### Abstract

The corrected least squares (CLS) approach gives a consistent estimate of a system model in the presence of input and output noises. However, when the input signal is band-limited or strongly correlated, and/or a transfer function model is identified by using an overdetermined model, the CLS estimate often becomes ill-conditioned. To overcome this problem, we propose a regularized CLS estimation method by introducing multiple regularization parameters to minimize the mean squares error (MSE) of the regularized CLS estimate. The asymptotic MSE can be evaluated by considering the third and fourth cross moments of the input and output noises, and an analytical expression of the optimal regularization parameters minimizing the MSE is also clarified. Furthermore, an effective regularization algorithm is given by using only accessible input-output data. The relationship between the regularization using multiple parameters and the truncation of small eigenvalues is investigated and then it is clarified that the proposed regularization scheme is also efficient to decide the order of a transfer function model.

Original language | English |
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Title of host publication | Proceedings of the IEEE Conference on Decision and Control |

Publisher | IEEE |

Pages | 1807-1814 |

Number of pages | 8 |

Volume | 2 |

Publication status | Published - 1995 |

Event | Proceedings of the 1995 34th IEEE Conference on Decision and Control. Part 1 (of 4) - New Orleans, LA, USA Duration: 1995 Dec 13 → 1995 Dec 15 |

### Other

Other | Proceedings of the 1995 34th IEEE Conference on Decision and Control. Part 1 (of 4) |
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City | New Orleans, LA, USA |

Period | 95/12/13 → 95/12/15 |

### Fingerprint

### ASJC Scopus subject areas

- Chemical Health and Safety
- Control and Systems Engineering
- Safety, Risk, Reliability and Quality

### Cite this

*Proceedings of the IEEE Conference on Decision and Control*(Vol. 2, pp. 1807-1814). IEEE.

**Minimum MSE based regularization for system identification in the presence of input and output noise.** / Xin, J.; Ohmori, Hiromitsu; Sano, A.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Proceedings of the IEEE Conference on Decision and Control.*vol. 2, IEEE, pp. 1807-1814, Proceedings of the 1995 34th IEEE Conference on Decision and Control. Part 1 (of 4), New Orleans, LA, USA, 95/12/13.

}

TY - GEN

T1 - Minimum MSE based regularization for system identification in the presence of input and output noise

AU - Xin, J.

AU - Ohmori, Hiromitsu

AU - Sano, A.

PY - 1995

Y1 - 1995

N2 - The corrected least squares (CLS) approach gives a consistent estimate of a system model in the presence of input and output noises. However, when the input signal is band-limited or strongly correlated, and/or a transfer function model is identified by using an overdetermined model, the CLS estimate often becomes ill-conditioned. To overcome this problem, we propose a regularized CLS estimation method by introducing multiple regularization parameters to minimize the mean squares error (MSE) of the regularized CLS estimate. The asymptotic MSE can be evaluated by considering the third and fourth cross moments of the input and output noises, and an analytical expression of the optimal regularization parameters minimizing the MSE is also clarified. Furthermore, an effective regularization algorithm is given by using only accessible input-output data. The relationship between the regularization using multiple parameters and the truncation of small eigenvalues is investigated and then it is clarified that the proposed regularization scheme is also efficient to decide the order of a transfer function model.

AB - The corrected least squares (CLS) approach gives a consistent estimate of a system model in the presence of input and output noises. However, when the input signal is band-limited or strongly correlated, and/or a transfer function model is identified by using an overdetermined model, the CLS estimate often becomes ill-conditioned. To overcome this problem, we propose a regularized CLS estimation method by introducing multiple regularization parameters to minimize the mean squares error (MSE) of the regularized CLS estimate. The asymptotic MSE can be evaluated by considering the third and fourth cross moments of the input and output noises, and an analytical expression of the optimal regularization parameters minimizing the MSE is also clarified. Furthermore, an effective regularization algorithm is given by using only accessible input-output data. The relationship between the regularization using multiple parameters and the truncation of small eigenvalues is investigated and then it is clarified that the proposed regularization scheme is also efficient to decide the order of a transfer function model.

UR - http://www.scopus.com/inward/record.url?scp=0029540583&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0029540583&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:0029540583

VL - 2

SP - 1807

EP - 1814

BT - Proceedings of the IEEE Conference on Decision and Control

PB - IEEE

ER -