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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

薛昱,  馮西安

薛昱, 馮西安. 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[J]. 電子與信息學(xué)報(bào), 2024, 46(11): 4295-4304. doi: 10.11999/JEIT240201
引用本文: 薛昱, 馮西安. 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[J]. 電子與信息學(xué)報(bào), 2024, 46(11): 4295-4304. doi: 10.11999/JEIT240201
XUE Yu, FENG Xi’an. Joint Multi-Gaussian Mixture Probability Hypothesis Density Filter for Bearings-only Multi-target Tracking[J]. Journal of Electronics & Information Technology, 2024, 46(11): 4295-4304. doi: 10.11999/JEIT240201
Citation: XUE Yu, FENG Xi’an. Joint Multi-Gaussian Mixture Probability Hypothesis Density Filter for Bearings-only Multi-target Tracking[J]. Journal of Electronics & Information Technology, 2024, 46(11): 4295-4304. doi: 10.11999/JEIT240201

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

  • 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)
詳細(xì)信息
    作者簡介:

    薛昱：男，博士生，研究方向?yàn)槎鄠鞲衅魅诤虾湍繕?biāo)跟蹤

    馮西安：男，教授，博士生導(dǎo)師，研究方向?yàn)樗曅盘柼幚?、陣列信號處理、水下目?biāo)跟蹤、多傳感器融合等

    通訊作者:

    馮西安　fengxa@nwpu.edu.cn

  • 中圖分類號: TN911.7; TP391

Joint Multi-Gaussian Mixture Probability Hypothesis Density Filter for Bearings-only Multi-target Tracking

  • School of Marine Science and Technology, Northwestern Polytechnical University, Xi’an 710072, China

Funds: The National Natural Science Foundation of China (62071386)
  • 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。
    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.
    • HTML全文

  • 圖  1  無漏檢和目標(biāo)新生時(shí)，高斯分量的1次迭代

    圖  2  主、被動(dòng)跟蹤中交叉合并的頻率曲線

    圖  3  跟蹤態(tài)勢與純方位量測

    圖  4  目標(biāo)軌跡和各濾波器的估計(jì)軌跡

    圖  5  各濾波器的似然曲線

    圖  6  各濾波器的模型概率估計(jì)誤差

    圖  7  多目標(biāo)跟蹤性能評估

    圖  8  不同轉(zhuǎn)移概率的平均OSPA誤差曲線

    圖  9  JMGM分量/高斯分量的數(shù)量

    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-PHD50.150 297.146 210.729 5
    MMF-GM-PHD74.883 5100.000 019.286 3
    JMGM-PHD41.452 362.084 08.463 9
    下載: 導(dǎo)出CSV

    表  2  各濾波器的平均運(yùn)行時(shí)間(s)

    MM-GM-PHDJMGM-PHD
    2.62422.2254
    下載: 導(dǎo)出CSV
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  • 收稿日期:  2024-03-25
  • 修回日期:  2024-09-29
  • 網(wǎng)絡(luò)出版日期:  2024-10-12
  • 刊出日期:  2024-11-10

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