Abstract <p>Weighted finite-rank time-series approximation is considered for signal estimation. Weights that lead to improved estimation accuracy are found. Quadratic optimization is used to construct and theoretically justify an efficient method for the numerical search of weights. The algorithm is made efficient by reducing the problem of quadratic optimization with a large number of linear constraints to a sequence of problems with a smaller number of constraints and a stopping criterion. The algorithm is justified by proving that different statements of the original optimization problem are equivalent. A numerical simulation is performed to confirm the efficiency of the algorithm and improve the accuracy of signal estimation.</p>