A method for estimating the direction of ballistic targets from satellite images under single-satellite conditions

Abstract

The present invention specifically discloses a method for estimating the direction of a ballistic target of a satellite image under single-satellite conditions. The method comprises the following steps: S1, obtaining the original image of the target and performing target detection on the original image obtained with a known time interval to extract the centroid coordinates of the target in the corresponding original image; S2, tracking the target according to the centroid coordinates of the target and its corresponding time information to obtain the motion trajectory of the target; S3, converting the motion trajectory posture data of the target into the earth coordinate system and finding the corresponding ballistic trajectory points in the earth coordinate system; S4, establishing a normal vector equation group corresponding to the ballistic trajectory plane according to the ballistic trajectory points; S5, establishing the coordinate equation of the target using the collinear equation, and calculating the target direction according to the coordinate equation and the normal vector equation group. The present invention can obtain accurate results without prior knowledge of the trajectory, and has the characteristics of easy availability of required data, small amount of calculation and short calculation time.

Description

Technical Field

[0001] The invention relates to the technical field of flight dynamics, and in particular to a method for estimating the direction of a ballistic target using a satellite image under a single-satellite condition. Background Art

[0002] In the process of building a space-based satellite system, the deployment of satellites is phased due to factors such as project expenses, preliminary experiments and feedback verification. In the development of space-based satellite systems, considering the possible failure of sensors and the development of high-orbit satellites, the initial development stage is still in the state of single-star detection. Ballistic target parameter estimation based on single-star observation is an important process that space-based optical satellite systems must go through.

[0003] The direction of a ballistic target is the angle between the plane of the ballistic target trajectory and the plane of the longitude circle where its launch point is located. When a ballistic target is flying in the active phase, the tail flame ejected during fuel combustion can be detected by the onboard infrared sensor in the space-based optical satellite system. However, the infrared sensor is a passive observation imaging and can only obtain the relative orientation information and angular observation of the ballistic target. It cannot measure the relative distance and speed, which is an incomplete observation for target positioning.

[0004] The existing ballistic target direction estimation methods mainly include the following:

[0005] (1) Use trajectory prior information to predict the type of target, and then use template matching to estimate trajectory parameters. Prior information requires the establishment of a nominal trajectory data template library for different types of targets. The accuracy of the parameters obtained by this method also depends to a large extent on the template library capacity and information accuracy. The incompleteness of the template library information and the existence of errors in the template will cause the estimation algorithm to fail. All countries have listed the trajectory of ballistic targets as extremely important information data, so it is very difficult to obtain target template information. In general, the trajectory data obtained by the camera cannot correspond to the standard trajectory defined in the satellite information library. Even if the template information is complete, the template library is large in size, resulting in a large amount of calculation, so it is difficult to ensure the real-time performance of the system.

[0006] (2) The dynamic modeling of the target is mainly to constrain the active segment of the target by constructing various constraint models. In essence, it still supplements the prior information, but replaces the template matching with model constraints. The active segment motion is complex, and its own model is also relatively complex. Therefore, how to reasonably simplify the active segment model and form a reasonable constraint relationship becomes a key factor affecting the accuracy of the results of this type of method. This method requires the target mass and mass change rate, the relative effective injection speed and thrust of the target high-temperature gas, etc., and these data are also not easy to obtain.

[0007] (3) The trajectory observation imaging model based on the imaging relationship constraint parameter estimation algorithm assumes that the first observation point is the launch point. Due to the limitation of fewer measurement data points, it is easy to have the problem of underdetermined equations and unsolvable problems. The Monte Carlo method is used to calculate the numerical solution, which is a statistical result. It is necessary to select the parameters appropriately based on prior knowledge, and the reliability is difficult to guarantee.

[0008] In view of this, it is a technical problem that technicians in this field need to urgently solve to develop a method for estimating the direction of ballistic targets from satellite images under single-star conditions, which has accurate results and does not require a priori template and priori knowledge of the ballistic trajectory. Summary of the invention

[0009] The purpose of the present invention is to overcome the shortcomings and deficiencies in the prior art. The present invention proposes a method for estimating the direction of a ballistic target from a satellite image under single-satellite conditions. The method does not require prior knowledge of the trajectory to obtain accurate results, and has the characteristics of easy availability of required data, small amount of calculation and short calculation time.

[0010] In order to solve the above technical problems, the present invention provides a method for estimating the direction of a ballistic target from a satellite image under a single-satellite condition, the method comprising the following steps:

[0011] S1. Using a satellite camera to obtain an original image of a target, and performing target detection on the original image obtained at a known time interval to extract the centroid coordinates of the target in the corresponding original image;

[0012] S2, tracking the target according to the center of mass coordinates of the target in step S1 and its corresponding time information to obtain the motion trajectory of the target;

[0013] S3, converting the target's motion trajectory posture data into the earth coordinate system, and finding the corresponding ballistic trajectory point in the earth coordinate system according to the target's motion trajectory;

[0014] S4, establishing a normal vector equation group corresponding to the ballistic trajectory plane according to the ballistic trajectory points;

[0015] S5. Use the collinear equation to establish the coordinate equation of the target, and calculate the target direction based on the coordinate equation and the normal vector equation group.

[0016] Preferably, the specific implementation of step S1 includes:

[0017] S11. Use a satellite camera to obtain the original image of the target, and then use Top-Hat filtering to suppress the background of the original image with a known time interval to obtain an image after background suppression. The Top-Hat filtering is expressed by the formula:

[0018] T H(f)=-open(f,e) (1)

[0019] In formula (1), open represents the opening operation, f represents the original image, and e represents the structural element;

[0020] S12, select the structural element with the same target feature to perform convolution processing on the background suppressed image, then set the threshold to segment the possible target points, and then obtain the target segmented image. The target segmented image is expressed by the formula:

[0021]

[0022] In formula (2), f represents the original image, f r represents the image after background suppression, E represents the image after convolution with the structural element, and Δ represents the parameter related to the false alarm rate;

[0023] S13. Use the Sobel operator to calculate the gradient of the target segmented image, and then obtain the number of targets and the centroid coordinates of the targets through cluster analysis.

[0024] Preferably, the specific implementation of step S2 includes:

[0025] S21, selecting multiple frames of images to extract the target centroid coordinates for frame integration, and using the meanshift algorithm to converge to the target motion area;

[0026] S22, performing pipeline filtering on the target in the target motion area to filter out noise interference outside the pipeline, and obtaining a pipeline filtered image;

[0027] S23, inputting the pipeline filtered image into a Kalman filter for target tracking, thereby obtaining the motion trajectory of the target.

[0028] Preferably, the specific implementation of step S3 includes:

[0029] S31. According to the satellite camera imaging model, the conversion relationship between the earth coordinate system and the satellite imaging coordinate system is obtained, and then the coordinates of the original image points in the satellite imaging coordinate system are inversely transformed to obtain the three-dimensional coordinates of the corresponding image points in the earth coordinate system. The conversion relationship between the earth coordinate system and the satellite imaging coordinate system is expressed by the formula:

[0030]

[0031] In formula (3), h=[0,0,-(r0+H0)] T , T represents matrix transpose, H0 represents satellite altitude, r0 represents the radius of the earth, α represents the positioning longitude of the satellite camera, β represents the inclination angle of the main optical axis of the satellite camera along the equator, (uc ,v c ) represents the two-dimensional coordinates of the image point in the satellite imaging coordinate system, (X c ,Y c ,Z c ) represents the three-dimensional coordinates of the image point in the satellite imaging coordinate system in the earth coordinate system;

[0032] S32. Find the corresponding ballistic trajectory point in the earth coordinate system according to the target's motion trajectory. The ballistic trajectory point satisfies the formula:

[0033]

[0034] In formula (4), (x, y, z) represents the coordinates of the trajectory point in the earth coordinate system, (X center ,Y center ,Z center ) represents the three-dimensional coordinates of the camera optical center in the earth coordinate system, (X image ,Y image ,Z image ) represents the three-dimensional coordinates of the image point corresponding to the target's motion trajectory in the earth coordinate system.

[0035] Preferably, the specific implementation of step S4 is:

[0036] S41, obtain the function expression of the spherical radius r of the sphere where the trajectory point is located, and establish the trajectory points p1 and p n The trajectory corresponds to the trajectory plane P n-1 The normal vector is expressed as:

[0037]

[0038] In formula (5), and They represent the points p1 and p2 from the center of the earth O to the ballistic trajectory. n The vector, X p1 (r1), Y p1 (r1) and Z p1 (r1) respectively represent vectors The components along the x, y, and z directions are expressed as functions of the spherical radius r1, X pn (r n ), Y pn (r n ) and Z pn (r n ) represents a vector The components along the x, y, and z directions are related to the spherical radius r n Function expressions;

[0039] S42, constructing a normal vector equation group according to the normal vector of the trajectory plane in step S41, which is expressed as:

[0040]

[0041] In formula (6), (λ 1x (r1,r2),λ 1y (r1,r2),λ 1z (r1, r2)) represents the function expression of the normal vector N1 about the spherical radius r1 and the spherical radius r2, λ 1x (r1,r2),λ 1y (r1,r2) and λ 1z (r1, r2) represent the normal vectors Functional expressions of the components along the x, y, and z directions with respect to the spherical radius r1 and the spherical radius r2; (λ (n-1)x (r1,r n ),λ (n-1)y (r1,r n ),λ (n-1)z (r1,r n )) represents the normal vector In the spherical radius r1 and spherical radius r n The function expression of λ (n-1)x (r1,r n ), λ (n-1)y (r1,r n ) and λ (n-1)z (r1,r n ) represent the normal vector The components along the x, y, and z directions are related to the spherical radius r1 and the spherical radius r n The function expression of .

[0042] Preferably, the specific implementation of step S5 includes:

[0043] S51, randomly select two image points A1 and A2 from the target's motion trajectory in step S2, and use the collinear equation to establish the target's coordinate equation, which can be expressed as:

[0044]

[0045]

[0046] In formula (7) and formula (8), represents the three-dimensional coordinates of the image point A1 in the earth coordinate system, represents the three-dimensional coordinates of the image point A2 in the earth coordinate system, f j(H0) represents a function about H0 (where j = 1, 2, 3, 4, 5, 6), where H0 represents the satellite altitude;

[0047] S52, calculating the target direction q according to the established coordinate equation and normal vector equation group, wherein the target direction q is expressed by the formula:

[0048]

[0049]

[0050] In formula (9) and formula (10), is the normal vector of trajectory plane P1, Represents the target launch point through the trajectory plane P l The normal vector of , l represents the target launch point in the earth coordinate system, represents the unit vector with the same direction as the Y axis in the Earth coordinate system, Represents the vector from the center of the earth O to the target launch point l.

[0051] Preferably, the Kalman filter time update equation is:

[0052]

[0053] The Kalman filter state update equation is:

[0054]

[0055] In formula (11) and formula (12), represents the state one-step prediction error covariance matrix, P k represents the state estimation error covariance matrix, P k-1 represents the state estimation error matrix at time k-1, R k represents the measurement uncertainty covariance matrix, A represents the state transfer matrix, Q represents the process noise matrix, represents the estimated value of the state, represents the state vector of the state estimation system at time k-1, represents the one-step prediction value at the current state, K k represents the Kalman gain, z k represents the measurement value, H represents the observation matrix, and I represents the identity matrix.

[0056] Compared with the prior art, the method for estimating the direction of a ballistic target using satellite images under single-satellite conditions provided by the present invention first obtains the motion trajectory of the target by performing target detection and target tracking on the original images with known time intervals; then converts the motion trajectory posture data of the target into the earth coordinate system and finds the corresponding ballistic trajectory points; finally, establishes a group of normal vector equations of the ballistic trajectory plane and the coordinate equation of the target, and then calculates the target direction. The method for estimating the direction of a ballistic target in the present invention only needs to obtain the position information of the target based on the original image collected by the satellite camera, and at the same time, infers the speed of the target at the launch point by combining the known time interval of the original image, and then solves the three groups of equations to obtain the accurate result of the target direction, without the need for prior knowledge of the target, and has the characteristics of easy data acquisition, small amount of calculation and short calculation time. BRIEF DESCRIPTION OF THE DRAWINGS

[0057] Figure 1 This is a flow chart of a method for estimating the direction of a ballistic target from a satellite image under single-satellite conditions in the present invention;

[0058] Figure 2 This is a schematic diagram of the satellite camera imaging model in the present invention;

[0059] Figure 3 It is a plane schematic diagram of the ballistic target trajectory in the present invention. DETAILED DESCRIPTION

[0060] In order to enable those skilled in the art to better understand the technical solutions of the present disclosure, the technical solutions in the embodiments of the present disclosure will be clearly and completely described below in conjunction with the drawings in the embodiments of the present disclosure. Obviously, the described embodiments are only embodiments of a part of the present disclosure, not all of the embodiments. Based on the embodiments in the present disclosure, all other embodiments obtained by ordinary technicians in this field without making creative work should fall within the scope of protection of the present disclosure.

[0061] like Figure 1 As shown, the present invention provides a method for estimating the direction of a ballistic target from a satellite image under single-satellite conditions, the method comprising the following steps:

[0062] S1. Using a satellite camera to obtain an original image of a target, and performing target detection on the original image obtained at a known time interval to extract the centroid coordinates of the target in the corresponding original image;

[0063] S2, tracking the target according to the center of mass coordinates of the target in step S1 and its corresponding time information to obtain the motion trajectory of the target;

[0064] S3, converting the target's motion trajectory posture data into the earth coordinate system, and finding the corresponding ballistic trajectory point in the earth coordinate system according to the target's motion trajectory;

[0065] S4, establishing a normal vector equation group corresponding to the ballistic trajectory plane according to the ballistic trajectory points;

[0066] S5. Use the collinear equation to establish the coordinate equation of the target, and calculate the target direction based on the coordinate equation and the normal vector equation group.

[0067] In this embodiment, first, a series of original images of the target are acquired by using a satellite camera, and target detection is performed on the original images with known time intervals, and then the centroid coordinates of the target in the original image are extracted; then, the target is tracked according to the centroid coordinates of the target in the original image and its corresponding time information, and the motion trajectory of the target is obtained; then, the motion trajectory posture data of the target is converted into the earth coordinate system and the corresponding ballistic trajectory points are found, and the normal vector equation group corresponding to the ballistic trajectory plane is established according to the ballistic trajectory points found; finally, the coordinate equation of the target is established using the collinear equation, and the target direction is calculated in combination with the established normal vector equation group. The ballistic target direction estimation method only needs to obtain the position information of the target based on the original images collected by the satellite camera, and the speed of the target at the launch point can be calculated in combination with the known time interval. At the same time, the accurate result of the target direction can be obtained by solving the equation group, and no prior knowledge of the target is required, and it has the characteristics of easy data acquisition, small amount of calculation and short calculation time.

[0068] The specific implementation of step S1 includes:

[0069] S11. Use a satellite camera to obtain the original image of the target, and then use Top-Hat (top hat or top hat) filtering to suppress the background of the original image obtained at a known time interval to obtain an image after background suppression. The Top-Hat filtering is expressed by the formula:

[0070] T H (f)=-open(f,e) (1)

[0071] In formula (1), open represents the opening operation, f represents the original image, and e represents the structural element;

[0072] S12, select the structural element with the same target feature to perform convolution processing on the background suppressed image, then set the threshold to segment the possible target points, and then obtain the target segmented image. The target segmented image is expressed by the formula:

[0073]

[0074] In formula (2), f represents the original image, f r represents the image after background suppression, E represents the image after convolution with the structural element, and Δ represents the parameter related to the false alarm rate;

[0075] S13. The gradient of the image after target segmentation is calculated using the Sobel operator, and then the number of targets and the centroid coordinates of the targets are obtained through cluster analysis.

[0076] The specific implementation of step S2 includes:

[0077] S21, selecting multiple frames of images to extract the target centroid coordinates for frame integration, and using the meanshift algorithm to converge to the target motion area, that is, the area with larger radiance;

[0078] S22, performing pipeline filtering on the target in the target motion area to filter out the noise interference outside the pipeline, and obtaining a pipeline filtered image. According to the continuity of the target motion, when there is a target at the pixel (a, b) in the pipeline filtered image of the Sth frame, the target must appear in a small neighborhood of the pixel (a, b) in the pipeline filtered image of the S+1th frame;

[0079] S23, inputting the pipeline filtered image into a Kalman filter for target tracking, thereby obtaining the motion trajectory of the target, wherein the Kalman filter time update equation is:

[0080]

[0081] The Kalman filter state update equation is:

[0082]

[0083] In formula (11) and formula (12), represents the state one-step prediction error covariance matrix, P k represents the state estimation error covariance matrix, P k-1 represents the state estimation error matrix at time k-1, R k represents the measurement uncertainty covariance matrix, A represents the state transfer matrix, Q represents the process noise matrix, represents the estimated value of the state, represents the state vector of the state estimation system at time k-1, represents the one-step prediction value at the current state, K k represents the Kalman gain, z k represents the measurement value, H represents the observation matrix, and I represents the identity matrix.

[0084] like Figure 2 As shown, the specific implementation of step S3 includes:

[0085] S31. Obtain the conversion relationship between the earth coordinate system and the satellite imaging coordinate system according to the satellite camera imaging model, and then perform an inverse transformation on the coordinates of the original image points in the satellite imaging coordinate system (i.e., the coordinates corresponding to the target original image points obtained by the satellite camera in step S1 in the satellite imaging coordinate system) to obtain the three-dimensional coordinates of the corresponding original image points in the earth coordinate system, wherein the conversion relationship between the earth coordinate system and the satellite imaging coordinate system is expressed by the formula:

[0086]

[0087] In formula (3), h=[0,0,-(r0+H0)] T , T represents matrix transpose, H0 represents satellite altitude, r0 represents the radius of the earth, α represents the positioning longitude of the satellite camera, β represents the inclination angle of the main optical axis of the satellite camera along the equator, (u c ,v c ) represents the two-dimensional coordinates of the original image point in the satellite imaging coordinate system, (X c ,Y c ,Z c ) represents the three-dimensional coordinates of the original image point in the satellite imaging coordinate system in the earth coordinate system;

[0088] S32. Find the corresponding ballistic trajectory point in the earth coordinate system based on the motion trajectory of the target, wherein the ballistic trajectory point satisfies the formula:

[0089]

[0090] In formula (4), (x, y, z) represents the coordinates of the trajectory point in the earth coordinate system, (X center ,Y center ,Z center ) represents the camera optical center O c The three-dimensional coordinates in the Earth coordinate system, (X image ,Y image ,Z image ) represents the three-dimensional coordinates of the target's motion trajectory corresponding to the image point i in the earth coordinate system.

[0091] In this embodiment, first, the conversion relationship between the earth coordinate system and the satellite imaging coordinate system is obtained according to the satellite camera imaging model, and the corresponding three-dimensional coordinates of the original image points in the satellite imaging coordinate system in the earth coordinate system are obtained; then, the ballistic trajectory point corresponding to the motion trajectory of the target is found in the earth coordinate system. According to the satellite camera imaging principle, the ballistic trajectory point is the corresponding image point i and the camera optical center O c The intersection point p is where the straight line formed intersects the spherical surface where the ballistic trajectory point is located.

[0092] like Figure 3 As shown, the specific implementation of step S4 is:

[0093] S41, obtain the function expression of the spherical radius r of the sphere where the trajectory point is located, and establish the trajectory points p1 and p n The trajectory corresponds to the trajectory plane P n-1 The normal vector is expressed as:

[0094]

[0095] In formula (5), and They represent the points p1 and p2 from the center of the earth O to the ballistic trajectory. n The vector, X p1 (r1), Y p1 (r1) and Z p1 (r1) respectively represent vectors The components along the x, y, and z directions are expressed as functions of the spherical radius r1, X pn (r n ), Y pn (r n ) and Z pn (r n ) represent vectors respectively The components along the x, y, and z directions are related to the spherical radius r n Function expressions;

[0096] S42, constructing a normal vector equation group according to the normal vector of the trajectory plane in step S41, which is expressed as:

[0097]

[0098] In formula (6), (λ 1x (r1,r2),λ 1y (r1,r2),λ 1z (r1, r2)) represents the function expression of the normal vector N1 about the spherical radius r1 and the spherical radius r2, λ 1x (r1,r2),λ 1y (r1,r2) and λ 1z (r1, r2) represent the normal vectors Functional expressions of the components along the x, y, and z directions with respect to the spherical radius r1 and the spherical radius r2; (λ (n-1)x (r1,r n ),λ (n-1)y (r1,r n ),λ (n-1)z (r1,r n )) represents the normal vector In the spherical radius r1 and spherical radius r n The function expression of λ (n-1)x (r1,r n ), λ (n-1)y (r1,r n ) and λ (n-1)z (r1,r n ) represent the normal vector The components along the x, y, and z directions are related to the spherical radius r1 and the spherical radius r n The function expression of .

[0099] In this embodiment, the function expression of the spherical radius r of the sphere where the ballistic trajectory point is located can be obtained according to the ballistic trajectory point (the ballistic trajectory point constitutes the motion trajectory of the target), from Figure 3 It can be seen that each trajectory of the target corresponds to a trajectory plane, and all trajectory planes pass through the center of the earth O. Using the ballistic trajectory points p1 and p n The corresponding spherical radius function expression can establish the ballistic trajectory points p1 and p n The trajectory plane P corresponding to the trajectory n-1 The normal vector of the ballistic trajectory points p1 and p2 is P1, because the trajectory plane corresponding to the trajectory of the ballistic trajectory points p1 and p2 is P1, k (k>1) The trajectory plane corresponding to the trajectory is P k-1 , so when n is 2 and k respectively, we can get the normal vector N1 of the trajectory plane P1 and the plane P k-1 The normal vector N k-1 At the same time, the trajectory points p1, p2 and p k Located on the same motion trajectory of the target, trajectory plane P1 and trajectory plane P k-1 should coincide, that is, the trajectory plane P1 and the trajectory plane P k-1 The normal vectors of the trajectory plane P1 and trajectory plane P k-1 Both pass through point O and point p1, so when the trajectory plane P1 and the trajectory plane P k-1 When they coincide, the normal vector equation group can be obtained, see formula (6) for details.

[0100] The specific implementation of step S5 includes:

[0101] S51. Select any two image points A1 and A2 from the target's motion trajectory, and use the collinear equation to establish the target's coordinate equation, which can be expressed as:

[0102]

[0103]

[0104] In formula (7) and formula (8), represents the three-dimensional coordinates of the image point A1 in the earth coordinate system, represents the three-dimensional coordinates of the image point A2 in the earth coordinate system, f j (H0) represents a function about H0 (where j = 1, 2, 3, 4, 5, 6), where H0 represents the satellite altitude;

[0105] S53, calculating the target direction q according to the established coordinate equation and normal vector equation group, wherein the target direction q is expressed by the formula:

[0106]

[0107]

[0108] In formula (9), is the normal vector of trajectory plane P1, Represents the target launch point through the trajectory plane P l The normal vector of , l represents the target launch point in the earth coordinate system, in formula (10), represents the unit vector with the same direction as the Y axis in the Earth coordinate system, Represents the vector from the center of the earth O to the target launch point l.

[0109] In this embodiment, the collinear equation can be used to establish the coordinate equation of the two selected image points with respect to the target height function. The values ​​of the spherical radii r1, r2 and r3 can be obtained according to the coordinate equation and the normal vector equation group. Then, the coordinates (X l ,Y l ,Z l ) can obtain the normal vector of the target through the launch point through the coil plane. The target's launch angle is calculated by the angle between the trajectory plane and the target launch point through the coil plane. The angle between the actual trajectory plane and the estimated trajectory plane is equal to the error of the estimated trajectory angle. The trajectory plane is calculated by taking the trajectory initial point p s And ballistic shutdown point p e Since the trajectory plane passes through the earth's center O, the center of the earth O and the initial point of the trajectory p s And ballistic shutdown point p e A plane can be uniquely determined from the center of the earth O to point p s Vector and the Earth's center O to point p e Vector The normal vector of the trajectory plane can be obtained, which is expressed as:

[0110]

[0111] At this time, by estimating the normal vector of the ballistic surface and the actual ballistic surface normal vector The error of the estimated direction angle can be obtained, which can be expressed as:

[0112]

[0113] The above description is only a preferred specific implementation manner of the present invention, but the protection scope of the present invention is not limited thereto. Any technician familiar with the technical field can make equivalent replacements or changes according to the technical scheme and inventive concept of the present invention within the technical scope disclosed by the present invention, which should be covered by the protection scope of the present invention.

Claims

1. A method for estimating the direction of a ballistic target from a satellite image under single-satellite conditions, characterized in that: The method comprises the following steps: S1. Using a satellite camera to obtain an original image of a target, and performing target detection on the original image obtained at a known time interval to extract the centroid coordinates of the target in the corresponding original image; S2, tracking the target according to the center of mass coordinates of the target in step S1 and its corresponding time information to obtain the motion trajectory of the target; S3, converting the target's motion trajectory posture data into the earth coordinate system, and finding the corresponding ballistic trajectory point in the earth coordinate system according to the target's motion trajectory; S4, establishing a normal vector equation group corresponding to the ballistic trajectory plane according to the ballistic trajectory points; S5. Use the collinear equation to establish the coordinate equation of the target, and calculate the target direction based on the coordinate equation and the normal vector equation group.

2. The method for estimating the direction of a ballistic target from a satellite image under single-satellite conditions according to claim 1, characterized in that: The specific implementation of step S1 includes: S11. Use a satellite camera to obtain the original image of the target, and then use Top-Hat filtering to suppress the background of the original image with a known time interval to obtain an image after background suppression. The Top-Hat filtering is expressed by the formula: T H (f)=-open(f,e) (1) In formula (1), open represents the opening operation, f represents the original image, and e represents the structural element; S12, select the structural element with the same target feature to perform convolution processing on the background suppressed image, then set the threshold to segment the possible target points, and then obtain the target segmented image. The target segmented image is expressed by the formula: In formula (2), f represents the original image, f r represents the image after background suppression, E represents the image after convolution with the structural element, and Δ represents the parameter related to the false alarm rate; S13. Use the Sobel operator to calculate the gradient of the target segmented image, and then obtain the number of targets and the centroid coordinates of the targets through cluster analysis.

3. The method for estimating the direction of a ballistic target from a satellite image under single-satellite conditions according to claim 2, characterized in that: The specific implementation of step S2 includes: S21, selecting multiple frames of images to extract the target centroid coordinates for frame integration, and using the meanshift algorithm to converge to the target motion area; S22, performing pipeline filtering on the target in the target motion area to filter out noise interference outside the pipeline, and obtaining a pipeline filtered image; S23, inputting the pipeline filtered image into a Kalman filter for target tracking, thereby obtaining the motion trajectory of the target.

4. The method for estimating the direction of a ballistic target from a satellite image under single-satellite conditions according to claim 3, characterized in that: The specific implementation of step S3 includes: S31. According to a preset satellite camera imaging model, a conversion relationship between the earth coordinate system and the satellite imaging coordinate system is obtained, and then the coordinates of the original image points in the satellite imaging coordinate system are inversely transformed to obtain the three-dimensional coordinates of the corresponding image points in the earth coordinate system. The conversion relationship between the earth coordinate system and the satellite imaging coordinate system is expressed by the formula: In formula (3), h=[0,0,-(r0+H0)] T , T represents matrix transpose, H0 represents satellite altitude, r0 represents the radius of the earth, α represents the positioning longitude of the satellite camera, β represents the inclination angle of the main optical axis of the satellite camera along the equator, (u c ,v c ) represents the two-dimensional coordinates of the image point in the satellite imaging coordinate system, (X c ,Y c ,Z c ) represents the three-dimensional coordinates of the image point in the satellite imaging coordinate system in the earth coordinate system; S32. Find the corresponding ballistic trajectory point in the earth coordinate system based on the motion trajectory of the target, wherein the ballistic trajectory point satisfies the formula: In formula (4), (x, y, z) represents the coordinates of the trajectory point in the earth coordinate system, (X center ,Y center ,Z center ) represents the three-dimensional coordinates of the camera optical center in the earth coordinate system, (X image ,Y image ,Z image ) represents the three-dimensional coordinates of the image point corresponding to the target's motion trajectory in the earth coordinate system.

5. The method for estimating the direction of a ballistic target from a satellite image under single-satellite conditions according to claim 4, characterized in that: The specific implementation of step S4 is: S41, obtain the function expression of the spherical radius r of the sphere where the trajectory point is located, and establish the trajectory points p1 and p n The trajectory corresponds to the trajectory plane P n-1 The normal vector is expressed as: In formula (5), and They represent the points p1 and p2 from the center of the earth O to the ballistic trajectory. n The vector, X p1 (r1), Y p1 (r1) and Z p1 (r1) respectively represent vectors The components along the x, y, and z directions are expressed as functions of the spherical radius r1, X pn (r n ), Y pn (r n ) and Z pn (r n ) represent vectors respectively The components along the x, y, and z directions are related to the spherical radius r n Function expressions; S42, constructing a normal vector equation group according to the normal vector of the trajectory plane in step S41, which is expressed as: In formula (6), (λ 1x (r1,r2),λ 1y (r1,r2),λ 1z (r1,r2)) represents the normal vector The function expression of spherical radius r1 and spherical radius r2 in 1x (r1,r2),λ 1y (r1,r2) and λ 1z (r1, r2) represent the normal vectors Functional expressions of the components along the x, y, and z directions with respect to the spherical radius r1 and the spherical radius r2; (λ (n-1)x (r1,r n ),λ (n-1)y (r1,r n ),λ (n-1)z (r1,r n )) represents the normal vector In the spherical radius r1 and spherical radius r n The function expression of λ (n-1)x (r1,r n ), λ (n-1)y (r1,r n ) and λ (n-1)z (r1,r n ) represent the normal vector The components along the x, y, and z directions are related to the spherical radius r1 and the spherical radius r n The function expression of .

6. The method for estimating the direction of a ballistic target from a satellite image under single-satellite conditions according to claim 5, characterized in that: The specific implementation of step S5 includes: S51, randomly select two image points A1 and A2 from the target's motion trajectory in step S2, and use the collinear equation to establish the target's coordinate equation, which can be expressed as: In formula (7) and formula (8), represents the three-dimensional coordinates of the image point A1 in the earth coordinate system, represents the three-dimensional coordinates of the image point A2 in the earth coordinate system, f j (H0) represents a function about H0 (where j = 1, 2, 3, 4, 5, 6), where H0 represents the satellite altitude; S52, calculating the target direction q according to the established coordinate equation and normal vector equation group, wherein the target direction q is expressed by the formula: In formula (9) and formula (10), is the normal vector of trajectory plane P1, represents the normal vector of the target launch point through the coil plane, l represents the target launch point in the earth coordinate system, represents the unit vector with the same direction as the Y axis in the Earth coordinate system, Represents the vector from the center of the earth, point O, to the target launch point, point l.

7. The method for estimating the direction of a ballistic target from a satellite image under single-satellite conditions according to claim 6, characterized in that: The Kalman filter time update equation is: The Kalman filter state update equation is: In formula (11) and formula (12), represents the state one-step prediction error covariance matrix, P k represents the state estimation error covariance matrix, P k-1 represents the state estimation error matrix at time k-1, R k represents the measurement uncertainty covariance matrix, A represents the state transfer matrix, Q represents the process noise matrix, represents the estimated value of the state, represents the one-step prediction value at the current state, represents the state vector of the state estimation system at time k-1, K k represents the Kalman gain, z k represents the measurement value, H represents the observation matrix, I represents the identity matrix, and T represents the matrix transpose.

Images