A journal of IEEE and CAA , publishes high-quality papers in English on original theoretical/experimental research and development in all areas of automation
Volume 3 Issue 1
Jan.  2016

IEEE/CAA Journal of Automatica Sinica

  • JCR Impact Factor: 7.847, Top 10% (SCI Q1)
    CiteScore: 13.0, Top 5% (Q1)
    Google Scholar h5-index: 64, TOP 7
Turn off MathJax
Article Contents
Xiao Lu, Linglong Wang, Haixia Wang and Xianghua Wang, "Kalman Filtering for Delayed Singular Systems with Multiplicative Noise," IEEE/CAA J. of Autom. Sinica, vol. 3, no. 1, pp. 51-58, 2016.
Citation: Xiao Lu, Linglong Wang, Haixia Wang and Xianghua Wang, "Kalman Filtering for Delayed Singular Systems with Multiplicative Noise," IEEE/CAA J. of Autom. Sinica, vol. 3, no. 1, pp. 51-58, 2016.

Kalman Filtering for Delayed Singular Systems with Multiplicative Noise

Funds:

This work was supported by National Natural Science Foundation of China (61273197, 61503224), Applied Fundamental Research of Qingdao (14-2-4-19-jch), Huangdao District Science and Technology Project (2014-1- 33), China Postdoctoral Science Foundation (2015M582115), and "Taishan Scholarship" Construction Engineering.

  • Kalman filtering problem for singular systems is dealt with, where the measurements consist of instantaneous measurements and delayed ones, and the plant includes multiplicative noise. By utilizing standard singular value decomposition, the restricted equivalent delayed system is presented, and the Kalman filters for the restricted equivalent system are given by using the well-known re-organization of innovation analysis lemma. The optimal Kalman filter for the original system is given based on the above Kalman filter by recursive Riccati equations, and a numerical example is presented to show the validity and efficiency of the proposed approach, where the comparison between the filter and predictor is also given.

     

  • loading
  • [1]
    Wiener N. Extrapolation, Interpolation, and Smoothing of Stationary Time Series. Cambridge, MA:The MIT Press, 1949.
    [2]
    Kalman R E. A new approach to linear filtering and prediction problems. Journal of Basic Engineering, 1960, 82(1):35-45
    [3]
    Hassibi B, Sayed A H, Kailath T. Linear estimation in Krein spaces. I. Theory. IEEE Transactions on Automatic Control, 1996, 41(1):18-33
    [4]
    Hassibi B, Sayed A H, Kailath T. Linear estimation in Krein spaces. II. Applications. IEEE Transactions on Automatic Control, 1996, 41(1):34-49
    [5]
    Hassibi B, Sayed A H, Kailath T. Indefinite-Quadratic Estimation and Control-A Unified Approach to H2 and H Theories. Englewood Cliffs, NJ:Prentice-Hall, 1999.
    [6]
    Zhang H S, Xie L H, Soh Y C. A unified approach to linear estimation for discrete-time systems. II. H estimation. In:Proceedings of the 40th IEEE Conference on Decision and Control. Orlando, FL:IEEE, 2001. 2923-2928
    [7]
    Zhang H S, Xie L H, Soh Y C. Risk-sensitive filtering, prediction and smoothing for discrete-time singular systems. Automatica, 2003, 39(1):57-66
    [8]
    Zhang H S, Chai T Y, Liu X J. A unified approach to optimal state estimation for stochastic singular systems. Automatica, 1998, 34(6):777-781
    [9]
    Dai L. Filtering and LQG problems for discrete-time stochastic singular systems. IEEE Transactions on Automatic Control, 1989, 34(10):1105-1108
    [10]
    Olemskoi A I. Theory of stochastic systems with singular multiplicative noise. Physics-Uspekhi, 2007, 41(3):269
    [11]
    Chu D S, Gao S W, Guo L. An augmented optimal filter for multichannel stochastic singular systems with multiplicative noise. In:Proceedings of the 2007 IEEE International Conference on Automation and Logistics. Jinan, China:IEEE, 2007. 378-382
    [12]
    Chu D S, Gao S W. State optimal estimation algorithm for singular systems with multiplicative noise. Periodical of Ocean University of China, 2008, 38(5):814-818(in Chinese)
    [13]
    Gao S W. Study of optimal estimation algorithm for singular systems with multiplicative noise[Master dissertation], Ocean University of China, China, 2008(in Chinese)
    [14]
    Lu X, Wang H X, Wu F. Optimal multi-step predictor for descriptor systems with multiplicative noise and delayed measurement. Control Theory and Applications, 2015, 32(6):787-793(in Chinese)
    [15]
    Lu X, Wang L L, Wang H X, Pu Q, Dong X. Optimal FSL smoothing for delayed descriptor systems. In:Proceedings of the 34th Chinese Control Conference. Hangzhou, China:IEEE, 2015. 131-134
    [16]
    Lu X, Dong X, Wang H X, Song B Y. On fixed-point smoothing for descriptor systems with multiplicative noise and single delayed observations. Mathematical Problems in Engineering, 2015, 2015:Article ID 658153
    [17]
    Ni Y H, Li X. Consensus seeking in multi-agent systems with multiplicative measurement noises. Systems and Control Letters, 2013, 62(5):430-437
    [18]
    Zhang H S, Xie L H, Zhang H S, Soh Y C. A reorganized innovation approach to linear estimation. IEEE Transactions on Automatic Control, 2004, 49(10):1810-1814
    [19]
    Lu X, Liu S, Luan S, Pu Q. Kalman filtering for singular WSN systems with multiplicative noise. In:Proceedings of the 2014 International Conference on Mechatronics and Control. Jinzhou, China:IEEE, 2014. 1319-1323
    [20]
    Lu X, Dong X, Wang H X. Optimal fixed-point smoothing for delayed descriptor systems with multiplicative noise. In:Proceedings of the 27th Chinese Control and Decision Conference. Qingdao, China:IEEE, 2015. 2810-2813

Catalog

    通讯作者: 陈斌, bchen63@163.com
    • 1. 

      沈阳化工大学材料科学与工程学院 沈阳 110142

    1. 本站搜索
    2. 百度学术搜索
    3. 万方数据库搜索
    4. CNKI搜索

    Article Metrics

    Article views (1020) PDF downloads(4) Cited by()

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return