Unbiased equation-error based algorithms for efficient system identification using noisy measurements

Based on the equation-error approach, two constrained weighted least squares algorithms are developed for unbiased infinite impulse response system identification. Both white input and output noise are present, and the ratio of the noise powers is known. Through a weighting matrix, the first algorithm uses a generalized unit-norm constraint which is a generalization of the Koopmans–Levin method. The second method employs a monic constraint which in fact is a relaxation algorithm for maximum likelihood estimation in Gaussian noise. Algorithm modifications for the input-noise-only or output-noise-only cases are also given. Via computer simulations, the effectiveness of the proposed estimators is demonstrated by contrasting with conventional benchmarks in different signal-to-noise ratio and data length conditions.