Abstract: Aiming at the problem of AR model order and parameters estimation,a novel algorithm based on sparse representation of atomic decomposition was proposed.Firstly,an over-completed sparse dictionary was constructed according to the characteristic of the autocorrelation coefficient of AR model.Secondly,for noisy signals,this paper used the slack variables to establish a new optimization model for sparsely recovery of the characteristic polynomial roots of AR model.Finally,we converted the parameters estimation problem into the problem of best basis selection which is solved by the modified affine scaling methodology.The experiments show that our algorithm is more effective than the traditional methods in terms of the forecasting precision and robustness.

Key words: AR model,Sparse representation,Over-completed basis,Parameters estimation