Study of a least-squares type method for noisy FIR filtering

In this paper, by assuming that the ratio between the output noise variance and the input noise variance is accessible, a modified least-squares (LS) type method with simplistic algorithmic structure is introduced to fulfil the task of FIR filtering with noisy input-output data. The mean convergence of the modified LS type method is comprehensively studied. The practical implication of the knowledge of the noise variance ratio is investigated through sensitivity analysis. This analysis results in the establishment of an alternative identification method that can work efficiently under a much relaxed condition on the knowledge of the noise variance ratio. Computer simulations are conducted to verify the theoretical discussions.