Subspace-based spectrum estimation in innovation models by mixed norm minimization

Abstract

In this paper, identification of discrete-time power spectra of multi-input/multi-output (MIMO) systems in innovation models from output-only time-domain measurements is considered.A hybrid identification algorithm unifying mixed norm minimization with subspace estimation method is proposed. The proposed algorithm first estimates a covariance matrix from measurements. A significant dimension reduction is achieved in this step. Next, a regularized nuclear norm optimization problem is solved to enforce sparsity on the selection of most parsimonious model structure. A modification of the covariance estimates in the proposed algorithm generates yet another algorithm capable of handling data records with sequentially and intermittently missing values. The new and the modified identification algorithms are tested on a numerical study and a real-life application example concerned with the estimation of joint power spectral density (PSD) of parallel road tracks.