Shorter Communication: Estimating the Parameters of Undamped Exponential Signals

Abstract

A nonlinear eigenvalue method is proposed for estimating the parameters of undamped exponential signals when the parameters are complex-valued. Such data arise in several areas of application, including communications radio location of objects, seismic signal processing, and computer-assisted medical diagnosis. Osborne proposed a method to estimate the parameters of exponential models when the parameters are real-valued. The method is generalized to the complex-parameters case. It is shown to perform better than existing methods due to Tufts and Kumaresan and Bai, Krishnaiah, and Zhao in the sense of having lower mean-squared errors. A simulation study showed that the observed mean-squared errors are close to the Cramer-Rao lower bound for frequency estimates.

KEY WORDS:

• Consistent estimator
• Nonlinear
• Normal equation
• Separable regression