Adaptive Weighting Least-Squares Estimation of Initial Residuals

Selection of initial residuals affects parameter estimation. Until now, the mean of the residuals was widely employed as an estimate of initial residuals. In this paper, the statistics of the conventional method (i.e., using the mean of residuals as an estimate of initial residuals) are investigated. It is shown that the statistics of the conventional method depend directly upon the parameters to be estimated and are quite poor in some cases. This behavior underlines the importance of initial residual estimation. In order to obtain a practical alternative to the conventional method, an adaptive estimate of the initial residuals is proposed. It is proven that the statistics of the adaptive estimate do not depend upon the parameters to be estimated and can possess excellent qualities for a variety of system parameters. Simulations illustrating the excellent properties of the statistics of the adaptive estimate and the poor properties of the statistics of the conventional method are included.