On bias compensated least squares method for noisy input-output system identification

In this paper a new type of bias compensated least squares (BCLS) method is proposed for noisy input-output system identification. It is known that BCLS method is based on compensation of asymptotic bias on the least squares estimate by making use of noise variances estimates. The main future of our proposed algorithm is introducing a forward output predictor to generate the cross-correlations of LS error and forward output prediction (FOP) error and with the help of auto-correlations of LS error and cross-correlations of LS and FOP errors unknown input and output noise variances can be estimated. On the basis of the obtained estimates of noise variances the consistent estimates of system parameters can be given. It is shown that the proposed algorithm can give consistent parameter estimates when the input is white noise, AR and MA process respectively. Simulations which compare the standard LS with BCLS algorithms indicate that the proposed algorithm is an efficient method for noisy input-output system identification