Parameter estimation of exponentially damped sinusoids using a higher order correlation-based approach

A very common problem in signal processing is parameter estimation of exponentially damped sinusoids from a finite subset of noisy observations. When the signal is contaminated with colored noise of unknown power spectral density, a cumulant-based approach provides an appropriate solution to this problem. We propose a new class of estimator, namely, a covariance-type estimator, which reduces the deterministic errors associated with imperfect estimation of higher order correlations from finite-data length. This estimator allows a higher order correlation sequence to be modeled as a damped exponential model in certain slices of the moments plane. This result shows a useful link with well-known linear-prediction-based methods, such as the minimum-norm principal-eigenvector method of Kumaresan and Tufts (1982), which can be subsequently applied to extracting frequencies and damping coefficients from the 1-D correlation sequence. This paper discusses the slices allowed in the moments plane, the uses and limitations of this estimator using multiple realizations, and a single record in a noisy environment. Monte Carlo simulations applied to standard examples are also performed, and the results are compared with the KT method and the standard biased-estimator-based approach. The comparison shows the effectiveness of the proposed estimator in terms of bias and mean-square error when the signals are contaminated with additive Gaussian noise and a single data record with short data length is available