On TLS estimation of autoregressive signals with noisy measurements

This paper is concerned with estimating the parameters of autoregressive (AR) signals from noise-contaminated measurements. This parameter estimation problem can be formulated as a total least-squares (TLS) identification problem. It is shown that under the assumption of the known variance ratio of the driving signal and the measurement noise, this TLS problem can be easily solved using the generalized eigenvalue decomposition technique. Furthermore, the sensitivity of the resulting AR parameter estimates with respect to the known variance ratio is analyzed, which reveals the possibility of relaxing this assumption in practical applications. Numerical results are described which compare the behavior of the proposed AR identification method with other typical methods.