### Abstract

In this paper, a new class of robust Kalman filtering problem is tackled for time-varying linear systems. Aside from the conventional problem settings, it is assumed that the measurement matrix be unknown and only a noise corrupted observation of it be available for state estimation. The influence of the noise contaminated measurement matrix on the Kalman filter estimate is analyzed in the sense of classical weighted leastsquares criterion. Stochastic approximations of estimation errors due to noisy measurement matrix make it possible to develop a less conservative robust estimation scheme. Reinterpreting the stochastic error compensation procedure, the less conservative robust Kalman filtering problem is defined as finding a unique minimum of an indefinite quadratic cost. By solving the single stage optimization problem, the robust filter recursion is derived. As well, its existence condition is recursively checked using the estimation error covariance. It is also shown that the proposed filter is consistent in probability. A practical design example related to frequency estimation of noisy sinusoidal signal is given to verify the estimation performance of the proposed scheme.

Original language | English |
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Title of host publication | 2009 IEEE International Conference on Industrial Technology, ICIT 2009 |

DOIs | |

Publication status | Published - 2009 Jul 17 |

Event | 2009 IEEE International Conference on Industrial Technology, ICIT 2009 - Churchill, VIC, Australia Duration: 2009 Feb 10 → 2009 Feb 13 |

### Publication series

Name | Proceedings of the IEEE International Conference on Industrial Technology |
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### Other

Other | 2009 IEEE International Conference on Industrial Technology, ICIT 2009 |
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Country | Australia |

City | Churchill, VIC |

Period | 09/2/10 → 09/2/13 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Computer Science Applications
- Electrical and Electronic Engineering

### Cite this

*2009 IEEE International Conference on Industrial Technology, ICIT 2009*[4939683] (Proceedings of the IEEE International Conference on Industrial Technology). https://doi.org/10.1109/ICIT.2009.4939683

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*2009 IEEE International Conference on Industrial Technology, ICIT 2009.*, 4939683, Proceedings of the IEEE International Conference on Industrial Technology, 2009 IEEE International Conference on Industrial Technology, ICIT 2009, Churchill, VIC, Australia, 09/2/10. https://doi.org/10.1109/ICIT.2009.4939683

**Less conservative robust Kalman filtering using noise corrupted measurement matrix for discrete linear time-varying system.** / Ra, Won Sang; Whang, Ick Ho; Park, Jin Bae.

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

TY - GEN

T1 - Less conservative robust Kalman filtering using noise corrupted measurement matrix for discrete linear time-varying system

AU - Ra, Won Sang

AU - Whang, Ick Ho

AU - Park, Jin Bae

PY - 2009/7/17

Y1 - 2009/7/17

N2 - In this paper, a new class of robust Kalman filtering problem is tackled for time-varying linear systems. Aside from the conventional problem settings, it is assumed that the measurement matrix be unknown and only a noise corrupted observation of it be available for state estimation. The influence of the noise contaminated measurement matrix on the Kalman filter estimate is analyzed in the sense of classical weighted leastsquares criterion. Stochastic approximations of estimation errors due to noisy measurement matrix make it possible to develop a less conservative robust estimation scheme. Reinterpreting the stochastic error compensation procedure, the less conservative robust Kalman filtering problem is defined as finding a unique minimum of an indefinite quadratic cost. By solving the single stage optimization problem, the robust filter recursion is derived. As well, its existence condition is recursively checked using the estimation error covariance. It is also shown that the proposed filter is consistent in probability. A practical design example related to frequency estimation of noisy sinusoidal signal is given to verify the estimation performance of the proposed scheme.

AB - In this paper, a new class of robust Kalman filtering problem is tackled for time-varying linear systems. Aside from the conventional problem settings, it is assumed that the measurement matrix be unknown and only a noise corrupted observation of it be available for state estimation. The influence of the noise contaminated measurement matrix on the Kalman filter estimate is analyzed in the sense of classical weighted leastsquares criterion. Stochastic approximations of estimation errors due to noisy measurement matrix make it possible to develop a less conservative robust estimation scheme. Reinterpreting the stochastic error compensation procedure, the less conservative robust Kalman filtering problem is defined as finding a unique minimum of an indefinite quadratic cost. By solving the single stage optimization problem, the robust filter recursion is derived. As well, its existence condition is recursively checked using the estimation error covariance. It is also shown that the proposed filter is consistent in probability. A practical design example related to frequency estimation of noisy sinusoidal signal is given to verify the estimation performance of the proposed scheme.

UR - http://www.scopus.com/inward/record.url?scp=67650292931&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=67650292931&partnerID=8YFLogxK

U2 - 10.1109/ICIT.2009.4939683

DO - 10.1109/ICIT.2009.4939683

M3 - Conference contribution

AN - SCOPUS:67650292931

SN - 1424435064

SN - 9781424435067

T3 - Proceedings of the IEEE International Conference on Industrial Technology

BT - 2009 IEEE International Conference on Industrial Technology, ICIT 2009

ER -