Initialized orbit determination method for projecting linearized orbital plane under conical surface

Abstract

The invention discloses an initialized orbit determination method for projecting a linearized orbital plane under a conical surface, and belongs to the technical field of calculation, reckoning or counting. The method comprises the steps of firstly obtaining preliminary estimation of a target track through three groups of observation data; determining a conical surface containing an initial orbit surface according to the initial orbit information and geometric knowledge; the lacked height information is estimated in combination with the conical surface, and more position information of the target is obtained in combination with the existing angle information; the position information of the target is projected into the two-dimensional cross section, and the orbit parameters are re-estimated by using the least square algorithm, so that more accurate orbit parameters can be obtained; and repeating the iteration process by using the newly obtained orbit information until a certain initial orbit determination precision requirement is met. According to the algorithm, the height information of the target is fitted by using the conical surface coordinate system for the first time, linear fitting of the position vector is realized by using the orbital plane projection method, the calculated amount is small, and the accuracy is high.

Description

Technical Field

[0001] The present invention relates to the technology of determining the initial orbit of a space target in space, including the research contents of analyzing the orbit from a geometric point of view, estimating the state parameters of the space target, etc., and specifically discloses an initialization orbit determination method of projecting a linearized orbital surface under a conical surface, which belongs to the technical field of calculation, estimation or counting. Background Art

[0002] With the vigorous development of the aerospace industry, space orbital resources are becoming increasingly scarce. Space debris, faulty satellites, and non-cooperative spacecraft can pose a huge threat to one's own missions, and space situational awareness has therefore developed rapidly. In the tracking and observation mission of non-cooperative spacecraft, the use of passive sensors such as visible light cameras for measurement has the advantages of good concealment, not easily affected by weather, and light measurement equipment. Most of the current initial orbit determination methods use the estimation of orbital parameters, and the orbital parameters have a nonlinear change law, which results in the inability to balance the estimation accuracy and the amount of calculation. For example, the Lambert initial orbit determination method only requires two position vectors and time intervals, has requirements on the time between observation points, and is very sensitive to the position vector error. In addition, the existing initial orbit determination method uses the least squares algorithm to make an approximate linear estimate of the nonlinear orbital parameters, and then uses the approximate estimated nonlinear orbital parameters to calculate the target position information. Although the linear estimation of the nonlinear orbital parameters can reduce the amount of calculation, the accuracy is low; while the nonlinear estimation method is used to estimate the orbital parameters and then calculate the target position information, which can improve the accuracy but the amount of calculation is large.

[0003] In geometry, the conic section problem is a very important branch, which is usually analyzed in projective geometry or analytic geometry. Conic sections can be generated in three-dimensional space by the intersection of a plane and a cone. According to the different angles between the plane and the cone's rotation axis, four cross-sectional shapes can be obtained, namely: circle, ellipse, parabola and hyperbola. The present invention aims to propose an initialization orbit determination method for projecting a linearized orbital surface under a cone surface to overcome the above-mentioned defects. Summary of the invention

[0004] The object of the present invention is to address the deficiencies of the above-mentioned background technology and to provide an initial orbit determination method based on a conic coordinate system and linearized using orbital plane projection. The method uses the geometric definition of conic sections to determine the orbit, performs data dimensionality reduction processing on the orbital plane and the space target position vector that retains the geometric features, and then performs linear fitting estimation on the space target position vector after dimensionality reduction processing, thereby achieving the technical effect of accurately calculating the target position and reducing the amount of calculation, and solving the technical problem that it is impossible to simultaneously take into account both accuracy and the amount of calculation in the task of determining the initial orbit of the space target.

[0005] The present invention adopts the following technical solutions to achieve the above-mentioned invention object: The method for initializing orbit determination by projecting a linearized orbital surface on a conical surface includes the following steps: Step 1, obtaining initial orbit information; Step 2, determine the conical surface containing the initial orbital surface and estimate the space target position vector; Step 3, projecting the space target position vector and the initial orbital plane onto a two-dimensional cross section, and linearly estimating the subsequent orbital information based on the projection information of the space target position vector on the two-dimensional cross section, where the two-dimensional cross section passes through the semi-major axis of the initial orbital plane and is perpendicular to the initial orbital plane; Step 4: When the current linear estimation value of the rear track information obtained in step 3 does not meet the accuracy requirement, update the initial track information to the current linear estimation value of the rear track information, return to step 2, and loop the iterative estimation process of the rear track information until the linear estimation value of the rear track information obtained meets the accuracy requirement.

[0006] As a further optimization scheme for the initialization orbit determination method of projecting the linearized orbital plane on the conical surface, the specific method of step 3 for linearly estimating the subsequent orbital information based on the projection information of the space target position vector on the two-dimensional section is as follows: under the constraint that the straight line projected from the initial orbital plane to the two-dimensional section passes through the center of the earth and is projected to the fixed point of the two-dimensional section, the least squares estimation method is used to perform linear fitting on the data scatter points obtained by projecting the space target position vector to the two-dimensional section. The straight line obtained by the linear fitting is the projection result of the precise orbital plane on the two-dimensional section. The projection result of the precise orbital plane on the two-dimensional section is converted into the precise orbital plane in the three-dimensional space of the conical coordinate system, and the orbital element number information of the precise orbital plane is recorded as the current estimated value of the subsequent orbital information.

[0007] As a further optimization scheme for the initialization orbit determination method of projecting the linearized orbital plane under the conical surface, the specific method of using the least squares estimation method to perform linear fitting on the data scatter points obtained by projecting the space target position vector to the two-dimensional cross section is: weighted calculation of the data scatter points according to the source of the height information; or weighted processing of different data scatter points according to the relative position relationship between the space-based observation platform and the space target.

[0008] As a further optimization scheme of the initialization orbit determination method of projecting the linearized orbital surface under the conical surface, the specific method of obtaining the initial orbit information in step 1 is: obtaining a set of position vectors of the space target, a set of position vectors includes position vectors at least three moments; determining the initial orbit information according to the set of position vectors of the space target.

[0009] As a further optimization scheme of the initialization orbit determination method of projecting the linearized orbital plane under the conical surface, the altitude information in the position vector at least three times is obtained by measurement, and the angle information in the position vector at least three times is obtained by a space-based observation platform.

[0010] As a further optimization scheme of the initialization orbit determination method of projecting the linearized orbital plane on the conical surface, according to the Gibbs initial orbit determination principle, the initial orbit information is determined according to a set of position vectors of the space target. The initial orbit information includes eccentricity and orbit inclination.

[0011] As a further optimization scheme of the initialization orbit determination method of projecting the linearized orbital surface under the conical surface, the specific method of step 2 to determine the conical surface containing the initial orbital surface and estimate the space target position vector is: A conical surface with a unique cone vertex angle is established according to the initial orbit information, and an elliptical initial orbital surface is obtained by intersecting a plane with the conical surface; In the cone coordinate system determined by the cone surface, the spatial target position vector is estimated according to the change trend of the cone surface height.

[0012] As a further optimization scheme for the initialization orbit determination method of projecting the linearized orbital surface on the conical surface, the specific method for establishing a conical surface with a unique cone vertex angle according to the initial orbit information is as follows: When the initial orbital plane is not perpendicular to the Earth's polar axis, the cone's rotation axis coincides with the Earth's polar axis and the initial orbital plane passes through the Earth's center, and a cone surface with a unique cone vertex angle is established based on the initial orbital information; When the initial orbital plane is perpendicular to the Earth's polar axis, the cone's rotation axis passes close to the focus of the initial orbital plane's perigee and the initial orbital plane passes through the Earth's center, and a conical surface with a unique cone vertex angle is established based on the initial orbital information.

[0013] As a further optimization scheme of the initialization orbit determination method of projecting the linearized orbital plane on the conical surface, in the conical coordinate system determined by the conical surface, the space target position vector is estimated according to the surface height change trend of the conical surface. Specifically, the direction vector of the observation platform and the height information of the initial orbital plane are calculated according to the angle data of the space-based observation platform, and the space target position vector is determined according to the angle information of the space-based observation platform and the height information of the initial orbital plane.

[0014] An electronic device comprises a memory and a processor, wherein a computer program running on the processor is stored in the memory, and the processor executes the steps of the above-mentioned initialization orbit determination method when running the computer program.

[0015] The present invention adopts the above technical solution and has the following beneficial effects: (1) The present invention abandons the process of approximating the nonlinearly changing orbital parameters using linear estimation methods. Instead, the geometric characteristics of the orbital surface and the conical surface determined by the space target position vector are considered. Under the premise of maintaining the geometric characteristics, the orbital parameters are linearly estimated using dimensionality reduction processing. The established conical surface containing the orbital surface has a clear meaning.

[0016] (2) After determining the conical surface, the present invention estimates the height information of the space target according to the rate of change of the conical surface in the conical coordinate system determined by the conical surface, which has a more accurate estimation result and a clearer meaning.

[0017] (3) Based on the geometric constraint that the orbital plane passes through the center of the earth, the present invention introduces the constraint that the straight line passes through a fixed point in the process of linearly estimating orbital parameters. The two-dimensional projection data scatter points of the spatial position vector are linearly fitted by the least squares estimation method to obtain the precise two-dimensional projection result of the orbital plane, and then the precise orbital parameters in three-dimensional space are obtained. Compared with the traditional least squares estimation method for estimating the parameters of the six elements of the orbit or other parameters, the present invention has the technical advantages of small calculation amount and high accuracy, and is not restricted by eccentricity and has clear geometric meaning, and does not have any requirements on the time interval between observation points. BRIEF DESCRIPTION OF THE DRAWINGS

[0018] Figure 1 The present invention is a flowchart of the method for initializing orbit determination by projecting a linearized orbital surface under a conical surface.

[0019] Figure 2 Schematic diagram of a conical surface containing a track surface determined for the present invention.

[0020] Figure 3 This is a schematic diagram of determining a conical surface containing a track surface in a special case of the present invention.

[0021] Figure 4 It is a schematic diagram of estimating the target position in combination with the surface change according to the present invention.

[0022] Figure 5 This is a schematic diagram of the trajectory of the projected linearized target position estimation of the present invention. DETAILED DESCRIPTION

[0023] The technical solution of the invention is described in detail below with reference to the accompanying drawings.

[0024] like Figure 1 As shown, the present invention provides a method for determining the initial orbit of a space target in a conic coordinate system by combining the geometric meaning of conic curves and using linear processing of projection dimension reduction. The method specifically includes steps 1 to 4.

[0025] Step 1: Get initial track information

[0026] First, the altitude information of three or more space targets is obtained. The time intervals between the altitude information obtained do not need to be equal. At the same time, the angle information of the space targets under the platform is obtained from the space-based observation platform. According to the existing angle and altitude information, a set of position vectors of the space targets can be determined. Then, according to the Gibbs initial orbit determination principle, the rough orbit information is determined and recorded as the initial orbit information or the previous orbit information. The previous orbit information includes two orbit parameters: eccentricity e and orbit inclination i.

[0027] Step 2: Determine the conical surface containing the initial orbital surface and estimate the space target position vector

[0028] First, a conical surface with a unique cone vertex angle is established based on the two orbital parameters contained in the initial orbital information. The rough initial orbital surface is generated by the intersection of the conical surface and a plane. Figure 2 As shown, the three geocentric position vectors determine the first rough initial orbital plane. In the Gibbs problem, the three coplanar geocentric position vectors can calculate the orbital information of the space target in space. The orbital information includes the semi-major axis, eccentricity, orbital inclination, right ascension of the ascending node, and argument of perigee. In the present invention, the eccentricity e and orbital inclination i are used to determine the cone vertex angle.

[0029] The cone vertex angle corresponding to the eccentricity and orbital inclination is unique. In the established conical surface, the rotation axis of the cone coincides with the polar axis of the earth. When a plane intersects with a cone, if the plane is perpendicular to the rotation axis, the cross section is a circle. As the angle between the plane and the polar axis decreases, the cross section is an ellipse, and the smaller the angle, the greater the eccentricity of the ellipse. If the angle between the rotation axis and the plane remains unchanged, the eccentricity of the ellipse formed by the intersection of the cone and the plane with a larger cone vertex angle is smaller. It can be concluded that a conical surface containing the target orbital plane can be determined by the eccentricity e and the orbital inclination i. However, this conical surface determination method cannot solve a special case, that is, the case where the elliptical orbital plane is perpendicular to the polar axis of the earth. If the conical surface is still determined according to the above method in this case, the elliptical orbit running in the equatorial plane of the earth cannot be solved. To solve this problem, a conical surface is established in which the rotation axis no longer coincides with the polar axis of the earth, but the rotation axis of the cone is still too close to the focus of the orbital perigee. The conical surface established in this special case is used in subsequent calculation processes, such as Figure 3 shown.

[0030] Next, estimate the height information of the space target. From the process of establishing the above conical surface, it can be seen that the height information of the space target shows irregular discontinuity characteristics with the change trend of the cone surface height. The use of approximate linear estimation methods or nonlinear estimation methods cannot well reflect the change of the height data of the space target. In the cone coordinate system determined by the cone surface, the height information of the space target is supplemented according to the change trend of the surface height of the cone surface. The angle information corresponding to the supplemented height information can be obtained from the space-based observation platform, and the position vector of the space target can be calculated. Figure 4 As shown in the figure, the specific method of completing the height information of the space target is: a set of position vectors of the space target a 1, a 2, a 3. The conical surface containing the elliptical orbital surface is determined. The height change trend of the conical surface and the angle data of the space-based observation platform can be used to calculate the direction vector of the observation platform and the height information of the orbital surface. Then, the position vector information of the space target can be obtained by combining the angle information of the space-based observation platform. b i .

[0031] Step 3: Project the space target position vector and the initial orbital plane onto a two-dimensional cross section, and linearly estimate the orbital information based on the projection information of the space target position vector on the two-dimensional cross section.

[0032] Select a section that passes through the semi-major axis of the elliptical orbital plane and is perpendicular to the orbital plane, project the spatial target position vector and the rough initial orbital plane in the three-dimensional space of the conical coordinate system into the section, and obtain the data scatter points of the spatial target position vector in the two-dimensional section. Since the orbital plane passes through the center of the earth, a constrained linear fit is performed on the data scatter points, and the fitting result is a more accurate projection of the orbital plane in the two-dimensional section, and the projection of the more accurate orbital plane in the two-dimensional section is converted to the accurate orbital plane in the three-dimensional space of the conical coordinate system, and the orbital element information converted to the accurate orbital plane in the three-dimensional space of the conical coordinate system is recorded as the post-orbital information.

[0033] like Figure 5 As shown in the figure, the basic principle of data linearization through dimensionality reduction processing is explained. In the elliptical orbital plane, the true anomaly angle data of the space target can be determined according to the space target position vector, and then the angle between the space target position vector and the semi-major axis of the elliptical orbital plane can be determined, as shown in Figure 5 As shown on the left side of the arrow, projecting the space target position vector to the section through the semi-major axis of the elliptical orbital plane and perpendicular to the orbital plane, we can get Figure 5 The two-dimensional cross-sectional projection result shown on the right side of the arrow, that is, the data scatter points obtained after the two-dimensional projection of the space target position vector are distributed on both sides of the straight line obtained after the two-dimensional projection of the orbital surface.

[0034] Among the data scatter points obtained after the two-dimensional projection of the space target position vector, the data scatter points can be divided into two categories according to the source of the height information: one is the data scatter points whose height comes from the actual measurement in step 1, and the other is the data scatter points whose height information is calculated in step 2. When estimating the orbital plane, the least squares estimation can be used to perform weighted calculations on the data scatter points according to the source of the height information, or the least squares estimation can be used to perform weighted processing on different data scatter points according to the relative position relationship between the space-based observation platform and the space target. Since the focus of the orbital plane is at the center of the earth, the projection of the orbital plane in the cross section must pass through the center of the earth. The least squares estimation process needs to add a point-through constraint that the straight line projected from the orbital plane to the two-dimensional cross section passes through the center of the earth and projects to the fixed point of the two-dimensional cross section.

[0035] Step 4: When the current linear estimation value of the rear track information obtained in step 3 does not meet the accuracy requirement, the initial track information is updated to the current linear estimation value of the rear track information, and the process returns to step 2 to cycle the iterative estimation process of the rear track information until the linear estimation value of the rear track information meets the accuracy requirement.

[0036] When the accuracy requirement is not met, the rear track information is used as the new front track information, and the above steps 2 to 3 are repeated. The information used in this process is still the angle information and target height information that have been measured. No new measurement is required, and the process of calculating the rear track information is repeated until the estimation result converges.

[0037] In one embodiment of the present invention, an electronic device is provided, including a memory and a processor, wherein the memory stores a computer program running on the processor, and the processor executes the steps of the above-mentioned initialization orbit determination method when running the computer program.

[0038] The above shows and describes the basic principles, main features and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited to the above specific embodiments. The above specific embodiments and the description in the specification are only for further illustrating the principles and preparation effects of the present invention. Without departing from the spirit and scope of the present invention, the present invention may have various changes and improvements, which fall within the scope of the present invention. The scope of the present invention is defined by the claims and their equivalents.

Claims

1. A method for initializing orbit determination by projecting a linearized orbital surface under a conical surface, characterized in that: The steps include: Step 1, obtaining initial orbit information; Step 2, determine the conical surface containing the initial orbital surface and estimate the space target position vector; Step 3, projecting the space target position vector and the initial orbital plane to a two-dimensional cross section, and linearly estimating the subsequent orbital information according to the projection information of the space target position vector on the two-dimensional cross section, wherein the two-dimensional cross section passes through the semi-major axis of the initial orbital plane and is perpendicular to the initial orbital plane; Step 4: When the current linear estimation value of the rear track information obtained in step 3 does not meet the accuracy requirement, update the initial track information to the current linear estimation value of the rear track information, return to step 2, and loop the iterative estimation process of the rear track information until the linear estimation value of the rear track information obtained meets the accuracy requirement.

2. The method for initializing orbit determination by projecting a linearized orbital surface under a conical surface according to claim 1, characterized in that: The specific method of step 3 for linearly estimating the subsequent orbital information based on the projection information of the space target position vector on the two-dimensional section is: under the constraint that the straight line projected from the initial orbital plane to the two-dimensional section passes through the center of the earth and is projected to a fixed point of the two-dimensional section, the least squares estimation method is used to perform linear fitting on the data scatter points obtained by projecting the space target position vector to the two-dimensional section. The straight line obtained by the linear fitting is the projection result of the precise orbital plane on the two-dimensional section. The projection result of the precise orbital plane on the two-dimensional section is converted into a precise orbital plane in the three-dimensional space of the conical coordinate system, and the orbital element number information of the precise orbital plane is recorded as the current estimated value of the subsequent orbital information.

3. The method for initializing orbit determination by projecting a linearized orbital surface under a conical surface according to claim 2, characterized in that: The specific method of using the least squares estimation method to perform linear fitting on the data scatter points obtained by projecting the space target position vector to the two-dimensional cross section is: weighting the data scatter points according to the source of the height information; or weighting different data scatter points according to the relative position relationship between the space-based observation platform and the space target.

4. The method for initializing orbit determination by projecting a linearized orbital surface under a conical surface according to claim 1, 2 or 3, characterized in that: The specific method of obtaining the initial orbit information in step 1 is: obtaining a set of position vectors of the space target, wherein the set of position vectors includes position vectors at least at three moments; and determining the initial orbit information according to the set of position vectors of the space target.

5. The method for initializing orbit determination by projecting a linearized orbital surface under a conical surface according to claim 4, characterized in that: The height information in the position vectors at least three times is obtained by measurement, and the angle information in the position vectors at least three times is obtained by a space-based observation platform.

6. The method for initializing orbit determination by projecting a linearized orbital surface under a conical surface according to claim 4, characterized in that: According to the Gibbs initial orbit determination principle, initial orbit information is determined according to a group of position vectors of the space target, and the initial orbit information includes eccentricity and orbit inclination.

7. The method for initializing orbit determination by projecting a linearized orbital surface under a conical surface according to claim 1, 2 or 3, characterized in that: The specific method of determining the conical surface including the initial orbital surface and estimating the space target position vector in step 2 is: Establish a conical surface with a unique cone vertex angle according to the initial orbit information, and obtain an elliptical initial orbital surface by intersecting a plane with the conical surface; In the conical surface coordinate system determined by the conical surface, the spatial target position vector is estimated according to the change trend of the curved surface height of the conical surface.

8. The method for initializing orbit determination by projecting a linearized orbital surface under a conical surface according to claim 7, characterized in that: The specific method of establishing a conical surface with a unique cone vertex angle according to the initial orbit information is as follows: When the initial orbital plane is not perpendicular to the polar axis of the earth, a cone surface with a unique cone vertex angle is established based on the initial orbital information, with the principle that the rotation axis of the cone coincides with the polar axis of the earth and the initial orbital plane passes through the center of the earth; When the initial orbital plane is perpendicular to the earth's polar axis, a cone surface with a unique cone vertex angle is established based on the initial orbital information, with the cone's rotation axis passing close to the focus of the perigee of the initial orbital plane and the initial orbital plane passing through the center of the earth.

9. The method for initializing orbit determination by projecting a linearized orbital surface under a conical surface according to claim 7, characterized in that: In the conical coordinate system determined by the conical surface, the space target position vector is estimated according to the surface height change trend of the conical surface, specifically: the direction vector of the observation platform and the height information of the initial orbital plane are calculated according to the angle data of the space-based observation platform, and the space target position vector is determined according to the angle information of the space-based observation platform and the height information of the initial orbital plane.

10. An electronic device comprising a memory and a processor, wherein the memory stores a computer program to be executed on the processor, and the processor executes the steps of the initialization orbit determination method according to claim 1 when executing the computer program.

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