A SEPARABLE NONLINEAR LEAST-SQUARES APPROACH FOR IDENTIFICATION OF LINEAR SYSTEMS WITH ERRORS IN VARIABLES

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. Previously, an extended version of compensated least-squares (ECLS), based on an overdetermined linear system of equations, was proposed as a method for handling problems where the input and output data are corrupted by white noise. This paper considers the problem where the noise is colored and, thus, extends previous results of the ECLS method. By considering the ECLS problem as a separable nonlinear LS problem, it is shown that the parameters, associated with the noise terms, can be obtained from solving a variable projection minimization problem. The accuracy of the parameter estimates is investigated, and it is also shown that the estimates, under some general assumptions, are consistent.