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On unbiased parameter estimation in FIR filtering of signals corrupted by noise

This paper addresses the problem of unbiased estimation of the FIR filter parameters in the face of corrupting noises at the filter input and output sides. The asymptotic analysis reveals that an unbiased parameter estimate is attainable provided that the variance of the input corrupting noise can be estimated. An objective function is properly introduced so that the input noise variance can be easily obtained as a minimum point of this objective function. Consequently this paves the way for achieving an unbiased estimate of the FIR filter parameters. The distinctive feature of the developed algorithm is that the estimation process of the input noise variance is detached from that of the FIR filter parameters and no alternating iterations are required. The performance of the developed unbiased parameter estimation algorithm is substantiated using simulation data.