Search of weights in the problem of finite-rank signal estimation in presence of noise

The problem of weighted finite-rank time-series approximation is considered for signal estimation in "signal plus noise" model, where the inverse covariance matrix of noise is $(2p+1)$-diagonal. Finding of weights, which improve the estimation accuracy, is examined. An effective method for the numerical search of the weights is constructed and proved. Numerical simulations are performed to study the improvement of the estimation accuracy for several noise models.