The problem of weighted finite-rank series approximation of a time-series aimed at estimating the signal in the "signal plus noise" model, where the inverse covariance noise matrix is (2p + 1) diagonal, is considered in this paper. The problem of searching for weights that improve the estimation accuracy is solved. An efficient numerical method for the search for weights is constructed and theoretically validated. A numerical simulation is performed for several noise models to study the improvement of accuracy of the signal estimation method.