A method and device for controlling a retrograde orbit in the event of a satellite mission conflict

Abstract

The application discloses a method and device for controlling a regression orbit of a satellite in a task conflict, and belongs to the field of spacecraft orbit determination and control, in particular to a method for controlling a regression orbit of a satellite in a task conflict. The method solves the problem that the prior art cannot adapt to a task conflict scenario in the regression orbit control of a satellite due to the dependence on a fixed periodic firing window, and thus causes the accumulation of orbit deviation, serious fuel waste and the decline of control precision. The method comprises phase deviation judgment and target orbit regeneration, step-by-step optimization of target orbit parameters, optimization and execution of orbit control parameters. The method and device are suitable for dynamic maintenance of a satellite orbit and a high-precision revisit scenario.

Description

Technical Field

[0001] This invention relates to the field of spacecraft orbit determination and control, and more particularly to a return-to-orbit control method for satellite mission conflicts. Background Technology

[0002] With the rapid development of the satellite industry, the demand for revisiting the same location on the ground is increasing. This requires high-precision control of satellite orbits to achieve high-precision revisiting of the nadir trajectory after the return cycle.

[0003] Because the characteristics of the revisit orbit are strongly correlated with the Earth's rotation period, orbital decay caused by the atmosphere needs to be corrected in a timely manner; otherwise, the regression deviation will become increasingly large, eventually failing to meet the regression deviation requirements within a certain range. This is especially true for the high-precision INSAR mission requirements of SAR satellites, which have even higher requirements for revisiting the space trajectory.

[0004] High-precision orbital control requires strict control intervals and firing windows. Most current orbital control methods are based on ideal control cycles and ignition points, relying on preset fixed control cycles and ignition windows (e.g., performing orbital corrections every fixed number of days) to compensate for orbital decay caused by atmospheric drag by periodically adjusting parameters such as the semi-major axis and eccentricity. This type of method has the following problems:

[0005] Unable to adapt to mission conflict scenarios: When a satellite encounters an emergency imaging mission or insufficient power, the preset control window is often missed. At this time, orbital decay continues to accumulate, causing the phase deviation to exceed the allowable threshold (e.g., exceeding 0.5°), and the nadir trajectory deviation after the return cycle can reach the kilometer level. Orbital control cannot be performed under these circumstances.

[0006] Significant fuel waste: Existing methods, after missing the target return trajectory, require a large amount of fuel for extensive corrections if the previously designed target trajectory deviates significantly. Actual data shows that fuel consumption for corrections after accumulated deviations is more than 20% higher than that for conventional maintenance.

[0007] The control strategy lacks dynamic optimization: Since the next control window time is uncertain, traditional methods cannot formulate a reasonable control strategy for the track, which leads to the continuous expansion of the deviation and further affects the track control accuracy.

[0008] Causes and technical challenges of the problem:

[0009] The root cause of the above problems lies in the rigid framework design of existing technologies:

[0010] Fixed-period dependency: The control strategy assumes that the satellite can always perform orbit control as planned, without considering the dynamic conflict scenarios that are common in space missions;

[0011] Target track rigidity: mechanically tracking the original track even when deviation exceeds the limit;

[0012] Historical data not utilized: It is impossible to optimize the window period control strategy based on historical data, and it is impossible to predict the optimal orbit control position and ignition duration in the future, resulting in a large regression bias.

[0013] The core challenge in overcoming these difficulties lies in how to simultaneously achieve dynamic optimization of orbital parameters and maximize fuel efficiency under conditions of uncertain control timing. Especially for revisit orbits, the semi-major axis deviation is amplified by the coupling effect of Earth's rotation, while fluctuations in eccentricity and perigee angle further reduce revisit accuracy. Summary of the Invention

[0014] This invention proposes a method and apparatus for return-to-orbit control in the event of satellite mission conflicts. It solves the problem that existing technologies for satellite return-to-orbit control cannot adapt to mission conflict scenarios due to their reliance on fixed-period ignition windows, resulting in accumulated orbital deviations, serious fuel waste, and decreased control accuracy.

[0015] The present invention discloses a method for return-to-orbit control during satellite mission conflicts, the method comprising the following steps:

[0016] Step S1: Phase deviation judgment and target orbit regeneration:

[0017] Obtain the six-element numbers of the current orbit and the original target orbit; the current orbit is the satellite orbit at the initial time t0, and its six-element number is... ;

[0018] Calculate the phase deviation Δλ between the current orbit and the original target orbit, and compare it with a preset threshold λ. limit Compare:

[0019] If Δλ≤λ limit Then, step S3 is executed to track the target orbit using the six roots of the original target orbit.

[0020] If △λ>λ limit If so, recalculate the new target orbit based on the current orbit and execute step S2 to obtain the six roots of the new target orbit;

[0021] Step S2: Optimize the target orbit parameters step by step:

[0022] Initial optimization: using the semi-major axis To optimize variables, minimize a regression period. T p The objective equation for the longitude deviation of the descending node is:

[0023]

[0024] Constraints: Orbital dynamics equations , ;

[0025] in:

[0026] x To optimize the variables, here x Indicates semi-major axis ;Δ longitude _ DN ( x ) indicates that the variable x The resulting change in the longitude of the descending node; Indicates a regression period T p End of terminal time t f , by optimization variables x The determined geographical longitude of the satellite's descending node; Indicates the initial time. t 0, determined by the optimization variable x The determined geographical longitude of the satellite's descending node; Represents the orbital dynamics model; Indicates the initial time. t 0, determined by the optimization variable x The initial state of the satellite was determined; Indicates at the terminal time t f , by optimization variables x The determined satellite terminal status; H represents the feasible region; Represents optimization variables x The j One component; express The lower bound; express The upper bound;

[0027] Second optimization: using eccentricity e The sum and the argument ω of the perigee are the optimization variables, and the goal is to minimize them. n The parameter fluctuations and target value deviations within each regression period are represented by the objective equation:

[0028]

[0029] in, Std () represents the standard deviation function; average () represents the mean function; ω_ tar The average perigee argument of the target; e _ tar The target is the average eccentricity; coef This is the magnification factor;

[0030] Constraints: Orbital dynamics equations , ;

[0031] in:

[0032] x To optimize the variables, here x Indicates eccentricity e And the argument ω of the perigee; Std () represents the standard deviation function; average () represents the mean function; ω(:) represents the time series data of the perigee argument ω over multiple regression periods; e (:) represents the eccentricity. e Time series data over multiple regression periods; coef Indicates the magnification factor; ω_tar is the target value of the perigee argument; e _tar represents the target value for the eccentricity; Indicates the stability of the perigee argument; Indicates the stability of the eccentricity; Indicates the accuracy of the argument of perigee; Indicates the accuracy of the eccentricity;

[0033] After the above step-by-step optimization, the number of six roots of the new target orbit is obtained; step S3 is executed to track using the number of six roots of the new target orbit;

[0034] Step S3: Track control parameter optimization and execution:

[0035] Based on the target trajectory, with the ignition initiation phase angle and ignition time To optimize the variables and minimize the squared track distance, the objective equation is as follows:

[0036]

[0037] The constraints are relative to the orbital dynamics equations: , ;

[0038] in, x To optimize the variables, the ignition start phase angle is used here. and ignition time ; J The square of the trace distance; X Δt represents the track distance; Δt represents the expected next control interval. t j This represents the time corresponding to Δt / 2 time. A dynamic model to describe the relative motion between a virtual satellite and a real satellite; For time t0, the optimization variables are...x The initial relative state between the virtual star and the actual star is determined; For at any time t j From optimization variables x The final relative state between the virtual star and the actual star;

[0039] Calculate the weighted optimal parameters based on historical track control interval data:

[0040]

[0041]

[0042]

[0043] in, These are the statistical weights calculated based on the historical interval distribution; This is the final ignition start phase angle; This refers to the final ignition duration; The optimal launch phase angle corresponds to the i-th orbital control mission in history; This represents the optimal firing duration for the i-th orbital control mission in history. n This represents the total number of data points in the historical track control interval data.

[0044] In obtaining and Then, the orbit control task will be executed according to these two parameters.

[0045] Furthermore, a preferred embodiment is provided, wherein in step S1:

[0046] The phase deviation Δλ is calculated using the angular distance of the nadir point trajectory.

[0047] The preset threshold λ limit The value range is 0.1° ≤ λ limit ≤1°.

[0048] Furthermore, a preferred implementation is provided, in the initial optimization of step S2:

[0049] Boundary constraints are satisfied ,in ;

[0050] The orbital dynamics model High-order orbital perturbation models or numerical integration models of order 20 or above are used.

[0051] Furthermore, a preferred embodiment is provided, in the second optimization of step S2:

[0052] ω_ tar The range of values ​​for ω is 85° ≤ ω_ tar ≤95°;

[0053] e _ tar The value range is 0.001≤ e _ tar ≤0.005;

[0054] Magnification factor coef Satisfy 10 3 ≤ coef ≤10 6 .

[0055] Furthermore, a preferred embodiment is provided, wherein in step S3:

[0056] The trajectory distance X is defined as the displacement of the satellite ground projection point along the orbital direction.

[0057] Furthermore, in a preferred embodiment, in step S3, after obtaining... and Then, when performing this orbital control task according to these two parameters:

[0058] The thrust direction is along the track direction;

[0059] Ignition time Satisfying 0< ≤1200s.

[0060] This invention also proposes a return-to-orbit control device for satellite mission conflicts, the device comprising the following modules:

[0061] Module S1: Phase Deviation Judgment and Target Orbit Regeneration

[0062] Obtain the six-element numbers of the current orbit and the original target orbit; the current orbit is the satellite orbit at the initial time t0, and its six-element number is... ;

[0063] Calculate the phase deviation Δλ between the current orbit and the original target orbit, and compare it with a preset threshold λ. limit Compare:

[0064] If Δλ≤λ limit Then, step S3 is executed to track the target orbit using the six roots of the original target orbit.

[0065] If △λ>λ limit If so, recalculate the new target orbit based on the current orbit and execute step S2 to obtain the six roots of the new target orbit;

[0066] Module S2: Step-by-step optimization of target orbit parameters:

[0067] Initial optimization: using the semi-major axis To optimize variables, minimize a regression period. T p The objective equation for the longitude deviation of the descending node is:

[0068]

[0069] Constraints: Orbital dynamics equations , ;

[0070] in:

[0071] x To optimize the variables, here x Indicates semi-major axis ;Δ longitude _ DN ( x ) indicates that the variable x The resulting change in the longitude of the descending node; Indicates a regression period T p End of terminal time t f , by optimization variables x The determined geographical longitude of the satellite's descending node; Indicates the initial time. t 0, determined by the optimization variable x The determined geographical longitude of the satellite's descending node; Represents the orbital dynamics model; Indicates the initial time. t 0, determined by the optimization variable x The initial state of the satellite was determined; Indicates at the terminal time t f , by optimization variables x The determined satellite terminal status; H represents the feasible region; Represents optimization variables x The j One component; express The lower bound; express The upper bound;

[0072] Second optimization: using eccentricity e The sum and the argument ω of the perigee are the optimization variables, and the goal is to minimize them. n The parameter fluctuations and target value deviations within each regression period are represented by the objective equation:

[0073]

[0074] in, Std () represents the standard deviation function; average () represents the mean function; ω_ tar The average perigee argument of the target; e _ tar The target is the average eccentricity; coef This is the magnification factor;

[0075] Constraints: Orbital dynamics equations , ;

[0076] in:

[0077] x To optimize the variables, here x Indicates eccentricity e And the argument ω of the perigee; Std () represents the standard deviation function; average () represents the mean function; ω(:) represents the time series data of the perigee argument ω over multiple regression periods; e (:) represents the eccentricity. e Time series data over multiple regression periods; coef Indicates the magnification factor; ω_tar is the target value of the perigee argument; e _tar represents the target value for the eccentricity; Indicates the stability of the perigee argument; Indicates the stability of the eccentricity; Indicates the accuracy of the argument of perigee; Indicates the accuracy of the eccentricity;

[0078] After the above step-by-step optimization, the number of six roots of the new target orbit is obtained; step S3 is executed to track using the number of six roots of the new target orbit;

[0079] Module S3: Track Control Parameter Optimization and Execution

[0080] Based on the target trajectory, with the ignition initiation phase angle and ignition time To optimize the variables and minimize the squared track distance, the objective equation is as follows:

[0081]

[0082] The constraints are relative to the orbital dynamics equations: , ;

[0083] in, xTo optimize the variables, the ignition start phase angle is used here. and ignition time ; J The square of the trace distance; X Δt represents the track distance; Δt represents the expected next control interval. t j This represents the time corresponding to Δt / 2 time. A dynamic model to describe the relative motion between a virtual satellite and a real satellite; For time t0, the optimization variables are... x The initial relative state between the virtual star and the actual star is determined; For at any time t j From optimization variables x The final relative state between the virtual star and the actual star;

[0084] Calculate the weighted optimal parameters based on historical track control interval data:

[0085]

[0086]

[0087]

[0088] in, These are the statistical weights calculated based on the historical interval distribution; This is the final ignition start phase angle; This refers to the final ignition duration; The optimal launch phase angle corresponds to the i-th orbital control mission in history; This represents the optimal firing duration for the i-th orbital control mission in history. n This represents the total number of data points in the historical track control interval data.

[0089] In obtaining and Then, the orbit control task will be executed according to these two parameters.

[0090] The present invention also proposes a computer device comprising: a processor and a memory, the memory for storing executable instructions of the processor, the processor being configured to execute, by executing the executable instructions, a return-to-orbit control method for satellite mission conflicts as described above.

[0091] The present invention also proposes a computer storage medium storing a computer program, wherein when the computer program is executed, it performs a return-to-orbit control method for satellite mission conflicts as described above.

[0092] The present invention also proposes a computer program product, including a computer program / instruction, which, when executed by a processor, implements the steps of the return-to-orbit control method for satellite mission conflicts as described above.

[0093] The present invention has the following beneficial effects:

[0094] 1. The revisit orbit control method for satellite mission conflicts described in this invention dynamically regenerates the target orbit when the phase deviation exceeds a preset threshold, and fixes the orbit inclination and right ascension of the ascending node to reduce out-of-plane adjustments. This effectively avoids the accumulation of deviations caused by forcibly tracking the original orbit, thereby significantly reducing orbit control errors (e.g., the track distance converges to the meter level) and improving the revisit accuracy of the nadir point trajectory, especially meeting the high requirements of SAR satellite InSAR missions.

[0095] 2. The regression orbit control method for satellite mission conflicts described in this invention optimizes the target orbit parameters in steps—first optimizing the semi-major axis to minimize the longitude deviation of the descending node, then optimizing the eccentricity and perigee argument to minimize multi-period parameter fluctuations and target deviations, and combining the amplification factor to balance the optimization weights. This can significantly reduce unnecessary orbit corrections, reduce fuel consumption by 15-20%, and ensure the long-term stability of orbit parameters.

[0096] 3. The regression orbit control method for satellite mission conflicts described in this invention calculates the optimal ignition initiation phase angle and ignition duration based on historical orbit control interval data using weighted average, and uses the relative orbit dynamics equation to constrain the minimization of the trajectory distance. This method can dynamically adapt to uncertain control windows, improve the stability of the regression cycle (e.g., reduce the standard deviation by 30%), effectively suppress the expansion of deviations, and improve orbit control accuracy.

[0097] 4. The regression orbit control method for satellite mission conflicts described in this invention overcomes the dependence of existing technologies on fixed control periods by integrating dynamic orbit re-optimization, step-by-step parameter priority adjustment, and historical data weighting strategies. It can minimize orbit control errors and improve orbit control accuracy when the optimal control window and period are missed. The regression period is relatively stable, and high-precision orbit revisit is achieved (such as a reduction in regression deviation of more than 50%). It has significant engineering implications and is applicable to satellite orbit dynamic maintenance and high-precision revisit applications in space mission conflict scenarios.

[0098] The present invention discloses a method and apparatus for revisiting orbits when satellite mission conflicts occur. It is applicable to scenarios of dynamic satellite orbit maintenance and high-precision revisit, and is particularly used to solve the problem of deviation accumulation when the control window is missed due to mission conflicts. It improves orbit control accuracy and fuel efficiency through step-by-step parameter optimization and historical data weighting strategies. Attached Figure Description

[0099] To more clearly illustrate the technical solutions in the embodiments of the present invention, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.

[0100] Figure 1 A flowchart of a method for reverting to orbit control when satellite mission conflicts occur, as described in one embodiment of the present invention;

[0101] Figure 2 This is a schematic diagram of the statistical distribution of historical track control mission intervals (historical track control intervals) in one embodiment of the present invention.

[0102] Figure 3 This is a schematic diagram of the eccentricity of the optimized new target orbit in one embodiment of the present invention;

[0103] Figure 4 This is a schematic diagram of the perigee argument of the optimized new target orbit in one embodiment of the present invention;

[0104] Figure 5 This is a schematic diagram showing the distance between the current star and the target star in one embodiment of the present invention. Detailed Implementation

[0105] To make the technical solutions and advantages of the present invention clearer, the specific embodiments of the present invention will be described in further detail and completely below with reference to the accompanying drawings. The various embodiments described below are only some preferred embodiments of the present invention, and not all of them; the various embodiments described below are intended to explain the present invention and should not be construed as limiting the present invention; reasonable combinations of the technical features defined in the various embodiments of the present invention, as well as all other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative effort, are all within the scope of protection of the present invention.

[0106] Implementation Method 1: A method for return orbit control during satellite mission conflicts, the method comprising the following steps:

[0107] Step S1: Phase deviation judgment and target orbit regeneration:

[0108] Obtain the six-element numbers of the current orbit and the original target orbit; the current orbit is the satellite orbit at the initial time t0, and its six-element number is... ;

[0109] Calculate the phase deviation Δλ between the current orbit and the original target orbit, and compare it with a preset threshold λ. limit Compare:

[0110] If Δλ≤λ limit Then, step S3 is executed to track the target orbit using the six roots of the original target orbit.

[0111] If △λ>λ limit If so, recalculate the new target orbit based on the current orbit and execute step S2 to obtain the six roots of the new target orbit;

[0112] Step S2: Optimize the target orbit parameters step by step:

[0113] Initial optimization: using the semi-major axis To optimize variables, minimize a regression period. T p The objective equation for the longitude deviation of the descending node is:

[0114]

[0115] Constraints: Orbital dynamics equations , ;

[0116] in:

[0117] x To optimize the variables, here x Indicates semi-major axis ;Δ longitude _ DN ( x ) indicates that the variable x The resulting change in the longitude of the descending node; Indicates a regression period T p End of terminal time t f , by optimization variables x The determined geographical longitude of the satellite's descending node; Indicates the initial time. t 0, determined by the optimization variable x The determined geographical longitude of the satellite's descending node; Represents the orbital dynamics model; Indicates the initial time. t 0, determined by the optimization variable x The initial state of the satellite was determined; Indicates at the terminal time t f , by optimization variables x The determined satellite terminal status; H represents the feasible region; Represents optimization variables x The j One component; express The lower bound; express The upper bound;

[0118] Second optimization: using eccentricity e The sum and the argument ω of the perigee are the optimization variables, and the goal is to minimize them. n Parameter fluctuations and target value deviations within each regression period (i.e., n (Minimize the changes in eccentricity and angle of permeability within each regression period), the objective equation is:

[0119]

[0120] in, Std () represents the standard deviation function; average () represents the mean function; ω_ tar The average perigee argument of the target; e _ tar The target is the average eccentricity; coef This is the magnification factor;

[0121] Constraints: Orbital dynamics equations , ;

[0122] in:

[0123] x To optimize the variables, here x Indicates eccentricity e And the argument ω of the perigee; Std () represents the standard deviation function; average () represents the mean function; ω(:) represents the time series data of the perigee argument ω over multiple regression periods; e (:) represents the eccentricity. e Time series data over multiple regression periods; coef Indicates the magnification factor; ω_tar is the target value of the perigee argument; e _tar represents the target value for the eccentricity; Indicates the stability of the perigee argument; Indicates the stability of the eccentricity; Indicates the accuracy of the argument of perigee; Indicates the accuracy of the eccentricity;

[0124] After the above step-by-step optimization, the number of six roots of the new target orbit is obtained; step S3 is executed to track using the number of six roots of the new target orbit;

[0125] Step S3: Track control parameter optimization and execution:

[0126] Based on the target trajectory, with the ignition initiation phase angle and ignition time To optimize the variables and minimize the squared track distance, the objective equation is as follows:

[0127]

[0128] The constraints are relative to the orbital dynamics equations: , ;

[0129] in, x To optimize the variables, the ignition start phase angle is used here. and ignition time ; J The square of the trace distance; X Δt represents the track distance; Δt represents the expected next control interval. t j This represents the time corresponding to Δt / 2 time. A dynamic model to describe the relative motion between a virtual satellite and a real satellite; For time t0, the optimization variables are... x The initial relative state between the virtual star and the actual star is determined; For at any time t j From optimization variables x The final relative state between the virtual star and the actual star;

[0130] Calculate the weighted optimal parameters based on historical track control interval data:

[0131]

[0132]

[0133]

[0134] in, These are the statistical weights calculated based on the historical interval distribution; This is the final ignition start phase angle; This refers to the final ignition duration; The optimal launch phase angle corresponds to the i-th orbital control mission in history; This represents the optimal firing duration for the i-th orbital control mission in history. n This represents the total number of data points in the historical track control interval data.

[0135] In obtaining and Then, the orbit control task will be executed according to these two parameters.

[0136] In this embodiment, the six-root number, or (Kepler) orbital six-root number, is a core parameter in aerospace dynamics that describes the orbital state of a satellite.

[0137] In this embodiment, the formula middle:

[0138] The superscript "°" indicates "the measured or reference value at the initial time t0", which is the starting point for optimization calculation.

[0139] It represents the semi-major axis of the initial orbit and describes the size of the orbital ellipse; it is the most important parameter that determines the orbital period of a satellite; unit: meter (m).

[0140] e ° represents the initial orbital eccentricity, describing the flattening of the orbital ellipse; e When = 0, it is a circular orbit; when 0 < 0, it is a circular orbit. e When <1, it is an elliptical orbit; dimensionless.

[0141] i ° represents the initial orbital inclination, the angle between the orbital plane and the Earth's equatorial plane; unit: degrees (°).

[0142] Ω° represents the right ascension of the initial ascending node, the angle between the direction of the vernal equinox and the ascending node of the orbit (the point where the satellite crosses the equatorial plane from south to north); unit: degrees (°).

[0143] ω° represents the initial perigee argument, which is the angle between the ascending node and the perigee (the point closest to the Earth's center) in the orbital plane; unit: degree (°).

[0144] M ° represents the initial mean anomaly angle, a calculated angle used to determine the satellite's specific position in its orbit; it assumes the satellite is moving at an average angular velocity; unit: degree (°).

[0145] These are the input data for the optimization algorithm; they come from the orbital state measured in real time by the GNSS receiver (such as GPS) on the satellite at time t0, representing a precise description of where the satellite is currently "located".

[0146] In this embodiment, the optimization strategy for step S2 is as follows:

[0147] Fixed parameters: i (Orbital inclination) and Ω (right ascension of the ascending node) are used as fixed parameters, based on the current orbital inclination ( i The orbital inclination and right ascension of the ascending node (Ω°) are optimized; this is because the out-of-plane adjustment of the orbital inclination and right ascension of the ascending node is not adjusted due to the large fuel consumption. That is, adjusting these two parameters (called "out-of-plane maneuvers") requires changing the direction of the orbital plane, which is extremely fuel-intensive. Therefore, only "in-plane maneuvers" are performed.

[0148] Optimize variables: (semi-major axis) e (Eccentricity) and ω° (argument of perigee) are the main variables adjusted in the optimization process; adjusting them can change the size, shape and orientation of the track, but not the track plane itself, thus greatly saving fuel.

[0149] Calculation reference: M (Mean anterior angle) is used as a known input condition or calculation benchmark to accurately calculate the initial phase of the satellite and is the starting point for extrapolating its future orbital position. M ° represents the instantaneous position of the satellite in its orbit at the initial time t0; it is a definite value obtained directly from GNSS measurements; in optimization calculations, the optimization objective is to adjust the geometry and spatial orientation of the orbit (through...). , e , i (, Ω, ω), rather than changing the instantaneous position of the satellite at the initial time t0, M The value of ° is known and constant; in the orbital dynamics equations In the initial state It includes M ° This value; for each new combination of optimization variables tried (e.g., a new semi-major axis) The algorithm needs to start from the same initial position (value). M Starting from °, using the model This is used to predict the future trajectory of the satellite, so that the optimization target (such as the future longitude deviation of the descending node) can be calculated.

[0150] This set of parameters This is the foundation and starting point of the entire optimization algorithm; by fixing the parameters for high fuel consumption ( i , Ω), optimize parameters for low fuel consumption ( , e To achieve an efficient and energy-saving track control strategy, we can use ω).

[0151] In this implementation, the objective equation and its constraints for the first optimization are as follows:

[0152] For the objective function (or objective equation) min H 1( x ):

[0153] min: short for minimize; it indicates that the objective function aims to find a value that minimizes the function. H 1( x The solution with the smallest value;

[0154] H 1( x This is a custom objective function. The subscript "1" indicates that this is the first optimization; the function's value depends on the optimization variables. x The goal is to find... H 1( x The smallest one x ;

[0155] x Optimization variables refer to unknown variables for which an algorithm aims to find the optimal value. Here, this... x Specifically refers to the semi-major axis of the satellite ;

[0156] Δ longitude _ DN ( x ): Δ (Delta) represents the "difference"; longitude _ DN It is the standard term for the descending node longitude; Δ longitude _ DN ( x This indicates that the variable is determined by... x The resulting change or deviation in the longitude of the descending node;

[0157] ‖ ... ‖: This is the norm symbol; it ensures that the calculated deviation is a positive number (because distance differences cannot be negative).

[0158] At the terminal time t f (i.e., one regression period) T p (The end time), determined by the optimization variables x The determined geographical longitude of the satellite's descending node;

[0159] At the initial moment t 0 (i.e., the moment when optimization begins), determined by the optimization variables. x The determined geographical longitude of the satellite's descending node;

[0160] Interpretation of the entire objective function:

[0161] Find an optimal semi-major axis of the orbit. This makes it possible to start from a regression cycle ( t 0) to the end ( t f When the satellite descends to its nadir, the absolute value of the change in geographical longitude is minimized; ideally, this difference should be zero, meaning the satellite accurately returns to its nadir trajectory.

[0162] For min H 1( x Constraints:

[0163] Constraints define the optimization variables Physical rules and engineering constraints that must be followed.

[0164] (Orbital dynamics equation constraints):

[0165] r : Represents the satellite's state vector; here it is the orbital root number ( , e , i , Ω, ω, M );

[0166] At the initial moment t 0, determined by the optimization variable x The initial state of the satellite was determined;

[0167] At the terminal time t f , by optimization variables x The determined satellite terminal status;

[0168] : Orbital dynamics model (or orbital propagator). This is a complex function calculated based on physical laws (such as universal gravitation, Earth's non-spherical perturbation J2, atmospheric drag, etc.) from the initial state. It begins, and spreads to some point in the future. t f The terminal status after ;

[0169] meaning: This equation constraint mandates that the final state calculated through optimization must conform to the laws of orbital dynamics; one cannot calculate a physically impossible orbit simply to minimize the longitude difference.

[0170] (Decision space constraints):

[0171] ∈: means "belongs to";

[0172] H: Represents the feasible region or set of constraints (or search space) of the optimization problem, i.e., the optimization variables. x The set of all possible values; in mathematics and optimization, H is often written in cursive script. For ease of editing, the special font is written as the ordinary font H here;

[0173] The superscript "1×1" indicates that the search space H is one-dimensional; because in this optimization, there is only one optimization variable. x (i.e., semi-major axis) ).

[0174] (Boundary constraints):

[0175] Optimization variables x The j One component; because j =1, so only here x 1, which is our optimization variable x ;

[0176] : The lower bound, l It is an abbreviation for lower;

[0177] : The upper bound of , u is an abbreviation for upper;

[0178] meaning: This inequality constraint forces that the optimization variable... x The value must be within a reasonable physical range (e.g., semi-major axis). The size of the satellite must be such that it falls into the atmosphere, or it must be such that it escapes; this is usually determined by mission safety and satellite capabilities.

[0179] In this implementation, the objective equation and its constraints for the second optimization are as follows:

[0180] For the objective function (or objective equation) min H 2( x ):

[0181] H 2( x This is the objective function for the second optimization. The subscript "2" connects it to the objective function for the first optimization. H 1( x Distinguish them;

[0182] x : Optimization variables; In the second optimization, this is a two-dimensional vector containing two orbital parameters to be optimized: eccentricity e and perigee argument ω. x =( e ,ω) T 。

[0183] The four components of the objective function:

[0184] objective function H 2( x It consists of four parts, designed to comprehensively evaluate the quality of the orbit from different perspectives:

[0185] Stability of perigee argument:

[0186] Std (): Standard Deviation function; calculates the dispersion of a set of data; the smaller the value, the more stable the data and the less volatile it is;

[0187] ω(:): The symbol (:) is a syntax in programming languages ​​such as MATLAB, indicating that all elements of a matrix / array are expanded into column vectors; in this context, ω(:) represents the time series data of the perigee argument ω over multiple regression periods;

[0188] meaning: This requirement requires that the optimized orbit have as little fluctuation as possible in its perigee argument ω over multiple periods, i.e., remain stable.

[0189] Stability of eccentricity (weighted):

[0190] e (:): Indicates eccentricity. e Time series data over multiple regression periods;

[0191] coef: Coefficient; this is a constant (e.g., 1 × 10⁻⁶). 5 Since the value of the eccentricity (e.g., 0.001) is usually much smaller than the change in the perigee angle (tens of degrees), a large coefficient is needed to amplify its influence so that the two items are comparable in magnitude, thus giving them a reasonable weight in the optimization.

[0192] meaning: This requirement stipulates that the eccentricity e of the optimized trajectory should fluctuate as little as possible over multiple periods.

[0193] Accuracy of perigee argument:

[0194] average (): Mean function; calculates the average of a set of data;

[0195] ω_tar: Target value of perigee angle; this is an ideal value preset according to mission requirements (e.g., 90°); tar is an abbreviation for target;

[0196] | |: Absolute value; ensures the difference is a positive number;

[0197] meaning: This requirement requires that the long-term average of the perigee argument ω of the optimized orbit be as close as possible to the set target value ω_tar.

[0198] Accuracy of eccentricity (weighted):

[0199] e _tar: Target value of eccentricity;

[0200] meaning: This requirement demands that the optimized orbit have an eccentricity. e The long-term average should be as close as possible to the set target value. e _tar; similarly, use coef To amplify the signal, the magnitude was adjusted.

[0201] The entire objective function min H 2( x A comprehensive interpretation of the meaning of )

[0202] Finding an optimal pair of eccentricities e and perigee argument ω , so that they:

[0203] It remains stable (with little change over time);

[0204] The long-term average value is close to the expected target value;

[0205] And through the magnification factor coef To reconcile the differences in the numerical value and importance of eccentricity and perigee argument.

[0206] Constraints :

[0207] Constraints define the optimization variables x Physical rules and engineering constraints that must be followed.

[0208] The superscript "2×1" indicates that the variables being optimized are 2-dimensional (i.e., e and ω (two variables)

[0209] j=2: indicates that there are two variables (i.e., ... e and ω (The upper and lower bounds need to be set separately.)

[0210] In this embodiment, based on the ignition start phase angle and ignition time To optimize the variables, the objective equation for minimizing the squared track distance is:

[0211] Optimize variable definitions: ;

[0212] x : Optimization variable, which is a column vector containing two parameters to be optimized;

[0213] : Ignition start phase angle; this determines at which phase angle of the satellite orbit the thrusters are activated; the unit is usually degrees (°) or radians (rad);

[0214] Ignition duration; refers to the length of time the thruster operates continuously; the unit is usually seconds (s);

[0215] : Transpose symbol; indicates converting a row of data into a column vector; here it means x It is a two-dimensional column vector;

[0216] meaning: This indicates that the core task of the objective equation is to find the optimal ignition timing for the satellite. ) and optimal ignition duration ( ).

[0217] Objective function (or objective equation) ;

[0218] J Objective function; here it is directly defined as the square of the trace distance;

[0219] X : Along-track distance; This is a key concept in satellite orbit control, referring to the distance between a virtual satellite in a target orbit and a real satellite (or actual satellite) in an actual orbit along their orbital path on the ground.

[0220] Δt: The expected next control interval; that is, the length of time from the current moment to the next planned track control.

[0221] X (Δt / 2): This represents the track distance between the virtual star (virtual satellite) and the actual star (actual satellite) after time Δt / 2 (i.e., halfway through the next control window).

[0222] The square operation is used to ensure that the distance value is positive, and to facilitate differentiation and optimization (such as the least squares method).

[0223] Interpretation of the entire objective function:

[0224] Finding the optimal ignition parameters x This ensures that, at half the time point of the next control window, the track distance between the target virtual satellite and the actual satellite is... X The square of the value is minimized; this design is ingenious, its purpose being to minimize the maximum deviation within the entire control interval, thereby maintaining good control performance throughout the entire cycle.

[0225] Constraints: This equation constraint forces the optimization to conform to the laws of physics:

[0226] G ref {}: Relative orbital dynamics equations; This is a mathematical model used to accurately calculate the relative motion between two satellites (in this case, a virtual satellite and an actual satellite), taking into account various perturbations (such as the Earth's non-spherical perturbation J2, atmospheric drag, etc.); It is called the dynamic model describing the relative motion between the virtual satellite and the actual satellite;

[0227] At the initial time t0, the optimization variables are... x The initial relative state (usually including relative position and relative velocity) between the virtual star and the actual star is determined by the ignition parameters.

[0228] At the terminal time t j (This refers to the time Δt / 2), determined by the optimization variables. x The terminal relative state between the virtual star and the actual star, determined by (i.e., ignition parameters);

[0229] meaning: This equality constraint implies that the relative state at the terminal moment... It must be based on a relative dynamics model G ref {} from the initial state The propagation is achieved. This ensures that the trajectory generated by the optimized ignition parameters is physically achievable, rather than a mathematical illusion.

[0230] Boundary constraints: This inequality constraint defines the reasonable range of values ​​for the optimization variable:

[0231] The superscript "2×1" indicates that this is a 2-dimensional feasible region (because...). x It is a two-dimensional vector, namely the ignition initiation phase angle and ignition duration.

[0232] Optimization variables x The j The lower bound of each component;

[0233] Optimization variables x The j The upper bound of each component;

[0234] (j=2): This indicates that there are 2 variables here. j =1 is , j =2 is (The upper and lower bounds need to be set separately.)

[0235] meaning: This means that the optimized ignition initiation phase and ignition duration must be within a reasonable engineering range. For example, It cannot be a negative angle. The upper and lower limits are determined by factors such as the satellite's fuel reserves, the maximum operating time of the thrusters, and its thermal control capabilities.

[0236] In this embodiment, regarding t 0、 t f and t j The differences between these three moments:

[0237] In step S2 (orbit parameter optimization):

[0238] t 0: Optimize initial timing.

[0239] t f The terminal moment of orbital propagation (such as the moment when a regression cycle ends).

[0240] In step S3 (control parameter optimization):

[0241] t 0: The initial moment of control optimization (compared to step S2) t 0 represents the same absolute point in time.

[0242] t j : The target time for evaluating the control effect (i.e., the time Δt / 2); here we use j As a subscript, it indicates that it is an intermediate evaluation point in the optimization process, and is the same as the subscript representing the "final state" in step S2. f Distinguish between them.

[0243] In this embodiment, the weighted optimal parameters are calculated based on historical track control interval data:

[0244] (1) Final ignition start phase angle: :

[0245] The final calculated optimized ignition start phase angle used for execution, also known as the final executed ignition start phase angle, final ignition start phase angle, or final ignition phase angle, is indicated by the subscript "". f "(final)" means "final". thrust_start Indicates "ignition start";

[0246] i: Index, representing the i-th data point in the historical data sequence (historical track control interval data, or the interval statistics of historical track control tasks); n This represents the total number of data points in the historical track control interval data. This "data point" refers to a complete record of a "control interval-optimization result" combination in history. The i-th data point includes the ignition duration used in the i-th control in history and the ignition start phase angle used in the i-th control in history.

[0247] The optimal launch phase angle corresponding to the i-th orbital control mission in history (this is obtained through optimization calculation, assuming the control interval is a certain specific value of the optimal solution);

[0248] The statistical weights calculated based on the historical interval distribution, i.e., the statistical weights assigned to the i-th historical data point, are used to reflect the probability of different (control) intervals occurring. For example, if historical data shows that the most frequent control interval is 3 days, then the statistical weight corresponding to the 3-day interval... The value will be the largest; the historical interval distribution refers to the length of the time interval between each orbit control mission in history, which can be expressed as Δ. t iThe set of historical interval distributions, where "distribution" describes the statistical regularity of different interval values ​​(e.g., the interval of 3 days appeared 3 times, the highest frequency); the data source for historical interval distributions can be the historical mission log database of the satellite operator (such as the aerospace tracking and control center). This database records the precise execution timestamp of each orbit control mission. By calculating the time difference between two adjacent orbit control missions, a historical control interval Δ is obtained. t i For example, if the first control is executed on Day 1 and the second control is executed on Day 4, then Δ t 1 = 4 - 1 = 3 days; by traversing the entire historical record, a series of Δ values ​​can be obtained. t 1, Δ t 2, Δ t 3, ..., Δ t m These data constitute the original dataset of the "historical interval distribution"; the weight calculation process is based on probability statistics, with the aim of giving more frequent intervals a greater weight in the final decision.

[0249] Final ignition start phase angle , is the weighted average of all historical best phase angles, which is to combine the best solutions in each historical case according to their probability (weight) of possible future occurrences to obtain a comprehensive optimal estimate.

[0250] (2) Final ignition duration: :

[0251] The final calculated optimized ignition duration used for execution, also known as the final executed ignition duration or final ignition duration;

[0252] The optimal launch duration for the i-th orbital control mission in history;

[0253] Final ignition duration It is the weighted average of the longest fire durations in all historical periods.

[0254] (3) Weight constraints: :

[0255] The premise for weighted average calculation to be valid is that all weights constitute a complete probability distribution.

[0256] In summary, the above formula describes a probability-based decision-making model:

[0257] Because the exact time of the next control is uncertain, and we do not say "the next interval will definitely be X days", but rather consider all possible scenarios.

[0258] By calculating a weighted average of the optimal solutions corresponding to various (control) intervals throughout history, a comprehensive solution with the highest expected return is obtained. This is a very high-order and intelligent optimization strategy.

[0259] In this embodiment, the statistical weights are calculated based on the historical interval distribution. Method:

[0260] (1) Data preparation: Extract m consecutive control time intervals Δ from the historical database. t i Data refers to the statistical interval length between each past track control operation and the next track control operation (i.e., all Δ...). t i )

[0261] For example, obtain 4 data points: [Δ t 1=2.5,Δ t 2=3.0,Δ t 3=3.0,Δ t 4 = 3.5).

[0262] Δ t i Δ represents the time interval (or control period) between the i-th historical orbit control task and its next control task, representing the temporal pattern of historical control behavior. Historical statistical information (historical orbit control interval data) contains many records of past orbit control tasks. Each historical record includes an actual control interval that occurred, i.e., how long the interval was between this control and the next control. t i This refers to the time interval corresponding to the i-th control task in this historical sequence.

[0263] (2) Statistical frequency: Count the number of times each different interval value appears.

[0264] For example, it occurs once every 2.5 days; twice every 3.0 days; and once every 3.5 days.

[0265] (3) Calculate the probability / weight: Divide the number of occurrences of each value by the total number of data points m to obtain its weight. The total weight is 1.

[0266] For example, ω 2.5 =1 / 4=0.25; ω 3.0 =2 / 4=0.50; ω 3.5 =1 / 4=0.25;

[0267] Total: 0.25 + 0.50 + 0.25 = 1.

[0268] (4) Application weight: This weight The final control parameters are used for weighted calculation. A weight is assigned to the optimization result corresponding to each interval based on the probability of these historical intervals occurring.

[0269] Predicting the future: When the next control window is uncertain, a weighted average calculation is used to obtain the most likely applicable comprehensive control parameters (i.e., the final ignition start phase angle and the final ignition duration), thereby optimizing the uncertainty.

[0270] Implementation Method 2: In step S1:

[0271] The phase deviation Δλ is calculated using the angular distance of the nadir point trajectory.

[0272] The preset threshold λ limit The value range is 0.1° ≤ λ limit ≤1°.

[0273] In another embodiment, the preset threshold λ limit The value is 0.5°. Note that "°" here represents degrees.

[0274] Implementation Method 3: In the initial optimization of step S2:

[0275] Boundary constraints are satisfied ,in ;

[0276] The orbital dynamics model The J2 perturbation model or the numerical integration model is adopted.

[0277] In this embodiment, the semi-major axis Optimization scope:

[0278] Optimize the semi-major axis of the variable The search space is limited to the current measurement value. Centered on a radius of 1000 meters, this ensures sufficient space to find the optimal solution while avoiding the algorithm searching for unrealistic orbits that satellites cannot reach due to fuel, structural, or mission requirements.

[0279] In this embodiment, the type of orbital propagation model is:

[0280] Orbital dynamics model used for constraint calculation It can be a high-order orbit (order 20 or above) perturbation model or a numerical integration model.

[0281] The high-order orbit (order 20 and above) perturbation model is a high-precision orbital dynamics model based on spherical harmonic function theory, which can finely characterize the complex gravitational field of the Earth and has high computational efficiency;

[0282] Numerical integral models can take into account more perturbations (such as atmospheric drag, lunar and solar gravitational pull), resulting in higher accuracy but more complex calculations.

[0283] Implementation Method 4: In the second optimization of step S2:

[0284] ω_ tar The range of values ​​for ω is 85° ≤ ω_ tar ≤95°;

[0285] e _ tar The value range is 0.001≤ e _ tar ≤0.005;

[0286] Magnification factor coef Satisfy 10 3 ≤ coef ≤10 6 .

[0287] In this embodiment, 85°≤ω_ tar ≤95°, which is a typical range close to 90°. Setting ω near 90° helps optimize orbital geometry and is suitable for many remote sensing satellite missions that require specific lighting conditions or ground coverage.

[0288] In this embodiment, 0.001 ≤ e _ tar ≤0.005, this range defines a near-circular orbit (an eccentricity of 0 indicates a perfect circle). Maintaining a near-circular orbit ensures stable nadir trajectory velocity and ground resolution.

[0289] In this embodiment, 10 3 ≤ coef ≤10 6 Due to eccentricity e The value (~0.001) is much smaller than the change in the perigee argument ω (tens of degrees), so an amplification factor must be used in the optimization objective function. coef This is used to balance the magnitude and importance of both, allowing them to be optimized simultaneously on a similar order of magnitude. This range gives a reasonable range of values ​​for this coefficient.

[0290] In another embodiment, coef It is 1e5 (in scientific notation), which is 1 × 10⁵. 5 .

[0291] Implementation method 5: In step S3:

[0292] The trajectory distance X is defined as the displacement of the satellite ground projection point along the orbital direction.

[0293] In this embodiment, the satellite ground projection point is the vertical projection point of the satellite on the Earth's surface.

[0294] In this embodiment, the displacement along the orbital direction is the distance component along the tangent direction of the satellite's ground trajectory.

[0295] Implementation Method 6: In step S3, after obtaining... and Then, when performing this orbital control task according to these two parameters:

[0296] The thrust direction is along the track direction;

[0297] Ignition time Satisfying 0< ≤1200s.

[0298] In this implementation, the thrust direction is required to be "along the track direction," meaning the thrust direction is collinear with the satellite's flight velocity direction. This is the most efficient way to adjust orbital energy and shape (change the semi-major axis, eccentricity, etc.), and it conforms to the basic principles of orbital control.

[0299] In this embodiment, the upper limit for ignition duration is required to be "≤ 1200s" (i.e., 20 minutes). This is an important engineering safety constraint to prevent thruster overheating, abnormal fuel supply, or other system failures caused by excessively long continuous ignition, thus ensuring the reliability of control and the safety of the satellite.

[0300] Implementation Method 7: A return-to-orbit control device for satellite mission conflicts, the device comprising the following modules:

[0301] Module S1: Phase Deviation Judgment and Target Orbit Regeneration

[0302] Obtain the six-element numbers of the current orbit and the original target orbit; the current orbit is the satellite orbit at the initial time t0, and its six-element number is... ;

[0303] Calculate the phase deviation Δλ between the current orbit and the original target orbit, and compare it with a preset threshold λ. limit Compare:

[0304] If Δλ≤λ limit Then, step S3 is executed to track the target orbit using the six roots of the original target orbit.

[0305] If △λ>λ limitIf so, recalculate the new target orbit based on the current orbit and execute step S2 to obtain the six roots of the new target orbit;

[0306] Module S2: Step-by-step optimization of target orbit parameters:

[0307] Initial optimization: using the semi-major axis To optimize variables, minimize a regression period. T p The objective equation for the longitude deviation of the descending node is:

[0308]

[0309] Constraints: Orbital dynamics equations , ;

[0310] in:

[0311] x To optimize the variables, here x Indicates semi-major axis ;Δ longitude _ DN ( x ) indicates that the variable x The resulting change in the longitude of the descending node; Indicates a regression period T p End of terminal time t f , by optimization variables x The determined geographical longitude of the satellite's descending node; Indicates the initial time. t 0, determined by the optimization variable x The determined geographical longitude of the satellite's descending node; Represents the orbital dynamics model; Indicates the initial time. t 0, determined by the optimization variable x The initial state of the satellite was determined; Indicates at the terminal time t f , by optimization variables x The determined satellite terminal status; H represents the feasible region; Represents optimization variables x The j One component; express The lower bound; express The upper bound;

[0312] Second optimization: using eccentricity eThe sum and the argument ω of the perigee are the optimization variables, and the goal is to minimize them. n The parameter fluctuations and target value deviations within each regression period are represented by the objective equation:

[0313]

[0314] in, Std () represents the standard deviation function; average () represents the mean function; ω_ tar The average perigee argument of the target; e _ tar The target is the average eccentricity; coef This is the magnification factor;

[0315] Constraints: Orbital dynamics equations , ;

[0316] in:

[0317] x To optimize the variables, here x Indicates eccentricity e And the argument ω of the perigee; Std () represents the standard deviation function; average () represents the mean function; ω(:) represents the time series data of the perigee argument ω over multiple regression periods; e (:) represents the eccentricity. e Time series data over multiple regression periods; coef Indicates the magnification factor; ω_tar is the target value of the perigee argument; e _tar represents the target value for the eccentricity; Indicates the stability of the perigee argument; Indicates the stability of the eccentricity; Indicates the accuracy of the argument of perigee; Indicates the accuracy of the eccentricity;

[0318] After the above step-by-step optimization, the number of six roots of the new target orbit is obtained; step S3 is executed to track using the number of six roots of the new target orbit;

[0319] Module S3: Track Control Parameter Optimization and Execution

[0320] Based on the target trajectory, with the ignition initiation phase angle and ignition time To optimize the variables and minimize the squared track distance, the objective equation is as follows:

[0321]

[0322] The constraints are relative to the orbital dynamics equations: , ;

[0323] in, x To optimize the variables, the ignition start phase angle is used here. and ignition time ; J The square of the trace distance; X Δt represents the track distance; Δt represents the expected next control interval. t j This represents the time corresponding to Δt / 2 time. A dynamic model to describe the relative motion between a virtual satellite and a real satellite; For time t0, the optimization variables are... x The initial relative state between the virtual star and the actual star is determined; For at any time t j From optimization variables x The final relative state between the virtual star and the actual star;

[0324] Calculate the weighted optimal parameters based on historical track control interval data:

[0325]

[0326]

[0327]

[0328] in, These are the statistical weights calculated based on the historical interval distribution; This is the final ignition start phase angle; This refers to the final ignition duration; The optimal launch phase angle corresponds to the i-th orbital control mission in history; This represents the optimal firing duration for the i-th orbital control mission in history. n This represents the total number of data points in the historical track control interval data.

[0329] In obtaining and Then, the orbit control task will be executed according to these two parameters.

[0330] Implementation Method 8: A computer device comprising: a processor and a memory, the memory for storing executable instructions of the processor, the processor being configured to execute, by executing the executable instructions, a return-to-orbit control method for satellite mission conflicts as described above.

[0331] Implementation Method 9: A computer storage medium storing a computer program, wherein when the computer program is executed, it performs a return-to-orbit control method for satellite mission conflicts as described in any of the above embodiments.

[0332] Implementation method 10: A computer program product, including a computer program / instructions, which, when executed by a processor, implement the steps of the return-to-orbit control method for satellite mission conflicts as described above.

[0333] Implementation Method 11: A specific embodiment is provided to illustrate a method for return orbit control in the event of satellite mission conflicts.

[0334] This embodiment details the application of the present invention in specific satellite mission conflict scenarios, where the satellite can be a SAR satellite or other spacecraft with high revisit accuracy requirements.

[0335] Step S1: Phase deviation judgment and target orbit regeneration:

[0336] Determine the phase deviation between the current orbital parameters (i.e., the parameters of the current orbit) and the original target orbit (i.e., the original target orbit). Specifically, obtain the GNSS orbital root count (i.e., the current orbital root count) at time t0 (UTC time 18 Aug 2025 00:55:10.000):

[0337] Current orbital (six) number of elements:

[0338] =6879405.40m, e °=0.001041505, i °=97.334626950°, Ω°=236.61379203°, ω°=28.50069265°, M °=93.441387992°

[0339] Simultaneous elements of the original target orbit:

[0340] =6878835.142m, e tr =0.001031, i tr =97.336°, Ω tr =236.619°, ω tr =21.909° M tr =98.301°

[0341] Note: Subscript " tr"(short for target)" is used to refer to "target value".

[0342] The calculated phase deviation Δλ = 1.73°. Since Δλ > λ... limit (With the threshold set to 0.5°), a new target orbit needs to be generated.

[0343] Among them, orbital inclination i And the right ascension of the ascending node Ω will not be adjusted due to high fuel consumption from out-of-plane adjustments, based on the current orbital inclination. i The right ascension of the ascending node (Ω°) was optimized.

[0344] Step S2: Optimize the target orbit parameters step by step:

[0345] When the phase deviation Δλ>λ limit After triggering the regeneration of the target orbit, the following step-by-step optimization process is executed:

[0346] (1) Initial optimization (semi-major axis optimization):

[0347] Based on the current orbital telemetry (six roots), the longitude of the initial descending node is calculated by recursively extrapolating to the nearest descending node:

[0348] .

[0349] Optimize variables: , or expressed as (semi-major axis) );

[0350] in, x It represents the optimization variable, the unknown variable whose optimal value is sought through calculation; x ° represents the optimization variable. x The initial value or initial guess value. The superscript ° here indicates the "initial", "nominal", or "reference" state; The initial or current value of the semi-major axis in the satellite orbital elements; the entire formula It means: to optimize variables x Defined as semi-major axis And at the beginning of the optimization calculation, x The initial value is set to the satellite's current time ( t Actual semi-major axis measurement value (0) .

[0351] Optimization objective: Minimize a regression period T p The objective equation for the longitude deviation of the descending node is:

[0352]

[0353] Constraints: Orbital dynamics equations and boundary constraints (conditions) ;

[0354] in, For orbital dynamics model, This is the satellite's initial position. This indicates the position at the end of the satellite.

[0355] More specifically, the location here refers to the "state vector"; that is... Initial time t A complete set of orbital parameters for a satellite with a value of 0, which is sufficient to uniquely determine the satellite's state at that moment and its future trajectory. The parameters refer to the six orbital elements of the satellite. To use the orbital dynamics model After propagation, the result is at some final moment in the future. t f The satellite state vector (i.e., the orbital root number).

[0356] formula It describes a process: given an optimization variable x (semi-major axis) The value of ) and the initial time t Satellite status 0 Through a high-precision orbital dynamics model Calculate the satellite at a specified time in the future t f status .

[0357] During the optimization process, we continuously tried to give... x (semi-major axis) Assigning different values ​​to each orbital is equivalent to assuming a new orbit. For each assumed orbit, a new orbital needs to be established from the same initial moment. t Starting from the true state of 0, using the model We need to extrapolate how it will change in the future in order to calculate the optimization objective (such as the future difference in longitude between the descending nodes). Therefore, the initial state... and final state They are all functions of the assumed new orbit.

[0358] Additionally, it should be noted that, middle:

[0359] H represents the feasible region or constraint set of the optimization problem. In mathematics and optimization, it is often written as a capital letter H in a fancy (or calligraphic) style. Here, for ease of editing, the special font is written as the ordinary font H.

[0360] After optimization calculations, the semi-major axis after the first optimization It is 6,879,326.952m.

[0361] (2) Second optimization (eccentricity and perigee argument optimization):

[0362] After the first optimization is completed, a second iteration of optimization is performed.

[0363] Optimize variables: x =( e °,ω°) T (eccentricity) e (with perigee argument ω).

[0364] Optimization objective: To make it 3 (i.e. n =3) Minimize the fluctuations of eccentricity and perigee angle and their deviations from the target value within 3 regression periods. The objective equation is:

[0365]

[0366] in, Std () is the standard deviation function. average () is the mean function, ω_ tar The target's average perigee argument (set to 90 deg in this example), e _ tar The target average eccentricity is set to 0.00125 in this example. coef This is the magnification factor (set to 1e5 in this example, expressed in scientific notation, i.e., 1 × 10⁻⁵). 5 ).

[0367] Constraints: Orbital dynamics equations and boundary constraints (conditions) ;

[0368] After optimization calculations, the final optimized orbital parameters were obtained: eccentricity. e =0.00109133, perigee argument ω=26.2572 deg.

[0369] Step S3: Track control parameter optimization and execution:

[0370] After the new target orbit (with parameters of 6879300.446m semi-major axis, 0.001091, orbital inclination 97.334°, right ascension of ascending node 236.615°, argument of perigee 26.257°, ​​and mean perigee 95.589°) is redefined, the orbital control parameters are optimized and executed.

[0371] S3.1 Optimize control variables:

[0372] Optimization variable: Ignition start phase angle and ignition time ;

[0373] Optimization objective: To optimize the trajectory distance between the virtual satellite and the current actual satellite in the target orbit after a time interval of Δt / 2. X Minimize. The objective optimization equation is as follows:

[0374]

[0375] in, J It is the square of the trace distance.

[0376] Constraints:

[0377] Relative orbital dynamics equation constraints: ;

[0378] in, To describe the dynamic model of the relative motion between the virtual satellite and the actual satellite, and These are the initial and Δt / 2 times, respectively (i.e.) t j The relative position vector (state quantity) of ).

[0379] Boundary constraints:

[0380]

[0381] in, .

[0382] S3.2 Weighted Calculation of Final Parameters:

[0383] Assume the next control window is in △t i After a period of time,

[0384] Based on the statistical information of historical orbit control mission intervals, multiple optimal firing parameters are weighted and calculated to obtain the final execution parameters.

[0385] The weighted calculation expression is:

[0386]

[0387]

[0388] in, The statistical weights are calculated based on the historical interval distribution. (), used to reflect the probability of occurrence at different intervals.

[0389] The orbit control task will be executed according to these two final execution parameters.

[0390] In this example, the thruster thrust is 20 mN and the satellite mass is 300 kg.

[0391] Based on the statistical distribution of historical track control mission intervals, the next control interval Δ is expected to be... t There are three main possibilities: Δ t 1 = 2.5 days, Δ t 2 = 3 days or Δ t 3 = 3.5 days. Statistically, the weighting coefficients for each interval are ω1 = 0.06, ω2 = 0.72, and ω3 = 0.22.

[0392] Based on the above weights, the ignition parameters optimized for each control interval are weighted and calculated to obtain the final integrated track control parameters:

[0393] Final ignition start phase angle:

[0394]

[0395] Final ignition time:

[0396]

[0397] Table 1: Weighted Calculation Table of Control Parameters

[0398]

[0399] Based on the final calculated parameters ϕ f =301.4 degrees and Δ T f High-precision orbit maintenance can be achieved by executing orbit control in 850.3 seconds.

[0400] In this embodiment, Figure 3 This is a schematic diagram of the eccentricity of the optimized new target trajectory; as can be seen from the diagram:

[0401] After the "second optimization" (i.e., optimization with eccentricity e and perigee argument ω as variables), the eccentricity of the new target orbit was successfully controlled within an extremely narrow and stable range.

[0402] Stability: Over a timescale of approximately 30,000 minutes (about 20.8 days), the eccentricity value remained consistently at 1.20 × 10⁻⁶. -3 Up to 1.30×10 -3 Fluctuations between.

[0403] Fluctuation amplitude: Throughout the entire time series, the maximum fluctuation amplitude of the eccentricity is only 0.1 × 10⁻⁶. -3 (i.e., 0.0001). This is a very small change, which fully demonstrates the optimization algorithm's ability to control the long-term stability of the orbital parameters.

[0404] Orbital characteristics: The eccentricity remains close to zero, indicating that the optimized orbit is a highly circular orbit, which is crucial for maintaining stable imaging geometry for Earth observation satellites (such as SAR satellites).

[0405] This figure demonstrates that the optimization algorithm can: "significantly reduce unnecessary orbital corrections, achieve lower fuel consumption, and ensure long-term stability of orbital parameters."

[0406] Because the high stability of the eccentricity means that the satellite does not need to frequently and significantly use the thrusters to correct its orbital shape, it directly achieves the dual goals of saving fuel and improving stability.

[0407] In this embodiment, Figure 4 This is a schematic diagram of the perigee argument of the optimized new target orbit; as can be seen from the diagram:

[0408] After the "second optimization" process, the perigee argument (ω) of the new target orbit was stably controlled within a reasonable range during the simulation period of more than 20 days, without any divergence or significant deviation.

[0409] Stability and Fluctuation Range: Over a timescale of approximately 30,000 minutes (about 20.8 days), the perigee argument fluctuated between approximately 88° and 93°. This fluctuation range (approximately 5°) is small and stable relative to its physical meaning. It indicates that the optimization algorithm successfully "anchored" the parameter near the target value (e.g., 90°).

[0410] and Figure 3 Comparative analysis:

[0411] Figure 3 The fluctuation of (eccentricity) is extremely small (0.0001), which reflects the precise control of the absolute value of the parameter by the optimization algorithm.

[0412] Figure 4 The fluctuation range of the (perigee angle) is relatively large (5°), but the trend is stable and there is no divergence, which reflects the optimization algorithm's ability to stabilize the long-term change trend of parameters.

[0413] The combination of these two methods demonstrates that the optimization algorithm can simultaneously handle parameters (e and ω) with different characteristics and achieve excellent optimization results in both cases.

[0414] This figure demonstrates that the optimization algorithm can: "improve the stability of the regression cycle, achieve a relatively stable regression cycle, and realize high-precision orbit revisiting."

[0415] Because the perigee argument is stable, it means that the spatial pointing of the orbital ellipse is stable. This is crucial for ensuring that the satellite can revisit the same ground area with the same geometry each time (i.e., achieving high-precision regression).

[0416] In this embodiment, Figure 5 This is a schematic diagram showing the distance between the current star and the target star; it can be seen from the diagram that:

[0417] After applying the optimized control strategy, the distance between the actual satellite and the target virtual satellite showed a clear downward trend with fluctuations. The initial distance was approximately 12 kilometers, and after a control cycle of about 5000 minutes (approximately 83.3 hours / 3.5 days), the distance significantly decreased to below approximately 2 kilometers and then stabilized. This demonstrates that the entire control process (from judgment and re-optimization to execution) is highly effective.

[0418] Control effectiveness: The overall trend of the distance curve decreased significantly, from 12 kilometers to 2 kilometers, and the deviation was reduced by more than 80%, proving that the optimization algorithm can calculate effective control commands and drive the satellite to reliably approach the target orbit.

[0419] Convergence characteristics: The curve stabilized after 5000 minutes, indicating that the main adjustment phase of the control system had been completed and the satellite had entered a stable cruise state.

[0420] Stability: After the main decline phase ended, the distance remained at a relatively stable low level without further divergence, demonstrating the long-term stability of the control effect.

[0421] This figure directly demonstrates that the invention can: "significantly reduce regression error (by more than 80%) when the control window is missed or the deviation is large, thereby significantly improving the accuracy of track control and laying a solid foundation for the ultimate realization of high-precision revisit missions."

[0422] in short, Figure 3 and Figure 4 This proves that the optimized "target trajectory" itself is stable and of high quality; and Figure 5 This demonstrates that implementing "control" along this trajectory is remarkably effective, significantly correcting large initial deviations.

[0423] This embodiment provides a computer device or system. The hardware device in this part is a general model and is not shown in the figure. The system includes a processor and a memory, wherein the processor and the memory can be connected by a bus or other means. The memory, as a non-transitory computer-readable storage medium, can be used to store non-transitory software programs, non-transitory computer-executable programs and modules, as well as corresponding program instructions / modules. The processor executes various functional applications and data processing by running the non-transitory software programs, instructions and modules stored in the memory, so as to realize the data quality enhancement method for data space entity parsing in the above method embodiment.

[0424] The memory may include a program storage area and a data storage area, wherein the program storage area may store the operating system and applications required for at least one function; the data storage area may store data created by the processor, etc. Furthermore, the memory may include high-speed random access memory and may also include non-transitory memory, such as at least one disk storage device, flash memory device, or other non-transitory solid-state storage device. In some embodiments, the memory may optionally include memory remotely located relative to the processor, which can be connected to the processor via a network. Examples of such networks include, but are not limited to, the Internet, corporate intranets, mobile communication networks, and combinations thereof.

[0425] One or more modules are stored in the memory. When the processor executes, it performs the method steps in the embodiments. In this way, the invention objective can be achieved through the method, apparatus and process of the present invention. The specific details of the computer device described above can be understood by referring to the relevant descriptions and effects in the embodiments, and will not be repeated here.

[0426] Those skilled in the art will understand that implementing all or part of the processes in the above embodiments can be accomplished by a computer program instructing related hardware. The program can be stored in a computer-readable storage medium, and when executed, it can include the processes of the embodiments of the above methods. The storage medium can be a magnetic disk, optical disk, read-only memory (ROM), random access memory (RAM), flash memory, hard disk drive (HDD), or solid-state drive (SSD), etc.; the storage medium can also include combinations of the above types of memory.

[0427] The above description of several specific embodiments further details the technical solution provided by the present invention in order to highlight the advantages and benefits of the technical solution provided by the present invention. However, the above-described specific embodiments are not intended to limit the present invention. Any reasonable modifications and improvements to the present invention, reasonable combinations of embodiments, and equivalent substitutions based on the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for controlling a retrograde orbit in the event of a satellite mission conflict, characterized in that, The method comprises the following steps: Step S1: Phase deviation judgment and target orbit regeneration: Obtaining six elements of the current orbit and the original target orbit; the current orbit is the satellite orbit at the initial time t0, and the six elements are ; the superscript ° indicates the reference value at the initial time t0; Calculate the phase deviation Δλ of the current orbit from the original target orbit, and compare it with the preset threshold λ limit Comparison: If Δλ < λ limit then proceed to step S3 to track using the six elements of the original target orbit; If Δλ > λ limit then recalculate the new target orbit from the current orbit and perform step S2 to obtain the six elements of the new target orbit; Step S2: Step-by-step optimization of target orbit parameters: First optimization: with semi-major axis Minimize a regression period for optimization variable T p The declination of the descending node, the target equation is: Constraint: Equations of orbital dynamics , ; Wherein: x For optimization variables, here x denotes the semi-major axis ; Δ longitude _ DN x denotes the change in the descending node longitude caused by the optimization variable x ; denotes the satellite descending node geodetic longitude determined by the optimization variable T at the initial time p ; t f at the terminal time x ; denotes the satellite descending node geodetic longitude determined by the optimization variable t at the initial time x 0; denotes the orbit dynamic model ; t denotes the satellite initial state determined by the optimization variable x at the initial time 0; t f at the terminal time x ; denotes the feasible region x ; j denotes the th component of the optimization variable ; denotes the lower bound of ; Second optimization: with eccentricity e and minimizing the parameter fluctuations and target value deviations over a regression period of 2 years, the target equation being: n = 0. wherein Std () is a standard deviation function; average () is a mean function; ω tar is a target mean argument of perigee; e tar is a target mean eccentricity; coef is a magnification factor;​ Constraint: Equations of orbital dynamics , ; Wherein: x For the optimization variables, here x denotes the eccentricity e and the argument of perigee ω; Std () is the standard deviation function; average () is the mean function; ω(:) denotes the time series data of the argument of perigee ω over multiple regression cycles; e (:) denotes the eccentricity e over multiple regression cycles; coef denotes the amplification factor; ω_tar is the target value of the argument of perigee; e _tar is the target value of the eccentricity; denotes the stability of the argument of perigee; denotes the stability of the eccentricity; denotes the accuracy of the argument of perigee; denotes the accuracy of the eccentricity; After the above step-by-step optimization, the six numbers of the new target orbit are obtained; Step S3 is performed to track the six numbers of the new target orbit; Step S3: Orbit control parameter optimization and execution: Based on the target orbit, with the ignition start phase angle and the ignition duration The objective function is as follows for optimization variables, minimizing the squared slant range distance: The constraints are the relative orbit dynamics equations constraints: , ; in, x To optimize the variables, the ignition start phase angle is used here. and ignition time ; J The square of the trace distance; X Δt represents the trajectory distance; Δt represents the expected next control interval. t j This represents the time corresponding to Δt / 2 time. A dynamic model to describe the relative motion between a virtual satellite and a real satellite; For time t0, the optimization variables are... x The initial relative state between the virtual star and the actual star is determined; For at any time t j From optimization variables x The final relative state between the virtual star and the actual star; Based on the historical orbit control interval data to calculate the weighted optimal parameters: wherein, is a statistical weight calculated according to the historical interval distribution; is a final ignition start phase angle; is a final ignition duration; is an optimal ignition start phase angle corresponding to the i-th orbit control task in history; is an optimal ignition duration corresponding to the i-th orbit control task in history; n is a total number of data points in the historical orbit control interval data; After obtaining and the present orbit control task is performed in accordance with these two parameters.

2. The method according to claim 1, wherein, In the step S1: The phase deviation Δλ is calculated by the subspace point trajectory angle distance; The preset threshold λ limit is in the range of 0.1°≤λ limit ≤1°.

3. The method according to claim 1, wherein, In the first optimization of step S2: Boundary constraint condition satisfied , wherein ; The orbit dynamics model A high-order orbit perturbation model or a numerical integration model of 20 orders or more is adopted.

4. The method of claim 1, wherein, In the second optimization of step S2: ω tar The value of ω tar ranges from 85° ≤ ω ≤ 95°. e tar the value range of a is 0.001≤a≤0.005 e tar the value range of a is 0.001≤a≤0.005​​ Amplification factor coef Satisfies 10 3 ≤ coef ≤10 6 .

5. The method of claim 1, wherein, In the step S3: The trace distance X is defined as the displacement of the satellite ground projection point along the orbit direction.

6. The method of claim 1, wherein, In the step S3, after obtaining and the two parameters, the orbit control task is performed according to the two parameters. The thrust direction is along the trace direction; Ignition duration satisfies 0 ≤ 1200 s.

7. A device for controlling a retro-orbit in case of conflict of satellite missions, characterized in that, The device comprises the following modules: Module S1: Phase deviation judgment and target orbit regeneration: Obtaining six elements of the current orbit and the original target orbit; the current orbit is the satellite orbit at the initial time t0, and the six elements are ; the superscript ° indicates the reference value at the initial time t0; Calculate the phase deviation Δλ of the current orbit from the original target orbit, and compare it with the preset threshold λ limit Comparison: If Δλ < λ limit then step S3 is executed to track using the six elements of the original target orbit; If Δλ > λ limit then recalculate the new target orbit from the current orbit and perform step S2 to obtain the six elements of the new target orbit; Module S2: Step-by-step optimization of target orbit parameters: First optimization: with semi-major axis Minimize a regression period for optimization variable T p The target equation is: Constraint: Equations of orbital dynamics , ; Wherein: x for optimization variables, here x denotes the semi-major axis ; Δ longitude _ DN x denotes the change in the descending node longitude caused by the optimization variable x ; denotes the descending node longitude at the initial time T p the terminal time t f , determined by the optimization variable x ; denotes the descending node longitude at the initial time t 0, determined by the optimization variable x ; denotes the orbit dynamics model denotes the initial state of the satellite at the initial time t 0, determined by the optimization variable x ; denotes the terminal state of the satellite at the terminal time t f , determined by the optimization variable x ; denotes the x th component of the optimization variable j ; denotes the lower bound of ; denotes the upper bound of ;​ Second optimization: with eccentricity e and minimizing the parameter fluctuations and target value deviations over a regression period of 2 years, the target equation being: n with the argument of perigee ω as optimization variable. wherein Std () is a standard deviation function; average () is a mean function; ω tar is the target mean argument of perigee; e tar is the target mean eccentricity; coef is a magnification factor;​ Constraint: Equations of orbital dynamics , ; Wherein: x For the optimization variables, here x denotes the eccentricity e and the argument of perigee ω; Std () is the standard deviation function; average () is the mean function; ω(:) denotes the time series data of the argument of perigee ω over multiple regression cycles; e (:) denotes the eccentricity e over multiple regression cycles; coef denotes the amplification factor; ω_tar is the target value of the argument of perigee; e _tar is the target value of the eccentricity; denotes the stability of the argument of perigee; denotes the stability of the eccentricity; denotes the accuracy of the argument of perigee; denotes the accuracy of the eccentricity; After the above step-by-step optimization, the six numbers of the new target orbit are obtained; Step S3 is performed to track the six numbers of the new target orbit; Module S3: Orbit control parameter optimization and execution: Based on the target orbit, with a firing start phase angle and a firing duration The objective equation is as follows for optimizing variables, minimizing the squared slant range distance: The constraints are the relative orbit dynamics equations constraints: , ; in, x To optimize the variables, the ignition start phase angle is used here. and ignition time ; J The square of the trace distance; X Δt represents the trajectory distance; Δt represents the expected next control interval. t j This represents the time corresponding to Δt / 2 time. A dynamic model to describe the relative motion between a virtual satellite and a real satellite; For time t0, the optimization variables are... x The initial relative state between the virtual star and the actual star is determined; For at any time t j From optimization variables x The final relative state between the virtual star and the actual star; Based on the historical orbit control interval data to calculate the weighted optimal parameters: wherein, is a statistical weight calculated according to the historical interval distribution; is a final ignition start phase angle; is a final ignition duration; is an optimal ignition start phase angle corresponding to the i-th orbit control task in history; is an optimal ignition duration corresponding to the i-th orbit control task in history; n is a total number of data points in the historical orbit control interval data; After obtaining and the present orbit control task is executed in accordance with these two parameters.

8. A computer device comprising: A processor and a memory, characterized in that the memory is used to store executable instructions of the processor, and the processor is configured to execute the method of claim 1-6 via execution of the executable instructions.

9. A computer storage medium, characterized in that The storage medium stores a computer program, and the computer program runs to execute the method of claim 1-6.

10. A computer program product comprising computer programs / instructions, characterized in that, The computer program / instructions are executed by the processor to implement the steps of the method of claim 1-6.

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