Filtering-Based Bias-Compensation Recursive Estimation Algorithm for an Output Error Model with Colored Noise

For the output error (OE) models whose outputs are contaminated by colored process noises (i.e., correlated noises), this paper derives a new form of bias compensation recursive least squares (BCRLS) algorithm by means of the data filtering technology and the bias compensation principle. The basic idea is to firstly transform the OE model disturbed by colored process noise into a simple OE model with the white noise by adopting the data filtering technology at each recursive calculation, and then to calculate the bias compensation term, based on the new OE model with the bias-compensation technique. Finally, eliminate this bias term in the biased RLS parameter estimation of the OE model to be identified, thereby achieving its unbiased parameter estimation. Unlike the previous BCRLS algorithm, this algorithm can still achieve unbiased parameter estimation of OE systems in the presence of colored process noise without calculating complex noise correlation functions. The performance of the proposed algorithm is demonstrated through three digital simulation examples.