Transformed Spiked Covariance Completion for Time Series Estimation

In this paper, we address the problem of estimating a noisy, incomplete time series of a dynamical system with an unknown state evolution. The technique that we will present is transformed spiked covariance completion (TSCC), a matrix completion method for signal estimation. This method exploits the spiked covariance model of the underlying signal to develop a linear estimator that is resilient to noise. We discuss the conditions in the signal model for which this technique is applicable and compare this method against other state-of-the-art time series estimation techniques with a numerical example. Our algorithm gives estimates that are more robust to noise in comparison to the current state-of-the-art techniques that address this same estimation problem.