Identification of linear systems with errors in variables using separable nonlinear least-squares
Abstract
It is well-known that the least-squares identification method generally gives biased parameter estimates when the observed input-output data are corrupted with noise. If the noise acting on both the input and output is white, and if the noise variances are known, or if estimates of the noise variances are available, then the principle of biased-compensated least-squares (CLS) can readily be used to obtain consistent estimates. In this paper an extended version of the CLS (ECLS) method based on an overdetermined linear system of equations is investigated. By considering the ECLS problem as a separable nonlinear LS problem, it is also shown that the noise variance parameters can be obtained from solving a variable projection minimization problem.
