一種純方位多目標(biāo)跟蹤的聯(lián)合多高斯混合概率假設(shè)密度濾波器
doi: 10.11999/JEIT240201
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西北工業(yè)大學(xué)航海學(xué)院 西安 710072
基金項(xiàng)目: 國家自然科學(xué)基金(62071386)
Joint Multi-Gaussian Mixture Probability Hypothesis Density Filter for Bearings-only Multi-target Tracking
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School of Marine Science and Technology, Northwestern Polytechnical University, Xi’an 710072, China
Funds: The National Natural Science Foundation of China (62071386)
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摘要: 現(xiàn)有的多模型-高斯混合-概率假設(shè)密度(MM-GM-PHD)濾波器被廣泛用于不確定機(jī)動(dòng)目標(biāo)跟蹤,但它不能在不同模型下保持并行的估計(jì),導(dǎo)致各模型的似然值滯后于目標(biāo)機(jī)動(dòng)。為此,該文提出一種聯(lián)合多高斯混合概率假設(shè)密度(JMGM-PHD)濾波器,并將其用于純方位多目標(biāo)跟蹤。首先,推導(dǎo)了JMGM模型,其中每個(gè)單目標(biāo)狀態(tài)估計(jì)由一組并行的、帶模型概率的高斯函數(shù)描述,該狀態(tài)估計(jì)的概率由一個(gè)非負(fù)的權(quán)重來表征。一組權(quán)值、模型概率、均值和協(xié)方差被統(tǒng)稱為JMGM分量。根據(jù)貝葉斯規(guī)則,推導(dǎo)了JMGM分量的更新方法。然后,利用JMGM模型近似多目標(biāo)PHD。根據(jù)交互式多模型(IMM)規(guī)則,推導(dǎo)出JMGM分量的交互、預(yù)測和估計(jì)方法。將所提JMGM-PHD濾波器應(yīng)用于純方位跟蹤(BOT)時(shí),針對同時(shí)執(zhí)行平移和旋轉(zhuǎn)的觀測站,基于復(fù)合函數(shù)求導(dǎo)規(guī)則推導(dǎo)出一種計(jì)算線性化觀測矩陣的方法。所提JMGM-PHD濾波器保持了單模型PHD濾波器的形式,但能夠自適應(yīng)地跟蹤不確定機(jī)動(dòng)目標(biāo)。仿真結(jié)果表明,JMGM-PHD濾波器克服了似然值滯后于目標(biāo)機(jī)動(dòng)的問題,在跟蹤精度和計(jì)算成本方面均優(yōu)于MM-GM-PHD濾波器。
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關(guān)鍵詞:
- 不確定機(jī)動(dòng)目標(biāo)跟蹤 /
- 概率假設(shè)密度濾波器 /
- 交互多模型 /
- 平移和旋轉(zhuǎn) /
- 純方位跟蹤
Abstract: The Multi-Model Gaussian Mixture-Probability Hypothesis Density (MM-GM-PHD) filter is widely used in uncertain maneuvering target tracking, but it does not maintain parallel estimates under different models, leading to the model-related likelihood lagging behind unknown target maneuvers. To solve this issue, a Joint Multi-Gaussian Mixture PHD (JMGM-PHD) filter is proposed and applied to bearings-only multi-target tracking in this paper. Firstly, a JMGM model is derived, where each single-target state estimate is described by a set of parallel Gaussian functions with model probabilities, and the probability of this state estimate is characterized by a nonegative weight. The weights, model-related probabilities, means and covariances are collectively called JMGM components. According to the Bayesian rule, the updating method of the JMGM components is derived. Then, the multi-target PHD is approximated using the JMGM model. According to the Interactive Multi-Model (IMM) rule, the interacting, prediction and estimation methods of the JMGM components are derived. When addressing Bearings-Only Tracking (BOT), a method based on the derivative rule for composite functions is derived to compute the linearized observation matrix of observers that simultaneously performs translations and rotations. The proposed JMGM-PHD filter preserves the form of regular single-model PHD filter but can adaptively track uncertain maneuvering targets. Simulations show that our algorithm overcomes the likelihood lag issue and outperforms the MM-GM-PHD filter in terms of tracking accuracy and computation cost. -
1 所提JMGM-PHD濾波應(yīng)用于BOT時(shí)的算法
輸入:上一時(shí)刻PHD vk−1、量測Zk、觀測站姿態(tài)(xOk,yOk), θOk (1) 根據(jù)式(12)–式(15)預(yù)測PHD,得到式(16)所述的vk|k−1 (2) 根據(jù)式(17)–式(21)更新vk|k−1,其中似然的計(jì)算見式(29)、
式(30)(3) 剔除權(quán)重小于λ\textq7j3ldu95的JMGM分量,后根據(jù)式(31)–式(35)執(zhí)行合并 (4) 根據(jù)式(24)–式(26)估計(jì)目標(biāo)數(shù)、目標(biāo)狀態(tài)和多目標(biāo)模型概率 輸出:當(dāng)前時(shí)刻PHDvk,多目標(biāo)的狀態(tài)估計(jì)ˆx(i)k和模型概率u(m)k 下載: 導(dǎo)出CSV
表 1 各濾波器平均OSPA誤差曲線的均值、最大值和標(biāo)準(zhǔn)差
濾波器 均值 最大值 標(biāo)準(zhǔn)差 MM-GM-PHD 50.150 2 97.146 2 10.729 5 MMF-GM-PHD 74.883 5 100.000 0 19.286 3 JMGM-PHD 41.452 3 62.084 0 8.463 9 下載: 導(dǎo)出CSV
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[1] 嚴(yán)靈杰, 顧杰, 姜余, 等. 基于隨機(jī)有限集的多目標(biāo)跟蹤技術(shù)綜述[J]. 電子信息對抗技術(shù), 2024, 39(1): 81–88. doi: 10.3969/j.issn.1674-2230.2024.01.013.YAN Lingjie, GU Jie, JIANG Yu, et al. Overview of multi-target tracking technology based on random finite set[J]. Electronic Information Warfare Technology, 2024, 39(1): 81–88. doi: 10.3969/j.issn.1674-2230.2024.01.013. [2] MAHLER R P S. Multitarget Bayes filtering via first-order multitarget moments[J]. IEEE Transactions on Aerospace and Electronic Systems, 2003, 39(4): 1152–1178. doi: 10.1109/TAES.2003.1261119. [3] MAHLER R. PHD filters of higher order in target number[J]. IEEE Transactions on Aerospace and Electronic Systems, 2007, 43(4): 1523–1543. doi: 10.1109/TAES.2007.4441756. [4] VO B T, VO B N, and CANTONI A. The cardinality balanced multi-target multi-Bernoulli filter and its implementations[J]. IEEE Transactions on Signal Processing, 2009, 57(2): 409–423. doi: 10.1109/TSP.2008.2007924. [5] 陳一梅, 劉偉峰, 孔明鑫, 等. 基于GLMB濾波和Gibbs采樣的多擴(kuò)展目標(biāo)有限混合建模與跟蹤算法[J]. 自動(dòng)化學(xué)報(bào), 2020, 46(7): 1445–1456. doi: 10.16383/j.aas.c180077.CHEN Yimei, LIU Weifeng, KONG Mingxin, et al. A modeling and tracking algorithm of finite mixture models for multiple extended target based on the GLMB filter and Gibbs sampler[J]. Acta Automatica Sinica, 2020, 46(7): 1445–1456. doi: 10.16383/j.aas.c180077. [6] üNEY M, CLARK D E, and JULIER S J. Distributed fusion of PHD filters via exponential mixture densities[J]. IEEE Journal of Selected Topics in Signal Processing, 2013, 7(3): 521–531. doi: 10.1109/JSTSP.2013.2257162. [7] LI Tiancheng and HLAWATSCH F. A distributed particle-PHD filter using arithmetic-average fusion of Gaussian mixture parameters[J]. Information Fusion, 2021, 73: 111–124. doi: 10.1016/j.inffus.2021.02.020. [8] 王奎武, 張秦, 虎小龍. 基于多目標(biāo)不確定性改進(jìn)的GM-PHD濾波器[J]. 兵工學(xué)報(bào), 2022, 43(12): 3113–3121. doi: 10.12382/bgxb.2021.0693.WANG Kuiwu, ZHANG Qin, and HU Xiaolong. Improved GM-PHD filter based on multi-target uncertainty[J]. Acta Armamentarii, 2022, 43(12): 3113–3121. doi: 10.12382/bgxb.2021.0693. [9] HUANG Qiao, XIE Lei, and SU Hongye. Estimations of time-varying birth cardinality distribution and birth intensity in Gaussian mixture CPHD filter for multi-target tracking[J]. Signal Processing, 2022, 190: 108321. doi: 10.1016/j.sigpro.2021.108321. [10] WANG Linxi, HU Xiaoxi, HAN Xun, et al. Simulation of CBMeMber multi-target tracking algorithm based on Gauss mixture[C]. The IEEE 19th International Conference on Communication Technology, Xi’an, China, 2019: 1524–1528. doi: 10.1109/ICCT46805.2019.8947076. [11] YANG Chaoqun, CAO Xianghui, and SHI Zhiguo. Road-map aided Gaussian mixture labeled multi-Bernoulli filter for ground multi-target tracking[J]. IEEE Transactions on Vehicular Technology, 2023, 72(6): 7137–7147. doi: 10.1109/TVT.2023.3240740. [12] 邵鵬飛, 王蕾, 王方勇. 基于序貫蒙特卡洛與概率假設(shè)密度濾波的主動(dòng)分布式聲納多目標(biāo)跟蹤[J]. 兵工學(xué)報(bào), 2020, 41(5): 941–949. doi: 10.3969/j.issn.1000-1093.2020.05.013.SHAO Pengfei, WANG Lei, and WANG Fangyong. Active distributed sonar multi-target tracking based on SMC-PHD filtering[J]. Acta Armamentarii, 2020, 41(5): 941–949. doi: 10.3969/j.issn.1000-1093.2020.05.013. [13] CAO Chenghu, ZHAO Yongbo, PANG Xiaojiao, et al. Sequential Monte Carlo cardinalized probability hypothesized density filter based on Track-Before-Detect for fluctuating targets in heavy-tailed clutter[J]. Signal Processing, 2020, 169: 107367. doi: 10.1016/j.sigpro.2019.107367. [14] WANG Haihuan, LYU Xiaoyong, and MA Long. Adaptive cardinality balanced multi-target multi-Bernoulli filter based on cubature Kalman[J]. The Journal of Engineering, 2019, 2019(21): 7667–7671. doi: 10.1049/joe.2019.0670. [15] HOU Liming, LIAN Feng, DE ABREU G T F, et al. Robust δ-generalized labeled multi-Bernoulli filter for nonlinear systems with heavy-tailed noises[C]. The IEEE 23rd International Conference on Information Fusion, Rustenburg, South Africa, 2020: 1–8. doi: 10.23919/FUSION45008.2020.9190250. [16] ZHAO Shunyi, AHN C K, SHI Peng, et al. Bayesian state estimation for Markovian jump systems: Employing recursive steps and pseudocodes[J]. IEEE Systems, Man, and Cybernetics Magazine, 2019, 5(2): 27–36. doi: 10.1109/MSMC.2018.2882145. [17] DU Xue, HU Xianbo, HU Junsheng, et al. An adaptive interactive multi-model navigation method based on UUV[J]. Ocean Engineering, 2023, 267: 113217. doi: 10.1016/j.oceaneng.2022.113217. [18] ZHOU Gongjian, ZHU Bin, and YE Xiaoping. Switch-constrained multiple-model algorithm for maneuvering target tracking[J]. IEEE Transactions on Aerospace and Electronic Systems, 2023, 59(4): 4414–4433. doi: 10.1109/TAES.2023.3242944. [19] PUNITHAKUMAR K, KIRUBARAJAN T, and SINHA A. Multiple-model probability hypothesis density filter for tracking maneuvering targets[J]. IEEE Transactions on Aerospace and Electronic Systems, 2008, 44(1): 87–98. doi: 10.1109/TAES.2008.4516991. [20] DA Kai, LI Tiancheng, ZHU Yongfeng, et al. Gaussian mixture particle jump-Markov-CPHD fusion for multitarget tracking using sensors with limited views[J]. IEEE Transactions on Signal and Information Processing over Networks, 2020, 6: 605–616. doi: 10.1109/TSIPN.2020.3016478. [21] 楊標(biāo), 朱圣棋, 余昆, 等. 貪婪的量測劃分機(jī)制下的多傳感器多機(jī)動(dòng)目標(biāo)跟蹤算法[J]. 電子與信息學(xué)報(bào), 2021, 43(7): 1962–1969. doi: 10.11999/JEIT200498.YANG Biao, ZHU Shengqi, YU Kun, et al. Multi-sensor multiple maneuvering targets tracking algorithm under greedy measurement partitioning mechanism[J]. Journal of Electronics & Information Technology, 2021, 43(7): 1962–1969. doi: 10.11999/JEIT200498. [22] CAO Chenghu and ZHAO Yongbo. A multiple-model generalized labeled multi-Bernoulli filter based on blocked Gibbs sampling for tracking maneuvering targets[J]. Signal Processing, 2021, 186: 108119. doi: 10.1016/j.sigpro.2021.108119. [23] WU Sunyong, DONG Xudong, ZHAO Jun, et al. A fast implementation of interactive-model generalized labeled multi-Bernoulli filter for interval measurements[J]. Signal Processing, 2019, 164: 345–353. doi: 10.1016/j.sigpro.2019.05.028. [24] TURNER J D, MCMAHON J, and ZAVLANOS M M. Receding horizon tracking of an unknown number of mobile targets using a bearings-only sensor[C]. 2022 International Conference on Robotics and Automation, Philadelphia, USA, 2022: 7327–7334. doi: 10.1109/ICRA46639.2022.9811882. [25] ZHANG Yuexing, LI Yiping, LI Shuo, et al. A multi-AUV bearings-only multi-target tracking method based on the fast LMB filter[C]. The 4th International Conference on Control and Robotics, Guangzhou, China, 2022: 446–451. doi: 10.1109/ICCR55715.2022.10053872. [26] CHEN Jinfeng, MA Hong, LIANG Chengguo, et al. OTHR multipath tracking using the Bernoulli filter[J]. IEEE Transactions on Aerospace and Electronic Systems, 2014, 50(3): 1974–1990. doi: 10.1109/TAES.2013.120659. [27] SCHUHMACHER D, VO B T, and VO B N. A consistent metric for performance evaluation of multi-object filters[J]. IEEE Transactions on Signal Processing, 2008, 56(8): 3447–3457. doi: 10.1109/TSP.2008.920469. -