Minimization of the estimation error of the Kalman filter with an H∞ error bound by Secant method

Bing-Fei Wu; Hung Hseng Hsu

doi:10.1109/CDC.1995.480356

Minimization of the estimation error of the Kalman filter with an H∞ error bound by Secant method

Bing-Fei Wu^*, Hung Hseng Hsu

^*Corresponding author for this work

Department of Electrical and Computer Engineering

Research output: Contribution to journal › Conference article › peer-review

3 Scopus citations

Abstract

Designing a Kalman filter with a constraint on the H_∞ norm of the estimation error was first developed by Bernstein and Haddad in 1989. The main result is a sufficient condition for characterizing the Kalman filter. Like the standard Kalman filter, the orthogonal principles are also shown to sustain. Furthermore, the uniqueness, as opposed to the H_∞ filter, of the filter is implied by the orthogonal principles. In this paper, an approach to get the minimum energy with a constraint on the H_∞ norm of the estimation error is proposed since the original work of Bernstein and Haddad does not, in general, reach the minimum energy of the estimation error. By means of Secant method, the energy of the estimation error can be reduced as minimum as possible, under the condition that the H_∞ error bound is still satisfied.

Original language	English
Article number	480356
Pages (from-to)	1538-1543
Number of pages	6
Journal	Proceedings of the IEEE Conference on Decision and Control
Volume	2
DOIs	https://doi.org/10.1109/CDC.1995.480356
State	Published - 13 Dec 1995
Event	Proceedings of the 1995 34th IEEE Conference on Decision and Control. Part 1 (of 4) - New Orleans, LA, USA Duration: 13 Dec 1995 → 15 Dec 1995

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10.1109/CDC.1995.480356

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title = "Minimization of the estimation error of the Kalman filter with an H∞ error bound by Secant method",

abstract = "Designing a Kalman filter with a constraint on the H∞ norm of the estimation error was first developed by Bernstein and Haddad in 1989. The main result is a sufficient condition for characterizing the Kalman filter. Like the standard Kalman filter, the orthogonal principles are also shown to sustain. Furthermore, the uniqueness, as opposed to the H∞ filter, of the filter is implied by the orthogonal principles. In this paper, an approach to get the minimum energy with a constraint on the H∞ norm of the estimation error is proposed since the original work of Bernstein and Haddad does not, in general, reach the minimum energy of the estimation error. By means of Secant method, the energy of the estimation error can be reduced as minimum as possible, under the condition that the H∞ error bound is still satisfied.",

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AU - Hsu, Hung Hseng

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N2 - Designing a Kalman filter with a constraint on the H∞ norm of the estimation error was first developed by Bernstein and Haddad in 1989. The main result is a sufficient condition for characterizing the Kalman filter. Like the standard Kalman filter, the orthogonal principles are also shown to sustain. Furthermore, the uniqueness, as opposed to the H∞ filter, of the filter is implied by the orthogonal principles. In this paper, an approach to get the minimum energy with a constraint on the H∞ norm of the estimation error is proposed since the original work of Bernstein and Haddad does not, in general, reach the minimum energy of the estimation error. By means of Secant method, the energy of the estimation error can be reduced as minimum as possible, under the condition that the H∞ error bound is still satisfied.

AB - Designing a Kalman filter with a constraint on the H∞ norm of the estimation error was first developed by Bernstein and Haddad in 1989. The main result is a sufficient condition for characterizing the Kalman filter. Like the standard Kalman filter, the orthogonal principles are also shown to sustain. Furthermore, the uniqueness, as opposed to the H∞ filter, of the filter is implied by the orthogonal principles. In this paper, an approach to get the minimum energy with a constraint on the H∞ norm of the estimation error is proposed since the original work of Bernstein and Haddad does not, in general, reach the minimum energy of the estimation error. By means of Secant method, the energy of the estimation error can be reduced as minimum as possible, under the condition that the H∞ error bound is still satisfied.

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Y2 - 13 December 1995 through 15 December 1995

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Minimization of the estimation error of the Kalman filter with an H∞ error bound by Secant method

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