Estimation Procedure for Parameters of Transfer Function by Using Estimates of Autocorrelation Function of Measurement Noise

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  • 観測雑音の自己相関関数の推定値を用いた伝達関数のパラメータ推定法
  • カンソク ザツオン ノ ジコ ソウカン カンスウ ノ スイテイチ オ モチイタ

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Abstract

This paper considers the problem of estimating the parameters, of the process transfer function G (z-1) by using the estimates of the noise autocorrelation function φv (l), from input data and output data containing colored measurement noise in the single-input/single-output linear discrete system. Based on the correlation analysis (instrumental variable (IV) method), a three-step estimation procedure is proposed, i. e.1st-step : an initial estimation of a transfer function model using N given by input, 2nd-step : an estimation of φv (l), and 3rd-step : a final estimation of parameters from the standpoint of the optimal IV estimation method. In the 2nd-step, the estimation for φv (l) is derived from solving simultaneous equations with relation between input/output correlation functions, G (z-1) and φv (l). Extending the input/output correlation information by selecting a model with higher order than the true order in the 1st-step, better estimates of the parameters of G (z-1) are obtained in the final step. The validity of our estimation procedure is demonstrated by computer simulations.

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