A Large-Scale Satellite Orbit Intelligent Calculation Method for Mega-Constellations

Abstract

The present invention discloses a large-scale satellite orbit intelligent calculation method for a giant constellation, designs multiple groups of satellite cluster configurations including nodal satellites, and accurately initializes the orbits of the nodal satellites through ground stations; taking the nodal satellites as a reference, uses a multi-population genetic algorithm including immigration strategies and fitness function optimization to solve the initial orbits of target satellites; based on a chain recurrence strategy, uses the satellites with determined orbits as new references, gradually calculates the positions of satellites in the same group, and combines extended Kalman filtering to suppress error accumulation. The present invention can calculate and obtain the absolute orbit parameters of each satellite with a relatively high accuracy on the basis of using a small amount of ground ranging data and making full use of inter-satellite ranging.

Description

Technical Field

[0001] The present invention relates to the technical field of spacecraft orbit determination, and specifically to a large-scale constellation satellite orbit determination algorithm that uses a small amount of ground ranging data and fully utilizes inter-satellite ranging. Background Technique

[0002] The premise for a satellite constellation to complete its mission is the maintenance of its configuration, and the premise for configuration maintenance is the precise relative orbit determination of the constellation members. For a large-scale constellation, due to the limited measurement capabilities of sensors, each sensor can usually only obtain partial measurement information (angle measurement or range measurement) of the system. Therefore, it is very important to invent a satellite constellation precise orbit determination technology that only uses partial measurement information.

[0003] Currently, there are various different studies on relative navigation orbit determination for angle-only or range-only measurements at home and abroad. Some perform initial orbit determination based on the iterative least squares method, some use dual-satellite cooperation combined with neural networks to solve the ambiguous orbit problem, some introduce sensor installation biases to avoid the influence of ambiguous orbits, and some perform orbit determination based on the optimization algorithm of the nonlinear dynamics model.

[0004] Currently, there are many precise orbit determination methods for angle-only or range-only measurements. However, for a large constellation, due to the large number of satellites, problems such as serious accumulation of orbit determination errors and inability to meet the requirements for spacecraft observation modes or sensor installations will occur, and the existing methods cannot solve this problem. Summary of the Invention

[0005] Aiming at the problems existing in the prior art, the present invention provides a large-scale orbit intelligent calculation method for a giant constellation. On the basis of using a small amount of ground ranging data and fully utilizing inter-satellite ranging, the absolute orbit parameters of each satellite with a relatively high accuracy are calculated, and the combination of nonlinear orbit dynamics and genetic algorithm is used to effectively solve the ambiguous orbit problem caused by range-only measurement.

[0006] A large-scale orbit intelligent calculation method for a giant constellation includes the following steps:

[0007] Step 1, design the observation configuration of the giant constellation. The giant constellation includes s groups of satellite clusters, each group of satellite clusters includes a satellites, and each satellite performs inter-satellite ranging with adjacent satellites; multiple node satellites are provided in each group of satellite clusters, and the ground station performs initial orbit determination on the node satellites, and the initial time positions r0 and velocities v0 of the node satellites are accurately known;

[0008] Step 2, use the multi-population genetic algorithm for range-only measurement with the node satellites as the observation satellites to determine the initial orbit of the target satellite;

[0009] Step 3: Using the already - orbited satellites as observation stars, starting from the nodal star, repeat the multi - population genetic algorithm described in Step 2, and calculate the initial positions of the satellites in the same group in sequence according to the chain - type recursive strategy. The orbit determination result of each satellite is used as the reference for the next satellite, and the positions and velocities of the satellites in the same group at the initial moment except the nodal star are obtained.

[0010] Step 4: Based on the ground station ranging data, inter - satellite ranging data, and the orbit initial values obtained by the multi - population genetic algorithm, use the extended Kalman filter to perform real - time correction on the predicted values of the orbit integration.

[0011] Preferably, Step 2 includes: Step 2.1: Construct a fitness function based on the difference between the satellite state and the ranging data; Step 2.2: Initialize multiple populations and perform selection, crossover, mutation, and immigration operations between populations according to the fitness function; Step 2.3: Determine the initial positions and velocities of the target satellites through elite population iteration and termination conditions.

[0012] Preferably, in Step 2.1, the fitness function is defined as the sum of the two - norm and the standard deviation between the predicted value of the distance between the target satellite state and the observation star and the actual ranging data, expressed as:

[0013] f = f1 + f2,

[0014] where, is the predicted value of the distance, is the actual ranging value, the subscript k represents the k - th measurement of the observation star on the target, and N represents the total number of measurements.

[0015] Preferably, in Step 2, the upper and lower limits X up , X down of the population initialization are determined according to the prior information of the initial value of the target satellite. The population individuals are generated according to the following formula: pop=(X up - X down )rand(0,1)+X down . The initialized population is denoted as pop i , i = 1, 2…m. The states of each individual and the corresponding observation moments of the observation stars are obtained through non - linear orbit dynamics integration, and the fitness of each individual is calculated through the objective function.

[0016] Preferably, in Step 2, the selection operation is: randomly select q individuals from the k - th generation population and retain the individual with the maximum fitness among them. Repeat n times, where n is the number of individuals in a single population, so that the retained individuals form a new population

[0017] Preferably, in step 2, a proportional crossover operator is used. For two parent individuals in the k-th generation population and the two offspring individuals in the (k + 1)-th generation population generated by them are expressed as:

[0018]

[0019] α and β are random numbers uniformly distributed in the interval [0, 1).

[0020] Preferably, in step 2, differential mutation operator is used for mutation. For two parent individuals in the k-th generation population and the two offspring individuals in the (k + 1)-th generation population generated by them are expressed as:

[0021]

[0022] F is a scaling factor.

[0023] Preferably, in step 2, a circular immigration strategy is adopted for the immigration operation between populations: in population i, v individuals with the highest fitness are selected according to the fitness f, and in population i + 1, v individuals with the lowest fitness are selected according to the fitness f, and the best individuals are used to replace the worst individuals, and the loop operation is performed to replace each population once.

[0024] Preferably, the best individuals in each population are selected to form an elite population Pop elite =[X 1max X 2max …], and the remaining individuals continue to perform population iteration. If the fitness of an individual in the next generation is better than that of a certain individual in the current elite population, replacement is performed; when the change of the optimal fitness individual in the current elite population from the previous generation is less than a certain threshold ε, that is the iteration terminates, and the position and velocity of the target satellite at the initial moment are obtained.

[0025] Preferably, in step 3, a chain recurrence strategy is adopted for satellite orbit calculation. The multi-population genetic algorithm only needs to input the position, velocity and actual ranging information of the observed satellite at the initial moment, and then the position and velocity of the target satellite at the initial moment can be output; in the calculation of a group of satellites, the position and velocity of the nodal satellite at the initial moment and the ranging data between adjacent satellites are known. The output of the genetic orbit determination of the nodal satellite a for satellite a + 1, that is, the position and velocity of satellite a + 1 at the initial moment, is used as the input and continues to be used to calculate the orbit of satellite a + 2, and so on to calculate the position and velocity of the entire group of satellites at the initial moment.

[0026] Preferably, to reduce the calculation time, b nodal satellites are set within a group of satellites, and the group of satellites is divided into b parts. Each part is independently calculated by the corresponding nodal satellite through a chain strategy. Given that the ground station has relatively mature satellite orbit determination technology, the initial positions and velocities of the nodal satellites in this application are precisely known. The genetic algorithm disclosed in this application has high robustness. Within a certain error range, the initial state of the observed satellite has little impact on the initial orbit determination result of the target. Therefore, a chain recursion strategy is used for the initial orbit determination of multiple satellites.

[0027] Preferably, in step 4, for the extended Kalman filter, the state equation is It is the non-linear orbit dynamics model of the satellite. The observation equation is Y = G(X, t), where Y is the distance measurement and X is the state of the satellite, i.e., the three-dimensional position and velocity. Then, conventional extended Kalman filtering is performed, namely state prediction, covariance prediction, calculation of gain, state update, and covariance update.

[0028] Beneficial effects:

[0029] (1) By combining the multi-population genetic algorithm with the non-linear orbit dynamics model, the present invention solves the ambiguous orbit problem caused by ranging only and can achieve high orbit determination accuracy.

[0030] (2) The immigration operator selected in the present invention can solve the local convergence problem of the traditional genetic algorithm and can achieve high optimization accuracy.

[0031] (3) Through the design of the fitness function with the second norm plus the standard deviation, the genetic algorithm of the present invention has high robustness and the sensitivity to the position and velocity errors of the observed satellite is reduced.

[0032] (4) By combining the robust genetic algorithm with the chain recursion strategy in the present invention, while effectively suppressing the error accumulation in the chain recursion orbit determination strategy, it also has high computational efficiency. Description of the Drawings

[0033] Figure 1 It is a schematic diagram of ranging between satellite constellations in an embodiment of the present invention;

[0034] Figure 2 It is a three-axis position error diagram of the initial orbit determination of satellite 2 in an embodiment of the present invention;

[0035] Figure 3 It is a three-axis position error diagram of the initial orbit determination of satellite 3 in an embodiment of the present invention;

[0036] Figure 4 It is a three-axis position error diagram of the initial orbit determination of satellite 4 in an embodiment of the present invention;

[0037] Figure 5Initial three-axis velocity error map of satellite 2 in an embodiment of the present invention;

[0038] Figure 6 Initial three-axis velocity error map of satellite 3 in an embodiment of the present invention;

[0039] Figure 7 Initial three-axis velocity error map of satellite 4 in an embodiment of the present invention; Detailed implementation manners

[0040] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of the present invention.

[0041] The present invention discloses a large-scale orbit intelligent calculation method for a giant constellation. Based on using a small amount of ground ranging data and making full use of inter-satellite ranging, a multi-population genetic algorithm is adopted for orbit determination of the target satellite, and absolute orbit parameters of each satellite with relatively high precision are calculated according to the designed observation configuration of the giant constellation.

[0042] As Figure 1 shown, in this configuration, each satellite can range to the surrounding satellites. Therefore, in each group of satellites, the orbit determination calculation of the multi-population genetic algorithm for single satellite to single satellite can start from the node satellite and take turns. The specific steps are as follows:

[0043] Step 1, design a calculation strategy for the giant constellation. The giant constellation includes s groups of satellite clusters, each group of satellite clusters includes a satellites, and each satellite performs inter-satellite ranging with adjacent satellites (for fitness function calculation); multiple node satellites are provided in each group of satellite clusters, and the ground station performs initial orbit determination on the node satellites, and the initial time positions and velocities of the node satellites are accurately known. The orbit of each group of satellites is calculated using a chain recurrence strategy.

[0044] Step 2, use the multi-population genetic algorithm with only ranging to determine the initial orbit of the target satellite with the node satellite as the observed satellite.

[0045] Specifically, it includes:

[0046] Step 2.1, construct a fitness function based on the difference between the satellite state and the ranging data.

[0047] According to the orbit determination characteristics of the only ranging target, construct a fitness function (genetic algorithm objective function) f, which is set to be the satellite position k at time t and the position of the observed satellite The predicted distance and the actual ranging information of the data link ranging sensor The sum of the two-norm and the standard deviation of the difference, that is:

[0048]

[0049] The position of the observed star and the satellite position It is calculated by the algorithm through non-linear dynamic orbit integration according to the input initial time position and velocity of the observed star and the corresponding population individuals (i.e., the initial time position and velocity of the target satellite). The specific steps are as follows: calculate the positions at their respective observation times, and then solve the distance between the two based on these position data. The initial position and velocity of the target satellite are the individuals in the population, and the corresponding function value is its fitness. The fitness function disclosed in this application can perform genetic algorithm optimization iterations only using ranging information. This function combines the two-norm and the standard deviation, enhancing the robustness of the genetic algorithm, specifically manifested as a reduced sensitivity to the position error of the observed star. Among them, the two-norm is used to measure the numerical difference between the predicted ranging data and the actual ranging data, while the standard deviation reflects the variation of these differences in the time series. This combined method not only improves the stability of the algorithm in complex environments but also makes the results more reliable and accurate. It enables the fitness function to more effectively guide the optimization process of the genetic algorithm and ensures the quality of the final solution.

[0050] Step 2.2, Initialize multiple populations and perform selection, crossover, mutation, and immigration operations between populations according to the fitness function.

[0051] According to the prior information of the initial value of the target satellite estimate the upper and lower limits X up , X down . The prior information is used to estimate the initial position and velocity of the target satellite. This estimate may have a large error, but the error is within a certain specific range. Therefore, when setting the upper and lower limits of the initial parameters, ensure that the limits exceed the error range to ensure that the population contains information on the initial position and velocity of the target satellite that is accurate enough to improve the accuracy of subsequent analysis or simulation and ensure the effectiveness and reliability of the results. According to the formula pop = (X up - X down )rand(0,1) + X down obtain the initialized population pop i , i = 1, 2,..., m, and calculate the fitness of each individual according to the fitness function.

[0052] Perform the selection operation separately within each population. In the population of this generation (the kth generation) Randomly select q individuals (q is determined according to the population size) from within, and retain the individual with the highest fitness. Repeat this n times (n is the size of the single population) so that the retained individuals form a new population

[0053] Perform the crossover operation separately within each population. Use the proportional crossover operator. Let and be two parent individuals in the k-th generation population. The two offspring individuals in the (k + 1)-th generation population they produce can be expressed as:

[0054]

[0055] α and β are random numbers uniformly distributed in the interval [0, 1). Perform crossover with a certain crossover probability p c to carry out the crossover

[0056] Mutation: Perform mutation separately within each population. Use the differential mutation operator. Let and be two parent individuals in the k-th generation population. The two offspring individuals in the (k + 1)-th generation population they produce can be expressed as:

[0057]

[0058] F is the scaling factor, generally taking values between 0 and 2. For the offspring after selection and crossover, perform mutation operation with a mutation probability p m to carry out the mutation operation

[0059] Immigration: Perform the operation between different populations to avoid the emergence of super individuals within a single population. Select two adjacent populations Select the number of immigrants as v. Specifically, in population i ((i = 1, 2... m), m is the number of populations), select v individuals with the highest fitness according to the fitness f, and in population i + 1, select v individuals with the worst fitness according to the fitness f, and replace the worst individuals with the best individuals. Perform the cyclic operation to replace each population once

[0060] Step 2.3: Select the best individuals in each population to form the elite population Pop elite = [X 1max X 2max ...]. The remaining individuals continue with population iteration. If an individual in the next generation has a fitness better than a certain individual in the current elite population, then replace it. When the change in the best fitness individual of the current elite population from the previous generation is less than a certain threshold ε, that is terminate. The result of the iteration is the population individual with the best fitness, and the value corresponding to this individual is the position and velocity of the target satellite at the initial moment

[0061] Step 3: Using the already-orbit-determined satellite as the observation satellite, starting from the nodal satellite, repeat the multi-population genetic algorithm described in Step 2, and calculate the initial positions of the satellites in the same group in sequence according to the chain recurrence strategy, where the orbit determination result of each satellite is used as the benchmark for the next satellite, and the positions and velocities of the satellites in the same group at the initial moment except the nodal satellite are obtained. If the relatively accurate initial orbit of satellite a in this group has been determined by the nodal satellite through orbit determination calculation, then use satellite a as the reference satellite to perform orbit determination calculation on satellite a+1.

[0062] Specifically, the chain recurrence strategy is adopted for the orbit calculation of the subsequent satellites. The multi-population genetic algorithm only needs to input the position, velocity, and actual ranging information of the observation satellite at the initial moment, and then it can output the position and velocity of the target satellite at the initial moment. In the calculation of a group of satellites, the position and velocity of the nodal satellite at the initial moment and the ranging data between adjacent satellites are known. Take the output of the genetic algorithm orbit determination of nodal satellite a for satellite a+1, that is, the position and velocity of satellite a+1 at the initial moment as the input, and continue to be used for the calculation of the orbit of satellite a+2, and so on to calculate the positions and velocities of the entire group of satellites at the initial moment. To reduce the calculation time, b nodal satellites are set in a group of satellites, and a group of satellites is divided into b parts, and each part is independently calculated through the chain strategy.

[0063] Step 4: Based on the ground station ranging data, inter-satellite ranging data, and the orbit initial value obtained by the multi-population genetic algorithm, use the extended Kalman filter to perform real-time correction on the orbit integral prediction value.

[0064] In the satellite orbit estimation, the state equation of the Kalman filter adopts a non-linear differential equation model based on orbit dynamics, which can be specifically expressed as X is the state of the satellite, that is, the three-dimensional position and velocity. The observation equation is modeled as Y = G(X, t), where Y is the distance measurement. For this non-linear system, this study constructs an extended Kalman filter framework: First, in the state prediction stage, the state equation is solved by the fourth-order Runge-Kutta method to obtain the prior estimate; then, the covariance prediction is carried out based on the state transition matrix, and then the Kalman gain k is calculated. Finally, the state update and covariance update are completed through the observation residual to achieve the optimal recursive estimation of the satellite orbit.

[0065] The feasibility of the present invention will be described in conjunction with the following examples.

[0066] Set the following calculation conditions and technical parameters:

[0067] 1) The parameters of the four satellites in this group are set as shown in Table 1 below.

[0068] 2) The observation duration is 10000 s, the ranging period is 50 s, the number of population individuals is set to 1000, and the number of populations is 6.

[0069] 3) The standard deviation of the ranging error is 30 m, the standard deviation of the initial satellite position error is 20000 m, and the standard deviation of the velocity error is 50 m / s.

[0070] 4) Set the initialization boundary of the genetic algorithm as the initial value of the target satellite xd_initial ± [120000 * [1; 1; 1]; 300 * [1; 1; 1]];

[0071] Table 1 Position parameters of the satellite at the initial moment

[0072]

[0073] The multi - population genetic algorithm initial orbit determination method using ranging data based on the present invention is verified by simulation with the above - set calculation conditions and technical parameters. The simulation time is 10000 s. Ranging data between satellites are obtained every 50 s. As Figures 2 to 7 shown is the initial orbit determination position and velocity error diagram of three satellites obtained by 150 times of shooting. It can be seen from the figure that according to the 3σ principle, for the satellite 2 whose orbit is determined using a reference satellite with known accurate position, the probability that the positioning error in the x - axis direction falls within [-70.5399 m, 69.5093 m], the y - axis error falls within [-306.5854 m, 277.4517 m], and the z - axis error falls within [-96.6937 m, 86.0663 m] is 99.7%. Similarly, for satellite 3, the probability that the three - axis xyz errors fall within [-90.4314 m, 86.4433 m], [-346.3854 m, 318.5431 m], [-116.9285 m, 107.4010 m], and for satellite 4, the probability that the three - axis xyz errors fall within [-112.6169 m, 118.2829 m], [-356.6019 m, 369.9996 m], [-120.7588 m, 124.5483 m] is 99.7%. For the 3σ range of the three - axis xyz velocity errors, for satellite 2: [-0.2100 m / s, 0.2336 m / s], [-0.1910 m / s, 0.2061 m / s], [-0.0384 m / s, 0.0331 m / s]; for satellite 3: [-0.2141 m / s, 0.2398 m / s], [-0.2173 m / s, 0.2350 m / s], [-0.0367 m / s, 0.0319 m / s]; for satellite 4: [-0.2406 m / s, 0.2288 m / s], [-0.2649 m / s, 0.2521 m / s], [-0.0359 m / s, 0.0375 m / s];

[0074] It can be seen that although the increase in the number of satellites will lead to an increase in the orbit determination error, it will not cause the orbit determination to diverge. By arranging appropriate nodal satellites, the orbit determination accuracy requirements of the entire constellation can be fully met.

[0075] Finally, it should be noted that the above are only preferred embodiments of the present invention and are not intended to limit the present invention. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art can still modify the technical solutions described in the foregoing embodiments or perform equivalent replacements for some of the technical features. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principle of the present invention shall be included within the protection scope of the present invention.

Claims

1. A large-scale satellite orbit intelligent calculation method for giant constellations, characterized in that It includes the following steps: Step 1: Design the observation configuration of the giant star constellation. The giant star constellation includes s groups of satellite clusters, each group of satellite clusters includes a satellites, and each satellite performs inter-satellite ranging with adjacent satellites. There are multiple nodal stars in each group of satellite clusters, and the ground station performs initial orbit determination on the nodal stars. The initial time positions r0 and velocities v0 of the nodal stars are accurately known; Step 2: Using the nodal stars as observation stars, use a multi-population genetic algorithm with only ranging to determine the initial orbit of the target satellite. Specifically, Step 2.1, construct a fitness function based on the difference between satellite states and ranging data. The fitness function f is defined as the sum of the two-norm f1 and the standard deviation f2 of the difference e between the target satellite state and the predicted distance values and the actual ranging data at each moment of the observed satellite, expressed as: k ​ f = f1 + f2, In the formula, is the predicted distance value, is the actual measured distance value. The subscript k represents the k-th measurement of the observed star pair to the target, and N represents the total number of measurements; Step 2.2: Initialize multiple populations and perform selection, crossover, mutation, and inter-population immigration operations according to the fitness function; Step 2.3: Determine the initial position and velocity of the target satellite through elite population iteration and termination conditions; Step 3: Use the satellites with determined orbits as observation stars, starting from the nodal stars, repeat the multi-population genetic algorithm described in Step 2, and calculate the initial positions of the satellites in the same group in sequence according to the chain recursion strategy. The orbit determination result of each satellite is used as the reference for the next satellite, and the positions and velocities of the satellites in the same group at the initial moment except the nodal stars are obtained; Step 4: Based on the ground station ranging data, inter-satellite ranging data, and the orbit initial values obtained by the multi-population genetic algorithm, use the extended Kalman filter to perform real-time correction on the orbit integral prediction value.

2. The method according to claim 1, wherein In step 2, the upper and lower limits X of population initialization up , X down are determined according to the prior information of the initial value of the target satellite . r t0 , v t0 are the three-dimensional position and velocity at the initial moment of the target respectively. The population individuals are generated according to the following formula: pop = (X up - X down )rand(0,1) + X down , initialize the population as pop i , i = 1, 2... m.

3. The method according to claim 1, characterized in that, In step 2, the selection operation is as follows: randomly select q individuals from the k-th generation population and retain the individual with the maximum fitness among them. Repeat this n times, where n is the number of individuals in a single population, so that the retained individuals form a new population 4. The method according to claim 1, wherein In step 2, the proportional crossover operator is used for crossover. For two parent individuals in the k-th generation population and the two offspring individuals in the (k + 1)-th generation population generated therefrom are represented as: α, β are random numbers uniformly distributed in the interval [0, 1).

5. The method according to claim 1, wherein In step 2, differential mutation operator is adopted for mutation. For two parent individuals of the k-th generation population and the two offspring individuals of the (k + 1)-th generation population generated thereby are expressed as: F is the scaling factor.

6. The method according to claim 1, wherein In Step 2, the inter-population immigration operation adopts a circular immigration strategy: In population i, v individuals with the largest fitness are selected according to the fitness f, and in population i + 1, v individuals with the worst fitness are selected according to the fitness f, and the best individuals are used to replace the worst individuals. The loop operation replaces each population once.

7. The method according to claim 6, wherein Select the optimal individuals in each population to form the elite population Pop elite = [X 1max X 2max …], and the remaining individuals continue the population iteration. If the fitness of an individual in the next generation is better than that of an individual in the current elite population, then replace it; when the change in the optimal fitness individual of the current elite population relative to the previous generation is less than a certain threshold ε during the population iteration, that is terminate, and obtain the position and velocity of the target satellite at the initial moment.

8. The method according to any one of claims 1-7, characterized in that In Step 3, the chain recursion strategy is adopted for satellite orbit calculation. The multi-population genetic algorithm only needs to input the position, velocity, and actual ranging information of the observation star at the initial moment to output the position and velocity of the target satellite at the initial moment; in the calculation of a group of satellites, the position and velocity of the nodal star at the initial moment and the ranging data between adjacent satellites are known. The output of the genetic algorithm orbit determination of nodal star a for satellite a + 1, that is, the position and velocity of satellite a + 1 at the initial moment, is used as the input to continue calculating the orbit of satellite a + 2, and so on to calculate the positions and velocities of the entire group of satellites at the initial moment.

9. The method according to claim 8, wherein Set b nodal stars in the group of satellites, divide the group of satellites into b parts, and each part is independently calculated through the chain strategy to reduce the calculation time.

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