[go: up one dir, main page]

CN113344039B - A multi-extended target tracking method based on spatiotemporal correlation - Google Patents

A multi-extended target tracking method based on spatiotemporal correlation Download PDF

Info

Publication number
CN113344039B
CN113344039B CN202110547305.4A CN202110547305A CN113344039B CN 113344039 B CN113344039 B CN 113344039B CN 202110547305 A CN202110547305 A CN 202110547305A CN 113344039 B CN113344039 B CN 113344039B
Authority
CN
China
Prior art keywords
target
matrix
gaussian
measurement
extended
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Expired - Fee Related
Application number
CN202110547305.4A
Other languages
Chinese (zh)
Other versions
CN113344039A (en
Inventor
甘露
林晨
徐政五
廖红舒
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Research Institute Of Yibin University Of Electronic Science And Technology
University of Electronic Science and Technology of China
Original Assignee
Research Institute Of Yibin University Of Electronic Science And Technology
University of Electronic Science and Technology of China
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Research Institute Of Yibin University Of Electronic Science And Technology, University of Electronic Science and Technology of China filed Critical Research Institute Of Yibin University Of Electronic Science And Technology
Priority to CN202110547305.4A priority Critical patent/CN113344039B/en
Publication of CN113344039A publication Critical patent/CN113344039A/en
Application granted granted Critical
Publication of CN113344039B publication Critical patent/CN113344039B/en
Expired - Fee Related legal-status Critical Current
Anticipated expiration legal-status Critical

Links

Images

Classifications

    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F18/00—Pattern recognition
    • G06F18/20—Analysing
    • G06F18/23—Clustering techniques
    • G06F18/232—Non-hierarchical techniques
    • G06F18/2321—Non-hierarchical techniques using statistics or function optimisation, e.g. modelling of probability density functions
    • G06F18/23213—Non-hierarchical techniques using statistics or function optimisation, e.g. modelling of probability density functions with fixed number of clusters, e.g. K-means clustering
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
    • G06F17/10—Complex mathematical operations
    • G06F17/15—Correlation function computation including computation of convolution operations
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
    • G06F17/10—Complex mathematical operations
    • G06F17/16—Matrix or vector computation, e.g. matrix-matrix or matrix-vector multiplication, matrix factorization

Landscapes

  • Engineering & Computer Science (AREA)
  • Physics & Mathematics (AREA)
  • General Physics & Mathematics (AREA)
  • Data Mining & Analysis (AREA)
  • Theoretical Computer Science (AREA)
  • Mathematical Physics (AREA)
  • Pure & Applied Mathematics (AREA)
  • Mathematical Optimization (AREA)
  • Mathematical Analysis (AREA)
  • Computational Mathematics (AREA)
  • General Engineering & Computer Science (AREA)
  • Computing Systems (AREA)
  • Algebra (AREA)
  • Databases & Information Systems (AREA)
  • Software Systems (AREA)
  • Bioinformatics & Cheminformatics (AREA)
  • Artificial Intelligence (AREA)
  • Evolutionary Computation (AREA)
  • Bioinformatics & Computational Biology (AREA)
  • Evolutionary Biology (AREA)
  • Computer Vision & Pattern Recognition (AREA)
  • Life Sciences & Earth Sciences (AREA)
  • Probability & Statistics with Applications (AREA)
  • Radar Systems Or Details Thereof (AREA)

Abstract

本发明涉及一种基于时空关联的多扩展目标跟踪方法。当目标占据传感器的多个分变率单元时，单个目标便会产生多个量测值，即为扩展目标。在这种背景下，当扩展目标产生交叉，一般的基于距离的划分方法会将不同目标的量测值划入同一量测集合中，造成滤波器的精度下降，势估计出现错误。本发明基于ET‑GM‑PHD算法，采用时空关联思想，利用扩展目标在相邻时刻量测值的关联性，并在一种有向图SNN划分基础上，对多扩展目标进行跟踪。本发明方法大大降低了扩展目标在交叉处的跟踪误差，对目标的个数和目标的位置实现了精确估计。同时将扩展目标与点目标的跟踪过程分离，大大降低了计算的计算量。

Figure 202110547305

The invention relates to a multi-expansion target tracking method based on space-time correlation. When the target occupies multiple sub-variable cells of the sensor, a single target will produce multiple measurement values, that is, an extended target. In this context, when the extended target intersects, the general distance-based division method will divide the measurement values of different targets into the same measurement set, resulting in a decrease in the accuracy of the filter and an error in the potential estimation. The invention is based on the ET-GM-PHD algorithm, adopts the idea of space-time correlation, utilizes the correlation of the measured values of the extended target at adjacent moments, and tracks multiple extended targets on the basis of a directed graph SNN division. The method of the invention greatly reduces the tracking error of the extended target at the intersection, and realizes accurate estimation of the number of targets and the position of the target. At the same time, the tracking process of the extended target and the point target is separated, which greatly reduces the amount of calculation.

Figure 202110547305

Description

一种基于时空关联的多扩展目标跟踪方法A multi-extended target tracking method based on spatiotemporal correlation

技术领域technical field

本发明属于信息融合领域，涉及一种基于时空关联的多扩展目标跟踪方法。The invention belongs to the field of information fusion, and relates to a multi-expansion target tracking method based on space-time correlation.

背景技术Background technique

随着现代传感器技术的发展，传感器的分辨率越来越高，单个目标会占据传感器的多个分辨率单元，同时得到多个关于目标的量测信息，该目标类型变为扩展目标。ET-GM-PHD (Extended Target Gaussian Mixture PHD)是在随机有限集的理论下对多扩展目标进行跟踪的滤波算法，该方法使用高斯混合形式表示多目标的强度函数，并以此来近似多目标的后验分布。基于随机有限集的多扩展目标的方法避免了数据关联，并降低了计算的复杂度，其中不可或缺的部分是对当前时刻量测集进行合理的划分，进而找到正确的量测集划分。目前广泛使用的划分方法是距离划分，该方法利用属于同一目标的量测值在空间上相隔较近的特性，对于满足距离门限的量测值都划分到同一个划分单元中，实现对量测集合的划分。但当目标距离较近的时候，不同目标的量测值会落入同一个量测集合中，造成滤波错误。With the development of modern sensor technology, the resolution of the sensor is getting higher and higher, a single target will occupy multiple resolution units of the sensor, and obtain multiple measurement information about the target at the same time, the target type becomes an extended target. ET-GM-PHD (Extended Target Gaussian Mixture PHD) is a filtering algorithm for tracking multiple extended targets under the theory of random finite sets. the posterior distribution of . The method based on random finite sets of multi-expansion targets avoids data association and reduces the computational complexity. The indispensable part is to reasonably divide the measurement set at the current moment, and then find the correct measurement set division. At present, the widely used division method is distance division. This method utilizes the characteristic that the measurement values belonging to the same target are relatively close in space. Division of collections. However, when the target distance is relatively close, the measurement values of different targets will fall into the same measurement set, resulting in filtering errors.

发明内容SUMMARY OF THE INVENTION

本发明目的在于克服现有方法的不足，提出一种基于时空关联的多扩展目标跟踪方法，解决多扩展目标距离较近和航迹交叉下目标状态和目标数估计问题，具有良好的性能，同时该方法也不受量测密度的影响。本发明主要是应用在杂波环境中单个传感器实现对多扩展目标跟踪的场景下。The purpose of the invention is to overcome the shortcomings of the existing methods, and propose a multi-expansion target tracking method based on space-time correlation, which solves the problem of estimating the target state and the number of targets when the distance between the multi-expansion targets is relatively short and the track crosses, and has good performance. The method is also unaffected by the measured density. The invention is mainly applied in the scenario where a single sensor realizes tracking of multiple extended targets in a clutter environment.

本发明的技术方案为：The technical scheme of the present invention is:

一种基于时空的多扩展目标跟踪方法，考虑了扩展目标相邻时刻量测值之间的关联性，具体包括：A spatiotemporal-based multi-extended target tracking method, which considers the correlation between the measurement values of the extended target at adjacent moments, specifically includes:

通过单传感器完成对扩展目标的探测，令k时刻传感器获得的量测集合为

Figure BDA0003074018230000011
zi为表示二维空间的单个量测值，nk为量测值数目；k时刻传感器检测区域中扩展目标状态集合为
Figure BDA0003074018230000012
其中Mk表示扩展目标的数目，
Figure BDA0003074018230000013
表示单个扩展目标的运动状态，xi，yi表示目标信息，
Figure BDA0003074018230000014
表示目标运动信息。The detection of the extended target is completed by a single sensor, and the measurement set obtained by the sensor at time k is
Figure BDA0003074018230000011
z i is a single measurement value representing a two-dimensional space, n k is the number of measurement values; the extended target state set in the sensor detection area at time k is:
Figure BDA0003074018230000012
where M k represents the number of extended targets,
Figure BDA0003074018230000013
represents the motion state of a single extended target, x i , y i represent target information,
Figure BDA0003074018230000014
Represents target motion information.

建立扩展目标的运动方程为：The equation of motion to establish the extended target is:

Xk＝FXk-1+vk X k =FX k-1 +v k

其中，

Figure BDA0003074018230000021
为状态转移矩阵，I为单位矩阵，Ts为采样间隔。vk表示协方差为
Figure BDA0003074018230000022
的过程噪声，σv为过程标准差。in,
Figure BDA0003074018230000021
is the state transition matrix, I is the identity matrix, and T s is the sampling interval. v k means that the covariance is
Figure BDA0003074018230000022
is the process noise, and σ v is the process standard deviation.

扩展目标的量测方程为：The measurement equation of the extended target is:

Zk＝HXk+wk Z k =HX k +w k

其中，

Figure BDA0003074018230000023
为观测方程，wk表示协方差为
Figure BDA0003074018230000024
的量测噪声，σε为量测噪声标准差。in,
Figure BDA0003074018230000023
is the observation equation, w k represents the covariance as
Figure BDA0003074018230000024
The measurement noise, σ ε is the standard deviation of the measurement noise.

基于时空关联的多扩展目标跟踪方法，如图1所示，主要包括以下步骤：The multi-extended target tracking method based on spatiotemporal correlation, as shown in Figure 1, mainly includes the following steps:

S1、当时刻k＝0时，初始化系统中的高斯分量为

Figure BDA0003074018230000025
其中w0为高斯分量的权重，m0为高斯分量均值，表示为运动状态，P0为对应的协方差矩阵，J0为初始高斯项数目；S1. When time k=0, the Gaussian component in the initialization system is
Figure BDA0003074018230000025
where w 0 is the weight of the Gaussian component, m 0 is the mean value of the Gaussian component, expressed as a motion state, P 0 is the corresponding covariance matrix, and J 0 is the number of initial Gaussian terms;

S2、当k≥1时，遍历高斯分量集合，按照状态转移矩阵作一步预测，并添加新生目标的高斯分量，表示为：S2. When k≥1, traverse the Gaussian component set, make one-step prediction according to the state transition matrix, and add the Gaussian component of the new target, which is expressed as:

Figure BDA0003074018230000026
Figure BDA0003074018230000026

式中，Jk-1为k-1时刻高斯分量数目，

Figure BDA0003074018230000027
和
Figure BDA0003074018230000028
分别为新生目标高斯分量的参数，JB表示新生目标高斯分量的数目；In the formula, J k-1 is the number of Gaussian components at time k-1,
Figure BDA0003074018230000027
and
Figure BDA0003074018230000028
are the parameters of the Gaussian component of the new target respectively, and J B represents the number of Gaussian components of the new target;

S3、选取高斯分量中权重大于0.5分量：

Figure BDA0003074018230000029
式中Jc为高斯分量的数目；并选择其位置分量
Figure BDA00030740182300000210
构建波门，距离门限设为τ；遍历整个量测集合Zk，对于落入波门中的量测值，形成量测集合
Figure BDA00030740182300000211
N表示量测集合的数目；S3. Select the Gaussian component with a weight greater than 0.5:
Figure BDA0003074018230000029
where J c is the number of Gaussian components; and select its position component
Figure BDA00030740182300000210
Construct a wave gate, the distance threshold is set as τ; traverse the entire measurement set Z k , and form a measurement set for the measurement values that fall into the wave gate
Figure BDA00030740182300000211
N represents the number of measurement sets;

S4、计算量测集合

Figure BDA00030740182300000212
的并集
Figure BDA00030740182300000213
采用K-means++算法进行聚类，得到L个聚类中心
Figure BDA00030740182300000214
采用点目标的GM-PHD算法，将聚类中心
Figure BDA00030740182300000215
更新高斯分量G，得到更新后的高斯分量：
Figure BDA00030740182300000216
式中
Figure BDA00030740182300000217
为高斯分量的数目；S4. Calculate the measurement set
Figure BDA00030740182300000212
union of
Figure BDA00030740182300000213
K-means++ algorithm is used for clustering, and L cluster centers are obtained
Figure BDA00030740182300000214
Using the GM-PHD algorithm of point target, the cluster center
Figure BDA00030740182300000215
Update the Gaussian component G to get the updated Gaussian component:
Figure BDA00030740182300000216
in the formula
Figure BDA00030740182300000217
is the number of Gaussian components;

S5、计算k时刻量测集合Zk与集合

Figure BDA00030740182300000218
的差集
Figure BDA00030740182300000219
利用DBSCAN聚类算法对集合
Figure BDA0003074018230000031
进行预处理，若此时有聚类单元，则转到S6；否则，转到S7；S5. Calculate the measurement set Z k and the set at time k
Figure BDA00030740182300000218
difference
Figure BDA00030740182300000219
Use the DBSCAN clustering algorithm to
Figure BDA0003074018230000031
Carry out preprocessing, if there are clustering units at this time, go to S6; otherwise, go to S7;

S6、对于S5产生的聚类单元，计算聚类单元的并集

Figure BDA0003074018230000032
利用有向图SNN聚类方法进行进一步处理，其聚类数目为K∈[Kl,Ku]，其中Kl为DBSCAN算法中的聚类数目，
Figure BDA0003074018230000033
n为集合
Figure BDA0003074018230000034
中量测值的数目，β为扩展目标的量测率；S6. For the clustering units generated by S5, calculate the union of the clustering units
Figure BDA0003074018230000032
The directed graph SNN clustering method is used for further processing, and the number of clusters is K∈[K l ,K u ], where K l is the number of clusters in the DBSCAN algorithm,
Figure BDA0003074018230000033
n is the set
Figure BDA0003074018230000034
The number of medium measurement values, β is the measurement rate of the expansion target;

S61、构建集合

Figure BDA0003074018230000035
的有向kNN邻接矩阵的相似度矩阵Wn×n，算法中选取k＝8；W中的元素为：S61. Build a collection
Figure BDA0003074018230000035
The similarity matrix W n×n of the directed kNN adjacency matrix, k=8 is selected in the algorithm; the elements in W are:

Figure BDA0003074018230000036
Figure BDA0003074018230000036

其中，zs为zi的第

Figure BDA0003074018230000037
个最邻近点，为zj的第
Figure BDA0003074018230000038
个最邻近点，Ni表示zi在kNN图中的k个最邻近点，Nj表示zj在kNN图中的k个最邻近点，zi、zj和zs分别为kNN图中的顶点； Ni∩Nj表示zi和zj之间的共享最临近点，定义为：Among them, z s is the th
Figure BDA0003074018230000037
the nearest neighbor point, which is the first point of z j
Figure BDA0003074018230000038
N i represents the k nearest neighbors of z i in the kNN graph, N j represents the k nearest neighbors of z j in the kNN graph, zi , z j and z s are the kNN graphs, respectively The vertices of ; N i ∩N j represents the shared closest point between z i and z j , defined as:

Figure BDA0003074018230000039
Figure BDA0003074018230000039

式中，zij为一个虚顶点，表示顶点zi和zj是相互的最邻近点。In the formula, zi ij is an imaginary vertex, indicating that vertices zi and z j are the closest points to each other.

S62、对于相似度矩阵W和聚类数目范围[Kl,Ku]，采用谱聚类的方法进行聚类，形成聚类单元；谱聚类的步骤为：S62, for the similarity matrix W and the range of the number of clusters [K l , K u ], use the spectral clustering method for clustering to form a clustering unit; the steps of spectral clustering are:

(1)依据相似度矩阵W计算未归一化的拉普拉斯矩阵L，(1) Calculate the unnormalized Laplacian matrix L according to the similarity matrix W,

Figure BDA00030740182300000310
Figure BDA00030740182300000310

式中，D为对角矩阵，为kNN图的度矩阵。In the formula, D is the diagonal matrix, which is the degree matrix of the kNN graph.

(2)计算归一化的拉普拉斯矩阵Ls＝D-1/2LD-1/2；(2) Calculate the normalized Laplacian matrix L s =D -1/2 LD -1/2 ;

(3)计算矩阵Ls的特征值λi和特征向量ui；(3) Calculate the eigenvalue λ i and the eigenvector ui of the matrix L s ;

(4)选取K个最小特征值对应的特征向量构成矩阵U；(4) Select the eigenvectors corresponding to the K minimum eigenvalues to form a matrix U;

(5)归一化矩阵U，得到矩阵Y，并将矩阵Y的每一行当作K维空间新的数据点，利用K-means++算法进行聚类。(5) Normalize the matrix U to obtain the matrix Y, and treat each row of the matrix Y as a new data point in the K-dimensional space, and use the K-means++ algorithm for clustering.

S7、在S6划分结果基础上，利用ET-GM-PHD算法更新高斯分量G,得到更新后的高斯分量为：

Figure BDA0003074018230000041
Figure BDA0003074018230000042
为高斯分量的数目。S7. On the basis of the division result of S6, the Gaussian component G is updated by using the ET-GM-PHD algorithm, and the updated Gaussian component is obtained as:
Figure BDA0003074018230000041
Figure BDA0003074018230000042
is the number of Gaussian components.

S8、对高斯分量

Figure BDA0003074018230000043
进行剪枝与合并，删除权重小于T的高斯分量，合并高斯分量之间距离小于μ的高斯分量。S8, for Gaussian components
Figure BDA0003074018230000043
Perform pruning and merging, delete Gaussian components whose weight is less than T, and merge Gaussian components whose distance between Gaussian components is less than μ.

S9、选择权重大于0.5的高斯分量作为目标的滤波结果，实现目标跟踪。S9 , selecting a Gaussian component with a weight greater than 0.5 as the filtering result of the target to achieve target tracking.

本发明的有益效果为：本发明方法降低滤波的计算量，并且能够有效处理扩展目标在交叉处的目标位置估计和目标数目估计。将扩展目标跟踪过程转换为扩展目标跟踪和点目标跟踪的形式，在提高运算效率的同时也使滤波算法有较好的鲁棒性，减少了杂波对估计结果的干扰。The beneficial effects of the present invention are: the method of the present invention reduces the calculation amount of filtering, and can effectively process the target position estimation and target number estimation of the extended target at the intersection. The extended target tracking process is converted into the form of extended target tracking and point target tracking, which not only improves the computing efficiency, but also makes the filtering algorithm have better robustness and reduces the interference of clutter on the estimation results.

附图说明Description of drawings

图1本发明应用于多扩展目标跟踪的流程图；Fig. 1 is applied to the flow chart of multi-expansion target tracking of the present invention;

图2实施例1下的航迹估计、真实航迹、量测值；Fig. 2 Track estimation, real track, and measured value under Embodiment 1;

图3实施例1下的OSPA误差对比；OSPA error contrast under Fig. 3 embodiment 1;

图4实施例1下目标数目估计对比；The number of targets estimated and contrasted under the embodiment 1 of Fig. 4;

图5实施例1下运行时间对比；Fig. 5 compares the running time under embodiment 1;

图6实施例2下的航迹估计、真实航迹、量测值；Track estimation, real track, and measured values under Embodiment 2 of FIG. 6;

图7实施例2下OSPA误差对比；OSPA error contrast under Fig. 7 embodiment 2;

图8实施例2下的目标数目估计；Estimated number of targets under Embodiment 2 of Fig. 8;

图9实施例2下运行时间对比；Fig. 9 compares the running time under embodiment 2;

具体实施方式Detailed ways

仿真参数设置如下：目标存活概率为Ps＝0.99，检测概率为PD＝0.99，扩展目标量测个数服从期望值为10的泊松分布；杂波量测个数服从期望值为20的泊松分布；最大高斯项分量个数为Jmax＝100，修剪门限T＝10-6，合并门限μ＝4；距离门限τ＝50。过程噪声的协方差为

Figure BDA0003074018230000044
sv＝2；观测噪声方差为
Figure BDA0003074018230000045
sε＝20，监视的区域大小为：[-1000，1000]×[-1000,1000]m。The simulation parameters are set as follows: the target survival probability is P s = 0.99, the detection probability is P D = 0.99, the number of extended target measurements obeys a Poisson distribution with an expected value of 10; the number of clutter measurements obeys a Poisson distribution with an expected value of 20 distribution; the maximum number of Gaussian term components is J max =100, the trimming threshold T=10 -6 , the merging threshold μ=4; the distance threshold τ=50. The covariance of the process noise is
Figure BDA0003074018230000044
s v = 2; the observed noise variance is
Figure BDA0003074018230000045
s ε = 20, the size of the monitored area is: [-1000, 1000]×[-1000, 1000]m.

实施例1、Embodiment 1,

本实施例的目的是验证所提方法在两个扩展目标距离较近且平行运动场景下目标的滤波性能。目标1初始状态为[-600m,-500m,0m/s,0m/s]T，存活时间为1～100s；目标2的初始状态为[-600m,-600m,0m/s,0m/s]T，存活时间为1～100s；此场景下新生目标的强度函数为：The purpose of this embodiment is to verify the filtering performance of the proposed method in a scenario where the distance between two extended targets is close and the targets are moving in parallel. The initial state of target 1 is [-600m,-500m,0m/s,0m/s] T , and the survival time is 1～100s; the initial state of target 2 is [-600m,-600m,0m/s,0m/s] T , the survival time is 1 to 100s; the intensity function of the new target in this scenario is:

Figure BDA0003074018230000051
Figure BDA0003074018230000051

式中

Figure BDA0003074018230000052
Pγ,t＝diag([100,100,25,25])。in the formula
Figure BDA0003074018230000052
P γ,t =diag([100, 100, 25, 25]).

图2是实施例1下本发明的目标状态估计和目标真实状态的对比。可以看出本发明在扩展目标相隔较近的情况下也能得到一个较好的跟踪结果。FIG. 2 is a comparison between the target state estimation of the present invention and the target real state under Embodiment 1. FIG. It can be seen that the present invention can also obtain a better tracking result under the condition that the extended targets are close to each other.

图3为实施例1下本发明方法和距离划分、有向图SNN划分方法的OSPA误差对比。可以看出，本发明方法的OSPA误差明显最小。3 is a comparison of OSPA errors between the method of the present invention and the distance division and directed graph SNN division methods under Embodiment 1. It can be seen that the OSPA error of the method of the present invention is obviously the smallest.

图4为实施例1下本发明方法和距离划分、有向图SNN划分方法的目标数估计对比。可以看出，本发明方法的目标数估计最为准确。4 is a comparison of the number of targets estimated by the method of the present invention and the distance division and directed graph SNN division methods under Embodiment 1. It can be seen that the estimation of the target number of the method of the present invention is the most accurate.

图5为实施例1下本发明方法和距离划分、有向图SNN划分方法的算法运行时间对比，可以看出，本发明方法的算法运行时间最低。5 is a comparison of the algorithm running time of the method of the present invention, the distance division and the directed graph SNN dividing method under Embodiment 1, and it can be seen that the algorithm of the method of the present invention has the lowest running time.

实施例2、Embodiment 2,

仿真参数如例1相同。本实施例的目的是验证算法在目标相交情况下的滤波性能。场景中存在2个目标，目标1的初始状态为[250m,250m,0m/s,0m/s]T，存活时间为1～100s；目标2的初始状态为[-250m,-250m,0m/s,0m/s]T，存活时间为1～100s；两个目标在56s 的时候相交。此场景下新生目标的强度函数为：The simulation parameters are the same as in Example 1. The purpose of this embodiment is to verify the filtering performance of the algorithm in the case of target intersection. There are 2 targets in the scene, the initial state of target 1 is [250m, 250m, 0m/s, 0m/s] T , and the survival time is 1 to 100s; the initial state of target 2 is [-250m, -250m, 0m/ s,0m/s] T , the survival time is 1 to 100s; the two targets intersect at 56s. The intensity function of the new target in this scenario is:

Figure BDA0003074018230000053
Figure BDA0003074018230000053

式中，

Figure BDA0003074018230000054
Pγ,t＝diag([100,100,25,25])。In the formula,
Figure BDA0003074018230000054
P γ,t =diag([100, 100, 25, 25]).

图6为实施例2下本发明的目标状态估计和目标真实状态的对比。可以看出，即使在目标航迹交叉时刻，也能得到一个较好的估计结果。FIG. 6 is a comparison between the target state estimation of the present invention and the target real state under the second embodiment. It can be seen that a better estimation result can be obtained even at the time of the target track crossing.

图7为实施例2下本发明方法和距离划分、有向图SNN划分方法的OSPA误差对比。可以看出，即使是在扩展目标航迹交叉时刻，本发明方法的OSPA误差也最小。FIG. 7 is a comparison of OSPA errors between the method of the present invention and the distance division and directed graph SNN division methods under Embodiment 2. It can be seen that even at the time of crossing the extended target track, the OSPA error of the method of the present invention is the smallest.

图8为实施例2下本发明方法和距离划分、有向图SNN划分方法的目标数估计对比。可以看出，在航迹交叉时刻，本发明方法的目标数估计最为准确。8 is a comparison of the number of targets estimated by the method of the present invention and the distance division and directed graph SNN division methods under Embodiment 2. It can be seen that at the time of track crossing, the method of the present invention estimates the number of targets most accurately.

图9为实施例2下本发明方法和距离划分、有向图SNN划分方法的算法运行时间对比，可以看出，本发明方法的算法运行时间最低。9 is a comparison of the algorithm running time of the method of the present invention and the distance division and the directed graph SNN dividing method under Embodiment 2. It can be seen that the algorithm of the method of the present invention has the lowest running time.

Claims (1)

1.一种基于时空的多扩展目标跟踪方法，其特征在于，包括：1. a multi-expanded target tracking method based on space and time, is characterized in that, comprises: 通过单传感器完成对扩展目标的探测，令k时刻传感器获得的量测集合为
Figure FDA0003074018220000011
zi为表示二维空间的单个量测值，nk为量测值数目；k时刻传感器检测区域中扩展目标状态集合为
Figure FDA0003074018220000012
其中Mk表示扩展目标的数目，
Figure FDA0003074018220000013
表示单个扩展目标的运动状态，xi，yi表示目标信息，
Figure FDA0003074018220000014
表示目标运动信息；The detection of the extended target is completed by a single sensor, and the measurement set obtained by the sensor at time k is
Figure FDA0003074018220000011
z i is a single measurement value representing a two-dimensional space, n k is the number of measurement values; the extended target state set in the sensor detection area at time k is:
Figure FDA0003074018220000012
where M k represents the number of extended targets,
Figure FDA0003074018220000013
represents the motion state of a single extended target, x i , y i represent target information,
Figure FDA0003074018220000014
Represents target motion information; 建立扩展目标的运动方程为：The equation of motion to establish the extended target is: Xk＝FXk-1+vk X k =FX k-1 +v k 其中，
Figure FDA0003074018220000015
为状态转移矩阵，I为单位矩阵，Ts为采样间隔；vk表示协方差为
Figure FDA0003074018220000016
的过程噪声，σv为过程标准差；in,
Figure FDA0003074018220000015
is the state transition matrix, I is the identity matrix, T s is the sampling interval; v k indicates that the covariance is
Figure FDA0003074018220000016
is the process noise, σ v is the process standard deviation; 扩展目标的量测方程为：The measurement equation of the extended target is: Zk＝HXk+wk Z k =HX k +w k 其中，
Figure FDA0003074018220000017
为观测方程，wk表示协方差为
Figure FDA0003074018220000018
的量测噪声，σε为量测噪声标准差；in,
Figure FDA0003074018220000017
is the observation equation, w k represents the covariance as
Figure FDA0003074018220000018
The measurement noise, σ ε is the standard deviation of the measurement noise; 对扩展目标进行跟踪，具体方法为：Track the expansion target, and the specific methods are as follows: S1、当时刻k＝0时，初始化系统中的高斯分量为
Figure FDA0003074018220000019
其中w0为高斯分量的权重，m0为高斯分量均值，表示为运动状态，P0为对应的协方差矩阵，J0为初始高斯项数目；S1. When time k=0, the Gaussian component in the initialization system is
Figure FDA0003074018220000019
where w 0 is the weight of the Gaussian component, m 0 is the mean value of the Gaussian component, expressed as a motion state, P 0 is the corresponding covariance matrix, and J 0 is the number of initial Gaussian terms; S2、当k≥1时，遍历高斯分量集合，按照状态转移矩阵作一步预测，并添加新生目标的高斯分量，表示为：S2. When k≥1, traverse the Gaussian component set, make one-step prediction according to the state transition matrix, and add the Gaussian component of the new target, which is expressed as:
Figure FDA00030740182200000110
Figure FDA00030740182200000110
 式中，Jk-1为k-1时刻高斯分量数目，
Figure FDA00030740182200000111
和
Figure FDA00030740182200000112
分别为新生目标高斯分量的参数，JB表示新生目标高斯分量的数目；In the formula, J k-1 is the number of Gaussian components at time k-1,
Figure FDA00030740182200000111
and
Figure FDA00030740182200000112
are the parameters of the Gaussian component of the new target respectively, and J B represents the number of Gaussian components of the new target; S3、选取高斯分量中权重大于0.5分量：
Figure FDA00030740182200000113
式中Jc为高斯分量的数目；并选择其位置分量
Figure FDA0003074018220000021
构建波门，距离门限设为τ；遍历整个量测集合Zk，对于落入波门中的量测值，形成量测集合
Figure FDA0003074018220000022
N表示量测集合的数目；S3. Select the Gaussian component with a weight greater than 0.5:
Figure FDA00030740182200000113
where J c is the number of Gaussian components; and select its position component
Figure FDA0003074018220000021
Construct a wave gate, the distance threshold is set as τ; traverse the entire measurement set Z k , and form a measurement set for the measurement values that fall into the wave gate
Figure FDA0003074018220000022
N represents the number of measurement sets; S4、计算量测集合
Figure FDA0003074018220000023
的并集
Figure FDA0003074018220000024
采用K-means++算法进行聚类，得到L个聚类中心
Figure FDA0003074018220000025
采用点目标的GM-PHD算法，将聚类中心
Figure FDA0003074018220000026
更新高斯分量G，得到更新后的高斯分量：
Figure FDA0003074018220000027
式中
Figure FDA0003074018220000028
为高斯分量的数目；S4. Calculate the measurement set
Figure FDA0003074018220000023
union of
Figure FDA0003074018220000024
K-means++ algorithm is used for clustering, and L cluster centers are obtained
Figure FDA0003074018220000025
Using the GM-PHD algorithm of point target, the cluster center
Figure FDA0003074018220000026
Update the Gaussian component G to get the updated Gaussian component:
Figure FDA0003074018220000027
in the formula
Figure FDA0003074018220000028
is the number of Gaussian components; S5、计算k时刻量测集合Zk与集合
Figure FDA0003074018220000029
的差集
Figure FDA00030740182200000210
利用DBSCAN聚类算法对集合
Figure FDA00030740182200000211
进行预处理，若此时有聚类单元，则转到S6；否则，转到S7；S5. Calculate the measurement set Z k and the set at time k
Figure FDA0003074018220000029
difference
Figure FDA00030740182200000210
Use the DBSCAN clustering algorithm to
Figure FDA00030740182200000211
Carry out preprocessing, if there are clustering units at this time, go to S6; otherwise, go to S7; S6、对于S5产生的聚类单元，计算聚类单元的并集
Figure FDA00030740182200000212
利用有向图SNN聚类方法进行进一步处理，其聚类数目为K∈[Kl,Ku]，其中Kl为DBSCAN算法中的聚类数目，
Figure FDA00030740182200000213
n为集合
Figure FDA00030740182200000214
中量测值的数目，β为扩展目标的量测率；S6. For the clustering units generated by S5, calculate the union of the clustering units
Figure FDA00030740182200000212
The directed graph SNN clustering method is used for further processing, and the number of clusters is K∈[K l ,K u ], where K l is the number of clusters in the DBSCAN algorithm,
Figure FDA00030740182200000213
n is the set
Figure FDA00030740182200000214
The number of medium measurement values, β is the measurement rate of the expansion target; S61、构建集合
Figure FDA00030740182200000215
的有向kNN邻接矩阵的相似度矩阵Wn×n，W中的元素为：S61. Build a collection
Figure FDA00030740182200000215
The similarity matrix W n×n of the directed kNN adjacency matrix, the elements in W are:
Figure FDA00030740182200000216
Figure FDA00030740182200000216
 其中，zs为zi的第
Figure FDA00030740182200000217
个最邻近点，为zj的第
Figure FDA00030740182200000218
个最邻近点，Ni表示zi在kNN图中的k个最邻近点，Nj表示zj在kNN图中的k个最邻近点，zi、zj和zs分别为kNN图中的顶点；Ni∩Nj表示zi和zj之间的共享最临近点，定义为：Among them, z s is the th
Figure FDA00030740182200000217
the nearest neighbor point, which is the first point of z j
Figure FDA00030740182200000218
N i represents the k nearest neighbors of z i in the kNN graph, N j represents the k nearest neighbors of z j in the kNN graph, zi , z j and z s are the kNN graphs, respectively The vertex of ; N i ∩N j represents the shared nearest point between zi and z j , defined as:
Figure FDA00030740182200000219
Figure FDA00030740182200000219
 式中，zij为一个虚顶点，表示顶点zi和zj是相互的最邻近点；In the formula, zi ij is an imaginary vertex, indicating that vertices zi and z j are the closest points to each other; S62、对于相似度矩阵W和聚类数目范围[Kl,Ku]，采用谱聚类的方法进行聚类，形成聚类单元；谱聚类的步骤为：S62, for the similarity matrix W and the range of the number of clusters [K l , K u ], use the spectral clustering method for clustering to form a clustering unit; the steps of spectral clustering are: (1)依据相似度矩阵W计算未归一化的拉普拉斯矩阵L，(1) Calculate the unnormalized Laplacian matrix L according to the similarity matrix W,
Figure FDA0003074018220000031
Figure FDA0003074018220000031
 式中，D为对角矩阵，表示kNN图的度矩阵；In the formula, D is the diagonal matrix, which represents the degree matrix of the kNN graph; (2)计算归一化的拉普拉斯矩阵Ls＝D-1/2LD-1/2；(2) Calculate the normalized Laplacian matrix L s =D -1/2 LD -1/2 ; (3)计算矩阵Ls的特征值λi和特征向量ui；(3) Calculate the eigenvalue λ i and the eigenvector ui of the matrix L s ; (4)选取K个最小特征值对应的特征向量构成矩阵U；(4) Select the eigenvectors corresponding to the K minimum eigenvalues to form a matrix U; (5)归一化矩阵U，得到矩阵Y，并将矩阵Y的每一行当作K维空间新的数据点，利用K-means++算法进行聚类(5) Normalize the matrix U to obtain the matrix Y, and treat each row of the matrix Y as a new data point in the K-dimensional space, and use the K-means++ algorithm for clustering S7、在S6划分结果基础上，利用ET-GM-PHD算法更新高斯分量G，得到更新后的高斯分量为：
Figure FDA0003074018220000032
Figure FDA0003074018220000033
为高斯分量的数目；S7. On the basis of the division result of S6, use the ET-GM-PHD algorithm to update the Gaussian component G, and obtain the updated Gaussian component as follows:
Figure FDA0003074018220000032
Figure FDA0003074018220000033
is the number of Gaussian components; S8、对高斯分量
Figure FDA0003074018220000034
进行剪枝与合并，删除权重小于T的高斯分量，合并高斯分量之间距离小于μ的高斯分量；S8, for Gaussian components
Figure FDA0003074018220000034
Perform pruning and merging, delete Gaussian components whose weight is less than T, and merge Gaussian components whose distance between Gaussian components is less than μ; S9、选择权重大于0.5的高斯分量作为目标的滤波结果。S9. Select a Gaussian component with a weight greater than 0.5 as the filtering result of the target.
CN202110547305.4A 2021-05-19 2021-05-19 A multi-extended target tracking method based on spatiotemporal correlation Expired - Fee Related CN113344039B (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN202110547305.4A CN113344039B (en) 2021-05-19 2021-05-19 A multi-extended target tracking method based on spatiotemporal correlation

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN202110547305.4A CN113344039B (en) 2021-05-19 2021-05-19 A multi-extended target tracking method based on spatiotemporal correlation

Publications (2)

Publication Number Publication Date
CN113344039A CN113344039A (en) 2021-09-03
CN113344039B true CN113344039B (en) 2022-04-26

Family

ID=77469540

Family Applications (1)

Application Number Title Priority Date Filing Date
CN202110547305.4A Expired - Fee Related CN113344039B (en) 2021-05-19 2021-05-19 A multi-extended target tracking method based on spatiotemporal correlation

Country Status (1)

Country Link
CN (1) CN113344039B (en)

Families Citing this family (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN116256746A (en) * 2023-05-12 2023-06-13 江苏亿连通信技术有限公司 Radar-based system and method for monitoring intrusion of foreign matters into perimeter airspace of preventive area
CN117214857B (en) * 2023-11-09 2024-02-02 中国人民解放军海军航空大学 Tracking method of Gaussian multi-hypothesis multi-expansion target in three-dimensional scene

Citations (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN110298865A (en) * 2019-05-22 2019-10-01 西华大学 The space-based Celestial Background small point target tracking of cluster device is separated based on threshold value
CN110297221A (en) * 2019-06-19 2019-10-01 西安电子科技大学 A kind of data correlation method based on gauss hybrid models

Family Cites Families (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US11408978B2 (en) * 2015-07-17 2022-08-09 Origin Wireless, Inc. Method, apparatus, and system for vital signs monitoring using high frequency wireless signals
CN109671096B (en) * 2017-10-13 2023-07-28 南京航空航天大学 A multi-extended target tracking method based on space-time neighbor target detection and grid clustering measurement division
CN109991570B (en) * 2019-04-05 2023-02-03 电子科技大学 Moving target direct positioning method based on quasi-Newton method
CN110992396A (en) * 2019-10-18 2020-04-10 河南科技大学 K-means + + clustering algorithm-based multi-extension target tracking method

Patent Citations (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN110298865A (en) * 2019-05-22 2019-10-01 西华大学 The space-based Celestial Background small point target tracking of cluster device is separated based on threshold value
CN110297221A (en) * 2019-06-19 2019-10-01 西安电子科技大学 A kind of data correlation method based on gauss hybrid models

Also Published As

Publication number Publication date
CN113344039A (en) 2021-09-03

Similar Documents

Publication Publication Date Title
CN109949375B (en) Mobile robot target tracking method based on depth map region of interest
CN111739053B (en) An online multi-pedestrian detection and tracking method in complex scenes
CN113344039B (en) A multi-extended target tracking method based on spatiotemporal correlation
CN110532921B (en) SSD-based generalized label detection multi-Bernoulli video multi-target tracking method
CN112085765B (en) Video object tracking method combining particle filtering and metric learning
CN110111362A (en) A kind of local feature block Similarity matching method for tracking target
CN103678949A (en) Tracking measurement set partitioning method for multiple extended targets based on density analysis and spectrum clustering
CN113160293A (en) Complex scene ground station point cloud automatic registration method based on feature probability
CN108667684A (en) A data flow anomaly detection method based on local vector dot product density
Qin et al. Application of an efficient graph-based partitioning algorithm for extended target tracking using GM-PHD filter
Cao et al. Correlation-based tracking of multiple targets with hierarchical layered structure
Hui RETRACTED ARTICLE: Motion video tracking technology in sports training based on Mean-Shift algorithm
CN114091578A (en) Ship track clustering method based on curve length distance
Fan et al. Adaptive crowd segmentation based on coherent motion detection
WO2023130842A1 (en) Camera pose determining method and apparatus
CN115508824A (en) Multi-target big data association fusion tracking method and system
CN112836582B (en) Online detection method of structural change points of high-dimensional flow systems based on dynamic sparse subspace
CN112509014B (en) Robust Interpolated Optical Flow Computation Method for Pyramid Occlusion Detection Block Matching
CN109671096A (en) A kind of space-time neighbour target detection and Grid Clustering measure more extension method for tracking target under dividing
CN111563904B (en) A wing fork ear point cloud segmentation method based on 3D feature descriptor
CN117557599B (en) 3D moving object tracking method and system and storage medium
CN110111353B (en) Image saliency detection method based on Markov background and foreground absorption chain
Jing et al. An improved target tracking method based on extraction of corner points
CN102800108B (en) Based on the visual target tracking method of local restriction least-squares estimation
CN117214857A (en) Tracking method of Gaussian multi-hypothesis multi-expansion target in three-dimensional scene

Legal Events

Date Code Title Description
PB01 Publication
PB01 Publication
SE01 Entry into force of request for substantive examination
SE01 Entry into force of request for substantive examination
GR01 Patent grant
GR01 Patent grant
CF01 Termination of patent right due to non-payment of annual fee
CF01 Termination of patent right due to non-payment of annual fee

Granted publication date: 20220426