A method and system for optimizing double-star orbital parameters

Abstract

The present invention discloses a method and system for optimizing the orbital parameters of a double star, including: Step 1) According to the six orbital elements of the primary star, calculate the time interval to obtain the <time, position, velocity> information matrix of the primary star and the theoretical solution set of the <time, position, velocity> information matrix of the secondary star; Step 2) Set the constraint conditions, establish an optimization model for the orbit of the secondary star, and according to the set solution granularity, use the dynamic mutation genetic algorithm. By setting the mutation operation probability that changes dynamically with the iteration step size, optimize the six orbital elements of the secondary star to obtain the actual solution of the <time, position, velocity> information matrix of the secondary star, and use the number of occurrences of the actual solution in the theoretical solution set as the fitness function; Step 3) Calculate the fitness function to obtain the continuous duration of maintaining communication between the two stars of the double star, and judge whether the continuous duration remains unchanged. If it is judged to be yes, go to Step 4), otherwise, go to Step 2); Step 4) Output the positions of the primary star and the secondary star that meet the conditions.

Description

Technical Field

[0001] The present invention belongs to the technical field of aerospace TT&C, and particularly relates to a method and system for optimizing the orbit parameters of double stars. Background Art

[0002] Due to different positions of space science satellites, they are affected differently by the space environment, geomagnetic field, etc. During the actual operation of space science missions, the information transfer between the two stars will be affected by the external environment, resulting in the inability to perform information transfer between the two stars during certain time periods. It is necessary to optimize the orbits of the double stars specifically. Under the condition of meeting the external constraints of the satellite orbits, the information transfer between the stars should be ensured to ensure the smooth progress of space science missions.

[0003] Currently existing algorithms usually optimize a single satellite orbit and do not involve the iterative optimization of double-star orbits. Therefore, there is an urgent need for a method for optimizing double-star orbit parameters to achieve iterative optimization of double-star orbits based on various constraints. Summary of the Invention

[0004] The purpose of the present invention is to overcome the defects of the prior art and propose a method and system for optimizing double-star orbit parameters.

[0005] In view of this, the present invention proposes a method for optimizing double-star orbit parameters, including:

[0006] Step 1) According to the six orbital elements of the primary star, calculate the time interval to obtain the <time, position, velocity> information matrix of the primary star and the theoretical solution set of the <time, position, velocity> information matrix of the secondary star;

[0007] Step 2) Set the constraint conditions, establish an optimization model for the orbit of the secondary star. According to the set solution granularity, adopt the dynamic mutation genetic algorithm, and by setting the mutation operation probability that changes dynamically with the iteration step size, optimize the six orbital elements of the secondary star to obtain the actual solution of the <time, position, velocity> information matrix of the secondary star, and use the number of occurrences of the actual solution in the theoretical solution set as the fitness function of the dynamic mutation genetic algorithm;

[0008] Step 3) Calculate the fitness function to obtain the continuous duration of maintaining communication between the two stars, and determine whether the continuous duration remains unchanged. If it is judged to be yes, go to Step 4); otherwise, go to Step 2);

[0009] Step 4) Output the positions of the primary star and the secondary star that meet the conditions.

[0010] Preferably, the six orbital elements in Step 1) include: the semi-major axis a of the orbit, the orbital eccentricity e, the orbital inclination i, the argument of perigee ω, the longitude of the ascending node Ω, and the true anomaly

[0011] Preferably, the <time, position, velocity> information matrix of the primary satellite in step 1) is a T×1 matrix, where T represents the T calculated time points, and the information matrix Y(t) at a certain time point t satisfies the following formula:

[0012]

[0013] where x(t), y(t), and z(t) are the position coordinates in three directions, and v x (t), v y (t), v z (t) are the velocity values in three directions respectively, and t_start and t_end represent the start time and end time of the time interval, respectively, and there are a total of T time points.

[0014] Preferably, the theoretical solution of the <time, position, velocity> information matrix of the slave satellite in step 1) includes:

[0015] Step s1): Set the information emission angles [P, Y] of the primary satellite at [x0, y0, z0], where P represents the pitch angle, and its value range is [0, π / 2], and Y represents the yaw angle, and its value range is [0, π / 2]. The units of P and Y are radians, and calculate the positions where the slave satellite can receive information:

[0016]

[0017] where dirx, diry, and dirz represent the emission directions transformed to the x-axis, y-axis, and z-axis respectively, and D represents the emission distance. When D is a set, each primary satellite position will correspond to multiple slave satellite positions;

[0018] Step s2): Loop step s1) to obtain the theoretical solutions of the <time, position, velocity> information matrices of all slave satellites.

[0019] Preferably, the constraint conditions in step 2) include: environmental constraints, satellite distance constraints, orbital altitude constraints, and slave satellite position constraints;

[0020] The environmental constraints satisfy the following formula:

[0021]

[0022] where X(t), Y(t), and Z(t) represent the position information of the slave satellite at time t, and Penv(t) represents the positions where the two satellites cannot establish communication at time t;

[0023] The satellite distance constraints satisfy the following formula:

[0024]

[0025] where D主从 (t) represents the distance information varying with time between the master and slave satellites, D 从-其他 (t) represents the distance information varying with time between the slave satellite and other existing satellites. Dsetting represents the minimum distance between the master and slave satellites, and Dglobal represents the minimum distance between the slave satellite and the existing satellites;

[0026] The orbital altitude constraint satisfies the following formula:

[0027] Hlower < Height < Hupper

[0028] where Height represents the orbital altitude of the slave satellite, and Hlower and Hupper respectively represent the lowest and highest orbital altitudes acceptable for the mission;

[0029] The slave satellite position constraint satisfies the following formula:

[0030]

[0031] i = 1, 2, 3,....n

[0032] where and represent the i-th theoretical slave satellite position at time t obtained from the theoretical solution of the <time, position, velocity> information matrix of the slave satellite in step 1). n represents the total number of theoretical slave satellite positions at this moment, and x cal (t), y cal (t) and z cal (t) represent the slave satellite position calculated according to the six orbital elements at time t, and D real_cal represents the maximum distance between the acceptable theoretical slave satellite position and the calculated slave satellite position.

[0033] Preferably, the optimization model of the slave satellite orbit in step 2) is:

[0034] max(durationT)

[0035]

[0036] where max(durationT) is the solution objective, that is, to maximize the communication duration. durationT represents the total communication duration that can be established between the master and slave satellites. The specific calculation method is:

[0037] Determine in sequence whether each point of the slave star satisfies the constraint. Then, determine whether the points of the slave star are in the set <time, position> of the slave star positions obtained in step 1). If the determination is yes, set FLAG = 1; otherwise, FLAG = 0. durationT = sum(FLAG(t)), where FLAG(t) is the value of FLAG at each time point after determination.

[0038] Preferably, the solution granularity of step 2) is determined according to the set calculation step. When the calculation step is less than 1, it is a fine granularity; otherwise, it is a coarse granularity.

[0039] The fitness function Value of the dynamic mutation genetic algorithm is:

[0040] Value = -sum(FLAG(t)),

[0041] The mutation operation probability alpha that changes dynamically with the iteration step is:

[0042] alpha = alpha0 + (1 - alpha0)(1 - e -Step )

[0043] where alpha0 represents the initial mutation operation probability, 0 < alpha < 1, Step represents the number of iteration steps, and e is the natural constant.

[0044] Preferably, step 4) includes:

[0045] Update the information matrix of the master star to: <master star, time, position, velocity, FLAG>, and the information matrix of the slave star to <slave star, time, position, velocity, FLAG>;

[0046] Three - dimensional visualization shows the positions of the master star and the slave star changing with time, and connects the positions of the master star and the slave star when FLAG = 1 to show that the current positions can achieve information transfer under the condition of satisfying external constraints.

[0047] On the other hand, the present invention proposes a double - star orbit parameter optimization system, including: an orbit information acquisition module, a multi - granularity double - star orbit optimization module, a communicable duration calculation module, and a visualization output module, where

[0048] The orbit information acquisition module is used to calculate the <time, position, velocity> information matrix of the master star and the theoretical solution set of the <time, position, velocity> information matrix of the slave star according to the six - orbital elements of the master star and the calculated time interval;

[0049] The multi-granularity dual-star orbit optimization module is used to set constraint conditions, establish an optimization model for the slave star orbit, and according to the set solution granularity, adopt a dynamic mutation genetic algorithm. By setting the mutation operation probability that changes dynamically with the iteration step size, optimize the six orbital elements of the slave star, obtain the actual solution of the <time, position, velocity> information matrix of the slave star, and use the number of occurrences of the actual solution in the theoretical solution set as the fitness function of the dynamic mutation genetic algorithm;

[0050] The communicable duration calculation module is used to calculate the fitness function, obtain the continuous duration of communication between the two stars, determine whether the continuous duration remains unchanged. If the determination result is yes, transfer to the visualization output module; otherwise, transfer to the multi-granularity dual-star orbit optimization module;

[0051] The visualization output module is used to output the positions of the master star and the slave star that meet the conditions.

[0052] Compared with the prior art, the advantages of the present invention are as follows:

[0053] Aiming at the problem of determining the orbits of dual stars in space science experiments, a method and system for optimizing the orbital parameters of dual stars for space science experiments are proposed. Under the constraints of the external space environment, the orbits of the dual stars are iteratively optimized. After initially setting the orbital elements of one satellite, solve the orbit of the other satellite and avoid the areas affected by external environmental interference as much as possible to ensure the continuity of communication between the two stars, and realize the simulation of the motion of the dual stars and the visualization display of communication. BRIEF DESCRIPTION OF THE DRAWINGS

[0054] Figure 1 is the flowchart of the method for optimizing the orbital parameters of the dual stars of the present invention;

[0055] Figure 2 is the position information of the master star and the slave star changing with time in the x-y plane;

[0056] Figure 3 is the visualization of the positions where the master star and the slave star can transmit information. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0057] The purpose of the present invention is to establish a method and system for optimizing the orbital parameters of dual stars for space science experiments. Under the constraints of the external space environment, the orbits of the dual stars are iteratively optimized. After initially setting the orbital elements of one satellite, solve the orbit of the other satellite and avoid the areas affected by external environmental interference as much as possible to ensure the continuity of communication between the two stars.

[0058] In space science missions, a formation of two satellites is used to conduct specific space science experiments. The two satellites establish satellite communication with each other under the influence of the space environment, and it is agreed that the two satellites are the primary satellite and the secondary satellite respectively. In order to obtain the orbital parameters of the two satellites, a method and system for optimizing the orbital parameters of the two satellites are constructed, and the motion orbits of the two satellites constrained by the external environment are optimized, specifically including an orbital information acquisition module, a multi-granularity two-satellite orbit optimization module, a communicable duration calculation module, and a visualization module.

[0059] The orbital information acquisition module includes the following steps:

[0060] Step 1) Input the matrix of six orbital elements, expressed as

[0061]

[0062] The six components of X in the above formula are, respectively, the semi-major axis a of the orbit, the orbital eccentricity e, the orbital inclination i, the argument of periapsis ω, the longitude of the ascending node Ω, and the true anomaly

[0063] Step 2) Input the start time, end time, and calculation step size of the calculation.

[0064] Step 3) According to the six orbital elements, obtain the T×1 matrix of <time, position, velocity> of the satellite within the range of the start time and end time, where T represents the T time points obtained by the calculation, and it is specifically expressed as follows:

[0065]

[0066] t_start and t_end represent the start time and end time of the time interval respectively, and a total of T time points are included.

[0067] Step 4) Save the obtained matrix of <time, position, velocity> of the satellite.

[0068] The multi-granularity two-satellite orbit optimization module includes a simulation granularity setting module and a secondary satellite orbit optimization module.

[0069] The simulation granularity setting module is: select an appropriate calculation granularity. Different calculation granularities result in different precisions and different calculation complexities. The difference in the calculation granularity is mainly reflected in the calculation step size t. Generally, the relationship between the calculation granularity and the step size is as follows:

[0070]

[0071] The secondary satellite orbit optimization module is used to optimize the position information of the secondary satellite according to the primary satellite orbit, and obtain the six orbital elements of the secondary satellite orbit based on the position of the secondary satellite at different times. This module includes the following steps:

[0072] Step 1) Set the constraint information of the secondary satellite orbit;

[0073] Step 1-1): Set the minimum distance Dsetting between the slave satellite and the master satellite;

[0074] Step 1-2): Obtain the position set Penv where communication cannot be established according to the space environment data; The set Penv is a time-varying data set, and the set is different according to different times.

[0075] Step 2): Input the master satellite <time, position, velocity> matrix;

[0076] Step 3): Obtain the theoretical solution of the slave satellite <time, position> matrix;

[0077] Step 3-1): Set the information emission angles [P, Y] of the master satellite [x0, y0, z0], where P represents the pitch angle and Y represents the yaw angle, and calculate the positions where the slave satellite can receive information.

[0078]

[0079] Among them, dirx, diry, and dirz represent the emission directions transformed to the x-axis, y-axis, and z-axis, P and Y are in radians, and D represents the emission distance. Among them, D can be a set. In this case, each master satellite position will correspond to multiple slave satellite positions.

[0080] Step 3-2): Loop Step 3-1) to obtain the set <time, position> of all slave satellite positions. It should be noted that a certain time point may correspond to multiple slave satellite positions, which is determined by whether D is a set.

[0081] Step 4): Optimize the slave satellite orbit to obtain the six orbital elements of the slave satellite.

[0082] Step 4-1): Randomly specify the six orbital elements of the slave satellite, and obtain the slave satellite position according to the orbit information acquisition module.

[0083] Step 4-2): The slave satellite orbit optimization modeling includes constraint condition modeling and optimization

[0084] Environmental constraint modeling, that is, the position of the slave satellite is not in the set Penv.

[0085]

[0086] Among them, X(t), Y(t), and Z(t) represent the position information of the slave satellite at time t, and Penv(t) represents the position where communication cannot be established between the two satellites at time t.

[0087] Satellite distance constraint modeling, that is, the constraints between the distance between the slave satellite and the current master satellite and the distance between the slave satellite and other existing satellites. The formula is as follows:

[0088]

[0089] Among them, D 主从 (t) represents the distance information that varies with time between the master and the slave, and D 从-其他 (t) represents the distance information that varies with time between the slave satellite and the existing satellites. Dsetting represents the minimum distance between the master and slave satellites, and Dglobal represents the minimum distance between the slave satellite and the existing satellites. Dsetting is set according to the needs of the actual mission, and Dglobal is set according to international conventions.

[0090] Orbit altitude constraint

[0091] Hlower < Height < Hupper (7)

[0092] Among them, Heigth represents the orbit altitude of the slave satellite, and Hlower and Hupper respectively represent the lowest and highest orbit altitudes acceptable for the mission.

[0093] The position constraint of the slave satellite, that is, the distance between the position of the slave satellite at time t and the position of the theoretical slave satellite derived from the master satellite at time t should be within an acceptable range, that is

[0094]

[0095] Among them, and represent the position of the slave satellite derived from the position of the master satellite at time t obtained in step 3, where i represents the i-th theoretical slave satellite position solved at this moment, n represents the total number of theoretical slave satellite positions at this moment, x cal (t), y cal (t) and z cal (t) represent the position of the slave satellite calculated according to the six orbital elements, and D real_cal represents the maximum distance between the acceptable theoretical slave satellite position and the calculated slave satellite position.

[0096] Optimization equation modeling, construct the following optimization model according to the above constraints.

[0097]

[0098] Among them, durationT represents the total communication duration that can be established between the master and slave satellites, and max(durationT) is the solution target, that is, to maximize the communication duration.

[0099] The calculation process of durationT is as follows:

[0100] Determine in sequence whether each point of the slave satellite satisfies the constraints. Then, determine whether the points of the slave satellite are in the set <time, position> of the slave satellite positions obtained in step 3-2). If the determination result is yes, set FLAG = 1; otherwise, set FLAG = 0. The calculation formula for durationT is

[0101] sum(FLAG(t))(10)

[0102] where FLAG(t) is the value of FLAG at each time point after determination.

[0103] Step 4-3) Optimize the above time-varying constraint conditions and objective function as the input of the dynamic mutation genetic algorithm. The fitness function of the dynamic mutation genetic algorithm is set as

[0104] Value=-sum(FLAG(t)) (11)

[0105] Optimize the six orbital elements of the slave satellite through the genetic algorithm to obtain the solution with the minimum fitness Value.

[0106] Step 4-4) Output the six orbital elements of the slave satellite corresponding to the maximum durationT, that is, the minimum Value of the dynamic mutation genetic algorithm, and output the sustainable duration durationT at the same time.

[0107] The dynamic mutation genetic algorithm is an algorithm developed on the basis of the traditional genetic algorithm to avoid the solution of the six orbital elements of the slave satellite falling into a local optimum. The difference between it and the traditional genetic algorithm is that the probability of the mutation operation in the genetic algorithm changes dynamically according to the number of iterations. The formula is expressed as

[0108] alpha=alpha0+(1-alpha0)(1-e -Step ) (12)

[0109] where alpha represents the probability of the mutation operation in the genetic algorithm, alpha0 represents the initial probability of the mutation operation, and 0 < alpha < 1. Step represents the number of iteration steps. It can be seen from the formula that as the iteration step increases, the mutation probability alpha gradually approaches 1, which is beneficial to avoiding the solution falling into a local optimum as the iteration step increases.

[0110] The communicable duration calculation module calculates whether the slave satellite can receive the information transmitted by the master satellite under the influence of the space environment within a certain period of time according to the positions of the master and slave satellites changing with time, and calculates the cumulative communicable duration. It includes the following steps:

[0111] Step 1: Input the six orbital elements of the master and slave satellites;

[0112] Step 2: Set the simulation duration, simulation step size, charged particle movement duration, and charged particle movement simulation step size;

[0113] Step 3: According to the orbit information acquisition module, calculate the position information of the master and slave satellites changing with time within the simulation duration, that is, the <master satellite, time, position> information matrix and the <slave satellite, time, position> information matrix;

[0114] Step 4: Input the set of positions Penv where communication cannot be established;

[0115] Step 5: Calculate in sequence whether communication can be established between the master satellite and the slave satellite at each time point. If so, set FLAG = 1, and update the information matrix to <master satellite, time, position, FLAG> and <slave satellite, time, position, FLAG>.

[0116] The visualization module includes the following steps:

[0117] Step 1: Input the six orbital elements of the master and slave satellites;

[0118] Step 2: Set the simulation duration parameter;

[0119] Step 3: Set the information transfer constraint;

[0120] Step 4: Obtain the <master satellite, time, position> and <slave satellite, time, position> information matrices changing with time according to the orbit information acquisition module;

[0121] Step 5: Calculate the time points at which information can be transferred according to the constraint, and update the information matrix to <master satellite, time, position, velocity, FLAG> and <slave satellite, time, position, velocity, FLAG>, where the value of FLAG is 0 or 1, indicating the time points, position, and velocity information at which the master satellite can send information and the slave satellite can receive it;

[0122] Step 6: Use three-dimensional visualization to display the positions of the master and slave satellites changing with time, and connect the positions of the master and slave satellites when FLAG = 1 to show that information transfer can be achieved at the current position under the condition of meeting external constraints.

[0123] The technical solution of the present invention will be described in detail below with reference to the accompanying drawings and embodiments.

[0124] Embodiment 1

[0125] As Figure 1 shown, Embodiment 1 of the present invention proposes a method for optimizing the orbital parameters of a double star, including the following steps:

[0126] Step S1) Calculate the time interval based on the six orbital elements of the primary star to obtain the <time, position, velocity> information matrix of the primary star and the theoretical solution set of the <time, position, velocity> information matrix of the secondary star;

[0127] In one embodiment, the six orbital elements of the primary star are set as [6971, 0.0093, 53.1, 288.86, 0.6767, 70.14] T , the elevation angle range of the transmitted information is [0, π / 2], the yaw angle range is [0, π / 2], and the transmission information distance is 100 km.

[0128] Specifically, it includes:

[0129] Step 1) Input the six-orbital-element matrix of the primary star, expressed as

[0130]

[0131] In the above formula, the six components of X are the semi-major axis a of the orbit, the orbital eccentricity e, the orbital inclination i, the argument of periapsis ω, the longitude of the ascending node Ω, and the true anomaly

[0132] Step 2) Input the start time of the calculation as 0, the end time as 1000, and the calculation step size as 1 s.

[0133] Step 3) Obtain a 100×1 matrix of the satellite's <time, position, velocity> within the start time and end time range according to the six orbital elements, specifically expressed as follows:

[0134]

[0135] Step 4) Save the obtained satellite <time, position, velocity> matrix.

[0136] Step S2) Set the constraint conditions, establish an optimization model for the secondary star's orbit, and adopt the dynamic mutation genetic algorithm according to the set solution granularity. By setting the mutation operation probability that changes dynamically with the iteration step size, optimize the six orbital elements of the secondary star to obtain the actual solution of the <time, position, velocity> information matrix of the secondary star, and use the number of occurrences of the actual solution in the theoretical solution set as the fitness function of the dynamic mutation genetic algorithm;

[0137] This includes the setting of the simulation granularity and the optimization of the secondary star's orbit.

[0138] In this embodiment, a coarse granularity is adopted, that is, the solution step size is 1 s.

[0139] This step obtains the position information of the secondary star according to the optimization of the primary star's orbit, and obtains the six orbital elements of the secondary star according to the position of the secondary star at a certain time. Specifically, it includes:

[0140] Step 1) Set the constraint information of the slave satellite orbit;

[0141] Step 1-1) Set the minimum distance Dsetting between the slave satellite and the master satellite to 100 km;

[0142] Step 1-2) Obtain the position set Penv where communication cannot be established according to the space environment data; the set Penv is a time-varying data set, and the set is different according to different times.

[0143] Step 2) Input the <time, position, velocity> matrix of the master satellite;

[0144] Step 3) Obtain the theoretical solution of the <time, position> matrix of the slave satellite;

[0145] Step 3-1) Set the emission information angles [P, Y] of the master satellite at [x0, y0, z0], where P represents the pitch angle, and the value range is [0, π / 2], and Y represents the yaw angle, and the value range is [0, π / 2], and calculate the positions where the slave satellite can receive information.

[0146]

[0147] Among them, dirx, diry, and dirz represent the emission directions transformed to the x-axis, y-axis, and z-axis, P and Y are in radians, and D represents the emission distance. Among them, D can be a set. In this case, each master satellite position will correspond to multiple slave satellite positions.

[0148] Step 3-2) Loop through Step 3-1) to obtain the set <time, position> of all slave satellite positions. Note that a certain time point may correspond to multiple slave satellite positions, which is determined by whether D is a set.

[0149] Step 4) Optimize the slave satellite orbit to obtain the six orbital elements of the slave satellite.

[0150] Step 4-1) Randomly specify the six orbital elements of the slave satellite orbit, and obtain the slave satellite position according to the orbit information acquisition module.

[0151] Step 4-2) The slave satellite orbit optimization modeling includes constraint condition modeling and optimization

[0152] Environmental constraint modeling, that is, the position of the slave satellite is not in the set Penv.

[0153]

[0154] Among them, X(t), Y(t), and Z(t) represent the position information of the slave satellite at time t, and Penv(t) represents the position where communication cannot be established between the two satellites at time t.

[0155] Satellite distance constraint modeling, that is, the constraints between the distance of the slave satellite from the current master satellite and the distances of the slave satellite from other existing satellites, are expressed by the following formulas:

[0156]

[0157] Among them, D 主从 (t) represents the distance information between the master and the slave that changes over time, D 从-其他 (t) represents the distance information between the slave satellite and the existing satellites that changes over time. Dsetting represents the minimum distance between the master and the slave satellites, which is set to 100 km here, and Dglobal represents the minimum distance between the slave satellite and the existing satellites, which is set to 60 km here.

[0158] Orbital altitude constraint

[0159] Hlower < Height < Hupper (18)

[0160] Among them, Heigth represents the orbital altitude of the slave satellite, and Hlower and Hupper respectively represent the lowest and highest orbital altitudes acceptable for the mission. Here, Hlower = 6900 km and Hupper = 7500 km are set.

[0161] The position constraint of the slave satellite means that the distance between the position of the slave satellite at time t and the position of the theoretical slave satellite at time t derived from the master satellite should be within an acceptable range, that is

[0162]

[0163] Among them, and represent the position of the slave satellite derived from the position of the master satellite at time t obtained in step 3. Here, i represents the i-th theoretical slave satellite position solved at this moment, n represents the total number of theoretical slave satellite positions at this moment, x cal (t), y cal (t) and z cal (t) represent the position of the slave satellite calculated according to the six orbital elements. D real_cal represents the maximum distance between the acceptable theoretical slave satellite position and the calculated slave satellite position.

[0164] Optimization equation modeling, an optimization model is constructed according to the above constraints as follows.

[0165]

[0166] Among them, durationT represents the total communication duration that can be established between the master and the slave satellites, and max(durationT) is the solution objective, that is, to maximize the communication duration.

[0167] The calculation process of durationT is as follows:

[0168] Determine whether each point of the slave star satisfies the constraint in sequence. Then, determine whether the points of the slave star are in the set <time, position> of the slave star positions obtained in step 3-2). If the determination is yes, set FLAG = 1; otherwise, FLAG = 0. The calculation formula of durationT is

[0169] sum(FLAG(t))(21)

[0170] where FLAG(t) is the value of FLAG at each time point after determination.

[0171] Step 4-3) Optimize the above time-varying constraint conditions and objective function as the input of the dynamic mutation genetic algorithm. The fitness function of the dynamic mutation genetic algorithm is set as

[0172] Value = -sum(FLAG(t)) (22)

[0173] Optimize the six orbital elements of the slave star through the genetic algorithm to obtain the solution with the minimum fitness Value.

[0174] Step 4-4) Output the six orbital elements of the slave star corresponding to the maximum durationT, that is, the minimum Value of the dynamic mutation genetic algorithm, and output the sustainable duration durationT at the same time.

[0175] The dynamic mutation genetic algorithm is an algorithm developed on the basis of the traditional genetic algorithm to avoid the solution of the six orbital elements of the slave star falling into a local optimum. The difference between it and the traditional genetic algorithm is that the probability of the mutation operation in the genetic algorithm changes dynamically according to the number of iterations. The formula is expressed as

[0176] alpha = alpha0+(1-alpha0)(1-e -Step ) (23)

[0177] where alpha represents the probability of the mutation operation in the genetic algorithm, alpha0 represents the initial probability of the mutation operation, and 0 < alpha < 1. Step represents the number of iteration steps. It can be seen from the formula that as the iteration step increases, the mutation probability alpha gradually approaches 1, which is beneficial to avoiding the solution falling into a local optimum as the iteration step increases.

[0178] Step S3) Calculate the fitness function to obtain the sustainable duration of communication between the two stars. Judge whether the sustainable duration remains unchanged. If the judgment is yes, go to step S4); otherwise, go to step S2).

[0179] Step S4) Output the positions of the primary star and the secondary star that meet the conditions.

[0180] After solving, the optimal six orbital elements of the secondary star are obtained as [6928, 0.001, 53.002, 0.0035, 0.004, 0.002].

[0181] As Figure 2 shown, it shows the position information of the primary star and the secondary star changing with time in the x-y plane; as Figure 3 shown, it shows the positions where the primary star and the secondary star can transmit information. The red line represents the primary star, the blue line represents the secondary star, and the colored line in the middle represents the area where information can be transmitted.

[0182] Embodiment 2

[0183] Embodiment 2 of the present invention proposes a dual-star orbital parameter optimization system, which is implemented based on the method of Embodiment 1 and includes: an orbital information acquisition module, a multi-granularity dual-star orbital optimization module, a communicable duration calculation module, and a visualization output module. Among them,

[0184] The orbital information acquisition module is used to calculate the <time, position, velocity> information matrix of the primary star and the theoretical solution set of the <time, position, velocity> information matrix of the secondary star according to the six orbital elements of the primary star and the calculated time interval.

[0185] The multi-granularity dual-star orbital optimization module is used to set constraint conditions, establish an optimization model for the secondary star's orbit, and adopt a dynamic mutation genetic algorithm according to the set solution granularity. By setting the mutation operation probability that changes dynamically with the iteration step, optimize the six orbital elements of the secondary star to obtain the actual solution of the <time, position, velocity> information matrix of the secondary star, and use the number of occurrences of the actual solution in the theoretical solution set as the fitness function of the dynamic mutation genetic algorithm.

[0186] The communicable duration calculation module is used to calculate the fitness function, obtain the continuous duration for which the two stars maintain communication, determine whether the continuous duration remains unchanged. If it is judged to be yes, go to the visualization output module; otherwise, go to the multi-granularity dual-star orbital optimization module.

[0187] The visualization output module is used to output the positions of the primary star and the secondary star that meet the conditions.

[0188] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit them. Although the present invention has been described in detail with reference to the embodiments, those of ordinary skill in the art should understand that any modification or equivalent replacement of the technical solutions of the present invention does not depart from the spirit and scope of the technical solutions of the present invention, and they should all be covered within the scope of the claims of the present invention.

Claims

1. A method for optimizing the orbital parameters of a double star, comprising: Step 1) According to the six orbital elements of the primary star, calculate the time interval, obtain the <time, position, velocity> information matrix of the primary star, and the theoretical solution set of the <time, position, velocity> information matrix of the secondary star; Step 2) Set the constraint conditions, establish an optimization model for the orbit of the secondary star. According to the set solution granularity, adopt the dynamic mutation genetic algorithm, and by setting the mutation operation probability that changes dynamically with the iteration step size, optimize the six orbital elements of the secondary star to obtain the actual solution of the <time, position, velocity> information matrix of the secondary star, and use the number of occurrences of the actual solution in the theoretical solution set as the fitness function of the dynamic mutation genetic algorithm; Step 3) Calculate the fitness function, obtain the continuous duration of the communication between the two stars, determine whether the continuous duration remains unchanged. If it is determined to be yes, go to Step 4); otherwise, go to Step 2); Step 4) Output the positions of the primary star and the secondary star that meet the conditions; The constraint conditions in Step 2) include: environmental constraint, satellite distance constraint, orbital altitude constraint, and secondary star position constraint; The environmental constraint satisfies the following formula: where X(t), Y(t), Z(t) represent the position information of the secondary star at time t, and Penv(t) represents the position where the two stars cannot establish communication at time t; The satellite distance constraint satisfies the following formula: Among them, D 主从 (t) represents the distance information changing with time between the master and slave satellites, D 从-其他 (t) represents the distance information changing with time between the slave satellite and other existing satellites, Dsetting represents the minimum distance between the master and slave satellites, and Dglobal represents the minimum distance between the slave satellite and the existing satellites; The orbital altitude constraint satisfies the following formula: Hlower < Height < Hupper where Height represents the orbital altitude of the secondary star, and Hlower and Hupper respectively represent the lowest and highest orbital altitudes that the mission can accept; The secondary star position constraint satisfies the following formula: Among them, and represent the position of the i-th theoretical slave satellite at time t obtained from the theoretical solution of the <time, position, velocity> information matrix of the slave satellites in step 1), n represents the total number of theoretical slave satellite positions at this time, x cal (t), y cal (t) and z cal (t) represent the position of the slave satellite calculated according to the six orbital elements at time t, D real_cal represents the maximum distance between the acceptable theoretical slave satellite position and the calculated slave satellite position; The optimization model of the orbit of the secondary star in Step 2) is: where max(durationT) is the solution target, that is, to maximize the communication duration. durationT represents the total communication duration that the primary and secondary satellites can establish, and the specific calculation method is: Determine whether each point of the secondary star meets the constraints in turn. Then, determine whether the point of the secondary star is in the set <time, position> of the positions of the secondary star obtained in Step 1). If it is determined to be yes, set FLAG = 1; otherwise, FLAG = 0. durationT = sum(FLAG(t)), where FLAG(t) is the value of FLAG at each time point after determination.

2. The double-star orbit parameter optimization method according to claim 1, characterized in that The six orbital elements in step 1) include: semi-major axis a of the orbit, orbital eccentricity e, orbital inclination i, argument of perigee ω, longitude of the ascending node Ω, and true anomaly 3. The method for optimizing the binary star orbital parameters according to claim 1, wherein The <time, position, velocity> information matrix of the primary star in Step 1) is a T×1 matrix, where T represents the T time points calculated. The information matrix Y(t) at a certain time point t satisfies the following formula: where x(t), y(t), z(t) are the position coordinates in three directions, and v x (t), v y (t), v z (t) are the velocity values in three directions, t_start and t_end represent the start time and end time of the time interval respectively, and there are a total of T time points.

4. The method for optimizing the double-star orbital parameters according to claim 1, wherein The theoretical solution of the <time, position, velocity> information matrix of the secondary star in Step 1) includes: Step s1) Set the information emission angles [P, Y] of the primary star [x0, y0, z0], where P represents the pitch angle, and the value range is [0, π / 2], Y represents the yaw angle, and the value range is [0, π / 2]. The units of P and Y are radians, and calculate the positions where the secondary star can receive information: where dirx, diry, and dirz respectively represent the emission directions transformed to the x-axis, y-axis, and z-axis, and D represents the emission distance. When D is a set, each primary star position will correspond to multiple secondary star positions; Step s2) Repeat step s1) to obtain the theoretical solutions of all <time, position, velocity> information matrices of the slave stars.

5. The method for optimizing double-star orbital parameters according to claim 1, wherein The solution granularity of step 2) is determined according to the set calculation step size. When the calculation step size is less than 1, it is fine-grained; otherwise, it is coarse-grained. The fitness function Value of the dynamic mutation genetic algorithm is as follows: Value = -sum(FLAG(t)), The mutation operation probability alpha that changes dynamically with the iteration step size is as follows: alpha = alpha0+(1 - alpha0)(1 - e -Step ) where alpha0 represents the probability of the initial mutation operation, 0 < alpha < 1, Step represents the number of iteration steps, and e is the natural constant.

6. The method for optimizing the binary star orbital parameters according to claim 5, wherein Step 4) includes: Update the information matrix of the master star to <master star, time, position, velocity, FLAG>, and the information matrix of the slave star to <slave star, time, position, velocity, FLAG>. Perform 3D visualization to display the positions of the master star and the slave star changing with time, and connect the positions of the master star and the slave star when FLAG = 1 to show that the current positions can achieve information transfer under the condition of meeting external constraints.

7. A system based on the double-star orbital parameter optimization method according to claim 1, characterized in that It includes: An orbital information acquisition module, a multi-granularity binary star orbital optimization module, a communicable duration calculation module, and a visualization output module. Among them, The orbital information acquisition module is used to calculate the <time, position, velocity> information matrix of the master star and the theoretical solution set of the <time, position, velocity> information matrix of the slave star according to the six orbital elements of the master star and the calculated time interval. The multi-granularity binary star orbital optimization module is used to set constraint conditions, establish an optimization model for the slave star's orbit, and use the dynamic mutation genetic algorithm according to the set solution granularity. By setting the mutation operation probability that changes dynamically with the iteration step size, optimize the six orbital elements of the slave star to obtain the actual solution of the <time, position, velocity> information matrix of the slave star, and use the number of occurrences of the actual solution in the theoretical solution set as the fitness function of the dynamic mutation genetic algorithm. The communicable duration calculation module is used to calculate the fitness function to obtain the continuous duration of communication between the two stars, and judge whether the continuous duration remains unchanged. If the judgment is yes, go to the visualization output module; otherwise, go to the multi-granularity binary star orbital optimization module. The visualization output module is used to output the positions of the master star and the slave star that meet the conditions.

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