基于变分边缘化粒子滤波的车载雷达扩展目标跟踪

周浩文; 王奇

doi:10.12000/JR25005

基于变分边缘化粒子滤波的车载雷达扩展目标跟踪

DOI: 10.12000/JR25005 CSTR: 32380.14.JR25005

周浩文^1, ,,
王奇²

1.
南京楚航科技有限公司南京 211800
2.
海拉南京研发中心南京 211106

详细信息

作者简介:
周浩文，博士，主要研究方向为车载毫米波雷达数据处理、信息融合、非线性估计与滤波

王　奇，硕士，主要研究方向为车载毫米波雷达数据处理

通讯作者:
周浩文 zhouhaowen@nuaa.edu.cn

责任主编：黄岩 Corresponding Editor: HUANG Yan
中图分类号: TN911.7
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出版历程
- 收稿日期: 2025-01-03
- 修回日期: 2025-05-01

Extended Object Tracking Based on Variational Marginalized Particle Filter for Automotive Radar

ZHOU Haowen^{1
, ,},
WANG Qi²

1.
Nanjing ChuHang Technology Co., Ltd., Nanjing 211800, China
2.
Hella Nanjing Technology Center, Nanjing 211106, China

More Information

Corresponding author: ZHOU Haowen, zhouhaowen@nuaa.edu.cn

摘要

摘要: 车载毫米波雷达量测由极坐标系下的位置坐标与多普勒速度组成，其与笛卡儿坐标系下建模的扩展目标状态具有复杂的非线性关系。针对以上非线性状态估计问题，提出一种基于变分边缘化粒子滤波的扩展目标跟踪算法。首先，采用椭圆对目标二维平面轮廓建模，显式定义轮廓朝向角，构建参数化的逆伽马分布作为轮廓尺寸的共轭先验分布；其次，引入量测源位置作为辅助变量，建立适用于毫米波雷达的扩展目标量测模型；然后，为了改善复杂机动目标轮廓估计性能，基于边缘化思想，利用粒子滤波算法独立估计轮廓朝向角的后验分布，并在变分贝叶斯推断框架内，迭代求解剩余状态变量(包括目标中心运动状态、轮廓尺寸)后验分布的近似解析表达式。仿真实验结果表明，所提算法相比于已有算法能够获得更高的状态估计精度，在跟踪机动目标时，对轮廓朝向角与尺寸的估计性能优势更加明显。
- 车载雷达 /
- 扩展目标跟踪 /
- 多普勒速度 /
- 变分贝叶斯 /
- 边缘化粒子滤波
Abstract: The measurement from automotive millimeter-wave radar consists of position coordinates in the polar coordinate system and doppler velocity, which has a complex, nonlinear relationship with the extended object state modeled in the Cartesian coordinate system. To address this nonlinear state estimation problem, a Variational Marginalized Particle Filter–based Extended Object Tracking (VMPF-EOT) algorithm is proposed. First, the object’s two-dimensional planar contour is modeled as an ellipse with an explicitly defined orientation angle. A parameterized inverse gamma distribution is constructed as the conjugate prior distribution for the contour size. Second, the measurement source position is introduced as an auxiliary variable to establish a measurement model for extended objects detected by automotive millimeter-wave radar. To enhance the contour estimation performance for maneuvering objects, the joint distribution of the extended object state is marginalized with respect to the contour orientation angle. The posterior distribution of the contour orientation angle is estimated independently using a particle filter. The approximate analytical solution for the posterior distributions of the remaining state variables—including the target’s center motion state and contour size—is derived using the variational Bayesian inference. The simulation results demonstrate that the proposed algorithm achieves higher state estimation accuracy than existing algorithms. In tracking maneuvering targets, the proposed algorithm offers a more significant advantage in terms of estimating the contour orientation angle and contour size.
- Automotive radar /
- Extended object tracking /
- Doppler velocity /
- Variational inference /
- Marginalized particle filter

HTML全文

图 1 基于车载毫米波雷达的扩展目标

Figure 1. Extended object tracking based on automotive millimeter-wave radar

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图 2 基于VMPF-EOT算法的扩展目标跟踪

Figure 2. Extended object tracking based on VMPF-EOT

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图 3 目标真实转弯率

Figure 3. True object turn rate

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图 4 目标轮廓估计结果

Figure 4. Estimation results of object contour state

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图 5 目标运动估计结果

Figure 5. Estimation results of object motion state

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图 6 VMPF-EOT算法在粒子数不同时的轮廓估计精度

Figure 6. Contour estimation accuracy of VMPF-EOT algorithm with different particle numbers

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图 7 VMPF-EOT算法在迭代次数不同时的估计结果

Figure 7. Estimation results of VMPF-EOT algorithm with different iteration numbers

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1 基于变分边缘化粒子滤波的扩展目标跟踪算法

1. Variational marginalized particle filtering based extended object tracking algorithm

输入：分布参数$\{{\bar{\boldsymbol{x}}}_{k-1\left\|k-1\right.}^{\left(i\right)},{\boldsymbol{P}}_{k-1\left\|k-1\right.}^{\left(i\right)},\{{\alpha }_{k-1\left\|k-1\right.}^{t,\left(i\right)} $, 　$ {\beta }_{k-1\left\|k-1\right.}^{t,\left(i\right)}\}_{t=1}^{{n}_{\boldsymbol{y}}^{p}},\;{\theta }_{k-1}^{\left(i\right)},\;{w}_{k-1}^{\left(i\right)}\}_{i=1}^{N} $，量测 $ {\boldsymbol{Y}}_{k} $.
输出：分布参数$ \{{\bar{\boldsymbol{x}}}_{k\left\|k\right.}^{\left(i\right)},{\boldsymbol{P}}_{k\left\|k\right.}^{\left(i\right)},{\{{\alpha }_{k\left\|k\right.}^{t,\left(i\right)},{\beta }_{k\left\|k\right.}^{t,\left(i\right)}\}}_{t=1}^{{n}_{\boldsymbol{y}}^{p}}, $ 　$ {\theta }_{k}^{\left(i\right)},{w}_{k}^{\left(i\right)}\}_{i=1}^{N} $.
步骤1　状态预测：
(1) 轮廓朝向角预测：根据式(17)，采样新粒子集　　　　 $ {\left\{{\theta }_{k}^{\left(i\right)}\right\}}_{k=1}^{N} $；
(2) 运动状态与轮廓尺寸预测：
for i = 1, 2, ···, N
根据式(20)和式(21)，计算$ p\left({\boldsymbol{x}}_{k}\left\|{\theta }_{k}^{\left(i\right)},{\boldsymbol{Y}}_{1:k-1}\right.\right) $；
根据式(23)和式(24)，计算$ p\left({\boldsymbol{X}}_{k}\left\|{\theta }_{k}^{\left(i\right)},{\boldsymbol{Y}}_{1:k-1}\right.\right) $；
end for
步骤2　量测更新：
(1) 运动状态与轮廓尺寸更新：
for i = 1, 2, ···, N
初始化：
$ {\bar{\boldsymbol{x}}}_{k\left\|k\right.}^{\left(i\right),0}={\bar{\boldsymbol{x}}}_{k\left\|k-1\right.}^{\left(i\right)},{\boldsymbol{P}}_{k\left\|k\right.}^{\left(i\right),0}={\boldsymbol{P}}_{k\left\|k-1\right.}^{\left(i\right)} $;
$ {\alpha }_{k\left\|k\right.}^{t,\left(i\right),0}={\alpha }_{k\left\|k\right.-1}^{t,\left(i\right)},{\beta }_{k\left\|k\right.}^{t,\left(i\right),0}={\beta }_{k\left\|k\right.-1}^{t,\left(i\right)}(t=1,2,\cdots, {n}_{\boldsymbol{y}}^{p}) $;
$ {\bar{\boldsymbol{z}}}_{k}^{p,\left(i\right),j,0}={\boldsymbol{y}}_{k}^{p,j},{\boldsymbol{\varSigma }}_{k}^{{\boldsymbol{z}}^{p},\left(i\right),j,0}=s{\bar{\boldsymbol{X}}}_{k}(j=1,2,\cdots ,{m}_{k}) $;
for l = 1, 2,···, $\ell_{\max} $
根据式(35)—式(37)，计算$ {q}_{\boldsymbol{x}}^{\left(i\right),\ell }\left({\boldsymbol{x}}_{k}\right) $；
根据式(42)—式(44)，计算$ {q}_{{\boldsymbol{X}}}^{\left(i\right),\ell }\left({\boldsymbol{X}}_{k}\right)； $
根据式(47)—式(49)，计算$ {q}_{{\boldsymbol{Z}}^{p}}^{\left(i\right),\ell }\left({\boldsymbol{Z}}_{k}^{p}\right)； $
end for
end for
(2) 轮廓朝向角更新：
for i = 1, 2,···, N
根据式(63)，计算$ p\left({\boldsymbol{Y}}_{k}\|{\theta }_{k}^{\left(i\right)},{\boldsymbol{Y}}_{1:k}\right)； $
根据式(60)，计算$ {w}_{k}^{\left(i\right)}； $
end for
根据式(67)，归一化权值；
若$ {N}_{e} $低于阈值，对粒子重采样.

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表 1 仿真参数

Table 1. Simulation parameters

参数	数值
粒子数N	10
最大迭代次数$ {\ell }_{\max} $	5
过程噪声参数$ {q}_{1} $	0.1
过程噪声参数$ {q}_{2} $	0.1
轮廓朝向角过程噪声方差$ {Q}_{k}^{\theta } $	0.005
遗忘因子$ {\rho }_{k} $	0.99
重采样阈值$ {N}_{{\mathrm{thr}}} $	$ 0.2N $
轮廓缩放系数s	$ 1/4 $

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表 2 各算法的平均单步长运行时间

Table 2. Average single-step running time of various algorithms

算法	运行时间(ms)
RM-EOT	0.0653
MEM-EKF	0.3274
MEM-EKF-D	0.4659
VMPF-EOT	0.7238
VMPF-EOT(并行计算)	0.2587

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