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Stiefel manifold particle filtering

Zhu Zhi-Yu Yang Guan-Xiao

Stiefel manifold particle filtering

Zhu Zhi-Yu, Yang Guan-Xiao
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  • In order to solve the problems of particle degeneration and lackness of diversity of particle filter, a new particle filter based on Stiefel manifold (SMPF) is proposed in this paper. In the SMPF the system model is based on Stiefel manifold, Langevin distribution is used as a prior density, the matrix normal distribution serves a as likelihood function, and particle is sampled on the manifold distribution. First, manifold is embedded in Euclidean space, then the mean of particles is calculated in Euclidean space and its result is projected back to embedded manifold. So the influence on variance of particle weight caused by statistic characteristics of noise is removed, and a kind of universal selecting scheme of important probability density function is acquired which is hardly restrained to system state model. The simulation results based on univariate nonstationary growth model nonlinear system indicate that the SMPF works much better than scentless particle filter in real-time performance, robustness, filtering precision and filtering efficiency.
    • Funds:
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    Igor M, Den Y 2010 Acta Phys. Sin. 59 1396 (in Chinese)

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    Xie W X, Xu W 2005 Acta Phys. Sin. 54 1105 (in Chinese) [谢文贤、 徐 伟 2005 物理学报 54 1105]

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    Xiao F H, Yan G R 2004 Acta Phys. Sin. 53 396 (in Chinese)[肖方红、 闫桂荣 2004 物理学报 53 396]

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    Cheng C, Ansari R 2005 IEEE Sig. Proc. Lett. 12 242

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    Gong Y X, Yang H W, Hu W D, Yu W X 2008 J. Electron. Inform. Techn. 34 941(in Chinese)[龚亚信、 杨宏文、 胡卫东、 郁文贤 2008 电子与信息学报 34 941]

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    Duan Z H, Cai Z X, Yu J X 2008 Acta Autom. Sin. 34 581 (in Chinese) [段琢华、 蔡自兴、 于金霞 2008 自动化学报 34 581]

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    Du Z C, Liu L X, Tang B 2006 Chin. Phys. 15 2481

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    Du Z C, Tang B, Li K 2006 Acta Phys. Sin. 55 999 (in Chinese)[杜正聪、 唐 斌、 李 可 2006 物理学报 55 999]

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    Torma P, Szepesvari C 2005 Proceedings of the 4th International Symposium on Image and Signal Processing and Analysis (Philadelphia: Springer) p58

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    Song Z H, Wu X D 2008 Chin. Phys. B 17 3241

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    Li L Q, Ji H B, Luo J H 2007 J. Xidian Univ. 34 233 (in Chinese)[李良群、 姬红兵、 罗军辉 2007 西安电子科技大学学报 34 233]

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    Sui S L, Zao X W 2008 J. Syst. Sim. 20 4971 (in Chinese) [隋树林、 赵晓伟 2008 系统仿真学报 20 4971]

    [14]

    Zhu Z Y, Jiang C S 2007 J. Syst. Eng. Electron. 29 1596 (in Chinese)[朱志宇、 姜长生 2007 系统工程与电子技术 29 1596]

    [15]

    Hayakawa T 1990 Ann. Inst. Statis. Math. 42 312

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    Chikuse Y 2006 Multivar. Anal. 97 1284

    [17]

    Zhou G H, Jing Z L, Hu H T 2006 J. Shanghai Jiaotong Univ. 40 1135 (in Chinese)[邹国辉、 敬忠良、 胡洪涛 2006 上海交通大学学报 40 1135]

  • [1]

    Cao W F, Ju Z P, Liu X W 2010 Acta Phys. Sin. 59 199 (in Chinese)[曹午飞、 鞠志萍、 刘小伟 2010 物理学报 59 199]

    [2]

    Igor M, Den Y 2010 Acta Phys. Sin. 59 1396 (in Chinese)

    [3]

    Xie W X, Xu W 2005 Acta Phys. Sin. 54 1105 (in Chinese) [谢文贤、 徐 伟 2005 物理学报 54 1105]

    [4]

    Xiao F H, Yan G R 2004 Acta Phys. Sin. 53 396 (in Chinese)[肖方红、 闫桂荣 2004 物理学报 53 396]

    [5]

    Cheng C, Ansari R 2005 IEEE Sig. Proc. Lett. 12 242

    [6]

    Gong Y X, Yang H W, Hu W D, Yu W X 2008 J. Electron. Inform. Techn. 34 941(in Chinese)[龚亚信、 杨宏文、 胡卫东、 郁文贤 2008 电子与信息学报 34 941]

    [7]

    Duan Z H, Cai Z X, Yu J X 2008 Acta Autom. Sin. 34 581 (in Chinese) [段琢华、 蔡自兴、 于金霞 2008 自动化学报 34 581]

    [8]

    Du Z C, Liu L X, Tang B 2006 Chin. Phys. 15 2481

    [9]

    Du Z C, Tang B, Li K 2006 Acta Phys. Sin. 55 999 (in Chinese)[杜正聪、 唐 斌、 李 可 2006 物理学报 55 999]

    [10]

    Torma P, Szepesvari C 2005 Proceedings of the 4th International Symposium on Image and Signal Processing and Analysis (Philadelphia: Springer) p58

    [11]

    Song Z H, Wu X D 2008 Chin. Phys. B 17 3241

    [12]

    Li L Q, Ji H B, Luo J H 2007 J. Xidian Univ. 34 233 (in Chinese)[李良群、 姬红兵、 罗军辉 2007 西安电子科技大学学报 34 233]

    [13]

    Sui S L, Zao X W 2008 J. Syst. Sim. 20 4971 (in Chinese) [隋树林、 赵晓伟 2008 系统仿真学报 20 4971]

    [14]

    Zhu Z Y, Jiang C S 2007 J. Syst. Eng. Electron. 29 1596 (in Chinese)[朱志宇、 姜长生 2007 系统工程与电子技术 29 1596]

    [15]

    Hayakawa T 1990 Ann. Inst. Statis. Math. 42 312

    [16]

    Chikuse Y 2006 Multivar. Anal. 97 1284

    [17]

    Zhou G H, Jing Z L, Hu H T 2006 J. Shanghai Jiaotong Univ. 40 1135 (in Chinese)[邹国辉、 敬忠良、 胡洪涛 2006 上海交通大学学报 40 1135]

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    [6] Zhang Meng, Yao Ruo-He, Liu Yu-Rong. A channel thermal noise model of nanoscaled metal-oxide-semiconductor field-effect transistor. Acta Physica Sinica, 2020, 69(5): 057101. doi: 10.7498/aps.69.20191512
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  • Received Date:  16 August 2009
  • Accepted Date:  05 July 2010
  • Published Online:  15 December 2010

Stiefel manifold particle filtering

  • 1. School of Electronics and Information, Jiangsu University of Science and Technology, Zhenjiang 212003, China

Abstract: In order to solve the problems of particle degeneration and lackness of diversity of particle filter, a new particle filter based on Stiefel manifold (SMPF) is proposed in this paper. In the SMPF the system model is based on Stiefel manifold, Langevin distribution is used as a prior density, the matrix normal distribution serves a as likelihood function, and particle is sampled on the manifold distribution. First, manifold is embedded in Euclidean space, then the mean of particles is calculated in Euclidean space and its result is projected back to embedded manifold. So the influence on variance of particle weight caused by statistic characteristics of noise is removed, and a kind of universal selecting scheme of important probability density function is acquired which is hardly restrained to system state model. The simulation results based on univariate nonstationary growth model nonlinear system indicate that the SMPF works much better than scentless particle filter in real-time performance, robustness, filtering precision and filtering efficiency.

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