Modeling and generation of 3-D random surface roughness data by the non-causal 2-D AR model (Part 2) - An algorithm for fast AR parameter estimation

In this paper, an algorithm for fast AR parameter estimation of the non-causal 2-D AR(auto-regressive) model is suggested and examined for modeling and generation of 3-D surface topography data. The problem of the AR parameter estimation of the non-causal 2-D AR model is a non-linear programming problem of minimization of the error of fitting multiplied by the correction term. A detailed algorithm for the AR parameter estimation based on the conjugate gradient method combined with the Newton method and some other techniques is described for reduction of the calculation time. To investigate the efficiency of the newly proposed algorithm, the direct search method and the proposed algorithm are applied to a set of generated data with the non-causal 2-D AR model with known parameter and compared from the standpoint of precision and the calculation time. Precision of AR parameter estimation with the proposed algorithm is equivalent to the direct search method. The calculation of the proposed algorithm is approximately one fiftieth that of the direct search method.