非平穩(wěn)異常噪聲條件下的擴展目標(biāo)跟蹤方法

陳輝; 張欣雨; 連峰; 韓崇昭; 張光華

doi:10.11999/JEIT240824

非平穩(wěn)異常噪聲條件下的擴展目標(biāo)跟蹤方法

doi: 10.11999/JEIT240824

1.
蘭州理工大學(xué)電氣工程與信息工程學(xué)院蘭州 730050
2.
西安交通大學(xué)自動化科學(xué)與工程學(xué)院西安 710049

基金項目: 國家自然科學(xué)基金(62163023, 61873116, 62366031, 62363023)，甘肅省科技計劃(25JRRA058, 25ZYJA040), 2024年度甘肅省重點人才項目(2024RCXM86)，2023年度甘肅省軍民融合發(fā)展專項資金

詳細(xì)信息

作者簡介:
陳輝：男，教授，博士生導(dǎo)師，研究方向為多目標(biāo)跟蹤、數(shù)據(jù)融合、最優(yōu)控制等

張欣雨：女，碩士生，研究方向為擴展目標(biāo)跟蹤和最優(yōu)濾波技術(shù)

連峰：男，教授，博士生導(dǎo)師，研究方向為目標(biāo)跟蹤、信息融合與傳感器管理

韓崇昭：男，教授，博士生導(dǎo)師，研究方向為多源信息融合、隨機控制與自適應(yīng)控制、非線性頻譜分析等

張光華：男，副教授，博士生導(dǎo)師，研究方向為多源信息融合、目標(biāo)跟蹤、傳感器管理

通訊作者:
陳輝　huich78@hotmail.com

中圖分類號: TN911.7; TP274
計量
- 文章訪問數(shù): 131
- HTML全文瀏覽量: 38
- PDF下載量: 112
- 被引次數(shù): 0
出版歷程
- 收稿日期: 2024-09-27
- 修回日期: 2025-02-23
- 網(wǎng)絡(luò)出版日期: 2025-03-01

Extended Target Tracking Method under Non-stationary Abnormal Noise Conditions

1.
School of electrical engineering and Information Engineering, Lanzhou University of Technology, Lanzhou 730050, China
2.
School of Automation Science and Engineering, Xi’an Jiaotong University, Xi’an 710049, China

Funds: The National Natural Science Foundation of China (62163023, 61873116, 62366031, 62363023), Gansu Provincial Science and Technology Plan Project of China (25JRRA058, 25ZYJA040), 2024 Gansu Provincial Key Talent Project of China (2024RCXM86), 2023 Gansu Provincial Special Fund for Military-Civilian Integration Development

摘要

摘要: 針對非平穩(wěn)異常噪聲環(huán)境下擴展目標(biāo)跟蹤問題，該文提出一種基于高斯-學(xué)生t混合(GSTM)擴展目標(biāo)跟蹤方法。首先，將過程噪聲和量測噪聲建模為GSTM分布，以表征非平穩(wěn)厚尾噪聲，并通過引入伯努利隨機變量，將目標(biāo)的運動狀態(tài)和量測似然函數(shù)建模為分層高斯形式。其次，在隨機矩陣(RMM)濾波框架下，使用變分貝葉斯方法詳細(xì)推導(dǎo)了非平穩(wěn)厚尾噪聲下的GSTM擴展目標(biāo)跟蹤算法。該算法通過建模高斯噪聲與厚尾噪聲之間的非平穩(wěn)過程，精確表征噪聲特性，從而在非平穩(wěn)異常噪聲環(huán)境下穩(wěn)健捕捉擴展目標(biāo)的質(zhì)心位置和輪廓形態(tài)。最后，構(gòu)建非平穩(wěn)異常噪聲環(huán)境下的擴展目標(biāo)跟蹤仿真實驗，并通過高斯-瓦瑟斯坦距離對實驗結(jié)果進(jìn)行效果評估，驗證了所提出算法的合理性。此外，真實場景實驗結(jié)果進(jìn)一步證明了該算法在實際應(yīng)用中的有效性和魯棒性。
- 擴展目標(biāo)跟蹤 /
- 隨機矩陣 /
- 高斯-學(xué)生t混合分布 /
- 變分貝葉斯方法
Abstract: Objective This paper addresses the problem of extended target tracking in the presence of non-stationary abnormal noise. Traditional Gaussian extended target filters and Student’s t filters rely on the assumption of stationary noise distributions, which limits their performance in environments with non-stationary abnormal noise. Non-stationary noise, common in practical applications, is especially prevalent in complex environments where the noise frequently shifts between Gaussian and heavy-tailed distributions. To overcome this challenge, a Gaussian-Student’s T Mixture (GSTM) distribution is proposed for modeling non-stationary abnormal noise in extended target tracking. The GSTM distribution is used to model the noise accurately, and a filter is developed to track the target’s kinematic state and shape effectively under non-stationary measurement and process noise conditions. This method is shown to be robust in complex environments, offering enhanced accuracy, robustness, and applicability for extended target tracking. Methods The GSTM distribution is employed to model both process and measurement noise, enabling dynamic adjustment of mixture parameters to capture the evolving characteristics of noise distributions in non-stationary environments. To optimize computation, Bernoulli random variables are introduced, and the target’s one-step prediction and measurement likelihood functions are reformulated as a hierarchical Gaussian model based on the GSTM distribution. This approach facilitates adaptive switching between Gaussian and Student’s t distributions, streamlining the inference process and simplifying posterior computation, which reduces the complexity of parameter estimation. Within the Random Matrix Model (RMM) framework, Variational Bayesian (VB) inference is applied to jointly estimate the target’s kinematic state, extension state, mixture parameters, and noise characteristics. During the filtering update phase, a dynamic adjustment mechanism is introduced for the one-step prediction error covariance matrix and observation noise covariance matrix, ensuring the model to maintain robustness and adaptability in complex, non-stationary noise environments. Results and Discussions The introduction of the GSTM distribution for modeling non-stationary abnormal noise enables robust tracking of both the centroid and shape contour of extended targets in such environments. Theoretical derivations and experimental validations confirm the effectiveness of the proposed method for single extended target tracking under non-stationary noise conditions. Simulation and real-world results demonstrate significant performance advantages. First, in terms of tracking accuracy, the proposed algorithm achieves a notably lower Root Mean Square Error (RMSE) for centroid tracking compared to other algorithms (Fig. 2, Fig. 6), effectively adapting to dynamic changes in non-stationary noise, and offering superior accuracy and stability. Second, for adaptive estimation of target shape, the algorithm shows considerable improvements in non-stationary noise environments, providing more accurate contour estimation (Fig. 3, Fig. 7). It also maintains high robustness under evolving target shapes. Moreover, the algorithm exhibits faster convergence and greater stability in complex environments (Fig. 2, Fig. 4), with a significantly lower Gaussian Wasserstein Distance (GWD) mean compared to other methods (Fig. 4, Fig. 8). In practical experiments, a vehicle operated in environments with obstacles like tree branches, where the noise is non-stationary, further validated the algorithm’s performance. Under these conditions, the proposed algorithm demonstrated exceptional stability and robustness throughout the tracking process (Fig. 9), outperforming other algorithms and highlighting its adaptability and reliability in complex dynamic environments. Conclusions This paper proposes an extended target tracking method based on the GSTM distribution, overcoming the limitations of traditional algorithms in adapting to non-stationary anomalous noise environments. The GSTM distribution is used for noise modeling, combined with the RMM framework, and the VB method along with hierarchical Gaussian modeling simplifies the computational process, enhancing the algorithm’s adaptability and robustness. Experimental results across shape-invariant, shape-evolving, and real-world scenarios demonstrate the following: (1) The proposed algorithm significantly outperforms existing methods in robustness, particularly in centroid tracking and shape estimation. (2) The noise model is adaptively adjusted under non-stationary noise and dynamic target evolution, enabling high-precision tracking of extended targets. (3) In complex real-world scenarios, the algorithm successfully tracks small vehicles, further validating its effectiveness in practical applications. Future research could explore integrating multi-target tracking theories, extending the algorithm to multi-extended target tracking scenarios, and addressing more complex environmental challenges to further enhance its practicality and performance in multi-target settings.
- Extended target tracking /
- Random matrix /
- Gaussian-Student's T Mixture (GSTM) distribution /
- Variational Bayesian (VB) method

HTML全文

圖 1 擴展目標(biāo)軌跡跟蹤圖

下載: 全尺寸圖片幻燈片

圖 2 目標(biāo)質(zhì)心跟蹤誤差

下載: 全尺寸圖片幻燈片

圖 3 不同階段的輪廓放大圖

下載: 全尺寸圖片幻燈片

圖 4 橢圓擴展目標(biāo)GWD

下載: 全尺寸圖片幻燈片

圖 5 擴展目標(biāo)軌跡跟蹤圖

下載: 全尺寸圖片幻燈片

圖 6 目標(biāo)質(zhì)心跟蹤誤差

下載: 全尺寸圖片幻燈片

圖 7 不同階段的輪廓放大圖

下載: 全尺寸圖片幻燈片

圖 8 橢圓擴展目標(biāo)GWD

下載: 全尺寸圖片幻燈片

圖 9 不同時刻效果圖

下載: 全尺寸圖片幻燈片

參考文獻(xiàn)(28)

[1]	JIANG Meiqiu, GUO Shisheng, LUO Haolan, et al. A robust target tracking method for crowded indoor environments using mmWave radar[J]. Remote Sensing, 2023, 15(9): 2425. doi: 10.3390/rs15092425.
[2]	ZHANG Jiwei, BHUIYAN M Z A, YANG Yu, et al. Trustworthy target tracking with collaborative deep reinforcement learning in EdgeAI-Aided IoT[J]. IEEE Transactions on Industrial Informatics, 2022, 18(2): 1301–1309. doi: 10.1109/TII.2021.3098317.
[3]	YANG Dongsheng, GUO Yunfei, YIN Tianxiang, et al. Cost-effective Gaussian processes based extended target tracking[J]. IEEE Transactions on Aerospace and Electronic Systems, 2023, 59(6): 8282–8296. doi: 10.1109/TAES.2023.3305320.
[4]	WANG Yi, CHEN Xin, GONG Chao, et al. Non-ellipsoidal infrared group/extended target tracking based on Poisson multi-Bernoulli mixture filter and B-spline[J]. Remote Sensing, 2023, 15(3): 606. doi: 10.3390/rs15030606.
[5]	KOCH J W. Bayesian approach to extended object and cluster tracking using random matrices[J]. IEEE Transactions on Aerospace and Electronic Systems, 2008, 44(3): 1042–1059. doi: 10.1109/TAES.2008.4655362.
[6]	FELDMANN M, FRANKEN D, and KOCH W. Tracking of extended objects and group targets using random matrices[J]. IEEE Transactions on Signal Processing, 2011, 59(4): 1409–1420. doi: 10.1109/TSP.2010.2101064.
[7]	LAN Jian and LI X R. Tracking of extended object or target group using random matrix: New model and approach[J]. IEEE Transactions on Aerospace and Electronic Systems, 2016, 52(6): 2973–2989. doi: 10.1109/TAES.2016.130346.
[8]	LAN Jian and LI X R. Tracking of extended object or target group using random matrix — part II: Irregular object[C]. 2012 15th International Conference on Information Fusion, Singapore, 2012: 2185–2192.
[9]	LI Mingkai, LAN Jian, and LI X R. Tracking of elliptical object with unknown but fixed lengths of axes[J]. IEEE Transactions on Aerospace and Electronic Systems, 2023, 59(5): 6518–6533. doi: 10.1109/TAES.2023.3276951.
[10]	THORMANN K and BAUM M. Fusion of elliptical extended object estimates parameterized with orientation and axes lengths[J]. IEEE Transactions on Aerospace and Electronic Systems, 2021, 57(4): 2369–2382. doi: 10.1109/TAES.2021.3057651.
[11]	BAUM M, FAION F, HANEBECK U D. Modeling the target extent with multiplicative noise[C]. 2012 15th International Conference on Information Fusion, Singapore, Singapore, 2012: 2406–2412.
[12]	BAUM M and HANEBECK U D. Random hypersurface models for extended object tracking[C]. Proceedings of 2009 IEEE International Symposium on Signal Processing and Information Technology (ISSPIT), Ajman, United Arab Emirates, 2009: 178–183. doi: 10.1109/ISSPIT.2009.5407526.
[13]	WAHLSTR?M N and ?ZKAN E. Extended target tracking using Gaussian processes[J]. IEEE Transactions on Signal Processing, 2015, 63(16): 4165–4178. doi: 10.1109/TSP.2015.2424194.
[14]	陳輝, 張星星. 基于多伯努利濾波的厚尾噪聲條件下多擴展目標(biāo)跟蹤[J]. 自動化學(xué)報, 2023, 49(7): 1573–1586. doi: 10.16383/j.aas.c201061. CHEN Hui and ZHANG Xingxing. Multiple extended target tracking in the presence of heavy-tailed noise using multi-Bernoulli filtering method[J]. Acta Automatica Sinica, 2023, 49(7): 1573–1586. doi: 10.16383/j.aas.c201061.
[15]	黃偉, 付紅坡, 李煜, 等. 一種高斯-重尾切換分布魯棒卡爾曼濾波器[J]. 哈爾濱工業(yè)大學(xué)學(xué)報, 2024, 56(4): 12–23. doi: 10.11918/202301052. HUANG Wei, FU Hongpo, LI Yu, et al. A Gaussian-heavy-tailed switching distribution robust Kalman filter[J]. Journal of Harbin Institute of Technology, 2024, 56(4): 12–23. doi: 10.11918/202301052.
[16]	王國慶, 楊春雨, 馬磊, 等. 基于高斯–廣義雙曲混合分布的非線性卡爾曼濾波[J]. 自動化學(xué)報, 2023, 49(2): 448–460. doi: 10.16383/j.aas.c220400. WANG Guoqing, YANG Chunyu, MA Lei, et al. Nonlinear Kalman filter based on Gaussian-generalized-hyperbolic mixing distribution[J]. Acta Automatica Sinica, 2023, 49(2): 448–460. doi: 10.16383/j.aas.c220400.
[17]	UROOJ A and RADHAKRISHNAN R. Maximum correntropy-based pseudolinear Kalman filter for passive bearings-only target tracking[J]. Control Theory and Technology, 2024, 22(2): 269–281. doi: 10.1007/s11768-024-00212-y.
[18]	ZHONG Shan, WANG Ziyi, WANG Gang, et al. Robust adaptive filtering based on M-estimation-based minimum error entropy criterion[J]. Information Sciences, 2024, 658: 120026. doi: 10.1016/j.ins.2023.120026.
[19]	CHEN Badong, DANG Lujuan, GU Yuantao, et al. Minimum error entropy Kalman filter[J]. IEEE Transactions on Systems, Man, and Cybernetics: Systems, 2021, 51(9): 5819–5829. doi: 10.1109/TSMC.2019.2957269.
[20]	HU Yue and ZHOU Weidong. A novel moving horizon estimation-based robust Kalman filter with heavy-tailed noises[J]. Circuits, Systems, and Signal Processing, 2024, 43(12): 8091–8107. doi: 10.1007/s00034-024-02831-x.
[21]	HUANG Yulong, ZHANG Yonggang, LI Ning, et al. A novel robust student's t-based Kalman filter[J]. IEEE Transactions on Aerospace and Electronic Systems, 2017, 53(3): 1545–1554. doi: 10.1109/TAES.2017.2651684.
[22]	HUANG Yulong, ZHANG Yonggang, ZHAO Yuxin, et al. A novel robust Gaussian-student's I mixture distribution based Kalman filter[J]. IEEE Transactions on Signal Processing, 2019, 67(13): 3606–3620. doi: 10.1109/TSP.2019.2916755.
[23]	FU Hongpo and CHENG Yongmei. A novel robust Kalman filter based on switching Gaussian-heavy-tailed distribution[J]. IEEE Transactions on Circuits and Systems II: Express Briefs, 2022, 69(6): 3012–3016. doi: 10.1109/TCSII.2022.3161263.
[24]	GILHOLM K, GODSILL S, MASKELL S, et al. Poisson models for extended target and group tracking[C]. SPIE 5913, Signal and Data Processing of Small Targets 2005, San Diego, USA, 2005: 59130R. doi: 10.1117/12.618730.
[25]	ORGUNER U. A variational measurement update for extended target tracking with random matrices[J]. IEEE Transactions on Signal Processing, 2012, 60(7): 3827–3834. doi: 10.1109/TSP.2012.2192927.
[26]	CHENG Yuanhao, CAO Yunhe, YEO T S, et al. Variation Bayesian interference for multiple extended targets or unresolved group targets tracking[EB/OL]. https://arxiv.org/abs/2407.15226, 2024.
[27]	陳輝, 王莉, 韓崇昭. 基于隨機矩陣建模的Student’s t逆Wishart濾波器[J]. 控制理論與應(yīng)用, 2022, 39(6): 1088–1097. doi: 10.7641/CTA.2022.11108. CHEN Hui, WANG Li, and HAN Chongzhao. Student’s t inverse Wishart filter based on random matrix modeling[J]. Control Theory & Applications, 2022, 39(6): 1088–1097. doi: 10.7641/CTA.2022.11108.
[28]	STEUERNAGEL S, THORMANN K and BAUM K. Evaluation scores for elliptic extended object tracking considering diverse object sizes[C]. 2023 26th International Conference on Information Fusion (FUSION), Charleston, SC, USA, 2023: 1–7. doi: 10.23919/FUSION52260.2023.10224112.