Application of Improved Simplex Quadrature Cubature Kalman Filter in Nonlinear Dynamic System

A novel spherical simplex Gauss–Laguerre quadrature cubature Kalman filter is proposed to improve the estimation accuracy of nonlinear dynamic system. The nonlinear Gaussian weighted integral has been approximately evaluated using the spherical simplex rule and the arbitrary order Gauss–Laguerre quadrature rule. Thus, a spherical simplex Gauss–Laguerre cubature quadrature rule is developed, from which the general computing method of the simplex cubature quadrature points and the corresponding weights are obtained. Then, under the nonlinear Kalman filtering framework, the spherical simplex Gauss–Laguerre quadrature cubature Kalman filter is derived. A high-dimensional nonlinear state estimation problem and a target tracking problem are utilized to demonstrate the effectiveness of the proposed spherical simplex Gauss–Laguerre cubature quadrature rule to improve the performance.

[1]  Shovan Bhaumik,et al.  Improved High-Degree Cubature Kalman Filter , 2015, 2015 Sensor Signal Processing for Defence (SSPD).

[2]  Arnold Neumaier,et al.  Introduction to Numerical Analysis , 2001 .

[3]  Jwu-Sheng Hu,et al.  Second-Order Extended $H_{\infty}$ Filter for Nonlinear Discrete-Time Systems Using Quadratic Error Matrix Approximation , 2011, IEEE Transactions on Signal Processing.

[4]  Ming Xin,et al.  The high-degree cubature Kalman filter , 2012, 2012 IEEE 51st IEEE Conference on Decision and Control (CDC).

[5]  Qinglin Wang,et al.  Event-Trigger Heterogeneous Nonlinear Filter for Wide-Area Measurement Systems in Power Grid , 2019, IEEE Transactions on Smart Grid.

[6]  I. P. Mysovskih.  Approximate Calculation of Integrals , 1969 .

[7]  Xiaohang Wu,et al.  Improved Student’s t-Based Unscented Filter and its Application to Trajectory Estimation for Maneuvering Target , 2019 .

[8]  David L. Darmofal,et al.  Higher-Dimensional Integration with Gaussian Weight for Applications in Probabilistic Design , 2005, SIAM J. Sci. Comput..

[9]  Torsten Söderström,et al.  Advanced point-mass method for nonlinear state estimation , 2006, Autom..

[10]  Fred Daum,et al.  Particle degeneracy: root cause and solution , 2011, Defense + Commercial Sensing.

[11]  An Li,et al.  Transformed Unscented Kalman Filter , 2013, IEEE Transactions on Automatic Control.

[12]  Gang Hao,et al.  Distributed fusion cubature Kalman filters for nonlinear systems , 2019, International Journal of Robust and Nonlinear Control.

[13]  Yuanli Cai,et al.  Adaptive Fifth-Degree Cubature Information Filter for Multi-Sensor Bearings-Only Tracking , 2018, Sensors.

[14]  Sheng-Fuu Lin,et al.  Robust Huber-Based Cubature Kalman Filter for GPS Navigation Processing , 2016, Journal of Navigation.

[15]  E. Yaz.  Linear Matrix Inequalities In System And Control Theory , 1998, Proceedings of the IEEE.

[16]  P. A. Ejegwa,et al.  Novel distance measures for Pythagorean fuzzy sets with applications to pattern recognition problems , 2019, Granular Computing.

[17]  Bin Liu,et al.  Recognition and Vulnerability Analysis of Key Nodes in Power Grid Based on Complex Network Centrality , 2018, IEEE Transactions on Circuits and Systems II: Express Briefs.

[18]  Chongzhao Han,et al.  A Bayesian Approach to Track Multiple Extended Targets Using Particle Filter for Nonlinear System , 2018 .

[19]  Xi Chen,et al.  Event-Trigger Particle Filter for Smart Grids With Limited Communication Bandwidth Infrastructure , 2018, IEEE Transactions on Smart Grid.

[20]  F. Crick,et al.  Molecular Structure of Nucleic Acids: A Structure for Deoxyribose Nucleic Acid , 1974, Nature.

[21]  Hongbin Li,et al.  Maximum Correntropy Derivative-Free Robust Kalman Filter and Smoother , 2018, IEEE Access.

[22]  Ming Xin,et al.  High-degree cubature Kalman filter , 2013, Autom..

[23]  Peng Shi,et al.  A survey on Markovian jump systems: Modeling and design , 2015 .

[24]  Thiagalingam Kirubarajan,et al.  Estimation with Applications to Tracking and Navigation , 2001 .

[25]  Jeffrey K. Uhlmann,et al.  Unscented filtering and nonlinear estimation , 2004, Proceedings of the IEEE.

[26]  John Monahan,et al.  Stochastic Integration Rules for Infinite Regions , 1998, SIAM J. Sci. Comput..

[27]  C. K. Michael Tse,et al.  Spherical Simplex-Radial Cubature Kalman Filter , 2014, IEEE Signal Processing Letters.

[28]  Neil J. Gordon,et al.  A tutorial on particle filters for online nonlinear/non-Gaussian Bayesian tracking , 2002, IEEE Trans. Signal Process..

[29]  Yun Li,et al.  Nonlinear weighted measurement fusion Unscented Kalman Filter with asymptotic optimality , 2015, Inf. Sci..

[30]  Xi Chen,et al.  A Nested Tensor Product Model Transformation , 2019, IEEE Transactions on Fuzzy Systems.

[31]  Simo Särkkä,et al.  On Gaussian Optimal Smoothing of Non-Linear State Space Models , 2010, IEEE Transactions on Automatic Control.

[32]  Fredrik Gustafsson,et al.  Particle filters for positioning, navigation, and tracking , 2002, IEEE Trans. Signal Process..

[34]  Xi Chen,et al.  Stochastic Event-Triggered Cubature Kalman Filter for Power System Dynamic State Estimation , 2019, IEEE Transactions on Circuits and Systems II: Express Briefs.

[35]  Zhaoming Li,et al.  A Novel Fifth-Degree Strong Tracking Cubature Kalman Filter for Two-Dimensional Maneuvering Target Tracking , 2018, Mathematical Problems in Engineering.

[36]  S. Haykin,et al.  Cubature Kalman Filters , 2009, IEEE Transactions on Automatic Control.

[37]  Abhinoy Kumar Singh,et al.  Cubature quadrature Kalman filter for maneuvering target tracking , 2015, 2015 International Conference on Smart Sensors and Application (ICSSA).

[38]  Dong Meng,et al.  A Seventh‐Degree Cubature Kalman Filter , 2018 .

[39]  Fred Daum,et al.  Generalized Gromov method for stochastic particle flow filters , 2017, Defense + Security.

[40]  Shovan Bhaumik,et al.  Higher degree cubature quadrature kalman filter , 2015 .

[41]  Yazhao Wang.  Multitarget Tracking by Improved Particle Filter Based on Unscented Transform , 2013 .

[42]  Shovan Bhaumik,et al.  Cubature quadrature Kalman filter , 2013, IET Signal Process..

[43]  Kazufumi Ito,et al.  Gaussian filters for nonlinear filtering problems , 2000, IEEE Trans. Autom. Control..