Large-scale satellite orbit intelligent calculation method for giant constellation

Abstract

The invention discloses a giant constellation-oriented large-scale satellite orbit intelligent calculation method, which comprises the following steps of: designing a multi-group satellite group configuration containing node stars, and accurately and initially determining the orbit of the node stars through a ground station; solving an initial orbit of a target satellite by using a multi-population genetic algorithm including an immigrant strategy and fitness function optimization on the basis of a node satellite; on the basis of a chain recursion strategy, orbit-determined satellites are used as new references, the positions of satellites in the same group are calculated step by step, and error accumulation is inhibited in combination with extended Kalman filtering. According to the method, on the basis of using a small amount of ground ranging data and fully utilizing inter-satellite ranging, the absolute orbit parameters of all satellites with quite high precision can be calculated and obtained.

Description

Technical Field

[0001] The present invention relates to the technical field of spacecraft orbit determination, and in particular 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 Art

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

[0003] At present, there are many different studies at home and abroad on relative navigation orbit determination based on only angle measurement or only distance measurement. Some are based on the iterative least squares method for initial orbit determination, some use dual-satellite collaboration combined with neural networks to solve the problem of ambiguous orbits, some introduce sensor installation bias to avoid the impact of ambiguous orbits, and some are based on nonlinear dynamic model optimization algorithms for orbit determination.

[0004] There are many precise orbit determination methods that only measure angles or distances. However, for large constellations, the large number of satellites will lead to serious orbit determination error accumulation, and the requirements for spacecraft observation mode or sensor installation cannot be met. Existing methods cannot solve this problem. Summary of the invention

[0005] In view of the problems existing in the prior art, the present invention provides a large-scale orbit intelligent calculation method for giant constellations. Based on the use of a small amount of ground ranging data and full use of inter-satellite ranging, the absolute orbit parameters of each satellite are calculated with considerable accuracy, and the combination of nonlinear orbital dynamics and genetic algorithms is used to effectively solve the ambiguous orbit problem caused by ranging alone.

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

[0007] Step 1: Design a giant star constellation observation configuration. The giant star constellation includes s satellite groups, each satellite group includes a satellites, and each satellite performs inter-satellite ranging with adjacent satellites. Each satellite group is provided with multiple node satellites, and the ground station performs initial orbit determination on the node satellites. The initial position of the node satellite at a given moment is and speed precisely known; Step 2, taking the node satellite as the observation satellite, the initial orbit of the target satellite is determined using a multi-population genetic algorithm with only ranging; Step 3, using the satellites that have been orbited as observation satellites, taking the node satellite as the starting point, repeating the multi-population genetic algorithm described in step 2, and calculating the initial positions of the satellites in the same group in sequence according to the chain recursive strategy, wherein 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 except the node satellite at the initial time are obtained; Step 4: Based on the ground station ranging data, the inter-satellite ranging data and the orbit initial value obtained by the multi-population genetic algorithm, an extended Kalman filter is used to perform real-time correction on the orbit integral prediction value.

[0008] Preferably, step 2 includes: step 2.1, constructing a fitness function based on the difference between satellite status and ranging data; step 2.2, initializing multiple populations and performing selection, crossover, mutation and inter-population immigration operations according to the fitness function; step 2.3, determining the initial position and velocity of the target satellite through elite population iteration and termination conditions.

[0009] Preferably, in step 2.1, the fitness function is defined as: the sum of the bi-norm and the standard deviation between the predicted value of the distance between the target satellite state and the observed satellite and the actual ranging data, expressed as: , where , , is the predicted distance value, The actual distance measurement value, the subscript k represents the kth measurement of the observing star to the target, and N represents the total number of measurements.

[0010] As a preference, in step 2, the upper and lower limits of population initialization , According to the initial value of the target satellite The prior information is determined, and the population individuals are generated according to the following formula: , the initial population is expressed as , i = 1, 2…m. The states of each individual and the observed star at the corresponding observation time are obtained through nonlinear orbital dynamics integration, and the fitness of each individual is calculated through the objective function.

[0011] As a preference, in step 2, the selection operation is: in the kth generation population Randomly select q individuals from the population and retain the individual with the largest fitness, repeat n times, where n is the number of individuals in a single population, so that the retained individuals form a new population .

[0012] As a preference, in step 2, the crossover uses a proportional crossover operator. For the two parent individuals of the kth generation population, and , the two offspring individuals of the k+1 generation population generated are expressed as: , , is A uniformly distributed random number in the interval.

[0013] As a preference, in step 2, the mutation uses a differential mutation operator. For the two parent individuals of the kth generation population, and , the two offspring individuals of the k+1 generation population generated are expressed as: , F is the scaling factor.

[0014] Preferably, in step 2, the inter-population migration operation adopts a circular migration strategy: select v individuals with the largest fitness in population i according to fitness f, select v individuals with the worst fitness in population i+1 according to fitness f, replace the worst individual with the best individual, and repeat the operation to replace each population once.

[0015] As a preference, select the best individuals in each population to form an elite population , the remaining individuals continue to iterate the population. If the fitness of an individual in the next generation is better than that of an individual in the current elite population, it will be replaced; the population iterates until the optimal fitness of the individual in the contemporary elite population changes less than a certain threshold relative to the previous generation ,Right now The process ends at this time, and the position and velocity of the target satellite at the initial time are obtained.

[0016] Preferably, in step 3, a chain recursive strategy is used to calculate the satellite orbit, and the multi-population genetic algorithm only needs to input the position, velocity and actual ranging information of the observed star at the initial moment, and 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 node star at the initial moment and the ranging data between adjacent satellites are known, and the output of the genetic algorithm orbit determination of the node star a for the satellite a+1, that is, the position and velocity of the satellite a+1 at the initial moment is used as input, and is continued to be used to calculate the orbit of the satellite a+2, and so on to calculate the position and velocity of the entire group of satellites at the initial moment.

[0017] Preferably, in order to reduce the calculation time, b node stars are set in a group of satellites, and a group of satellites is divided into b parts, each of which is independently calculated by the corresponding node star through a chain strategy. In view of the relatively mature satellite orbit determination technology of the ground station, the present application sets the node star position and velocity at the initial moment to be accurately known. The genetic algorithm disclosed in the present application has high robustness. Within a certain error range, the initial state of the observed star has little effect on the initial orbit determination result of the target, so a chain recursive strategy is used to perform the initial orbit determination of multiple satellites.

[0018] As a preference, in step 4, the extended Kalman filter, the state equation is , is the nonlinear orbital dynamics model of the satellite, and the observation equation , 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, i.e., state prediction, covariance prediction, gain calculation, state update, and covariance update.

[0019] Beneficial effects: (1) The present invention solves the fuzzy orbit problem caused by only ranging by combining a multi-population genetic algorithm with a nonlinear orbit dynamics model, and can achieve a higher orbit determination accuracy; (2) The immigration operator selected by the present invention can solve the local convergence problem of traditional genetic algorithms and achieve higher optimization accuracy; (3) The present invention designs a fitness function of the binary norm plus the standard deviation, so that the genetic algorithm has a higher robustness and the sensitivity to the influence of the position and velocity errors of the observed satellite is reduced; (4) The present invention combines a robust genetic algorithm with a chain recursive strategy, which effectively suppresses the error accumulation in the chain recursive orbit determination strategy while having high computational efficiency. BRIEF DESCRIPTION OF THE DRAWINGS

[0020] Figure 1 A schematic diagram of inter-satellite constellation ranging according to an embodiment of the present invention; Figure 2 A three-axis position error diagram of initial orbit determination of satellite 2 according to an embodiment of the present invention; Figure 3 A three-axis position error diagram of initial orbit determination of satellite 3 according to an embodiment of the present invention; Figure 4 A three-axis position error diagram of initial orbit determination of satellite 4 according to an embodiment of the present invention; Figure 5 A three-axis velocity error diagram of initial orbit determination of satellite 2 according to an embodiment of the present invention; Figure 6 A three-axis velocity error diagram of initial orbit determination of satellite 3 according to an embodiment of the present invention; Figure 7 This is a three-axis velocity error diagram of the initial orbit determination of satellite 4 according to an embodiment of the present invention. DETAILED DESCRIPTION

[0021] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0022] The present invention discloses a large-scale orbit intelligent calculation method for giant constellations. On the basis of using a small amount of ground ranging data and making full use of inter-satellite ranging, a multi-population genetic algorithm is used to determine the orbit of the target satellite, and the absolute orbit parameters of each satellite with considerable accuracy are calculated according to the designed giant constellation observation configuration.

[0023] like Figure 1 As shown in the figure, in this configuration, each satellite can measure the distance to the satellites around it. Therefore, in each group of satellites, the orbit determination calculation of the multi-population genetic algorithm of single-star to single-star can be carried out starting from the node satellite. The specific steps are as follows:

[0024] Step 1: Design a giant star constellation calculation strategy. The giant star constellation includes s satellite groups, each satellite group includes a satellites, and each satellite performs inter-satellite distance measurement with adjacent satellites (for fitness function calculation). Each satellite group is equipped with multiple node satellites, and the ground station performs initial orbit determination on the node satellites. The initial position and velocity of the node satellites are precisely known. A chain recursive strategy is used to calculate the orbit of each satellite group.

[0025] Step 2: Using the node satellite as the observation satellite, the initial orbit of the target satellite is determined using a multi-population genetic algorithm with only ranging.

[0026] Specifically include: Step 2.1, construct a fitness function based on the difference between satellite status and ranging data.

[0027] According to the characteristics of only ranging target orbit determination, the fitness function (genetic algorithm objective function) f is constructed and set as Satellite position at the moment Observed star position The predicted distance between and data link ranging sensor actual ranging information The second norm of the difference and the sum of the standard deviations, that is: , , .

[0028] Observe star position and satellite position The algorithm is calculated by nonlinear dynamic orbit integration based on the input initial position and velocity of the observed star and the corresponding population individual (i.e., the initial position and velocity of the target satellite). The specific steps are: calculating the position at each observation time, and then solving the distance between the two based on these position data. The initial position velocity of the target satellite is the individual in the population, and the corresponding function value is its fitness. The fitness function disclosed in the present application can perform genetic algorithm optimization iteration using only ranging information. The function combines the bi-norm and the standard deviation to enhance the robustness of the genetic algorithm, which is specifically manifested in the reduced sensitivity to the error of the observed star position. Among them, the bi-norm is used to measure the numerical difference between the predicted ranging data and the actual ranging data, and the standard deviation reflects the change of these differences in the time series. This combination method not only improves the stability of the algorithm in complex environments, but also makes the results more reliable and accurate. This fitness function can more effectively guide the optimization process of the genetic algorithm and ensure the quality of the final solution.

[0029] Step 2.2, initialize multiple populations and perform selection, crossover, mutation and immigration operations between populations according to the fitness function.

[0030] According to the initial value of the target satellite The prior information estimates the upper and lower limits of the population individual initialization , The prior information is used to estimate the initial position and velocity of the target satellite. This estimation may have a large error, but the error is within a certain range. Therefore, when setting the upper and lower limits of the initial parameters, ensure that the limits are beyond the error range to ensure that the population contains sufficiently accurate information on the initial position and velocity of the target satellite, so as to improve the accuracy of subsequent analysis or simulation and ensure the validity and reliability of the results. According to the formula Get the initial population , i=1,2,…,m, and calculate the fitness of each individual according to the fitness function.

[0031] A selection operation is performed separately in each population, and in the current generation (kth generation) Randomly select q (q depends on the number of populations) individuals from the population, and retain the individual with the largest fitness, repeat n times (n is the number of individuals in a single population) so that the retained individuals form a new population .

[0032] Each population is crossovered separately, using a proportional crossover operator. and are two parent individuals of the k-th generation population, and the two offspring individuals of the k+1 generation population generated by them can be expressed as: , , is A random number uniformly distributed within the interval with a certain crossover probability Make a crossover.

[0033] Mutation, each population mutates separately, using the differential mutation operator, set and are two parent individuals of the k-th generation population, and the two offspring individuals of the k+1 generation population generated by them can be expressed as: , F is the scaling factor, which is generally between 0 and 2. Perform mutation operation.

[0034] Immigration, operating between different populations to avoid the emergence of super individuals in a single population. Select two adjacent populations , , select v immigrants. Specifically, select v individuals with the highest fitness according to fitness f in population i (i=1,2...m, m is the number of populations), select v individuals with the lowest fitness according to fitness f in population i+1, and replace the worst individuals with the best individuals. Repeat the operation to replace each population once.

[0035] Step 2.3, select the best individuals in each population to form an elite population , the remaining individuals continue to iterate the population. If the fitness of an individual in the next generation is better than that of an individual in the current elite population, it will be replaced. The population iterates to the point where the change in the optimal fitness of the individual in the current elite population relative to the previous generation is less than a certain threshold ,Right now The iteration is terminated, and the result is the population individual with the best fitness. The value corresponding to this individual is the position and speed of the target satellite at the initial moment.

[0036] Step 3, using the satellites that have been orbited as observation stars, taking the node star as the starting point, 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 recursive strategy, wherein the orbit determination result of each satellite is used as the reference for the next satellite, and the initial positions and velocities of the satellites in the same group except the node star are obtained. If the satellite a in this group has been orbited by the node star to obtain a relatively accurate initial orbit, the orbit determination calculation of satellite a+1 is performed using satellite a as the reference star.

[0037] Specifically, a chain recursive strategy is used to calculate the orbit of the receiving satellite. 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 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 node star at the initial moment and the ranging data between adjacent satellites are known. The output of the genetic algorithm orbit determination of the node star a on the satellite a+1, that is, the position and velocity of the satellite a+1 at the initial moment is used as input and continued to be used to calculate the orbit of the satellite a+2. And so on, the position and velocity of the entire group of satellites at the initial moment are calculated. In order to reduce the calculation time, b node stars are set in a group of satellites, and a group of satellites is divided into b parts, and each part is calculated independently through the chain strategy.

[0038] Step 4: Based on the ground station ranging data, the inter-satellite ranging data and the orbit initial value obtained by the multi-population genetic algorithm, an extended Kalman filter is used to perform real-time correction on the orbit integral prediction value.

[0039] In satellite orbit estimation, the state equation of the Kalman filter adopts a nonlinear differential equation model based on orbital dynamics, which can be specifically expressed as: X is the state of the satellite, i.e. the three-dimensional position and velocity, and the observation equation is modeled as, Y For distance measurement. For this nonlinear 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 a priori estimates; then, the covariance prediction is performed based on the state transfer matrix, and then the Kalman gain k is calculated, and finally the state update and covariance update are completed through the observation residual to achieve the optimal recursive estimation of the satellite orbit.

[0040] The feasibility of the present invention is illustrated with reference to the following examples.

[0041] Set the following calculation conditions and technical parameters: 1) The parameter settings of the four satellites in this group are shown in Table 1 below; 2) The observation time is 10000s, the ranging period is 50s, the number of individuals in the population is set to 1000, and the number of populations is set to 6; 3) The standard deviation of ranging error is 30m, the standard deviation of satellite initial position error is 20000m, and the standard deviation of velocity error is 50m / s; 4) Set the genetic algorithm initialization boundary to the target satellite initial value xd_initial±[120000*[1;1;1];300*[1;1;1]].

[0042] Table 1 Satellite position parameters at initial time .

[0043] The multi-population genetic algorithm initial orbit determination method based on the present invention using ranging data is simulated and verified with the above-mentioned calculation conditions and technical parameters. The simulation time is 10000s. The ranging data between each satellite is obtained every 50 seconds. Figures 2 to 7 The figure shows the initial orbit position and velocity error diagram of the three satellites obtained by 150 target shootings. According to the 3σ principle, the probability that the positioning error of Satellite 2 using the known precise position reference satellite for orbit determination falls within [-70.5399m, 69.5093m] on the x-axis, [-306.5854m, 277.4517m] on the y-axis, and [-96.6937m, 86.0663m] on the z-axis is 99.7%. Similarly, the probability that the three-axis xyz error of satellite 3 falls within [-90.4314m, 86.4433m], [-346.3854m, 318.5431m], [-116.9285m, 107.4010m], and the probability that the three-axis xyz error of satellite 4 falls within [-112.6169m, 118.2829m], [-356.6019m, 369.9996m], [-120.7588m, 124.5483m] is 99.7%. The three-axis xyz velocity error 3σ range is: Satellite 2: [-0.2100m / s, 0.2336m / s], [-0.1910m / s, 0.2061m / s], [-0.0384m / s, 0.0331m / s]; Satellite 3: [-0.2141m / s, 0.2398m / s], [ -0.2173m / s, 0.2350m / s], [ -0.0367m / s, 0.0319m / s]; Satellite 4: [-0.2406m / s, 0.2288m / s], [ -0.2649m / s, 0.2521m / s], [ -0.0359m / s, 0.0375m / s].

[0044] It can be seen that although the orbit determination error will increase with the increase in the number of satellites, it will not cause the orbit determination to diverge. By arranging appropriate node satellites, the orbit determination accuracy requirements of the entire constellation can be fully met.

[0045] Finally, it should be noted that the above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art can still modify the technical solutions described in the aforementioned embodiments or replace some of the technical features therein by equivalents. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A large-scale satellite orbit intelligent calculation method for giant constellations, characterized in that: The following steps are involved: Step 1: Design a giant star constellation observation configuration. The giant star constellation includes s satellite groups, each satellite group includes a satellites, and each satellite performs inter-satellite ranging with adjacent satellites. Each satellite group is provided with multiple node satellites, and the ground station performs initial orbit determination on the node satellites. The initial position of the node satellite at a given moment is and speed precisely known; Step 2: Using the node satellite as the observation satellite, the initial orbit of the target satellite is determined using a multi-population genetic algorithm with only ranging. Specifically, Step 2.1, construct a fitness function based on the difference between satellite status and ranging data; 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, using the satellites that have been orbited as observation satellites, taking the node satellite as the starting point, repeating the multi-population genetic algorithm described in step 2, and calculating the initial positions of the satellites in the same group in sequence according to the chain recursive strategy, wherein 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 except the node satellite at the initial time are obtained; Step 4: Based on the ground station ranging data, the inter-satellite ranging data and the orbit initial value obtained by the multi-population genetic algorithm, an extended Kalman filter is used to perform real-time correction on the orbit integral prediction value.

2. The method according to claim 1, characterized in that In step 2, the fitness function is defined as: the sum of the bi-norm and standard deviation between the predicted value of the distance between the target satellite state and the observed satellite and the actual ranging data, expressed as: , where , , is the predicted distance value, The actual distance measurement value, the subscript k represents the kth measurement of the observing star to the target, and N represents the total number of measurements.

3. The method according to claim 2, characterized in that In step 2, the upper and lower limits of population initialization , According to the initial value of the target satellite The prior information is determined, and the population individuals are generated according to the following formula: , the initial population is expressed as , i=1,2…m.

4. The method according to claim 2, characterized in that: In step 2, the selection operation is: in the kth generation population Randomly select q individuals from the population and retain the individual with the largest fitness, repeat n times, where n is the number of individuals in a single population, so that the retained individuals form a new population .

5. The method according to claim 2, characterized in that: In step 2, the crossover uses the proportional crossover operator. For the two parent individuals of the kth generation population and , the two offspring individuals of the k+1 generation population generated are expressed as: , is A uniformly distributed random number in the interval.

6. The method according to claim 2, characterized in that In step 2, the mutation uses the differential mutation operator. For the two parent individuals of the kth generation population and , the two offspring individuals of the k+1 generation population generated are expressed as: F is the scaling factor.

7. The method according to claim 2, characterized in that: In step 2, the inter-population migration operation adopts a circular migration strategy: select v individuals with the largest fitness in population i according to fitness f, select v individuals with the worst fitness in population i+1 according to fitness f, replace the worst individual with the best individual, and repeat the operation to replace each population once.

8. The method according to claim 7, characterized in that Select the best individuals in each population to form an elite population , the remaining individuals continue to iterate the population. If the fitness of an individual in the next generation is better than that of an individual in the current elite population, it will be replaced; the population iterates until the optimal fitness of the individual in the contemporary elite population changes less than a certain threshold relative to the previous generation ,Right now The process ends at this time, and the position and velocity of the target satellite at the initial time are obtained.

9. The method according to any one of claims 2 to 8, characterized in that: In step 3, a chain recursive strategy is used to calculate the satellite orbit. The multi-population genetic algorithm only needs to input the position, velocity and actual ranging information of the observed star at the initial moment, and 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 node star at the initial moment and the ranging data between adjacent satellites are known. The output of the genetic algorithm orbit determination of node star a for satellite a+1, that is, the position and velocity of satellite a+1 at the initial moment, is used as input and continued to be used to calculate the orbit of satellite a+2. The position and velocity of the entire group of satellites at the initial moment are calculated in this way.

10. The method according to claim 9, characterized in that B node stars are set in the group of satellites, and the group of satellites is divided into b parts, each of which is independently calculated through a chain strategy to reduce the calculation time.

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