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This paper is concerned with infinite impulse response (IIR) filtering where the measurements of both the input and the output of the Alter are corrupted by noise. Making use of the ratio of the variances of the input noise and the output noise which decide the estimation bias, a least-squares (LS) based method is developed for unbiased IIR Altering. One algorithmic feature is that the proposed method is fully based upon the standard LS method in the sense that no evaluation of the average LS errors and other covariances is required. Then the sensitivity of the proposed LS based method with respect to the ratio of the input and output noise variances is studied. The sensitivity analysis reveals that the assumption of the given noise variance ratio can be relaxed to that of a rough range of this ratio, thereby broadening the application domain of the proposed method for noisy IIR filtering. The theoretical findings are corroborated with numerical results.