| Summary: | Recently, the time-updating <inline-formula> <tex-math notation="LaTeX">$q$ </tex-math></inline-formula>-norm sparse covariance-based estimator (<inline-formula> <tex-math notation="LaTeX">$q$ </tex-math></inline-formula>-SPICE) was developed for online spectral estimation of stationary signals. In this work, this development is furthered to deal with non-stationary signals. By introducing a weighting matrix defined by a forgetting factor, the generalized least absolute shrinkage and selection operator (LASSO) is generalized, in order to allow for changes in the spectral content. As shown here, the resulting LASSO formulation can be solved in a simple manner using cyclic minimization, enabling recursive estimation for non-stationary signals. The proposed generalized time-updating <inline-formula> <tex-math notation="LaTeX">$q$ </tex-math></inline-formula>-SPICE offers the same benefits as the original estimator, including being computationally efficient at constant computational and storage cost, but also allows for substantial improvements when dealing with non-stationary signals. The performance of the method is evaluated using both stationary and non-stationary signals, indicating the preferable performance of the generalized formulation as compared to the original time-updating SPICE algorithm.
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