Time-domain identification of rational spectra with missing data

Abstract

In this paper, we study modelling of rational spectra from time-domain measurements when the measurement information is not complete. We propose a three-stage estimation scheme. In the first-stage, rational spectra are identified by a modified covariance-based subspace identification algorithm in the innovation form. Accuracy of this stage is further enhanced by integrating a regularized nuclear norm optimization step with the subspace algorithm, which makes the model order selection easier. When the covariance estimates are not reliable, a modification of the optimization criterion is suggested. The second-stage of the scheme extracts a spectral factor via the recently introduced the regularized and re-weighted nuclear norm heuristic. In the third-stage, the missing values are recovered by one-step/multi-step prediction filters or fixed-interval smoothing filters. The predictors or the smoothers are built on the second-stage models in the innovation form.