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| DOI： |
| Received:December 18, 2011Revised:January 23, 2013 |
| 基金项目:This work was supported by the Fundamental Research Funds for the Central Universities (No. DL13BB14). |
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| Krein-space approach to robust filtering for uncertain systems with time-varying bias |
| Heming JIA,Wenlong SONG,Jin FENG |
| (College of Mechanical and Electrical Engineering, Northeast Forestry University;College of Automation, Harbin Engineering University) |
| Abstract: |
| In this paper, a novel Krein space approach to robust estimation for uncertain systems with accumulated bias is proposed. The bias is impacted by system uncertainties and exists in both state transition and observer matrices. Initial conditions and cross-correlated uncertainty inputs are described by the sum quadratic constraint (SQC). Without modifying the SQC, the minimal state of the SQC is obtained through Krein space method. The inertia condition for a minimum of a deterministic quadratic form is derived when the coefficient of observer uncertainty input is non-unit matrix. Recursions of Krein space state filtering and bias filtering are developed respectively. Since the cross correlation between uncertainties is considered, a cross correlation gain is introduced into the posteriori estimator. Finally, a numerical example illustrates the performance of the proposed filter. |
| Key words: Linear system Parameter uncertainty Time-varying bias Sum quadratic form Krein space linear estimation |
