Unbiased identification of a class of multi-input single-output systems with correlated disturbances using bias compensation methods

This paper studies the modelling and identification problems for multi-input single-output (MISO) systems with colored noises. In order to obtain the unbiased recursive estimates of the systems, this paper presents a recursive least squares (RLS) identification algorithm based on bias compensation technique. The basic idea is to eliminate the estimation bias by adding a correction term in the least squares (LS) estimates, a set of stable digital prefilters are suitably designed to preprocess the input sampled data from multi-input channels for the purpose of getting the bias term arisen by colored noises in LS estimates, and further to derive a bias compensation based RLS algorithm. The performance of the developed method is both analyzed theoretically and shown by means of simulation results.