WO2022022023A1 - 激光末制导飞行器组网控制方法 - Google Patents
激光末制导飞行器组网控制方法 Download PDFInfo
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
- G01S17/00—Systems using the reflection or reradiation of electromagnetic waves other than radio waves, e.g. lidar systems
- G01S17/86—Combinations of lidar systems with systems other than lidar, radar or sonar, e.g. with direction finders
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
- G01S17/00—Systems using the reflection or reradiation of electromagnetic waves other than radio waves, e.g. lidar systems
- G01S17/02—Systems using the reflection of electromagnetic waves other than radio waves
- G01S17/06—Systems determining position data of a target
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
- G01S7/00—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00
- G01S7/48—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S17/00
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- G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
- G01S7/00—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00
- G01S7/48—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S17/00
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Definitions
- the invention relates to a control method for a laser terminal guidance aircraft, in particular to a network control method for a laser terminal guidance aircraft.
- the basic working principle of the laser-guided aircraft is: at the end of the ballistic trajectory, the laser irradiator begins to illuminate the target, and the laser detector on the bomb detects the laser signal diffusely reflected by the target in real time; when the target enters the field of view of the detector, the laser detector can The deviation signal that deviates from the center of the field of view controls the corresponding pulse engine or steering gear, corrects the flight trajectory, achieves precise strikes on the target, and greatly improves the aircraft's point target killing ability.
- the present inventor has conducted in-depth research on the existing networking control methods, expecting to design a new networking control method for laser terminal-guided aircraft that can solve the above problems.
- the inventors have carried out keen research and designed a network control method for laser terminal guidance aircraft.
- the observation drone cruising in the target area cooperates with the lure aircraft to obtain target position information in a timely and accurate manner, and then guide the subsequent aircraft to fly to the target by emitting laser light from the observation drone, thereby completing the present invention.
- the purpose of the present invention is to provide the following aspects: a method for networking control of a laser terminal-guided aircraft, the method comprising the following steps:
- Step 1 Launch at least two aircraft 2 towards the target area through the launch unit 1, and the first aircraft arrives at the target area at least 5-10 seconds earlier than the other aircraft;
- step 2 the radar signal is captured by the radar signal receiving module 21 installed on the first aircraft, and the position information of the radar transmitting vehicle is obtained accordingly;
- Step 3 control the observation drone 3 to cruise in the target area in real time, and find the target by taking pictures of the target area in real time through the camera 31 installed on it;
- Step 4 the target is irradiated by the laser irradiator 32 installed on the observation drone 3 .
- the camera 31 on the observation UAV 3 takes pictures of the target before and after the landing of the aircraft, and transmits them to the command unit 4, so as to judge the landing point of the aircraft and the damage of the target.
- step 2 the first aircraft sends the obtained position information of the radar transmitting vehicle to the observation drone 3, so that the observation drone can find and lock the target.
- the first aircraft controls itself to fly to the radar transmitting vehicle;
- At least one of the other aircraft is guided by the laser irradiator 32 to fly towards the radar transmitting vehicle.
- each target is irradiated with a laser irradiator 32, and each laser irradiator 32 emits irradiation lasers of different frequencies.
- the command unit 4 calculates the accurate countdown information in real time, and controls the laser irradiator 32 to emit the irradiating laser 1-3 seconds before the aircraft enters the final guidance section according to the countdown information.
- step 3 includes the following sub-steps:
- Sub-step 1 the observation drone 3 continues to obtain photos of the target area through the camera 31 during the movement;
- Sub-step 3 converting the preprocessed image into a grayscale image
- Sub-step 4 establishes a transformation model according to the grayscale image, and the transformation model is used to convert the previous frame image in the adjacent two frame images into a matching image, and the background of the matching image is the same as the background of the current frame image;
- Sub-step 5 Calculate the target optical flow field according to the matching image and the current frame image, and then determine the target.
- establishing the transformation model includes the following sub-steps:
- x' represents the X-axis coordinate of a point in the matching image
- y' represents the Y-axis coordinate of a point in the matching image
- x represents the X-axis coordinate of a point in the previous frame of image
- y represents the Y-axis coordinate of a point in the previous frame of image
- Sub-sub-step b retrieve the current frame image and the previous frame image, and use the same method to divide the two frame images into multiple sub-blocks that do not completely overlap,
- Sub-sub-step c find the best matching block of each sub-block in the current frame image from the sub-blocks of the previous frame image;
- (x i , y i ) represents the center coordinates of the ith sub-block in the current frame image
- (x i , y i ) ' i , y' i ) represents the center coordinate of the best matching block of the i-th sub-block in one frame of image;
- Sub-step d use the least squares method to solve the conversion parameters in equation (1), as shown in the following equation (2):
- N represents the number of sub-blocks divided in the current frame image
- a sub-block in the current frame image is arbitrarily selected, and the gray of each sub-block in the previous frame image and all the pixel points of the sub-block in the current frame image are calculated one by one by formula (3).
- the sum of the absolute values of the degree difference, and the sub-block in the previous frame image with the smallest value is selected as the best matching block;
- I current block (m, n) represents the gray value of the pixel at position (m, n) in the image sub-block of the current frame
- I matching block (m, n) represents (m, n) in the image sub-block of the previous frame.
- n) the grayscale value of the pixel at the position
- p represents the number of pixels in the X-axis direction of the sub-block
- q represents the number of pixels in the Y-axis direction of the sub-block;
- E(p) represents the energy function in the matching image and the current frame image
- E m represents the optical flow constraint term
- E s represents the smooth constraint term
- ⁇ represents all areas of the current frame image
- the function f represents the position (x, y) of any pixel in the image at a certain moment, f x represents the partial derivative of the function f in the X-axis direction; f y represents the partial derivative of the function f in the Y-axis direction; f t represents the partial derivative of the function f at time t;
- u represents the velocity component of any pixel in the image in the X-axis direction
- v represents the velocity component of any pixel in the image in the Y-axis direction
- dx represents the differential symbol
- ⁇ is a positive number, which represents the weight of the smooth constraint term E m .
- the position information of the radar launch vehicle in the target area is captured by using the first aircraft as an inducing aircraft;
- the target position can be accurately and timely found and locked, and then the target position can be accurately and accurately detected by guiding the laser Control the subsequent aircraft to fly to the target.
- Fig. 1 shows the overall logic diagram of a network control method for a laser terminal-guided aircraft according to a preferred embodiment of the present invention
- FIG. 2 shows a schematic diagram of the signal connection relationship between various components in a method for controlling a laser terminal-guided aircraft network according to a preferred embodiment of the present invention
- FIG. 3 shows a schematic diagram of a motion trajectory in an embodiment of the present invention
- FIG. 4 shows a partial enlarged view of FIG. 3 .
- the targets targeted by the aircraft are often hidden under specific bunkers or camouflages, and it is difficult to find and lock the targets.
- different targets will have different stress responses.
- the radar car will send a radar signal when it enters the working state.
- the target is a command vehicle or an interceptor car, it will enter the working state. It will continue to maneuver at high speed, or change the station at predetermined intervals, and it is easier to detect when the target is moving from stationary to moving or from moving to stationary, and the radar vehicle is also easier to detect when it sends out detection radar.
- the present invention provides a network control method for a laser terminal-guided aircraft. As shown in FIG. 1 , the method includes the following steps:
- Step 1 Launch at least two aircraft 2 towards the target area through the launch unit 1, and the first aircraft arrives at the target area at least 5-10 seconds earlier than the other aircraft;
- step 2 the radar signal is captured by the radar signal receiving module 21 installed on the first aircraft, and the position information of the radar transmitting vehicle is obtained accordingly;
- Step 3 control the observation drone 3 to cruise in the target area in real time, and find the target by taking pictures of the target area in real time through the camera 31 installed on it;
- Step 4 the target is irradiated by the laser irradiator 32 installed on the observation drone 3 .
- the target area mentioned in this application refers to a larger area where the target may exist, generally a fan-shaped area of 3 ⁇ 10 to 3 ⁇ 20 km 2 .
- the plurality of aircraft can be launched at a predetermined time interval, or can be launched simultaneously and the time to reach the target area can be changed by adjusting their respective flight speeds.
- the first aircraft arrives at the target area 5 seconds earlier than the second aircraft, when When the aircraft reaches the target area, it is very likely to be discovered by the radar vehicle in the target area. After being discovered, it will cause a chain reaction. The enemy's interceptor vehicles and command vehicles are very likely to start moving, which will give the observation drone. Find the target to provide convenience.
- the radar signal receiving module can be selected from Zhang Jiaoyun. Research on Modeling and Simulation of Monopulse Radar Seeker [D]. Shaanxi: Xidian University, 2006. The radar signal receiving module introduced in Radar signal to find the location of the radar transmitter car.
- the observation drone can start cruising in the target area before the aircraft is launched. Due to the small size of the observation drone, it is difficult for the radar launch vehicle to find the observation drone. When the target is stationary and camouflaged, it is difficult for the observation drone to find the target.
- the step 3 includes the following sub-steps:
- Sub-step 1 the observation drone 3 continues to obtain the target area photo by the camera 31 during the moving process;
- Sub-step 2 pre-processing the photos obtained by the camera 31, specifically, reducing random noise through median filtering, and enhancing image clarity through image sharpening;
- Sub-step 3 converting the preprocessed image into a grayscale image
- Sub-step 4 establishes a transformation model according to the grayscale image, and the transformation model is used to convert the previous frame image in the adjacent two frame images into a matching image, and the background of the matching image is the same as the background of the current frame image;
- Sub-step 5 Calculate the target optical flow field according to the matching image and the current frame image, and then determine the target.
- establishing the transformation model includes the following sub-steps:
- x' represents the X-axis coordinate of a point in the matching image
- y' represents the Y-axis coordinate of a point in the matching image
- x represents the X-axis coordinate of a point in the previous frame of image
- y represents the Y-axis coordinate of a point in the previous frame of image
- Sub-sub-step b retrieve the current frame image and the previous frame image, and use the same rule to divide the two frame images into multiple complementary and partially overlapping sub-blocks,
- Sub-sub-step c find the best matching block of each sub-block in the current frame image from the sub-blocks of the previous frame image;
- (x i , y i ) represents the center coordinates of the ith sub-block in the current frame image
- (x i , y i ) ' i , y' i ) represents the center coordinate of the best matching block of the i-th sub-block in one frame of image;
- Sub-step d use the least squares method to solve the conversion parameters in equation (1), as shown in the following equation (2):
- N represents the number of sub-blocks divided in the current frame image
- the six parameters affect each other, so the combination of the optimal value of each parameter is not the global optimal solution; the iterative optimization of Equation 2 is carried out with the help of a computer.
- the solution method is to enumerate many groups (a, b, c, d, e, f) in the global scope, and substitute them into formula (2), and the group of parameters with the smallest output value is the optimal solution.
- the formula (1) can be used to convert the previous frame of image into a matching image.
- the method for dividing the sub-blocks is to obtain the overall number of pixels P ⁇ Q of the image, that is, there are P pixels in the X-axis direction of the rectangular image, and Q pixels in the Y-axis direction. pixel.
- the sub-blocks are also rectangular image blocks, and each sub-block has a total of P/10 pixels in the X-axis direction and Q/10 pixels in the Y-axis direction.
- the lower right corner pixel of the first sub-block coincides with the lower right corner pixel of the current frame image/previous frame image; the X-axis between the lower right corner pixel of the second sub-block and the lower right corner pixel of the first sub-block
- the interval is P/1000 pixels in the direction, and/or, the interval is Q/1000 pixels in the Y-axis direction; the interval between the lower-right corner pixel of the third sub-block and the lower-right corner pixel of the second sub-block is in the X-axis direction P/1000 pixels, and/or, at intervals of Q/1000 pixels in the Y-axis direction; according to this rule, all sub-blocks that satisfy this condition are continuously segmented and selected.
- a sub-block in the current frame image is arbitrarily selected, and the relationship between each sub-block in the previous frame image and the current frame image is calculated by formula (3) one by one.
- the sum of the absolute values of the grayscale differences of all pixels in the sub-block, and the sub-block in the previous frame image with the smallest value is selected as the best matching block;
- I current block (m, n) represents the gray value of the pixel at position (m, n) in the current frame image sub-block (that is, the current block), and I matching block (m, n) represents the previous frame image sub-block
- p represents the number of pixels in the X-axis direction of the sub-block
- q represents the number of pixels in the Y-axis direction of the sub-block;
- the minimum value of the energy function expression is obtained by the following formula (4):
- E(p) represents the energy function in the matching image and the current frame image
- both Em and E s are obtained by integrating the values of each point in the image
- E m represents the optical flow constraint item, the purpose is to ensure that the image sequence reaches the optical flow constraint with a constant gray level
- E s represents the smoothness constraint item, the purpose is to ensure that the optical flow field of the image sequence has been kept globally smooth;
- ⁇ represents all areas of the current frame/matching image
- the function f represents the position (x, y) of any pixel in the image at a certain moment
- f x represents the partial derivative of the function f in the X-axis direction
- land f y represents the partial derivative of the function f in the direction of the Y axis
- f t represents the partial derivative of the function f at time t
- u represents the velocity component of any pixel in the image in the X-axis direction
- v represents the velocity component of any pixel in the image in the Y-axis direction
- dx represents the differential symbol
- ⁇ is a positive number, which represents the weight of the smooth constraint item E m , and the smaller the value is, the more complex the optical flow field is.
- the method further includes step 5, by observing the camera 31 on the UAV 3 to take pictures of the target before and after the aircraft landed, and transmit them to the command unit 4, and then Determine the landing point of the aircraft and the damage to the target.
- the camera 31 captures and obtains a photo of the target in real time, and the observation drone 3 sends the target photo to the calculation module of the command unit in real time.
- the calculation module evaluates the damage effect according to the change degree of the pixel gray level of the target photo before and after the aircraft landing.
- the pixel value of the target photo after the aircraft has landed refers to the pixel value of the target photo 10 to 15 seconds after the aircraft has landed, preferably the pixel value of the target photo after 12 seconds.
- the camera 31 continuously shoots the target 10 seconds after the aircraft lands to obtain a photo of the target, and the target photo refers to a photo of a circular area with a diameter of 3 to 5 meters including the target.
- the camera 31 It can also directly judge whether the target is moving according to the target photo. If the target moves, it can be considered that the target damage effect has not reached the expectation. If the target does not move, the target photo of the aircraft 12 seconds after landing is collected for further analysis and evaluation.
- the specific further analysis and evaluation method is as follows: First, the grayscale change of the target photo image is solved by the following formula (5):
- p t0 is the pixel value of the target photo before the aircraft landed
- P t1 is the pixel value of the target photo after the aircraft has landed
- N b is the number of pixels in the target photo
- H b is the average grayscale change of the target photo.
- H b evaluate the degree of grayscale change of the target photo image pixels. For each pixel of the target photo, when
- the command unit displays the target damage effect value.
- the first aircraft sends the obtained position information of the radar transmitting vehicle to the observation drone 3, so that the observation drone can find and lock the target.
- the observation drone 3 determines the position of the radar launch vehicle in the photo through coordinate transformation, and can then quickly lock the target.
- the first aircraft controls itself to fly to the radar transmitter vehicle; since the radar transmitter vehicle has already discovered the first aircraft, the first aircraft The probability of being intercepted is relatively high.
- At least one of the other aircraft flies to the radar launch vehicle, that is, the radar launch vehicle is regarded as an important strike target.
- each target is irradiated with a laser irradiator 32, and each laser irradiator 32 emits irradiation lasers of different frequencies.
- the observation drone 3 sends the captured target information to the command unit 4 in real time, and the command unit can temporarily increase the number of aircraft according to the target information and target damage status, and control the launch unit to launch more aircraft to fly to the target area.
- a laser encoder is pre-stored in the aircraft, which can randomly select a variety of pseudo-random frequencies, and control the laser irradiator 32 to emit laser light of this frequency to irradiate the target.
- the pseudo-random frequency family can simultaneously reduce the target detection laser signal and the active interference of the laser signal. possibility.
- the laser seeker of the aircraft is equipped with a laser frequency decoder, which can calculate the laser frequency emitted by the laser irradiator according to the same coding rules, so that the laser seeker can capture the guiding laser in time and complete the laser terminal guidance.
- the accurate countdown information is calculated in real time by the command unit 4, and according to the countdown information, the laser irradiator 32 is controlled to emit an irradiating laser 1-3 seconds before the aircraft enters the final guidance segment.
- the command unit 4 calculates the countdown information according to the target position information and the position information and speed information of the aircraft. Preferably, 1 second after the countdown is over, the aircraft just enters the terminal guidance section, and the laser seeker starts to work. At this time, the laser irradiator 32 on the observation drone 3 also starts to work, just so that the aircraft captures the target position information, And control the aircraft to fly to the target.
- Three aircraft are launched towards the target area 20km away from the launch unit, the first aircraft arrives at the target area at least 5 seconds earlier than the other two aircraft; the second aircraft and the third aircraft arrive at the target area at the same time; it is known that the aircraft's The effective flight distance is 25km; the launch unit contains three launch vehicles, and the three aircraft are launched by three launch vehicles;
- the radar signal receiving module installed on the first aircraft captures the radar wave signal when entering the target area, and obtains the position information of the radar transmitter vehicle accordingly; 3 seconds later, the interceptor vehicle in the target area launches the interceptor aircraft and starts move, the radar transmitter also starts to move,
- the observation drone takes pictures of the target area in real time through the camera installed on it. After the radar launch vehicle and the interceptor vehicle move, the position of the radar launch vehicle and the interceptor vehicle is found, and the second and third aircraft enter the terminal guidance. In the first 1 second of the segment, irradiation lasers with different frequencies are emitted to irradiate the two targets respectively, and guide the second and third aircraft to fly to the targets.
- Figures 3 and 4 The motion trajectories of the first, second, third, radar launch vehicle and interceptor vehicle are shown in Figures 3 and 4, wherein Figure 4 is a partial enlarged view of Figure 3, and Figure 4 mainly shows three The trajectory of the aircraft as it approaches the landing and the trajectory of the two targets. As can be seen from the picture, the first aircraft was intercepted, the second aircraft hit the radar launch vehicle, and the third aircraft hit the interceptor vehicle.
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Abstract
Description
Claims (10)
- 一种激光末制导飞行器组网控制方法,其特征在于,该方法包括如下步骤:步骤1,通过发射单元(1)朝向目标区域发射至少两个飞行器(2),第一个飞行器至少比其他飞行器早5~10秒到达目标区域;步骤2,通过安装在第一个飞行器上的雷达信号接收模块(21)捕获雷达波信号,并据此获得雷达发射车的位置信息;步骤3,控制观测无人机(3)实时在目标区域巡航,并通过其上安装的摄像机(31)实时拍摄目标区域照片来寻找目标;步骤4,通过安装在观测无人机(3)上的激光照射器(32)照射目标。
- 根据权利要求1所述的激光末制导飞行器组网控制方法,其特征在于,该方法还包括步骤5,通过观测无人机(3)上的摄像机(31)拍摄飞行器着陆前后的目标照片,并将之传送给指挥单元(4),进而判断飞行器落点和目标毁伤情况。
- 根据权利要求1所述的激光末制导飞行器组网控制方法,其特征在于,在步骤2中,第一个飞行器将获得的雷达发射车的位置信息发送给观测无人机(3),以便于观测无人机发现并锁定该目标。
- 根据权利要求1所述的激光末制导飞行器组网控制方法,其特征在于,所述第一个飞行器在获得雷达发射车的位置信息后,控制其自身飞向该雷达发射车;其他飞行器中至少有一个飞行器在激光照射器(32)的导引下飞向该雷达发射车。
- 根据权利要求1所述的激光末制导飞行器组网控制方法, 其特征在于,当步骤3中寻找到两个或两个以上目标时,在步骤4中,每个目标都用一个激光照射器(32)进行照射,且各个激光照射器(32)发射不同频率的照射激光。
- 根据权利要求1所述的激光末制导飞行器组网控制方法,其特征在于,通过指挥单元(4)实时解算准确的倒计时信息,并根据该倒计时信息在飞行器进入末制导段前1-3秒时控制激光照射器(32)发出照射激光。
- 根据权利要求1所述的激光末制导飞行器组网控制方法,其特征在于,所述步骤3包括如下子步骤:子步骤1,观测无人机(3)在移动过程中持续通过摄像机(31)获得目标区域照片;子步骤2,对摄像机(31)获得的照片做预处理,子步骤3,将预处理后的图像转换为灰度图像;子步骤4,根据灰度图像建立变换模型,所述变换模型用于将相邻两帧图像中上一帧图像转换为匹配图像,所述匹配图像的背景与当前帧图像的背景相同;子步骤5,根据匹配图像和当前帧图像计算目标光流场,进而确定目标。
- 根据权利要求7所述的激光末制导飞行器组网控制方法,其特征在于,建立变换模型包括如下亚子步骤:亚子步骤a,建立变换模型为下式(一)其中,x'表示匹配图像中一个点的X轴坐标,y'表示匹配图像中的一个点的Y轴坐标;x表示上一帧图像中一个点的X轴坐标,y表示上一帧图像中一个点的Y轴坐标,a、b、c、d、e、f都表示转换参数,亚子步骤b,调取当前帧图像和上一帧图像,采用相同的方法将两帧图像都分割为不完全重叠的多个子块,亚子步骤c,从上一帧图像的子块中找到当前帧图像中每个子块的最佳匹配块;(x i,y i)表示当前帧图像中第i个子块的中心坐标,(x i',y i')表示该第i个子块在上一帧图像中最佳匹配块的中心坐标;亚子步骤d,用最小二乘法求解式(一)中的转换参数,如下式(二)中所示:其中,N表示当前帧图像中分割的子块数量。
- 根据权利要求8所述的激光末制导飞行器组网控制方法,其特征在于,在所述亚子步骤c中,任意选择一个当前帧图像中的子块,通过式(三)逐一解算上一帧图像中每个子块与该当前帧图像中子块所有像素点灰度差值的绝对值之和,并选择使得取值最小的上一帧图像中子块作为最佳匹配块;其中,I 当前块(m,n)表示当前帧图像子块中(m,n)位置处像素 点的灰度值,I 匹配块(m,n)表示上一帧图像子块中(m,n)位置处像素点的灰度值;p表示子块X轴方向像素点的个数,q表示子块Y轴方向像素点的个数;待确定一个当前帧图像中子块的最佳匹配块后,继续选择另一个当前帧图像中子块,继续通过式(三)寻找对应的最佳匹配块,直至找到当前帧图像中所有子块的最佳匹配块。
- 根据权利要求1所述的激光末制导飞行器组网控制方法,其特征在于,在子步骤5中,通过下式(四)获得能量函数表达式最小值:min(E(p))=min(E m+E s) (四)其中,E(p)表示匹配图像和当前帧图像中的能量函数,E m表示光流约束项;E s表示平滑约束项;其中,Ω表示当前帧图像的所有区域;函数f表示图像中任意像素点在某一时刻所处的位置(x,y),f x表示函数f在X轴方向上的偏导数;f y表示函数f在Y轴方向上的偏导数;f t表示函数f在时间t上的偏导数;u表示图像中任意像素点在X轴方向上的速度分量,v表示图像中任意像素点在Y轴方向上的速度分量;dx表示微分符号;α为正数,表示光滑约束项E m的权重。
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