The Covariance Least-Squares Algorithm for Spectral Estimation of Processes of Short Data Length

A new method for generating the autoregressive (AR) process parameters for spectral estimation is introduced. The method fits AR models to the data optimally in the sense of minimizing the sum of squares of the error covariance function within the model prediction region, and is thus designated as the Covariance Least-Squares (CLS) algorithm. This minimization is shown to be identical with minimizing the weighted average one-step, linear prediction errors with adaptive weights corresponding to the energy of the data within the prediction region. The CLS algorithm is compared to the Least-Squares (LS) algorithm [1], [2] by simulation and asymptotic properties. It is shown that the CLS method combines all the desirable properties of the comparison algorithm with improved robustness in the presence of nonstationarity, namely, additive transients and envelope modulation. It is also shown that the CLS algorithm provides asymptotically unbiased AR parameters, a property also shared by the comparison LS algorithm.