Bias-Compensated Least-Squares Estimation and Parameter Transformation in Identification with Over-Parameterized Models

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  • オーバーパラメータモデルを用いた同定におけるパラメータ変換とバイアス補償最小2乗推定
  • オーバーパラメータ モデル オ モチイタ ドウテイ ニ オケル パラメータ ヘンカン ト バイアス ホショウ サイショウ 2ジョウ スイテイ

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Abstract

For the problem of estimating unknown parameters of the transfer function model from input and output (I/O) data contaminated by colored measurement noise, a three-step estimation procedure has been previously proposed to exploit the I/O correlation information with respect to the correlation time. This paper analyzes this procedure from the compatibility between the parameter transformation and the bias-compensated least-squares (BCLS) estimation used in the third step. The transformation is made from the over-parameterized model in the first and second steps to the final model with the true order in the final step, and is based on the minimization of the mean square error (MSE) between the outputs of the two models. The BCLS estimation is based on the minimization of MSE between the final model output and the process output. It is verified that the condition for compatibility, i.e. the equivalence of two minimizations, is a consequence of the two over-parameterized estimation equations in the first two steps, and that the over-parameterization assures an inclusive expansion of the I/O correlation information. Simulation results are presented to demonstrate the equivalence.

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