Least squares identification of FIR systems subject to noise

The bias compensation principle is used to develop a simple method for least-squares (LS) identification of finite impulse response (FIR) systems in the presence of input and output noises. It is shown that the variance of the input noise, which determines the bias in the standard LS estimate of the FIR filter coefficients, can be estimated by simply using the average LS errors when the ratio between the output noise variance and the input noise variance is known or obtainable in some way. Compared with the other LS type method recently developed, the proposed method produces better parameter estimates, requires fewer computations and has a simpler algorithmic structure. Numerical results are included to illustrate the performance of the proposed method.