An efficient identification algorithm for FIR filtering with noisy data

This paper is concerned with FIR filtering with noise-corrupted input-output measurements. With an analysis of the algebraic structure of the correlation matrix, it is shown that an unbiased estimate of FIR parameters can be obtained by solving a special bilinear equation. Then a bilinear equation method (BEM) is developed for solving the bilinear equation associated with the unbiased solution of the FIR filtering under the unknown ratio of the input noise variance to the output noise variance (NNR). Being different from the existing unbiased estimators, the main advantage is that the proposed method exploits much sufficiently the special structure of the correlation matrix and obtains much accurate estimation for FIR filtering in the presence of input and output noises. Simulation results are presented to validate the good performance of the proposed method.