Method and device for obtaining strict regression orbit parameters

Abstract

The present disclosure relates to a method and device for obtaining rigorous regression orbit parameters, and relates to the technical field of spacecraft, which can solve the problem of long time consumption of existing algorithms. The specific technical solution is: an orbit analytical method is adopted, and the J2 and J3 perturbation terms of the earth flattening are considered to obtain a set of rough regression orbit root numbers; a calculation function of the plane-instantaneous conversion is adopted to obtain the instantaneous orbit root numbers corresponding to the rough regression orbit root numbers; a numerical method is used to recursively correct the semi-major axis in the parameters of the instantaneous orbit root numbers, and the optimized initial value of the regression orbit root numbers is obtained; each orbit parameter and the regression period in the optimized initial value of the regression orbit root numbers are optimized and improved in a small range by using a nonlinear equation set, so that the rigorous regression orbit parameters with high regression accuracy are obtained. The present disclosure is simple and easy to understand in the calculation process, has high solving efficiency, short calculation time consumption, and can save a large amount of time for the design and analysis stage of the rigorous regression orbit.

Description

Technical Field

[0001] This disclosure relates to the field of spacecraft technology, and in particular to a method and apparatus for obtaining rigorous regression orbit parameters. Background Technology

[0002] A strictly regress orbit is a novel satellite orbit designed for recent satellite re-orbiting Earth observation missions. A key feature of a strictly regress orbit is the closure of its initial and final states. The nadir trajectory of a strictly regress orbit, obtained through iterative design, is shown below. Figure 1 As shown, the trajectory is a set of completely defined reference points in the Earth-fixed coordinate system. After obtaining the starting point orbit parameters and regression period of the strict regression orbit, ignoring other space environment perturbations, and considering only the Earth's gravitational field model for high-precision orbit extrapolation prediction, the target reference nominal trajectory can be obtained. This allows for strict regression orbit maintenance control, enabling satellite re-orbit Earth observation missions and meeting the satellite payload's requirements for orbital accuracy. For example, for long-term Earth deformation or geological disaster monitoring revisit measurement missions, the satellite orbit is controlled to move near a pre-set strict regression orbit throughout its lifespan, with a maximum deviation of approximately several hundred meters.

[0003] Existing traditional regression orbit design methods only consider the Earth's oblateness term J2 perturbation and use analytical methods to design coarse regression orbits. These methods result in poor ground trajectory revisit accuracy, with deviations ranging from several kilometers to tens of kilometers. Such regression orbits can only meet the requirements of general-precision satellite re-orbit Earth observation missions. Another type of rigorous regression orbit design method uses intelligent optimization algorithms, such as genetic algorithms. However, obtaining the initial values ​​for these intelligent optimization algorithms is difficult. For example, using differential iterative algorithms to solve for the initial values ​​requires deriving numerous partial derivative formulas to correct the analytical design results; or constructing a high-order Poincaré mapping of the satellite's orbital state changes after one regression cycle from its initial state requires deriving high-order Taylor expansions, a complex process. Furthermore, genetic algorithms simulate the process of gene mutation and selection in nature, undergoing multiple trials. The computational efficiency for finding the optimal solution is related to the mutation probability setting, and to ensure the success of finding the global optimum, the computation time is generally long. Summary of the Invention

[0004] To overcome the problems existing in related technologies, this disclosure provides a method and apparatus for obtaining rigorous regression orbit parameters. The technical solution is as follows:

[0005] According to a first aspect of the present disclosure, a method for obtaining rigorous regression orbit parameters is provided, comprising:

[0006] Using the orbital analysis method, considering the Earth's oblateness perturbation terms J2 and J3, a set of rough regression orbit square roots are obtained;

[0007] The instantaneous orbital elements corresponding to the coarse regression orbital elements are obtained by using the calculation function of the instantaneous-to-flat conversion.

[0008] The orbit is recursively derived using a numerical method, and the semi-major axis in the parameters of the instantaneous orbital elements is iteratively corrected to obtain the initial value of the optimized regression orbital elements.

[0009] A set of nonlinear equations was used to optimize and improve the orbital parameters and regression period in the initial value of the regression orbital elements within a small range, so as to obtain strict regression orbital parameters with higher regression accuracy.

[0010] In one embodiment, the use of an orbital analysis method, considering the Earth's oblateness perturbation terms J2 and J3, to obtain coarse regression orbital elements includes:

[0011] Based on the constraint relationship between the satellite orbital intersection period and the stellar period parameter, the semi-major axis a is calculated using the following iterative formula. k+1 :

[0012]

[0013] Among them, normalized units are used. Calculate and iteratively calculate the initial value a. k =1,

[0014]

[0015] when|a k+1 -a k When | < 0.00000001, the iteration ends, and the semi-major axis a is obtained. k+1 ;

[0016] According to the formula a′0=a k+1 ·R e Perform denormalization calculations;

[0017] Based on the relationship between the semi-major axis and the ground trajectory, the following formula is used to correct a′0:

[0018] a0 = a′0 + Δa;

[0019] in,

[0020]

[0021]

[0022]

[0023] Wherein, the N day N represents the number of days for the regression; cir The total number of revolutions; μ is the Earth's gravitational constant; R e The mean radius of the Earth's equator is given; e0 is the eccentricity; i0 is the orbital inclination; and ω0 is the perigee argument.

[0024] In one embodiment, the method further includes:

[0025] The orbital inclination angle i0 is obtained according to the following formula:

[0026]

[0027] The semi-major axis a′0 is initially estimated by the following formula:

[0028]

[0029] Wherein, T is the satellite orbital period.

[0030] In one embodiment, the method further includes:

[0031] The eccentricity is calculated based on the characteristics of the frozen track and the following iterative formula:

[0032]

[0033] Wherein, the e n The initial value is (0, 0.002);

[0034]

[0035]

[0036] when|e n+1 -e n |<10 -7 The iteration ends, and the eccentricity e0 is obtained.

[0037] In one embodiment, obtaining the instantaneous orbital elements corresponding to the coarse regression orbital elements using the calculation function of the instantaneous-to-flat transformation includes:

[0038] The instantaneous orbital elements corresponding to the rough regression orbital elements are obtained using the following formula:

[0039]

[0040] Wherein, Mean2Osc(σ) is the calculation function for the mean-to-instantaneous conversion; a0 is the semi-major axis; e0 is the eccentricity; i0 is the orbital inclination; Ω0 is the original right ascension of the ascending node; ω0 is the argument of perigee; and M0 is the mean perigee angle.

[0041] In one embodiment, the step of using a numerical method to recursively derive the orbit and iteratively correcting the semi-major axis of the instantaneous orbital elements to obtain the initial value for the optimized regression orbital elements includes:

[0042] The instantaneous orbital elements σ at the initial epoch t0 osc Convert the position and velocity to the J2000 inertial coordinate system, and calculate the longitude Lon0 of the nadir point in the ECEF coordinate system;

[0043] The regression period is calculated using the following formula:

[0044]

[0045] The numerical integration method is used to calculate σ. osc Extrapolate to predict a regression period T regress The satellite's position and velocity in the J2000 inertial frame at the end of its period are obtained, and the longitude Lon of the nadir point in the ECEF coordinate system is calculated. T ;

[0046] Based on the relationship between the satellite orbital period and the semi-major axis, the initial value of the semi-major axis of the regression orbital parameter is improved using the numerical iteration method of the following formula:

[0047]

[0048] in, ΔLon=Lon T -Lon0; the ω e This is the Earth's rotational angular rate;

[0049] Substitute the new orbital parameter semi-major axis as the initial value into the formula corresponding to the regression period, and repeat the above steps until |ΔT| is reached. orbit |<ΔT eps , where ΔT eps Iteratively correct the convergence threshold for the LEO strict regression trajectory;

[0050] After the iteration is completed, the orbital parameters obtained from the iteration are σ. osc The regression period is T regress .

[0051] In one embodiment, the step of using a system of nonlinear equations to perform small-scale optimization and improvement on each orbital parameter and regression period in the initial value of the regression orbital roots to obtain rigorous regression orbital parameters with higher regression accuracy includes:

[0052] Based on the Earth's gravity field data model file, a higher-order Earth gravity field perturbation model is selected, and the initial orbital parameters (t0, σ) are used. osc The initial position and velocity of the satellite in the ECEF coordinate system are calculated using the coordinate transformation function and denoted as (r0, v0).

[0053] A regression period T is calculated for the satellite orbit. regress Calculate the position and velocity at the end of the regression period, and use the coordinate transformation function to calculate the satellite's position and velocity in the Earth-Fixed Coordinate System (ECEF) at the initial moment, denoted as (r f v f );

[0054] Calculate the position and velocity errors at the start and end times of the next regression cycle in the Earth-Fixed Coordinate System (ECEF):

[0055] Δr=|r f -r0|

[0056] Δv=|v f -v f |;

[0057] The above process is considered as a system of nonlinear equations to be solved by the minpack algorithm:

[0058] {Δr x , Δr y , Δr z ,1000·Δv x ,1000·Δv y ,1000·Δv z}=F(σ osc T regress )≈0;

[0059] Even a small velocity error, when accumulated over time, will cause the position error to diverge rapidly, failing to meet the accuracy requirements of rigorous regression. Here, the velocity error is multiplied by 1000 as an amplification factor, similar to the constraint penalty coefficient when constructing the optimization objective in intelligent optimization algorithms.

[0060] Based on the range of variation of each orbital parameter searched and solved in the Minpack algorithm, and utilizing the nonlinear equation solving capability of the Minpack algorithm, a set of initial orbital roots and corresponding strict regression periods are obtained, ensuring that the regression revisit accuracy of the reference trajectory under the Earth-Fixed system can satisfy the following equation:

[0061]

[0062] According to a second aspect of the present disclosure, an apparatus for obtaining strictly regressed orbital parameters is provided, comprising:

[0063] The first acquisition module is used to obtain a set of rough regression orbital square root numbers by employing an orbital analysis method, considering the Earth's oblateness perturbation terms J2 and J3. a0 is the semi-major axis; e0 is the eccentricity; i0 is the orbital inclination; Ω0 is the original right ascension of the ascending node; ω0 is the argument of perigee; M0 is the level anterior angle.

[0064] The second acquisition module is used to obtain the instantaneous orbital elements corresponding to the coarse regression orbital elements using the calculation function of the flat-instantaneous conversion;

[0065] The third acquisition module is used to recursively deduce the orbit using a numerical method, iteratively correct the semi-major axis in the parameters of the instantaneous orbital elements, and obtain the initial value σ for the optimized regression orbital elements. osc (a1, e1, i1, Ω1, ω1, M1);

[0066] The fourth acquisition module is used to perform small-scale optimization and improvement on each orbital parameter and regression period in the initial value of the regression orbital root optimization using a system of nonlinear equations, so as to obtain the rigorous regression orbital parameter σ with higher regression accuracy. * (a * e * i * Ω * ω * M * ).

[0067] According to a third aspect of the present disclosure, an apparatus for obtaining strictly regressive orbital parameters is provided, comprising:

[0068] processor;

[0069] Memory used to store processor-executable instructions;

[0070] The processor is configured as follows:

[0071] Using an analytical orbital method, considering the Earth's oblateness perturbation terms J2 and J3, a set of coarse regression orbital square roots is obtained. a0 is the semi-major axis; e0 is the eccentricity; i0 is the orbital inclination; Ω0 is the original right ascension of the ascending node; ω0 is the argument of perigee; M0 is the level anterior angle.

[0072] The instantaneous orbital elements corresponding to the coarse regression orbital elements are obtained by using the calculation function of the instantaneous-to-flat conversion.

[0073] By using a numerical method to recursively derive the orbit, the semi-major axis of the instantaneous orbital elements is iteratively corrected to obtain the initial value σ for the optimized regression orbital elements. osc (a1, e1, i1, Ω1, ω1, M1);

[0074] A set of nonlinear equations was used to perform small-scale optimization and improvement on each orbital parameter and regression period in the initial value of the regression orbital elements, so as to obtain a rigorous regression orbital parameter σ with higher regression accuracy. * (a * e * i * Ω * ω * M * ).

[0075] According to a fourth aspect of the present disclosure, a computer-readable storage medium is provided that stores computer instructions thereon, which, when executed by a processor, implement the steps of the method described in any of the first aspects.

[0076] It should be understood that the above general description and the following detailed description are exemplary and explanatory only, and are not intended to limit this disclosure. Attached Figure Description

[0077] The accompanying drawings, which are incorporated in and form a part of this specification, illustrate embodiments consistent with this disclosure and, together with the description, serve to explain the principles of this disclosure.

[0078] Figure 1 This is a schematic diagram of the sub-satellite point trajectory of a strictly regressed orbit obtained through iterative design, according to an exemplary embodiment.

[0079] Figure 2 This is a flowchart illustrating a method for obtaining strict regression orbital parameters according to an exemplary embodiment.

[0080] Figure 3 This is a flowchart illustrating a method for obtaining strict regression orbital parameters according to an exemplary embodiment.

[0081] Figure 4 This is a block diagram illustrating an apparatus for acquiring strictly regressed orbital parameters according to an exemplary embodiment. Detailed Implementation

[0082] Exemplary embodiments will now be described in detail, examples of which are illustrated in the accompanying drawings. When the following description relates to the drawings, unless otherwise indicated, the same numerals in different drawings denote the same or similar elements. The embodiments described in the following exemplary embodiments do not represent all embodiments consistent with this disclosure. Rather, they are merely examples of apparatuses and methods consistent with some aspects of this disclosure as detailed in the appended claims.

[0083] To address the shortcomings of existing regression trajectory design methods, this invention proposes a simple and rigorous regression trajectory design method that combines analytical and numerical methods to design rigorous regression trajectory parameters that satisfy input constraints. The design method of this invention can be described as follows:

[0084] The input parameters are the given orbital inclination, number of days of return, and total number of orbits. First, using the analytical method of orbital design, considering the Earth's oblateness perturbation terms J2 and J3, and performing iterative correction calculations, a set of rough root values ​​of the return orbit is designed. Then, a mean-instantaneous conversion is performed to convert it into instantaneous orbital elements. Next, a numerical method is used to recursively derive the orbit, iteratively correcting the semi-major axis a0 in the instantaneous root parameters to reduce the longitude deviation of the satellite's nadir trajectory after one regression cycle, thus obtaining the optimized initial value σ for the regression orbital elements. osc (a1, e1, i1, Ω1, ω1, M1); Finally, the regression position error and weighted velocity error of the strictly regressed orbit are transformed into a nonlinear equation system problem of the initial orbit parameters and regression period. The nonlinear equation system solution tool minpack is used to solve the initial value σ. osc By making small-scale optimizations and improvements to the orbital parameters and regression period, a rigorous regression orbital parameter σ with higher regression accuracy can be obtained. * (a * e * i * Ω * ω * M * The following details the method steps of the present invention.

[0085] Figure 2 and Figure 3 This is a flowchart illustrating a method for obtaining rigorous regression orbital parameters according to an exemplary embodiment, such as... Figure 2 and Figure 3 As shown, the method includes the following steps S101-S104:

[0086] In step S101, the orbital analysis method is used, taking into account the Earth's oblateness perturbation terms J2 and J3, to obtain a set of rough regression orbital root numbers. a0 is the semi-major axis; e0 is the eccentricity; i0 is the orbital inclination; Ω0 is the original right ascension of the ascending node; ω0 is the argument of perigee; M0 is the level anterior angle.

[0087] Before executing step S101, input parameters can be obtained, including:

[0088] Number of days N day Total number of regression cycles N cit Initial epoch t0, eccentricity e0, perigee argument ω0, orbital inclination i0 (if the mission requires a sun-synchronous orbit, the inclination must first be calculated from the semi-major axis), Earth oblateness perturbation terms J2 and J3, Earth's gravitational constant μ = G·M e The average radius of the Earth's equator, R e When the mission requires a near-circular orbit, let the eccentricity e0 = 0, and the perigee argument ω0 can be any value; when the mission requires a non-circular orbit, e0 and ω0 take given values.

[0089] Calculate the initial value a0 of the semi-major axis:

[0090] Furthermore, if the mission requires a sun-synchronous return orbit, the orbital inclination i0 needs to be determined first; if the mission requires a non-sun-synchronous orbit, i.e. the orbital inclination i0 is known, the initial value of the semi-major axis can be calculated directly through iteration.

[0091] In one embodiment, the method further includes:

[0092] Based on the characteristics of a sun-synchronous orbit, the orbital inclination i0 is obtained using the following formula:

[0093]

[0094] The semi-major axis a′0 is initially estimated using the following formula:

[0095]

[0096] Where T is the satellite orbital period.

[0097] In one embodiment, an analytical orbital method is employed, considering the Earth's oblateness perturbations J2 and J3, to obtain a coarse regression orbital element. Includes the following sub-steps:

[0098] A1. Utilizing the constraint relationship between the satellite orbital intersection period and the stellar period parameter, the semi-major axis a is calculated using the following iterative formula. k+1 :

[0099]

[0100] Calculations using normalized units, i.e. Let the initial value a be calculated iteratively. k =1;;

[0101]

[0102]

[0103] when|a k+1 -a k When | < 0.00000001, the iteration ends, and we obtain a. k+1 ;

[0104] A2. Perform denormalization calculations according to the following formula;

[0105] a′0=a k+1 ·R e (6)

[0106] A3. Based on the relationship between the semi-major axis and the ground trajectory, a′0 is corrected using the following formula:

[0107] a0=a′0+Δa (7);

[0108] in,

[0109]

[0110]

[0111] n is the orbital angular velocity:

[0112]

[0113] Where, N day N represents the number of days since the return; cir R is the total number of cycles; μ is the Earth's gravitational constant; e ω0 is the average radius of the Earth's equator; e0 is the eccentricity; i0 is the orbital inclination; ω0 is the perigee argument.

[0114] Calculate the eccentricity:

[0115] Furthermore, if the task requires a circular orbit, or if the eccentricity is not specified, the eccentricity e0 is calculated using the frozen orbit property and the following formula. This eccentricity can be called the frozen eccentricity. If the task requires the eccentricity e0 to be specified, this step is skipped.

[0116] A frozen orbit is a stable equilibrium solution to the dynamic equations, with zero long-term variations in eccentricity and perigee argument. Once the orbit is adjusted to near these nominal values, the subsequent camber will oscillate within a small range, requiring no active control. Based on the characteristics of a frozen orbit, the stability of the satellite orbit camber within the orbital plane can be achieved, which is beneficial for ensuring the consistency of orbital altitude during nadir revisits.

[0117] At this point, the above method also includes:

[0118] Calculate the freezing eccentricity using the following iterative formula:

[0119]

[0120] Among them, e n The initial value can be arbitrarily selected within the range (0, 0.002);

[0121]

[0122]

[0123] when|e n+1 -e n |<10 -7 The iteration ends, and the eccentricity e0 is obtained.

[0124] The core of obtaining frozen orbit parameters is calculating the frozen eccentricity. Taking a perigee argument ω0 = 90° as an example, the eccentricity e n The initial value can be arbitrarily selected within the range (0, 0.002), and the formula for calculating the freezing eccentricity iteratively is shown in (12).

[0125] Transformation from flat to instantaneous:

[0126] In step S102, the instantaneous orbital elements corresponding to the coarse regression orbital elements are obtained using the calculation function of the instantaneous-to-flat conversion.

[0127] After the above steps, a0, e0, i0, and ω0 are determined. The initial right ascension of the ascending node Ω0 and the angle of approach m0 can be arbitrarily specified. This yields the approximate regression orbital elements. These orbital elements are average elements, and they need to be converted into instantaneous elements before proceeding with the next step of numerical integration extrapolation.

[0128] In one embodiment, the instantaneous orbital elements corresponding to the coarse regression orbital elements are obtained using the calculation function of the instantaneous-to-flat transformation, including:

[0129] The instantaneous orbital elements corresponding to the rough regression orbital elements can be obtained using the following formula:

[0130]

[0131] Where Mean2Osc(σ) is the calculation function for the mean-to-instantaneous transformation; a0 is the semi-major axis; e0 is the eccentricity; i0 is the orbital inclination; Ω0 is the original right ascension of the ascending node; ω0 is the argument of perigee; and M0 is the mean perigee angle.

[0132] Mean2Osc(σ) is a common function for calculating instantaneous functional transitions in the field, which will not be elaborated here.

[0133] Correct the semi-major axis and calculate the regression period:

[0134] In step S1+3, the numerical method is used to recursively derive the orbit, and the semi-major axis in the parameters of the instantaneous orbital elements is iteratively corrected to obtain the initial value σ for the optimized regression orbital elements. osc0 (a1, e1, i1, Ω1, ω1, M1);

[0135] Since the orbital parameters calculated by the above algorithms only consider the J2 and J3 terms of the Earth's non-spherical gravitational perturbation, to meet the high-precision regression orbit characteristics, it is necessary to use a high-precision numerical integration method to integrate the higher-order Earth gravitational field perturbation acceleration term to obtain more accurate regression orbit parameters. The numerical integration orbit extrapolation algorithm in this step considers the 30×30 order Earth non-spherical gravitational perturbation term. Ephem represents the orbit extrapolation algorithm, and Convert represents the conversion of satellite position and velocity into orbital elements; both are common functionals in the field and will not be elaborated further here.

[0136] Specifically, the numerical method is used to recursively derive the orbit, and the semi-major axis of the instantaneous orbital elements is iteratively corrected to obtain the initial value σ for the optimized regression orbital elements. osc0 (a1, e1, i1, Ω1, ω1, M1), including:

[0137] The instantaneous orbital elements σ at the initial epoch t0 osc Convert the position and velocity to the J2000 inertial coordinate system, and calculate the longitude Lon0 of the nadir point in the ECEF coordinate system;

[0138] Using a0, calculate the regression period according to the following formula:

[0139]

[0140] To ensure computational accuracy and convergence of subsequent iterations, the regression period should be calculated and verified using numerical integration, comparing the square root phase angle at the initial moment. extrapolation regression cycle number N cir Satellites behind the circle To determine the actual regression period, based on experience, the threshold can generally be set as the amplitude value of the LEO satellite's operation in 1 second, which is approximately 0.06°.

[0141] Using numerical integration method to σ osc Extrapolate to predict a regression period T regress The satellite's position and velocity in the J2000 inertial frame at the end of its period are obtained, and the longitude Lon of the nadir point in the ECEF coordinate system is calculated. T Then we have:

[0142] ΔLon=Lon T -Lon0 (17)

[0143] According to the Earth's rotation angular rate ω e Furthermore,

[0144]

[0145] Based on the relationship between the satellite orbital period and the semi-major axis, the initial value of the semi-major axis of the regression orbital parameter is improved using the numerical iteration method of the following formula:

[0146]

[0147] Substitute the new orbital parameter semi-major axis as the initial value into the formula (16) corresponding to the regression period, and repeat the above steps until |ΔT orbit |<ΔT eps , where ΔT eps This is the convergence threshold for the above iterative process.

[0148] Based on experience, the iterative correction convergence threshold ΔT for the LEO strict regression trajectory is... eps A value of 0.02s is generally acceptable.

[0149] At this point, for the design of the sun-synchronous return orbit, since the semi-major axis has undergone a large range of corrections and adjustments, the orbital inclination angle i0 needs to be recalculated based on the new semi-major axis a0 using equation (1).

[0150] After the iteration is completed, the orbital parameters obtained from the iteration are σ. osc The regression period is T regress .

[0151] Optimize and improve the strict regression trajectory parameters:

[0152] In step S104, a set of nonlinear equations is used to perform small-scale optimization and improvement on each orbital parameter and regression period in the initial value of the regression orbital elements, so as to obtain a rigorous regression orbital parameter σ with higher regression accuracy. * (a * e *i * Ω * ω * M * ).

[0153] The orbital parameters generated by the above algorithm already possess good regression characteristics. To obtain high-precision, strictly regressed orbital parameters, this step uses the nonlinear problem-solving toolkit minpack to further improve and optimize the initial values ​​of the orbital parameters. minpack is a function toolkit for solving nonlinear equations using the Jacobian matrix; here, it is used to solve for accurate regression orbits, which can improve the optimization solution speed. The specific steps are as follows:

[0154] Based on the Earth's gravity field data model file, select a high-order Earth gravity field perturbation model (for example, choose the highest possible order, such as 90×90). Then, based on the initial orbital parameters (t0, σ...) osc The initial position and velocity of the satellite in the ECEF coordinate system are calculated using the coordinate transformation function and denoted as (r0, v0).

[0155] A regression period T is calculated for the satellite orbit. regress Calculate the position and velocity at the end of the regression period, and use the coordinate transformation function to calculate the satellite's position and velocity in the Earth-Fixed Coordinate System (ECEF) at the initial moment, denoted as (r f v f );

[0156] Calculate the position and velocity errors at the start and end times of the next regression cycle in the Earth-Fixed Coordinate System (ECEF):

[0157]

[0158] The above process is considered as a system of nonlinear equations to be solved by the minpack algorithm:

[0159] {Δr x , Δr y , Δr z ,1000·Δv x ,1000·Δv y ,1000·Δv z}=F(σ osc T regress )≈0;

[0160] Even a small velocity error, when accumulated over time, will cause the position error to diverge rapidly, failing to meet the accuracy requirements of rigorous regression. Here, the velocity error is multiplied by 1000 as an amplification factor, similar to the constraint penalty coefficient when constructing the optimization objective in intelligent optimization algorithms.

[0161] Based on the range of variation of each orbital parameter searched and solved in the Minpack algorithm, and utilizing the nonlinear equation solving capability of the Minpack algorithm, a set of initial orbital roots and corresponding strict regression periods are obtained, ensuring that the regression revisit accuracy of the reference trajectory under the Earth-Fixed system can satisfy the following equation:

[0162]

[0163] The range of variation for the search and solution of each orbital parameter in the Minpack algorithm is set as shown in Table 1.

[0164] Table 1 Optimization Adjustment Range in Targeting Algorithm

[0165] parameter Δa Δe Δi ΔΩ Δω ΔM <![CDATA[ΔT regress ]]> scope ±500m ±0.0002 0° 0° ±0.5° ±1.5° ±2s

[0166] The implementation process is described in detail through the following examples.

[0167] 1. Obtain the following input parameters:

[0168]

[0169] The initial epoch time t0 is 12:00:00.00 Beijing time on April 18, 2022.

[0170] The right ascension of the ascending node Ω0 and the angle of approach M0 do not affect the design process and can be arbitrarily specified. Here, they are all set to 0.

[0171] Other parameters are fixed constants, using standard values ​​commonly used in this field.

[0172] 2. Calculate the initial value of the semi-major axis.

[0173] Based on the iterative algorithm in step 2, the initial value of the semi-major axis, a0, is calculated to be 6938016.696m.

[0174] 3. Calculate the freezing eccentricity.

[0175] The freezing eccentricity was obtained as e0 = 0.001068497.

[0176] 4. Transition from flat to instantaneous

[0177] The flat root obtained from the above steps is:

[0178]

[0179] After transformation, the instantaneous root is obtained as:

[0180]

[0181] 5. Correct the semi-major axis and calculate the regression period.

[0182] Choosing an order of 30×30 for the Earth's gravitational field perturbation, the semi-major axis was corrected using numerical integration to obtain the instantaneous root semi-major axis as a0 = 6928656.468m. The convergence condition was met in the first iteration, therefore the semi-major axis remained unchanged. At this point, the regression period of the regression orbit is: T regress =86379s;

[0183] The regression position error under the Earth-fixed system is:

[0184] 6. Solving for the strict regression orbital parameters

[0185] Substituting the orbital parameters and precise regression period obtained in the previous step into the minpack algorithm module, and selecting the order of the Earth's gravitational field perturbation as 70×70, after iterative optimization, the final strictly regressed orbital parameters can be obtained as follows:

[0186] The initial instantaneous root parameters of the orbit are:

[0187]

[0188] The regression period is: T regress =86379s;

[0189] The regression error under the Earth-Solid System is:

[0190] refer to Figure 3 It can be seen that the regression error of the strictly regressed orbit parameters is greatly reduced, and they can be used as reference orbit parameters for maintaining the corresponding pipeline radius control, thus completing high-precision revisit missions similar to those of SAR remote sensing satellites for Earth observation.

[0191] The analytical and numerical combined optimization design method proposed in this disclosure simplifies the theoretical formula derivation in previous regression trajectory design processes. It uses a simple analytical method to iteratively calculate initial values, and then utilizes a high-precision numerical method to recursively derive the trajectory to further improve the initial values ​​of the trajectory parameters, combining the advantages of both approaches. Furthermore, the regression position error and weighted velocity error of the strict regression trajectory are transformed into a nonlinear equation system problem involving the initial trajectory parameters and the regression period. This problem is solved using the mature nonlinear equation system solving tool Minpack, enabling rapid optimization of the strict regression trajectory parameters. Due to the adoption of a step-by-step design and optimization method, the calculation process is simple and easy to understand, with high solution efficiency and short computation time, saving significant time in the design and analysis phase of the strict regression trajectory.

[0192] Based on the above Figure 1 The method for obtaining the strict regression orbit parameters described in the corresponding embodiments is described below as an embodiment of the apparatus of this disclosure, which can be used to execute the method embodiments of this disclosure.

[0193] This disclosure provides an apparatus for obtaining strictly regressive orbital parameters, such as... Figure 4 As shown, it includes:

[0194] The first acquisition module 11 is used to obtain a set of rough regression orbital square roots by using an orbital analysis method, considering the Earth's oblateness perturbation terms J2 and J3. a0 is the semi-major axis; e0 is the eccentricity; i0 is the orbital inclination; Ω0 is the original right ascension of the ascending node; ω0 is the argument of perigee; M0 is the level anterior angle.

[0195] The second acquisition module 12 is used to obtain the instantaneous orbital elements corresponding to the coarse regression orbital elements using the calculation function of the flat-instantaneous conversion;

[0196] The third acquisition module 13 is used to recursively deduce the orbit using a numerical method, iteratively correct the semi-major axis in the parameters of the instantaneous orbital elements, and obtain the initial value σ for the optimized regression orbital elements. osc (a1, e1, i1, Ω1, ω1, M1);

[0197] The fourth acquisition module 14 is used to perform small-scale optimization and improvement on each orbital parameter and regression period in the initial value of the regression orbital root optimization using a system of nonlinear equations, so as to obtain a rigorous regression orbital parameter σ with higher regression accuracy. * (a * e * i * Ω * ω * M * ).

[0198] In one embodiment, the first acquisition module is specifically used for:

[0199] Based on the constraint relationship between the satellite orbital intersection period and the stellar period parameter, the semi-major axis a is calculated using the following iterative formula. k+1 :

[0200]

[0201] Among them, normalized units are used. Calculate and iteratively calculate the initial value a. k =1,

[0202]

[0203] when|a k+1 -a k When | < 0.00000001, the iteration ends, and the semi-major axis a is obtained. k+1 ;

[0204] According to the formula a′0=a k+1 ·R e Perform denormalization calculations;

[0205] Based on the relationship between the semi-major axis and the ground trajectory, the following formula is used to correct a′0:

[0206] a0 = a′0 + Δa;

[0207] in,

[0208]

[0209]

[0210]

[0211] Wherein, the N day N represents the number of days for the regression; cir The total number of revolutions; μ is the Earth's gravitational constant; R e The mean radius of the Earth's equator is given; e0 is the eccentricity; i0 is the orbital inclination; and ω0 is the perigee argument.

[0212] In one embodiment, the first acquisition module is specifically used for:

[0213] The orbital inclination angle i0 is obtained according to the following formula:

[0214]

[0215] The semi-major axis a′0 is initially estimated by the following formula:

[0216]

[0217] Wherein, T is the satellite orbital period.

[0218] In one embodiment, the first acquisition module is specifically used for:

[0219] The eccentricity is calculated based on the characteristics of the frozen track and the following iterative formula:

[0220]

[0221] Wherein, the e n The initial value is (0, 0.002);

[0222]

[0223]

[0224] when|e n+1 -e n |<10 -7 The iteration ends, and the eccentricity e0 is obtained.

[0225] In one embodiment, the second acquisition module is specifically used for:

[0226] The instantaneous orbital elements corresponding to the rough regression orbital elements are obtained using the following formula:

[0227]

[0228] Wherein, Mean2Osc(σ) is the calculation function for the mean-to-instantaneous conversion; a0 is the semi-major axis; e0 is the eccentricity; i0 is the orbital inclination; Ω0 is the original right ascension of the ascending node; ω0 is the argument of perigee; and M0 is the mean perigee angle.

[0229] In one embodiment, the third acquisition module is specifically used for:

[0230] The instantaneous orbital elements σ at the initial epoch t0 osc Convert the position and velocity to the J2000 inertial coordinate system, and calculate the longitude Lon0 of the nadir point in the ECEF coordinate system;

[0231] The regression period is calculated using the following formula:

[0232]

[0233] The numerical integration method is used to calculate σ. osc Extrapolate to predict a regression period T regress The satellite's position and velocity in the J2000 inertial frame at the end of its period are obtained, and the longitude Lon of the nadir point in the ECEF coordinate system is calculated. T ;

[0234] Based on the relationship between the satellite orbital period and the semi-major axis, the initial value of the semi-major axis of the regression orbital parameter is improved using the numerical iteration method of the following formula:

[0235]

[0236] in, ΔLon=Lon T -Lon0; the ω e This is the Earth's rotational angular rate;

[0237] Substitute the new orbital parameter semi-major axis as the initial value into the formula corresponding to the regression period, and repeat the above steps until |ΔT| is reached. orbit |<ΔT eps , where ΔT epsIteratively correct the convergence threshold for the LEO strict regression trajectory;

[0238] After the iteration is completed, the orbital parameters obtained from the iteration are σ. osc The regression period is T regress .

[0239] In one embodiment, the fourth acquisition module is specifically used for:

[0240] Based on the Earth's gravity field data model file, a higher-order Earth gravity field perturbation model is selected, and the initial orbital parameters (t0, σ) are used. osc The initial position and velocity of the satellite in the ECEF coordinate system are calculated using the coordinate transformation function and denoted as (r0, v0).

[0241] A regression period T is calculated for the satellite orbit. regress Calculate the position and velocity at the end of the regression period, and use the coordinate transformation function to calculate the satellite's position and velocity in the Earth-Fixed Coordinate System (ECEF) at the initial moment, denoted as (r f v f );

[0242] Calculate the position and velocity errors at the start and end times of the next regression cycle in the Earth-Fixed Coordinate System (ECEF):

[0243] Δr=|r f -r0|

[0244] Δv=|v f -v f |;

[0245] The above process is considered as a system of nonlinear equations to be solved by the minpack algorithm:

[0246] {Δr x , Δr y , Δr z ,1000·Δv x ,1000·Δv y ,1000·Δv z}=F(σ osc T regress )≈0;

[0247] Even a small velocity error, when accumulated over time, will cause the position error to diverge rapidly, failing to meet the accuracy requirements of rigorous regression. Here, the velocity error is multiplied by 1000 as an amplification factor, similar to the constraint penalty coefficient when constructing the optimization objective in intelligent optimization algorithms.

[0248] Based on the range of variation of each orbital parameter searched and solved in the Minpack algorithm, and utilizing the nonlinear equation solving capability of the Minpack algorithm, a set of initial orbital roots and corresponding strict regression periods are obtained, ensuring that the regression revisit accuracy of the reference trajectory under the Earth-Fixed system can satisfy the following equation:

[0249]

[0250] Based on the above Figure 1 In addition to the method for obtaining the strict regression trajectory parameters described in the corresponding embodiments, this disclosure also provides a computer-readable storage medium. For example, a non-transitory computer-readable storage medium may be a read-only memory (ROM), a random access memory (RAM), a CD-ROM, magnetic tape, a floppy disk, or an optical data storage device. This storage medium stores computer instructions for executing the above-described... Figure 1 The method for obtaining the strict regression orbital parameters described in the corresponding embodiments will not be repeated here.

[0251] Other embodiments of this disclosure will readily occur to those skilled in the art upon consideration of the specification and practice of the disclosure herein. This application is intended to cover any variations, uses, or adaptations of this disclosure that follow the general principles of this disclosure and include common knowledge or customary techniques in the art not disclosed herein. The specification and examples are to be considered exemplary only, and the true scope and spirit of this disclosure are indicated by the following claims.

[0252] It should be understood that this disclosure is not limited to the precise structures described above and shown in the accompanying drawings, and various modifications and changes can be made without departing from its scope. The scope of this disclosure is limited only by the appended claims.

Claims

1. A method for obtaining rigorous regression orbital parameters, characterized in that, The method comprises the following steps: The orbit analytical method is used to obtain a set of rough regression orbit plane roots by considering the Earth's flattening perturbation terms J2 and J3; The instantaneous orbit roots corresponding to the rough regression orbit plane roots are obtained by using the calculation function of the plane-instantaneous conversion; The semi-major axis in the parameters of the instantaneous orbit roots is iteratively corrected by using the numerical method to recursively track the orbit, so that the regression orbit root optimization initial value is obtained; The small-range optimization and improvement are performed on each orbit parameter and the regression period in the regression orbit root optimization initial value by using the nonlinear equation set, so that the strict regression orbit parameter with high regression accuracy is obtained.

2. The method of claim 1, wherein, The orbit analytical method is used to obtain a set of rough regression orbit plane roots by considering the Earth's flattening perturbation terms J2 and J3, and the method comprises the following steps: According to the constraint relationship between the satellite orbit intersection period and the star period parameter, the semi-major axis a is calculated according to the following iterative formula k+1 : wherein the normalized units are adopted The calculation is made and the initial value a is iterated k = 1, When |a k+1 -a k | < 0.00000001, the iteration ends, and the semi-major axis a is obtained k+1 ; According to the formula a'0 = a k+1 • R e A denormalization calculation is performed; According to the relationship between the semi-major axis and the ground track, the following formula is used to correct a'0: a0=a0'+Δa wherein wherein the N day is the number of revolutions; the N cir is the total number of revolutions; the μ = is the gravitational constant of the Earth; the R e is the average radius of the Earth's equator; the e0is the eccentricity; the i0is the orbital inclination; and the ω0is the argument of perigee.

3. The method of claim 2, wherein, The method further comprises the following steps: The orbit inclination i0 is obtained according to the following formula: The semi-major axis a'0 is preliminarily estimated according to the following formula: The T is the satellite orbit period.

4. The method of claim 1, wherein, The method further comprises the following steps: The eccentricity is calculated according to the frozen orbit characteristics and the following iterative formula: wherein the e n belongs to (0, 0.002); When |e n+1 - e n | < 10 -7 The iteration ends, and the eccentricity e0 is obtained.

5. The method of claim 1, wherein, The instantaneous orbit roots corresponding to the rough regression orbit plane roots are obtained by using the calculation function of the plane-instantaneous conversion, and the method comprises the following steps: The instantaneous orbit roots corresponding to the rough regression orbit plane roots are obtained by using the following formula: The Mean2Osc(σ) is the calculation function of the plane-instantaneous conversion; the a0 is the semi-major axis; the e0 is the eccentricity; the i0 is the orbit inclination; the Ω0 is the original longitude of the ascending node; the ω0 is the argument of perigee; and the M0 is the mean anomaly.

6. The method of claim 1, wherein, The semi-major axis in the parameters of the instantaneous orbit roots is iteratively corrected by using the numerical method to recursively track the orbit, so that the regression orbit root optimization initial value is obtained, and the method comprises the following steps: The instantaneous orbital elements σ at the initial epoch t0 osc Convert to position and velocity in J2000 inertial frame and calculate the sub-satellite point longitude Lon0 in the Earth-centered Earth-fixed (ECEF) frame. The regression period is calculated according to the following formula: The σ osc is obtained by numerical integration method regress , the position and velocity of the satellite at the end of the cycle are obtained in J2000 inertial system, and the sub-satellite point longitude Lon T in the ECEF coordinate system is calculated According to the relationship between the satellite orbit period and the semi-major axis, the numerical iterative method of the following formula is used to improve the initial value of the semi-major axis of the regression orbit parameter: wherein, ΔLon = Lon T - Lon0; said ω e is the earth rotation angular rate; The new orbital parameter semi-major axis is substituted as the initial value into the formula corresponding to the regression period, and the above steps are repeated until |ΔT orbit |<ΔT eps , wherein the ΔT eps is the iteration correction convergence threshold of the LEO rigorous regression orbit. After the iteration is completed, the track parameter obtained by the iteration is taken as σ osc , and the regression period is T regress .

7. The method of claim 1, wherein, The small-range optimization and improvement are performed on each orbit parameter and the regression period in the regression orbit root optimization initial value by using the nonlinear equation set, so that the strict regression orbit parameter with high regression accuracy is obtained, and the method comprises the following steps: According to the earth gravity field data model file, select high order earth gravity field perturbation model order, according to the initial orbit parameter (t0, sigma osc ), the position and velocity of the satellite at the initial time in the earth fixed coordinate system ECEF are calculated by using the coordinate conversion function, which are denoted as (r0, v0). Recursion of satellite orbit for one revolution T regress , the position and velocity at the end of the revolution are calculated, and the position and velocity of the satellite at the initial time in the ECEF coordinate system are calculated using the coordinate transformation function, denoted as (r f ,v f ). The position error and the velocity error of the start and end time of the next regression period in the Earth-fixed coordinate system ECEF are calculated: Δr = |r f -r0| Δv = |v f -v f |; The above process is taken as the nonlinear equation set to be solved in the minpack algorithm: {Δr x ,Δr y ,Δr z ,1000·Δv x ,1000·Δv y ,1000·Δv z}=F(σ osc ,T regress )≈0; Due to the very small velocity error, the position error will soon diverge under the time accumulation, and the accuracy requirement of the strict regression cannot be met. Here, the velocity error is multiplied by 1000 as an amplification coefficient, which is similar to the constraint penalty coefficient in the construction of the optimization objective in the intelligent optimization algorithm; According to the search and solution change range of each orbit parameter in the Minpack algorithm, the nonlinear equation set of the minpack algorithm is used to obtain a set of orbit initial roots and the corresponding strict regression period, so that the regression revisit accuracy of the reference track in the Earth-fixed system can meet the following formula:

8. An apparatus for obtaining rigorous regression orbital parameters, characterized by, The method comprises the following steps: The first acquisition module is configured to use the orbit analytical method to obtain a set of rough regression orbit plane roots by considering the Earth's flattening perturbation terms J2 and J3; The second obtaining module is configured to obtain the instantaneous orbital elements corresponding to the rough regression orbital elements by using a calculation function of plane-instantaneous conversion. The third obtaining module is configured to correct the semi-major axis in the parameters of the instantaneous orbital elements by using a numerical method to recursively calculate the orbit, so as to obtain an optimized initial value of the regression orbital elements. The fourth obtaining module is configured to perform small-range optimization and improvement on each orbital parameter and the regression period in the optimized initial value of the regression orbital elements by using a nonlinear equation set, so as to obtain strict regression orbital parameters with high regression accuracy.

9. An apparatus for obtaining rigorous regression orbital parameters, characterized by, The method comprises the following steps: a processor; a memory for storing processor-executable instructions; wherein the processor is configured to: obtain a set of rough regression orbital elements by using an orbital analytical method and considering the J2 and J3 perturbation terms of the earth's flattening; obtain the instantaneous orbital elements corresponding to the rough regression orbital elements by using a calculation function of plane-instantaneous conversion; correct the semi-major axis in the parameters of the instantaneous orbital elements by using a numerical method to recursively calculate the orbit, so as to obtain an optimized initial value of the regression orbital elements; perform small-range optimization and improvement on each orbital parameter and the regression period in the optimized initial value of the regression orbital elements by using a nonlinear equation set, so as to obtain strict regression orbital parameters with high regression accuracy.

10. A computer readable storage medium having stored thereon computer instructions, wherein, The instructions are executed by the processor to implement the method of any one of claims 1 to 7.

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