Initialization method of orbit determination by projecting linearized orbital plane under conic surface

Abstract

The application discloses an initialization method of a conic surface under a projection linearization track surface, and belongs to the technical field of calculation, reckoning or counting. The method first obtains a preliminary estimation of a target track through three groups of observation data; determines a conic surface containing an initial track surface according to initial track information and geometric knowledge; estimates the missing height information in combination with the conic surface, and obtains more position information of the target in combination with the existing angle information; projects the position information of the target into a two-dimensional section, re-estimates the track parameters by using a least square algorithm, and more accurate track parameters can be obtained; then the iteration process is repeated by using the newly obtained track information until a certain initial orbit determination accuracy requirement is met. The algorithm firstly fits the height information of the target by using a conic surface coordinate system, and realizes linear fitting of the position vector by using a track surface projection method, so that the calculation amount is small and the accuracy is high.

Description

Technical Field

[0001] This invention relates to the technology for determining the initial trajectory of a space target in space, including research on trajectory analysis from a geometric perspective and estimation of the state parameters of the space target. Specifically, it discloses an initial trajectory determination method that projects a linearized trajectory surface under a conical surface, belonging to the technical field of calculation, estimation, or counting. Background Technology

[0002] With the rapid development of the aerospace industry, space orbital resources are becoming increasingly scarce. Space debris, faulty satellites, and non-cooperative spacecraft pose significant threats to missions, leading to the rapid development of space situational awareness. In tracking and observing non-cooperative spacecraft, using passive sensors such as visible light cameras offers advantages such as good concealment, resistance to weather conditions, and lightweight measurement equipment. Many current initial orbit determination methods rely on estimating orbital parameters, which exhibit nonlinear variations. This makes it difficult to balance estimation accuracy and computational complexity. For example, the Lambert initial orbit determination method requires only two position vectors and a time interval, placing demands on the time between observation points and being highly sensitive to position vector errors. Furthermore, existing initial orbit determination methods use least squares algorithms to approximate linear estimates of nonlinear orbital parameters before calculating target position information. While linear estimation of nonlinear orbital parameters reduces computational load, it results in low accuracy. Conversely, using nonlinear estimation methods to estimate orbital parameters before calculating target position information improves accuracy but incurs significant computational costs.

[0003] In geometry, conic sections are a very important branch, usually analyzed within projective or analytic geometry. Conic sections can be generated in three-dimensional space by the intersection of a plane and a cone. Depending on the angle between the plane and the cone's axis of rotation, four cross-sectional shapes can be obtained: a circle, an ellipse, a parabola, and a hyperbola. This invention aims to propose an initial orbit determination method that projects a linearized orbital surface onto the conical surface to overcome the aforementioned shortcomings. Summary of the Invention

[0004] The purpose of this invention is to address the shortcomings of the aforementioned background technology by providing an initial trajectory determination method based on a conical coordinate system and linearized using orbital plane projection. This method uses the geometric definition of conic sections for trajectory determination, performs data dimensionality reduction processing on the orbital plane and the spatial target position vector while preserving geometric features, and then performs linear fitting estimation on the dimensionality-reduced spatial target position vector. This achieves the technical effect of accurately calculating the target position while reducing the computational load, thus solving the technical problem of not being able to simultaneously consider accuracy and computational load in the task of determining the initial trajectory of a spatial target.

[0005] To achieve the above-mentioned objectives, the present invention employs the following technical solution:

[0006] The initial orbit determination method for projecting a linearized orbital surface onto a conical surface includes the following steps:

[0007] Step 1: Obtain initial orbital information;

[0008] Step 2: Determine the conical surface containing the initial orbital plane and estimate the spatial target position vector;

[0009] Step 3: Project the spatial target position vector and the initial orbital plane onto the two-dimensional cross section. Linearly estimate the orbital information based on the projection information of the spatial target position vector onto the two-dimensional cross section. The two-dimensional cross section passes through the semi-major axis of the initial orbital plane and is perpendicular to the initial orbital plane.

[0010] Step 4: If the current linear estimate of the subsequent orbit information obtained in Step 3 does not meet the accuracy requirements, update the initial orbit information to the current linear estimate of the subsequent orbit information, return to Step 2, and repeat the iterative estimation process of the subsequent orbit information until the linear estimate of the subsequent orbit information obtained meets the accuracy requirements.

[0011] As a further optimization of the initial orbit determination method for projecting a linearized orbital surface under a conical surface, step 3, which linearly estimates the orbital information based on the projection information of the spatial target position vector on the two-dimensional section, is as follows: Under the constraint that the straight line projected from the initial orbital surface to the two-dimensional section passes through a fixed point projected from the geocenter to the two-dimensional section, the least squares estimation method is used to linearly fit the scattered data points obtained by projecting the spatial target position vector to the two-dimensional section. The straight line obtained by the linear fitting is the projection result of the precise orbital surface on the two-dimensional section. The projection result of the precise orbital surface on the two-dimensional section is converted into the precise orbital surface in the three-dimensional space of the conical coordinate system. The orbital element information of the precise orbital surface is recorded as the current estimated value of the orbital information.

[0012] As a further optimization of the initial orbit determination method that projects a linearized orbital plane onto a conical surface, the specific method for linearly fitting the data scatter points obtained by projecting the position vector of the space target onto a two-dimensional section using the least squares estimation method is as follows: the data scatter points are weighted according to the source of the altitude information; or, different data scatter points are weighted according to the relative positional relationship between the space-based observation platform and the space target.

[0013] As a further optimization of the initial orbit determination method for projecting a linearized orbital surface under a conical surface, the specific method for obtaining the initial orbit information in step 1 is as follows: obtain a set of position vectors of the space target, which includes position vectors at least three times; determine the initial orbit information based on the set of position vectors of the space target.

[0014] As a further optimization of the initial orbit determination method that projects a linearized orbital plane onto a conical surface, the altitude information in the position vector at at least three time points is obtained through measurement, and the angle information in the position vector at at least three time points is obtained through a space-based observation platform.

[0015] As a further optimization of the initial orbit determination method that projects a linearized orbital surface under a conical surface, based on 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 orbital inclination.

[0016] As a further optimization of the initial orbit determination method that projects a linearized orbital surface onto a conical surface, step 2, which determines the conical surface containing the initial orbital surface and estimates the spatial target position vector, is as follows:

[0017] Based on the initial trajectory information, a cone surface with a unique apex angle is established, and an elliptical initial trajectory surface is obtained by intersecting the cone surface with a plane;

[0018] In the conical coordinate system defined by the conical surface, the spatial target position vector is estimated based on the trend of the change in the surface height of the conical surface.

[0019] As a further optimization of the initial orbit determination method that projects a linearized orbit surface onto a conical surface, the specific method for establishing a conical surface with a unique apex angle based on the initial orbit information is as follows:

[0020] When the initial orbital plane is not perpendicular to the Earth's polar axis, a cone surface with a unique apex angle is established based on the principle that the axis of rotation of the cone coincides with the Earth's polar axis and the initial orbital plane passes through the Earth's center.

[0021] When the initial orbital plane is perpendicular to the Earth's polar axis, a cone with a unique apex angle is established based on the principle that the axis of rotation of the cone passes through the focus of the perigee of the initial orbital plane and the initial orbital plane passes through the Earth's center.

[0022] As a further optimization of the initial orbit determination method that projects a linearized orbital plane under a conical surface, the position vector of the space target is estimated based on the trend of the curvature height change of the conical surface in the conical coordinate system determined by the conical surface. Specifically, the direction vector of the observation platform and the height information of the initial orbital plane are calculated based on the angle data of the space-based observation platform, and the position vector of the space target is determined based on the angle information of the space-based observation platform and the height information of the initial orbital plane.

[0023] An electronic device includes a memory and a processor, wherein the memory stores a computer program that runs on the processor, and the processor executes the steps of the above-described initialization and orbit determination method when running the computer program.

[0024] The present invention, by adopting the above technical solution, has the following beneficial effects:

[0025] (1) This invention abandons the approximate estimation process of nonlinearly changing orbital parameters using linear estimation methods. Instead, it combines the geometric features of the conical surface determined by the orbital surface and the spatial target position vector, and uses dimensionality reduction to linearly estimate the orbital parameters while maintaining the geometric features. The established conical surface containing the orbital surface has a clear meaning.

[0026] (2) After determining the conical surface, the present invention estimates the height information of the spatial target based on the rate of change of the conical surface in the conical coordinate system determined by the conical surface, which has more accurate estimation results and clearer significance.

[0027] (3) Based on the geometric constraint that the orbital plane passes through the Earth's center, this invention introduces the constraint that the straight line passes through a fixed point in the process of linearly estimating the orbital parameters. By using the least squares estimation method to linearly fit the two-dimensional projection data of the spatial position vector, the two-dimensional projection result of the accurate orbital plane is obtained. Then, the accurate orbital parameters in three-dimensional space are obtained. Compared with the traditional least squares estimation method that estimates the parameters of the six orbital roots or other parameters, it has the technical advantages of low computational cost and high accuracy. It is not limited by eccentricity, has clear geometric meaning, and does not require time intervals between observation points. Attached Figure Description

[0028] Figure 1 This is a flowchart of the initial orbit determination method for projecting a linearized orbital surface onto a conical surface, as proposed in this invention.

[0029] Figure 2 This is a schematic diagram illustrating the conical surface containing the track surface as defined in this invention.

[0030] Figure 3 This is a schematic diagram illustrating the determination of a conical surface containing a track surface under special circumstances according to the present invention.

[0031] Figure 4 This is a schematic diagram illustrating the method of estimating the target position by incorporating surface changes according to the present invention.

[0032] Figure 5 This is a schematic diagram of the trajectory estimation for the target position using projection linearization according to the present invention. Detailed Implementation

[0033] The technical solution of the invention will now be described in detail with reference to the accompanying drawings.

[0034] like Figure 1 As shown, this invention provides a method for determining the initial trajectory of a space target in a conical coordinate system, combining the geometric meaning of conic sections and utilizing linearization processing through projection dimensionality reduction. This method specifically includes steps 1 to 4.

[0035] Step 1, Obtain initial orbit information

[0036] First, the altitude information of three or more space targets is acquired. The time intervals between the acquired altitude information do not need to be equal. At the same time, the angle information of the space targets below the platform is also acquired from the space-based observation platform. Based on the existing angle and altitude information, a set of position vectors of the space targets can be determined. Next, according to the Gibbs initial orbit determination principle, the rough orbit information is determined and recorded as the initial orbit information or the forward orbit information. The forward orbit information includes two orbital parameters: eccentricity e and orbital inclination i.

[0037] Step 2: Determine the conical surface containing the initial orbital plane and estimate the spatial target position vector.

[0038] First, a conical surface with a unique vertex angle is established based on the two orbital parameters contained in the initial orbital information. A rough initial orbital surface is generated by the intersection of this conical surface and a plane. For example... Figure 2 As shown, three geocentric position vectors determine the first rough initial orbital plane. In the Gibbs problem, the orbital information of a space target in space can be calculated from three coplanar geocentric position vectors. The orbital information includes the semi-major axis, eccentricity, orbital inclination, right ascension of the ascending node, and argument of perigee. In this invention, the eccentricity e and the orbital inclination i are used to determine the cone apex angle.

[0039] The eccentricity and orbital inclination correspond uniquely to the cone apex angle. In the established conical surface, the cone's axis of rotation coincides with the Earth's polar axis. A plane intersects the cone; if the plane is perpendicular to the axis of rotation, the cross-section is circular. As the angle between the plane and the polar axis decreases, the cross-section becomes elliptical, and the smaller the angle, the greater the eccentricity of the ellipse. If the angle between the axis of rotation and the plane remains constant, the larger the cone apex angle, the smaller the eccentricity of the ellipse formed by the intersection of the cone and the plane. Therefore, 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 method for determining the conical surface cannot solve a special case: when the elliptical orbital plane is perpendicular to the Earth's polar axis. If the conical surface is still determined using the above method in this case, it is impossible to solve for elliptical orbits within the Earth's equatorial plane. To solve this problem, a conical surface is established where the axis of rotation no longer coincides with the Earth's polar axis, but the cone's axis of rotation is still too close to the focus of the orbital perigee. The conical surface established in this special case is used in subsequent calculations, such as... Figure 3 As shown.

[0040] Next, the altitude information of the space target is estimated. As seen in the process of establishing the conical surface, the altitude information of the space target exhibits an irregular and discontinuous trend with the change in the cone's height. Neither approximately linear nor nonlinear estimation methods can accurately reflect the changes in the space target's altitude data. Within the conical coordinate system determined by the conical surface, the altitude information of the space target is supplemented based on the trend of the conical surface's height change. The angle information corresponding to the supplemented altitude information can be obtained from the space-based observation platform, allowing the calculation of the space target's position vector. For example... Figure 4 As shown, the specific method for supplementing the altitude information of a space target is as follows: a set of position vectors of the space target a 1, a 2, a 3. A conical surface containing an elliptical orbital plane was identified. Utilizing the trend of the conical surface's height variation and based on the angle data of the space-based observation platform, the orientation vector of the observation platform and the height information of the orbital plane can be calculated. Combined with the angle information of the space-based observation platform, the position vector information of the space target can then be obtained. b i .

[0041] Step 3: Project the spatial 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 spatial target position vector onto the two-dimensional cross section.

[0042] A cross-section passing through the semi-major axis of the elliptical orbital plane and perpendicular to the orbital plane is selected. The spatial target position vector in the three-dimensional space of the conical coordinate system and the rough initial orbital plane are projected onto the cross-section, resulting in a scatter plot of the spatial target position vector in the two-dimensional cross-section. Since the orbital plane passes through the Earth's center, a constrained linear fit is performed on the scatter plot. The resulting fit is a more accurate projection of the orbital plane onto the two-dimensional cross-section. This more accurate projection of the orbital plane onto the two-dimensional cross-section is then converted into an accurate orbital plane in the three-dimensional space of the conical coordinate system. The orbital element information of the accurate orbital plane converted to the three-dimensional space of the conical coordinate system is recorded as the subsequent orbital information.

[0043] like Figure 5 As shown, this illustrates the basic principle of data linearization through dimensionality reduction. In an elliptical orbit, the true anomaly angle of the target can be determined based on its position vector, and subsequently, the angle between the target's position vector and the semi-major axis of the elliptical orbit can be determined, such as... Figure 5 As shown to the left of the arrow, by projecting the spatial target position vector onto a section passing through the semi-major axis of the elliptical orbital plane and perpendicular to the orbital plane, we can obtain... Figure 5 The two-dimensional cross-section projection result shown to the right of the arrow, that is, the data scatter points obtained after the two-dimensional projection of the spatial target position vector, are distributed on both sides of the straight line obtained after the two-dimensional projection of the orbital plane.

[0044] In the scattered data obtained after two-dimensional projection of the space target's position vector, the scattered data can be divided into two categories based on the source of the altitude information: one category consists of scattered data with altitudes obtained from the actual measurements in step 1, and the other category consists of scattered data with altitude information calculated in step 2. When estimating the orbital plane, least squares estimation can be used to weight the scattered data based on the source of the altitude information. Alternatively, least squares estimation can be used to weight different scattered data based on the relative positional relationship between the space-based observation platform and the space target. Since the orbital plane's focus is located at the Earth's center, the projection of the orbital plane onto the cross-section must pass through the Earth's center. Therefore, the least squares estimation process requires adding a constraint that the straight line projected from the orbital plane onto the two-dimensional cross-section passes through a fixed point projected from the Earth's center onto the two-dimensional cross-section.

[0045] Step 4: If the current linear estimate of the subsequent orbit information obtained in Step 3 does not meet the accuracy requirements, update the initial orbit information to the current linear estimate of the subsequent orbit information, return to Step 2, and repeat the iterative estimation process of the subsequent orbit information until the linear estimate of the subsequent orbit information meets the accuracy requirements.

[0046] If the accuracy requirements are not met, the rear track information is used as the new front track information, and steps 2 to 3 above are repeated. The information used in this process is still the already measured angle information and target height information. No new measurements are needed. The process of calculating the rear track information is repeated until the estimation result converges.

[0047] In one embodiment of the present invention, an electronic device is also provided, including a memory and a processor. The memory stores a computer program that runs on the processor. When the processor runs the computer program, it executes the steps of the above-described initialization orbit determination method.

[0048] The foregoing has shown and described 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 specific embodiments described above. The specific embodiments and descriptions in the specification are merely for further illustrating the principles and preparation effects of the present invention. Various changes and modifications can be made to the present invention without departing from its spirit and scope, and all such changes and modifications fall within the scope of protection claimed by the present invention. The scope of protection of the present invention is defined by the claims and their equivalents.

Claims

1. An initialization method for orbit determination of a linearized track surface projected under a conic surface, characterized in that, The method comprises the following steps: Step 1, obtaining initial orbit information; Step 2, determining a conical surface containing the initial orbit plane and estimating a position vector of the space target; Step 3, projecting the position vector of the space target and the initial orbit plane to a two-dimensional section, and linearly estimating post-orbit information according to the projection information of the position vector of the space target on the two-dimensional section, wherein the two-dimensional section passes through the semi-major axis of the initial orbit plane and is perpendicular to the initial orbit plane, and wherein The specific method of linearly estimating post-orbit information according to the projection information of the position vector of the space target on the two-dimensional section is that, under the constraint that the straight line obtained by projecting the initial orbit plane to the two-dimensional section passes through a fixed point of the two-dimensional section projected to the center of the Earth, the data scatter points obtained by projecting the position vector of the space target to the two-dimensional section are linearly fitted by using a least square estimation method, the straight line obtained by linear fitting is the projection result of the accurate orbit plane on the two-dimensional section, the projection result of the accurate orbit plane on the two-dimensional section is converted into the accurate orbit plane in the three-dimensional space of the conical surface coordinate system, and the orbital element information of the accurate orbit plane is recorded as the current estimation value of the post-orbit information, The specific method of linearly fitting the data scatter points obtained by projecting the position vector of the space target to the two-dimensional section by using the least square estimation method is that the data scatter points are weighted calculated according to the source of the height information, or different data scatter points are weighted processed according to the relative position relationship between the space-based observation platform and the space target; Step 4, when the current linear estimation value of the post-orbit information obtained in step 3 does not meet the accuracy requirement, the initial orbit information is updated to the current linear estimation value of the post-orbit information, and the iteration estimation process of the post-orbit information is returned to step 2, and the iteration estimation process of the post-orbit information is cycled until the linear estimation value of the post-orbit information obtained meets the accuracy requirement.

2. The initialization method of a conic under-projection linearization of an orbital plane according to claim 1, characterized in that, The specific method of obtaining the initial orbit information in step 1 is that a group of position vectors of the space target are obtained, the group of position vectors comprises position vectors at at least three time points, and the initial orbit information is determined according to the group of position vectors of the space target.

3. The initialization method of claim 2, wherein, The height information in the position vectors at the at least three time points is obtained by measurement, and the angle information in the position vectors at the at least three time points is obtained by the space-based observation platform.

4. The initialization method of claim 2, wherein, According to the initial orbit determination principle of Gibbs, the initial orbit information is determined according to the group of position vectors of the space target, and the initial orbit information comprises an eccentricity and an orbital inclination.

5. The initialization method of claim 1, wherein, The specific method of step 2 is as follows: An elliptical initial orbit plane is obtained by intersecting a plane with a conical surface with a unique conical top angle according to the initial orbit information; In a conical surface coordinate system determined by the conical surface, the position vector of the space target is estimated according to the variation trend of the curved surface height of the conical surface.

6. The initialization method of claim 5, wherein, The specific method of establishing a conical surface with a unique conical top angle according to the initial orbit information is as follows: When the initial orbit plane is not perpendicular to the polar axis of the Earth, a conical surface with a unique conical top angle is established according to the initial orbit information, with the principle that the rotation axis of the conical surface coincides with the polar axis of the Earth and the initial orbit plane passes through the center of the Earth. When the initial orbital plane is perpendicular to the polar axis of the earth, a conical surface is established according to the initial orbit information, with the principle that the rotation axis of the cone passes through the focus of the initial orbit plane near the perigee and the initial orbit plane passes through the center of the earth.

7. The initialization method of claim 5, wherein, In the conical surface coordinate system determined by the conical surface, the spatial target position vector is estimated according to the height variation trend of the curved surface of the conical surface, specifically: the direction vector of the space-based observation platform is calculated according to the angle data of the space-based observation platform, and the height information of the initial orbit plane is calculated according to the angle data of the space-based observation platform and the height information of the initial orbit plane, and the spatial target position vector is determined according to the angle information of the space-based observation platform and the height information of the initial orbit plane. 8.An electronic device comprising a memory and a processor, wherein the memory stores a computer program which is run on the processor, and the processor executes the steps of the initialization orbit determination method of claim 1 when running the computer program.

Images