### Abstract

Multiscale wavelet-based representation of data has shown great noise removal abilities when used in data filtering. In this paper, a multiscale Kalman filtering (MSKF) algorithm is developed, in which the filtering advantages of multiscale representation are combined with those of the Kaiman filter to further enhance its estimation performance. The MSKF algorithm relies on representing the data at multiple scales using Stationary Wavelet Transform (SWT), applying Kalman filtering on the scaling coefficients at each scales, and then selecting the optimum scale at which the Kaiman filter minimizes a cross validation mean square error criterion. The multiscale state space models Used in MSKF are also derived using the SWT representation. The MSKF algorithm is shown to outperform the conventional Kalman filter through a simulated example, and the reason behind this improvement is the additional filtering advantage gained by the low pass filters used in SWT.

Original language | English |
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Title of host publication | Proceedings of the 45th IEEE Conference on Decision and Control 2006, CDC |

Pages | 1679-1684 |

Number of pages | 6 |

Publication status | Published - 1 Dec 2006 |

Event | 45th IEEE Conference on Decision and Control 2006, CDC - San Diego, CA, United States Duration: 13 Dec 2006 → 15 Dec 2006 |

### Other

Other | 45th IEEE Conference on Decision and Control 2006, CDC |
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Country | United States |

City | San Diego, CA |

Period | 13/12/06 → 15/12/06 |

### Fingerprint

### ASJC Scopus subject areas

- Control and Systems Engineering
- Modelling and Simulation
- Control and Optimization

### Cite this

*Proceedings of the 45th IEEE Conference on Decision and Control 2006, CDC*(pp. 1679-1684). [4177666]

**Enhanced state estimation using multiscale Kalman filtering.** / Nounou, Mohamed.

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

*Proceedings of the 45th IEEE Conference on Decision and Control 2006, CDC.*, 4177666, pp. 1679-1684, 45th IEEE Conference on Decision and Control 2006, CDC, San Diego, CA, United States, 13/12/06.

}

TY - GEN

T1 - Enhanced state estimation using multiscale Kalman filtering

AU - Nounou, Mohamed

PY - 2006/12/1

Y1 - 2006/12/1

N2 - Multiscale wavelet-based representation of data has shown great noise removal abilities when used in data filtering. In this paper, a multiscale Kalman filtering (MSKF) algorithm is developed, in which the filtering advantages of multiscale representation are combined with those of the Kaiman filter to further enhance its estimation performance. The MSKF algorithm relies on representing the data at multiple scales using Stationary Wavelet Transform (SWT), applying Kalman filtering on the scaling coefficients at each scales, and then selecting the optimum scale at which the Kaiman filter minimizes a cross validation mean square error criterion. The multiscale state space models Used in MSKF are also derived using the SWT representation. The MSKF algorithm is shown to outperform the conventional Kalman filter through a simulated example, and the reason behind this improvement is the additional filtering advantage gained by the low pass filters used in SWT.

AB - Multiscale wavelet-based representation of data has shown great noise removal abilities when used in data filtering. In this paper, a multiscale Kalman filtering (MSKF) algorithm is developed, in which the filtering advantages of multiscale representation are combined with those of the Kaiman filter to further enhance its estimation performance. The MSKF algorithm relies on representing the data at multiple scales using Stationary Wavelet Transform (SWT), applying Kalman filtering on the scaling coefficients at each scales, and then selecting the optimum scale at which the Kaiman filter minimizes a cross validation mean square error criterion. The multiscale state space models Used in MSKF are also derived using the SWT representation. The MSKF algorithm is shown to outperform the conventional Kalman filter through a simulated example, and the reason behind this improvement is the additional filtering advantage gained by the low pass filters used in SWT.

UR - http://www.scopus.com/inward/record.url?scp=39649101040&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=39649101040&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:39649101040

SN - 1424401712

SN - 9781424401710

SP - 1679

EP - 1684

BT - Proceedings of the 45th IEEE Conference on Decision and Control 2006, CDC

ER -