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CN110986947A - Multi-target self-propelled ship model trajectory tracking measurement method - Google Patents

Multi-target self-propelled ship model trajectory tracking measurement method Download PDF

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CN110986947A
CN110986947A CN201911206118.9A CN201911206118A CN110986947A CN 110986947 A CN110986947 A CN 110986947A CN 201911206118 A CN201911206118 A CN 201911206118A CN 110986947 A CN110986947 A CN 110986947A
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CN110986947B (en
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吴俊�
舒岳阶
张绪进
周世良
李晓飚
周远航
马御风
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Chongqing Jiaotong University
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    • G—PHYSICS
    • G01—MEASURING; TESTING
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Abstract

本发明公开了一种多目标自航船模轨迹跟踪测量方法，包括如下步骤：S1.获取自航船模的初始方位角序列；S2.获取自航船模运动过程中的方位角序列；S3.计算方位角序列与初始方位角序列的残差矩阵；S4.根据残差矩阵，对方位角序列的方位角进行重匹配，得到新的方位角序列；S5.根据新的方位角序列，计算自航船模靶标的坐标；S6.按照步骤S2‑S5类推，直到试验结束，得到自航船模靶标的坐标集；S7.根据自航船模靶标的坐标集，计算自航船模的运行轨迹。本发明的一种多目标自航船模轨迹跟踪测量方法，能够在保持高精度、高频响的优势下，对多条自航船模轨迹同时进行跟踪测量。

Figure 201911206118

The invention discloses a method for tracking and measuring the trajectory of a multi-target self-propelled ship model. Residual matrix between the angle sequence and the initial azimuth sequence; S4. According to the residual matrix, re-match the azimuth of the azimuth sequence to obtain a new azimuth sequence; S5. Calculate the self-propelled ship model according to the new azimuth sequence The coordinates of the target; S6. According to the analogy of steps S2-S5, until the end of the test, the coordinate set of the self-propelled ship model target is obtained; S7. According to the coordinate set of the self-propelled ship model target, calculate the running trajectory of the self-propelled ship model. The multi-target self-propelled ship model trajectory tracking method of the invention can simultaneously track and measure multiple self-propelled ship model trajectories while maintaining the advantages of high precision and high frequency response.

Figure 201911206118

Description

多目标自航船模轨迹跟踪测量方法Multi-target self-propelled ship model trajectory tracking measurement method

技术领域technical field

本发明涉及自航船模跟踪测量领域，具体涉及一种多目标自航船模轨迹跟踪测量方法。The invention relates to the field of self-propelled ship model tracking and measurement, in particular to a multi-target self-propelled ship model trajectory tracking and measurement method.

背景技术Background technique

航行轨迹是自航船模通航试验关键参数，多船通航条件是近年来水工物理模型自航船模试验研究热点和难点，目前自航船模轨迹测量方法主要有两种：Navigation trajectory is the key parameter of the navigation test of the self-propelled ship model. The multi-ship navigation condition is the hotspot and difficulty in the research of the self-propelled ship model test of the hydraulic physical model in recent years. At present, there are two main methods for measuring the trajectory of the self-propelled ship model:

①激光测角交叉定位法，在自航船模首尾安装两个反光靶标，利用两台激光测角扫描系统扫描两靶标的方位角，基于交叉定位法，实时计算自航船模航行轨迹。该方法测量精度高、实时性好，是目前广为认可的方法。但由于交叉定位法会产生虚假交汇点，现有算法无法剔除这些虚假交汇点，所以目前该方法仅能实现单自航船模轨迹测量。①Laser angle measurement cross positioning method, install two reflective targets at the fore and aft of the self-propelled ship model, use two laser angle measurement scanning systems to scan the azimuth angles of the two targets, and calculate the navigation trajectory of the self-propelled ship model in real time based on the cross positioning method. This method has high measurement accuracy and good real-time performance, and is a widely recognized method at present. However, since the cross-location method will generate false junctions, the existing algorithms cannot eliminate these false junctions, so the current method can only measure the trajectory of a single self-propelled ship model.

②图像识别跟踪测量法，在物理模型上方安装摄像机，基于机器视觉方法，跟踪测量自航船模航行轨迹。相比于激光测角交叉定位法，该方法对自航船模数量没有限制，可实现对多船运动轨迹同时跟踪测量，但该方法计算效率极度依赖硬件资源，实时性差，同时由于边缘畸变难以矫正、环境光照条件复杂以及测量精度较激光测角交叉定位法要低，所以目前仍处于试验改进阶段。②Image recognition tracking measurement method, a camera is installed above the physical model, and based on the machine vision method, the navigation trajectory of the self-propelled ship model is tracked and measured. Compared with the laser angle measurement cross positioning method, this method has no limit on the number of self-propelled ship models, and can track and measure the motion trajectories of multiple ships at the same time. However, the calculation efficiency of this method is extremely dependent on hardware resources, and the real-time performance is poor. At the same time, it is difficult to correct due to edge distortion. , The ambient lighting conditions are complex and the measurement accuracy is lower than that of the laser angle measurement cross-location method, so it is still in the stage of experimental improvement.

因此，为解决以上问题，需要一种多目标自航船模轨迹跟踪测量方法，能够在保持高精度、高频响的优势下，对多条自航船模轨迹同时进行跟踪测量。Therefore, in order to solve the above problems, a multi-target self-propelled ship model trajectory tracking and measurement method is needed, which can simultaneously track and measure multiple self-propelled ship model trajectories while maintaining the advantages of high precision and high frequency response.

发明内容SUMMARY OF THE INVENTION

有鉴于此，本发明的目的是克服现有技术中的缺陷，提供多目标自航船模轨迹跟踪测量方法，能够在保持高精度、高频响的优势下，对多条自航船模轨迹同时进行跟踪测量。In view of this, the purpose of the present invention is to overcome the defects in the prior art, and to provide a multi-target self-propelled ship model trajectory tracking measurement method, which can simultaneously carry out multiple self-propelled ship model trajectories while maintaining the advantages of high precision and high frequency response. Track measurements.

本发明的多目标自航船模轨迹跟踪测量方法，包括如下步骤：The multi-target self-propelled ship model trajectory tracking measurement method of the present invention comprises the following steps:

S1.试验开始前，将n条自航船模依次排开，使得n条自航船模的船头朝向一致，并为n条自航船模分别设置船头靶标与船尾靶标，使用两套扫描仪同时对n条自航船模的船头靶标以及船尾靶标进行扫描，得到n条自航船模靶标的初始左方位角序列G0：

Figure BDA0002296964310000021
与初始右方位角序列H0：
Figure BDA0002296964310000022
其中，n＝1,2,3,…,N；i＝1,2,…,n；i为自航船模编号；
Figure BDA0002296964310000023
以及
Figure BDA0002296964310000024
分别为其中一套扫描仪对第i条自航船模进行扫描得到的船头方位角与船尾方位角；
Figure BDA0002296964310000025
以及
Figure BDA0002296964310000026
分别为其中另外一套扫描仪对第i条自航船模进行扫描得到的船尾方位角与船头方位角；方位角的下标为靶标的编号；S1. Before the test starts, arrange the n self-propelled ship models in turn so that the bows of the n self-propelled ship models are in the same direction, and set the bow target and the stern target for the n self-propelled ship models respectively, and use two sets of scanners at the same time. Scan the bow targets and the stern targets of n self-propelled ship models to obtain the initial left azimuth sequence G 0 of the n self-propelled ship model targets:
Figure BDA0002296964310000021
with the initial right azimuth sequence H 0 :
Figure BDA0002296964310000022
Among them, n=1,2,3,…,N; i=1,2,…,n; i is the number of the self-propelled ship model;
Figure BDA0002296964310000023
as well as
Figure BDA0002296964310000024
are the bow azimuth and stern azimuth obtained by scanning the i-th self-propelled ship model by one of the scanners respectively;
Figure BDA0002296964310000025
as well as
Figure BDA0002296964310000026
are the stern azimuth angle and the bow azimuth angle obtained by scanning the i-th self-propelled ship model by another set of scanners; the subscript of the azimuth angle is the target number;

S2.试验开始后，对n条自航船模的船头靶标与船尾靶标进行扫描，得到n条自航船模靶标的左方位角序列G1：(α1,α2,…,α2i-1,α2i,…,α2n-1,α2n)与右方位角序列H1：(β1,β2,…,β2i-1,β2i,…,β2n-1,β2n)；S2. After the test starts, scan the bow target and the stern target of the n self-propelled ship models to obtain the left azimuth sequence G 1 of the n self-propelled ship model targets: (α 1 ,α 2 ,…,α 2i-1 ,α 2i ,…,α 2n-1 ,α 2n ) and the right azimuth sequence H 1 : (β 1 ,β 2 ,…,β 2i-1 ,β 2i ,…,β 2n-1 ,β 2n );

S3.计算左方位角序列G1与初始左方位角序列G0的残差矩阵Δdα；计算右方位角序列H1与初始右方位角序列H0的残差矩阵Δdβ；S3. Calculate the residual matrix Δd α of the left azimuth sequence G 1 and the initial left azimuth sequence G 0 ; calculate the residual matrix Δd β of the right azimuth sequence H 1 and the initial right azimuth sequence H 0 ;

S4.根据残差矩阵Δdα对左方位角序列G1中方位角的顺序进行调整，使得左方位角匹配所属靶标，得到新的左方位角序列

Figure BDA0002296964310000027
根据残差矩阵Δdβ对右方位角序列H1中右方位角的顺序进行调整，使得右方位角匹配所属靶标，得到新的右方位角序列
Figure BDA0002296964310000028
S4. Adjust the order of the azimuth angles in the left azimuth angle sequence G 1 according to the residual matrix Δd α , so that the left azimuth angle matches the target to which it belongs, and a new left azimuth angle sequence is obtained
Figure BDA0002296964310000027
The order of the right azimuth angles in the right azimuth angle sequence H 1 is adjusted according to the residual matrix Δd β , so that the right azimuth angle matches the target to which it belongs, and a new right azimuth angle sequence is obtained.
Figure BDA0002296964310000028

S5.根据新的左方位角序列

Figure BDA0002296964310000029
与右方位角序列
Figure BDA00022969643100000210
计算n条自航船模的船头靶标坐标序列
Figure BDA00022969643100000211
与船尾靶标坐标序列
Figure BDA00022969643100000212
S5. According to the new left azimuth sequence
Figure BDA0002296964310000029
with the right azimuth sequence
Figure BDA00022969643100000210
Calculate the bow target coordinate sequence of n self-propelled ship models
Figure BDA00022969643100000211
with the stern target coordinate sequence
Figure BDA00022969643100000212

S6.将每次扫描到的新的左方位角序列与右方位角序列分别作为下次扫描的初始左方位角序列与初始右方位角序列，按照步骤S2-S5类推，直到试验结束，最后得到n条自航船模的船头靶标坐标序列集CH与船尾靶标坐标序列集CT；S6. Take the new left azimuth sequence and right azimuth sequence obtained by each scan as the initial left azimuth sequence and the initial right azimuth sequence of the next scan, respectively, according to steps S2-S5 and so on, until the end of the test, and finally get The bow target coordinate sequence set CH and the stern target coordinate sequence set CT of the n self-propelled ship models;

S7.根据n条自航船模的船头靶标坐标序列集CH与船尾靶标坐标序列集CT计算n条自航船模的运行轨迹。S7. Calculate the running trajectories of the n self-propelled ship models according to the bow target coordinate sequence set CH and the stern target coordinate sequence set CT of the n self-propelled ship models.

进一步，步骤S2中，当自航船模靶标出现遮挡时，扫描到的左方位角序列G：(α1,α2,…,αk,…,αp)或右方位角序列H：(β1,β2,…,βl,…,βq)中方位角个数会减少，则需要对左方位角序列或右方位角序列进行补全；其中，k以及p为左方位角下标，取值均为正整数，且k<p，p<2n；l以及q为右方位角下标，取值均为正整数，且l<q，q<2n。Further, in step S2, when the self-propelled ship model target is blocked, the scanned left azimuth sequence G: (α 1 ,α 2 ,...,α k ,...,α p ) or right azimuth sequence H: (β 1 ,β 2 ,…,β l ,…,β q ), the number of azimuths will decrease, so the left azimuth sequence or the right azimuth sequence needs to be completed; where k and p are the left azimuth subscripts , the values are all positive integers, and k<p, p<2n; l and q are the subscripts of the right azimuth, and the values are all positive integers, and l<q, q<2n.

进一步，根据如下步骤对左方位角序列G进行补全：Further, complete the left azimuth sequence G according to the following steps:

S31.计算左方位角序列G与初始左方位角序列G0的残差矩阵

Figure BDA0002296964310000031
S31. Calculate the residual matrix of the left azimuth sequence G and the initial left azimuth sequence G 0
Figure BDA0002296964310000031

Figure BDA0002296964310000032
Figure BDA0002296964310000032

S32.将残差矩阵

Figure BDA0002296964310000033
第k行的元素按照从小到大的顺序排列，取出第k行的前两个元素作为数据对
Figure BDA0002296964310000034
计算数据对差值
Figure BDA0002296964310000035
Figure BDA0002296964310000036
其中，u以及v分别为残差矩阵
Figure BDA0002296964310000037
第u列以及第v列；S32. Convert the residual matrix
Figure BDA0002296964310000033
The elements of the kth row are arranged in ascending order, and the first two elements of the kth row are taken out as the data pair
Figure BDA0002296964310000034
Calculate data pair difference
Figure BDA0002296964310000035
Figure BDA0002296964310000036
Among them, u and v are the residual matrix, respectively
Figure BDA0002296964310000037
Column u and column v;

S33.按照步骤S32类推，得到残差矩阵

Figure BDA0002296964310000038
每行的数据对差值，将所得数据对差值组成数据对差值序列
Figure BDA0002296964310000039
S33. According to the analogy of step S32, the residual matrix is obtained
Figure BDA0002296964310000038
The difference between the data pairs for each row, and the resulting data pair differences are formed into a data pair difference sequence
Figure BDA0002296964310000039

S34.将数据对差值序列中数据对差值按照从小到大的顺序排列，取出前2n-p个数据对差值，查找2n-p个数据对差值分别对应的左方位角填补到左方位角序列中；S34. Arrange the data pair differences in the data pair difference sequence in ascending order, take out the first 2n-p data pair differences, and find the left azimuth corresponding to the 2n-p data pair differences and fill them to the left in the azimuth sequence;

根据如下步骤对右方位角序列H进行补全：Complete the right azimuth sequence H according to the following steps:

S35.计算右方位角序列H与初始右方位角序列H0的残差矩阵

Figure BDA00022969643100000310
S35. Calculate the residual matrix of the right azimuth sequence H and the initial right azimuth sequence H 0
Figure BDA00022969643100000310

Figure BDA00022969643100000311
Figure BDA00022969643100000311

S36.将残差矩阵

Figure BDA00022969643100000312
第l行的元素按照从小到大的顺序排列，取出第l行的前两个元素作为数据对
Figure BDA00022969643100000313
计算数据对差值
Figure BDA00022969643100000314
其中，d以及w分别为残差矩阵
Figure BDA00022969643100000315
第d列以及第w列；S36. Convert the residual matrix
Figure BDA00022969643100000312
The elements of the lth row are arranged in ascending order, and the first two elements of the lth row are taken out as the data pair
Figure BDA00022969643100000313
Calculate data pair difference
Figure BDA00022969643100000314
Among them, d and w are the residual matrix respectively
Figure BDA00022969643100000315
Column d and column w;

S37.按照步骤S36类推，得到残差矩阵

Figure BDA00022969643100000316
每行的数据对差值，将所得数据对差值组成数据对差值序列
Figure BDA0002296964310000041
S37. According to the analogy of step S36, the residual matrix is obtained
Figure BDA00022969643100000316
The difference between the data pairs for each row, and the resulting data pair differences are formed into a data pair difference sequence
Figure BDA0002296964310000041

S38.将数据对差值序列中数据对差值按照从小到大的顺序排列，取出前2n-q个数据对差值，查找2n-q个数据对差值分别对应的右方位角填补到右方位角序列中。S38. Arrange the data pair differences in the data pair difference sequence in ascending order, take out the first 2n-q data pair differences, and find the right azimuths corresponding to the 2n-q data pair differences and fill them to the right in the azimuth sequence.

进一步，步骤S3中，根据如下公式确定残差矩阵Δdα：Further, in step S3, the residual matrix Δd α is determined according to the following formula:

Figure BDA0002296964310000042
Figure BDA0002296964310000042

其中，左方位角序列G1为(α1,α2,…,α2i-1,α2i,…,α2n-1,α2n)；初始左方位角序列G0为

Figure BDA0002296964310000043
Among them, the left azimuth sequence G 1 is (α 1 ,α 2 ,…,α 2i-1 ,α 2i ,…,α 2n-1 ,α 2n ); the initial left azimuth sequence G 0 is
Figure BDA0002296964310000043

根据如下公式确定残差矩阵Δdβ：The residual matrix Δd β is determined according to the following formula:

Figure BDA0002296964310000044
Figure BDA0002296964310000044

其中，右方位角序列H1为(β1,β2,…,β2i-1,β2i,…,β2n-1,β2n)；初始右方位角序列H0为

Figure BDA0002296964310000045
Among them, the right azimuth sequence H 1 is (β 1 ,β 2 ,…,β 2i-1 ,β 2i ,…,β 2n-1 ,β 2n ); the initial right azimuth sequence H 0 is
Figure BDA0002296964310000045

进一步，步骤S4中，根据如下步骤得到新的左方位角序列

Figure BDA0002296964310000046
Further, in step S4, a new left azimuth sequence is obtained according to the following steps
Figure BDA0002296964310000046

a.确定残差矩阵Δdα中与左方位角α1差值最小的初始左方位角序列中的方位角

Figure BDA0002296964310000047
将α1调整到左方位角序列中第s个靶标所在的位置，记为
Figure BDA0002296964310000048
其中，
Figure BDA0002296964310000049
为自航船模第s个靶标对应的左方位角；下标s为所属靶标编号；s为奇数时表示船头靶标，s为偶数时表示船尾靶标；上标1为第1次测量；a. Determine the azimuth in the initial left azimuth sequence with the smallest difference from the left azimuth α 1 in the residual matrix Δd α
Figure BDA0002296964310000047
Adjust α 1 to the position of the s-th target in the left azimuth sequence, denoted as
Figure BDA0002296964310000048
in,
Figure BDA0002296964310000049
is the left azimuth angle corresponding to the s-th target of the self-propelled ship model; the subscript s is the target number; when s is an odd number, it means the bow target, and when s is an even number, it means the stern target; the superscript 1 is the first measurement;

b.删除残差矩阵Δdα的第1行以及第s列，确定残差矩阵Δdα中与左方位角α2差值最小的初始左方位角序列中的方位角

Figure BDA00022969643100000410
将α2调整到左方位角序列中第r个靶标所在的位置，记为
Figure BDA00022969643100000411
其中，r＝1,2,…,2n；
Figure BDA00022969643100000412
为自航船模第r个靶标对应的左方位角；下标r为所属靶标编号；r为奇数时表示船头靶标，r为偶数时表示船尾靶标；上标1为第1次测量；b. Delete the 1st row and the sth column of the residual matrix Δd α , and determine the azimuth in the initial left azimuth sequence with the smallest difference from the left azimuth angle α 2 in the residual matrix Δd α
Figure BDA00022969643100000410
Adjust α 2 to the position of the rth target in the left azimuth sequence, denoted as
Figure BDA00022969643100000411
Among them, r=1,2,...,2n;
Figure BDA00022969643100000412
is the left azimuth angle corresponding to the rth target of the self-propelled ship model; the subscript r is the target number; when r is an odd number, it means the bow target, and when r is an even number, it means the stern target; the superscript 1 is the first measurement;

c.按照步骤b类推，调整左方位角序列G1中其他方位角的顺序，得到新的左方位角序列

Figure BDA0002296964310000051
Figure BDA0002296964310000052
c. According to step b and so on, adjust the order of other azimuth angles in the left azimuth angle sequence G 1 to obtain a new left azimuth angle sequence
Figure BDA0002296964310000051
Figure BDA0002296964310000052

根据如下步骤得到新的右方位角序列

Figure BDA0002296964310000053
Obtain a new right azimuth sequence according to the following steps
Figure BDA0002296964310000053

e.确定残差矩阵Δdβ中与右方位角β1差值最小的初始右方位角序列中的方位角

Figure BDA0002296964310000054
将β1调整到右方位角序列中第s个靶标所在的位置，记为
Figure BDA0002296964310000055
其中，
Figure BDA0002296964310000056
为自航船模第s个靶标对应的右方位角；下标s为所属靶标编号；s为奇数时表示船尾靶标，s为偶数时表示船头靶标；上标1为第1次测量；e. Determine the azimuth in the initial right azimuth sequence with the smallest difference from the right azimuth angle β 1 in the residual matrix Δd β
Figure BDA0002296964310000054
Adjust β 1 to the position of the s-th target in the right azimuth sequence, denoted as
Figure BDA0002296964310000055
in,
Figure BDA0002296964310000056
is the right azimuth corresponding to the s-th target of the self-propelled ship model; the subscript s is the target number; when s is an odd number, it means the stern target, and when s is an even number, it means the bow target; the superscript 1 is the first measurement;

f.删除残差矩阵Δdβ的第1行以及第s列，确定残差矩阵Δdβ中与右方位角β2差值最小的初始右方位角序列中的方位角

Figure BDA0002296964310000057
将β2调整到右方位角序列中第r个靶标所在的位置，记为
Figure BDA0002296964310000058
其中，r＝1,2,…,2n；
Figure BDA0002296964310000059
为自航船模第r个靶标对应的右方位角；下标r为所属靶标编号；r为奇数时表示船尾靶标，r为偶数时表示船头靶标；上标1为第1次测量；f. Delete the 1st row and the sth column of the residual matrix Δd β , and determine the azimuth in the initial right azimuth sequence with the smallest difference from the right azimuth angle β 2 in the residual matrix Δd β
Figure BDA0002296964310000057
Adjust β 2 to the position of the rth target in the right azimuth sequence, denoted as
Figure BDA0002296964310000058
Among them, r=1,2,...,2n;
Figure BDA0002296964310000059
is the right azimuth corresponding to the rth target of the self-propelled ship model; the subscript r is the target number; when r is an odd number, it means the stern target, and when r is an even number, it means the bow target; the superscript 1 is the first measurement;

g.按照步骤f类推，调整右方位角序列H1中其他方位角的顺序，得到新的右方位角序列

Figure BDA00022969643100000510
Figure BDA00022969643100000511
g. According to the analogy of step f, adjust the order of other azimuth angles in the right azimuth angle sequence H 1 to obtain a new right azimuth angle sequence
Figure BDA00022969643100000510
Figure BDA00022969643100000511

进一步，对新的左方位角序列

Figure BDA00022969643100000512
以及新的右方位角序列
Figure BDA00022969643100000513
中方位角所属自航船模靶标进行校验，包括：Further, for the new left azimuth sequence
Figure BDA00022969643100000512
and the new right azimuth sequence
Figure BDA00022969643100000513
The self-propelled ship model target belonging to the middle azimuth is verified, including:

S41.计算第i条自航船模的船头坐标

Figure BDA00022969643100000514
以及船尾坐标
Figure BDA00022969643100000515
其中，
Figure BDA00022969643100000516
Figure BDA00022969643100000517
S41. Calculate the bow coordinates of the i-th self-propelled ship model
Figure BDA00022969643100000514
and the stern coordinates
Figure BDA00022969643100000515
in,
Figure BDA00022969643100000516
Figure BDA00022969643100000517

S42.计算第i条自航船模的船头靶标与船尾靶标之间距离

Figure BDA00022969643100000518
S42. Calculate the distance between the bow target and the stern target of the i-th self-propelled ship model
Figure BDA00022969643100000518

Figure BDA00022969643100000519
Figure BDA00022969643100000519

S43.判断

Figure BDA00022969643100000520
是否大于3σi；如是，则第i条自航船模靶标对应的方位角有误，需要对方位角序列中方位角的顺序进行重新调整；否则，不做任何操作；S43. Judgment
Figure BDA00022969643100000520
Whether it is greater than 3σ i ; if so, the azimuth angle corresponding to the i-th self-propelled ship model target is wrong, and the order of the azimuth angles in the azimuth angle sequence needs to be readjusted; otherwise, do nothing;

其中，Li为第i条自航船模靶标间的实际距离，σi为靶标间距离测量值的离散阈值。Among them, Li is the actual distance between the targets of the i -th self-propelled ship model, and σ i is the discrete threshold of the distance measurement between the targets.

进一步，根据如下公式确定靶标间距离测量值的离散阈值σi：Further, the discrete threshold σ i of the distance measurement value between the targets is determined according to the following formula:

Figure BDA0002296964310000061
Figure BDA0002296964310000061

其中，

Figure BDA0002296964310000062
为自航船模i在开始试验前自航船模静止时，第j次被扫描到的靶标间距离；M为自航船模在开始试验前被扫描的次数；j＝1,2,…,M；Li为第i条自航船模靶标间的实际距离。in,
Figure BDA0002296964310000062
is the distance between the targets scanned for the jth time when the self-propelled ship model i is stationary before the start of the test; M is the number of scans of the self-propelled ship model before the start of the test; j=1,2,…,M; Li is the actual distance between the i -th self-propelled ship model targets.

进一步，步骤S43中，根据如下步骤对第i条自航船模的方位角序列中方位角的顺序进行重新调整：Further, in step S43, the order of the azimuth angles in the azimuth angle sequence of the i-th self-propelled ship model is readjusted according to the following steps:

S431.将第i条自航船模两靶标对应的左方位角

Figure BDA0002296964310000063
以及
Figure BDA0002296964310000064
移至左方位角序列G1的最后，按照步骤a-b类推，再次对左方位角序列G1中方位角的顺序进行调整，得到左方位角序列
Figure BDA0002296964310000065
S431. Set the left azimuth corresponding to the two targets of the i-th self-propelled ship model
Figure BDA0002296964310000063
as well as
Figure BDA0002296964310000064
Move to the end of the left azimuth sequence G 1 , follow steps ab and so on, adjust the order of the azimuth angles in the left azimuth sequence G 1 again, and obtain the left azimuth sequence
Figure BDA0002296964310000065

S432.根据左方位角序列

Figure BDA0002296964310000066
与右方位角序列
Figure BDA0002296964310000067
Figure BDA0002296964310000068
执行步骤S41-S42，得到距离差值
Figure BDA0002296964310000069
S432. According to the left azimuth sequence
Figure BDA0002296964310000066
with the right azimuth sequence
Figure BDA0002296964310000067
Figure BDA0002296964310000068
Execute steps S41-S42 to obtain the distance difference
Figure BDA0002296964310000069

S433.将第i条自航船模两靶标对应的右方位角

Figure BDA00022969643100000610
以及
Figure BDA00022969643100000611
移至右方位角序列H1的最后，按照步骤e-f类推，再次对右方位角序列H1中方位角的顺序进行调整，得到右方位角序列
Figure BDA00022969643100000612
S433. Set the right azimuth corresponding to the two targets of the i-th self-propelled ship model
Figure BDA00022969643100000610
as well as
Figure BDA00022969643100000611
Move to the end of the right azimuth angle sequence H 1 , follow steps ef and so on, adjust the order of the azimuth angles in the right azimuth angle sequence H 1 again, and obtain the right azimuth angle sequence
Figure BDA00022969643100000612

S434.根据右方位角序列

Figure BDA00022969643100000613
与左方位角序列
Figure BDA00022969643100000614
Figure BDA00022969643100000615
执行步骤S41-S42，得到距离差值
Figure BDA00022969643100000616
S434. According to the right azimuth sequence
Figure BDA00022969643100000613
sequence with left azimuth
Figure BDA00022969643100000614
Figure BDA00022969643100000615
Execute steps S41-S42 to obtain the distance difference
Figure BDA00022969643100000616

S435.根据左方位角序列

Figure BDA00022969643100000617
与右方位角序列
Figure BDA00022969643100000618
执行步骤S41-S42，得到距离差值
Figure BDA00022969643100000619
S435. According to the left azimuth sequence
Figure BDA00022969643100000617
with the right azimuth sequence
Figure BDA00022969643100000618
Execute steps S41-S42 to obtain the distance difference
Figure BDA00022969643100000619

S436.计算距离差值A、B以及C中的最小值min；S436. Calculate the minimum value min among the distance differences A, B and C;

S437.判断最小值min是否大于3σi；如是，继续执行步骤S431-S436，直到min≤3σi，当执行次数超过10次时，则丢弃扫描到的左右方位角序列；否则，将最小值min所对应的方位角调整结果作为最终的方位角修正结果。S437. Determine whether the minimum value min is greater than 3σ i ; if so, continue to perform steps S431-S436 until min≤3σ i , when the number of executions exceeds 10 times, discard the scanned left and right azimuth sequence; otherwise, set the minimum value min The corresponding azimuth angle adjustment result is used as the final azimuth angle correction result.

本发明的有益效果是：本发明公开的一种多目标自航船模轨迹跟踪测量方法，通过扫描得到自航船模靶标的方位角序列，对自航船模靶标所属方位角进行调整匹配，使得测量的方位角对应到相应的自航船模靶标上，对方位角的匹配结果进行校验，当匹配结果有误差时，再次对方位角所属靶标进行匹配，保证匹配结果的准确性，从而在保持高精度、高频响的优势下，实现对多条自航船模轨迹同时进行跟踪测量。The beneficial effects of the invention are as follows: the method for tracking and measuring the trajectory of a multi-target self-propelled ship model disclosed by the invention obtains the azimuth angle sequence of the self-propelled ship model target by scanning, and adjusts and matches the azimuth angle to which the self-propelled ship model target belongs, so that the measured The azimuth angle corresponds to the corresponding self-propelled ship model target, and the matching result of the azimuth angle is verified. When there is an error in the matching result, the target to which the azimuth angle belongs is matched again to ensure the accuracy of the matching result, so as to maintain high precision. With the advantages of high-frequency response and high-frequency response, it can track and measure multiple self-propelled ship model trajectories at the same time.

附图说明Description of drawings

下面结合附图和实施例对本发明作进一步描述：Below in conjunction with accompanying drawing and embodiment, the present invention is further described:

图1为本发明的方法流程示意图；Fig. 1 is the method flow schematic diagram of the present invention;

图2为本发明的激光自航船模轨迹仪测量示意图；Fig. 2 is the measurement schematic diagram of the laser self-propelled ship model locator of the present invention;

图3为本发明的多目标自航船模初始条件示意图；3 is a schematic diagram of the initial conditions of the multi-target self-propelled ship model of the present invention;

图4为本发明的多目标自航船模方位角遮挡示意图；4 is a schematic diagram of azimuth angle shielding of a multi-target self-propelled ship model of the present invention;

图5为本发明的多目标自航船模方位角干扰示意图。FIG. 5 is a schematic diagram of the azimuth interference of the multi-target self-propelled ship model of the present invention.

具体实施方式Detailed ways

以下结合说明书附图对本发明做出进一步的说明，如图所示：The present invention is further described below in conjunction with the accompanying drawings of the description, as shown in the figure:

本发明的多目标自航船模轨迹跟踪测量方法，包括如下步骤：The multi-target self-propelled ship model trajectory tracking measurement method of the present invention comprises the following steps:

S1.试验开始前，将n条自航船模依次排开，使得n条自航船模的船头朝向一致，并为n条自航船模分别设置船头靶标与船尾靶标，使用两套扫描仪同时对n条自航船模的船头靶标以及船尾靶标进行扫描，得到n条自航船模靶标的初始左方位角序列G0：

Figure BDA0002296964310000071
与初始右方位角序列H0：
Figure BDA0002296964310000072
其中，n＝1,2,3,…,N；i＝1,2,…,n；i为自航船模编号；
Figure BDA0002296964310000073
以及
Figure BDA0002296964310000074
分别为其中一套扫描仪对第i条自航船模进行扫描得到的船头方位角与船尾方位角；
Figure BDA0002296964310000075
以及
Figure BDA0002296964310000076
分别为其中另外一套扫描仪对第i条自航船模进行扫描得到的船尾方位角与船头方位角；方位角的下标为靶标的编号；S1. Before the test starts, arrange the n self-propelled ship models in turn so that the bows of the n self-propelled ship models are in the same direction, and set the bow target and the stern target for the n self-propelled ship models respectively, and use two sets of scanners at the same time. Scan the bow targets and the stern targets of n self-propelled ship models to obtain the initial left azimuth sequence G 0 of the n self-propelled ship model targets:
Figure BDA0002296964310000071
with the initial right azimuth sequence H 0 :
Figure BDA0002296964310000072
Among them, n=1,2,3,…,N; i=1,2,…,n; i is the number of the self-propelled ship model;
Figure BDA0002296964310000073
as well as
Figure BDA0002296964310000074
are the bow azimuth and stern azimuth obtained by scanning the i-th self-propelled ship model by one of the scanners respectively;
Figure BDA0002296964310000075
as well as
Figure BDA0002296964310000076
are the stern azimuth angle and the bow azimuth angle obtained by scanning the i-th self-propelled ship model by another set of scanners; the subscript of the azimuth angle is the target number;

S2.试验开始后，对n条自航船模的船头靶标与船尾靶标进行扫描，得到n条自航船模靶标的左方位角序列G1：(α1,α2,…,α2i-1,α2i,…,α2n-1,α2n)与右方位角序列H1：(β1,β2,…,β2i-1,β2i,…,β2n-1,β2n)；S2. After the test starts, scan the bow target and the stern target of the n self-propelled ship models to obtain the left azimuth sequence G 1 of the n self-propelled ship model targets: (α 1 ,α 2 ,…,α 2i-1 ,α 2i ,…,α 2n-1 ,α 2n ) and the right azimuth sequence H 1 : (β 1 ,β 2 ,…,β 2i-1 ,β 2i ,…,β 2n-1 ,β 2n );

S3.计算左方位角序列G1与初始左方位角序列G0的残差矩阵Δdα；计算右方位角序列H1与初始右方位角序列H0的残差矩阵Δdβ；S3. Calculate the residual matrix Δd α of the left azimuth sequence G 1 and the initial left azimuth sequence G 0 ; calculate the residual matrix Δd β of the right azimuth sequence H 1 and the initial right azimuth sequence H 0 ;

S4.根据残差矩阵Δdα对左方位角序列G1中方位角的顺序进行调整，使得左方位角匹配所属靶标，得到新的左方位角序列

Figure BDA0002296964310000081
根据残差矩阵Δdβ对右方位角序列H1中右方位角的顺序进行调整，使得右方位角匹配所属靶标，得到新的右方位角序列
Figure BDA0002296964310000082
S4. Adjust the order of the azimuth angles in the left azimuth angle sequence G 1 according to the residual matrix Δd α , so that the left azimuth angle matches the target to which it belongs, and a new left azimuth angle sequence is obtained
Figure BDA0002296964310000081
The order of the right azimuth angles in the right azimuth angle sequence H 1 is adjusted according to the residual matrix Δd β , so that the right azimuth angle matches the target to which it belongs, and a new right azimuth angle sequence is obtained.
Figure BDA0002296964310000082

S5.根据新的左方位角序列

Figure BDA0002296964310000083
与右方位角序列
Figure BDA0002296964310000084
计算n条自航船模的船头靶标坐标序列
Figure BDA0002296964310000085
与船尾靶标坐标序列
Figure BDA0002296964310000086
S5. According to the new left azimuth sequence
Figure BDA0002296964310000083
with the right azimuth sequence
Figure BDA0002296964310000084
Calculate the bow target coordinate sequence of n self-propelled ship models
Figure BDA0002296964310000085
with the stern target coordinate sequence
Figure BDA0002296964310000086

S6.将每次扫描到的新的左方位角序列与右方位角序列分别作为下次扫描的初始左方位角序列与初始右方位角序列，按照步骤S2-S5类推，直到试验结束，最后得到n条自航船模的船头靶标坐标序列集CH与船尾靶标坐标序列集CT；S6. Take the new left azimuth sequence and right azimuth sequence obtained by each scan as the initial left azimuth sequence and the initial right azimuth sequence of the next scan, respectively, according to steps S2-S5 and so on, until the end of the test, and finally get The bow target coordinate sequence set CH and the stern target coordinate sequence set CT of the n self-propelled ship models;

S7.根据n条自航船模的船头靶标坐标序列集CH与船尾靶标坐标序列集CT计算n条自航船模的运行轨迹。S7. Calculate the running trajectories of the n self-propelled ship models according to the bow target coordinate sequence set CH and the stern target coordinate sequence set CT of the n self-propelled ship models.

激光自航船模轨迹仪测量原理如图2所示，自航船模首尾立有两个反光杆A和B，LSR1和LSR2为两套激光扫描测角系统，用来检测A、B所处位置的方位角信息。LSR1与LSR2间的距离为L，测量过程中保持不变。以LSR1为原点，以LSR1与LSR2连线为x轴，建立直角坐标系。LSR1逆时针扫描，得到A、B两点的左方位角分别为α1、α2。LSR2顺时针扫描，得到A、B两点的右方位角分别为β2、β1。The measurement principle of the laser self-propelled ship model tracker is shown in Figure 2. There are two reflective rods A and B at the fore and aft of the self-propelled ship model. LSR1 and LSR2 are two sets of laser scanning angle measuring systems, which are used to detect the position of A and B. Azimuth information. The distance between LSR1 and LSR2 is L, which remains unchanged during the measurement. Taking LSR1 as the origin, and taking the line connecting LSR1 and LSR2 as the x-axis, a Cartesian coordinate system is established. LSR1 scans counterclockwise, and the left azimuth angles of points A and B are obtained as α 1 and α 2 respectively. The LSR2 scans clockwise, and the right azimuth angles of points A and B are obtained as β 2 and β 1 , respectively.

根据测点方位角及三角形正弦定理，可得到A、B两点二维坐标：According to the azimuth angle of the measuring point and the triangular sine theorem, the two-dimensional coordinates of points A and B can be obtained:

A的坐标为(x1,y1)，其中，

Figure BDA0002296964310000087
The coordinates of A are (x 1 , y 1 ), where,
Figure BDA0002296964310000087

B的坐标为(x2,y2)，其中，

Figure BDA0002296964310000088
The coordinates of B are (x 2 , y 2 ), where,
Figure BDA0002296964310000088

根据式(1)与式(2)可得自航船模运动轨迹。According to formula (1) and formula (2), it can be obtained from the motion trajectory of the ship model.

其中，本发明所述自航船模为人为遥控运动的船模，通过遥控对船模的运动进行控制。Wherein, the self-propelled ship model of the present invention is a ship model that is manually moved by remote control, and the movement of the ship model is controlled by remote control.

本实施例中，步骤S1中，设有n条自航船模，每条自航船模上有2个靶标，共有2n个靶标。在进入试验河段前(也就是在试验开始前，各条自航船模保持静止)，调整自航船模间位置，将n条自航船模依次排开，且船头均朝向试验河段，对于每条自航船模，激光扫描测角系统LSR1扫描得到一组左方位角：

Figure BDA0002296964310000091
i为自航船模编号，共有n组，n为正整数，将其进行合并，得到左方位角序列
Figure BDA0002296964310000092
调整各自航船模相对位置，使其满足：In this embodiment, in step S1, there are n self-propelled ship models, each self-propelled ship model has 2 targets, and there are 2n targets in total. Before entering the test section (that is, before the test starts, each self-propelled ship model remains stationary), adjust the position between the self-propelled ship models, arrange the n self-propelled ship models in sequence, and the bows of the boats are all facing the test section. For each self-propelled ship model, the laser scanning angle measuring system LSR1 scans to obtain a set of left azimuth angles:
Figure BDA0002296964310000091
i is the number of the self-propelled ship model, there are n groups in total, n is a positive integer, and they are combined to obtain the left azimuth sequence
Figure BDA0002296964310000092
Adjust the relative positions of the respective ship models to satisfy:

Figure BDA0002296964310000093
Figure BDA0002296964310000093

满足式(3)的各自航船模方位角相互错开，将距试验河段最近的自航船模编号为1号，其它依次编号为2号自航船模，…，n号自航船模。则有：The azimuth angles of the respective ship models that satisfy the formula (3) are staggered, and the self-propelled ship model closest to the test river section is numbered as No. 1, and the others are numbered as the No. 2 self-propelled ship model, ..., and No. Then there are:

1号自航船模船头、船尾两个靶标方位角分别为：

Figure BDA0002296964310000094
The azimuth angles of the two targets at the bow and stern of the No. 1 self-propelled ship model are:
Figure BDA0002296964310000094

i号自航船模船头、船尾两个靶标方位角分别为：

Figure BDA0002296964310000095
The azimuth angles of the two targets at the bow and stern of the self-propelled ship model i are:
Figure BDA0002296964310000095

n号自航船模船头、船尾两个靶标方位角分别为：

Figure BDA0002296964310000096
The azimuth angles of the two targets at the bow and stern of the No. n self-propelled ship model are:
Figure BDA0002296964310000096

同理，激光扫描测角系统LSR2扫描得到一组右方位角序列：

Figure BDA0002296964310000097
则有：Similarly, the laser scanning angle measuring system LSR2 scans to obtain a set of right azimuth sequences:
Figure BDA0002296964310000097
Then there are:

1号自航船模船头、船尾两个靶标方位角分别为：

Figure BDA0002296964310000098
The azimuth angles of the two targets at the bow and stern of the No. 1 self-propelled ship model are:
Figure BDA0002296964310000098

i号自航船模船头、船尾两个靶标方位角分别为：

Figure BDA0002296964310000099
The azimuth angles of the two targets at the bow and stern of the self-propelled ship model i are:
Figure BDA0002296964310000099

n号自航船模船头、般尾两个靶标方位角分别为：

Figure BDA00022969643100000910
The azimuth angles of the two targets at the bow and stern of the No. n self-propelled ship model are:
Figure BDA00022969643100000910

以方位角序列

Figure BDA00022969643100000911
Figure BDA00022969643100000912
确定的多目标自航船模位置作为自航船模试验的初始条件。in azimuth sequence
Figure BDA00022969643100000911
Figure BDA00022969643100000912
The determined multi-objective self-propelled ship model position is used as the initial condition for the self-propelled ship model test.

本实施例中，步骤S2中，激光测角扫描系统得到的方位角数据序列，少数情况下，多条自航船模在运动过程中，某些靶标可能会被其它靶标遮挡，导致激光扫描测角系统输出的方位角序列长短不一。如图4所示，当自航船模1靶标、自航船模2靶标、激光出射点三点共线时，自航船模2的靶标将被遮挡，左方位角数据序列会减少1个，LSR1输出数据序列长度为2n-1，数据缺失，需要对缺失数据进行填补。由于自航船模1与自航船模2的船尾左方位角相等，可在数据序列中填入相同的方位角数据，以补全数据。缺失数据填补的原理即是找到共线时的方位角，并将原方位角序列进行扩充。In this embodiment, in step S2, in the azimuth data sequence obtained by the laser angle measurement scanning system, in a few cases, some targets may be blocked by other targets during the movement of multiple self-propelled ship models, resulting in laser scanning angle measurement. The azimuth sequence output by the system varies in length. As shown in Figure 4, when the target of self-propelled ship model 1, the target of self-propelled ship model 2, and the laser exit point are collinear, the target of self-propelled ship model 2 will be blocked, the left azimuth data sequence will be reduced by one, and LSR1 will output The length of the data sequence is 2n-1, the data is missing, and the missing data needs to be filled. Since the stern left azimuth angles of the self-propelled ship model 1 and the self-propelled ship model 2 are equal, the same azimuth data can be filled in the data sequence to complete the data. The principle of missing data filling is to find the azimuth when collinear, and expand the original azimuth sequence.

具体地，填补方法如下：Specifically, the filling method is as follows:

1.LSR1测得的方位角序列(α1,α2,…,αk,…,αp)，若没有遮挡，应有2n个数据，则说明共有2n-p个靶标被遮挡。计算当前测量的方位角与初始条件下的方位角的残差矩阵

Figure BDA0002296964310000101
1. The azimuth angle sequence (α 1 ,α 2 ,…,α k ,…,α p ) measured by LSR1, if there is no occlusion, there should be 2n data, which means a total of 2n-p targets are occluded. Calculate the residual matrix of the currently measured azimuth and the azimuth in the initial conditions
Figure BDA0002296964310000101

Figure BDA0002296964310000102
Figure BDA0002296964310000102

其中，上述方位角序列

Figure BDA0002296964310000103
为方便表示，可以采用通项
Figure BDA0002296964310000104
形式，得到方位角序列的另一种表示为
Figure BDA0002296964310000105
下面描述的左方位角序列与右方位角序列中含有通项的与此处理方式相同，不再进行赘述。Among them, the above azimuth sequence
Figure BDA0002296964310000103
For convenience, the general term can be used
Figure BDA0002296964310000104
form, another representation of the azimuth sequence is obtained as
Figure BDA0002296964310000105
The left azimuth sequence and the right azimuth sequence described below contain general terms in the same processing manner, and will not be repeated here.

2.在残差矩阵

Figure BDA0002296964310000106
每行中取最小的前两个值，对于第k行，前两个最小值组成数据对：
Figure BDA0002296964310000107
k表示第几行，u和v表示第几列。计算数据对差值，得到：
Figure BDA0002296964310000108
同理，可得到残差矩阵
Figure BDA0002296964310000109
中其他行的数据对差值。2. In the residual matrix
Figure BDA0002296964310000106
Take the smallest first two values in each row, and for the kth row, the first two smallest values make up the data pair:
Figure BDA0002296964310000107
k represents the row, and u and v represent the column. Calculate the difference between the data pairs and get:
Figure BDA0002296964310000108
Similarly, the residual matrix can be obtained
Figure BDA0002296964310000109
The data pair difference of the other rows in .

3.将数据对差值组成序列：3. Combine the data pair differences into a sequence:

Figure BDA00022969643100001010
Figure BDA00022969643100001010

对序列(9)的元素按照从小到大的顺序排列，取该序列中前2n-p个最小值所对应的数据对，若没有2n-p个数据时，则将序列(9)中的数据全部取出，设其中的一个数据对为

Figure BDA00022969643100001011
其位于式(8)中的第k行，说明αk与
Figure BDA00022969643100001012
Figure BDA00022969643100001013
接近，从而导致自航船模运动过程中出现遮挡现象，以αk填充缺失数据集，将αk加到序列(α1,α2,…,αk,…,αp)的末尾即可。具体地，可将从序列(9)中取出的多个最小值按照从小到大的顺序排序，并依照此排序顺序，找出2n-p个数据进行依次填补，不够2n-p个数据时，可将找到的最后一个数据进行多次填补，使得方位角序列得以完整，实现如下转换：Arrange the elements of sequence (9) in ascending order, and take the data pairs corresponding to the first 2n-p minimum values in the sequence. If there are no 2n-p data, the data in sequence (9) All are taken out, and one of the data pairs is set as
Figure BDA00022969643100001011
It is located in the kth row in Eq. (8), indicating that α k and
Figure BDA00022969643100001012
Figure BDA00022969643100001013
approaching, resulting in occlusion during the motion of the self-propelled ship model, fill the missing data set with α k , and add α k to the end of the sequence (α 1 ,α 2 ,…,α k ,…,α p ). Specifically, the multiple minimum values taken out from the sequence (9) can be sorted in ascending order, and according to this sorting order, 2n-p pieces of data can be found and filled in sequence, and when there are not enough 2n-p pieces of data, The last data found can be filled multiple times to make the azimuth sequence complete, and the following conversions can be achieved:

(α1,α2,…,αk,…,αp)→(α1,α2,…,αj,…,α2n) (10)(α 1 ,α 2 ,…,α k ,…,α p )→(α 1 ,α 2 ,…,α j ,…,α 2n ) (10)

若LSR2测得的方位角序列(β1,β2,…,βl,…,βq)，q<2n，则数据也发生缺失，同理，根据上述步骤1-3，对右方位角序列进行填补，实现如下转换：If the azimuth sequence (β 1 ,β 2 ,…,β l ,…,β q ) measured by LSR2, q<2n, the data is also missing. Similarly, according to the above steps 1-3, for the right azimuth The sequence is filled to achieve the following conversion:

(β1,β2,…,βl,…,βq)→(β1,β2,…,βj,…,β2n) (11)(β 1 ,β 2 ,…,β l ,…,β q )→(β 1 ,β 2 ,…,β j ,…,β 2n ) (11)

最终的左方位角序列为(α1,α2,…,α2i-1,α2i,…,α2n-1,α2n)，右方位角序列为(β1,β2,…,β2i-1,β2i,…,β2n-1,β2n)，其中，i＝1,2,…,n。The final left azimuth sequence is (α 1 ,α 2 ,…,α 2i-1 ,α 2i ,…,α 2n-1 ,α 2n ), and the right azimuth sequence is (β 1 ,β 2 ,…,β 2i-1 ,β 2i ,...,β 2n-1 ,β 2n ), where i=1, 2,...,n.

本实施例中，步骤S3中，初始状态时，

Figure BDA0002296964310000111
是第i条自航船模的船头与船尾的左方位角，
Figure BDA0002296964310000112
是第i条自航船模的船头与船尾右方位角。由于每条自航船模船速、运动方向、运动轨迹等没有相关性，因此，自航船模运动后，测得的左方位角序列中的α2i-1、α2i并不一定是第i条船的左方位角，右方位角序列中的β2j、β2j-1也并不一定是第i条船的右方位角。需要将测量得到的方位角重新分配到各个对应的靶标上。In this embodiment, in step S3, in the initial state,
Figure BDA0002296964310000111
is the left azimuth angle of the bow and stern of the i-th self-propelled ship model,
Figure BDA0002296964310000112
is the right azimuth angle of the bow and stern of the i-th self-propelled ship model. Since each self-propelled ship model has no correlation with its speed, motion direction, and motion trajectory, after the self-propelled ship model moves, α 2i-1 and α 2i in the measured left azimuth sequence are not necessarily the i-th item. The ship's left azimuth and β 2j -1 in the right azimuth sequence are not necessarily the right azimuth of the i-th ship. The measured azimuths need to be reassigned to each corresponding target.

自航船模运动过程中，其方位角是连续变化的，激光扫描测角系统扫描频率50Hz，自航船模运动速度相对很慢，可以认为，同一个靶标相邻两次测量的方位角变化极小。基于这一思想，通过计算相邻两次测量的方位角的残差矩阵，对当前测量的方位角所属靶标进行区分。During the motion of the self-propelled ship model, the azimuth angle changes continuously. The scanning frequency of the laser scanning angle measuring system is 50 Hz, and the motion of the self-propelled ship model is relatively slow. It can be considered that the azimuth angle of the same target measured twice adjacent to each other changes very little. . Based on this idea, the target to which the currently measured azimuth belongs is distinguished by calculating the residual matrix of the azimuths of two adjacent measurements.

当前测得的左方位角与初始条件左方位角的残差矩阵Δdα：The residual matrix Δd α of the currently measured left azimuth and the initial condition left azimuth:

Figure BDA0002296964310000113
Figure BDA0002296964310000113

其中，第j行表示测得的左方位角αj与初始条件下各靶标左方位角初始值之差的绝对值。Among them, the jth row represents the absolute value of the difference between the measured left azimuth angle α j and the initial value of the left azimuth angle of each target under the initial conditions.

本实施例中，步骤S4中，根据如下步骤确定左方位角αj(j＝1,2,…,2n)所属靶标：In this embodiment, in step S4, the target to which the left azimuth angle α j (j=1,2,...,2n) belongs is determined according to the following steps:

a.对残差矩阵Δdα的第一行进行排序，若α1与初始条件下第s(s＝1,2,…,2n)个方位角

Figure BDA0002296964310000121
的差值最小，则将α1作为第s个靶标的当前测量值，记为：a. Sort the first row of the residual matrix Δd α , if α 1 is the same as the sth (s=1,2,...,2n) azimuth angle under the initial condition
Figure BDA0002296964310000121
The difference is the smallest, then α 1 is taken as the current measurement value of the s-th target, which is recorded as:

Figure BDA0002296964310000122
Figure BDA0002296964310000122

其中，

Figure BDA0002296964310000123
为第s个靶标对应的方位角，下标s表示所属靶标编号，s为奇数表示船头，偶数表示船尾，上标1表示第1次测量。in,
Figure BDA0002296964310000123
is the azimuth angle corresponding to the s-th target, the subscript s represents the target number to which it belongs, the odd number s represents the bow, the even number represents the stern, and the superscript 1 represents the first measurement.

b.删除残差矩阵Δdα的第1行以及第s列，对残差矩阵Δdα的第二行进行排序，若α2与初始条件下第r(r＝1,2,…,2n)个方位角

Figure BDA0002296964310000124
差值最小，则将α2作为第r个靶标的当前测量值，记为：b. Delete the 1st row and the sth column of the residual matrix Δd α , and sort the second row of the residual matrix Δd α . If α 2 is the same as the rth (r=1,2,...,2n) azimuth
Figure BDA0002296964310000124
The difference is the smallest, then α 2 is taken as the current measurement value of the rth target, which is recorded as:

Figure BDA0002296964310000125
Figure BDA0002296964310000125

其中，

Figure BDA0002296964310000126
为第r个靶标对应的方位角，下标r表示所属靶标编号，r为奇数表示船头，偶数表示船尾，上标1表示第1次测量。in,
Figure BDA0002296964310000126
is the azimuth angle corresponding to the rth target, the subscript r represents the target number to which it belongs, the odd number r represents the bow, the even number represents the stern, and the superscript 1 represents the first measurement.

c.按照步骤b类推，依次确定左方位角序列(α1,α2,…αj,…,α2n)中各个方位角所属靶标编号，实现如下变换：c. According to the analogy of step b, sequentially determine the target number of each azimuth in the left azimuth sequence (α 1 ,α 2 ,...α j ,...,α 2n ), and realize the following transformation:

Figure BDA0002296964310000127
Figure BDA0002296964310000127

原始测量的左方位角序列(α1,α2,…,αj,…,α2n)无法区分每个测量值所属靶标，变换后的左方位角序列

Figure BDA0002296964310000128
与自航船模的靶标对应关系如下：The original measured left azimuth sequence (α 1 ,α 2 ,…,α j ,…,α 2n ) cannot distinguish the target to which each measurement value belongs, and the transformed left azimuth sequence
Figure BDA0002296964310000128
The corresponding relationship with the target of the self-propelled ship model is as follows:

1号自航船模船头、船尾两个靶标方位角分别为：

Figure BDA0002296964310000129
The azimuth angles of the two targets at the bow and stern of the No. 1 self-propelled ship model are:
Figure BDA0002296964310000129

i号自航船模船头、船尾两个靶标方位角分别为：

Figure BDA00022969643100001210
The azimuth angles of the two targets at the bow and stern of the self-propelled ship model i are:
Figure BDA00022969643100001210

n号自航船模船头、船尾两个靶标方位角分别为：

Figure BDA00022969643100001211
The azimuth angles of the two targets at the bow and stern of the No. n self-propelled ship model are:
Figure BDA00022969643100001211

同理，根据步骤S3，计算当前测得的右方位角与初始条件下右方位角的残差矩阵Δdβ：Similarly, according to step S3, calculate the residual matrix Δd β of the currently measured right azimuth angle and the right azimuth angle under the initial conditions:

Figure BDA00022969643100001212
Figure BDA00022969643100001212

根据步骤S4，具体地，根据上述步骤a至c进行类推，对当前测量的右方位角序列进行变换：According to step S4, specifically, by analogy according to the above steps a to c, the currently measured right azimuth sequence is transformed:

Figure BDA0002296964310000131
Figure BDA0002296964310000131

变换后的右方位角序列

Figure BDA0002296964310000132
是按靶标先后顺序进行排列，其与自航船模的靶标对应关系如下：Transformed right azimuth sequence
Figure BDA0002296964310000132
It is arranged in the order of the target, and its corresponding relationship with the target of the self-propelled ship model is as follows:

1号自航船模船头、船尾两个靶标方位角分别为：

Figure BDA0002296964310000133
The azimuth angles of the two targets at the bow and stern of the No. 1 self-propelled ship model are:
Figure BDA0002296964310000133

i号自航船模船头、船尾两个靶标方位角分别为：

Figure BDA0002296964310000134
The azimuth angles of the two targets at the bow and stern of the self-propelled ship model i are:
Figure BDA0002296964310000134

n号自航船模船头、般尾两个靶标方位角分别为：

Figure BDA0002296964310000135
The azimuth angles of the two targets at the bow and stern of the No. n self-propelled ship model are:
Figure BDA0002296964310000135

对左右方位角进行变换后，理想情况下可根据式(1)和式(2)计算每条自航船模每个靶标的运动轨迹，但由于多船运动轨迹相互交叉干扰，易产生方位角误判。例如，如图5所示，理想情况下自航船模1方位角变化值为θ1，自航船模2方位角变化值为θ2。由于两条自航船模方位角较接近，使用方位角匹配算法可能将自航船模1的方位角变化值误判为θ3，将自航船模2的方位角变化值误判为θ4，从而产生错误，影响了自航船模跟踪精度。After transforming the left and right azimuth angles, ideally, the trajectory of each target of each self-propelled ship model can be calculated according to equations (1) and (2). sentence. For example, as shown in FIG. 5 , ideally, the azimuth angle change value of the self-propelled ship model 1 is θ 1 , and the azimuth angle change value of the self-propelled ship model 2 is θ 2 . Since the azimuth angles of the two self-propelled ship models are relatively close, using the azimuth matching algorithm may misjudge the azimuth angle change value of the self-propelled ship model 1 as θ 3 and the azimuth angle change value of the self-propelled ship model 2 as θ 4 . An error occurred, which affected the tracking accuracy of the self-propelled ship model.

对变换结果进行检验与修正：Check and correct the transformation results:

1)靶标匹配误判检验1) Target matching misjudgment test

自航船模上两靶标间的距离是固定值，基于该特征对靶标匹配结果进行检验。根据式(15)与式(17)，得到第i条自航船模船头坐标为

Figure BDA0002296964310000136
船尾坐标为
Figure BDA0002296964310000137
其中，The distance between the two targets on the self-propelled ship model is a fixed value, and the target matching results are checked based on this feature. According to formula (15) and formula (17), the bow coordinates of the i-th self-propelled ship model are obtained as
Figure BDA0002296964310000136
The coordinates of the stern are
Figure BDA0002296964310000137
in,

Figure BDA0002296964310000138
Figure BDA0002296964310000138

Figure BDA0002296964310000139
Figure BDA0002296964310000139

则第i条自航船模的船头靶标与船尾靶标之间距离

Figure BDA00022969643100001310
Then the distance between the bow target and the stern target of the i-th self-propelled ship model
Figure BDA00022969643100001310

Figure BDA00022969643100001311
Figure BDA00022969643100001311

靶标匹配误判检验标准：若

Figure BDA00022969643100001312
则说明第i条自航船模靶标的方位角匹配有误，需要进行重新匹配；否则不需要进行重新匹配。其中，Li为第i条自航船模靶标间的实际距离，σi表示靶标间距离测量值的离散性；Target matching misjudgment test standard: if
Figure BDA00022969643100001312
It means that the azimuth angle of the i-th self-propelled ship model target is incorrectly matched and needs to be re-matched; otherwise, re-matching is not required. Among them, Li is the actual distance between the targets of the i -th self-propelled ship model, and σ i represents the discreteness of the measured distance between the targets;

2)方位角修正方法2) Azimuth correction method

设第i条自航船模的靶标方位角匹配有误，但不确定是哪个方位角匹配错误。则根据如下方式对方位角进行修正：It is assumed that the target azimuth of the i-th self-propelled ship model is incorrectly matched, but it is uncertain which azimuth is incorrectly matched. The azimuth is corrected as follows:

①左方位角重匹配① Left azimuth rematch

根据方位角匹配算法，第i条自航船模两靶标左方位角的测量值

Figure BDA0002296964310000141
以及
Figure BDA0002296964310000142
对应序列(α1,α2,…,αj,…,α2n)中的αe、αg，方位角αe的残差项
Figure BDA0002296964310000143
Figure BDA0002296964310000144
位于残差矩阵Δdα(式(12))中的第e行，方位角αg的残差项
Figure BDA0002296964310000145
位于残差矩阵Δdα中的第g行。将第e行和第g行移至残差矩阵Δdα的最后两行(不分先后)，根据方位角匹配算法重新计算第i条自航船模两靶标左方位角测量值
Figure BDA0002296964310000146
以及
Figure BDA0002296964310000147
的对应值，并生成新的匹配序列
Figure BDA0002296964310000148
According to the azimuth matching algorithm, the measured value of the left azimuth of the two targets of the i-th self-propelled ship model
Figure BDA0002296964310000141
as well as
Figure BDA0002296964310000142
Corresponding to α e , α g in the sequence (α 1 ,α 2 ,…,α j ,…,α 2n ), the residual term of the azimuth α e
Figure BDA0002296964310000143
Figure BDA0002296964310000144
In the e-th row of the residual matrix Δd α (Eq. (12)), the residual term of the azimuth α g
Figure BDA0002296964310000145
Located at row g in the residual matrix Δd α . Move the e-th row and the g-th row to the last two rows of the residual matrix Δd α (in no particular order), and recalculate the left azimuth measurement value of the i-th self-propelled ship model and two targets according to the azimuth matching algorithm
Figure BDA0002296964310000146
as well as
Figure BDA0002296964310000147
the corresponding value of , and generate a new matching sequence
Figure BDA0002296964310000148

②右方位角重匹配②Right azimuth rematch

根据方位角匹配算法，第i条自航船模两靶标右方位角的测量值

Figure BDA0002296964310000149
以及
Figure BDA00022969643100001410
对应序列(β1,β2,…,βj,…,β2n)中的βf、βh，方位角βf的残差项
Figure BDA00022969643100001411
Figure BDA00022969643100001412
位于残差矩阵Δdβ(式(16))中的第f行，方位角βh的残差项
Figure BDA00022969643100001413
位于残差矩阵Δdβ中的第h行。将第f行和第h行移至残差矩阵Δdβ的最后两行(不分先后)，根据方位角匹配算法重新计算第i条自航船模两靶标右方位角测量值
Figure BDA00022969643100001414
以及
Figure BDA00022969643100001415
的对应值，并生成新的匹配序列
Figure BDA00022969643100001416
According to the azimuth matching algorithm, the measured value of the right azimuth of the two targets of the i-th self-propelled ship model
Figure BDA0002296964310000149
as well as
Figure BDA00022969643100001410
Corresponding to β f , β h in the sequence (β 1 ,β 2 ,…,β j ,…,β 2n ), the residual term of the azimuth β f
Figure BDA00022969643100001411
Figure BDA00022969643100001412
In the f-th row of the residual matrix Δd β (Eq. (16)), the residual term for the azimuth β h
Figure BDA00022969643100001413
Located at row h in the residual matrix Δd β . Move the fth and hth rows to the last two rows of the residual matrix Δd β (in no particular order), and recalculate the right azimuth measurement value of the i-th self-propelled ship model two targets according to the azimuth matching algorithm
Figure BDA00022969643100001414
as well as
Figure BDA00022969643100001415
the corresponding value of , and generate a new matching sequence
Figure BDA00022969643100001416

③左右方位角同时重匹配③ The left and right azimuths are rematched at the same time

根据上述①与②，对左右方位角同时重匹配。According to ① and ② above, rematch the left and right azimuths at the same time.

根据式(20)，计算上述三种情况(①、②以及③)下的靶标间距离，并计算每种情况的

Figure BDA00022969643100001417
值。若三种情况下，
Figure BDA00022969643100001418
则取最小值所对应的匹配结果作为最终的方位角修正结果。若三种情况下，
Figure BDA00022969643100001419
Figure BDA00022969643100001420
则继续三种情况下的重匹配过程，当迭代(重匹配)n次(一般设置为10次)后，若仍无法满足靶标匹配误判检验标准，则迭代终止，并丢弃本次测量的方位角数据；若满足靶标匹配误判检验标准，则找到三种情况下的
Figure BDA0002296964310000151
Figure BDA0002296964310000152
并取
Figure BDA0002296964310000153
所对应的匹配结果作为最终的方位角修正结果。According to formula (20), calculate the distance between the targets in the above three cases (①, ②, and ③), and calculate the distance between the targets in each case
Figure BDA00022969643100001417
value. In three cases,
Figure BDA00022969643100001418
Then take the matching result corresponding to the minimum value as the final azimuth correction result. In three cases,
Figure BDA00022969643100001419
Figure BDA00022969643100001420
Then continue the rematching process in the three cases. After n times of iteration (rematching) (usually set to 10 times), if the target matching misjudgment test standard still cannot be met, the iteration will be terminated and the measured orientation will be discarded. angle data; if the target matching misjudgment test standard is met, find the three cases of
Figure BDA0002296964310000151
Figure BDA0002296964310000152
and take
Figure BDA0002296964310000153
The corresponding matching result is used as the final azimuth correction result.

本实施例中，步骤S5中，基于校验修正后的左方位角序列

Figure BDA0002296964310000154
与右方位角序列
Figure BDA0002296964310000155
根据式子(1)以及式子(2)，计算n条自航船模开始试验后第一次扫描时船头靶标坐标与船尾靶标坐标，其中，第i条自航船模船头坐标为
Figure BDA0002296964310000156
船尾坐标为
Figure BDA0002296964310000157
按照自航船模的编号顺序，依次将自航船模对应的船头坐标放入坐标序列
Figure BDA0002296964310000158
中，则得到n条自航船模的船头靶标坐标序列
Figure BDA0002296964310000159
Figure BDA00022969643100001510
同理，得到n条自航船模的船尾靶标坐标序列
Figure BDA00022969643100001511
Figure BDA00022969643100001512
In this embodiment, in step S5, based on the corrected left azimuth sequence after checking
Figure BDA0002296964310000154
with the right azimuth sequence
Figure BDA0002296964310000155
According to Equation (1) and Equation (2), calculate the bow target coordinates and the stern target coordinates of the n self-propelled ship models in the first scan after the test, where the i-th self-propelled ship model bow coordinates are
Figure BDA0002296964310000156
The coordinates of the stern are
Figure BDA0002296964310000157
According to the numbering sequence of the self-propelled ship model, put the bow coordinates corresponding to the self-propelled ship model into the coordinate sequence in turn.
Figure BDA0002296964310000158
, then the bow target coordinate sequences of n self-propelled ship models are obtained
Figure BDA0002296964310000159
Figure BDA00022969643100001510
In the same way, the stern target coordinate sequence of n self-propelled ship models is obtained
Figure BDA00022969643100001511
Figure BDA00022969643100001512

本实施例中，步骤S6中，In this embodiment, in step S6,

1)以校验修正后的左方位角序列

Figure BDA00022969643100001513
与右方位角序列
Figure BDA00022969643100001514
确定的多目标自航船模位置作为自航船模试验的新的初始条件。1) To check the corrected left azimuth sequence
Figure BDA00022969643100001513
with the right azimuth sequence
Figure BDA00022969643100001514
The determined multi-objective self-propelled ship model position is used as a new initial condition for the self-propelled ship model test.

2)使用LSR1与LSR2开始第2次扫描，并再次进行缺失数据填补、执行方位角匹配算法、并对方位角校验及修正，得到第2次的左方位角匹配序列

Figure BDA00022969643100001515
与右方位角匹配序列
Figure BDA00022969643100001516
以左方位角匹配序列以及右方位角匹配序列确定的多目标自航船模位置作为第3次扫描数据的初始条件。以此类推，对自航船模进行多次扫描。2) Use LSR1 and LSR2 to start the second scan, and fill in the missing data again, perform the azimuth matching algorithm, and check and correct the azimuth to obtain the second left azimuth matching sequence
Figure BDA00022969643100001515
match sequence with right azimuth
Figure BDA00022969643100001516
The position of the multi-target self-propelled ship model determined by the left azimuth matching sequence and the right azimuth matching sequence is used as the initial condition of the third scan data. By analogy, multiple scans are performed on the self-propelled ship model.

3)LSR1与LSR2扫描过程中，依次计算每次方位角匹配序列，直至试验结束。其中，第w次的左方位角匹配序列为

Figure BDA00022969643100001517
右方位角匹配序列为
Figure BDA00022969643100001518
3) During the scanning process of LSR1 and LSR2, each azimuth matching sequence is calculated in turn until the end of the test. Among them, the wth left azimuth matching sequence is
Figure BDA00022969643100001517
The right azimuth matching sequence is
Figure BDA00022969643100001518

4)根据式(1)与式(2)，计算自航船模试验过程中每条自航船模船头靶标与船尾靶标的坐标，得到每次扫描的n条自航船模的船头靶标坐标序列与船尾靶标坐标序列，其中，第w次扫描得到的自航船模的船头靶标坐标序列与船尾靶标坐标序列分别为

Figure BDA0002296964310000161
最终得到n条自航船模的船头靶标坐标序列集CH：
Figure BDA0002296964310000162
与船尾靶标坐标序列集CT：
Figure BDA0002296964310000163
4) According to formula (1) and formula (2), calculate the coordinates of the bow target and the stern target of each self-propelled ship model during the test process of the self-propelled ship model, and obtain the bow target coordinate sequence of n self-propelled ship models for each scan. and the stern target coordinate sequence, wherein the bow target coordinate sequence and the stern target coordinate sequence of the self-propelled ship model obtained by the wth scan are respectively
Figure BDA0002296964310000161
Finally, the set CH of the bow target coordinate sequence of n self-propelled ship models is obtained:
Figure BDA0002296964310000162
with the stern target coordinate sequence set C T :
Figure BDA0002296964310000163

本实施例中，步骤S7中，取出n条自航船模的船头靶标坐标序列集CH中第一次扫描得到的船头靶标坐标序列

Figure BDA0002296964310000164
与船尾靶标坐标序列
Figure BDA0002296964310000165
再从序列
Figure BDA0002296964310000166
中取出编号为1的自航船模的船头靶标坐标
Figure BDA0002296964310000167
从序列
Figure BDA0002296964310000168
中取出编号为1的自航船模的船尾靶标坐标
Figure BDA0002296964310000169
计算编号为1的自航船模第1次被扫描得到的坐标为
Figure BDA00022969643100001610
其中，
Figure BDA00022969643100001611
同理，计算编号为1的自航船模第w次被扫描得到的坐标为
Figure BDA00022969643100001612
其中，
Figure BDA00022969643100001613
编号为1的自航船模的第w次被扫描得到的船头靶标坐标为
Figure BDA00022969643100001614
船尾靶标坐标为
Figure BDA00022969643100001615
则得到编号为1自航船模的坐标序列为(C11,C12,…,C1w,…)；按照得到编号为1的自航船模坐标序列的方法类推，得到所有自航船模在整个试验过程中的坐标序列；其中，编号为i的自航船模的坐标序列为(Ci1,Ci2,…,Ciw,…)；In this embodiment, in step S7, the bow target coordinate sequence obtained by the first scan in the bow target coordinate sequence set CH of the n self-propelled ship models is taken out
Figure BDA0002296964310000164
with the stern target coordinate sequence
Figure BDA0002296964310000165
from the sequence
Figure BDA0002296964310000166
Take out the target coordinates of the bow of the self-propelled ship model numbered 1
Figure BDA0002296964310000167
from the sequence
Figure BDA0002296964310000168
Take out the stern target coordinates of the self-propelled ship model numbered 1
Figure BDA0002296964310000169
The coordinates obtained by the first scan of the self-propelled ship model numbered 1 are:
Figure BDA00022969643100001610
in,
Figure BDA00022969643100001611
In the same way, the coordinates obtained by calculating the wth scan of the self-propelled ship model numbered 1 are:
Figure BDA00022969643100001612
in,
Figure BDA00022969643100001613
The coordinates of the bow target obtained by the wth scan of the self-propelled ship model numbered 1 are:
Figure BDA00022969643100001614
The coordinates of the stern target are
Figure BDA00022969643100001615
Then the coordinate sequence of the self-propelled ship model numbered 1 is obtained as (C1 1 , C1 2 ,…,C1 w ,…); according to the method of obtaining the coordinate sequence of the self-propelled ship model numbered 1, by analogy, all the self-propelled ship models in the whole test are obtained by analogy. The coordinate sequence in the process; wherein, the coordinate sequence of the self-propelled ship model numbered i is (Ci 1 ,Ci 2 ,…,Ci w ,…);

将编号为i的自航船模的坐标序列(Ci1,Ci2,…,Ciw,…)从左至右依次取出，展示到上述建立的直角坐标系上，并将坐标点按照取出的先后顺序依次顺连，得到编号为i的自航船模的运行轨迹；同理，按照上述所述方式，生成其他自航船模的运行轨迹。同时，根据自航船模的轨迹以及试验运行的时间可以得到自航船模的航速、漂角等数据。从而实现对多目标自航船模运动轨迹的跟踪测量。Take the coordinate sequence (Ci 1 ,Ci 2 ,…,Ci w ,…) of the self-propelled ship model numbered i from left to right and display it on the rectangular coordinate system established above, and place the coordinate points in the order in which they are taken out. The sequence is followed in order to obtain the running trajectory of the self-propelled ship model numbered i; in the same way, the running trajectories of other self-propelled ship models are generated according to the above-mentioned method. At the same time, data such as speed and drift angle of the self-propelled ship model can be obtained according to the trajectory of the self-propelled ship model and the time of test operation. In this way, the tracking and measurement of the motion trajectory of the multi-target self-propelled ship model is realized.

最后说明的是，以上实施例仅用以说明本发明的技术方案而非限制，尽管参照较佳实施例对本发明进行了详细说明，本领域的普通技术人员应当理解，可以对本发明的技术方案进行修改或者等同替换，而不脱离本发明技术方案的宗旨和范围，其均应涵盖在本发明的权利要求范围当中。Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit them. Although the present invention has been described in detail with reference to the preferred embodiments, those of ordinary skill in the art should understand that the technical solutions of the present invention can be Modifications or equivalent substitutions without departing from the spirit and scope of the technical solutions of the present invention should be included in the scope of the claims of the present invention.

Claims (8)

1.一种多目标自航船模轨迹跟踪测量方法，其特征在于：包括如下步骤：1. a multi-target self-propelled ship model trajectory tracking measurement method, is characterized in that: comprise the steps: S1.试验开始前，将n条自航船模依次排开，使得n条自航船模的船头朝向一致，并为n条自航船模分别设置船头靶标与船尾靶标，使用两套扫描仪同时对n条自航船模的船头靶标以及船尾靶标进行扫描，得到n条自航船模靶标的初始左方位角序列G0：
Figure FDA0002296964300000011
与初始右方位角序列H0：
Figure FDA0002296964300000012
其中，n＝1,2,3,…,N；i＝1,2,…,n；i为自航船模编号；
Figure FDA0002296964300000013
以及
Figure FDA0002296964300000014
分别为其中一套扫描仪对第i条自航船模进行扫描得到的船头方位角与船尾方位角；
Figure FDA0002296964300000015
以及
Figure FDA0002296964300000016
分别为其中另外一套扫描仪对第i条自航船模进行扫描得到的船尾方位角与船头方位角；方位角的下标为靶标的编号；S1. Before the test starts, arrange the n self-propelled ship models in turn so that the bows of the n self-propelled ship models are in the same direction, and set the bow target and the stern target for the n self-propelled ship models respectively, and use two sets of scanners at the same time. Scan the bow targets and the stern targets of n self-propelled ship models to obtain the initial left azimuth sequence G 0 of the n self-propelled ship model targets:
Figure FDA0002296964300000011
with the initial right azimuth sequence H 0 :
Figure FDA0002296964300000012
Among them, n=1,2,3,…,N; i=1,2,…,n; i is the number of the self-propelled ship model;
Figure FDA0002296964300000013
as well as
Figure FDA0002296964300000014
are the bow azimuth and stern azimuth obtained by scanning the i-th self-propelled ship model by one of the scanners respectively;
Figure FDA0002296964300000015
as well as
Figure FDA0002296964300000016
are the stern azimuth angle and the bow azimuth angle obtained by scanning the i-th self-propelled ship model by another set of scanners; the subscript of the azimuth angle is the target number; S2.试验开始后，对n条自航船模的船头靶标与船尾靶标进行扫描，得到n条自航船模靶标的左方位角序列G1：(α1,α2,…,α2i-1,α2i,…,α2n-1,α2n)与右方位角序列H1：(β1,β2,…,β2i-1,β2i,…,β2n-1,β2n)；S2. After the test starts, scan the bow target and the stern target of the n self-propelled ship models to obtain the left azimuth sequence G 1 of the n self-propelled ship model targets: (α 1 ,α 2 ,…,α 2i-1 ,α 2i ,…,α 2n-1 ,α 2n ) and the right azimuth sequence H 1 : (β 1 ,β 2 ,…,β 2i-1 ,β 2i ,…,β 2n-1 ,β 2n ); S3.计算左方位角序列G1与初始左方位角序列G0的残差矩阵Δdα；计算右方位角序列H1与初始右方位角序列H0的残差矩阵Δdβ；S3. Calculate the residual matrix Δd α of the left azimuth sequence G 1 and the initial left azimuth sequence G 0 ; calculate the residual matrix Δd β of the right azimuth sequence H 1 and the initial right azimuth sequence H 0 ; S4.根据残差矩阵Δdα对左方位角序列G1中方位角的顺序进行调整，使得左方位角匹配所属靶标，得到新的左方位角序列
Figure FDA00022969643000000111
根据残差矩阵Δdβ对右方位角序列H1中右方位角的顺序进行调整，使得右方位角匹配所属靶标，得到新的右方位角序列
Figure FDA0002296964300000017
S4. Adjust the order of the azimuth angles in the left azimuth angle sequence G 1 according to the residual matrix Δd α , so that the left azimuth angle matches the target to which it belongs, and a new left azimuth angle sequence is obtained
Figure FDA00022969643000000111
The order of the right azimuth angles in the right azimuth angle sequence H 1 is adjusted according to the residual matrix Δd β , so that the right azimuth angle matches the target to which it belongs, and a new right azimuth angle sequence is obtained.
Figure FDA0002296964300000017
 S5.根据新的左方位角序列
Figure FDA0002296964300000018
与右方位角序列
Figure FDA00022969643000000112
计算n条自航船模的船头靶标坐标序列
Figure FDA0002296964300000019
与船尾靶标坐标序列
Figure FDA00022969643000000110
S5. According to the new left azimuth sequence
Figure FDA0002296964300000018
with the right azimuth sequence
Figure FDA00022969643000000112
Calculate the bow target coordinate sequence of n self-propelled ship models
Figure FDA0002296964300000019
with the stern target coordinate sequence
Figure FDA00022969643000000110
 S6.将每次扫描到的新的左方位角序列与右方位角序列分别作为下次扫描的初始左方位角序列与初始右方位角序列，按照步骤S2-S5类推，直到试验结束，最后得到n条自航船模的船头靶标坐标序列集CH与船尾靶标坐标序列集CT；S6. Take the new left azimuth sequence and right azimuth sequence obtained by each scan as the initial left azimuth sequence and the initial right azimuth sequence of the next scan, respectively, according to steps S2-S5 and so on, until the end of the test, and finally get The bow target coordinate sequence set CH and the stern target coordinate sequence set CT of the n self-propelled ship models; S7.根据n条自航船模的船头靶标坐标序列集CH与船尾靶标坐标序列集CT计算n条自航船模的运行轨迹。S7. Calculate the running trajectories of the n self-propelled ship models according to the bow target coordinate sequence set CH and the stern target coordinate sequence set CT of the n self-propelled ship models. 2.根据权利要求1所述的多目标自航船模轨迹跟踪测量方法，其特征在于：步骤S2中，当自航船模靶标出现遮挡时，扫描到的左方位角序列G：(α1,α2,…,αk,…,αp)或右方位角序列H：(β1,β2,…,βl,…,βq)中方位角个数会减少，则需要对左方位角序列或右方位角序列进行补全；其中，k以及p为左方位角下标，取值均为正整数，且k<p，p<2n；l以及q为右方位角下标，取值均为正整数，且l<q，q<2n。2. The multi-target self-propelled ship model trajectory tracking measurement method according to claim 1, wherein in step S2, when the self-propelled ship model target is blocked, the scanned left azimuth sequence G: (α 1 ,α 2 ,…,α k ,…,α p ) or the right azimuth sequence H: (β 1 ,β 2 ,…,β l ,…,β q ), the number of azimuths will decrease, then the left azimuth Sequence or right azimuth sequence to complete; among them, k and p are left azimuth subscripts, and their values are positive integers, and k<p, p<2n; l and q are right azimuth subscripts, taking values All are positive integers, and l<q, q<2n. 3.根据权利要求2所述的多目标自航船模轨迹跟踪测量方法，其特征在于：根据如下步骤对左方位角序列G进行补全：3. multi-target self-propelled ship model trajectory tracking measurement method according to claim 2, is characterized in that: the left azimuth sequence G is complemented according to the following steps: S31.计算左方位角序列G与初始左方位角序列G0的残差矩阵
Figure FDA0002296964300000022
S31. Calculate the residual matrix of the left azimuth sequence G and the initial left azimuth sequence G 0
Figure FDA0002296964300000022
Figure FDA0002296964300000021
Figure FDA0002296964300000021
 S32.将残差矩阵
Figure FDA0002296964300000029
第k行的元素按照从小到大的顺序排列，取出第k行的前两个元素作为数据对
Figure FDA0002296964300000024
计算数据对差值
Figure FDA0002296964300000023
Figure FDA0002296964300000028
其中，u以及v分别为残差矩阵
Figure FDA0002296964300000025
第u列以及第v列；S32. Convert the residual matrix
Figure FDA0002296964300000029
The elements of the kth row are arranged in ascending order, and the first two elements of the kth row are taken out as the data pair
Figure FDA0002296964300000024
Calculate data pair difference
Figure FDA0002296964300000023
Figure FDA0002296964300000028
Among them, u and v are the residual matrix, respectively
Figure FDA0002296964300000025
Column u and column v; S33.按照步骤S32类推，得到残差矩阵
Figure FDA0002296964300000026
每行的数据对差值，将所得数据对差值组成数据对差值序列
Figure FDA0002296964300000027
S33. According to the analogy of step S32, the residual matrix is obtained
Figure FDA0002296964300000026
The difference between the data pairs for each row, and the resulting data pair differences are formed into a data pair difference sequence
Figure FDA0002296964300000027
 S34.将数据对差值序列中数据对差值按照从小到大的顺序排列，取出前2n-p个数据对差值，查找2n-p个数据对差值分别对应的左方位角填补到左方位角序列中；S34. Arrange the data pair differences in the data pair difference sequence in ascending order, take out the first 2n-p data pair differences, and find the left azimuth corresponding to the 2n-p data pair differences and fill them to the left in the azimuth sequence; 根据如下步骤对右方位角序列H进行补全：Complete the right azimuth sequence H according to the following steps: S35.计算右方位角序列H与初始右方位角序列H0的残差矩阵
Figure FDA00022969643000000210
S35. Calculate the residual matrix of the right azimuth sequence H and the initial right azimuth sequence H 0
Figure FDA00022969643000000210
Figure FDA0002296964300000031
Figure FDA0002296964300000031
 S36.将残差矩阵
Figure FDA0002296964300000034
第l行的元素按照从小到大的顺序排列，取出第l行的前两个元素作为数据对
Figure FDA0002296964300000035
计算数据对差值
Figure FDA0002296964300000036
其中，d以及w分别为残差矩阵
Figure FDA0002296964300000037
第d列以及第w列；S36. Convert the residual matrix
Figure FDA0002296964300000034
The elements of the lth row are arranged in ascending order, and the first two elements of the lth row are taken out as the data pair
Figure FDA0002296964300000035
Calculate data pair difference
Figure FDA0002296964300000036
Among them, d and w are the residual matrix respectively
Figure FDA0002296964300000037
Column d and column w; S37.按照步骤S36类推，得到残差矩阵
Figure FDA0002296964300000038
每行的数据对差值，将所得数据对差值组成数据对差值序列
Figure FDA0002296964300000039
S37. According to the analogy of step S36, the residual matrix is obtained
Figure FDA0002296964300000038
The difference between the data pairs in each row, and the resulting data pair differences are formed into a data pair difference sequence
Figure FDA0002296964300000039
 S38.将数据对差值序列中数据对差值按照从小到大的顺序排列，取出前2n-q个数据对差值，查找2n-q个数据对差值分别对应的右方位角填补到右方位角序列中。S38. Arrange the data pair differences in the data pair difference sequence in ascending order, take out the first 2n-q data pair differences, and find the right azimuths corresponding to the 2n-q data pair differences and fill them to the right in the azimuth sequence. 4.根据权利要求1所述的多目标自航船模轨迹跟踪测量方法，其特征在于：步骤S3中，根据如下公式确定残差矩阵Δdα：4. The multi-target self-propelled ship model trajectory tracking measurement method according to claim 1, characterized in that: in step S3, the residual matrix Δd α is determined according to the following formula:
Figure FDA0002296964300000032
Figure FDA0002296964300000032
 其中，左方位角序列G1为(α1,α2,…,α2i-1,α2i,…,α2n-1,α2n)；初始左方位角序列G0为
Figure FDA00022969643000000310
Among them, the left azimuth sequence G 1 is (α 1 ,α 2 ,…,α 2i-1 ,α 2i ,…,α 2n-1 ,α 2n ); the initial left azimuth sequence G 0 is
Figure FDA00022969643000000310
 根据如下公式确定残差矩阵Δdβ：The residual matrix Δd β is determined according to the following formula:
Figure FDA0002296964300000033
Figure FDA0002296964300000033
 其中，右方位角序列H1为(β1,β2,…,β2i-1,β2i,…,β2n-1,β2n)；初始右方位角序列H0为
Figure FDA00022969643000000311
Among them, the right azimuth sequence H 1 is (β 1 ,β 2 ,…,β 2i-1 ,β 2i ,…,β 2n-1 ,β 2n ); the initial right azimuth sequence H 0 is
Figure FDA00022969643000000311
 5.根据权利要求1所述的多目标自航船模轨迹跟踪测量方法，其特征在于：步骤S4中，根据如下步骤得到新的左方位角序列
Figure FDA0002296964300000041
5. The multi-target self-propelled ship model trajectory tracking measurement method according to claim 1, wherein in step S4, a new left azimuth sequence is obtained according to the following steps
Figure FDA0002296964300000041
 a.确定残差矩阵Δdα中与左方位角α1差值最小的初始左方位角序列中的方位角
Figure FDA0002296964300000044
将α1调整到左方位角序列中第s个靶标所在的位置，记为
Figure FDA0002296964300000042
其中，
Figure FDA0002296964300000043
为自航船模第s个靶标对应的左方位角；下标s为所属靶标编号；s为奇数时表示船头靶标，s为偶数时表示船尾靶标；上标1为第1次测量；a. Determine the azimuth in the initial left azimuth sequence with the smallest difference from the left azimuth α 1 in the residual matrix Δd α
Figure FDA0002296964300000044
Adjust α 1 to the position of the s-th target in the left azimuth sequence, denoted as
Figure FDA0002296964300000042
in,
Figure FDA0002296964300000043
is the left azimuth angle corresponding to the s-th target of the self-propelled ship model; the subscript s is the target number; when s is an odd number, it means the bow target, and when s is an even number, it means the stern target; the superscript 1 is the first measurement; b.删除残差矩阵Δdα的第1行以及第s列，确定残差矩阵Δdα中与左方位角α2差值最小的初始左方位角序列中的方位角
Figure FDA0002296964300000046
将α2调整到左方位角序列中第r个靶标所在的位置，记为
Figure FDA0002296964300000045
其中，r＝1,2,…,2n；
Figure FDA00022969643000000412
为自航船模第r个靶标对应的左方位角；下标r为所属靶标编号；r为奇数时表示船头靶标，r为偶数时表示船尾靶标；上标1为第1次测量；b. Delete the 1st row and the sth column of the residual matrix Δd α , and determine the azimuth in the initial left azimuth sequence with the smallest difference from the left azimuth angle α 2 in the residual matrix Δd α
Figure FDA0002296964300000046
Adjust α 2 to the position of the rth target in the left azimuth sequence, denoted as
Figure FDA0002296964300000045
Among them, r=1,2,...,2n;
Figure FDA00022969643000000412
is the left azimuth angle corresponding to the rth target of the self-propelled ship model; the subscript r is the target number; when r is an odd number, it means the bow target, and when r is an even number, it means the stern target; the superscript 1 is the first measurement; c.按照步骤b类推，调整左方位角序列G1中其他方位角的顺序，得到新的左方位角序列
Figure FDA0002296964300000047
c. According to step b and so on, adjust the order of other azimuth angles in the left azimuth angle sequence G 1 to obtain a new left azimuth angle sequence
Figure FDA0002296964300000047
 根据如下步骤得到新的右方位角序列
Figure FDA00022969643000000413
Obtain a new right azimuth sequence according to the following steps
Figure FDA00022969643000000413
 e.确定残差矩阵Δdβ中与右方位角β1差值最小的初始右方位角序列中的方位角
Figure FDA0002296964300000048
将β1调整到右方位角序列中第s个靶标所在的位置，记为
Figure FDA00022969643000000414
其中，
Figure FDA0002296964300000049
为自航船模第s个靶标对应的右方位角；下标s为所属靶标编号；s为奇数时表示船尾靶标，s为偶数时表示船头靶标；上标1为第1次测量；e. Determine the azimuth in the initial right azimuth sequence with the smallest difference from the right azimuth angle β 1 in the residual matrix Δd β
Figure FDA0002296964300000048
Adjust β 1 to the position of the s-th target in the right azimuth sequence, denoted as
Figure FDA00022969643000000414
in,
Figure FDA0002296964300000049
is the right azimuth corresponding to the s-th target of the self-propelled ship model; the subscript s is the target number; when s is an odd number, it means the stern target, and when s is an even number, it means the bow target; the superscript 1 is the first measurement; f.删除残差矩阵Δdβ的第1行以及第s列，确定残差矩阵Δdβ中与右方位角β2差值最小的初始右方位角序列中的方位角
Figure FDA00022969643000000411
将β2调整到右方位角序列中第r个靶标所在的位置，记为
Figure FDA00022969643000000410
其中，r＝1,2,…,2n；
Figure FDA00022969643000000415
为自航船模第r个靶标对应的右方位角；下标r为所属靶标编号；r为奇数时表示船尾靶标，r为偶数时表示船头靶标；上标1为第1次测量；f. Delete the 1st row and the sth column of the residual matrix Δd β , and determine the azimuth in the initial right azimuth sequence with the smallest difference from the right azimuth angle β 2 in the residual matrix Δd β
Figure FDA00022969643000000411
Adjust β 2 to the position of the rth target in the right azimuth sequence, denoted as
Figure FDA00022969643000000410
Among them, r=1,2,...,2n;
Figure FDA00022969643000000415
is the right azimuth corresponding to the rth target of the self-propelled ship model; the subscript r is the target number; when r is an odd number, it means the stern target, and when r is an even number, it means the bow target; the superscript 1 is the first measurement; g.按照步骤f类推，调整右方位角序列H1中其他方位角的顺序，得到新的右方位角序列
Figure FDA00022969643000000416
g. According to the analogy of step f, adjust the order of other azimuth angles in the right azimuth angle sequence H 1 to obtain a new right azimuth angle sequence
Figure FDA00022969643000000416
 6.根据权利要求5所述的多目标自航船模轨迹跟踪测量方法，其特征在于：对新的左方位角序列
Figure FDA00022969643000000417
以及新的右方位角序列
Figure FDA00022969643000000418
中方位角所属自航船模靶标进行校验，包括：6. The multi-target self-propelled ship model trajectory tracking measurement method according to claim 5, characterized in that: to the new left azimuth sequence
Figure FDA00022969643000000417
and the new right azimuth sequence
Figure FDA00022969643000000418
The self-propelled ship model target belonging to the middle azimuth is verified, including: S41.计算第i条自航船模的船头坐标
Figure FDA0002296964300000055
以及船尾坐标
Figure FDA0002296964300000056
其中，
Figure FDA0002296964300000051
Figure FDA0002296964300000052
S41. Calculate the bow coordinates of the i-th self-propelled ship model
Figure FDA0002296964300000055
and the stern coordinates
Figure FDA0002296964300000056
in,
Figure FDA0002296964300000051
Figure FDA0002296964300000052
 S42.计算第i条自航船模的船头靶标与船尾靶标之间距离
Figure FDA0002296964300000057
S42. Calculate the distance between the bow target and the stern target of the i-th self-propelled ship model
Figure FDA0002296964300000057
Figure FDA0002296964300000053
Figure FDA0002296964300000053
 S43.判断
Figure FDA0002296964300000058
是否大于3σi；如是，则第i条自航船模靶标对应的方位角有误，需要对方位角序列中方位角的顺序进行重新调整；否则，不做任何操作；S43. Judgment
Figure FDA0002296964300000058
Whether it is greater than 3σ i ; if so, the azimuth angle corresponding to the i-th self-propelled ship model target is wrong, and the order of the azimuth angles in the azimuth angle sequence needs to be readjusted; otherwise, do nothing; 其中，Li为第i条自航船模靶标间的实际距离，σi为靶标间距离测量值的离散阈值。Among them, Li is the actual distance between the targets of the i -th self-propelled ship model, and σ i is the discrete threshold of the distance measurement between the targets. 7.根据权利要求6所述的多目标自航船模轨迹跟踪测量方法，其特征在于：根据如下公式确定靶标间距离测量值的离散阈值σi：7. The multi-target self-propelled ship model trajectory tracking measurement method according to claim 6, wherein the discrete threshold σ i of the distance measurement value between the targets is determined according to the following formula:
Figure FDA0002296964300000054
Figure FDA0002296964300000054
 其中，
Figure FDA0002296964300000059
为自航船模i在开始试验前自航船模静止时，第j次被扫描到的靶标间距离；M为自航船模在开始试验前被扫描的次数；j＝1,2,…,M；Li为第i条自航船模靶标间的实际距离。in,
Figure FDA0002296964300000059
is the distance between the targets scanned for the jth time when the self-propelled ship model i is stationary before the start of the test; M is the number of scans of the self-propelled ship model before the start of the test; j=1,2,…,M; Li is the actual distance between the i -th self-propelled ship model targets. 8.根据权利要求6所述的多目标自航船模轨迹跟踪测量方法，其特征在于：步骤S43中，根据如下步骤对第i条自航船模的方位角序列中方位角的顺序进行重新调整：8. multi-target self-propelled ship model trajectory tracking measurement method according to claim 6, is characterized in that: in step S43, according to the following steps, the order of the azimuth angle in the azimuth angle sequence of the i-th self-propelled ship model is readjusted: S431.将第i条自航船模两靶标对应的左方位角
Figure FDA00022969643000000510
以及
Figure FDA00022969643000000511
移至左方位角序列G1的最后，按照步骤a-b类推，再次对左方位角序列G1中方位角的顺序进行调整，得到左方位角序列
Figure FDA00022969643000000512
S431. Set the left azimuth corresponding to the two targets of the i-th self-propelled ship model
Figure FDA00022969643000000510
as well as
Figure FDA00022969643000000511
Move to the end of the left azimuth sequence G 1 , follow steps ab and so on, adjust the order of the azimuth angles in the left azimuth sequence G 1 again, and obtain the left azimuth sequence
Figure FDA00022969643000000512
 S432.根据左方位角序列
Figure FDA00022969643000000513
与右方位角序列
Figure FDA00022969643000000514
执行步骤S41-S42，得到距离差值
Figure FDA0002296964300000061
S432. According to the left azimuth sequence
Figure FDA00022969643000000513
with the right azimuth sequence
Figure FDA00022969643000000514
Execute steps S41-S42 to obtain the distance difference
Figure FDA0002296964300000061
 S433.将第i条自航船模两靶标对应的右方位角
Figure FDA0002296964300000063
以及
Figure FDA0002296964300000064
移至右方位角序列H1的最后，按照步骤e-f类推，再次对右方位角序列H1中方位角的顺序进行调整，得到右方位角序列
Figure FDA0002296964300000062
S433. Set the right azimuth corresponding to the two targets of the i-th self-propelled ship model
Figure FDA0002296964300000063
as well as
Figure FDA0002296964300000064
Move to the end of the right azimuth angle sequence H 1 , follow steps ef and so on, adjust the order of the azimuth angles in the right azimuth angle sequence H 1 again, and obtain the right azimuth angle sequence
Figure FDA0002296964300000062
 S434.根据右方位角序列
Figure FDA0002296964300000065
与左方位角序列
Figure FDA0002296964300000066
执行步骤S41-S42，得到距离差值
Figure FDA0002296964300000067
S434. According to the right azimuth sequence
Figure FDA0002296964300000065
sequence with left azimuth
Figure FDA0002296964300000066
Execute steps S41-S42 to obtain the distance difference
Figure FDA0002296964300000067
 S435.根据左方位角序列
Figure FDA0002296964300000068
与右方位角序列
Figure FDA00022969643000000610
执行步骤S41-S42，得到距离差值
Figure FDA0002296964300000069
S435. According to the left azimuth sequence
Figure FDA0002296964300000068
with the right azimuth sequence
Figure FDA00022969643000000610
Execute steps S41-S42 to obtain the distance difference
Figure FDA0002296964300000069
 S436.计算距离差值A、B以及C中的最小值min；S436. Calculate the minimum value min among the distance differences A, B and C; S437.判断最小值min是否大于3σi；如是，继续执行步骤S431-S436，直到min≤3σi，当执行次数超过10次时，则丢弃扫描到的左右方位角序列；否则，将最小值min所对应的方位角调整结果作为最终的方位角修正结果。S437. Determine whether the minimum value min is greater than 3σ i ; if so, continue to perform steps S431-S436 until min≤3σ i , when the number of executions exceeds 10 times, discard the scanned left and right azimuth sequence; otherwise, set the minimum value min The corresponding azimuth angle adjustment result is used as the final azimuth angle correction result.
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