Time series modeling via general linear estimation theory

A procedure for time series modeling is presented which combines a general linear estimation approach with a smoothing singular value decomposition operation. The linear estimator is allowed to possess both causal and anticausal terms. This structure is found to yield better performance capabilities than strictly causal or anticausal structures. Upon using this less restrictive linear estimator with the smoothing properties of a singular value decomposition operation, a time series modeling procedure with superresolution capabilities in low signal-to-noise environments is evolved. The optimality of this approach is analytically established for the important case of two closely spaced (in frequency) sinusoids in white noise.