Algorithm for Maneuvering Target Tracking Based on Robust Cubature Kalman Filter

doi:10.3969/j.issn.1009-086x.2026.04.017

Abstract

Abstract:

To address the issues of severe deviation of filtering results from true states caused by heavy-tailed noise and time-delay errors brought by detection information transmission during target tracking of high-speed maneuvering aircraft， this paper proposed an algorithm for maneuvering target tracking based on the robust cubature Kalman filter to achieve accurate tracking of target states. First， the Student’s t-distribution was employed to approximate the heavy-tailed characteristics of noise， and an unknown scale matrix and auxiliary variables were jointly estimated via the variational Bayesian method， significantly improving the tracking accuracy of the algorithm under noise containing outliers. Second， kinematic extrapolation was applied to time-delayed measurement information， improving the tracking accuracy of maneuvering targets under time-delay conditions. Finally， simulation experiments demonstrate that， compared with existing target tracking algorithms， this algorithm maintains stable estimation performance for maneuvering target states under the conditions of noise containing outliers and time delays and achieves higher tracking accuracy.

Key words: high-speed maneuvering aircraft, heavy-tailed noise, student’s t-distribution, variational Bayesian, time-delay compensation, robust filtering

摘要：

针对高速机动飞行器目标跟踪中重尾噪声导致滤波结果严重偏离真实状态，以及探测信息传输带来时延误差问题，提出了一种基于鲁棒容积卡尔曼滤波的机动目标跟踪算法，以实现对目标状态的精确跟踪。采用学生t分布对噪声的重尾特性进行近似，通过变分贝叶斯方法联合估计未知尺度矩阵和辅助变量，显著提升了算法在含野值噪声下的跟踪精度。通过对时滞量测信息的运动学外推，提高了时延条件下机动目标的跟踪精度。仿真实验表明，相较于现有目标跟踪算法，该算法在噪声存在野值和时延条件下仍能保持对机动目标状态稳定的估计性能，且跟踪精度更高。

关键词: 高速机动飞行器, 重尾噪声, 学生t分布, 变分贝叶斯, 时延补偿, 鲁棒滤波

CLC Number:

TP27

Zhiying ZHANG, Yufei WEI. Algorithm for Maneuvering Target Tracking Based on Robust Cubature Kalman Filter[J]. Modern Defense Technology, 2026, 54(4): 159-169.

张智蓥, 魏宇飞. 基于鲁棒容积卡尔曼滤波的机动目标跟踪算法[J]. 现代防御技术, 2026, 54(4): 159-169.

Figures/Tables 22

Fig. 1 Schematic diagram of detection system

Fig. 2 Comparison of probability density distributions for different distributions

Fig. 3 True and estimated trajectories of non-maneuvering target

Fig. 4 Comparison of root mean square errors of position

Fig. 5 Comparison of root mean square errors of velocity

Table 1 ARMSE of different algorithms for non-maneuvering target

滤波方法	位置ARMSE/m	速度ARMSE/（m·s^-1）
CKF	26.684 8	7.592 4
VBAIEKF	16.721 1	6.760 9
RCKF-MTT	12.528 1	6.240 1

Fig. 6 Comparison of position RMSE under different degree-of-freedom parameters

Fig. 7 Comparison of velocity RMSE under different degree-of-freedom parameters

Table 2 ARMSE of non-maneuvering target under different degree-of-freedom parameters

自由度参数ν	位置ARMSE/m	速度ARMSE/（m·s^-1）
3	14.321 4	6.439 6
4	12.853 2	6.292 7
5	12.528 1	6.240 1
6	12.485 5	6.218 6
7	12.622 3	6.224 5

Fig. 8 True and estimated trajectories of maneuvering target

Fig. 9 Comparison of root mean square errors of maneuvering target position

Fig. 10 Comparison of root mean square errors of maneuvering target velocity

Fig. 11 Comparison of position root mean square errors for different degrees of freedom

Fig. 12 Comparison of velocity root mean square errors for different degrees of freedom

Table 3 ARMSE of different algorithms for maneuvering target

滤波方法	位置ARMSE/m	速度ARMSE/（m·s^-1）
CKF	1 369.289 0	119.971 3
VBAIEKF	1 229.585 8	112.614 1
RCKF-MTT	882.018 3	96.645 9

Table 4 ARMSE under different degree-of-freedom parameters

自由度参数ν	位置ARMSE/m	速度ARMSE/（m·s^-1）
3	1 182.195 4	107.285 0
4	988.862 4	100.488 0
5	882.018 3	96.645 9
6	817.000 1	94.262 5
7	774.432 0	92.672 0

Fig. 13 Comparison of root mean square errors of target position under time-varying noise

Fig. 14 Comparison of root mean square errors of target velocity under time-varying noise

Table 5 ARMSE of different algorithms for maneuvering target under time-varying noise

滤波方法	位置ARMSE/m	速度ARMSE/（m·s^-1）
CKF	1 339.527 3	119.225 2
VBAIEKF	1 147.780 4	108.618 5
RCKF-MTT	885.626 9	99.783 9

Fig. 15 Comparison of position （95~100 s）

Fig. 16 Comparison of position root mean square errors for different algorithms

Table 6 Position ARMSE under different algorithms m

算法	位置ARMSE
无补偿CKF	2 105.698 9
有补偿CKF	1 320.666 6
有补偿VBAIEKF	823.954 3
有补偿RCKF-MTT	704.943 6

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