A nonlinear eigenvalue method is proposed for estimating the parameter
s of undamped exponential signals when the parameters are complex-valu
ed. Such data arise in several areas of application, including communi
cations radio location of objects, seismic signal processing, and comp
uter-assisted medical diagnosis. Osborne proposed a method to estimate
the parameters of exponential models when the parameters are real-val
ued. The method is generalized to the complex-parameters case. It is s
hown to perform better than existing methods due to Tufts and Kumaresa
n and Bai, Krishnaiah, and Zhao in the sense of having lower mean-squa
red errors. A simulation study showed that the observed mean-squared e
rrors are close to the Cramer-Rao lower bound for frequency estimates.