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Estimation of autoregressive (AR) signals measured in noise is considered. A well known fact is that the measurement noise causes the least-squares (LS) estimate of the AR parameters to be biased. The kernel of an alternative method to be proposed is that, unlike the previous LS based methods, a non-iterative estimation scheme is established for the measurement noise variance - the source of the bias. Numerical results demonstrate that the proposed method is much more cost effective in terms of computations and accuracy than the previous LS based methods. The establishment of this non-iterative unbiased estimation method also provides a mechanism for better understanding of the family of LS based methods.