Design of Decentralized $H^\infty$ Filter using the Generalization of $H^\infty$ Filter in Indefinite Inner Product Spaces

부정 내적 공간에서의$H^\infty$ 필터의 일반화를 통한 분산 $H^\infty$ 필터의 설계

  • Kim, Gyeong-Geun (Agency for Defense Development) ;
  • Jin, Seung-Hui (Dept.of Electric Electronics Engineering, Engineering College, Yonsel University) ;
  • Yun, Tae-Seong (Dept.of Electric Engineering, Engineering College, Changwon National University) ;
  • Park, Jin-Bae (Dept.of Electric Engineering, Engineering College, Yonsel University)
  • Published : 1999.06.01

Abstract

We design the robust and inherently fault tolerant decetralized$$H^infty$$ filter for the multisensor state estimation problem when there are insufficient priori informations on the statistical properties of external disturbances. For developing the proposed algorithm, an alternative form of suboptimal$$H^infty$$ filter equations are formulated by applying an alternative form of Kalman filter equations to the indefinite inner product space state model of suboptimal$$H^infty$$ filtering problems. The decentralized$$H^infty$$ filter that consists of local and central fusion filters can be designed effciently using the proposed alternative$$H^infty$$ filiter gain equations. The proposed decentralized$$H^infty$$ filter is robust against un-known external disturbances since it bounds the maximum energy gain from the external disturbances to the estimation errors under the prescribed level$$r^2$$ in both local and central fusion filters and is also fault tolerant due to its inherent redundancy. In addition, the central fusion equations between the global and local data can reduce the unnecessary calculation burden effectively. Computer simulations are made to ceritfy the robustness and fault tolerance of the proposed algorithm.

Keywords

References

  1. Introduction to Random Signals and Applied Kalman Filtering Robert Grover Brown;Patrick Y. C. Hwang
  2. Optimal Control and Estimation Theory Siouris
  3. Estimation and Tracking Yaakov Bar-Shalom;Xiao-Rong Li
  4. IEEE Trans. on Aerospace and Electronic Systems v.AES-23 no.6 A Fault-Tolerant Multisensor Navigation System Design B. D. Brumback;M. D. Srinath
  5. IEEE. Trans. Aerospace and Electronic Systems v.23 no.1 Decentralized Filtering and Redundancy Management for Multisensor Navigation Thomas Kerr
  6. IEEE Trans. on Automatic Control v.AC-24 no.2 Computation and Transmission Require ments for a Decentralized Linear-Quadratic-Gaussian Control Problem Jason L. Speyer
  7. IEEE Trans. on Automatic Control v.AC-27 no.4 Combining and Updating of Local Estimates and Regional Maps Along Sets of One-Dimensional Tracks Alan S. Willsky;Martin G. Bello;David A. Castanon;Bernard C. Levy;George C. Verghese
  8. IEEE Trans. Automatic Control v.33 no.1 Decentralized Structures for Parallel Kalman Filtering Hamid R. Hassimipour;Sumit Roy;Alan J. Laub
  9. The International Journal of Robotics Research v.12 no.1 A Fully Decentralized Multi-Sensor System For Tracking and Surveillance B.S.Y. Rao;H.F. Durrant-Whyte;J. A. Sheen
  10. Systems & Control Letters v.12 Steady-state Kalman filtering with an $H^{\infty}$ error bound Dennis S. Bernstein;Wassim M. Haddad
  11. Proc. IEEE CDC $H^{\infty}$ Optimal Estimation: A Tutorial U. Shaked;Y. Theodor
  12. Proc. of the IEEE v.85 no.1 Sensor Fusion for Mobile Robot Navigation Moshe Kam;Xiaoxun Zhu;Paul Kalate
  13. The Annals of Statistics v.12 no.3 Optimal Fixed Size Confidence Procedures for a Restricted Parameter Space Mehmet Zeytinoglu;Max Mintz
  14. The Annals of Statistics v.16 no.3 Robust Fixed Size Confidence Procedures for a Restricted Parameter Space Mehmat Zeytinoglu;Max Mintz
  15. Proc. Int. Conf. on. Robot. Automat. Robust Fusion of Location Information R. McKendall;M. Mintz
  16. IEEE Trans. on Automatic Control v.41 no.1 Linear Estimation in Krein Spaces-Part I; Theory Babak Hassibi;Ali H. Sayed;Thomas Kailath
  17. IEEE Trans. on Automatic Control v.41 no.1 Linear Estimation in Krein Spaces-Part II;Applications Babak Hassibi;Ali H. Sayed;Thomas Kailath
  18. Mathmatics and Its Applications Inner Product Structures, Theory and Applications V. I. Istratescu
  19. Mathematical Techniques in Multisensor Data Fusion David L. Hall
  20. Robust and Optimal Control Kemin Zhou;John C. Doyle;Keith Glover
  21. IEEE Trans. on Automatic Control v.AC-34 no.8 State-Space Solutions to Standard $H_2$ and $H_{\infty}$ Control Problems J. C. Doyle;K. Glover;P. P. Khargonekar;B. A. Francis
  22. IEEE Trans. on Automatic Control v.AC-36 no.2 Filtering and Smoothing in an $H_{\infty}$ Setting K. M. Nagpal;P. P. Khargonekar
  23. $H^{\infty}$ Optimal Control and Related Minimax Design Problems: A Dynamic Game Approach T. Basar;P. Bernhard