A method and device for satellite orbit determination based on space-based observations

Abstract

A satellite orbit determination method and device based on space-based observation, which relates to the field of computer simulation. It solves the problems that domestic aerospace simulation software is limited in terms of accuracy and generality, and that when the Laplace method and the Gauss method encounter extremely short arcs of dozens of seconds or even more than ten seconds, large errors often occur between the solution and the true value due to the intrinsic ill-conditioning when solving equations. The method includes: using Spacesim to randomly plan and simulate two satellite orbits; using an observation satellite to photograph a target satellite on the tracking satellite orbit to obtain a series of images of the target satellite; using Opencv to identify and process the series of images of the obtained target satellite to determine the trajectory of the target satellite obtained by the observation satellite; and processing the short-arc orbit determination problem of the trajectory of the target satellite obtained by the observation satellite according to the particle swarm algorithm to determine the target satellite orbit. It is applied to the field of space-based observation.

Description

Technical Field

[0001] It relates to the field of computer simulation, and particularly to a method for determining the orbit of a space-based observation satellite. Background Art

[0002] Since the launch of the first artificial satellite in 1957, the number of space vehicles around the Earth has increased geometrically. Among the artificial satellites in space, only a small part is still in effective operation, and the rest have become space debris. Excessive space debris will increase the risk of collision with other vehicles. Therefore, the control system of satellites urgently needs a method for measuring the orbit of a vehicle to obtain the position and velocity information of all space targets, so as to avoid space debris and prevent collisions. Since the orbits of space targets are usually medium and low orbits with fast movement, whether it is a space-based observation platform or a ground-based observation platform, at most only the orbits of dozens of seconds or even more than a dozen seconds can be measured. Using traditional Laplace and Gauss orbit determination methods often results in a large error from the correct value due to less known information and lack of prior conditions.

[0003] Currently, domestic generally uses foreign commercial software such as Satellite Tool Kit and SATSOFT. However, the use is often restricted, resulting in certain limitations in the accuracy and versatility of domestic aerospace simulation software. Summary of the Invention

[0004] The present invention solves the problems that the main software used in domestic aerospace research is foreign commercial software, and domestic aerospace simulation software has certain limitations in terms of accuracy and versatility, and when the Laplace method and Gauss method encounter extremely short arc problems of dozens of seconds or even more than ten seconds, there are often large errors from the true value due to the intrinsic ill-conditioning when solving equations.

[0005] The present invention provides a method for determining the orbit of a satellite based on space-based observation, and the method includes:

[0006] Using Spacesim to randomly plan and simulate two satellite orbits; one satellite orbit is the predicted target satellite orbit, and the other satellite orbit is the tracking satellite orbit;

[0007] Using an observation satellite to photograph the target satellite on the tracking satellite orbit to obtain a series of images of the target satellite;

[0008] Using Opencv to identify and process the series of images of the obtained target satellite to determine the trajectory of the target satellite obtained by the observation satellite;

[0009] Solve the short-arc orbit determination problem of the target satellite's trajectory obtained by the observation satellite according to the particle swarm algorithm, and determine the target satellite's orbit.

[0010] Furthermore, a preferred implementation is also provided. The observation satellite includes: a tracking satellite and a camera;

[0011] The camera's swing direction is [1, 0, 0], the full field of view angle is 15°, the pitch resolution is 800 pixels, the azimuth resolution is 800 pixels, the near plane is specifically 1m, the far plane is specifically 100000m, the pitch angle is 180°, and the azimuth angle is 0°.

[0012] Furthermore, a preferred implementation is also provided. The method of using Opencv to identify and process the series of images of the target satellite is as follows:

[0013] Obtain the grayscale image of each photo in the series of images of the target satellite, and perform thresholding on the grayscale image.

[0014] Furthermore, a preferred implementation is also provided. The method further includes: obtaining the direction vector from the observation satellite to the target satellite according to the trajectory of the target satellite obtained by the observation satellite, specifically:

[0015]

[0016] Among them, R1 is the rotation matrix from the celestial system to the absolute coordinate system, R2 is the rotation matrix rotating 180° around the y-axis, R3 is the rotation matrix rotating 90° around the z-axis, f x 、f y 、c x 、c y are the internal parameters of the camera, f x is the focal length of the camera in the x-axis direction, f y is the focal length of the camera in the y-axis direction, c x is the x-coordinate of the camera's optical center, c y is the y-coordinate of the camera's optical center, x, y, z are the direction vectors from the observation satellite to the target satellite, and (u, v) are the pixel coordinates of the target satellite.

[0017] Furthermore, a preferred implementation is also provided. The f x 、f y 、c x 、c y are obtained according to the conversion between the perspective camera parameters and the OpenGL camera internal parameters, specifically:

[0018]

[0019] Wherein, w is the number of horizontal pixels of the captured image, h is the number of vertical pixels of the captured image, n is the near-plane distance, f is the far-plane distance, and θ is the field of view angle in the pitch direction.

[0020] Further, a preferred implementation manner is also provided. The determination of the target satellite orbit is specifically as follows:

[0021] v i+1 = v i + c1 × rand × (pbest i - x i ) + c2 × rand × (gbest i - x i ),

[0022] x i+1 = x i + v i+1 ,

[0023] Wherein, v i is the velocity of the i-th generation particle, v i+1 is the velocity of the (i + 1)-th generation particle, c1 and c2 are learning factors to be adjusted, rand is a random number between (0, 1), pbest i is the best position searched by a single particle after the i-th iteration, x i is the current position of the i-th generation particle, x i+1 is the current position of the (i + 1)-th generation particle, and gbest i is the best position searched by the particle swarm after the i-th iteration.

[0024] The present invention also provides a satellite orbit determination device based on space-based observation. The device includes:

[0025] A satellite orbit planning unit, configured to randomly plan and simulate two satellite orbits by using Spacesim; one satellite orbit is a predicted target satellite orbit, and the other satellite orbit is a tracking satellite orbit;

[0026] A series of images acquisition unit of the target satellite, configured to use an observation satellite to capture the target satellite on the tracking satellite orbit to obtain a series of images of the target satellite;

[0027] A trajectory acquisition unit of the target satellite, configured to use Opencv to identify and process the series of images of the target satellite obtained, and determine the trajectory of the target satellite obtained by the observation satellite;

[0028] A target satellite orbit determination unit, configured to process the short-arc orbit determination problem of the trajectory of the target satellite obtained by the observation satellite according to an evolutionary algorithm, and determine the target satellite orbit.

[0029] Furthermore, a preferred implementation is also provided. The observation satellite includes: a tracking satellite and a camera;

[0030] The camera has a camera swing direction of [1, 0, 0], a full field of view angle of 15°, a pitch resolution of 800 pixels, an azimuth resolution of 800 pixels, a near plane specifically of 1 m, a far plane specifically of 100,000 m, a pitch angle of 180°, and an azimuth angle of 0°.

[0031] The present invention also provides a computer device, including a memory and a processor. A computer program is stored in the memory. When the processor runs the computer program stored in the memory, the processor executes a satellite orbit determination method based on space-based observation described in any one of the above.

[0032] The present invention also provides a computer-readable storage medium. A computer program is stored on the computer-readable storage medium. When the computer program is run by a processor, it executes a satellite orbit determination method based on space-based observation described in any one of the above.

[0033] The advantages of the present invention are as follows:

[0034] The present invention solves the problems that the main commercial software used in domestic aerospace research at present is from foreign countries, and domestic aerospace simulation software is limited in terms of accuracy and generality, and when the Laplace method and the Gauss method encounter extremely short arc problems of dozens of seconds or even more than ten seconds, large errors often occur between the solution of the equation and the true value due to the intrinsic ill-conditioning of the equation-solving process.

[0035] For the satellite orbit determination method based on space-based observation described in the present invention, the short arc orbit determination problem of the trajectory of the target satellite obtained by the observation satellite is processed according to the particle swarm algorithm to determine the target satellite orbit. Through the particle swarm algorithm, extremely short arc orbit information of dozens of seconds or even more than ten seconds can be effectively identified, the orbit determination speed is fast, the error is small, and it has strong practicability. For the short arc orbit determination problem, within an observation time of 10 s, the space-based observation images are processed to obtain the target orbit. The semi-major axis error of the obtained orbit is less than 10 km, the eccentricity error is less than 0.001, and the errors of the orbit inclination, argument of perigee, right ascension of the ascending node, and mean anomaly are all better than 5%.

[0036] A satellite orbit determination method based on space-based observation according to the present invention uses domestic spacecraft system simulation software Spacesim to avoid restrictions during use. The satellite orbit is designed by using Spacesim, and then the pictures taken by the tracking satellite are obtained and processed. Finally, the direction vector from the tracking satellite to the target satellite in the camera coordinate system is obtained through the OpenGL camera coordinate principle, and the particle swarm algorithm is used to solve the short arc orbit determination problem to determine the target satellite orbit.

[0037] The present invention is applied to the field of space-based observation. BRIEF DESCRIPTION OF THE DRAWINGS

[0038] Figure 1 A flowchart of a satellite orbit determination method based on space-based observation according to Embodiment 1;

[0039] Figure 2 An effect diagram of a satellite designed by Spacesim according to Embodiment 11;

[0040] Figure 3 A schematic diagram showing the change of the pitch angle and azimuth angle in the absolute coordinate system according to Embodiment 11; wherein, Figure 3 (a) is a schematic diagram of the azimuth angle change, and Fig. (b) is a schematic diagram of the pitch angle change;

[0041] Figure 4 A schematic diagram of the Hough line detection result according to Embodiment 11;

[0042] Figure 5 A graph showing the change of the fitness function with the number of iterations according to Embodiment 11;

[0043] Figure 6 A photo of a single target satellite according to Embodiment 11;

[0044] Figure 7 An overlapped trajectory diagram according to Embodiment 11;

[0045] Figure 8 An OpenGL camera principle diagram according to Embodiment 11. SPECIFIC EMBODIMENTS

[0046] To make the technical solutions and advantages of the present invention more clearly expressed, the following further describes several embodiments of the present invention in detail with reference to the drawings. However, the following described embodiments are only several preferred embodiments of the present invention and are not used to limit the invention.

[0047] Embodiment 1. Refer to Figure 1 This embodiment is described. A satellite orbit determination method based on space-based observation according to this embodiment includes:

[0048] Two satellite orbits are planned and simulated using Spacesim randomly; one of the satellite orbits is the predicted target satellite orbit, and the other satellite orbit is the tracking satellite orbit;

[0049] An observation satellite is used to photograph the target satellite on the tracking satellite orbit to obtain a series of images of the target satellite;

[0050] Opencv is used to identify and process the series of images of the obtained target satellite to determine the trajectory of the target satellite obtained by the observation satellite;

[0051] The short arc orbit determination problem of the trajectory of the target satellite obtained by the observation satellite is processed according to the particle swarm algorithm to determine the target satellite orbit.

[0052] In practical applications, medium-short orbits are selected to replace the extremely short arc orbits, which is easier to verify the reliability of the results; the observation satellite needs to set reasonable camera parameters, such as the full field of view angle, the distance between the near and far planes, and the resolution; Opencv is used to identify and process the series of images of the obtained target satellite, including synthesizing and performing dilation and erosion operations on the obtained series of images, and then performing probabilistic Hough transform line detection to obtain the trajectory of the target satellite.

[0053] For the method for determining a satellite orbit based on space-based observation described in this embodiment, the short arc orbit determination problem of the trajectory of the target satellite obtained by the observation satellite is processed according to the particle swarm algorithm to determine the target satellite orbit. Through the particle swarm algorithm, the extremely short arc orbit information of dozens of seconds or even more than a dozen seconds can be effectively identified, with fast orbit determination speed, small error, and strong practicability.

[0054] The domestic spacecraft system simulation software Spacesim is used to avoid restrictions during use. By using Spacesim to design satellite orbits, then obtaining and processing the pictures taken by the tracking satellite. Finally, the direction vector from the tracking satellite to the target satellite in the camera coordinate system is obtained through the principle of the OpenGL virtual camera coordinates, and the particle swarm algorithm is used to solve the short arc orbit determination problem to determine the target satellite orbit.

[0055] Embodiment 2: This embodiment further limits the method for determining a satellite orbit based on space-based observation described in Embodiment 1. The observation satellite includes: a tracking satellite and a camera;

[0056] The camera swing direction of the camera is [1, 0, 0], the full field of view angle is 15°, the pitch resolution is 800 pixels, the azimuth resolution is 800 pixels, the near plane is specifically 1 m, the far plane is specifically 100,000 m, the pitch angle is 180°, and the azimuth angle is 0°.

[0057] The camera used in this embodiment is an OpenGL virtual camera. Parameters such as the camera orientation, full field of view angle, resolution, and pitch azimuth angle need to be adjusted to capture the trajectory map of the target satellite.

[0058] Embodiment 3: This embodiment further limits a satellite orbit determination method based on space-based observation described in Embodiment 1. The method uses Opencv to identify and process a series of images of the target satellite. The specific method is as follows:

[0059] Obtain the grayscale image of each photo in the series of images of the target satellite, and perform thresholding processing on the grayscale image.

[0060] Specifically, use an Opencv virtual camera to process the photos taken by the camera. After the simulation ends, 165 photos containing the target satellite taken by the observation satellite are obtained. To prevent the starry sky background in the photos from turning white during the process of superimposing the photos, it is first necessary to sequentially read the grayscale images of each photo and perform thresholding processing on them.

[0061] Embodiment 4: This embodiment further limits a satellite orbit determination method based on space-based observation described in Embodiment 1. The method further includes: obtaining the direction vector from the observation satellite to the target satellite according to the trajectory of the target satellite obtained by the observation satellite. Specifically:

[0062]

[0063] Among them, R1 is the rotation matrix from the celestial body system to the absolute coordinate system, R2 is the rotation matrix rotating 180° around the y-axis, R3 is the rotation matrix rotating 90° around the z-axis, f x 、f y 、c x 、c y are the internal parameters of the camera, f x is the focal length of the camera in the x-axis direction, f y is the focal length of the camera in the y-axis direction, c x is the x-coordinate of the optical center of the camera, c y is the y-coordinate of the optical center of the camera, x, y, z are the direction vectors from the observation satellite to the target satellite, and (u, v) are the pixel coordinates of the target satellite.

[0064] Specifically, solve the direction vector from the observation satellite to the target satellite according to the trajectory of the target satellite in the photo. In the software Spacesim, space targets are imaged using an OpenGL virtual camera. The three-dimensional model of the space target needs to be transformed in 5 coordinate systems before finally being imaged onto the image window. Considering the position and attitude of the camera during installation and the setting of the observation direction, it is necessary to obtain the direction vector in the absolute coordinate system, that is, the direction vector from the observation satellite to the target satellite.

[0065] Embodiment 5. This embodiment further limits a satellite orbit determination method based on space-based observation described in Embodiment 4, where the f x and f y and c x and c y are obtained according to the conversion between perspective camera parameters and OpenGL camera internal parameters, specifically:

[0066]

[0067] where w is the number of pixels in the horizontal direction of the captured image, h is the number of pixels in the horizontal direction of the captured image, n is the near-plane distance, f is the far-plane distance, and θ is the field of view angle in the pitch direction.

[0068] Embodiment 6. This embodiment further limits a satellite orbit determination method based on space-based observation described in Embodiment 4. The determination of the target satellite orbit is specifically as follows:

[0069] v i+1 = v i + c1 × rand × (pbest i - x i ) + c2 × rand × (gbest i - x i ),

[0070] x i+1 = x i + v i+1 ,

[0071] where v i is the velocity of the i-th generation of particles, v i+1 is the velocity of the (i + 1)-th generation of particles, that is, both v i and v i+1 are the increments of the variables [a, e, M] and [i, Ωω]. c1 and c2 are learning factors to be adjusted, rand is a random number between (0, 1), pbest i is the best position searched by a single particle after the i-th iteration, x i is the current position of the i-th generation of particles, x i+1 is the current position of the (i + 1)-th generation of particles, and gbest i is the best position searched by the particle swarm after the i-th iteration.

[0072] Specifically, the particle swarm algorithm is used to solve the six orbital elements of the target satellite. When generating the initial population using the particle swarm algorithm, the value range and search space of the optimization parameters need to be set according to some prior knowledge or constraint conditions.

[0073] Design the following two relatively reasonable medium and low Earth orbit satellites for orbit determination simulation according to the basic information of the currently launched satellites:

[0074]

[0075] Table 1 Six orbital elements of the designed observation satellite and target satellite

[0076] Among them, a is the semi-major axis of the orbit, e is the orbital eccentricity, M is the mean anomaly, i is the orbital inclination, Ω is the right ascension of the ascending node, and ω is the argument of perigee.

[0077] The initial population value range and search space designed in this embodiment according to the satellite orbit altitude are as follows:

[0078]

[0079]

[0080] Table 2 Population value range for different orbit altitudes

[0081] First, optimize the six orbital elements in two times. The variables selected for the first optimization are λ1 = [a, e, M], and the second time λ2 = [i, Ω, ω]. By optimizing the fitness function of the variable λ1, for any set of optimization variables [a, e, M0], according to Kepler's equation, the mean anomaly M at any time and the difference between the true anomaly and the initial time can be obtained

[0082]

[0083] M = E - e sin E

[0084]

[0085]

[0086] Then, according to the formula:

[0087] r2 = a(1 - e cos E)

[0088] where μ is the Earth's gravitational constant, E is the eccentric anomaly, is the true anomaly at time t, is the true anomaly at the initial time, is the difference in true anomaly, and r2 is the position vector of the target satellite.

[0089] The magnitude of the position vector of the target satellite at any time can be obtained.

[0090] Using the cosine theorem and the direction vector at this time The distance d between the target satellite and the observation satellite is obtained:

[0091]

[0092] r1 2 +d 2 -2r1d cos(π - θ) = r2 2

[0093] Where r1 is the position vector of the observation satellite.

[0094] Solving, the distance d between the target satellite and the observation satellite is obtained as:

[0095]

[0096] Obtain the position vector of the target satellite and the true anomaly difference deduced from the direction vector

[0097]

[0098]

[0099] In summary, for the direction vectors at the previously obtained N moments, the fitness function P1 for the variable λ1 is:

[0100]

[0101] Where the true anomaly difference obtained by Keplerian recursion from the i-th moment to the j-th moment, the true anomaly difference obtained from the direction vector from the i-th moment to the j-th moment.

[0102] The smaller the fitness function value corresponding to the optimization variable λ1, the closer the optimization variable λ1 is to the true value.

[0103] After searching for the variables [a, e, M], for the known orbital six elements [a, e, M, i, Ω, ω] of the target satellite, according to the Keplerian recursion and the conversion relationship between the orbital six elements and the position vector, the position vector of the target satellite at any moment can be obtained According to the above formula, the direction vector obtained from the Kepler equation can be calculated

[0104] Therefore, the fitness function P2 for the optimization variable λ2 is:

[0105]

[0106] After knowing the fitness functions of the optimization variables λ1 and λ2, the global optimal solutions of the optimization variables λ1 and λ2 in the search space can be found according to the particle swarm velocity-position update formula.

[0107] v i+1 = v i + c1 × rand × (pbest i - x i ) + c2 × rand × (gbest i - x i ),

[0108] x i+1 = x i + v i+1 .

[0109] Finally, using the particle swarm algorithm, a comparison graph of the six orbital elements of the partial orbit and the true values is obtained, as shown in the following figure:

[0110]

[0111] Table 3 Partial six-element values obtained by solving

[0112] Embodiment 7. A satellite orbit determination device based on space-based observation according to this embodiment, the device includes:

[0113] A satellite orbit planning unit for randomly planning and simulating two satellite orbits using Spacesim; one satellite orbit is the predicted target satellite orbit, and the other satellite orbit is the tracking satellite orbit;

[0114] A series of image acquisition units of the target satellite for taking pictures of the target satellite using an observation satellite on the tracking satellite orbit to obtain a series of images of the target satellite;

[0115] A trajectory acquisition unit of the target satellite for using Opencv to identify and process the series of images of the target satellite obtained to determine the trajectory of the target satellite obtained by the observation satellite;

[0116] A target satellite orbit determination unit for processing the short-arc orbit determination problem of the trajectory of the target satellite obtained by the observation satellite according to the particle swarm algorithm to determine the target satellite orbit.

[0117] Embodiment 8. This embodiment further limits the satellite orbit determination device based on space-based observation described in Embodiment 7, and the observation satellite includes: a tracking satellite and a camera;

[0118] The camera orientation of the camera is [1, 0, 0], the full field of view angle is 15°, the pitch resolution is 800 pixels, the azimuth resolution is 800 pixels, the near plane is specifically 1 m, the far plane is specifically 100,000 m, the pitch angle is 180°, and the azimuth angle is 0°.

[0119] Embodiment Nine. A computer device described in this embodiment includes a memory and a processor. A computer program is stored in the memory. When the processor runs the computer program stored in the memory, the processor executes a method for determining a satellite orbit based on space-based observation described in any one of Embodiments One to Four or Embodiment Six.

[0120] Embodiment Ten. A computer-readable storage medium described in this embodiment has a computer program stored thereon. When the computer program is run by a processor, it executes a method for determining a satellite orbit based on space-based observation described in any one of Embodiments One to Four or Embodiment Six.

[0121] Embodiment Eleven. Refer to Figures 2 to 8 Describe this embodiment. This embodiment provides a specific implementation for a method for determining a satellite orbit based on space-based observation described in Embodiment One, and is also used to explain Embodiments One to Six. Specifically:

[0122] Step 1: Use Spacesim to design two satellite orbits. The satellites designed by Spacesim are as Figure 1 shown. The satellite carrying a camera for space-based observation is called an observation satellite, and the satellite whose orbit information needs to be determined and is photographed by the observation satellite is called a target satellite. According to the basic information of currently launched satellites, the following two relatively reasonable medium and low Earth orbit satellites are designed for orbit determination simulation. The six orbital elements of the designed observation satellite and target satellite are shown in Table 1:

[0123]

[0124] Table 1 Six orbital elements of the designed observation satellite and target satellite

[0125] Step 2: Adjust the parameters of the camera installed in the observation satellite. The simulation camera used in Spacesim is an OpenGL camera. Parameters such as the camera orientation, full field of view angle, resolution, and pitch and azimuth angles need to be adjusted to capture the trajectory map of the target satellite. The specific parameter settings are shown in Table 2:

[0126]

[0127] Table 2 Camera parameters in Spacesim

[0128] Step 3: Process the photos taken by the camera using Opencv. After the simulation, 165 photos containing the target satellite taken by the observation satellite are obtained. To prevent the starry sky background in the photos from turning white during the process of superimposing the photos, it is first necessary to sequentially read the grayscale images of each photo and perform thresholding on them. The images before and after superimposition are as Figure 6 and Figure 7 shown.

[0129] After superimposition, individual stars and satellites will form a trajectory segment. Since there are gaps between satellite trajectories, it is necessary to perform erosion and dilation operations on the image before performing probabilistic Hough line detection. And because the distance from the observation satellite to the target satellite is much smaller than its distance to the stars, the longest line segment in the detection results is the trajectory of the target satellite taken by the observation satellite.

[0130] Step 4: Solve the direction vector from the observation satellite to the target satellite according to the target satellite trajectory described in Step 3. In the software Spacesim, spatial targets are imaged using an OpenGL virtual camera. The three-dimensional model of the spatial target needs to be transformed in 5 coordinate systems before it can be finally imaged onto the image window. Considering the position and attitude of the camera during installation and the setting of the observation direction, the solution formula for the direction vector in the absolute coordinate system can be obtained:

[0131]

[0132] where the matrix R1 is the rotation matrix from the celestial body system to the absolute coordinate system, and R2 and R3 are the rotation matrices for rotating 180° around the y-axis and 90° around the z-axis respectively. The parameters f x 、f y 、c x 、c y can be obtained from the conversion formula from perspective camera parameters to OpenGL camera internal parameters:

[0133]

[0134] where the OpenGL camera model is as Figure 8 shown, and fovy represents the camera's visual width. When the object is between the far plane far and the near plane near, the camera can take pictures and obtain an image with the number of pixels w*h.

[0135] Step 5: Use the particle swarm optimization algorithm to solve the six orbital elements of the target satellite. When generating the initial population using the particle swarm optimization algorithm, it is necessary to set the value range and search space of the optimization parameters according to some prior knowledge or constraints.

[0136] Based on the basic information of the currently launched satellites, the following two relatively reasonable medium and low Earth orbit satellites are designed for orbit determination simulation. The six orbital elements of the designed observation satellite and target satellite are shown in Table 3:

[0137]

[0138] Table 3 Six orbital elements of the designed observation satellite and target satellite

[0139] Among them, a is the semi-major axis of the orbit, e is the orbital eccentricity, M is the mean anomaly, i is the orbital inclination, Ω is the right ascension of the ascending node, and ω is the argument of perigee.

[0140] The value range of the initial population and the search space designed according to the satellite orbit altitude in this embodiment are shown in Table 4:

[0141]

[0142] Table 4 Value range of the population for different orbit altitudes

[0143] First, the six orbital elements are optimized in two steps. The variables selected for the first optimization are λ1 = [a, e, M], and for the second step, λ2 = [i, Ω, ω]. By optimizing the fitness function of the variable λ1, for any set of optimization variables [a, e, M0], according to Kepler's equation, the mean anomaly M at any time and the difference in the true anomaly from the initial time can be obtained

[0144]

[0145] M = E - e sin E

[0146]

[0147]

[0148] Then, according to the formula:

[0149] r2 = a(1 - e cos E)

[0150] where μ is the Earth's gravitational constant, E is the eccentric anomaly, is the true anomaly at time t, is the true anomaly at the initial time, is the difference in the true anomaly, and r2 is the position vector of the target satellite.

[0151] The magnitude of the position vector of the target satellite at any time can be obtained.

[0152] Using the cosine theorem and the direction vector at this time The distance d between the target satellite and the observation satellite is obtained:

[0153]

[0154] r1 2 +d 2 -2r1d cos(π-θ)=r2 2

[0155] Among them, r1 is the observed satellite position vector.

[0156] Solve and obtain the distance d as:

[0157]

[0158] Get the position vector of the target satellite and the direction vector True anomaly difference

[0159]

[0160]

[0161] In summary, for the direction vectors at the N moments obtained previously, the fitness function P1 for the variable λ1 is:

[0162]

[0163] in, The true anomaly difference obtained by Kepler recursion from time i to time j is, The true anomaly difference obtained from the direction vector from time i to time j.

[0164] The smaller the fitness function value corresponding to the optimization variable λ1 is, the closer the optimization variable λ1 is to the true value.

[0165] After searching for the variables [a, e, M], for the known six orbital numbers of the target satellite [a, e, M, i, Ω, ω], the position vector of the target satellite at any time can be calculated based on Kepler recursion and the conversion relationship between the six orbital numbers and the position vector According to the above formula, the direction vector obtained by Kepler's equation can be obtained

[0166] Therefore, the fitness function P2 for the optimization variable λ2 is:

[0167]

[0168] When the fitness functions of the optimization variables λ1 and λ2 are known, the global optimal solution of the optimization variables λ1 and λ2 in the search space can be found according to the particle swarm velocity position update formula.

[0169] v i+1 = v i + c1 × rand × (pbest i - x i ) + c2 × rand × (gbest i - x i ),

[0170] x i+1 = x i + v i+1 。

[0171] Finally, the comparison chart of the six orbital elements of the partial orbit obtained by the particle swarm algorithm and the true values is shown in Table 5 below:

[0172]

[0173] Table 5 The values of the partial six elements obtained by the solution

[0174] It can be seen from Table 5 that the orbital error of the target satellite obtained by adopting this embodiment is very small.

[0175] The above has described the present application in detail through specific embodiments, but the above are only the preferred embodiments of the present application and are not used to limit the present application. Any modifications, combinations of embodiments, equivalent replacements, and improvements made within the spirit and principle scope of the present application shall be included in the protection scope of the present application.

Claims

1. A satellite orbit determination method based on space-based observations, characterized in that, The method includes: Using Spacesim to randomly plan and simulate two satellite orbits; one satellite orbit is the predicted target satellite orbit, and the other satellite orbit is the tracking satellite orbit; Using an observation satellite to photograph the target satellite on the tracking satellite orbit to obtain a series of images of the target satellite; Using Opencv to identify and process the series of images of the target satellite obtained, and determining the trajectory of the target satellite obtained by the observation satellite; Processing the short-arc orbit determination problem of the trajectory of the target satellite obtained by the observation satellite according to the particle swarm algorithm to determine the target satellite orbit; The observation satellite includes: a tracking satellite and a camera; The camera has a camera swing direction of [1, 0, 0], a full field of view angle of 15°, a pitch resolution of 800 pixels, an azimuth resolution of 800 pixels, a near plane specifically of 1 m, a far plane specifically of 100,000 m, a pitch angle of 180°, and an azimuth angle of 0°.

2. The satellite orbit determination method based on space-based observation according to claim 1, wherein The specific method of using Opencv to identify and process the series of images of the target satellite obtained is: Obtaining the grayscale image of each photo in the series of images of the target satellite and performing thresholding processing on the grayscale image.

3. A satellite orbit determination method based on space-based observation according to claim 1, characterized in that The method further includes: obtaining the direction vector from the observation satellite to the target satellite according to the trajectory of the target satellite obtained by the observation satellite, specifically: ； Among them, is the rotation matrix from the star system to the absolute coordinate system, is the rotation matrix for rotating 180° around the y-axis, is the rotation matrix for rotating 90° around the z-axis, is the internal parameter of the camera, is the focal length in the x-axis direction of the camera, is the focal length in the y-axis direction of the camera, is the x coordinate of the optical center of the camera, is the y coordinate of the optical center of the camera, and and is the direction vector from the observed satellite to the target satellite, is the pixel coordinate of the target satellite.

4. A method for determining a satellite orbit based on space-based observations according to claim 3, wherein, The said Obtained according to the conversion between the perspective camera parameters and the OpenGL camera internal parameters, specifically: ， Among them, is the number of horizontal pixels of the captured image, is the number of vertical pixels of the captured image, is the near plane distance, is the far plane distance, is the field of view angle in the pitch direction.

5. A satellite orbit determination method based on space-based observation according to claim 1, wherein, Determining the target satellite orbit, specifically: ， ， Among them, is the velocity of the i-th generation of particles, is the velocity of the (i + 1)-th generation of particles, is the learning factor to be adjusted, is between is a random number, is the best position found by a single particle after the i-th iteration, is the current position of the i-th generation of particles, is the current position of the (i + 1)-th generation of particles, is the best position found by the particle swarm after the i-th iteration.

6. A satellite orbit determination device based on space-based observations, characterized in that The device includes: A satellite orbit planning unit for using Spacesim to randomly plan and simulate two satellite orbits; one satellite orbit is the predicted target satellite orbit, and the other satellite orbit is the tracking satellite orbit; A unit for obtaining a series of images of the target satellite, which is used to use an observation satellite to photograph the target satellite on the tracking satellite orbit to obtain a series of images of the target satellite; A unit for obtaining the trajectory of the target satellite, which is used to use Opencv to identify and process the series of images of the target satellite obtained, and determining the trajectory of the target satellite obtained by the observation satellite; A target satellite orbit determination unit for processing the short-arc orbit determination problem of the trajectory of the target satellite obtained by the observation satellite according to the particle swarm algorithm to determine the target satellite orbit; The observation satellite includes: a tracking satellite and a camera; The camera has a camera swing direction of [1, 0, 0], a full field of view angle of 15°, a pitch resolution of 800 pixels, an azimuth resolution of 800 pixels, a near plane specifically of 1 m, a far plane specifically of 100,000 m, a pitch angle of 180°, and an azimuth angle of 0°.

7. A computer device, characterized in that: It includes a memory and a processor. A computer program is stored in the memory. When the processor runs the computer program stored in the memory, the processor executes the method for determining a satellite orbit based on space-based observation described in any one of claims 1-5.

8. A computer-readable storage medium, characterized in that, A computer program is stored on this computer-readable storage medium. When the computer program is run by a processor, it executes the method for determining a satellite orbit based on space-based observation described in any one of claims 1-5.

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