A fast algorithm for AR parameter estimation using a novel noise-constrained least-squares method

In this paper, a novel noise-constrained least-squares (NCLS) method for online autoregressive (AR) parameter estimation is developed under blind Gaussian noise environments, and a discrete-time learning algorithm with a fixed step length is proposed. It is shown that the proposed learning algorithm converges globally to an AR optimal estimate. Compared with conventional second-order and high-order statistical algorithms, the proposed learning algorithm can obtain a robust estimate which has a smaller mean-square error than the conventional least-squares estimate. Compared with the learning algorithm based on the generalized least absolute deviation method, instead of minimizing a non-smooth linear L(1) function, the proposed learning algorithm minimizes a quadratic convex function and thus is suitable for online parameter estimation. Simulation results confirm that the proposed learning algorithm can obtain more accurate estimates with a fast convergence speed.