基于变尺度变换减少Sigma点的粒子滤波算法研究
|
摘要
为了减少传统无味粒子滤波(Unscented particle filter,UPF)算法的计算负担,提出了最小斜度单形无味转换(Minimal skew simplex UT,MSSUT)方法,这种方法是用最小斜度无味卡尔曼滤波来产生粒子的重要性函数.它不仅能够扩大重要性分布与系统状态的后验概率密度的重叠性,而且能够通过减少Sigma点来减少计算负担.但是,随着状态空间维数的增加,Sigma点集的覆盖半径增大,导致了Sigma点集的聚集性变差.辅助随机变量变尺度无味变换(Auxiliary random variable formulation of the scaled unscented transformation,ASUT)能够克服Sigma点集分布扩展的缺点.所以,提出了一种高维空间中改进的变尺度最小斜度无味粒子滤波(Scaled minimal skew simplex unscented particle filter,SMSSUPF)算法.仿真结果表明:在高维状态空间中,与传统的无味粒子滤波(UPF)相比,计算复杂度和计算负担显著减少.与最小斜度无味粒子滤波(Minimal skew simplex unscented particle filter,MSSUPF)相比,SMSSUPF减少了系统噪声方差和测量噪声方差所带来的估计误差.
In order to reduce the computation burden of conventional unscented particle filter(UPF), a method for particle filter based on minimal skew simplex unscented transformation(MSSUT) is proposed. This method uses a minimal skew simplex unscented Kalman filter to generate importance distribution of the particle filter. It can extend its overlaps and posterior probability density, and reduce the computation burden by reducing sigma points. However, the sigma point set coverage radius expands over dimension of state space, which results in the deterioration of the aggregation of sigma points. Auxiliary random variable formulation of the scaled transformation can overcome the defect of sigma point set distribution expansion. So a scaled minimal skew simplex unscented particle filter(SMSSUPF) is introduced. It is shown by simulation that compared with conventional unscented particle filter, the computation complexity of SMSSUPF can be reduced, the computation burden can be reduced, and compared with spherical simplex unscented particle filter(MSSUPF), SMSSUPF can reduce the system noise and the measurement noise variance estimation error.
In order to reduce the computation burden of conventional unscented particle filter(UPF), a method for particle filter based on minimal skew simplex unscented transformation(MSSUT) is proposed. This method uses a minimal skew simplex unscented Kalman filter to generate importance distribution of the particle filter. It can extend its overlaps and posterior probability density, and reduce the computation burden by reducing sigma points. However, the sigma point set coverage radius expands over dimension of state space, which results in the deterioration of the aggregation of sigma points. Auxiliary random variable formulation of the scaled transformation can overcome the defect of sigma point set distribution expansion. So a scaled minimal skew simplex unscented particle filter(SMSSUPF) is introduced. It is shown by simulation that compared with conventional unscented particle filter, the computation complexity of SMSSUPF can be reduced, the computation burden can be reduced, and compared with spherical simplex unscented particle filter(MSSUPF), SMSSUPF can reduce the system noise and the measurement noise variance estimation error.
引文
1 Rigatos G G.A derivative-free Kalman filtering approach to state estimation-based control of nonlinear systems.IEEE Transactions on Industrial Electronics,2012,59(10):3987-3997
2 Kong L,Kong L F,Wu P L.Adaptive Gaussian particle filter for nonlinear state estimation.In:Proceedings of the31 st Chinese Control Conference.Hefei,China:IEEE,2012.2146-2150
3 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
4 Hu J P,Liu Z X,Wang J H,Wang L,Hu X M.Estimation,intervention and interaction of multi-agent systems.Acta Automatica Sinica,2013,39(11):1796-1804
5 Wen Xin-Yu.Disturbance observer based control for a class of nonlinear systems with input time-delay.Acta Automatica Sinica,2014,40(9):1882-1888)(文新宇.一类含输入时滞非线性系统的干扰观测器控制.自动化学报,2014,40(9):1882-1888)
6 Novara C,Ruiz F,Milanes M.A new approach to optimal filter design for nonlinear systems.In:Proceedings of the48 th IEEE Conference on Decision and Control and 28th Chinese Control Conference.Shanghai,China:IEEE,2009.5484-5489
7 Zhang F R,Cao J S,Xu Z H.An improved particle swarm optimization particle filtering algorithm.In:Proceedings of the International Conference on 2013 Communications,Circuits and Systems.Chengdu,China:IEEE,2013.173-177
8 Zuo Jun-Yi,Zhang Yi-Zhe,Liang Yan.Particle filter based on adaptive part resampling.Acta Automatica Sinica,2012,38 (4):647-652(左军毅,张怡哲,梁彦.自适应不完全重采样粒子滤波器.自动化学报,2012,38(4):647-652)
9 Zhu J,Wang X L,Fang Q S.The improved particle filter algorithm based on weight optimization.In:Proceedings of the 2013 International Conference on Information Science and Cloud Computing Companion.Guangzhou,China:IEEE,2013.351-356
10 Ouyang Cheng,Ji Hong-Bing,Guo Zhi-Qiang.Improved multiple model particle PHD and CPHD filtering algorithm.Acta Automatica Sinica,2012,38(3):341-348(欧阳成,姬红兵,郭志强.改进的多模型粒子PHD和CPHD滤波算法.自动化学报,2012,38(3):341-348)
11 Li L Q,Ji H B,Luo J H.The iterated extended Kalman particle filtering.Journal of Xidian University(Natural Science),2007,34(2):233-238
12 Charalampidis A C,Papavassilopoulos G P.Improved auxiliary and unscented particle filter variants.In:Proceedings of the 52nd IEEE Annual Conference on Decision and Control.Florence,Italy:IEEE,2013.7040-7046
13 Julier S J.The scaled unscented transformation.In:Proceedings of the American Control Conference.Anchorage,AK:IEEE,2002.4555-4559
14 Julier S J.The spherical simplex unscented transformation.In:Proceedings of the American Control Conference.Denver,USA:IEEE,2003.2430-2434
15 Guo W Y,Han C Z,Lei M.Research on particle filter based on spherical unscented transformation.In:Proceedings of the 7th Word Congress on Intelligent Control and Automation.Chongqing,China:IEEE,2008.8388-8392
16 Tian Jun,Qian Jian-Sheng,Li Shi-Yin.Unscented particle filter using iterative minimal skew simplex UKF.Control and Decision,2011,26(6):888-892(田隽,钱建生,李世银.迭代最小斜度单型Sigma采样UPF算法.控制与决策,2011,26(6):888-892)
17 Ning Xiao-Lin,Fang Jian-Cheng,Ma Xin.Impact of UPF filter parameters on spacecraft celestial navigation performance.Chinese Space Science and Technology,2010,30(3):1 -11(宁晓琳,房建成,马辛.UPF滤波参数对航天器天文导航性能的影响.中国空间科学技术,2010,30(3):1-11)
18 Guo Ying-Shi,Wang Chang,Zhang Ya-Qi.Analysis of noise variance s effect on Kalman filter result.Computer Engineering and Design,2014,35(2):641-645(郭应时,王畅,张亚岐.噪声方差对卡尔曼滤波结果影响分析.计算机工程与设计,2014,35(2):641-645)
19 Jiang Wei-Nan,Zhou Hai-Yin,Duan Xiao-Jun,Pan XiaoGang.Adaptive selecting method for scaling factor of scaled unscented transformation.Chinese Space Science and Technology,2008,28(3):1-6(姜伟南,周海银,段晓君,潘晓刚.比例UT变换的一种比例因子自适应选取方法.2008,28(3):1-6)
20 Cheng Shui-Ying.Unscented transformation and unscented Kalman filtering.Computer Engineering and Applications,2008,44(24):25-35(程水英.无味变换与无味卡尔曼滤波.计算机工程与应用,2008,44(24):25-35)
2 Kong L,Kong L F,Wu P L.Adaptive Gaussian particle filter for nonlinear state estimation.In:Proceedings of the31 st Chinese Control Conference.Hefei,China:IEEE,2012.2146-2150
3 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
4 Hu J P,Liu Z X,Wang J H,Wang L,Hu X M.Estimation,intervention and interaction of multi-agent systems.Acta Automatica Sinica,2013,39(11):1796-1804
5 Wen Xin-Yu.Disturbance observer based control for a class of nonlinear systems with input time-delay.Acta Automatica Sinica,2014,40(9):1882-1888)(文新宇.一类含输入时滞非线性系统的干扰观测器控制.自动化学报,2014,40(9):1882-1888)
6 Novara C,Ruiz F,Milanes M.A new approach to optimal filter design for nonlinear systems.In:Proceedings of the48 th IEEE Conference on Decision and Control and 28th Chinese Control Conference.Shanghai,China:IEEE,2009.5484-5489
7 Zhang F R,Cao J S,Xu Z H.An improved particle swarm optimization particle filtering algorithm.In:Proceedings of the International Conference on 2013 Communications,Circuits and Systems.Chengdu,China:IEEE,2013.173-177
8 Zuo Jun-Yi,Zhang Yi-Zhe,Liang Yan.Particle filter based on adaptive part resampling.Acta Automatica Sinica,2012,38 (4):647-652(左军毅,张怡哲,梁彦.自适应不完全重采样粒子滤波器.自动化学报,2012,38(4):647-652)
9 Zhu J,Wang X L,Fang Q S.The improved particle filter algorithm based on weight optimization.In:Proceedings of the 2013 International Conference on Information Science and Cloud Computing Companion.Guangzhou,China:IEEE,2013.351-356
10 Ouyang Cheng,Ji Hong-Bing,Guo Zhi-Qiang.Improved multiple model particle PHD and CPHD filtering algorithm.Acta Automatica Sinica,2012,38(3):341-348(欧阳成,姬红兵,郭志强.改进的多模型粒子PHD和CPHD滤波算法.自动化学报,2012,38(3):341-348)
11 Li L Q,Ji H B,Luo J H.The iterated extended Kalman particle filtering.Journal of Xidian University(Natural Science),2007,34(2):233-238
12 Charalampidis A C,Papavassilopoulos G P.Improved auxiliary and unscented particle filter variants.In:Proceedings of the 52nd IEEE Annual Conference on Decision and Control.Florence,Italy:IEEE,2013.7040-7046
13 Julier S J.The scaled unscented transformation.In:Proceedings of the American Control Conference.Anchorage,AK:IEEE,2002.4555-4559
14 Julier S J.The spherical simplex unscented transformation.In:Proceedings of the American Control Conference.Denver,USA:IEEE,2003.2430-2434
15 Guo W Y,Han C Z,Lei M.Research on particle filter based on spherical unscented transformation.In:Proceedings of the 7th Word Congress on Intelligent Control and Automation.Chongqing,China:IEEE,2008.8388-8392
16 Tian Jun,Qian Jian-Sheng,Li Shi-Yin.Unscented particle filter using iterative minimal skew simplex UKF.Control and Decision,2011,26(6):888-892(田隽,钱建生,李世银.迭代最小斜度单型Sigma采样UPF算法.控制与决策,2011,26(6):888-892)
17 Ning Xiao-Lin,Fang Jian-Cheng,Ma Xin.Impact of UPF filter parameters on spacecraft celestial navigation performance.Chinese Space Science and Technology,2010,30(3):1 -11(宁晓琳,房建成,马辛.UPF滤波参数对航天器天文导航性能的影响.中国空间科学技术,2010,30(3):1-11)
18 Guo Ying-Shi,Wang Chang,Zhang Ya-Qi.Analysis of noise variance s effect on Kalman filter result.Computer Engineering and Design,2014,35(2):641-645(郭应时,王畅,张亚岐.噪声方差对卡尔曼滤波结果影响分析.计算机工程与设计,2014,35(2):641-645)
19 Jiang Wei-Nan,Zhou Hai-Yin,Duan Xiao-Jun,Pan XiaoGang.Adaptive selecting method for scaling factor of scaled unscented transformation.Chinese Space Science and Technology,2008,28(3):1-6(姜伟南,周海银,段晓君,潘晓刚.比例UT变换的一种比例因子自适应选取方法.2008,28(3):1-6)
20 Cheng Shui-Ying.Unscented transformation and unscented Kalman filtering.Computer Engineering and Applications,2008,44(24):25-35(程水英.无味变换与无味卡尔曼滤波.计算机工程与应用,2008,44(24):25-35)