Masato Ikenoue

On bias compensated least squares method for noisy input-output system identification

In this paper a new type of bias compensated least squares (BCLS) method is proposed for noisy input-output system identification. It is known that BCLS method is based on compensation of asymptotic bias on the least squares estimate by making use of noise variances estimates. The main future of our proposed algorithm is introducing a forward output predictor to generate the cross-correlations of LS error and forward output prediction (FOP) error and with the help of auto-correlations of LS error and cross-correlations of LS and FOP errors unknown input and output noise variances can be estimated. On the basis of the obtained estimates of noise variances the consistent estimates of system parameters can be given. It is shown that the proposed algorithm can give consistent parameter estimates when the input is white noise, AR and MA process respectively. Simulations which compare the standard LS with BCLS algorithms indicate that the proposed algorithm is an efficient method for noisy input-output system identification.

Identification of noisy input-output system using bias-compensated least-squares method

In this paper, a new bias-compensated least-squares (BCLS) based algorithm is proposed for identification of noisy input-output system. It is well known that BCLS method is based on compensation of asymptotic bias on the least-squares (LS) estimates by making use of noise variances estimates. The main feature of the proposed algorithm is to introduce a generalized least-squares type estimator in order to obtain the good estimates of noise variances. The results of a simulated example indicate that the proposed algorithm provides good estimates.

Bias-compensation based method for errors-in-variables model identification

Abstract It is well known that least-squares (LS) method gives biased parameter estimates when the input and output measurements are corrupted by noise. One possible approach for solving this bias problem is the bias-compensation based method such as the bias-compensated least-squares (BCLS) method. In this paper, a new bias-compnesation based method is proposed for identification of noisy input-output system. The proposed method is based on compensation of asymptotic bias on the instrumental variables type (IV-type) estimates by making use of noise covariances estimates. In order to obtain the noise covariances estimates, an overdetermined system of equations is introduced, and the noise covariances estimation algorithm is derived by solving this overdetermined system of equations. From the combination of the parameter estimation algorithm and the noise covariances estimation algorithm, the proposed bias-compensated instrumental variables type (BCIV-type) method can be established. The results of a simulated example indicate that the proposed algorithm provides good estimates.

Generalized eigenvector method for errors-in-variables models identification

This paper addresses the problem of identifying errors-in-variables models, where the both input and output measurements are corrupted by white noise. The Koopmans-Levin method, which is a computationally simple consistent estimation method for errors-in-variables situations, requires a priori knowledge about the values of variances or the ratio to measurement noises. To achieve the consistent estimation without a priori knowledge about the measurement noise variances, the method presented in this paper uses the idea that removes the bias induced by the output measurement noise using instrumental variable technique. Then the parameter estimation problem can be solved as the generalized eigenvalue problem, hence the proposed method is computationally simple. The results of simulated example indicate that the proposed method provides good parameter estimates.