综述部分

📌 分配轨道（数据关联）的方法：

1. The algorithm of Multiple Hypothesis Tracking (MHT) (多重假设跟踪)evaluates the likelihood of a target based on a sequence of measurements.The track hypothesis for each candidate forms a tree. To select the best track hypothesis, it prunes out the spurious hypotheses for each track independently and discards the deleted items [26,”Multiple hypothesis tracking revisited”]
2. In contrast, the algorithm of Joint Probabilistic Data Association (JPDA) (联合概率数据关联)considers all the potential hypotheses. It is a sub-optimal Bayesian algorithm that calculates a marginalized probability on the joint data association space.In each frame, a joint probability is calculated to associate the measurement with the corresponding track [27,”Joint probabilistic data association revisited”]

上述两种方法的计算量太大！

3. In [28,“Multi-3D-object tracking by fusing rgb and 3D-LIDAR data”], a method fusing RGB and 3D-LiDAR data（融合RGB图像和激光雷达数据进行数据关联） is proposed to track the perceived objects. It detected the appearance feature in RGB frame and geometrical feature in 3D pints cloud to associate the same obstacle. As the associated features are from different sensors, the method is limited by the overlap areas and lighting conditions.

4. In [29,“Multi-object tracking of 3D cuboids using aggregated features,”], a model with five states is proposed based on a Markov decision process. It considered the multiple aggregated features like color, semantic class, geometric properties, orientation and positional descriptor in the data association.（考虑了颜色、语义类、几何属性、方向和位置描述符等多个聚合特征，该方法能够很好地区分多种类型的障碍。但是，对于我们解决的车辆跟踪问题来说，它太复杂了）。

5. In our proposed algorithm, we consider the data association step as an assignment problem. In order to solve the problem of deformation and missing objects caused by occlusion and change of viewing angles, we retain the previously determined tracking list and use the Hungarian algorithm to achieve the match between the measurements and the targets.（在我们提出的算法中，我们将数据关联步骤视为分配问题。为了解决遮挡和视角变化导致的物体变形和丢失的问题，我们保留了之前确定的跟踪列表，并使用匈牙利算法来实现测量与目标的匹配。）**

数据关联使用的卡尔曼滤波方法：

1. In [32,“Low-Cost Lidar Based Vehicle Pose Estimation and Tracking,”], a vehicle tracking system with Multi-Model Association (MMA) is built upon the data segmentation result.(基于数据分割结果构建了具有多模型关联（MMA）的车辆跟踪系统，该系统考虑预拟合残差的协方差来选择最佳的车辆模型和卡尔曼滤波参数。)
2. In [34,”Generic vehicle tracking framework capable of handling occlusions based on modified mixture particle filter”,], a generic vehicle tracking framework based on a modified mixture particle filter is proposed. It can adapt the number of tracking targets to real-time observations and track all the vehicles within sensor range simultaneously, which is implemented in a uniform framework without explicit data association.(一种基于改进的混合粒子滤波器的通用车辆跟踪框架。它可以使跟踪目标的数量适应实时观测，同时跟踪传感器范围内的所有车辆，这是在一个统一的框架中实现的，无需明确的数据关联。)

本论文方法：
In this paper, we propose an L-shape fitting algorithm to fit vehicles with rectangular bounding boxes. We consider the velocity of the target vehicle to estimate the orientation of the target vehicle which greatly reduces the orientation error caused by incomplete observations. To identify different vehicles with consistent tracker IDs, we track the corner of the target vehicle by the RBPF, which estimates the position and the orientation separately.

算法部分

L-SHAPE EXTRACTION

A. 数据预处理

📌 1. 路边检测
降低了检测和跟踪的复杂性，假设可行驶边界由两侧路缘石的位置定义。
基于缘石的几何特征，高度大约在10-15cm，并且是凸起的（the elevation changes sharply in the vertical direction）Based on these features, a robust approach in [4,“A real-time curb detection and tracking method for UGVs by using a 3D-LIDAR sensor,”] was proposed to recognize curbs.
2. 拟合路面
分离的点包含障碍物部分和地面部分。障碍物的高度通常高于地面。因此，这些点按其高程升序排序，并选择 ξ% 的点用于拟合地面。[35]–[37]

B. L形拟合

📌 1. L形拟合的常规方法：
我们想找到一个矩形来适应分割的点云簇。使用两个垂直的线表示L形：
$$\begin{gathered} xcos\theta +ysin\theta =c1 \\ -xsin\theta +ycos\theta =c2 \end{gathered}$$
因此，L形拟合可以概括为如下优化问题：

然而上述方法计算量太大，难以实时运行

2.本文L形拟合的方法：
We instead rely on a corner-edge based algorithm to find the best-fit rectangle approximately.相反，我们依靠基于角边的算法来近似找到最佳拟合矩形。
The basic idea is that we find the nearest corner of the target vehicle first, and then fit the edges of the target vehicle using RANSAC.基本思想是我们先找到目标车辆最近的边角点，然后使用RANSAC拟合目标车辆的边缘。
A corner-edge based L-shape fitting method has also been proposed in [38]. However, the method proposed in [38,“L-shape model switching-based precise motion tracking of moving vehicles using laser scanners,”] assumes that all clustered points have a complete L-shape(完整的L形假设). In fact, due to occlusion and different viewing angles, the complete L-shape cannot be observed in most cases,（现实并非如此）

拟合过程：

1. 计算某一个聚类簇的所有点到传感器的距离和角度，选择出距离传感器最近的一个点D
2. 根据D点的角度，将聚类簇中点分成2类，A和B（根据是否大于D点角度）
3. A和B分别拟合出一条线LA和LB，然后计算两条线的夹角$\Delta \delta$
4. 如果$\Delta \delta$大于阈值，则LA和LB为需要的L形，那么车辆的航向就是LA或者LB的指向，否则将A和B合并，提取出一条线L,该条线是车辆和一个边缘，且L的方向就是车辆的方向(?)

According to the Ackerman principle(阿克曼理论), we can get the angle between the velocity and the orientation of a target（我们可以得到目标的速度和方向之间的夹角）

其中v是目标车辆的速度，Δt是两次采样之间的间隔，r是转弯半径，α是速度方向，φ是车辆滑动角。因此，我们用 α 确定哪条拟合线是目标车辆的方向。
观测量包括两种：One is the dynamic measurement ZD =[xc,yc]T for an update of the position. The other is the shape measurement ZS =[l1,l2,θ]T for an update of the shape state in the L-shape tracking.一种是用于更新位置的动态测量 ZD =[xc,yc]T。另一个是形状测量 ZS =[l1,l2,θ]T 用于更新 L 形跟踪中的形状状态。

L-SHAPE TRACKING

📌 本文通过跟踪车辆最近的边角点而非车辆的几何形状和车辆中心来实现车辆的跟踪，这样做的好处是可以避免由于视点的遮挡和变化导致每次扫描中的不稳定！

A. Data Association

📌 我们通过带有门函数的匈牙利算法来解决数据关联问题。The potential observation at a particular frame should be located in a gate area [40,“An algorithm for tracking multiple targets,”].
门控需要设置一个阈值$\epsilon$满足下式的观测值才会通过门控

B. Tracking Model

📌 车辆有三种运动模式：

1. 静止状态
2. 匀速状态
3. 匀加速状态
   前两种运动状态是第三种运动状态的特例，因此采用匀加速模型作为tracking的运动模型
   其中匀加速状态下，车辆的朝向可能和速度方向不一致，如下图所示：

状态向量如下：

$x(t)=[x(t),y(t),vx(t),vy(t),ax(t),ay(t){]}^T$

The constant acceleration model is:

where Δt is the sampling time and u is the system noise.

C. L-Shape Tracking

📌 采用Rao-Blackwellized粒子滤波器
将状态向量$x(t)=[x(t),y(t),vx(t),vy(t),ax(t),ay(t){]}^T$分成两部分：
$x(t)=[x_k(t);x_p(t)]$其中$x_k(t)$表示向量 x 在时间 t 的线性部分，$x_p(t)$表示非线性部分。
因此，状态空间方程和观测方程可以概括如下：

D. L-Shape to Box Model

📌 根据车辆的某个边角点恢复车辆的边界框

实验部分

📌 1. 拟合部分使用不同的拟合方式作对照实验
车辆有几种不同的拟合方式：
We compare the proposed algorithm with the variance criterion, area criterion and closeness criterion proposed in [20,“Efficient l-shape fitting for vehicle detection using laser scanners,”]方差标准、面积标准和接近标准
单一的拟合方式对视点和视角变化很敏感。
本文提出的L形拟合方式比上述几种拟合方式稳定（通过计算拟合出的车辆的朝向和真实朝向的误差来量化）

拟合的角度误差应该要小于5度

2.跟踪部分使用KF和Multiple Model Association (MMA)[38,“L-shape model switching-based precise motion tracking of moving vehicles using laser scanners,”]作对照实验
计算在横向位置、纵向位置和方向方面车辆跟踪的精度：

总结：

📌 本篇论文的创新点：

1. 基于车辆边角点的L形拟合：
   基本思想是我们先找到目标车辆最近的边角点，然后使用RANSAC拟合目标车辆的边缘。
2. 基于粒子滤波的L形跟踪：
   观测量是边角点到传感器的距离以及边角点到传感器的方位角，同时将状态向量分成两部分，线性部分和非线性部分。粒子滤波。

本篇论文值得借鉴的地方：

1. 基于车辆边角点的L形拟合，对视角和视点不敏感，较为稳定。衡量拟合结果优劣的标准是车辆方向的拟合误差，可以与其他几种拟合方法（ variance criterion, area criterion and closeness criterion）进行对照。
2. 车辆的运动模型，采用匀加速的运动模型，因为匀速模型和静止模型都可以看做是匀加速运动模型的特例。本篇论文采用的是粒子滤波，还有其他的滤波的方式，例如KF、MMA,可以作对照实验。衡量跟踪性能的标准是跟踪的横向、纵向、航向角的误差。

本篇论文未解决的问题：
车辆相距过近时很容易将两个车辆聚为一类，从而会影响车辆跟踪的稳定性和正确率。