Information Geometric Approach for Nonlinear filtering
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- 英文论文题名：Information Geometric Approach for Nonlinear filtering
- 论文作者：Yubo Li ; Yongqiang Cheng ; Xiang Li ; Hongqiang Wang ; Xiaoqiang Hua ; Yuliang Qin
- 英文论文作者：Yubo Li ; Yongqiang Cheng ; Xiang Li ; Hongqiang Wang ; Xiaoqiang Hua ; Yuliang Qin ; College of Electronic Science and Engineering ; National University of Defense Technology
- 年：2017
- 作者机构：College of Electronic Science and Engineering,National University of Defense Technology;
- 英文论文关键词：Bayesian Filtering ; Information Geometry ; Riemannian Metric ; Kalman filter ; Natural Gradient Descent
- 会议召开时间：2017-07-26
- 会议录名称：第36届中国控制会议论文集（A）
- 英文会议录名称：Proceedings of the 36th Chinese Control Conference（A）
- 语种：英文
- 分类号：TN713
- 学会代码：KZLL
- 会议名称：第36届中国控制会议
- 会议地点：中国辽宁大连
- 主办单位：中国自动化学会控制理论专业委员会
- 学会名称：中国自动化学会控制理论专业委员会
- 页数：6
- 文件大小：241k
- 原文格式：D
- 会议级别：全国
摘要
In this paper, we consider the nonlinear filtering by using information geometric approach. Under the principle of Bayesian, the filtering problem has been converted to Bayesian estimation. Based on the estimation conditional on the measurement, the posterior probability density functions(PDFs) have constructed a statistical manifold. With the information geometric approach, the nonlinear characteristic has been convert to the Riemannian metric tensor, and the Bayesian estimation has been obtained by the natural gradient descent technique. Further, the information geometric nonlinear filtering has been induced. For the linear and Gaussian case, the metric tensor is constant, and the proposed method will be equivalent to the traditional Kalman filter. While the nonlinear case, the metric tensor is variable in which need be computed at each point on the statistical manifold, and the proposed method will be convergence along the optimal direction. The numerical experiment will show the better performance of our proposed method.
In this paper, we consider the nonlinear filtering by using information geometric approach. Under the principle of Bayesian, the filtering problem has been converted to Bayesian estimation. Based on the estimation conditional on the measurement, the posterior probability density functions(PDFs) have constructed a statistical manifold. With the information geometric approach, the nonlinear characteristic has been convert to the Riemannian metric tensor, and the Bayesian estimation has been obtained by the natural gradient descent technique. Further, the information geometric nonlinear filtering has been induced. For the linear and Gaussian case, the metric tensor is constant, and the proposed method will be equivalent to the traditional Kalman filter. While the nonlinear case, the metric tensor is variable in which need be computed at each point on the statistical manifold, and the proposed method will be convergence along the optimal direction. The numerical experiment will show the better performance of our proposed method.
In this paper, we consider the nonlinear filtering by using information geometric approach. Under the principle of Bayesian, the filtering problem has been converted to Bayesian estimation. Based on the estimation conditional on the measurement, the posterior probability density functions(PDFs) have constructed a statistical manifold. With the information geometric approach, the nonlinear characteristic has been convert to the Riemannian metric tensor, and the Bayesian estimation has been obtained by the natural gradient descent technique. Further, the information geometric nonlinear filtering has been induced. For the linear and Gaussian case, the metric tensor is constant, and the proposed method will be equivalent to the traditional Kalman filter. While the nonlinear case, the metric tensor is variable in which need be computed at each point on the statistical manifold, and the proposed method will be convergence along the optimal direction. The numerical experiment will show the better performance of our proposed method.
引文
[1]A.Haug,Bayesian Estimation and Tracking:A Practical Guide,John Wiley&Sons:Hoboken,NJ,USA,2012.
[2]S.Julier,and J.Uhlmann,Unscented filtering and nonlinear estimation.Proc.IEEE,92(3):401–422,2004.
[3]I.Arasaratnam,and S.Haykin,Cubature Kalman filters.IEEE Trans.Auto.Control,54(6):1254–1269,2009.
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[5]R.Zanetti,Recursive Update Filtering for Nonlinear Estimation.IEEE Trans.Auto.Control,57(6):1481–1490,2012.
[6]R.Zanetti,Adaptable Recursive Update Filter.J.Guid.Control Dyn.,38(7):1295–1299,2015.
[7]M.Fatemi,L.Svensson,L.Hammarstrand,and M.Morelande,A study of MAP estimation techniques for nonlinear filtering.Proc.15th International Conference on Information Fusion,1058–1065,2012.
[8]B.Bell,and F.Cathey,The iterated Kalman filter update as a Gauss-Newton method.IEEE Trans.Auto.Control,38:294–297,1993
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[12]S.Amari,and H.Nagaoka,Methods of Information Geometry,American Mathematical Society:Providence,RI,USA,2007.
[13]S.Amari,Natural gradient works efficiently in learning.Neural Comput,10:251–276,2008.
[14]G.Raskutti,and S.Mukherjee,The Information Geometry of Mirror Descent.IEEE Trans.Inf.Theory,61(3):1451–1457,2015.
[15]I.Arasaratnam,S.Haykin,and R.Elliott,Discrete-Time Nonlinear Filtering Algorithms Using Gauss-Hermite Quadrature,Proc.IEEE,95(5):953–977,May 2007.
[16]Y.Lee,and A.Majda,State estimation and prediction using clustered particle filters,PNAS,113(51):14609–14614.2016.
[17].García-Fernández,M.Morelande,and J.Grajal,Truncated unscented Kalman filtering.IEEE Trans.Signal Process.,60(7):3372–3386,2012.
[18]J.Dunik,O.Ejstraka,M.Simandl,and E.Blasch,RandomPoint-Based Filters:Analysis and Comparison in Target Tracking,IEEE Trans.Aerosp.Electron.Syst.,51:1403–1421,2015.
[19]S.Gillijns,O.Mendoza,J.Chandrasekar,B.De Moor,D.Bernstein,and A.Ridley,What is the ensemble Kalman filter and how well does it work?Proceedings of the 2006 American Control Conference,4448–4453,2006.
[2]S.Julier,and J.Uhlmann,Unscented filtering and nonlinear estimation.Proc.IEEE,92(3):401–422,2004.
[3]I.Arasaratnam,and S.Haykin,Cubature Kalman filters.IEEE Trans.Auto.Control,54(6):1254–1269,2009.
[4]M.Arulampalam,S.Maskell,and N.Gordon,A tutorial on particle filters for online nonlinear/non-gaussian bayesian tracking.IEEE Trans.Signal Process.,50(2):174–188,2000.
[5]R.Zanetti,Recursive Update Filtering for Nonlinear Estimation.IEEE Trans.Auto.Control,57(6):1481–1490,2012.
[6]R.Zanetti,Adaptable Recursive Update Filter.J.Guid.Control Dyn.,38(7):1295–1299,2015.
[7]M.Fatemi,L.Svensson,L.Hammarstrand,and M.Morelande,A study of MAP estimation techniques for nonlinear filtering.Proc.15th International Conference on Information Fusion,1058–1065,2012.
[8]B.Bell,and F.Cathey,The iterated Kalman filter update as a Gauss-Newton method.IEEE Trans.Auto.Control,38:294–297,1993
[9]R.Bellaire,E.Kamen,and S.Zabin,A new nonlinear iterated filter with applications to target tracking.Proc.SPIE Signal Data Process.Small Targets,2561:240–251,1995.
[10]T.Lefebvre,H.Bruyninckx,and J.Schutter,Kalman filters for nonlinear systems:A comparison of performance.Int.J.Control,77:639–653,2004
[11]R.Zhan and J.Wan,Iterated Unscented Kalman Filter for Passive target tracking,IEEE Trans.Aerosp.Electron.Syst.,43(3):1155–1163,2007.
[12]S.Amari,and H.Nagaoka,Methods of Information Geometry,American Mathematical Society:Providence,RI,USA,2007.
[13]S.Amari,Natural gradient works efficiently in learning.Neural Comput,10:251–276,2008.
[14]G.Raskutti,and S.Mukherjee,The Information Geometry of Mirror Descent.IEEE Trans.Inf.Theory,61(3):1451–1457,2015.
[15]I.Arasaratnam,S.Haykin,and R.Elliott,Discrete-Time Nonlinear Filtering Algorithms Using Gauss-Hermite Quadrature,Proc.IEEE,95(5):953–977,May 2007.
[16]Y.Lee,and A.Majda,State estimation and prediction using clustered particle filters,PNAS,113(51):14609–14614.2016.
[17].García-Fernández,M.Morelande,and J.Grajal,Truncated unscented Kalman filtering.IEEE Trans.Signal Process.,60(7):3372–3386,2012.
[18]J.Dunik,O.Ejstraka,M.Simandl,and E.Blasch,RandomPoint-Based Filters:Analysis and Comparison in Target Tracking,IEEE Trans.Aerosp.Electron.Syst.,51:1403–1421,2015.
[19]S.Gillijns,O.Mendoza,J.Chandrasekar,B.De Moor,D.Bernstein,and A.Ridley,What is the ensemble Kalman filter and how well does it work?Proceedings of the 2006 American Control Conference,4448–4453,2006.