量测随机延迟下带厚尾噪声的鲁棒Student's t随机容积卡尔曼滤波器

卢春光, 张永顺, 李志汇, 葛启超

电子学报 ›› 2019, Vol. 47 ›› Issue (9) : 1830-1840.

PDF(6939 KB)
PDF(6939 KB)
电子学报 ›› 2019, Vol. 47 ›› Issue (9) : 1830-1840. DOI: 10.3969/j.issn.0372-2112.2019.09.003
学术论文

量测随机延迟下带厚尾噪声的鲁棒Student's t随机容积卡尔曼滤波器

  • 卢春光1, 张永顺1,2, 李志汇1, 葛启超1
作者信息 +

Robust Student’s t-Based Stochastic Cubature Kalman Filter with Heavy-Tailed Noises and Randomly Delayed Measurements

  • LU Chun-guang1, ZHANG Yong-shun1,2, LI Zhi-hui1, GE Qi-chao1
Author information +
文章历史 +

摘要

针对量测随机延迟下带厚尾过程噪声和量测噪声的非线性状态估计问题,本文通过充分考虑量测一步随机延迟特性及过程噪声和量测噪声的"厚尾"特性,推导了一种新的鲁棒Student's t滤波器框架,并采用随机Student's t-球面相径容积规则近似计算Student's t权值积分,从而设计了一种新的鲁棒Student's t随机容积滤波器.首先,采用一组服从伯努利分布的随机序列来描述系统中可能存在的量测一步随机延迟现象,并采用Student's t分布刻画过程噪声和量测噪声中存在的"厚尾"特性;其次,从理论上证明了当自由度参数趋于无穷以及随机延迟概率为零时,该鲁棒Student's t滤波器就自动地降为标准的非线性高斯近似滤波器;最后,采用随机Student's t-球面相径容积规则给出了一种新的鲁棒Student's t随机容积滤波器,并通过协同转弯模型验证了该滤波器的有效性和优越性.

Abstract

Aiming at the nonlinear state estimation problem with heavy-tailed process measurement noise and randomly delayed measurements, this paper deduces a new robust student's t filter framework by taking into one-step random delay characteristics and heavy-tailed characteristics of process noise and measurement noise account fully. Meanwhile, this paper proposes a new robust Student's t-based stochastic cubature filter(RSTCF)by approximately calculating the Student's t weight integral using stochastic Student's t-spherical radial cubature rule. Firstly, this paper uses a set of stochastic sequences obeying the Bernoulli distribution to describe the possible one-step random delay phenomenon in the system,what's more,this paper also uses the student's t distribution to characterize the heavy-tailed characteristics of the process noise and measurement noise. Secondly, it's theoretically proved that the robust Student's t filter automatically will be reduced to a standard nonlinear Gaussian approximation filter when the degrees of freedom in the posterior probability density function of the state and measurement noise are increasing continuously and randomly delay probability is equal to zero. Finally, this paper presentes a new robust Student's t-based stochastic cubature filter by use of stochastic Student's t-spherical radial cubature rule. The effectiveness and superiority of the filter are verified by the coordinated turn maneuvers model.

关键词

随机延迟 / 厚尾噪声 / Student's t权值积分 / 伯努利分布 / 矩匹配方法 / 非线性估计

Key words

randomly delay / heavy-tailed noises / student's t weighted integrals / Bernoulli distribution / moment matching method / nonlinear estimation

引用本文

导出引用
卢春光, 张永顺, 李志汇, 葛启超. 量测随机延迟下带厚尾噪声的鲁棒Student's t随机容积卡尔曼滤波器[J]. 电子学报, 2019, 47(9): 1830-1840. https://doi.org/10.3969/j.issn.0372-2112.2019.09.003
LU Chun-guang, ZHANG Yong-shun, LI Zhi-hui, GE Qi-chao. Robust Student’s t-Based Stochastic Cubature Kalman Filter with Heavy-Tailed Noises and Randomly Delayed Measurements[J]. Acta Electronica Sinica, 2019, 47(9): 1830-1840. https://doi.org/10.3969/j.issn.0372-2112.2019.09.003
中图分类号: TN97   

参考文献

[1] HU J,HU X.Nonlinear filtering in target tracking using cooperative mobile sensors[J].Automatica,2010,46(12):2041-2046.
[2] LENG S H,Posch C,Benosman R.Asychronous neuro-morphicevent-driven image filtering[J].Proceedings of the IEEE,2014,102(10):1485-1499.
[3] WEBESTER S E,WALLS J M,WHITCOMB L L,et al.Decentralized extended information filter for single-beacon cooperative acoustic navigation:Theory and experiments[J].IEEE Transactions on Robotics,2013,29(4):957-974.
[4] WANG S,FENG J,TSE C K.A class of stable square-root nonlinear information filters[J].IEEE Transactions on Automatic Control,2014,59(7):1893-1898.
[5] JULIERu S J,UHLMANN J K,DURRANT H F.A new method for the nonlinear transformation of means and covariances in filters and estimators[J].IEEE Transactions on Automatic Control,2000,45(3):477-482.
[6] 王磊,程向红,李双喜.高斯和高阶无迹卡尔曼滤波算法[J].电子学报,2017,45(2):424-430. WANG L,CHENG X H,LI S X.Gaussian sum high order unscented kalman filtering algorithm[J].Acta Electronica Sinica,2017,45(2):424-430.(in Chinese)
[7] ARASARATNAM I,HAYKIN S.Cubature Kalman filter[J].IEEE Transactions on Automatic Control,2010,54(8):1254-1269.
[8] BIN J,MING X,YANG C.High-degree cubature Kalman filter[J].Automatica,2013,49(2):510-518.
[9] Wang X X,Liang Y,Pan Q,et al.Gaussian filter for nonlinear systems with one-step randomly delayed measurements[J].Automatica,2013,49(4):976-986.
[10] Wang X X,Liang Y,Pan Q,et al.Measurement random latency probability identification[J].IEEE Transactions on Automatic Control,2016,61(12):4210-4216.
[11] AGAMENNONI G,NEBOT E M.Robust estimation in nonlinear state space models with state dependent noise[J].IEEE Signal Process,2014,62(8):112-116.
[12] ROTH M,OZKAN E,GUSTAFSSON F.A student's filter for heavy tailed process and measurement noise[A].Rabab W.2013 IEEE International Conference on Acoustics,Speech and Signal Processing (ICASSP)[C].Vancouver:IEEE,2013.5770-5774.
[13] HERMOSO C A,LINARES P J.Extended and unscented filtering algorithms using one-step randomly delayed observations[J].Applied Mathematics and Computation,2007,190(2):1375-1393.
[14] HERMOSO C A,LINARES P J.Unscented filtering algorithms using two-step randomly delayed observations[J].Applied Mathematics and Modeling,2009,33(9):3705-3717.
[15] 于浛,张秀杰,陈建伟,宋申民,李鹏.考虑随机时滞和同步相关噪声的改进高斯滤波算法[J].控制理论与应用,2016,33(2):133-145. YU H,ZHANG X J,CHEN J W,et al.An improved Gaussian fiter with randomly delayed measurements and synchronously correlated noises[J].Control Theory&Applications,2016,33(2):133-145.(in Chinese)
[16] EL-HAWARY F,JING Y.Robust regression based EKF for tracking under water targets[J].IEEE Journal of Oceanic Engineering,1995,20(1):31-41.
[17] KARLGAARD C D,SCHAUB H.Huber based divided difference filtering[J].Journal of Guidance,Control and Dynamics,2007,30(3):885-891.
[18] CHEN B,XING L,ZHENG N,et al.Steady state mean-square error analysis for adaptive filtering under the maximum correntropy criterion[J].IEEE Signal Process,2014,21(7):880-884.
[19] LIU X,CHEN B D,XU B,et al.Maximum correntropy unscented filter[J].IEEE Signal Process,2014,21(7):880-884.
[20] MA W,QU H,GUI G,et al.Maximum correntropy criterion based sparse adaptive filtering algorithms for robust channel estimation under non-Gaussian environments[J].IEEE Signal Process,2015,352(7):2708-2727.
[21] HUANG Y L,ZHANG Y G,LI N.Robust student's based nonlinear filter and smoother[J].IEEE Transactions on Aerospace and Electronic Systems,2016,52(5):2586-2596.
[22] Yulong Huang,Yonggang Zhang,Zhemin Wu,Ning Li,Jonathon Chambers.A novel robust Student's t based Kalman filter[J].IEEE Transactions on Aerospace and Electronic Systems,2017,53(3):1545-1554.
[23] HUANG Y L,ZHANG Y G,LI N,et al.A robust Gaussian approximate fixed-interval smoother for nonlinear systems with heavy-tailed process and measurement noises[J].IEEE Signal Processing Letters,2016,23(4):1-3.
[24] HUANG Y L,ZHANG Y G.Design of high-degree Student's t based cubature filters[J].Circuits,Systems,and Signal Processing,2017,37(5):2206-2225.
[25] HUANG Y L,ZHANG Y G.Robust student's based stochastic cubature for nonlinear systems with heavy-tailed process and measurement noises[J].IEEE Acess,2016,52(5):2586-2596.
[26] HUANG Y L,ZHANG Y G,XU B,et al.A new outlier-robust Student's t based Gaussian approximate filter for cooperative localization[J].IEEE-ASME Transactions on Mechatronics,2017,22(5):2380-2386.
[27] HUANG Y L,ZHANG Y G,XU B,et al.A new adaptive extended Kalman filter for cooperative localization[J].IEEE Transactions on Aerospace and Electronic Systems,2017,54(1):353-368.
[28] GENZ A,MONAHAN J.Stochastic integration rules for infinite regions[J].SIAM Journal on Scientific Computing,1998,19(2):426-439.

基金

国家自然科学基金 (No.61571459)
PDF(6939 KB)

1463

Accesses

0

Citation

Detail

段落导航
相关文章

/