CN102818561A

CN102818561A - Method for measuring motion parameters of projectile in shooting range based on digital slit shooting technology

Info

Publication number: CN102818561A
Application number: CN2012102356469A
Authority: CN
Inventors: 文贡坚; 赵竹新; 回丙伟
Original assignee: National University of Defense Technology
Current assignee: National University of Defense Technology
Priority date: 2012-07-09
Filing date: 2012-07-09
Publication date: 2012-12-12

Abstract

The invention provides a method for measuring motion parameters of projectiles in a shooting range based on digital slit camera technology. The technical scheme includes the following three steps: the first step is to arrange a three-dimensional digital slit measurement system; the second step is to determine the imaging model of the three-dimensional line array camera; the third step is to measure the motion parameters of the projectile. The second step includes: Step 1, determine the inner orientation elements and outer orientation elements of the front camera and the bottom camera respectively; Step 2, determine the imaging model expressions of the front camera and the bottom camera respectively. The third step includes: Step 1, select feature points, and calculate the initial estimated value of the projectile motion parameters; Step 2, construct a motion parameter optimization solution model based on the three-dimensional digital model of the projectile, and calculate the optimal estimated value of the projectile motion parameters. The invention solves the problem of high-precision measurement of motion parameters such as target speed, attitude and angle of attack of shooting range projectiles, and realizes digitization and automation of shooting range slit technology.

Description

Measuring method of shooting range projectile motion parameters based on digital slit camera technology

技术领域 technical field

本发明涉及摄影测量、图像处理领域，尤其涉及一种基于数字狭缝摄像技术的靶场弹丸运动参数的测量方法。 The invention relates to the fields of photogrammetry and image processing, in particular to a method for measuring motion parameters of shooting range projectiles based on digital slit camera technology. the

背景技术 Background technique

炮射武器（弹丸、导弹等）的靶场测试为武器性能的鉴定和改进提供重要的依据。弹丸出膛之后的姿态、速度、攻角等参数是影响其射程、射击精度的主要因素，因此这些参数的精确测量是靶场测试的主要任务。 Range testing of gun-launched weapons (projectiles, missiles, etc.) provides an important basis for the identification and improvement of weapon performance. The attitude, speed, angle of attack and other parameters of the projectile after it is released from the chamber are the main factors affecting its range and shooting accuracy, so the accurate measurement of these parameters is the main task of the shooting range test. the

与其他方法相比，光学测量的方法具有测量精度高、数据可视化效果好、抗干扰等优点，因此在靶场弹丸等高速目标的测量和测试中具有不可替代的地位。目前采用光测法分析弹丸目标的运动主要有两种途径：一是框幅式成像的方法，通过框幅式摄像机的高速成像得到弹丸运动的一系列序列图像，通过计算弹丸在不同帧之间弹丸运动的距离来计算弹丸的速度等运动参数；二是狭缝成像的方法，通过狭缝摄像机的扫描成像获取弹丸运动的狭缝图像，可以同时记录弹丸成像过程中的时间和空间信息，以此计算其运动参数。前者起步较早，但框幅式成像方法的成像原理决定了该类摄影机难以实现对弹丸速度方向及攻角的测量，因而在弹丸参数测量方面应用价值大大削弱。采用狭缝成像的方法在记录弹丸的速度和姿态参数的同时，也可以很好的反映弹丸出膛后的攻角变化，因此在常规靶场中成为对弹丸等高速目标测量和测试的重要方式。 Compared with other methods, the optical measurement method has the advantages of high measurement accuracy, good data visualization effect, and anti-interference, so it has an irreplaceable position in the measurement and testing of high-speed targets such as shooting range projectiles. At present, there are two main ways to analyze the movement of projectile targets by photometric method: one is the method of frame-and-frame imaging, which obtains a series of sequence images of projectile motion through high-speed imaging of frame-and-frame cameras, and calculates the distance between different frames of the projectile. The moving distance of the projectile is used to calculate the speed and other motion parameters of the projectile; the second is the method of slit imaging, the slit image of the projectile movement is obtained through the scanning imaging of the slit camera, and the time and space information in the process of projectile imaging can be recorded at the same time, so as to This calculates its motion parameters. The former started earlier, but the imaging principle of the frame-and-frame imaging method determines that it is difficult for this type of camera to measure the velocity direction and angle of attack of the projectile, so its application value in the measurement of projectile parameters is greatly weakened. The method of using slit imaging can not only record the speed and attitude parameters of the projectile, but also reflect the change of the angle of attack of the projectile after it exits the chamber. Therefore, it has become an important way to measure and test high-speed targets such as projectiles in conventional shooting ranges. the

目前通过狭缝成像的方法测量弹丸的运动参数存在一些难以克服的技术瓶颈，主要有：一是狭缝摄影要求弹丸的速度与狭缝摄像机的扫描速度达到弹道同步条件，由于事先无法获取弹丸准确的速度，因此在实际成像中是难以达到的；二是为了获得弹丸运动参数的三维信息，往往采用立体正交交会测量，目前的设备布置方法落后，操作不便，空间关系的精确性难以保证；三是仅采用弹丸图像上有限个特征点来计算运动参数，特征点选取的不确定性会引起较大的测量误差。 At present, there are some insurmountable technical bottlenecks in measuring the motion parameters of the projectile through the slit imaging method. The main ones are: first, the slit photography requires the velocity of the projectile and the scanning speed of the slit camera to reach the ballistic synchronization condition. Therefore, it is difficult to achieve in actual imaging; second, in order to obtain the three-dimensional information of projectile motion parameters, three-dimensional orthogonal cross-section measurement is often used. The current equipment layout method is backward, the operation is inconvenient, and the accuracy of the spatial relationship is difficult to guarantee; The third is to use only a limited number of feature points on the projectile image to calculate the motion parameters, and the uncertainty of feature point selection will cause large measurement errors. the

随着数字技术的发展，人们尝试将以线阵传感器为成像器件的线阵像机代替传统使用以胶片成像的狭缝摄像机。本发明将采用线阵像机获取弹丸图像并测量弹丸运动参数的技术称之为数字狭缝摄像技术。目前该技术的研究除了存在传统狭缝技术中的固有困难外，还由于线阵像机扫描频率的限制，出现了弹道同步条件远远无法达到的难题。 With the development of digital technology, people try to replace the traditional film-based slit cameras with line-scan cameras with line-scan sensors as imaging devices. In the present invention, the technology of acquiring projectile images and measuring projectile motion parameters by using a line array camera is called digital slit camera technology. In addition to the inherent difficulties in the traditional slit technology, the current research on this technology also has the problem that the ballistic synchronization condition is far from being achieved due to the limitation of the scanning frequency of the line array camera. the

为了解决这些困难，实现狭缝技术的数字化，本发明提出了基于数字狭缝摄像技术的靶场弹丸目标运动参数的测量方法。 In order to solve these difficulties and realize the digitization of the slit technology, the present invention proposes a method for measuring the motion parameters of the shooting range projectile target based on the digital slit camera technology. the

发明内容 Contents of the invention

本发明要解决的技术问题是靶场弹丸目标速度、姿态和攻角等运动参数的高精度测量。本发明的目的是提供一种基于数字狭缝摄像技术的靶场弹丸运动参数测量方法，通过本发明设计的立体数字狭缝测量系统和基于弹丸三维数字模型的运动参数测量方法，实现了靶场狭缝技术的数字化、自动化改进需求。 The technical problem to be solved by the present invention is the high-precision measurement of motion parameters such as velocity, attitude and angle of attack of projectiles in the shooting range. The purpose of the present invention is to provide a method for measuring the motion parameters of shooting range projectiles based on digital slit camera technology. Through the three-dimensional digital slit measurement system designed by the present invention and the method for measuring motion parameters based on the three-dimensional digital model of the projectile, the shooting range slit is realized. Digitization and automation improvement requirements of technology. the

结合附图1对本发明的技术方案进行描述： The technical scheme of the present invention is described in conjunction with accompanying drawing 1:

第一步，布置立体数字狭缝测量系统。 The first step is to arrange the three-dimensional digital slit measurement system. the

在火炮口附近2-3米弹丸出膛后弹道的正下方放置由矩形平面镜制作而成的双像器，双像器的镜面与地面成45°放置，同时在距离双像器5-10米的位置放置一台线阵像机，使得线阵像机的主光轴大约成45°入射双像器的平面镜。调整线阵像机的焦距，使得放置的线阵像机（以下称为前像机）和双像器中线阵像机的像（以下称为底像机）的视场中都能够观测到飞行过双像器上方的弹丸。前像机和底像机组成了立体数字狭缝测量系统中的立体线阵像机，立体线阵像机获得的一幅图像包括前像机的图像和底像机的图像，记录了弹丸在两个方向上的成像结果，本发明称之为弹丸的立体线阵图像。 Place a dual-image device made of a rectangular plane mirror directly below the trajectory of the projectile after it exits the chamber at 2-3 meters near the gun mouth. Place a line-scan camera so that the main optical axis of the line-scan camera is approximately 45° into the plane mirror of the double-imager. Adjust the focal length of the line-scan camera so that the flying can be observed in the field of view of the placed line-scan camera (hereinafter referred to as the front camera) and the image of the line-scan camera in the dual-imager (hereinafter referred to as the bottom camera). projectile over the binoculars. The front camera and the bottom camera constitute the stereo line camera in the stereo digital slit measurement system. One image obtained by the stereo line camera includes the image of the front camera and the image of the bottom camera, recording the projectile in the The imaging results in two directions are called the three-dimensional line array image of the projectile in the present invention. the

立体数字狭缝测量系统的布置如附图2所示。 The layout of the three-dimensional digital slit measurement system is shown in Figure 2. the

第二步，确定立体线阵像机的成像模型。 The second step is to determine the imaging model of the stereo line camera. the

为了描述立体数字狭缝测量系统的空间关系，定义3个坐标系： In order to describe the spatial relationship of the stereo digital slit measurement system, three coordinate systems are defined:

靶场坐标系o_p-x_py_pz_p：以靶场的基准点作为坐标系的原点o_p，弹丸弹道方向为坐标轴x_p的正方向，垂直于靶场地地面向上的方向为坐标轴z_p的正方向，o_p-x_py_p平面与坐标轴z_p构成右手系。靶场坐标系是测量坐标系，前像机和底像机的外方位元素和弹丸的运动参数都在靶场坐标系中定义。 Shooting range coordinate system o _p -x _p y _p z _p : take the reference point of the shooting range as the origin of the coordinate system o _p , the projectile trajectory direction is the positive direction of the coordinate axis x _p , and the upward direction perpendicular to the ground of the shooting range is the coordinate axis z The positive direction of _p , the o _p -x _p y _p plane and the coordinate axis z _p form a right-handed system. The shooting range coordinate system is a measurement coordinate system, and the outer orientation elements of the front camera and the bottom camera and the motion parameters of the projectile are all defined in the shooting range coordinate system.

前像机像空间坐标系o_f-x_fy_fz_f：以前像机的摄影中心作为原点o_f，顺着弹丸飞行方向并垂直于前像机的线阵传感器的方向为x_f轴正方向，沿着线阵传感器向下的方向为y_f轴正方向，沿着主光轴朝向目标的方向为z_f轴的正方向，o_f-x_fy_f平面与坐标轴z_f构成右手系，如附图2所示。 The front camera image space coordinate system o _f -x _f y _f z _f : the center of photography of the front camera is taken as the origin o _f , and the direction along the flight direction of the projectile and perpendicular to the line array sensor of the front camera is the positive x _f axis direction, the downward direction along the line array sensor is the positive direction of the y _f axis, the direction along the main optical axis towards the target is the positive direction of the z _f axis, and the o _f -x _f y _f plane and the coordinate axis z _f constitute the right hand system, as shown in Figure 2.

底像机像空间坐标系o_b-x_by_bz_b：根据镜面对称原理，底像机像空间坐标系是前像机像空间坐标系的镜面对称像。 Bottom camera image space coordinate system o _b _-x by y _b z _b : According to the principle of mirror symmetry, the bottom camera image space coordinate system is the mirror image of the front camera image space coordinate system.

立体线阵像机的成像模型包括前像机的成像模型和底像机的成像模型。确定立体线阵像机的成像模型的具体步骤如下: The imaging model of the stereoscopic line scan camera includes the imaging model of the front camera and the imaging model of the bottom camera. The specific steps for determining the imaging model of the stereo line scan camera are as follows:

第1步，分别确定前像机和底像机的内方位元素和外方位元素。 The first step is to determine the inner orientation elements and outer orientation elements of the front camera and the bottom camera respectively. the

进行前像机的标定，得到前像机的内方位元素和外方位元素。前像机的内方位元素包括前像机的焦距f，像主点偏移量y₀；外方位元素包括前像机的位置参数（用摄影中心的坐标o_f(X_s,Y_s,Z_s)表示）和姿态参数（用前像机像空间坐标系与靶场坐标系的坐标轴之间旋转过的角度

ω_f，κ_f表示）。量取双像器在靶场坐标系中确定的位置坐标，根据双像器在靶场坐标系中摆放位置和姿态，确定双像器的平面镜所在平面在靶场坐标系中的方程表达式。 Carry out the calibration of the front camera to obtain the inner and outer orientation elements of the front camera. The inner orientation element of the front camera includes the focal length f of the front camera and the offset of the principal point y ₀ ; the outer orientation element includes the position parameters of the front camera (using the coordinates o _f of the photography center (X _s , Y _s , Z _s )) and attitude parameters (rotated angles between the coordinate axes of the front camera image space coordinate system and the shooting range coordinate system

ω _f , κ _f represents). Measure the position coordinates of the dual imager in the shooting range coordinate system, and determine the equation expression of the plane where the plane mirror of the dual imager is located in the shooting range coordinate system according to the position and attitude of the dual imager in the shooting range coordinate system.

底像机的内方位元素与前像机相同，根据前像机和底像机的镜面对称关系，计算出底像机的外方位元素，包括位置参数（用底像机摄影中心的坐标o_b(X′_s,Y′_s,Z′_s)表示）和姿态参数（用底像机像空间坐标系与靶场坐标系的坐标轴之间旋转过的角度

ω_b，κ_b表示）。 The inner orientation elements of the bottom camera are the same as those of the front camera, and the outer orientation elements of the bottom camera are calculated according to the mirror symmetry relationship between the front camera and the bottom camera, including position parameters (using the coordinates o _b of the photography center of the bottom camera (X′ _s , Y′ _s , Z′ _s )) and attitude parameters (use the rotated angle between the coordinate system of the image space coordinate system of the base camera and the coordinate axis of the shooting range coordinate system

ω _b , κ _b represents).

第2步，分别确定前像机和底像机的成像模型表达式。 The second step is to determine the imaging model expressions of the front camera and the bottom camera respectively. the

假设P(X,Y,Z)为靶场坐标系中落在o_f-y_fz_f平面上的任意一点，点P(X,Y,Z)与其对应的前像机成像点p(x,y)之间的成像几何关系，即前像机的成像模型表示为： Assuming that P(X,Y,Z) is any point falling on the o _f -y _f z _f plane in the shooting range coordinate system, the point P(X,Y,Z) and its corresponding front camera imaging point p(x, y), that is, the imaging model of the front camera is expressed as:

$\{\begin{matrix} x x = = 00 = = {a a}_{11} ((X x - - {X x}_{S S})) + + {b b}_{11} ((Y Y - - {Y Y}_{S S})) + + {c c}_{11} ((Z Z - - {Z Z}_{S S})) \\ y the y = = {y the y}_{00} = = - - f f \cdot \cdot \frac{{a a}_{22} ((X x - - {X x}_{S S})) + + {b b}_{22} ((Y Y - - {Y Y}_{S S})) + + {c c}_{22} ((Z Z - - {Z Z}_{S S}))}{{a a}_{33} ((X x - - {X x}_{S S})) + + {b b}_{33} ((Y Y - - {Y Y}_{S S})) + + {c c}_{33} ((Z Z - - {Z Z}_{S S}))} \end{matrix}$

其中，a_i,b_i,c_i(i＝1,2,3)是与前像机姿态参数

ω_f，κ_f有关的9个元素，表示为： Among them, a _i , b _i , c _i (i=1,2,3) are the attitude parameters of the front camera

ω _f , 9 elements related to κ _f , expressed as:

同理，点P(X,Y,Z)与其对应的底像机成像点p′(x,y)之间的成像几何关系，即底像机的成像模型表示为： Similarly, the imaging geometric relationship between the point P(X, Y, Z) and its corresponding base camera imaging point p′(x, y), that is, the imaging model of the base camera is expressed as:

$\{\begin{matrix} x x = = 00 = = {a a}_{11}^{' '} ((X x - - {X x}_{S S}^{' '})) + + {b b}_{11}^{' '} (({Y Y}^{' '} - - {Y Y}_{S S})) + + {c c}_{11}^{' '} ((Z Z - - {Z Z}_{S S}^{' '})) \\ y the y - - {y the y}_{00} = = - - f f \cdot &Center Dot; \frac{{a a}_{22}^{' '} ((X x - - {X x}_{S S}^{' '})) + + {b b}_{22}^{' '} ((Y Y - - {Y Y}_{S S}^{' '})) + + {c c}_{22}^{' '} ((Z Z - - {Z Z}_{S S}^{' '}))}{{a a}_{33}^{' '} ((X x - - {X x}_{S S}^{' '})) + + {b b}_{33}^{' '} ((Y Y - - {Y Y}_{S S}^{' '})) + + {c c}_{33}^{' '} ((Z Z - - {Z Z}_{S S}^{' '}))} \end{matrix}$

其中，a′_i,b′_i′,c′_i(i＝1,2,3)是与底像机姿态参数

ω_b，κ_b有关的9个元素，表示方式与前像机中相同。 Among them, a′ _i , b′ _i ′, c′ _i (i=1,2,3) are the attitude parameters of the bottom camera

ω _b , 9 elements related to κ _b , expressed in the same way as in the front camera.

第三步，测量弹丸的运动参数。 The third step is to measure the motion parameters of the projectile. the

本发明在测量弹丸运动参数时，首先选取弹丸立体线阵图像中的特征点，计算运动参数的初始估计值，然后通过基于弹丸三维数字模型的运动参数优化求解模型，进一步得到弹丸运动参数的优化估计值。具体过程可以分为两个步骤： When measuring projectile motion parameters, the present invention firstly selects the feature points in the three-dimensional line array image of the projectile, calculates the initial estimated value of the motion parameters, and then obtains the optimization of the projectile motion parameters by optimizing the motion parameters based on the three-dimensional digital model of the projectile to solve the model estimated value. The specific process can be divided into two steps:

第1步，选择特征点，计算弹丸运动参数的初始估计值。 Step 1, select the feature points and calculate the initial estimated value of the projectile motion parameters. the

选取运动弹丸弹尖A、弹尾B在立体线阵图像中对应的成像点a和a′、b和b′作为特征点（如附图2）。假设弹丸的速度矢量V(V_x,V_y,V_z)，把前像机拍摄到弹丸弹尖时刻作为初始时刻，假设此时弹尖的空间坐标A(X_a,Y_a,Z_a)，弹丸的中轴线矢量L(L_x,L_y，L_z)，则此时弹尾的空间坐标为B(X_a-L_x,Y_a-L_y,Z_a-L_z)。弹丸的速度、姿态和位置参数就可以通过V_x,V_y,V_z,X_a,Y_a,Z_a,L_x,L_y,L_z9个参数来描述。通过弹丸弹尖、弹尾在立体线阵图像中的成像关系，构建关于这9个参数的方程式。 Select the imaging points a, a', b, and b' corresponding to the moving projectile's tip A and tail B in the three-dimensional line array image as feature points (see Figure 2). Assuming the velocity vector V(V _x ,V _y ,V _z ) of the projectile, the moment when the front camera captures the tip of the projectile is taken as the initial moment, assuming the spatial coordinates A(X _a ,Y _a ,Z _a ) of the projectile at this time , the central axis vector L(L _x ,L _y ,L _z ) of the projectile, then the spatial coordinates of the bullet tail at this time are B(X _a -L _x ,Y _a -L _y ,Z _a -L _z ). The velocity, attitude and position parameters of the projectile can be described by 9 parameters V _x , V _y , V _z , X _a , Y _a , Z _a , L _x , Ly _y , L _z . According to the imaging relationship of the projectile tip and tail in the three-dimensional line array image, the equations about these 9 parameters are constructed.

假设前像机拍摄到弹丸弹尖的时刻为0，根据前像机成像模型，有： Assuming that the moment when the front camera captures the projectile tip is 0, according to the front camera imaging model, there are:

$\{\begin{matrix} a_{1} (X_{a} - X_{S}) + b_{1} (Y_{a} - Y_{S}) + c_{1} (Z_{a} - Z_{S}) = 0 \\ y_{a} - y_{0} = - f \cdot \frac{a_{2} (X_{a} - X_{S}) + b_{2} (Y_{a} - Y_{S}) + c_{2} (Z_{a} - Z_{S})}{a_{3} (X_{a} - X_{S}) + b_{3} (Y_{a} - Y_{S}) + c_{3} (Z_{a} - Z_{S})} \end{matrix}$ （方程1和方程2） $\{\begin{matrix} a_{1} (x_{a} - x_{S}) + b_{1} (Y_{a} - Y_{S}) + c_{1} (Z_{a} - Z_{S}) = 0 \\ {the y}_{a} - {the y}_{0} = - f \cdot \frac{a_{2} (x_{a} - x_{S}) + b_{2} (Y_{a} - Y_{S}) + c_{2} (Z_{a} - Z_{S})}{a_{3} (x_{a} - x_{S}) + b_{3} (Y_{a} - Y_{S}) + c_{3} (Z_{a} - Z_{S})} \end{matrix}$ (Equation 1 and Equation 2)

其中，y_a为此时弹尖成像点在的y_f方向上的坐标。 Among them, y _a is the coordinate of the imaging point of the projectile tip in the y _f direction at this time.

假设底像机拍摄到弹丸弹尖的时刻为t₁，根据底像机的成像模型，有： Assuming that the moment when the base camera captures the tip of the projectile is t ₁ , according to the imaging model of the base camera, there are:

$\{\begin{matrix} a_{1}^{'} (X_{a} + V_{x} t_{1} - X_{S}^{'}) + b_{1}^{'} (Y_{a} + V_{y} t_{1} - Y_{S}^{'}) + c_{1}^{'} (Z_{a} + V_{z} t_{1} - Z_{S}^{'}) = 0 \\ y_{a^{'}} - y_{0} = - f \cdot \frac{a_{2}^{'} (X_{a} + V_{x} t_{1} - X_{S}^{'}) + b_{2}^{'} (Y_{a} + V_{y} t_{1} - Y_{S}^{'}) + c_{2}^{'} (Z_{a} + V_{z} t_{1} - Z_{S}^{'})}{a_{3}^{'} (X_{a} + V_{x} t_{1} - X_{S}^{'}) + b_{3}^{'} (Y_{a} + V_{y} t_{1} - Y_{S}^{'}) + c_{3}^{'} (Z_{a} + V_{z} t_{1} - Z_{S}^{'})} \end{matrix}$ （方程3和方程4） $\{\begin{matrix} a_{1}^{'} (x_{a} + V_{x} t_{1} - x_{S}^{'}) + b_{1}^{'} (Y_{a} + V_{the y} t_{1} - Y_{S}^{'}) + c_{1}^{'} (Z_{a} + V_{z} t_{1} - Z_{S}^{'}) = 0 \\ {the y}_{a^{'}} - {the y}_{0} = - f &Center Dot; \frac{a_{2}^{'} (x_{a} + V_{x} t_{1} - x_{S}^{'}) + b_{2}^{'} (Y_{a} + V_{the y} t_{1} - Y_{S}^{'}) + c_{2}^{'} (Z_{a} + V_{z} t_{1} - Z_{S}^{'})}{a_{3}^{'} (x_{a} + V_{x} t_{1} - x_{S}^{'}) + b_{3}^{'} (Y_{a} + V_{the y} t_{1} - Y_{S}^{'}) + c_{3}^{'} (Z_{a} + V_{z} t_{1} - Z_{S}^{'})} \end{matrix}$ (Equation 3 and Equation 4)

其中，y_a′为此时弹尖成像点在y_b方向上的坐标。 Among them, y _a' is the coordinate of the imaging point of the projectile tip in the direction of y _b at this time.

假设前像机拍摄到弹丸弹尾的时刻为t₂，根据前像机成像模型，有： Assuming that the moment when the front camera captures the tail of the projectile is t ₂ , according to the imaging model of the front camera, there are:

$\{\begin{matrix} {a a}_{11} (({X x}_{a a} - - {L L}_{x x} + + {V V}_{x x} {t t}_{22} - - {X x}_{S S})) + + {b b}_{11} (({Y Y}_{a a} - - {L L}_{y the y} + + {V V}_{y the y} {t t}_{22} - - {Y Y}_{S S})) + + {c c}_{11} (({Z Z}_{a a} - - {L L}_{z z} + + {V V}_{z z} {t t}_{22} - - {Z Z}_{S S})) = = 00 \\ {y the y}_{b b} - - {y the y}_{00} = = - - f f \cdot &Center Dot; \frac{{a a}_{22} (({X x}_{a a} - - {L L}_{x x} + + {V V}_{x x} {t t}_{22} - - {X x}_{S S})) + + {b b}_{22} (({Y Y}_{a a} - - {L L}_{y the y} + + {V V}_{y the y} {t t}_{22} - - {Y Y}_{S S})) + + {c c}_{22} (({Z Z}_{a a} - - {L L}_{z z} + + {V V}_{z z} {t t}_{22} - - {Z Z}_{S S}))}{{a a}_{33} (({X x}_{a a} - - {L L}_{x x} + + {V V}_{x x} {t t}_{22} - - {X x}_{S S})) + + {b b}_{33} (({Y Y}_{a a} - - {L L}_{y the y} + + {V V}_{y the y} {t t}_{22} - - {Y Y}_{S S})) + + {c c}_{33} (({Z Z}_{a a} - - {L L}_{z z} + + {V V}_{z z} {t t}_{22} - - {Z Z}_{S S}))} \end{matrix}$

（方程5和方程6） (Equation 5 and Equation 6)

其中，y_b为此时弹尾成像点在y_f方向上的坐标。 Among them, y _b is the coordinate of the imaging point of the missile tail in the y _f direction at this time.

假设底像机拍摄到弹丸弹尾的时刻为t3，根据底像机的成像模型，有： Assuming that the moment when the base camera captures the tail of the projectile is t3, according to the imaging model of the base camera, there are:

$\{\begin{matrix} {a a}_{11}^{' '} (({X x}_{a a} - - {L L}_{x x} + + {V V}_{x x} {t t}_{33} - - {X x}_{S S}^{' '})) + + {b b}_{11}^{' '} (({Y Y}_{a a} - - {L L}_{y the y} + + {V V}_{y the y} {t t}_{33} - - {Y Y}_{S S}^{' '})) + + {c c}_{11}^{' '} (({Z Z}_{a a} - - {L L}_{z z} + + {V V}_{z z} {t t}_{33} - - {Z Z}_{S S}^{' '})) = = 00 \\ {y the y}_{{b b}^{' '}} - - {y the y}_{00} = = - - f f \cdot &Center Dot; \frac{{a a}_{22}^{' '} (({X x}_{a a} - - {L L}_{x x} + + {V V}_{x x} {t t}_{33} - - {X x}_{S S}^{' '})) + + {b b}_{22}^{' '} (({Y Y}_{a a} - - {L L}_{y the y} + + {V V}_{y the y} {t t}_{33} - - {Y Y}_{S S}^{' '})) + + {c c}_{22}^{' '} (({Z Z}_{a a} - - {L L}_{z z} + + {V V}_{z z} {t t}_{33} - - {Z Z}_{S S}^{' '}))}{{a a}_{33}^{' '} (({X x}_{a a} - - {L L}_{x x} + + {V V}_{x x} {t t}_{33} - - {X x}_{S S}^{' '})) + + {b b}_{33}^{' '} (({Y Y}_{a a} - - {L L}_{y the y} + + {V V}_{y the y} {t t}_{33} - - {Y Y}_{S S}^{' '})) + + {c c}_{33}^{' '} (({Z Z}_{a a} - - {L L}_{z z} + + {V V}_{z z} {t t}_{33} - - {Z Z}_{S S}^{' '}))} \end{matrix}$

（方程7和方程8） (Equation 7 and Equation 8)

其中，y_b′为此时弹尾成像点在y_b方向上的坐标。 Among them, y _{b' is} the coordinates of the imaging point of the missile tail in the direction of y _b at this time.

通过弹尖、弹尾成像点在x_f(x_b)方向上相对a点的像素点覆盖数，结合前像机的扫描频率，可以得到t₁,t₂,t₃。这样，通过弹尖、弹尾在立体线阵图像上所形成的4个成像点，共可以得到关于弹丸运动参数的8个方程。 According to the number of pixels covered by the tip and tail imaging points relative to point a in the x _f (x _b ) direction, combined with the scanning frequency of the front camera, t ₁ , t ₂ , t ₃ can be obtained. In this way, through the four imaging points formed by the tip and the tail of the projectile on the three-dimensional line array image, a total of 8 equations about the motion parameters of the projectile can be obtained.

另外，弹丸的长度L是已知的，且： Additionally, the length L of the projectile is known and:

L_x ²+L_y ²+L_z ²＝L² （方程9） L _x ² +L _y ² +L _z ² =L ² (Equation 9)

综上，可以得到关于弹丸9个运动参数的9个方程。前8个方程是线性方程，最后一个是非线性方程。其中，L_x,V_x都为正数，以此为约束条件可以得到唯一解。求解这9个方程，得到弹丸运动参数初始估计值。 In summary, 9 equations about the 9 motion parameters of the projectile can be obtained. The first 8 equations are linear equations and the last one is nonlinear equation. Among them, L _x and V _x are both positive numbers, and a unique solution can be obtained by taking this as a constraint condition. Solve these 9 equations to get the initial estimate of projectile motion parameters.

第2步，构建基于弹丸三维数字模型的运动参数优化求解模型，计算弹丸运动参数的优化估计值。 The second step is to construct a motion parameter optimization solution model based on the three-dimensional digital model of the projectile, and calculate the optimal estimated value of the projectile motion parameters. the

根据已知的弹丸外形数据，利用3D MAX软件建立弹丸三维数字模型，根据立体线阵像机的成像模型，仿真生成弹丸的三维数字模型在弹丸运动参数初始估计值情况下的理论模拟成像结果。通过比较理论模拟成像结果的边缘梯度信息与立体线阵像机拍摄的实测图像中弹丸图像的边缘梯度信息之间的差异，构建以弹丸运动参数为输入值的优化求解模型。优化求解模型通过不断修正弹丸运动参数输入值（优化求解模型的初始输入值设定为弹丸运动参数初始估计值），使得弹丸三维数字模型的理论模拟成像结果与立体线阵像机拍摄的实测图像中弹丸图像实现最优化匹配，并将此时的弹丸运动参数输入值作为弹丸运动参数的优化估计值。本发明的有益效果：本发明采用线阵像机标定的方法确定立体线阵像机的成像模型，既保证了立体数字狭缝测量系统空间关系的精确性，又克服了线阵像机由于扫描频率低而无法实现弹道同步的困难。通过基于弹丸三维数字模型的运动参数优化求解模型计算弹丸的运动参数，减少了传统方法中仅采用有限个特征点计算弹丸运动参数存在的不稳定性，提高了弹丸运动参数测量的精度。 According to the known shape data of the projectile, the 3D digital model of the projectile is established by using 3D MAX software, and the theoretical simulation imaging results of the 3D digital model of the projectile under the condition of the initial estimated value of the projectile motion parameters are generated by simulation according to the imaging model of the stereo line camera. By comparing the difference between the edge gradient information of the theoretical simulation imaging results and the edge gradient information of the projectile image in the measured image captured by the stereo line scan camera, an optimal solution model with projectile motion parameters as input values was constructed. The optimal solution model continuously corrects the input value of the projectile motion parameters (the initial input value of the optimal solution model is set as the initial estimated value of the projectile motion parameter), so that the theoretical simulation imaging results of the three-dimensional digital model of the projectile are consistent with the measured images taken by the three-dimensional line scan camera. The projectile image in the middle is optimized for matching, and the input value of the projectile motion parameter at this time is used as the optimal estimated value of the projectile motion parameter. Beneficial effects of the present invention: the present invention adopts the calibration method of the line array camera to determine the imaging model of the three-dimensional line array camera. The difficulty of synchronizing ballistics due to the low frequency. The motion parameters of the projectile are calculated by optimizing the solution model of the motion parameters based on the three-dimensional digital model of the projectile, which reduces the instability of the traditional method of calculating the motion parameters of the projectile by only using a limited number of feature points, and improves the accuracy of the measurement of the motion parameters of the projectile. the

附图说明 Description of drawings

图1是本发明提供的基于数字狭缝摄像技术的靶场弹丸运动参数测量方法的原理流程示意图； Fig. 1 is the schematic flow chart of the principle of the shooting range projectile motion parameter measurement method based on the digital slit camera technology provided by the present invention;

图2是本发明所述的立体数字狭缝测量系统示意图； Fig. 2 is a schematic diagram of a three-dimensional digital slit measurement system of the present invention;

图3是弹丸运动参数优化求解模型构建的示意图； Fig. 3 is a schematic diagram of projectile motion parameter optimization solution model construction;

图4是弹丸三维数字模型及其构成三角形面片示意图； Figure 4 is a schematic diagram of the three-dimensional digital model of the projectile and its triangular facets;

图5是弹丸三维数字模型理论模拟成像示意图； Fig. 5 is a schematic diagram of the theoretical simulation imaging of the three-dimensional digital model of the projectile;

图6是t_n时刻理论模拟成像示意图。 Fig. 6 is a schematic diagram of theoretical simulation imaging at time t _n .

具体实施方式Detailed ways

下面结合附图对本发明作进一步说明。 The present invention will be further described below in conjunction with accompanying drawing. the

图1是本发明提供的基于数字狭缝摄像技术的靶场弹丸运动参数测量方法的某一具体实施例的原理示意图。如图所示，本发明的技术方案包括以下三步：第一步，布置立体数字狭缝测量系统；第二步，确定立体线阵像机成像模型；第三步，测量弹丸的运动参数。 Fig. 1 is a principle schematic diagram of a specific embodiment of a method for measuring projectile motion parameters in a shooting range based on digital slit camera technology provided by the present invention. As shown in the figure, the technical solution of the present invention includes the following three steps: the first step is to arrange the three-dimensional digital slit measurement system; the second step is to determine the imaging model of the three-dimensional line array camera; the third step is to measure the motion parameters of the projectile. the

需要再说明的以下两点是： The following two points need to be explained:

第一点，线阵传感器的标定以及成像模型 The first point, the calibration and imaging model of the line array sensor

本发明中采用的是线阵像机作为摄影测量的工具。线阵像机采用线阵传感器作为图像采集元器件，线阵传感器可以看做是面阵传感器的一种特例，因此其成像模型也可以从面阵传感器的成像模型引申而来，成像模型中包含了传感器的内方位元素和外方位元素，这些方位元素是通过线阵传感器的标定来获取的。线阵传感器的标定以及成像模型的描述具体参见：C.A.Luna,M.Mazo,et al，Calibration of Line-Scan Cameras,IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT,2010,59,(8),pp.2185–2190. What adopted in the present invention is the line array camera as the tool of photogrammetry. A line array camera uses a line array sensor as an image acquisition component. The line array sensor can be regarded as a special case of an area array sensor, so its imaging model can also be derived from the imaging model of an area array sensor. The imaging model includes The inner orientation elements and outer orientation elements of the sensor are defined, and these orientation elements are obtained through the calibration of the linear array sensor. For the calibration of the line array sensor and the description of the imaging model, see: C.A.Luna, M.Mazo, et al, Calibration of Line-Scan Cameras, IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, 2010, 59, (8), pp.2185–2190 .

第二点，优化求解模型的求解 The second point is to optimize the solution of the solution model

在本发明的第三步中的第2步，构建基于弹丸三维数字模型的运动参数优化求解模型，计算弹丸运动参数的优化估计值。参照附图3，具体过程为： In the second step of the third step of the present invention, a motion parameter optimization solution model based on the three-dimensional digital model of the projectile is constructed, and an optimal estimated value of the projectile motion parameter is calculated. Referring to accompanying drawing 3, the specific process is:

第（1）步，理论模拟成像 Step (1), theoretical simulation imaging

根据立体线阵像机的成像模型、弹丸的三维数字模型和弹丸运动参数的初始估计值生成弹丸三维数字模型的理论模拟成像结果，具体过程是： Generate the theoretical simulation imaging results of the three-dimensional digital model of the projectile based on the imaging model of the stereo line camera, the three-dimensional digital model of the projectile and the initial estimated value of the projectile motion parameters. The specific process is as follows:

1）、根据已知的弹丸的外形几何参数，在3D MAX三维建模软件中，构建弹丸的三维数字模型，如附图4的左图所示。 1) According to the known shape and geometric parameters of the projectile, in the 3D MAX three-dimensional modeling software, construct the three-dimensional digital model of the projectile, as shown in the left figure of attached drawing 4. the

2）、将三维数字模型数据保存，并以3DS格式文件形式导出。在3D MAX中构建的三维数字模型的结构是由许多三角形面片拼接而成，如附图4的右图所示。弹丸目标三维结构的所有信息，如目标的名称，顶点坐标，映射坐标，多边形列表，表面的颜色等等都包含在3DS文件。编写3DS文件读取程序，读取弹丸三维数字模型所有的顶点、线段以及它们构成三角形面片的数据列表。 2) Save the 3D digital model data and export it as a 3DS format file. The structure of the 3D digital model built in 3D MAX is composed of many triangle faces, as shown in the right figure of attached drawing 4. All information about the 3D structure of the projectile target, such as the name of the target, vertex coordinates, mapping coordinates, polygon list, surface color, etc. are contained in the 3DS file. Write a 3DS file reading program to read all the vertices and line segments of the projectile 3D digital model and the data list of their triangular faces. the

3）、根据3D MAX建模的特点，弹丸三维数字模型由许多个小三角形拼接而成，以底像机的成像为例，视平面与弹丸三维数字模型相交的结果是一系列由切面与三维数字模型的小三角形的边的相交点。如附图5所示，ΔABC是被切面切过的小三角形，切面与三角形的两条边AB和BC的交点分别为P1,P2。 3) According to the characteristics of 3D MAX modeling, the three-dimensional digital model of the projectile is composed of many small triangles. Taking the imaging of the base camera as an example, the result of the intersection of the viewing plane and the three-dimensional digital model of the projectile is a series of cut planes and three-dimensional The point where the sides of the small triangles of the digital model intersect. As shown in Fig. 5, ΔABC is a small triangle cut by the cut plane, and the intersection points of the cut plane and the two sides AB and BC of the triangle are P1 and P2 respectively. the

在t_n时刻，弹丸三维数字模型的所有与x_f＝0平面相交的三角形的交点为Pi(1,2,3...)，经过中心投影落到像片上，成像点y_f坐标的集合为[pl.y,p2.y,p3.y...]，比较之后，选取集合中最大值，定义为nymax，选取集合中最小值，定义为nymin（如附图6所示），连接最大、最小值点获得的成像条带l_n即为本模拟的成像。 At time t _n , the intersection point of all the triangles intersecting the x _f =0 plane of the three-dimensional digital model of the projectile is Pi(1,2,3...), which falls on the photo through the central projection, and the set of coordinates of the imaging point y _f is [pl.y, p2.y, p3.y...], after comparison, select the maximum value in the set, defined as nymax, select the minimum value in the set, defined as nymin (as shown in Figure 6), connect The imaging strip l _n obtained at the maximum and minimum points is the imaging of this simulation.

模拟立体线阵像机的拍摄的过程，每次拍摄都会得到弹丸三维数字模型成像的线阵条带，当弹丸三维数字模型完全通过成像区域时，就可以得到整个弹丸三维数字模型的理论模拟成像结果。 Simulate the shooting process of the three-dimensional line-scan camera. Every time you take a shot, you will get the linear strip of the three-dimensional digital model of the projectile. When the three-dimensional digital model of the projectile completely passes through the imaging area, you can get the theoretical simulation imaging of the entire three-dimensional digital model of the projectile. result. the

第（2）步，构建优化求解模型 Step (2), build an optimization solution model

具体过程是： The specific process is:

1）、获得弹丸实际成像和理论模拟成像的梯度图 1) Obtain the gradient map of the actual imaging of the projectile and the theoretical simulation imaging

假设(x_i,y_j)，i＝1…N,j＝1…M是弹丸实际成像I的N×M个像素点。由于立体线阵图像是由一维扫描线组成，因此其梯度图是通过在一维方向上取梯度模来获得的，假设其梯度图为G，则： Assuming ( _xi , y _j ), i=1...N, j=1...M are the N×M pixels of the actual imaging I of the projectile. Since the three-dimensional line array image is composed of one-dimensional scanning lines, its gradient map is obtained by taking the gradient modulus in the one-dimensional direction. Assuming that its gradient map is G, then:

G(x_i,y_j)＝|I(x_i,y_j+1)-I(x_i,y_j)|,i＝1…N,j＝1…M-1 G(x _i ,y _j )=|I(x _i ,y _j+1 )-I(x _i ,y _j )|,i=1…N,j=1…M-1

假设(x′_i,y′_j),i＝1…N,j＝1…M是三维数字模型模拟成像I′的N×M个像素点。同理，假设其梯度图为G′，则： Suppose (x' _i , y' _j ), i=1...N, j=1...M are N×M pixels of the three-dimensional digital model simulation imaging I'. Similarly, assuming that its gradient map is G′, then:

G′(x′_i,y′_j)＝|I(x′_i,y′_j+1)-I(x′_i,y′_j)|,i＝1…N,j＝1…M-1 G′(x′ _i ,y′ _j )=|I(x′ _i ,y′ _j+1 )-I(x′ _i ,y′ _j )|,i=1…N,j=1…M- 1

2）、构建运动参数求解的最优化模型 2) Construct an optimization model for solving motion parameters

根据获得的梯度图，建立表征模拟成像与实际成像匹配关系的能量函数： According to the obtained gradient map, an energy function that characterizes the matching relationship between simulated imaging and actual imaging is established:

$ϵ ϵ = = {Σ Σ}_{i i = = 11}^{N N} {Σ Σ}_{j j = = 11}^{M m - - 11} {[[{G G}^{' '} (({x x}_{i i}^{' '},, {y the y}_{j j}^{' '})) - - G G (({x x}_{i i},, {y the y}_{j j}))]]}^{22}$

根据能量函数构建最优化模型： Build an optimization model based on the energy function:

$min min ϵ ϵ = = min min {{{Σ Σ}_{i i = = 11}^{N N} {Σ Σ}_{j j = = 11}^{M m - - 11} {[[{G G}^{' '} (({x x}_{i i}^{' '},, {y the y}_{j j}^{' '})) - - G G (({x x}_{i i},, {y the y}_{j j}))]]}^{22}}}$

最优化模型通过改变三维数字模型的运动参数(用向量X＝[X_a,Y_a,Z_a,V_x,V_y,V_z,L_x,L_y,L_z]表示)，来减小能量函数的值。当三维数字模型的运动参数使得能量函数值最小时，此时的运动参数即为最优化模型的解，也是弹丸运动参数的优化估计值。 The optimized model is reduced by changing the motion parameters of the three-dimensional digital model (expressed by vector X=[X _a , Y _a , Z _a , V _x , V _y , V _z , L _x , L _y , L _z ]). The value of the energy function. When the motion parameters of the three-dimensional digital model minimize the value of the energy function, the motion parameters at this time are the solution of the optimal model and the optimal estimated value of the motion parameters of the projectile.

第（3）步，优化模型求解 Step (3), optimization model solution

采用Powell算法求解最优化模型。具体过程是： The Powell algorithm is used to solve the optimization model. The specific process is:

1）将利用特征点求得的运动参数初始估计值作为最优化模型的初始值，设为X⁽⁰⁾，设定收敛阈值δ（收敛阈值δ的选取与测量需要得到的精度以及实际应用中对计算量的要求有关，对本领域的技术人员而言，如何确定该值是公知常识。），置k＝1，给定9个线性无关的方向，一般采用单位方向向量： 1) The initial estimated value of the motion parameters obtained by using the feature points is used as the initial value of the optimization model, and is set to X ⁽⁰⁾ , and the convergence threshold δ is set (the selection of the convergence threshold δ and the accuracy required for measurement and practical application It is related to the requirement of the amount of calculation, for those skilled in the art, how to determine this value is common knowledge.), set k=1, given 9 linearly independent directions, generally adopt the unit direction vector:

d^(1,1),d^(1,2),...d^(1,n),n＝1,...9； d ^(1,1) ,d ^(1,2) ,...d ^(1,n) ,n=1,...9;

2）置X^(k，0)＝X^(k-1)，从X^(k，0)出发，依次沿9个方向向量对能量函数ε进行一维搜索，得到X^(k，1)，X^(k，2),...,X^(k，n)； 2) Set X ^{(k, 0)} = X ^(k-1) , start from X ^{(k, 0)} , conduct a one-dimensional search on the energy function ε along nine direction vectors in sequence, and obtain X ^{(k, 1)} , X ^(k,2) ,...,X ^(k,n) ;

3）再沿着X^(k，n)出发，沿着方向d^(k，n+1)＝X^(k，n)-X^(k，0)对能量函数ε进行一维搜索，得到X^(k)。 3) Start along X ^{(k, n)} , and perform a one-dimensional search on the energy function ε along the direction d ^{(k, n+1)} = X ^{(k, n)} -X ^{(k, 0)} , and get X ^{( k)} .

4）若X^(k)-X^(k-1)||＜δ，则停止迭代，得到X^(k)；否则，令d^(k+1，j)＝d^(k，，j+1),j＝1,...,n，置k＝k+1，返回2）。 4) If X ^(k) -X ^(k-1) ||<δ, then stop the iteration and get X ^(k) ; otherwise, set d ^{(k+1, j)} = d ^{(k,, j+1)} ,j=1,...,n, set k=k+1, return 2).

初始估计值经过不断修正后的值X_a,Y_a,Z_a,V_x,V_y,V_z,L_x,L_y,L_z，即为我们所要优化求解的结果。在得到了弹丸的位置、姿态和速度三维矢量参数之后，就可以进一步得到弹丸的速度和攻角的大小。设速度为v，攻角为φ，则： The values X _a , Y _a , Z _a , V _x , V _y , V _z , L _x , L _y , and L _z of the initial estimated value after continuous correction are the results we want to optimize and solve. After obtaining the three-dimensional vector parameters of the projectile's position, attitude and velocity, the velocity and angle of attack of the projectile can be further obtained. Let the velocity be v and the angle of attack be φ, then:

$v v = = \sqrt{{V V}_{x x}^{22} + + {V V}_{y the y}^{22} + + {V V}_{z z}^{22}}$

本发明中弹丸运动参数是通过对优化求解模型的求解获得的，所述的Powell法参见：陈宝林，最优化理论与算法，清华大学出版社，1989，pp.420-422。

The motion parameters of the projectile in the present invention are obtained by solving the optimization solution model. For the Powell method, refer to: Chen Baolin, Optimization Theory and Algorithm, Tsinghua University Press, 1989, pp.420-422.

Claims

1. A shooting range projectile motion parameter measurement method based on digital slit camera technology, is characterized in that comprising the following steps:

The first step is to arrange the three-dimensional digital slit measurement system:

Place a dual-imager 2-3 meters near the gun mouth and directly below the trajectory of the projectile after it exits the bore. The mirror surface of the dual-imager is placed at 45o to the ground, and a line array imager is placed at a distance of 5-10 meters from the dual-imager. machine, so that the projectile flying above the dual imager can be observed in the field of view of the placed line array camera and the image of the line array imager in the dual imager; the line array camera is called the front camera, and the line array camera The image of the camera is called the bottom camera, the front camera and the bottom camera constitute the stereoscopic line array camera in the stereo digital slit measurement system, and the image obtained by the stereoscopic line array camera is called the stereoscopic line array image of the projectile;

The second step is to determine the imaging model of the stereo line scan camera:

Define the following three coordinate systems:

Shooting range coordinate system o _p -x _p y _p z _p : take the reference point of the shooting range as the origin of the coordinate system o _p , the projectile trajectory direction is the positive direction of the coordinate axis x _p , and the upward direction perpendicular to the ground of the shooting range is the coordinate axis z The positive direction of _p , the o _p -x _p y _p plane and the coordinate axis z _p form a right-handed system;

The front camera image space coordinate system o _f -x _f y _f z _f : the center of photography of the front camera is taken as the origin o _f , and the direction along the flight direction of the projectile and perpendicular to the line array sensor of the front camera is the positive x _f axis direction, the downward direction along the line array sensor is the positive direction of the y _f axis, the direction along the main optical axis towards the target is the positive direction of the z _f axis, and the o _f -x _f y _f plane and the coordinate axis z _f constitute the right hand Tie;

Bottom camera image space coordinate system o _b -x _b y _b z _b : According to the principle of mirror symmetry, the bottom camera image space coordinate system is the mirror symmetric image of the front camera image space coordinate system;

The specific steps for determining the imaging model of the stereo line scan camera are as follows:

Step 1, determine the inner orientation elements and outer orientation elements of the front camera and the bottom camera respectively;

Carry out the calibration of the front camera to obtain the inner orientation element and the outer orientation element of the front camera; the inner orientation element of the front camera includes the focal length f of the front camera, and the offset y ₀ of the principal point of the image; the outer orientation element includes the front image The position parameters of the camera are represented by the coordinates o _f (X _s , Y _s , Z _s ) of the camera center, and the attitude parameters are represented by the rotated angle between the coordinate axes of the front camera image space coordinate system and the shooting range coordinate system

ω _f , κ _f represent; measure the position coordinates determined by the dual imager in the shooting range coordinate system, and according to the position and attitude of the dual imager in the shooting range coordinate system, determine that the plane where the plane mirror of the dual imager is located is in the shooting range coordinate system The equation expression;

The inner orientation element of the bottom camera is the same as that of the front camera. According to the mirror symmetry relationship between the front camera and the bottom camera, the outer orientation element of the bottom camera is calculated, including the coordinates o _b ( X′ _s , Y′ _s , Z′ _s ), the attitude parameters are represented by the rotated angle between the coordinate system of the image space coordinate system of the base camera and the coordinate axis of the shooting range coordinate system

ω _b , κ _b means;

Step 2, respectively determine the imaging model expressions of the front camera and the bottom camera;

Assuming that P(X,Y,Z) is any point falling on the o _f -y _f z _f plane in the shooting range coordinate system, the point P(X,Y,Z) and its corresponding front camera imaging point p(x, y), that is, the imaging model of the front camera is expressed as:

\{\begin{matrix} x x = = 00 = = {a a}_{11} ((X x - - {X x}_{S S})) + + {b b}_{11} ((Y Y - - {Y Y}_{S S})) + + {c c}_{11} ((Z Z - - {Z Z}_{S S})) \\ y the y - - {y the y}_{00} = = - - f f \cdot \cdot \frac{{a a}_{22} ((X x - - {X x}_{S S})) + + {b b}_{22} ((Y Y - - {Y Y}_{S S})) + + {c c}_{22} ((Z Z - - {Z Z}_{S S}))}{{a a}_{33} ((X x - - {X x}_{S S})) + + {b b}_{33} ((Y Y - - {Y Y}_{S S})) + + {c c}_{33} ((Z Z - - {Z Z}_{S S}))} \end{matrix}

Among them, a _i , b _i , c _i , i=1, 2, 3 are the attitude parameters of the front camera

ω _f , 9 elements related to κ _f , expressed as:

Similarly, the imaging geometric relationship between the point P(X, Y, Z) and its corresponding base camera imaging point p′(x, y), that is, the imaging model of the base camera is expressed as:

\{\begin{matrix} x x = = 00 = = {a a}_{11}^{' '} ((X x - - {X x}_{S S}^{' '})) + + {b b}_{11}^{' '} (({Y Y}^{' '} - - {Y Y}_{S S})) + + {c c}_{11}^{' '} ((Z Z - - {Z Z}_{S S}^{' '})) \\ y the y - - {y the y}_{00} = = - - f f \cdot &Center Dot; \frac{{a a}_{22}^{' '} ((X x - - {X x}_{S S}^{' '})) + + {b b}_{22}^{' '} ((Y Y - - {Y Y}_{S S}^{' '})) + + {c c}_{22}^{' '} ((Z Z - - {Z Z}_{S S}^{' '}))}{{a a}_{33}^{' '} ((X x - - {X x}_{S S}^{' '})) + + {b b}_{33}^{' '} ((Y Y - - {Y Y}_{S S}^{' '})) + + {c c}_{33}^{' '} ((Z Z - - {Z Z}_{S S}^{' '}))} \end{matrix}

Among them, a′ _i , b′ _i , c′ _i , i=1, 2, 3 are the attitude parameters of the bottom camera ω _b , 9 elements related to κ _b , expressed in the same way as in the front camera;

The third step is to measure the motion parameters of the projectile:

Step 1, select the feature points and calculate the initial estimate of the projectile motion parameters:

Select the imaging points a, a', b, and b' corresponding to the tip and tail of the moving projectile in the three-dimensional linear array image as feature points; assuming the velocity vector V(V _x , V _y , V _z ) of the projectile, the front The moment when the camera captures the tip of the projectile is taken as the initial moment, assuming that the space coordinates A(X _a , Y _a , Z _a ) of the projectile tip at this time, and the central axis vector L(L _x ,L _y ,L _z ) of the projectile, then At this time, the spatial coordinates of _the bullet _tail are B( _X _a -L _x ,Y _a -L _y ,Z _a _-L _z ); Y _a , Z _a , L _x , L _y , L _z are described by 9 parameters; through the imaging relationship of the projectile tip and tail in the three-dimensional line array image, the equations about these 9 parameters are constructed;

Assuming that the moment when the front camera captures the projectile tip is 0, according to the front camera imaging model, there are:

\{\begin{matrix} a_{1} (x_{a} - x_{S}) + b_{1} (Y_{a} - Y_{S}) + c_{1} (Z_{a} - Z_{S}) = 0 \\ {the y}_{a} - {the y}_{0} = - f &Center Dot; \frac{a_{2} (x_{a} - x_{S}) + b_{2} (Y_{a} - Y_{S}) + c_{2} (Z_{a} - Z_{S})}{a_{3} (x_{a} - x_{S}) + b_{3} (Y_{a} - Y_{S}) + c_{3} (Z_{a} - Z_{S})} \end{matrix}

(Equation 1 and Equation 2)

Among them, y _a is the coordinate of the imaging point of the projectile tip in the y _f direction at this time;

Assuming that the moment when the base camera captures the tip of the projectile is t ₁ , according to the imaging model of the base camera, there are:

\{\begin{matrix} a_{1}^{'} (x_{a} + V_{x} t_{1} - x_{S}^{'}) + b_{1}^{'} (Y_{a} + V_{the y} t_{1} - Y_{S}^{'}) + c_{1}^{'} (Z_{a} + V_{z} t_{1} - Z_{S}^{'}) = 0 \\ {the y}_{a^{'}} - {the y}_{0} = - f \cdot \frac{a_{2}^{'} (x_{a} + V_{x} t_{1} - x_{S}^{'}) + b_{2}^{'} (Y_{a} + V_{the y} t_{1} - V_{S}^{'}) + c_{2}^{'} (Z_{a} + V_{z} t_{1} - Z_{S}^{'})}{a_{3}^{'} (x_{a} + V_{x} t_{1} - x_{S}^{'}) + b_{3}^{'} (Y_{a} + V_{the y} t_{1} - Y_{S}^{'}) + c_{3}^{'} (Z_{a} + V_{z} t_{1} - Z_{S}^{'})} \end{matrix}

(Equation 3 and Equation 4)

Among them, y _a' is the coordinate of the imaging point of the projectile tip in the direction of y _b at this time;

Assuming that the moment when the front camera captures the tail of the projectile is t ₂ , according to the imaging model of the front camera, there are:

\{\begin{matrix} {a a}_{11} (({X x}_{a a} - - {L L}_{x x} + + {V V}_{x x} {t t}_{22} - - {X x}_{S S})) + + {b b}_{11} (({Y Y}_{a a} {- - L L}_{y the y} + + {V V}_{y the y} {t t}_{22} - - {Y Y}_{S S})) + + {c c}_{11} (({Z Z}_{a a} - - {L L}_{z z} + + {V V}_{z z} {t t}_{22} - - {Z Z}_{S S})) = = 00 \\ {y the y}_{b b} - - {y the y}_{00} = = - - f f \cdot \cdot \frac{{a a}_{22} (({X x}_{a a} - - {L L}_{x x} + + {V V}_{x x} {t t}_{22} - - {X x}_{S S})) + + {b b}_{22} (({Y Y}_{a a} - - {L L}_{y the y} + + {V V}_{y the y} {t t}_{22} - - {Y Y}_{S S})) + + {c c}_{22} (({Z Z}_{a a} - - {L L}_{z z} + + {V V}_{z z} {t t}_{22} - - {Z Z}_{S S}))}{{a a}_{33} (({X x}_{a a} - - {L L}_{x x} + + {V V}_{x x} {t t}_{22} - - {X x}_{S S})) + + {b b}_{33} (({Y Y}_{a a} - - {L L}_{y the y} + + {V V}_{y the y} {t t}_{22} - - {Y Y}_{S S})) + + {c c}_{33} (({Z Z}_{a a} - - {L L}_{z z} + + {V V}_{z z} {t t}_{22} - - {Z Z}_{S S}))} \end{matrix}

(Equation 5 and Equation 6)

Wherein, y _b is the coordinates of the imaging point of the missile tail in the y _f direction at this time;

Assuming that the moment when the base camera captures the tail of the projectile is t ₃ , according to the imaging model of the base camera, there are:

\{\begin{matrix} {a a}_{11}^{' '} (({X x}_{a a} - - {L L}_{x x} + + {V V}_{x x} {t t}_{33} - - {X x}_{S S}^{' '})) + + {b b}_{11}^{' '} (({Y Y}_{a a} - - {L L}_{y the y} + + {V V}_{y the y} {t t}_{33} - - {Y Y}_{S S}^{' '})) + + {c c}_{11}^{' '} (({Z Z}_{a a} - - {L L}_{z z} + + {V V}_{z z} {t t}_{33} - - {Z Z}_{S S}^{' '})) = = 00 \\ {y the y}_{{b b}^{' '}} - - {y the y}_{00} = = - - f f \cdot \cdot \frac{{a a}_{22}^{' '} (({X x}_{a a} - - {L L}_{x x} + + {V V}_{x x} {t t}_{33} - - {X x}_{S S}^{' '})) + + {b b}_{22}^{' '} (({Y Y}_{a a} - - {L L}_{y the y} + + {V V}_{y the y} {t t}_{33} - - {Y Y}_{S S}^{' '})) + + {c c}_{22}^{' '} (({Z Z}_{a a} - - {L L}_{z z} + + {V V}_{z z} {t t}_{33} - - {Z Z}_{S S}^{' '}))}{{a a}_{33}^{' '} (({X x}_{a a} - - {L L}_{x x} + + {V V}_{x x} {t t}_{33} - - {X x}_{S S}^{' '})) + + {b b}_{33}^{' '} (({Y Y}_{a a} - - {L L}_{y the y} + + {V V}_{y the y} {t t}_{33} - - {Y Y}_{S S}^{' '})) + + {c c}_{33}^{' '} (({Z Z}_{a a} - - {L L}_{z z} + + {V V}_{z z} {t t}_{33} - - {Z Z}_{S S}^{' '}))} \end{matrix}

(Equation 7 and Equation 8)

Wherein, y _{b '} is the coordinates of the imaging point of the missile tail in the y _b direction at this time;

According to the number of pixels covered by the tip and tail imaging points in the direction of x _f (x _b ) relative to point a, combined with the scanning frequency of the front camera, t ₁ , t ₂ and t ₃ can be obtained; The 4 imaging points formed by the tail on the three-dimensional line array image can obtain 8 equations about the motion parameters of the projectile in total;

Additionally, the length L of the projectile is known and:

L _x ² +L _y ² +L _z ² =L ² (Equation 9)

In summary, 9 equations about the 9 motion parameters of the projectile can be obtained; by solving these 9 equations, the initial estimated value of the projectile motion parameters can be obtained;

The second step is to construct a motion parameter optimization solution model based on the three-dimensional digital model of the projectile, and calculate the optimal estimated value of the projectile motion parameters;

According to the known shape data of the projectile, use 3D MAX software to establish a three-dimensional digital model of the projectile, and according to the imaging model of the three-dimensional line array camera, simulate the theoretical simulation imaging results of the three-dimensional digital model of the projectile under the condition of the initial estimated value of the projectile motion parameters; By comparing the difference between the edge gradient information of the theoretical simulation imaging results and the edge gradient information of the projectile image in the measured image taken by the stereo line scan camera, an optimal solution model with projectile motion parameters as input values is constructed; Correct the input value of the projectile motion parameters, so that the theoretical simulation imaging results of the three-dimensional digital model of the projectile and the projectile image in the actual measurement image taken by the stereo line array camera achieve optimal matching, and the input value of the projectile motion parameters at this time is used as the projectile motion parameter. Optimize estimates.