A General Framework Solution to Gaussian Filter with Multiple-step Randomly-delayed Measurements
-
摘要: 提出了一种适用于线性和非线性系统的带多步随机延迟量测高斯滤波器的一般框架解. 为了完成状态的递归更新估计, 噪声向量和先前时刻状态向量被扩展到当前时刻状态向量中. 然后基于贝叶斯方法推导了扩展后状态向量的一般框架解. 对于非线性系统, 通过利用不同的数值计算方法计算贝叶斯解中的高斯加权积分可以推导获得不同的高斯近似滤波器. 最后本文利用三阶球径容积准则来实施提出的方法, 并通过量测被随机延迟多步的目标跟踪模型对所提出的方法进行了仿真, 仿真结果验证了提出方法的有效性和优点.Abstract: This paper provides a general framework solution to state estimation of Gaussian filter for both linear and nonlinear dynamic systems with multiple step randomly delayed measurements. Noise and previous state vectors are added into the current state vector to facilitate its recursive update estimation. A general framework of Bayesian solution to the augmented state estimation is then derived. For nonlinear systems, different Gaussian approximation filters can be developed by utilizing different numerical methods for computing Gaussian weighted integrals involved in the Bayesian solution. Finally, the third-degree spherical-radial cubature rule is used to implement the proposed method. Simulation is performed based on a target tracking model, in which measurements are randomly delayed for multiple steps. The simulation results illustrate the efficiency and advantages of the proposed method.
-
[1] Arasaratnam I, Haykin S. Cubature Kalman filter. IEEE Transactions on Automatic Control, 2009, 54(6): 1254-1269 [2] Wang X X, Liang Y, Pan Q, Zhao C H. Gaussian filter for nonlinear systems with one-step randomly delayed measurements. Automatica, 2013, 49(4): 976-986 [3] Jia B, Xin M, Cheng Y. High-degree cubature Kalman filter. Automatica, 2013, 49(2): 510-518 [4] Jia B, Xin M, Cheng Y. Sparse-grid quadrature nonlinear filtering. Automatica, 2012, 48(2): 327-341 [5] Dunik J, Straka O, Simandl M. Stochastic integration filter. IEEE Transactions on Automatic Control, 2013, 58(6): 1561-1566 [6] Zhang X C. A novel cubature Kalman filter for nonlinear state estimation. In: Proceedings of the 52nd IEEE Conference on Decision and Control. Florence, Italy: IEEE, 2013. 7797-7802 [7] Wang S Y, Feng J C, Tse C K. Spherical simplex-radial cubature Kalman filter. IEEE Signal Processing Letter, 2014, 21(1): 43-46 [8] Wang Lu, Li Guang-Chun, Qiao Xiang-Wei, Wang Zhao-Long, Ma Tao. An adaptive UKF algorithm based on maximum likelihood principle and expectation maximization algorithm. Acta Automatica Sinica, 2012, 38(7): 1200-1210(王璐, 李光春, 乔相伟, 王兆龙, 马涛.基于极大似然准则和最大期望算法的自适应UKF 算法. 自动化学报, 2012,38(7): 1200-1210) [9] Zhang Yong-Gang, Huang Yu-Long, Wu Zhe-Min, Li Ning. A high order unscented Kalman filtering method. Acta Automatica Sinica, 2014, 40(5): 838-848(张勇刚, 黄玉龙, 武哲民, 李宁. 一种高阶无迹卡尔曼滤波方法.自动化学报, 2014, 40(5): 838-848) [10] Chang L B, Hu B Q, Li A, Qin F J. Transformed unscented Kalman filter. IEEE Transactions on Automatic Control, 2013 58(1): 252-257 [11] Wang Xiao-Xu, Liang Yan, Pan Quan, Zhao Chun-Hui, Li Han-Zhou. Unscented Kalman filter for nonlinear systems with colored measurement noise. Acta Automatica Sinica, 2012, 38(6): 986-998(王小旭, 梁彦, 潘泉, 赵春晖, 李汉舟.带有色量测噪声的非线性系统Unscented卡尔曼滤波器. 自动化学报, 2012,38(6): 986-998) [12] Yang F W, Wang Z D, Feng G, Liu X H. Robust filtering with randomly varying sensor delay: the finite-horizon case. IEEE Transactions on Circuits and Systems --- I, 2009, 56(3): 664-672 [13] Chen S J, Li Y Y, Qi G Q, Sheng A D. Adaptive Kalman estimation in target tracking mixed with random one-step delays, stochastic-bias measurements, and missing measurements. Discrete Dynamics in Nature and Society, 2013, 2013: Article ID 716915 [14] Hermoso-Carazo A, linares-Pérez J. Extended and unscented filtering algorithms using one-step randomly delayed observations. Applied Mathematics Computation, 2007, 190(2): 1375-1393 [15] Hermoso-Carazo A, linares-Pérez J. Unscented filtering algorithm using two-step randomly delayed obserations in nonlinear systems. Applied Mathematical Modelling, 2009, 33(9): 3705-3717 [16] Wang X X, Pan Q, Liang Y, Yang F. Gaussian smoothers for nonlinear systems with one-step randomly delayed measurements. IEEE Transactions on Automatic Control, 2013, 58(7): 1828-1835
点击查看大图
计量
- 文章访问数: 1821
- HTML全文浏览量: 79
- PDF下载量: 850
- 被引次数: 0