A new class of robust spectral estimation algorithms based on minimum covariance recursion error and their application in cardiac data analysis
Chrysostomos L. Nikias · 1982
A new class of algorithms for generating the autoregressive (AR) coefficients for one-dimensional (1-D) spectral estimation is introduced. The selected coefficients achieve the minimum square-error in fitting a recursion among the single-point unbiased estimated covariance elements of the data which would be satisfied exactly if the statistics were known exactly, and the data process fit the model assumptions. This minimization is shown to be identical with minimizing the average one-step prediction error with adaptive weights determined by the energy of the measured data. Specifically, three new algorithms for generating the AR coefficients for 1-D spectral estimation are introduced, namely, the Forward Covariance Least-Squares (FCLS), the Energy-Weighted (EW) and Covariance Least-Squares (CLS) algorithms. The EW method employs the lattice formulation of an AR model in which the estimated AR parameters are constrained to satisfy the Levinson recursion. On the other hand, the FCLS and CLS schemes are unconstrained optimization procedures leading to a linear system of equations. The new algorithms are compared, by means of computer simulations in most of the cases, to the Yule-Walker (YW), Burg and Least-Square (LS) algorithms. It is shown that the FCLS, EW and CLS algorithms combine all the desirable properties of the comparison algorithms with improved robustness in the presence of noise, envelope modulation and additive transients, thus extending the range of usefulness of AR type techniques to nonstationary data. It is also shown that the new class of algorithms provides asymptotically unbiased AR coefficients, a property shared by all comparison algorithms. The notion of Minimum Covariance Recursion Error of the 1-D linear prediction filter extends in a straightforward way to two-dimensions. Thereby, a new method of two-dimensional (2-D) spectral estimation is introduced, based on unconstrained minimization of the estimated Covariance Recursion Error of the Minimum Variance Filters (causal, semicausal, noncausal). The 2-D power spectra computed by this algorithm are shown to have improved resolution performance over spectra computed by standard techniques such as Conventional and 2-D Autoregressive. . . . (Author's abstract exceeds stipulated maximum length. Discontinued here with permission of school.) UMI