  The problem of time series approximation by series of finite rank is
considered from the viewpoint of signal extraction. For signal estimation, a
weighted least-squares method is applied to the trajectory matrix of the
considered time series. Matrix weights are chosen to obtain equal or
approximately equal weights in the equivalent problem of time-series
least-squares approximation. Several new methods are suggested and examined
together with the Cadzow's iterative method. The questions of convergence,
computational complexity, and accuracy are considered for the proposed methods.
The methods are compared on numeric examples.
