%0 Journal Article %1 Ruiz.Carrion.ea1995 %A Ruiz, D.P. %A Carrion, M.C. %A Gallego, A. %A Medouri, A. %D 1995 %J Signal Processing, IEEE Transactions on %K Carlo Gaussian Monte analysis; analysis;estimation coefficients;deterministic correlation correlation;higher damped data density;short error;minimum-norm errors estimation;power estimation;prediction estimator;damped exponential length;higher length;signal method;moments methods;covariance methods;mean-square model;damping noise;colored noise;correlation noise;covariance-type observations;parameter order plane;noisy principal-eigenvector processing;Gaussian processing;spectral reduction;exponentially sequence;linear-prediction-based simulations;additive sinusoids;finite-data spectral statistics;parameter theory;higher theory;signal %N 11 %P 2665 -2677 %R 10.1109/78.482116 %T Parameter estimation of exponentially damped sinusoids using a higher order correlation-based approach %V 43 %X 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

@article{Ruiz.Carrion.ea1995, abstract = {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}, added-at = {2011-09-01T13:26:03.000+0200}, author = {Ruiz, D.P. and Carrion, M.C. and Gallego, A. and Medouri, A.}, biburl = {https://www.bibsonomy.org/bibtex/2edfd66804f8edcaf367d30fa904b6ff7/procomun}, doi = {10.1109/78.482116}, file = {Ruiz.Carrion.ea1995.pdf:Ruiz.Carrion.ea1995.pdf:PDF}, interhash = {42e4f297a6b632875fa2f1a85704f7ad}, intrahash = {edfd66804f8edcaf367d30fa904b6ff7}, issn = {1053-587X}, journal = {Signal Processing, IEEE Transactions on}, keywords = {Carlo Gaussian Monte analysis; analysis;estimation coefficients;deterministic correlation correlation;higher damped data density;short error;minimum-norm errors estimation;power estimation;prediction estimator;damped exponential length;higher length;signal method;moments methods;covariance methods;mean-square model;damping noise;colored noise;correlation noise;covariance-type observations;parameter order plane;noisy principal-eigenvector processing;Gaussian processing;spectral reduction;exponentially sequence;linear-prediction-based simulations;additive sinusoids;finite-data spectral statistics;parameter theory;higher theory;signal}, month = {nov.}, number = 11, pages = {2665 -2677}, timestamp = {2011-09-02T08:25:25.000+0200}, title = {Parameter estimation of exponentially damped sinusoids using a higher order correlation-based approach}, volume = 43, year = 1995 }