Least-squares identification of a class of multivariable systems with correlated disturbances

A valuable new way of taking advantage of signal processing techniques to implement unbiased parameter estimation was reported in Feng and Zheng (IEE Proc.-Control Theory Appl. 138 (1991) 484–492). In this paper, some extensions to the recently developed bias-eliminated least-squares method are made such that the method can be employed to perform unbiased identification of multi-input–single-output systems subject to colored noise. A set of digital prefilters are suitably designed to pre-process the input data sampled from multi-input channels, which gives rise to a system of linear equality constraints with respect to system parameters. Then combined with a bias correction procedure, the colored-noise-induced bias in the least-squares parameter estimators can be removed efficiently. The performance of the developed method is both analyzed theoretically and illustrated by means of simulation results.