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 $ {v_{k - 1}} $、量測$ {{\boldsymbol{Z}}_k} $、觀測站姿態(tài)$ (x_k^{\text{O}},y_k^{\text{O}}) $, $ \theta _k^{\text{O}} $ (1) 根據(jù)式(12)–式(15)預(yù)測PHD，得到式(16)所述的$ {v_{k|k - 1}} $ (2) 根據(jù)式(17)–式(21)更新$ {v_{k|k - 1}} $，其中似然的計(jì)算見式(29)、
式(30)(3) 剔除權(quán)重小于$ {\lambda _{\textq7j3ldu95}} $的JMGM分量，后根據(jù)式(31)–式(35)執(zhí)行合并 (4) 根據(jù)式(24)–式(26)估計(jì)目標(biāo)數(shù)、目標(biāo)狀態(tài)和多目標(biāo)模型概率 輸出：當(dāng)前時(shí)刻PHD$ {v_k} $，多目標(biāo)的狀態(tài)估計(jì)$ \hat {\boldsymbol{x}}_k^{(i)} $和模型概率$ u_k^{(m)} $ 
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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
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