Method and system for optimizing orbit parameters of double satellites

Abstract

The invention discloses a double-satellite orbit parameter optimization method and system, and the method comprises the steps: 1), obtaining the lt of a main satellite according to the six orbital elements of the main satellite and a calculated time interval; gt, time, position and speed; an information matrix, and the lt of the slave satellites; gt, time, position and speed; a theoretical solution set of an information matrix; step 2) setting constraint conditions, establishing an optimization model of a slave satellite orbit, and according to the set solving granularity, adopting a dynamic variation genetic algorithm, and by setting a variation operation probability dynamically changing along with an iteration step length and optimizing six orbit elements of the slave satellite, obtaining the lt of the slave satellite; gt, time, position and speed; an actual solution of the information matrix is obtained, and the occurrence frequency of the actual solution in the theoretical solution set serves as a fitness function; (3) calculating a fitness function, obtaining the duration of keeping communication between the two stars, judging whether the duration is constant or not, if so, turning to the step (4), otherwise, turning to the step (2); and 4) outputting the positions of the master satellite and the slave satellite meeting the conditions.

Description

Technical Field

[0001] The present invention belongs to the field of aerospace measurement and control technology, and specifically relates to a method and system for optimizing binary satellite orbital parameters. Background Art

[0002] Space science satellites are located in different positions and are affected differently by the space environment, geomagnetic field, etc. In the actual operation of space science missions, the information transmission between the two satellites will be affected by the external environment, resulting in the inability to transmit information between the two satellites during certain time periods. It is necessary to optimize the orbits of the two satellites in a targeted manner to ensure the transmission of information between the two satellites while meeting the external constraints of the satellite orbits, so as to ensure the smooth implementation of space science missions.

[0003] The existing algorithms usually optimize a single satellite orbit and do not involve iterative optimization of dual satellite orbits. Therefore, there is an urgent need for a dual satellite orbit parameter optimization method to achieve iterative optimization of dual satellite 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 the orbital parameters of a binary star.

[0005] In view of this, the present invention proposes a method for optimizing binary satellite orbit parameters, comprising:

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

[0007] Step 2) Set constraints, establish an optimization model for the satellite orbit, and use a dynamic mutation genetic algorithm according to the set solution granularity. By setting the probability of mutation operation that changes dynamically with the iteration step, optimize the six orbit numbers of the satellite, obtain the actual solution of the <time, position, speed> information matrix of the satellite, 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 duration of communication between the two stars, and determine whether the duration remains unchanged. If yes, go to step 4); otherwise, go to step 2);

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

[0010] Preferably, the six orbital parameters in step 1) include: orbital semi-major axis a, orbital eccentricity e, orbital inclination i, pericentric argument ω, ascending node longitude Ω and true anomaly angle

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

[0012]

[0013] Among them, x(t), y(t), z(t) are the position coordinates in three directions respectively, v x (t),v y (t),v z (t) are the speed values ​​in three directions respectively, t_start and t_end represent the start time and end time of the time interval respectively, which includes T time points in total.

[0014] Preferably, the step 1) is based on the theoretical solution of the <time, position, velocity> information matrix of the star, including:

[0015] Step s1) Set the information transmission angle [P, Y] of the master satellite [x0, y0, z0], where P represents the pitch angle, the value range is [0, π / 2], Y represents the yaw angle, the value range is [0, π / 2], the units of P and Y are radians, and calculate the position where the slave satellite can receive information:

[0016]

[0017] Among them, dirx, diry and dirz represent the launch directions converted to the x-axis, y-axis and z-axis respectively, and D represents the launch distance. When D is a set, each master satellite position will correspond to multiple slave satellite positions;

[0018] Step s2) loops through step s1) to obtain the theoretical solution of the <time, position, velocity> information matrix of all slave stars.

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

[0020] The environmental constraints satisfy the following formula:

[0021]

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

[0023] The satellite distance constraint satisfies the following formula:

[0024]

[0025] Among them, D主从 (t) represents the distance information between the master and slave satellites that changes over time, D 从-其他 (t) represents the distance information between the slave satellite and other existing satellites that changes over time, Dsetting represents the minimum distance between the master and slave satellites, and Dglobal represents the minimum distance between the slave satellite and existing satellites;

[0026] The track height constraint satisfies the following formula:

[0027] Hlower<Height<Hupper

[0028] Among them, Height represents the orbital height from the satellite, Hlower and Hupper represent the lowest and highest orbital heights acceptable to the mission respectively;

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

[0030]

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

[0032] in, and represents the theoretical position of the satellite at time t obtained from the theoretical solution of the satellite's <time, position, velocity> information matrix in step 1), n ​​represents the total number of n theoretical satellite positions at that time, x cal (t), y cal (t) and z cal (t) represents the satellite position calculated based on the six orbital elements at time t, D real_cal Indicates the maximum acceptable distance between the theoretical slave star position and the calculated slave star position.

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

[0034] max(durationT)

[0035]

[0036] Among them, max(durationT) is the solution target, that is, to maximize the communication duration, and durationT represents the total duration that the master and slave satellites can establish communication. The specific calculation method is:

[0037] Determine in sequence whether each point of the slave star satisfies the constraints. 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 demonstrate 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 binary star orbit parameter optimization system, including: an orbit information acquisition module, a multi - granularity binary 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 binary satellite orbit optimization module is used to set constraint conditions, establish an optimization model for the satellite orbit, and use a dynamic mutation genetic algorithm according to the set solution granularity to optimize the six orbit numbers of the satellite by setting a mutation operation probability that changes dynamically with the iteration step size, and obtain the actual solution of the <time, position, speed> information matrix of the satellite, 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 communication duration calculation module is used to calculate the fitness function, obtain the duration of communication between the two stars, and determine whether the duration is constant. If it is, it will be transferred to the visualization output module, otherwise, it will be transferred to the multi-granularity binary orbit optimization module;

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

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

[0053] Aiming at the problem of determining the binary satellite orbits for space science experiments, a binary satellite orbit parameter optimization method and system for space science experiments is proposed. Under the constraints of the external space environment, the binary satellite motion orbit is iteratively optimized. After the orbital elements of one satellite are initially set, the orbit of the other satellite is solved, and the area affected by the external environment is avoided as much as possible to ensure the continuity of the communication between the two satellites, so as to realize the binary satellite motion simulation and communication visualization display. BRIEF DESCRIPTION OF THE DRAWINGS

[0054] Figure 1 is a flow chart of the binary satellite orbit parameter optimization method of the present invention;

[0055] Figure 2 It is the position information of the master star and the slave star changing with time on the xy plane;

[0056] Figure 3 The main star and the slave star can transmit information and visualize their positions. DETAILED DESCRIPTION

[0057] The purpose of the present invention is to establish a method and system for optimizing the orbital parameters of a binary satellite for space science experiments. Under the constraints of the external space environment, the binary satellite motion orbit is iteratively optimized. After the orbital elements of one satellite are initially set, the orbit of the other satellite is solved, and the area affected by the external environment is avoided as much as possible to ensure the continuity of communication between the binary satellites.

[0058] In space science missions, a binary star formation is used to conduct specific space science experiments. The binary stars establish satellite communications with each other under the influence of the space environment, and the binary stars are agreed to be the master star and the slave star. In order to obtain the orbital parameters of the binary stars, a binary star orbit parameter optimization method and system are constructed to optimize the binary star motion orbit constrained by the external environment, which specifically includes an orbit information acquisition module, a multi-granular binary star orbit optimization module, a communication duration calculation module, and a visualization module.

[0059] The track information acquisition module comprises the following steps:

[0060] Step 1) Input the orbital six-element matrix, expressed as

[0061]

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

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

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

[0065]

[0066] t_start and t_end represent the start time and end time of the time interval respectively, which includes T time points in total.

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

[0068] The multi-granularity dual-star orbit optimization module includes a simulation granularity setting module and a slave star orbit optimization module.

[0069] The simulation granularity setting module is to select a suitable calculation granularity. Different calculation granularities result in different precisions and calculation complexities. The difference in calculation granularity is mainly reflected in the calculation step length t. Usually, the relationship between calculation granularity and step length is as follows:

[0070]

[0071] The slave star orbit optimization module is used to obtain the slave star position information according to the master star orbit optimization, and obtain the six numbers of the slave star orbit according to the slave star time position. The module includes the following steps:

[0072] Step 1) Setting the constraint information of the slave star orbit;

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

[0074] Step 1-2) A set of locations Penv where communication cannot be established is obtained based on the spatial environment data; the set Penv is a time-varying data set, and the set is different depending on the time.

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

[0076] Step 3) obtaining the theoretical solution of the star <time, position> matrix;

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

[0078]

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

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

[0081] Step 4) Optimize the slave star orbit and obtain six numbers of the slave star orbit.

[0082] Step 4-1) Randomly specify six numbers of slave star orbits, and obtain the slave star position according to the orbit information acquisition module.

[0083] Step 4-2) Star orbit optimization modeling includes constraint modeling and optimization

[0084] Modeling of environmental constraints, i.e. from the positions of stars not in the Penv set.

[0085]

[0086] Where 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 the two satellites cannot establish communication at time t.

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

[0088]

[0089] 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) indicates the distance information between the slave satellite and the existing satellite over time, Dsetting indicates the minimum distance between the master and slave satellites, and Dglobal indicates the minimum distance between the slave satellite and the existing satellite. Dsetting is set according to the needs of the actual mission, and Dglobal is set according to international conventions.

[0090] Track height constraint

[0091] Hlower<Height<Hupper (7)

[0092] Among them, Heigth represents the orbit height from the satellite, Hlower and Hupper represent the lowest and highest orbital heights acceptable to the mission respectively.

[0093] The position constraint of the slave star is that the position of the slave star at time t must be within an acceptable range from the theoretical position of the slave star at time t derived from the master star, that is,

[0094]

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

[0096] Optimization equation modeling, based on the above constraints, builds the following optimization model.

[0097]

[0098] Among them, durationT represents the total duration that the master and slave satellites can establish communication, and max(durationT) is the solution target, that is, maximizing the communication duration.

[0099] The calculation process of durationT is:

[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 is yes, set FLAG = 1; otherwise, 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 length increases, the mutation probability alpha gradually approaches 1, which is beneficial to avoiding the solution falling into a local optimum as the iteration step length 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, charged particle motion duration, and charged particle motion simulation step;

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

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

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

[0116] The visualization module comprises the following steps:

[0117] Step 1: Input the six orbital numbers of the master and slave stars;

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

[0119] Step 3: Set information transfer constraints;

[0120] Step 4: Obtain the information matrix of <master star, time, position> and <slave star, time, position> that changes with time according to the orbit information acquisition module;

[0121] Step 5: Calculate the time point at which information can be transmitted according to the constraints, and update the information matrix to <master satellite, time, position, speed, FLAG>, <slave satellite, time, position, speed, FLAG>, where FLAG takes the value of 0 or 1, indicating the time point and position speed information that the slave satellite can receive when the master satellite sends the information;

[0122] Step 6: Use 3D visualization to display the positions of the master and slave satellites that change over time, and connect the positions of the master and slave satellites when FLAG=1 to show that the current position can achieve information transmission under the condition of satisfying external constraints.

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

[0124] Example 1

[0125] like Figure 1 As shown, embodiment 1 of the present invention proposes a method for optimizing binary satellite orbit parameters, comprising the following steps:

[0126] Step S1) According to the six orbital elements of the master star, the time interval is calculated to obtain the theoretical solution set of the <time, position, speed> information matrix of the master star and the <time, position, speed> information matrix of the slave star;

[0127] In one embodiment, the six numbers of the main star orbit are set to [6971, 0.0093, 53.1, 288.86, 0.6767, 70.14] T The pitch angle range of transmitted information is [0, π / 2], the yaw angle range is [0, π / 2], and the information sending distance is 100 kilometers.

[0128] Specifically include:

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

[0130]

[0131] The six components of X in the above formula are orbital semi-major axis a, orbital eccentricity e, orbital inclination i, pericentric angle ω, ascending node longitude Ω and true anomaly angle

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

[0133] Step 3) According to the six numbers, a 100×1 matrix of satellite <time, position, speed> within the start time and end time range is obtained, which is specifically expressed as follows:

[0134]

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

[0136] Step S2) setting constraint conditions, establishing an optimization model for the satellite orbit, using a dynamic mutation genetic algorithm according to the set solution granularity, optimizing the six orbit numbers of the satellite by setting a mutation operation probability that changes dynamically with the iteration step, and obtaining the actual solution of the <time, position, speed> information matrix of the satellite, and using 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 simulation granularity settings and star orbit optimization.

[0138] This embodiment adopts coarse granularity, that is, the solution step length is 1 s.

[0139] This step obtains the position information of the slave star based on the master star orbit optimization, and obtains the six numbers of the slave star orbit based on the slave star time position. Specifically includes:

[0140] Step 1) Setting the constraint information of the slave star orbit;

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

[0142] Step 1-2) A set of locations Penv where communication cannot be established is obtained based on the spatial environment data; the set Penv is a time-varying data set, and the set is different depending on the time.

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

[0144] Step 3) obtaining the theoretical solution of the star <time, position> matrix;

[0145] Step 3-1) Set the information transmission angle [P, Y] of the master satellite [x0, y0, z0], where P represents the pitch angle, ranging from [0, π / 2], and Y represents the yaw angle, ranging from [0, π / 2], and calculate the position where the slave satellite can receive information.

[0146]

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

[0148] Step 3-2) loops through step 3-1) to obtain the set <time, position> of all slave star positions. It should be noted that a certain time point may correspond to multiple slave star positions, which is determined by whether D is a set.

[0149] Step 4) Optimize the slave star orbit and obtain six numbers of the slave star orbit.

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

[0151] Step 4-2) Star orbit optimization modeling includes constraint modeling and optimization

[0152] Modeling of environmental constraints, i.e. from the positions of stars not in the Penv set.

[0153]

[0154] Where 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 the two satellites cannot establish communication at time t.

[0155] Satellite distance constraint modeling, that is, the constraint between the distance between the slave satellite and the current master satellite and the constraint between the distance between the slave satellite and other existing satellites, is expressed as follows:

[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 satellite that changes with time. Dsetting represents the minimum distance between the master and slave satellites, which is set to 100 km here. Dglobal represents the minimum distance between the slave satellite and the existing satellite, which is set to 60 km here.

[0158] Track height constraint

[0159] Hlower<Height<Hupper (18)

[0160] Among them, Heigth represents the orbital height from the satellite, Hlower and Hupper represent the lowest and highest orbital heights acceptable to the mission respectively. Here, Hlower is set to 6900km and Hupper is set to 7500km.

[0161] The position constraint of the slave star is that the position of the slave star at time t must be within an acceptable range from the theoretical position of the slave star at time t derived from the master star, that is,

[0162]

[0163] in, and represents the position of the slave star derived from the position of the master star at time t obtained in step 3, where i represents the i-th theoretical slave star position solved at that time, n represents the total number of n theoretical slave star positions at that time, and x cal (t), y cal (t) and z cal (t) represents the satellite position calculated based on the six orbital elements, D real_cal Indicates the maximum acceptable distance between the theoretical slave star position and the calculated slave star position.

[0164] Optimization equation modeling, based on the above constraints, builds the following optimization model.

[0165]

[0166] Among them, durationT represents the total duration that the master and slave satellites can establish communication, and max(durationT) is the solution target, that is, maximizing the communication duration.

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

[0168] Determine whether each point of the slave satellite satisfies the constraints in sequence. 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 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 satellite 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 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.

[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 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

[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 length increases, the mutation probability alpha gradually approaches 1, which is beneficial to avoiding the solution falling into a local optimum as the iteration step length increases.

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

[0179] Step S4) outputs the positions of the master star and the slave star that meet the conditions.

[0180] After solving, the optimal six numbers of the satellite orbit are [6928, 0.001, 53.002, 0.0035, 0.004, 0.002].

[0181] like Figure 2 As shown in the figure, the position information of the master star and the slave star on the xy plane changes with time; Figure 3 As shown, it shows the location where the master star and the slave star can transmit information. The red line represents the master star, the blue line represents the slave star, and the colored line in the middle represents the area where information can be transmitted.

[0182] Example 2

[0183] Embodiment 2 of the present invention proposes a binary satellite orbit parameter optimization system, which is implemented based on the method of embodiment 1 and includes: an orbit information acquisition module, a multi-granularity binary satellite orbit optimization module, a communication duration calculation module and a visualization output module, wherein:

[0184] The orbit information acquisition module is used to obtain the theoretical solution set of the <time, position, speed> information matrix of the master star and the <time, position, speed> information matrix of the slave star according to the time interval calculated based on the six orbital numbers of the master star;

[0185] The multi-granularity binary satellite orbit optimization module is used to set constraint conditions, establish an optimization model for the satellite orbit, and use a dynamic mutation genetic algorithm according to the set solution granularity to optimize the six orbit numbers of the satellite by setting a mutation operation probability that changes dynamically with the iteration step size, and obtain the actual solution of the <time, position, speed> information matrix of the satellite, 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 communication duration calculation module is used to calculate the fitness function, obtain the duration of communication between the two stars, and determine whether the duration is constant. If it is, it will be transferred to the visualization output module, otherwise, it will be transferred to the multi-granularity binary orbit optimization module;

[0187] The visualization output module is used to output the positions of the master satellite and the slave satellite 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 are not intended to limit the present invention. Although the present invention is described in detail with reference to the embodiments, it should be understood by those skilled in the art 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 should be included in the scope of the claims of the present invention.

Claims

1. A method for optimizing binary satellite orbital parameters, comprising: Step 1) According to the six orbital elements of the master star, the time interval is calculated to obtain the theoretical solution set of the <time, position, velocity> information matrix of the master star and the <time, position, velocity> information matrix of the slave star; Step 2) Set constraints, establish an optimization model for the satellite orbit, and use a dynamic mutation genetic algorithm according to the set solution granularity. By setting the probability of mutation operation that changes dynamically with the iteration step, optimize the six orbit numbers of the satellite, obtain the actual solution of the <time, position, speed> information matrix of the satellite, 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 to obtain the duration of communication between the two stars, and determine whether the duration remains unchanged. If yes, go to step 4); otherwise, go to step 2); Step 4) Output the positions of the master star and slave star that meet the conditions.

2. The method for optimizing binary satellite orbit parameters according to claim 1, characterized in that: The six orbital parameters in step 1) include: orbital semi-major axis a, orbital eccentricity e, orbital inclination i, pericentric argument ω, ascending node longitude Ω and true anomaly angle 3. The method for optimizing binary satellite orbit parameters according to claim 1, characterized in that: In step 1), the <time, position, speed> information matrix of the master satellite is a T×1 matrix, where T represents T calculated time points, and the information matrix Y(t) at a certain time point t satisfies the following formula: Among them, x(t), y(t), z(t) are the position coordinates in three directions respectively, v x (t),v y (t),v z (t) are the speed values ​​in three directions respectively, t_start and t_end represent the start time and end time of the time interval respectively, which includes T time points in total.

4. The method for optimizing binary satellite orbit parameters according to claim 1, characterized in that: The step 1) is based on the theoretical solution of the <time, position, velocity> information matrix of the star, including: Step s1) Set the information transmission angle [P, Y] of the master satellite [x0, y0, z0], where P represents the pitch angle, the value range is [0, π / 2], Y represents the yaw angle, the value range is [0, π / 2], the units of P and Y are radians, and calculate the position where the slave satellite can receive information: Among them, dirx, diry and dirz represent the launch directions converted to the x-axis, y-axis and z-axis respectively, and D represents the launch distance. When D is a set, each master satellite position will correspond to multiple slave satellite positions; Step s2) loops through step s1) to obtain the theoretical solution of the <time, position, velocity> information matrix of all slave stars.

5. The method for optimizing binary satellite orbit parameters according to claim 1, characterized in that: The constraints of step 2) include: environmental constraints, satellite distance constraints, orbital altitude constraints and satellite position constraints; The environmental constraints satisfy the following formula: Among them, X(t), Y(t), Z(t) represent the position information of the slave satellite at time t, and Penv(t) represents the position where the binary satellite cannot establish communication at time t; The satellite distance constraint satisfies the following formula: Among them, D 主从 (t) represents the distance information between the master and slave satellites that changes over time, D 从-其他 (t) represents the distance information between the slave satellite and other existing satellites that changes over time, Dsetting represents the minimum distance between the master and slave satellites, and Dglobal represents the minimum distance between the slave satellite and existing satellites; The track height constraint satisfies the following formula: Hlower<Height<Hupper Among them, Height represents the orbital height from the satellite, Hlower and Hupper represent the lowest and highest orbital heights acceptable to the mission respectively; The slave star position constraint satisfies the following formula: in, and represents the theoretical position of the satellite at time t obtained from the theoretical solution of the satellite's <time, position, velocity> information matrix in step 1), n ​​represents the total number of n theoretical satellite positions at that time, x cal (t), y cal (t) and z cal (t) represents the satellite position calculated based on the six orbital elements at time t, D real_cal Indicates the maximum acceptable distance between the theoretical slave star position and the calculated slave star position.

6. The method for optimizing binary satellite orbit parameters according to claim 5, characterized in that: The optimization model of the star orbit in step 2) is: Among them, max(durationT) is the solution target, that is, to maximize the communication duration, and durationT represents the total duration that the master and slave satellites can establish communication. The specific calculation method is: Determine in sequence whether each point of the slave star satisfies the constraints. 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.

7. The method for optimizing binary satellite orbit parameters according to claim 6, characterized in that: 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 a fine granularity; otherwise, it is a coarse granularity. The fitness function Value of the dynamic mutation genetic algorithm is as follows: Value = -sum(FLAG(t)), The mutation operation probability alpha that varies 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.

8. The method for optimizing binary satellite orbit parameters according to claim 7, characterized in that: 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 three-dimensional 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 satisfying external constraints.

9. A binary satellite orbit parameter optimization system, characterized in that: It includes: An orbit information acquisition module, a multi-granularity binary star orbit optimization module, a communication duration calculation module, and a visualization output module. Among them, 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. The multi-granularity binary star orbit optimization module is used to set constraint conditions, establish an optimization model for the slave star orbit, adopt a dynamic mutation genetic algorithm according to the set solution granularity, optimize the six orbital elements of the slave star by setting the mutation operation probability that varies dynamically with the iteration step size, 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 communication 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 the determination is yes, transfer to the visualization output module; otherwise, transfer to the multi-granularity binary star orbit 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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