Journal ArticleDOI
Estimation of frequencies of multiple sinusoids: Making linear prediction perform like maximum likelihood
Donald W. Tufts,Ramdas Kumaresan +1 more
- Vol. 70, Iss: 9, pp 975-989
TLDR
In this paper, the frequency estimation performance of the forward-backward linear prediction (FBLP) method was improved for short data records and low signal-to-noise ratio (SNR) by using information about the rank M of the signal correlation matrix.Abstract:
The frequency-estimation performance of the forward-backward linear prediction (FBLP) method of Nuttall/Uhych and Clayton, is significantly improved for short data records and low signal-to-noise ratio (SNR) by using information about the rank M of the signal correlation matrix. A source for the improvement is an implied replacement of the usual estimated correlation matrix by a least squares approximation matrix having the lower rank M. A second, related cause for the improvement is an increase in the order of the prediction filter beyond conventional limits. Computationally, the recommended signal processing is the same as for the FBLP method, except that the vector of prediction coefficients is formed from a linear combination of the M principal eigenvectors of the estimated correlation matrix. Alternatively, singular value decomposition can be used in the implementation. In one special case, which we call the Kumaresan-Prony (KP) case, the new prediction coefficients can be calculated in a very simple way. Philosophically, the improvement can be considered to result from a preliminary estimation of the explainable, predictable components of the data, rather than attempting to explain all of the observed data by linear prediction.read more
Citations
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Book
Spectral analysis of signals
Petre Stoica,Randolph L. Moses +1 more
TL;DR: 1. Basic Concepts. 2. Nonparametric Methods. 3. Parametric Methods for Rational Spectra.
Journal ArticleDOI
MUSIC, maximum likelihood, and Cramer-Rao bound
Petre Stoica,Nehorai Arye +1 more
TL;DR: The Cramer-Rao bound (CRB) for the estimation problems is derived, and some useful properties of the CRB covariance matrix are established.
Journal ArticleDOI
Matrix pencil method for estimating parameters of exponentially damped/undamped sinusoids in noise
Yingbo Hua,Tapan K. Sarkar +1 more
TL;DR: It is found through perturbation analysis and simulation that, for signals with unknown damping factors, the pencil method is less sensitive to noise than the polynomial method.
Journal ArticleDOI
Using the matrix pencil method to estimate the parameters of a sum of complex exponentials
Tapan K. Sarkar,O. Pereira +1 more
TL;DR: The matrix pencil method is described, which is more robust to noise in the sampled data and has a lower variance of the estimates of the parameters of interest than a polynomial-type method, and is also computationally more efficient.
Journal ArticleDOI
Coherent signal-subspace processing for the detection and estimation of angles of arrival of multiple wide-band sources
H. Wang,Mostafa Kaveh +1 more
TL;DR: In this paper, a method of constructing a single signal subspace for high-resolution estimation of the angles of arrival of multiple wide-band plane waves is presented, which relies on an approximately coherent combination of the spatial signal spaces of the temporally narrow-band decomposition of the received signal vector from an array of sensors.
References
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Book
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Journal ArticleDOI
High-resolution frequency-wavenumber spectrum analysis
TL;DR: In this article, a high-resolution frequency-wavenumber power spectral density estimation method was proposed, which employs a wavenumber window whose shape changes and is a function of the wave height at which an estimate is obtained.
Journal ArticleDOI
Linear prediction: A tutorial review
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Journal ArticleDOI
The approximation of one matrix by another of lower rank
Carl Eckart,Gale Young +1 more
TL;DR: In this paper, the problem of approximating one matrix by another of lower rank is formulated as a least-squares problem, and the normal equations cannot be immediately written down, since the elements of the approximate matrix are not independent of one another.
Journal ArticleDOI
The Retrieval of Harmonics from a Covariance Function
TL;DR: In this paper, a new method for retrieving harmonics from a covariance function is introduced, based on a theorem of Caratheodory about the trigonometrical moment problem.