For the problem of estimating superimposed complex exponential signals, the state-space algorithm is shown to be also equivalent to the previous matrix pencil algorithms to the first-order approximation. The second-order perturbation and the threshold phenomenon are illustrated by simulation results based on a damped sinusoidal signal. An improved state-space algorithm is found to be the most robust to noise.<>

A study of a matrix pencil method for estimating frequencies and damping factors of exponentiallydamped and/or undamped sinusoids in noise is presented. Comparison of this method to a polynomialmethod (SVD-Prony method) shows that the matrix pencil method and the polynomial method are two special cases of a matrix prediction approach and that the pencil method is more efficient in computation and less restrictive about signal probes. It is found through perturbation analysis and simulation that, for signals with unknown damping factors, the pencil method is less sensitive to noisethan the polynomial method. An expression of the Cramer-Rao bound for the exponential signals is presented.<>

A simple structured 2-D array, the L-shaped array, is presented. The L-shaped array consists of two uniform linear arrays (ULA) connected orthogonally at one end of each ULA. It is shown that the Cramer-Rao bounds (CRB) of the estimated wave directions based on the L-shaped array are about 37% smaller than those for the cross array. The CRB indicates the accuracy potential because it is the (reachable) lower bound on the variance of any unbiased estimate. An efficient maximum likelihood algorithm is developed utilizing the ULA structure inherent in the L-shaped array.<>