δ-广义标签多伯努利滤波算法的非线性扩展

doi:10.12305/j.issn.1001-506X.2021.12.19

摘要/Abstract

摘要：

针对高斯混合(Gaussian mixture, GM)实现的变分贝叶斯-δ-广义标签多伯努利(variational Bayesian-δ-generalized labeled multi-Bernoulli, VB-δ-GLMB)滤波算法在非线性场景下跟踪性能较低这一问题, 结合基于临近点算法(proximal point algorithm, PPA)和变分贝叶斯(variational Bayesian, VB)的迭代优化与容积卡尔曼滤波(cubature Kalman filtering, CKF), 提出一种适用于非线性模型的机动多目标跟踪算法。该算法在GM-VB-δ-GLMB的基础上采用逆伽马(inverse-Gamma, IG)和高斯乘积混合分布近似量测噪声协方差和状态联合后验分布; 利用PPA-CKF-VB(PCKF-VB)方法对传递过程中的高斯项参数进行预测更新; 最后为提高滤波精度进行变分贝叶斯容积RTS(VB cubature Rauch-Tung-Striebel, VB-CRTS)平滑。仿真结果表明, 对于量测噪声未知的非线性系统, 所提的算法与现有的VB-δ-GLMB算法相比目标跟踪精度有显著提高。

关键词: δ-广义标签多伯努利算法, 非线性模型, 容积卡尔曼滤波, 临近点算法, 变分贝叶斯近似

Abstract:

Aiming at the low tracking performance of the Gaussian mixture(GM)variational Bayesian-δ-generalized labeled multi-Bernoulli (VB-δ-GLMB) filtering algorithm in nonlinear scenes, a maneuvering multi-target tracking algorithm is proposed, which combined with the iterative optimization based on proximal point algorithm (PPA) and (variational Bayesian, VB) approximate and cubature Kalman filter (CKF), to suit for nonlinear models. Based on GM-VB-δ-GLMB, the proposed algorithm uses inverse Gamma (IG) and Gaussian product mixture distribution to approximate the joint posterior density of the measurement noise covariance and state. Then, PPA-CKF-VB (PCKF-VB) method is used to predict and update the Gaussian term parameters in the transfer process. Finally, smoothing of variational Bayesian cubature Rauch-Tung-Striebel (VB-CRTS) is utilized to improve the filtering accuracy. Simulation results indicate that the target tracking accuracy of the proposed algorithm is obviously improved compared with the existing VB-δ-GLMB algorithm for the nonlinear system with unknown measurement noise.

Key words: δ-generalized labeled multi-Bernoulli (δ-GLMB) algorithm, nonlinear model, cubature Kalman filter (CKF), proximal point algorithm, variational Bayesian approximation

中图分类号:

TN953

齐美彬, 胡晶晶, 程佩琳, 靳学明. δ-广义标签多伯努利滤波算法的非线性扩展[J]. 系统工程与电子技术, 2021, 43(12): 3571-3578.

Meibin QI, Jingjing HU, Peilin CHENG, Xueming JIN. Nonlinear extension of δ-generalized labeled multi-Bernoulli filtering algorithm[J]. Systems Engineering and Electronics, 2021, 43(12): 3571-3578.

图/表 6

表1

图1

图2

图3

表2

图4

参考文献 30

1	KOSUGE Y. Maneuvering target tracking using multiple maneuver model joint probabilistic data association[C]//Proc. of the IEEE Industrial Electronics Society Conference, 1991: 2059-2064.
2	FAN E, XIE W X, LIU Z X, et al. Combinige generalized JDPA and FRLS filter for tracking multiple maneuvering targets[C]//Proc. of the IEEE International Conference on Signal Processing, 2014: 239-245.
3	ZHAO S J , WANG Y , WANG P Y , et al. Adaptive non-linear joint probabilistic data association for vehicle target tracking[J]. IEEE Access, 2021, 9, 14138- 14147. doi: 10.1109/ACCESS.2021.3052555
4	WHANG I H, LEE J G. Multiple hypotheses tracking for maneuvering targets in clutter environment[C]//Proc. of the Conference on International Session Papers, 1995: 1493-1498.
5	BLACKMAN S S . Multiple hypothesis tracking for multiple target tracking[J]. IEEE Aerospace & Electronic Systems Magazine, 2009, 19 (1): 5- 18.
6	LEXA M, CORALUPPI S, CARTHEL C. Distributed MHT and ML-PMHT approaches to multi-sensor passive sonar tracking[C]//Proc. of the IEEE Aerospace Conference, 2020.
7	MAHLER R , EBRARY I . Statistical multisource multitarget information fusion[M]. Norwood: Artech House, 2007: 565- 682.
8	VO B N , VO B T , PHUNG D . Labeled random finite sets and the bayes multi-target tracking filter[J]. IEEE Trans.on Signal Processing, 2014, 62 (24): 6554- 6567. doi: 10.1109/TSP.2014.2364014
9	VO B T , VO B N . Labeled random finite sets and multi-object conjugate priors[J]. IEEE Trans.on Signal Processing, 2013, 61 (13): 3460- 3475. doi: 10.1109/TSP.2013.2259822
10	VO B , VO B , HOANG H G . An efficient implementation of the generalized labeled multi-bernoulli filter[J]. IEEE Trans.on Signal Processing, 2016, 65 (8): 1975- 1987.
11	HOANG H, VO BA N, VO B T. A fast implementation of the generalized labeled multi-Bernoulli filter with joint prediction and update[C]//Proc. of the International Conference on Information Fusion, 2015: 999-1006.
12	CAO C H , ZHAO Y B , PANG X J , et al. An efficient implementation of multiple weak targets tracking filter with labeled random finite sets for marine radar[J]. Digital Signal Processing, 2020, 101, 102710. doi: 10.1016/j.dsp.2020.102710
13	LI C Y , FAN Z H , SHI R Z . A generalized labelled multi-bernoulli filter for extended targets with unknown clutter rate and detection profile[J]. IEEE Access, 2020, 8, 213772- 213782. doi: 10.1109/ACCESS.2020.3036900
14	BEARD M , VO B T , VO B , A solution for large-scale multi-object tracking[J] . IEEE Trans[J]. on Signal Processing, 2020, 68, 2754- 2769.
15	SARKKA S , NUMMENMAA A . Recursive noise adaptive kalman filtering by variational Bayesian approximations[J]. IEEE Trans.on Automatic Control, 2009, 54 (3): 596- 600. doi: 10.1109/TAC.2008.2008348
16	LI W L, JIA Y M, DU J P, et al. PHD filter for multi-target tracking by variational Bayesian approximation[C]//Proc. of the IEEE Conference on Decision & Control, 2013: 7815-7820.
17	ZHANG G, LIAN F, HAN C, et al. An improved PHD filter based on variational Bayesian method for multi-target tracking[C]// Proc. of the 17th International Conference on Information Fusion, 2014.
18	YANG J L , GE H W . An improved multi-target tracking algorithm based on CBMeMBer filter and variational Bayesian approximation[J]. Signal Processing, 2013, 93 (9): 2510- 2515. doi: 10.1016/j.sigpro.2013.03.027
19	袁常顺, 王俊, 向洪, 等. 基于VB近似的自适应δ-GLMB滤波算法[J]. 系统工程与电子技术, 2017, 39 (2): 237- 243.
	YUAN C S , WANG J , XIANG H , et al. Adaptive δ-GLMB filtering algorithm based on VB approximation[J]. Systems Engineering and Electronics, 2017, 39 (2): 237- 243.
20	WANG S Y , YIN C , DUAN S K , et al. A modified variational bayesian noise adaptive Kalman filter[J]. Circuits Systems and Signal Processing, 2017, 36 (10): 4260- 4277. doi: 10.1007/s00034-017-0497-6
21	闫文旭, 兰华, 王增福, 等. 基于变分贝叶斯的星载雷达非线性滤波[J]. 航空学报, 2020, 41 (S2): 220- 228.
	YAN W X , LAN H , WANG Z F , et al. Nonlinear filtering of spaceborne radar Based on variational Bayes[J]. Acta Aeronautica et Astronautica Sinica, 2020, 41 (S2): 220- 228.
22	TSENG P . An analysis of the EM algorithm and entropy-like proximal point methods[J]. Mathematics of Operations Research, 2004, 29 (1): 27- 44. doi: 10.1287/moor.1030.0073
23	HU Y M , WANG X Z , LAN H , et al. An iterative nonlinear filter using variational Bayesian optimization[J]. Sensors, 2018, 18 (12): 4222. doi: 10.3390/s18124222
24	KHAN M E, BAQUÉ P, FLEURET F, et al. Kullback-Leibler proximal variational inference[C]//Proc. of the Advances in Neural Information Processing Systems, 2015: 3402-3410.
25	HE J , SUN C , ZHANG B , et al. Variational Bayesian-based maximum correntropy cubature Kalman filter with both adaptivity and robustness[J]. IEEE Sensors Journal, 2021, 21 (2): 1982- 1992. doi: 10.1109/JSEN.2020.3020273
26	母晓慧, 杨风暴, 刘哲, 等. 基于均方根容积卡尔曼的δ-GLMB多目标跟踪算法[J]. 计算机应用与软件, 2020, 37 (4): 164- 170. doi: 10.3969/j.issn.1000-386x.2020.04.027
	MU X H , YANG F B , LIU Z , et al. δ-GLMB filter multi-target tracking algorithm based on square-rooted cubature Kalman[J]. Computer Applications and Software, 2020, 37 (4): 164- 170. doi: 10.3969/j.issn.1000-386x.2020.04.027
27	HOU L M, LIAN F. Extension of nonlinear δ-generalized labeled multi-Bernoulli filter in multi-target tracking[C]//Proc. of the Chinese Automation Congress, 2018: 2301-2306.
28	WANG B , YE W , LIU Y H . Variational Bayesian cubature RTS smoothing for transfer alignment of DPOS[J]. IEEE Sensors Journal, 2020, 20 (6): 3270- 3279. doi: 10.1109/JSEN.2019.2958335
29	张磊, 郭健, 钱晨, 等. 基于变分贝叶斯的容积平滑变结构滤波[J]. 南京理工大学学报: 自然科学版, 2019, 43 (3): 255- 260.
	ZHANG L , GUO J , QIAN C , et al. Variational Bayesian based cubature smooth variable structure filter[J]. Journal of Nanjing University of Science and Technology, 2019, 43 (3): 255- 260.
30	SCHUHMACHER D , VO B T , VO B N . A consistent metric for performance evaluation of multi-object filters[J]. IEEE Trans.on Signal Processing, 2008, 56 (8): 3447- 3457. doi: 10.1109/TSP.2008.920469

目标	起始时刻/s	结束时刻/s	目标初始状态	转弯频率rad/s
1	1	100	[1 000, －10, 1 500, -10]^T	π/120
2	1	100	[－250, 20, 1 000, 3]^T	π/60
3	10	100	[－1 500, 11, 250, 10]^T	－π/120
4	10	100	[1 000, 5, 1 500, -15]^T	π/60
5	20	80	[250, -8, 750, -15]^T	π/120
6	20	100	[－250, -12, 1 000, -12]^T	π/60
7	30	90	[－1 500, 11, 250, -10]^T	π/80
8	30	80	[250, -25, 750, 0]^T	－π/120
9	40	100	[1 000, -20, 1 500, -10]^T	π/120
10	60	100	[250, -5, 750, 20]^T	π/120

滤波器	OSPA距离	OSPA势估计
VB-δ-GLMB	34.06	8.589
VB-δ-GLMB平滑之后	20.11	7.475
PCKF-VB-δ-GLMB	29.43	7.579
PCKF-VB-δ-GLMB平滑之后	18.03	6.353

[1]	史浩然, 卢发兴, 祁江鑫, 杨光. 基于辅助信标的无人机协同目标跟踪[J]. 系统工程与电子技术, 2022, 44(7): 2302-2310.
[2]	张平安, 汪伟, 高敏, 王毅. SR-CH∞KF用于弹丸飞行姿态测量研究[J]. 系统工程与电子技术, 2022, 44(1): 262-269.
[3]	李春辉, 马健, 杨永建, 肖冰松, 邓有为, 盛涛. 基于修正的自适应平方根容积卡尔曼滤波算法[J]. 系统工程与电子技术, 2021, 43(7): 1824-1830.
[4]	胥彪, 李翔, 李爽, 张金鹏. 基于非线性模型预测控制的火星大气进入智能制导方法[J]. 系统工程与电子技术, 2021, 43(7): 1943-1953.
[5]	卢雨, 王海滨. 空基无源相干定位系统的机动目标跟踪算法[J]. 系统工程与电子技术, 2021, 43(4): 875-882.
[6]	卢雨, 周正. 空基外辐射源定位系统的观测站航迹优化[J]. 系统工程与电子技术, 2020, 42(12): 2708-2715.
[7]	赵春明, 姚跃民, 金文, 宋蔚阳, 方海红. 全捷联被动雷达末制导系统设计[J]. 系统工程与电子技术, 2020, 42(11): 2607-2613.
[8]	宋敏, 戴静, 孔韬. 基于NMPC的无人机自主防撞控制方法[J]. 系统工程与电子技术, 2019, 41(9): 2092-2099.
[9]	张浩为, 谢军伟, 葛佳昂, 宗彬锋, 路文龙. 自适应CS模型的强跟踪平方根容积卡尔曼滤波算法[J]. 系统工程与电子技术, 2019, 41(6): 1186-1194.
[10]	许红, 谢文冲, 王永良. 角闪烁噪声下的高斯和容积卡尔曼滤波算法[J]. 系统工程与电子技术, 2019, 41(2): 229-235.
[11]	董萍, 程建华, 刘利强, 牟宏杰. 基于相对信息观测量的INS/USBL非线性组合导航方法[J]. 系统工程与电子技术, 2019, 41(2): 402-408.
[12]	王超, 张胜修, 宋仔标, 杨建业, 吴晓露. 飞行器抗饱和鲁棒自适应非线性模型预测控制[J]. 系统工程与电子技术, 2018, 40(2): 393-400.
[13]	郭肖亭, 孙长库, 王鹏. 矩阵对角化变换鲁棒QCKF在视觉和惯性融合姿态测量中的应用[J]. 系统工程与电子技术, 2018, 40(2): 402-408.
[14]	刘振亚, 高敏, 程呈. 基于理想弹道鲁棒容积卡尔曼滤波视线角估计[J]. 系统工程与电子技术, 2018, 40(2): 409-416.
[15]	林孝工, 焦玉召, 李恒, 梁坤, 聂君. 基于容积变换的平滑变结构滤波及应用[J]. 系统工程与电子技术, 2018, 40(1): 159-164.