On convergence of a BCLS algorithm for noisy autoregressive process estimation

The identification of AR processes whose measurement are corrupted by additive noise is considered. A bias compensated least squares (BCLS) algorithm is derived on the framework of solving nonlinear bias compensation equation (BCE). The framework is convenience for investigating the convergence property of the algorithm. Convergence analysis of the proposed algorithm is performed from the numerical analysis viewpoint. The algorithm is to find a fixed point of the BCE. By examination of the BCE and their Jacobian, a theoretical result is obtained to make clear that the relationship of convergence and the parameters of the AR process as well as the ratio of noise to signal. Based on the results of convergence analysis, it can be expected that more effective estimation algorithms are developed.