On Asymptotic Bias of Linear Least Squares Estimator

Abstract The bias problem of the linear least Squares estimator is dealt. In the case of a color noise, the asymptotic bias of the estimator is analytically obtained and is expressed in terms of physical quantities for first and second order systems. The condition for the asymptotic bias to be null is derived. It is also shown that the asymptotic bias is not necessarily larger when a noise is color and/or SN ratio is low, than when a noise is white and/or SN ratio is high. It should be noticed that the validity of parameter estimation method might not be judged only from simulation results which depend on the model structure. The experimental results of digital simulation are presented to verify the validity of the theoretical discussions.