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Research on Non-Hilbert Space Filtering

Author: GeLei
Tutor: YuFei
School: Harbin Engineering University
Course: System theory
Keywords: Hilbert space Indefinite metric space Krein space Kalman filtering H_∞filtering Norm weighted H_∞filtering
CLC: TN713
Type: Master's thesis
Year: 2009
Downloads: 11
Quote: 0
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Abstract


Kalman filtering is commonly used in state estimation theory, but traditional Kalman filter is based on Hilbert space, so the application condition of which should be met the quality of Hilbert space, that is the disturbance of the system must be white noise, which restricts the application area of the filter.This paper pulls in non-classical Functional space-indefinite metric space, and study the Krein space Kalman filter in this space, which is extended from the traditional Kalman filter. Then we compare the filters in two different spaces detailed in theory, and point out explicitly that both of them have the same structure expression, but Krein space Kalman filter has wilder existence conditions.Then we study an application of Krein space Kalman filter-constructing indefinite metric space H(?) filter, and find out the similarity and difference with Hilbert Kalman filter in theory. By analyzing the robustness mechanism of H(?) filter deeply, we illustrate that the filtering precision will decline when system noise and measured noise exist substantial difference, and in view of this situation, we proposed norm weighted H(?) filter. To the system whose covariance can be estimated approximately, higher state estimation precision can be obtained, and its robustness are kept at the same time. And it transforms into Hilbert space Kalman filter with noise covariance Qi, Ri whenγ-> (?).So it has higher state estimation precision than normal H(?) filter, whenever in the conditions of white noise or colored noise.At last we make numerical simulation comparison among the filters and the result shows that indefinite metric space H(?) filter has better robustness than Kalman filter, which can be used in colored noise environment. It also shows that the filtering precision is not satisfied when there exists a substantial difference between system noise and measured noise. However, the norm weighted H(?) filter proposed in this paper can overcome this defect and can improve filtering precision effectively on the condition of the disturbance of the system are known approximately.

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CLC: > Industrial Technology > Radio electronics, telecommunications technology > Basic electronic circuits > Filtering techniques,the filter
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