Satellite atmospheric resistance modeling method based on geometric effective area and relative flow direction
By calculating the effective windward area and drag coefficient angle model based on the satellite geometric model, the problem of high parameter correlation in the satellite atmospheric drag model was solved, and higher accuracy orbit prediction was achieved.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- CHANGGUANG SATELLITE TECH CO LTD
- Filing Date
- 2026-01-09
- Publication Date
- 2026-04-28
AI Technical Summary
In existing satellite atmospheric drag models, the drag coefficient is modeled as a constant and the geometric changes of the satellite structure are ignored, resulting in large errors and high parameter correlation, which affects the accuracy of orbit prediction.
An improved atmospheric drag acceleration model is constructed by calculating the effective windward area based on a detailed satellite geometric model and combining it with a drag coefficient angle model, thereby reducing parameter correlation and improving orbit prediction accuracy.
By introducing a geometric model to accurately calculate the change in windward area, the correlation of parameters is reduced, the accuracy of orbit prediction and the stability of the solution are improved, thus enhancing the accuracy of orbit prediction.
Smart Images
Figure CN121936352A_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of aerospace dynamics and satellite orbit determination technology, specifically relating to a satellite atmospheric drag modeling method based on geometric effective area and relative flow direction. Background Technology
[0002] In recent decades, the number of low-Earth orbit satellites and space debris has continued to grow rapidly, with orbital altitudes typically ranging from 200 km to 1000 km. Atmospheric drag is one of the dominant non-conservative perturbations within this altitude range, significantly and over the long term attenuating orbital elements such as the semi-major axis and eccentricity. It is also a key factor affecting the accuracy of space collision early warning and avoidance decisions. Traditional orbital dynamics models typically use drag acceleration in the following form: (1) in, Atmospheric density, The drag coefficient is a dimensionless coefficient. For reference, windward area For satellite quality, The magnitude of the satellite's velocity relative to the atmosphere. It is a unit vector in the direction of relative velocity.
[0003] In existing technologies, atmospheric density... Research on thermosphere density is relatively mature. Through ground-based observations, satellite accelerometer data, and years of observations from missions such as CHAMP, GOCE, and GRACE, multiple empirical or semi-empirical thermosphere density models have been developed. In contrast, the drag coefficient... Modeling development is relatively lagging, and in engineering, the projectile model is still commonly used, that is, the satellite is regarded as an equivalent sphere, and only the drag coefficient is considered. Treating it as a constant variable for overall calibration. Newer methods innovate upon this model, for example, by keeping the reference windward area constant and adjusting the drag coefficient... The model is constructed as an angle function between the relative flow direction and the stellar coordinate system, and expanded using a two-dimensional Fourier series. This approach can characterize the impact of attitude changes on atmospheric drag to some extent, but it neglects the significant changes in the geometric projected area of the complex satellite structure under different flow directions, thus passively absorbing the atmospheric drag modeling error. The empirical coefficients do not have a clear physical meaning and are easily confused with errors in atmospheric density models.
[0004] On the other hand, for satellites with large solar arrays, antennas, and anisotropic structures, the variation in windward area with the relative flow angle is often the main source of drag variation. Existing methods will... Fixed parameters will force the same type of geometric effects to be reflected in the angle function through higher-order Fourier coefficients, increasing the parameter dimension and correlation, which is not conducive to the stable estimation of resistance parameters using batch least squares method. Summary of the Invention
[0005] To overcome the limitations of existing satellite atmospheric drag models that only consider the drag coefficient... Modeling, and using the reference area To address the shortcomings of fixing the angle as a constant, this invention provides an atmospheric drag modeling method based on a detailed satellite geometric model to calculate the effective windward area and combined with a drag coefficient angle model. This allows for a more physically consistent representation of the effect of relative flow direction angles on airflow during orbit determination and batch least squares parameter estimation. and This reduces the impact of parameters, lowers their correlation, and improves the accuracy of orbit prediction.
[0006] The method includes the following steps: S1. Definition of relative velocity and coordinate system: In the geocentric inertial coordinate system, define the velocity vector of the satellite relative to the atmosphere, establish the satellite body-fixed coordinate system, transform the relative incoming flow unit vector to the body-fixed coordinate system and invert it to obtain the relative incoming flow direction vector in the body-fixed coordinate system, and define the azimuth and pitch angles of the relative incoming flow direction vector in the body-fixed coordinate system. S2. Calculation of effective windward area based on geometric model: Construct a satellite geometric model and calculate the satellite's effective windward area; S3. Construction of drag coefficient angle model: The drag coefficient angle model is constructed by using the azimuth and pitch angles of the relative flow direction in the body-fixed coordinate system. S4. Define the effective windward area-coefficient combination: Combine the drag coefficient angle model with the satellite's geometric effective windward area to define the effective windward area-coefficient combination. S5. Construct an improved atmospheric drag acceleration model: Construct an improved atmospheric drag acceleration model by combining the effective windward area and coefficient.
[0007] Furthermore, the satellite's velocity vector relative to the atmosphere is obtained through: Obtain, among which This represents the satellite's velocity vector relative to the atmosphere. Represents the satellite's velocity vector. This represents the velocity vector of the atmosphere as the Earth rotates.
[0008] Furthermore, the relative flow direction vector passes through Obtain, among which, This represents the vector relative to the incoming flow direction. Let be the direction cosine matrix, representing the attitude of the satellite's body-fixed coordinate system with respect to the geocentric inertial coordinate system; .
[0009] Furthermore, the azimuth angle of the relative incoming flow direction vector in the body-fixed coordinate system is obtained through... The pitch angle relative to the incoming flow direction vector in the body-fixed coordinate system is obtained through... get.
[0010] Furthermore, when constructing the satellite geometric model, it is assumed that the satellite geometric model is composed of... It consists of several rigid planes, each with an area of [area] in the satellite's body-fixed coordinate system. The unit normal vector is Pointing outwards refers to the given relative direction of incoming flow. The effective geometric frontal area of a satellite is defined as the sum of the projected areas of each plane at normal incidence. ,in, This represents the satellite's geometrically effective windward area.
[0011] Furthermore, the drag coefficient angle model is obtained through... Obtain, among which, This represents the drag coefficient angle model. , , , and For the parameter to be estimated, and This is the truncation order.
[0012] Furthermore, the effective windward area-coefficient combination is obtained through... Obtain, among which, This represents the effective windward area combined with the coefficient.
[0013] Furthermore, the improved atmospheric drag acceleration model is achieved through... Obtain, among which, This indicates atmospheric density.
[0014] This invention also provides a satellite orbit prediction method based on atmospheric drag modeling. The satellite orbit prediction method adopts the satellite atmospheric drag modeling method described above and includes the following steps: S91. Data Acquisition: Collect satellite observation data and auxiliary data within the time arc to be processed through ground-based telemetry and control systems, spaceborne GNSS receivers, or ground-based measurement equipment; S92. Observation preprocessing and relative inflow calculation: The collected data is unified in time system, outlier is removed and coordinate transformation is performed; In the geocentric inertial coordinate system, the velocity vector of the satellite relative to the atmosphere is calculated based on the satellite velocity and the velocity of the atmosphere with the rotation of the Earth, and the relative inflow direction is transformed to the satellite body-fixed coordinate system by combining the attitude direction cosine matrix, so as to obtain the relative inflow direction vector and its corresponding azimuth and pitch angles in the body-fixed coordinate system. S93. Calculation of effective geometric frontal area: Based on the satellite geometric model, for the relative incoming flow direction under the solid-body system obtained in step S92, the effective geometric frontal area at that moment is calculated by summing the normal incident projection areas of each plane in the incoming flow direction. S94. Drag Coefficient Angle Modeling and Parameterization: In the satellite body-fixed coordinate system, the drag coefficient is modeled as a function of the relative flow azimuth and pitch angle obtained in step 92, and parameterized expansion is performed using a finite-order Fourier series to form a set of drag parameters to be estimated. S95. Construct and introduce a satellite atmospheric drag modeling method: Combine the geometric effective windward area and drag coefficient angle model to construct an effective windward area-coefficient combination quantity, and apply the satellite atmospheric drag modeling method to obtain an improved atmospheric drag model; use the improved atmospheric drag model as the atmospheric drag term in the satellite dynamics model, realize the relevant partial derivatives, and participate in the subsequent orbital dynamics integral and state transition calculations. S96. Precise orbit determination and drag parameter calculation: Within a given time arc, based on an improved atmospheric drag model, the orbit determination method using batch least squares or Kalman filtering is employed to jointly estimate the satellite's initial state and drag parameters, thereby obtaining the precise orbit solution and drag parameter solution for that arc. S97. Model Update and Orbit Prediction: The calculated drag parameters are updated into the improved atmospheric drag model, and the updated improved atmospheric drag acceleration model is used to predict the satellite orbit, so as to improve the accuracy of satellite orbit prediction.
[0015] Furthermore, the collected data includes at least: orbital observation data, attitude data, satellite geometric model data, and space environment or atmospheric model-driven data.
[0016] The beneficial effects of the atmospheric drag modeling method described in this invention are as follows: (1) By using the formula to calculate the effective windward area based on the geometric model, the detailed geometric model of the satellite is introduced, so that the change of the windward area with the relative flow direction angle is accurately given by the geometric model, avoiding the passive fitting of the same geometric effect by the Fourier term of the higher-order drag coefficient.
[0017] (2) By defining the effective windward area-coefficient combination, the drag coefficient is... Geometric effective windward area of the satellite By modeling them separately, the drag coefficient reflects only the effects of satellite surface characteristics and surface materials, thus improving the physical interpretability of the drag parameters.
[0018] (3) In batch least squares or Kalman filtering, the parameters to be estimated are mainly concentrated on a finite number of atmospheric drag coefficients, and the geometric part is regarded as a deterministic quantity, thereby reducing parameter correlation and improving the stability of the solution and the accuracy of orbit prediction.
[0019] (4) The analytical form of the partial derivatives of atmospheric drag acceleration with respect to satellite position, velocity state and parameters is given, which is convenient for integration with conventional orbit variational equations to realize efficient calculation of large-scale satellite formation or precise orbit determination and orbit prediction. Attached Figure Description
[0020] Figure 1 This is a schematic diagram of the satellite geometry model and the relative incoming flow direction in an embodiment of the present invention; Figure 2 This is a schematic diagram illustrating the calculation of the effective windward area in an embodiment of the present invention. Detailed Implementation
[0021] The technical solution of the present invention will now be clearly and completely described with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the protection scope of the present invention.
[0022] Example 1 This embodiment provides a satellite atmospheric drag modeling method based on geometric effective area and relative flow direction.
[0023] The purpose of this embodiment is to overcome the limitations of existing satellite atmospheric drag models that only consider the drag coefficient. Modeling, and using the reference area To address the shortcomings of fixing the angle as a constant, this paper proposes an atmospheric drag modeling method based on a detailed satellite geometric model to calculate the effective windward area, combined with a drag coefficient angle model. This method enables a more physically consistent representation of the effect of relative flow direction angle on the orbit determination and batch least squares parameter estimation. and This reduces the impact of parameters, lowers their correlation, and improves the accuracy of orbit prediction.
[0024] The specific technical solution is as follows: 1. Relative velocity and coordinate system definition In a geocentric inertial coordinate system, the satellite position vector is denoted as... The velocity vector is The velocity vector of the atmosphere as the Earth rotates is Define the satellite's velocity vector relative to the atmosphere as: (2) Establish a body-fixed coordinate system for the satellite, whose attitude relative to the geocentric inertial frame is determined by the direction cosine matrix. Represented by transforming the relative incoming flow unit vector to the body-fixed coordinate system and inverting it, we obtain the relative incoming flow direction vector in the body-fixed coordinate system: (3) Satellite geometry model and schematic diagram of relative incoming flow direction are shown below Figure 1 As shown.
[0025] Define the azimuth angle of the relative incoming flow direction vector in the body-solid coordinate system. With pitch angle for: (4) 2. Calculation of effective windward area based on geometric model Assuming the satellite geometric model is composed of It consists of several rigid planes, each with an area of . Its outward normal unit vector is For a given relative incoming flow direction, The effective geometric frontal area of a satellite is defined as the sum of the projected areas of each plane at normal incidence. (5) Figure 2 This is a schematic diagram illustrating the calculation of the effective windward area in this embodiment. The effective areas corresponding to the four outward normal vectors a, b, c, and d are calculated based on... According to the calculation rule, the effective areas of planes a, b, and d are all 0, and only the calculation result of plane c is retained.
[0026] 3. Drag Coefficient Angle Model The drag coefficient is expressed as the relative flow direction angle in a body-solid coordinate system. and The function is expanded using a finite-order Fourier series: (6) in, For constant terms; and They are respectively and Harmonic order of direction, for The maximum truncation order in the direction; for The maximum truncation order in the direction; , , and For the corresponding expansion coefficients, and with Both are coefficients to be estimated.
[0027] 4. Effective windward area - coefficient combination The effective windward area is defined by combining the drag coefficient with the geometrically effective windward area: (7) 5. Improved atmospheric drag acceleration model The improved atmospheric drag acceleration model can then be expressed as: (8) Example 2 This embodiment further defines Embodiment 1, using the method described in Embodiment 1 for satellite orbit prediction. Specifically: Step 1: Data Collection Satellite observation data and auxiliary data within the time arc to be processed are collected through ground-based telemetry and control systems, spaceborne GNSS receivers, or ground-based surveying equipment; the data includes at least: 1) Orbital observation data (e.g., GNSS pseudorange, carrier phase, ranging, etc.) or equivalent ephemeris and status observations; 2) Attitude data (e.g., attitude quaternions, attitude angles, or direction cosine matrices); 3) Satellite geometric model data; 4) Space environment or atmospheric model-driven data (e.g., necessary parameters for calculating atmospheric density).
[0028] Step 2: Observation Preprocessing and Relative Incoming Flow Calculation The collected data undergoes time system unification, outlier removal, and coordinate transformation. In the geocentric inertial coordinate system, the satellite velocity vector relative to the atmosphere is calculated based on the satellite velocity and the atmospheric velocity due to the Earth's rotation. The relative incoming flow direction is then transformed to the satellite body-fixed coordinate system using the attitude direction cosine matrix, yielding the relative incoming flow direction vector and its corresponding azimuth and pitch angles in the body-fixed coordinate system.
[0029] Step 3: Calculation of Geometric Effective Windward Area Based on the satellite geometric model, the effective windward area at that moment is calculated by summing the normal incident projection areas of each plane in the direction of the flow, taking into account the relative incoming flow direction under the solid-body system obtained in the previous step.
[0030] Step 4: Drag Coefficient Angle Modeling and Parameterization In the satellite body-fixed coordinate system, the drag coefficient is modeled as a function of the relative flow azimuth and pitch angles obtained in step 2, and parameterized expansion is performed using finite-order Fourier series to form a set of drag parameters to be estimated.
[0031] Step 5: Construct and introduce an improved atmospheric drag acceleration model By combining the geometric effective windward area and drag coefficient angle model, an effective windward area-coefficient combination quantity is constructed, and an improved atmospheric drag model is obtained based on this. This improved drag model is used as the atmospheric drag term in the satellite dynamics model, and the relevant partial derivatives are realized to participate in the subsequent orbital dynamics integration and state transition calculations.
[0032] Step 6: Precise track determination and resistance parameter calculation Within a given time arc, based on a dynamic model that includes an improved drag term, and using orbit determination methods such as batch least squares or Kalman filtering, the initial state and drag parameters of the satellite are jointly estimated to obtain the precise orbit solution and drag parameter solution for that arc.
[0033] Step 7: Model Update and Orbit Prediction The calculated drag parameters are updated into the improved atmospheric drag model, and the updated improved atmospheric drag acceleration model is used to predict the satellite orbit, thereby improving the accuracy of satellite orbit prediction.
[0034] Example 3 This embodiment further defines Embodiment 1, applying the technical solution from Embodiment 1 to the solution of the partial derivatives of atmospheric drag acceleration with respect to satellite position and velocity.
[0035] To facilitate integration with batch least squares orbit determination methods, the relationship between atmospheric drag acceleration and the satellite state vector needs to be provided. The partial derivatives. First, define the scalar factor: (9) Equation (8) can then be written as: (10) For any vector independent variable ,have: (11) 1. Partial derivatives of the scalar factor with respect to position and velocity From equation (9), the partial derivative of the scalar factor with respect to the position vector is: (12) Similarly, the partial derivative of the scalar factor with respect to the velocity vector is (assuming that atmospheric density is independent of velocity): (13) From equation (2), the partial derivatives of the relative velocity vector with respect to position and velocity are: (14) The partial derivatives of the relative velocity scalar magnitude with respect to position and velocity are: (15) 2. Partial derivatives of the relative velocity unit vector with respect to position and velocity Unit vector right The partial derivative is: (16) in, It is a 3×3 identity matrix; for The unit vector.
[0036] 3. Effective frontal area - partial derivative of the coefficient with respect to position and velocity. because By relative incoming flow direction Indirectly dependent on and You can first find the correct answer. The gradient is then used, and the chain rule is applied. From equation (3), we have: (17) right about The gradient is expressed as: (18) Among them, the geometric effective windward area right The gradient is (in plane set superior): (19) drag coefficient The gradient can be obtained by using angle and The chain rule is used to obtain: (20) From equation (4) and the trigonometric differentiation formula, we can obtain: (twenty one) In summary, using the chain rule, we can obtain... The partial derivatives with respect to position and velocity are: (twenty two) Substituting equations (12), (13), (16), and (22) into equation (11), we can obtain the partial derivative matrix of atmospheric drag acceleration with respect to satellite position and velocity. and The analytical expression of it can be directly used to construct the Jacobian matrix in the orbital variational equation.
[0037] Example 4 This embodiment further defines Embodiment 1, applying the technical solution from Embodiment 1 to the partial derivative of atmospheric drag acceleration with respect to the solution parameters.
[0038] In batch least squares or filtered solutions, the atmospheric drag coefficient in equation (6) is usually selected. , , , and As parameters to be estimated. Since the density model and relative velocity do not depend on these parameters, atmospheric drag acceleration is insensitive to any parameter to be estimated. The partial derivative can be directly given by equation (8): (twenty three) From equation (7), we know that the geometrically effective windward area is independent of the parameters to be estimated, therefore: (twenty four) Based on the expansion of equation (6), the partial derivatives of each parameter can be obtained: (25) thereby: (26) (27) (28) (29) (30) When establishing the orbital variational equations, the partial derivatives of atmospheric drag acceleration with respect to parameters can be introduced as non-homogeneous terms for the extended state vector. By taking the derivative, the state transition matrix and sensitivity matrix required by the batch least squares or filtering algorithm can be obtained.
Claims
1. A satellite atmospheric drag modeling method based on geometric effective area and relative flow direction, characterized in that, The method includes the following steps: S1. Definition of relative velocity and coordinate system: In the geocentric inertial coordinate system, define the velocity vector of the satellite relative to the atmosphere, establish the satellite body-fixed coordinate system, transform the relative incoming flow unit vector to the body-fixed coordinate system and invert it to obtain the relative incoming flow direction vector in the body-fixed coordinate system, and define the azimuth and pitch angles of the relative incoming flow direction vector in the body-fixed coordinate system. S2. Calculation of effective windward area based on geometric model: Construct a satellite geometric model and calculate the satellite's effective windward area; S3. Construction of drag coefficient angle model: The drag coefficient angle model is constructed by using the azimuth and pitch angles of the relative flow direction in the body-fixed coordinate system. S4. Define the effective windward area-coefficient combination: Combine the drag coefficient angle model with the satellite's geometric effective windward area to define the effective windward area-coefficient combination. S5. Construct an improved atmospheric drag acceleration model: Construct an improved atmospheric drag acceleration model by combining the effective windward area and coefficient.
2. The satellite atmospheric drag modeling method based on geometric effective area and relative flow direction according to claim 1, characterized in that, The satellite's velocity vector relative to the atmosphere passes through: Obtain, among which This represents the satellite's velocity vector relative to the atmosphere. Represents the satellite's velocity vector. This represents the velocity vector of the atmosphere as the Earth rotates.
3. The satellite atmospheric drag modeling method based on geometric effective area and relative flow direction according to claim 2, characterized in that, Relative to the direction vector of the incoming flow Obtain, among which, This represents the vector relative to the incoming flow direction. Let be the direction cosine matrix, representing the attitude of the satellite's body-fixed coordinate system with respect to the geocentric inertial coordinate system; .
4. The satellite atmospheric drag modeling method based on geometric effective area and relative flow direction according to claim 3, characterized in that, The azimuth angle of the relative inflow direction vector in the body-solid coordinate system is obtained through The pitch angle relative to the incoming flow direction vector in the body-fixed coordinate system is obtained through... get.
5. The satellite atmospheric drag modeling method based on geometric effective area and relative flow direction according to claim 4, characterized in that, When constructing the satellite geometric model, it is assumed that the satellite geometric model is composed of It consists of several rigid planes, each with an area of [area] in the satellite's body-fixed coordinate system. The unit normal vector is Pointing outwards refers to the given relative direction of incoming flow. The effective geometric frontal area of a satellite is defined as the sum of the projected areas of each plane at normal incidence. ,in, This represents the satellite's geometrically effective windward area.
6. The satellite atmospheric drag modeling method based on geometric effective area and relative flow direction according to claim 5, characterized in that, The drag coefficient angle model is passed through Obtain, among which, This represents the drag coefficient angle model. , , , and For the parameter to be estimated, and This is the truncation order.
7. The satellite atmospheric drag modeling method based on geometric effective area and relative flow direction according to claim 6, characterized in that, Effective windward area-coefficient combination quantity through Obtain, among which, This represents the effective windward area combined with the coefficient.
8. The satellite atmospheric drag modeling method based on geometric effective area and relative flow direction according to claim 7, characterized in that, The improved atmospheric drag acceleration model is achieved through Obtain, among which, This indicates atmospheric density.
9. A satellite orbit prediction method based on atmospheric drag modeling, characterized in that, The satellite orbit prediction method employs the satellite atmospheric drag modeling method as described in any one of claims 1-8, and the method includes the following steps: S91. Data Acquisition: Collect satellite observation data and auxiliary data within the time arc to be processed through ground-based telemetry and control systems, spaceborne GNSS receivers, or ground-based measurement equipment; S92. Observation preprocessing and relative inflow calculation: Perform time system unification, outlier removal and coordinate transformation on the collected data; In the geocentric inertial coordinate system, the velocity vector of the satellite relative to the atmosphere is calculated based on the satellite velocity and the velocity of the atmosphere as the Earth rotates. The relative incoming flow direction is then transformed to the satellite body-fixed coordinate system by combining the attitude direction cosine matrix, and the relative incoming flow direction vector and its corresponding azimuth and pitch angles in the body-fixed coordinate system are obtained. S93. Calculation of effective geometric frontal area: Based on the satellite geometric model, for the relative incoming flow direction under the solid-body system obtained in step S92, the effective geometric frontal area at that moment is calculated by summing the normal incident projection areas of each plane in the incoming flow direction. S94. Drag Coefficient Angle Modeling and Parameterization: In the satellite body-fixed coordinate system, the drag coefficient is modeled as a function of the relative flow azimuth and pitch angle obtained in step 92, and parameterized expansion is performed using a finite-order Fourier series to form a set of drag parameters to be estimated. S95. Construct and introduce a satellite atmospheric drag modeling method: Combine the geometric effective windward area and drag coefficient angle model to construct an effective windward area-coefficient combination quantity, and apply the satellite atmospheric drag modeling method to obtain an improved atmospheric drag model; use the improved atmospheric drag model as the atmospheric drag term in the satellite dynamics model, realize the relevant partial derivatives, and participate in the subsequent orbital dynamics integral and state transition calculations. S96. Precise orbit determination and drag parameter calculation: Within a given time arc, based on an improved atmospheric drag model, the orbit determination method using batch least squares or Kalman filtering is employed to jointly estimate the satellite's initial state and drag parameters, thereby obtaining the precise orbit solution and drag parameter solution for that arc. S97. Model Update and Orbit Prediction: The calculated drag parameters are updated into the improved atmospheric drag model, and the updated improved atmospheric drag acceleration model is used to predict the satellite orbit, so as to improve the accuracy of satellite orbit prediction.
10. The satellite orbit prediction method based on atmospheric drag modeling according to claim 9, characterized in that, The collected data includes at least: orbital observation data, attitude data, satellite geometric model data, and space environment or atmospheric model-driven data.