### Abstract

A block orthogonal projection algorithm is proposed as a technique to balance convergence speed with computational complexity. However, if the observed noise is convolved with the output signal of an unknown system, a shortcoming of the block orthogonal projection algorithm is the susceptibility of the convergence characteristics to noise. To prevent degradation of the estimation accuracy, usually an operation is adopted to control the step gain in the adaptive algorithm by some technique or to average the coefficient vectors. Sometimes the expected results are not achieved by methods employing these techniques. In this paper, taking the perspective of the general theory of an orthogonal projection algorithm represented by a Moore-Penrose generalized inverse matrix, we propose an algorithm that attains excellent estimation accuracy by averaging over time the components constructed from the observed signal contained in the corrected direction vectors. This algorithm can be applied only under the conditions of the signal being uncorrelated to the observed noise and the noise having a zero mean. The convergence characteristics are examined by a computer simulation.

Original language | English |
---|---|

Pages (from-to) | 47-55 |

Number of pages | 9 |

Journal | Electronics and Communications in Japan, Part III: Fundamental Electronic Science (English translation of Denshi Tsushin Gakkai Ronbunshi) |

Volume | 84 |

Issue number | 2 |

DOIs | |

Publication status | Published - Jan 1 2001 |

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### All Science Journal Classification (ASJC) codes

- Electrical and Electronic Engineering

### Cite this

*Electronics and Communications in Japan, Part III: Fundamental Electronic Science (English translation of Denshi Tsushin Gakkai Ronbunshi)*,

*84*(2), 47-55. https://doi.org/10.1002/1520-6440(200102)84:2<47::AID-ECJC6>3.0.CO;2-4

**Robust block adaptive algorithm using the average of the divided direction vectors for the observed noise.** / Yoshimoto, Sadanobu; Furukawa, Toshihiro; Urahama, Kiichi.

Research output: Contribution to journal › Article

*Electronics and Communications in Japan, Part III: Fundamental Electronic Science (English translation of Denshi Tsushin Gakkai Ronbunshi)*, vol. 84, no. 2, pp. 47-55. https://doi.org/10.1002/1520-6440(200102)84:2<47::AID-ECJC6>3.0.CO;2-4

}

TY - JOUR

T1 - Robust block adaptive algorithm using the average of the divided direction vectors for the observed noise

AU - Yoshimoto, Sadanobu

AU - Furukawa, Toshihiro

AU - Urahama, Kiichi

PY - 2001/1/1

Y1 - 2001/1/1

N2 - A block orthogonal projection algorithm is proposed as a technique to balance convergence speed with computational complexity. However, if the observed noise is convolved with the output signal of an unknown system, a shortcoming of the block orthogonal projection algorithm is the susceptibility of the convergence characteristics to noise. To prevent degradation of the estimation accuracy, usually an operation is adopted to control the step gain in the adaptive algorithm by some technique or to average the coefficient vectors. Sometimes the expected results are not achieved by methods employing these techniques. In this paper, taking the perspective of the general theory of an orthogonal projection algorithm represented by a Moore-Penrose generalized inverse matrix, we propose an algorithm that attains excellent estimation accuracy by averaging over time the components constructed from the observed signal contained in the corrected direction vectors. This algorithm can be applied only under the conditions of the signal being uncorrelated to the observed noise and the noise having a zero mean. The convergence characteristics are examined by a computer simulation.

AB - A block orthogonal projection algorithm is proposed as a technique to balance convergence speed with computational complexity. However, if the observed noise is convolved with the output signal of an unknown system, a shortcoming of the block orthogonal projection algorithm is the susceptibility of the convergence characteristics to noise. To prevent degradation of the estimation accuracy, usually an operation is adopted to control the step gain in the adaptive algorithm by some technique or to average the coefficient vectors. Sometimes the expected results are not achieved by methods employing these techniques. In this paper, taking the perspective of the general theory of an orthogonal projection algorithm represented by a Moore-Penrose generalized inverse matrix, we propose an algorithm that attains excellent estimation accuracy by averaging over time the components constructed from the observed signal contained in the corrected direction vectors. This algorithm can be applied only under the conditions of the signal being uncorrelated to the observed noise and the noise having a zero mean. The convergence characteristics are examined by a computer simulation.

UR - http://www.scopus.com/inward/record.url?scp=0035193154&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0035193154&partnerID=8YFLogxK

U2 - 10.1002/1520-6440(200102)84:2<47::AID-ECJC6>3.0.CO;2-4

DO - 10.1002/1520-6440(200102)84:2<47::AID-ECJC6>3.0.CO;2-4

M3 - Article

AN - SCOPUS:0035193154

VL - 84

SP - 47

EP - 55

JO - Electronics and Communications in Japan, Part III: Fundamental Electronic Science (English translation of Denshi Tsushin Gakkai Ronbunshi)

JF - Electronics and Communications in Japan, Part III: Fundamental Electronic Science (English translation of Denshi Tsushin Gakkai Ronbunshi)

SN - 1042-0967

IS - 2

ER -