CN111680360A - Optimal design method for navigation constellation on-orbit backup scheme - Google Patents
Optimal design method for navigation constellation on-orbit backup scheme Download PDFInfo
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Abstract
The invention discloses an on-orbit backup scheme optimization design method of a navigation constellation, which comprises the steps of determining an optimization variable, an objective function and a constraint condition of an on-orbit backup star orbit position optimization model according to parameters of the navigation constellation; based on a track position optimization model of the on-track backup satellite, obtaining the optimal track position of the on-track backup satellite by using a multi-objective optimization algorithm; and determining a replacement optimization model for replacing the fault satellite by the on-orbit backup satellite by combining the optimal orbit position of the on-orbit backup satellite, and determining an optimal replacement method according to the replacement optimization model. The invention can obviously improve the service performance of the navigation constellation, enhance the stability and robustness of the navigation constellation, and can finish the replacement of the fault satellite with lower energy in a short time.
Description
Technical Field
The invention relates to an on-orbit backup scheme optimization design method for a navigation constellation, and belongs to the technical field of navigation constellations.
Background
In order to meet the strict requirements of the system on availability, continuity and integrity, a plurality of backup satellites are usually deployed in space, and if a satellite in the constellation fails, the backup satellite in orbit is replaced by changing the orbit of the backup satellite in orbit. For example, a gps (global Positioning system) constellation deploys backup satellites near a satellite with the highest failure probability to form a 'satellite pair', so that when one of the satellites fails, the backup satellites can rapidly replace the failed satellite through orbital maneuver in a short time, thereby reducing the influence on users. The optimization design of the on-orbit backup scheme relates to the service performance of the whole navigation constellation during operation, and also relates to the problems of maintenance and utilization of space track resources and the like, so the on-orbit backup scheme must be reasonably designed.
Disclosure of Invention
The application aims to provide an on-orbit backup scheme optimization design method of a navigation constellation so as to solve the technical problem that the service performance of an operation device is poor in the conventional navigation constellation.
The invention discloses an on-orbit backup scheme optimization design method of a navigation constellation, which comprises the following steps:
determining an optimization variable, an objective function and a constraint condition of a track position optimization model of the on-track backup satellite according to the parameters of the navigation constellation;
based on the track position optimization model of the on-track backup satellite, obtaining the optimal track position of the on-track backup satellite by using a multi-objective optimization algorithm;
and determining a replacement optimization model for replacing the fault satellite by the on-orbit backup satellite by combining the optimal orbit position of the on-orbit backup satellite, and determining an optimal replacement method according to the replacement optimization model.
Preferably, the optimization variables, the objective function and the constraint conditions of the track bit optimization model of the on-track backup satellite are determined according to the parameters of the navigation constellation, and specifically:
taking the track position of the on-track backup star on each track surface as an optimization variable of the track position optimization model;
determining an objective function of the rail position optimization model according to the precision attenuation factor value of the constellation position and the number of visible satellites in a set elevation angle range;
and taking the track position angle of the on-track backup star as a constraint condition of the track position optimization model.
Preferably, the track bits of the on-track backup star on each track surface are represented in an encoded form, and the encoding adopts floating point number encoding.
Preferably, the objective function of the orbit optimization model determined according to the constellation position accuracy attenuation factor value and the number of visible satellites in the set elevation angle range specifically includes:
carrying out grid division on the service area of the navigation constellation by adopting a grid analysis method;
acquiring the constellation position precision attenuation factor values and the number of visible satellites of all grid points at each moment;
acquiring an average value of the constellation position precision attenuation factor values and an average value of the number of visible satellites in a set simulation time period;
and determining an objective function of the orbit optimization model according to the average value of the precision attenuation factor values of the constellation positions and the average value of the number of the visible satellites.
Preferably, the obtaining of the optimal track position of the on-orbit backup satellite by using a multi-objective optimization algorithm based on the on-orbit backup satellite track position optimization model specifically includes:
and obtaining the optimal track position of the on-orbit backup star by using a non-dominated sorting genetic algorithm based on the on-orbit backup star track position optimization model.
Preferably, a replacement optimization model for replacing the failed satellite by the on-orbit backup satellite is determined by combining the optimal orbit position of the on-orbit backup satellite, and an optimal replacement method is determined according to the replacement optimization model, specifically:
determining a replacement mode of the in-orbit backup satellite according to the relationship between the phase of the fault satellite and the phase of the in-orbit backup satellite; the replacement mode comprises a phase lead replacement and a phase lag replacement;
and determining an objective function and constraint conditions of the replacement optimization model by combining the replacement mode to obtain a replacement optimization model for replacing the fault satellite by the on-orbit backup satellite, and determining an optimal replacement method according to the replacement optimization model.
Preferably, an objective function and a constraint condition of the replacement optimization model are determined in combination with the replacement mode to obtain a replacement optimization model for replacing the failed satellite by the on-orbit backup satellite, and an optimal replacement method is determined according to the replacement optimization model, specifically:
determining a semi-major axis of a transition orbit when the on-orbit backup satellite replaces the fault satellite according to the replacement mode;
determining an objective function and constraint conditions of a replacement optimization model by combining the semi-major axis of the transition orbit to obtain a replacement optimization model for replacing the fault satellite by the on-orbit backup satellite;
and determining an optimal replacement method based on the replacement optimization model.
Preferably, the objective function of the replacement optimization model is the minimum speed increment or the minimum replacement time when the on-orbit backup satellite replaces the failed satellite, which is determined in combination with the semi-major axis of the transition orbit.
Preferably, the constraint conditions of the replacement optimization model are the semimajor axis of the transition orbit, the number of turns of the on-orbit backup satellite running on the transition orbit and the number of turns of the fault satellite position running on the original orbit.
Compared with the prior art, the navigation constellation on-orbit backup scheme optimization design method has the following beneficial effects:
the optimal design method of the on-orbit backup scheme of the navigation constellation can obviously improve the service performance of the navigation constellation, enhance the stability and robustness of the navigation constellation, and simultaneously realize the replacement of the failed satellite by adopting the orbital maneuver mode of the on-orbit backup satellite, and can complete the replacement of the satellite with lower energy in a short time.
Drawings
FIG. 1 is a flow chart of an on-orbit backup scheme optimization design method of a navigation constellation according to the present invention;
FIG. 2 is a schematic illustration of chromosome coding in an embodiment of the present invention;
FIG. 3 is a flow chart of the NSGA-II algorithm of the present invention;
FIG. 4 is a result of on-orbit backup satellite-orbit bit optimization;
FIG. 5 is a schematic diagram of an on-orbit backup star orbit bit;
fig. 6 is a constellation PDOP value comparison;
FIG. 7 is a comparison of the number of satellites visible in a constellation;
FIG. 8 is a schematic diagram of phase advance substitution;
FIG. 9 is an alternate schematic of phase lag;
FIG. 10 is an optimized design result with minimum speed increment as the optimization goal;
FIG. 11 is an optimized design result with minimum replacement time as the optimization goal.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more clearly apparent, the present invention is further described in detail below with reference to the accompanying drawings and embodiments. It should be noted that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.
Fig. 1 is a flowchart of an on-orbit backup scheme optimization design method of a navigation constellation according to the present invention.
The invention discloses an on-orbit backup scheme optimization design method of a navigation constellation, which comprises the following steps:
taking the track position of the on-track backup star on each track surface as an optimization variable of the track position optimization model; the track bit of the on-track backup star on each track surface is represented in a coding mode, and the coding adopts floating point number coding;
the objective function of the rail position optimization model determined according to the constellation position precision attenuation factor value and the number of visible satellites in the set elevation angle range specifically comprises the following steps:
carrying out grid division on the service area of the navigation constellation by adopting a grid analysis method;
acquiring the constellation position precision attenuation factor values and the number of visible satellites of all grid points at each moment;
acquiring an average value of the constellation position precision attenuation factor values and an average value of the number of visible satellites in a set simulation time period;
and determining an objective function of the orbit optimization model according to the average value of the precision attenuation factor values of the constellation positions and the average value of the number of the visible satellites.
And taking the track position angle of the on-track backup star as a constraint condition of the track position optimization model.
obtaining the optimal track position of the on-orbit backup star by utilizing a non-dominated sorting genetic algorithm based on the on-orbit backup star track position optimization model;
determining a replacement mode of the in-orbit backup satellite according to the relationship between the phase of the fault satellite and the phase of the in-orbit backup satellite; the replacement mode comprises a phase lead replacement and a phase lag replacement;
determining an objective function and constraint conditions of a replacement optimization model by combining the replacement mode to obtain a replacement optimization model for replacing the fault satellite by the on-orbit backup satellite, and determining an optimal replacement method according to the replacement optimization model, wherein the method specifically comprises the following steps:
determining a semi-major axis of a transition orbit when the on-orbit backup satellite replaces the fault satellite according to the replacement mode;
determining an objective function and constraint conditions of a replacement optimization model by combining the semi-major axis of the transition orbit to obtain a replacement optimization model for replacing the fault satellite by the on-orbit backup satellite; wherein an objective function of the replacement optimization model is the minimum speed increment or the minimum replacement time when the on-orbit backup satellite replaces the failed satellite, which is determined by combining the semimajor axis of the transition orbit; and the constraint conditions of the replacement optimization model are the semimajor axis of the transition orbit, the number of turns of the on-orbit backup satellite running on the transition orbit and the number of turns of the fault satellite position running on the original orbit.
And determining an optimal replacement method based on the replacement optimization model.
The method comprises the steps that the condition that service is provided by an orbit backup satellite and a working satellite together in the operation period of a constellation is considered, an orbit position optimization model of the orbit backup satellite is established, a constellation position precision attenuation factor (PDOP) value and the number of visible satellites are selected as an orbit position optimization objective function, and the influence of the orbit backup satellite on the service performance of the system under different orbit positions is analyzed by an NSGA-II algorithm;
for example, in the embodiment of the present invention, a middle orbit Walker navigation constellation is used as an analysis object, the constellation is composed of 24 satellites, the constellation parameter is 24/3/1, the orbit height is 21528km, the inclination angle is 55 °, and meanwhile, two in-orbit backup satellites are respectively deployed on each orbit surface in the model:
(1) optimizing variables
In the on-orbit backup satellite orbit position optimization design, the model optimization variable is the orbit position f of the on-orbit backup satellite on each orbit surfacei,jWherein i ∈ (1,2,3), j ∈ (1,2), i is the track surface number, j is the on-track backup star number, such as f1,2The track position of the 2 nd on-track backup star on the 1 st track surface is shown.
(2) Objective function
In a navigation constellation, the positioning accuracy is an important index for performance evaluation, and the index is also related to the geometrical configuration of the constellation besides being influenced by each pseudo-range measurement value, and the configuration can be quantitatively evaluated by calculating the value of a constellation position accuracy decay factor (PDOP). Therefore, the PDOP value is selected as one of the evaluation indexes for backup star-orbit bit optimization, and is calculated as follows:
suppose the user coordinates are (X)0,Y0,Z0) At this time, in the local coordinate system of the user, the N satellite coordinates satisfying the minimum observation elevation α can be expressed as:
ri＝[Xi,Yi,Zi],(i＝1,2,...,N) (1)
the corresponding coefficient matrix H is then:
in the formula (I), the compound is shown in the specification,
the distance between the satellite and the user. Let matrix Q be:
the PDOP values for the end user coordinates are:
meanwhile, the visible satellite number is also selected as another evaluation index for backup satellite orbit optimization. The visible satellite number is the number of satellites in a certain elevation angle range, which can receive satellite navigation signals by a user, and the value of the visible satellite number determines the accuracy of the calculation result of the precision factor, so that the visible satellite number is also an important index for measuring the performance of a navigation constellation.
In order to more comprehensively evaluate the performance of the service area of the navigation constellation, a grid analysis method is adopted to carry out grid division on the service area of the navigation constellation, the PDOP value and the number of visible satellites of all grid points at each moment are counted, the average value of the PDOP value and the number of visible satellites of the service area in simulation time is finally obtained, and F is respectively used forP(X) and FM(X) represents. In conclusion, the mathematical model of the on-orbit backup satellite orbit bit optimization design of the navigation constellation is as follows:
(3) constraint conditions
In the optimization design of the orbit position of the on-orbit backup star, the constraint condition of the model is the orbit position f of the on-orbit backup stari,j∈[0°,360°]Meanwhile, due to the existence of the working satellite, the rail position of the on-orbit backup satellite cannot be taken as the rail position of the existing working satellite in the same orbit plane.
After various parameters of the model are determined, the optimal orbit position of the on-orbit backup satellite is obtained by utilizing the multi-objective optimization design of the NSGA-II algorithm.
(1) Coding mode of rail position optimization variable
The on-orbit backup star-orbit bit optimization variable belongs to a continuous variable, and the optimization variable needs to be coded when the on-orbit backup star-orbit bit optimization variable is solved by using an NSGA-II algorithm. Variable coding has multiple coding modes, the most widely applied mode is a binary coding mode, however, when the value range of the model optimization variable is large, in order to ensure that the optimization variable has high precision, the number of bits of a binary character string needs to be increased, which causes the chromosome gene to be too long, thereby reducing the search efficiency and influencing the convergence rate of the algorithm. Therefore, the floating-point number coding method is adopted, each gene in the chromosome represents one variable, the coding method can effectively reduce the coding length of the chromosome, improve the operation efficiency and simultaneously ensure that the variable has higher precision. After each variable is encoded, it is concatenated into a chromosome to complete the encoding of an individual, as shown in FIG. 2.
(2) Selection mechanism based on Pareto dominance
Unlike the single-objective optimization problem, the optimal solution of the multi-objective optimization problem is a set of optimal solutions because it is difficult to obtain an ideal solution that can optimize all objective functions, and when one objective is further optimized, other objectives are usually degraded. A large number of scholars develop research on solving the multi-objective optimization problem and provide corresponding solving ideas, wherein the optimization method based on the Pareto dominant thought is widely applied.
Assuming that the multi-objective optimization is to solve the minimum of the objective function, if x is a feasible solution1Any corresponding objective function value fk(x1) Are all less than or equal to feasible solution x2Corresponding objective function value fk(x2) And there is an objective function value fl(x1) Less than x2Corresponding objective function value fl(x2) Then called feasible solution x1Compared with x2Predominance or x1Dominating x2：
If the feasible solution x is not dominated by any other solution, the feasible solution is called a non-dominated solution, and after iterative evolution of the algorithm, all the non-dominated solutions can be obtained and form a non-dominated solution set called a Pareto front. Adopting a Pareto dominant selection mechanism in an NSGA-II algorithm to obtain a Pareto leading edge, wherein the formula is as follows:
in the formula, mui,gAs test vector, Xi,gIs the target vector.
(3) Optimization process of NSGA-II algorithm
The non-dominated ranking genetic algorithm (NSGA) is a multi-objective optimization algorithm based on Pareto dominant selection proposed by Srinivas and Deb in 1994. On the basis, Deb et al further propose an improved NSGA-II algorithm in 2002, and the advantage of the algorithm is mainly reflected in that the NSGA-II algorithm adopts a rapid non-dominated sorting method, so that the complexity of searching non-dominated solutions is reduced, the crowding degree between midpoints of each layer is calculated by defining a crowding distance, the use of a sharing function in the NSGA algorithm is replaced, the influence of manually determined sharing parameters on the solution space distribution is avoided, the diversity of a population is kept, simultaneously an elite strategy is introduced, the non-dominated sequence is determined by layering solution spaces, the superiority of the solutions in the population is kept, and the sampling space is also expanded. The NSGA-ii algorithm mainly includes initialization, selection, crossover, mutation, and the like, and the specific flow is shown in fig. 3.
And optimally designing the on-orbit backup star orbit position according to the model and the optimization algorithm, wherein the service area of the middle orbit Walker navigation constellation is a global area, the service area is subjected to grid division according to a longitude and latitude line with the angle of 5 degrees multiplied by 5 degrees, the simulation time is a constellation regression period, the minimum observation elevation angle alpha of a user is 5 degrees, and the data statistics step length is 600 s. The initial parameters of the optimization algorithm are: the population number N is 50, the maximum evolution generation G is 50, the cross factor is 1, and the variation factor is 0.16. The on-orbit backup star-orbit bit optimization result is shown in 4.
As can be seen from fig. 4, in the optimized solution set obtained by the iteration of the algorithm, the interval corresponding to the number of satellites is [10.3303, 10.3306], and the interval corresponding to the PDOP value is [1.665, 1.695 ]. Meanwhile, for different solutions in the optimization solution set, the variation range of the number of visible satellites is small, and in the small range, the PDOP values corresponding to the different solutions show a trend of increasing along with the increase of the number of visible satellites. Finally, the non-dominated solution set, i.e., Pareto level 1 in fig. 4, is selected from the optimized solution set and sorted in ascending order according to PDOP values, as shown in table 1.
TABLE 1
As can be seen from the non-dominated solution set in table 1, the satellite number variation range is small, and therefore, the solution with the minimum PDOP value in the non-dominated solution set is selected as the optimal solution for the analysis of the optimization result. Fig. 5 shows an on-orbit backup satellite-orbit bit diagram of the optimal solution, where M11 in (b) of fig. 5 represents a satellite numbered 1 on the 1 st orbital plane, and the other same principles are applied.
For the on-orbit backup satellite-orbit position of the optimal solution, the middle orbit Walker navigation constellation in the global area, the PDOP value of the constellation added after the on-orbit backup satellite and the number of visible satellites are compared and analyzed, as shown in fig. 6 and 7. It can be seen that the maximum PDOP value of the mid-orbit Walker navigation constellation in the global region is 1.8889, the minimum PDOP value is 1.8759, and the average PDOP value is 1.8824. After the on-orbit backup star is added, the maximum PDOP value of the constellation is reduced to 1.6797, and the reduction amplitude is 11.1%; the minimum PDOP value is reduced to 1.6618, the reduction amplitude is 11.4%; the average PDOP value dropped to 1.6697, with a reduction of 11.3%. Similarly, for the number of visible satellites in the constellation, the maximum value of the middle orbit Walker navigation constellation is 8.2845, the minimum value is 8.2476, and the average value is 8.2642. After the on-orbit backup satellite is added, the maximum value of the number of visible satellites is increased to 10.3529, and the increase amplitude is 24.9%; the minimum value is increased to 10.3075, and the increase amplitude is 24.9%; the average value rises to 10.3304, with an increase of 25%. Therefore, the on-orbit backup star has a remarkable enhancement effect on the performance of the navigation constellation.
Based on the optimization result of the on-orbit backup satellite-orbit position, establishing a corresponding on-orbit backup satellite replacement orbit maneuvering model, namely a replacement optimization model, according to the relation between the phase of the fault satellite and the phase of the on-orbit backup satellite, and analyzing and comparing an on-orbit backup satellite replacement scheme by taking the minimum speed increment and the minimum replacement time as optimization targets to obtain a final on-orbit backup satellite replacement scheme;
in order to describe the method for replacing the on-orbit backup satellite and the failed satellite in detail, the present application describes a specific embodiment.
The adjustment method of the satellite phase can be divided into the phase adjustment of the same orbital plane and the phase adjustment of the different orbital plane according to whether the change of the orbital plane is involved in the satellite phase adjustment process. Because of the large fuel consumption of the adjustment of the out-of-plane orbit, the on-orbit backup satellite usually only replaces the failed satellite in the same orbit plane. According to the relation between the phase of the failed satellite and the phase of the on-orbit backup satellite, the replacement of the backup satellite on the same orbit plane can be divided into two conditions of phase advance and phase lag.
(1) Phase advance
In phase advance, the earth center angle θ e [180 °,360 °) between the on-orbit backup satellite to the failed satellite along the direction of travel. At the moment, the on-orbit backup star can enter the high-orbit transition elliptical orbit by lifting the height of the orbit and applying impulse once at the initial position, and the semimajor axis a of the transition orbit needs to satisfy the following conditions:
a0＜a (7)
in the formula, a0Is the semi-major axis of the original orbit.
After the in-orbit backup satellite runs for a plurality of circles on the transition orbit, the position of the fault satellite just runs to the initial position of the in-orbit backup satellite, and at the moment, impulse is applied to the in-orbit backup satellite once again to enable the in-orbit backup satellite to enter the original orbit from the transition orbit, so that the fault satellite can be replaced, as shown in fig. 8.
(2) Phase lag
With phase lag, the earth center angle θ e (0 °,180 °) between the on-orbit backup satellite along the direction of travel to the failed satellite. At this time, the on-orbit backup star can enter the low-orbit transition elliptical orbit by reducing the height of the orbit and applying impulse once at the initial position, and the semimajor axis a of the transition orbit needs to satisfy:
in the formula, a0Is the semi-major axis of the original orbit and R is the radius of the earth.
After the in-orbit backup satellite runs for a plurality of circles on the transition orbit, the position of the fault satellite just runs to the initial position of the in-orbit backup satellite, and at the moment, impulse is applied to the in-orbit backup satellite once again to enable the in-orbit backup satellite to enter the original orbit from the transition orbit, so that the fault satellite can be replaced, as shown in fig. 9.
According to the orbit maneuver model, a mathematical model for replacing a fault satellite by an on-orbit backup satellite can be obtained, wherein the speed of the on-orbit backup satellite on an original orbit is v1Velocity v at the point of transition on the transition track2Since two passes of the track change, the total energy Δ V required for the replacement is twice the velocity increment:
ΔV＝2|v2-v1| (11)
where μ is the earth's gravitational constant.
In the replacement process of the orbit backup satellite, the number of running circles of the orbit backup satellite on the transition orbit is n, the number of running circles of the fault satellite position on the original orbit is m, and if the number of running circles is less than 1, the number of running circles is 0. The time required for the on-orbit backup star to complete replacement is Δ T, and then:
and analyzing the replacement results of the on-orbit backup satellites on 8 working satellites on the same orbit plane by taking the minimum speed increment required when the on-orbit backup satellites replace the fault satellites as an optimization target. Because each orbit surface in the middle orbit Walker navigation constellation is respectively provided with two on-orbit backup satellites, the minimum speed increment required when different fault satellites are replaced in each orbit surface can be obtained according to the replacement results of the two on-orbit backup satellites. The model objective function is:
F＝min(ΔVx,y,z),x∈(1,2,3),y∈(1,2),z∈(1,2,...8) (14)
in the formula,. DELTA.Vx,y,zThe on-orbit backup star numbered y replaces the speed increment required for the failed satellite numbered z for the x-th orbital plane.
Model constraint conditions: and simultaneously, aiming at the practical situation, the number of turns n of the orbit backup satellite running on the transition orbit and the number of turns m of the fault satellite running on the original orbit are both less than or equal to 10.
Finally, the result of the optimization design with the minimum velocity increment as the optimization target is shown in fig. 10, (a) of fig. 10 is the minimum velocity increment required when different satellites are replaced on each orbital plane, and (b) of fig. 10 is the replacement time corresponding to the replacement scheme. As can be seen from the figure, the maximum value of the speed increment is 0.1062km/s, and the minimum value is 0.015km/s, however, although the speed increment required for the replacement is small, the time required for the replacement is long, the shortest replacement time requires 126.4 hours, and the longest replacement time requires 134.5 hours.
And in addition, the minimum replacement time required when the on-orbit backup satellite replaces the fault satellite is taken as an optimization target, and the optimization results of 8 working satellites in the on-orbit backup satellite replacement orbit plane are analyzed again. And comparing the replacement results of the two in-orbit backup satellites in each orbital plane to obtain the minimum replacement time required by replacing different fault satellites in each orbital plane. The model objective function is:
F＝min(ΔTx,y,z),x∈(1,2,3),y∈(1,2),z∈(1,2,...8) (15)
in the formula,. DELTA.Tx,y,zThe replacement time required to replace the failed satellite numbered z for the on-orbit backup satellite numbered y in the x-th orbital plane.
Model constraint conditions: and when the phase of the on-orbit backup satellite advances, the high-orbit phase transformation is adopted, and when the phase lags, the low-orbit phase transformation is adopted, and meanwhile, the number of turns n of the on-orbit backup satellite running on the transition orbit and the number of turns m of the fault satellite running on the original orbit are less than or equal to 10.
Finally, the result of the optimization design with the minimum replacement time as the optimization goal is shown in fig. 11, (a) of fig. 11 is the minimum replacement time required when different satellites are replaced on each orbital plane, and (b) of fig. 11 is the corresponding replacement speed increment of the replacement scheme. As can be seen from the figure, when the minimum replacement time is taken as an optimization target, the minimum time required for replacing the satellite is 8.8 hours, and the maximum replacement time is 18.5 hours, so that the time required for replacing is greatly shortened. Meanwhile, although the speed increment required for replacement is larger than that when the minimum speed increment is taken as an optimization target, the maximum value of the speed increment is 1.16km/s, and the minimum value is 0.14km/s, which is still at a lower level.
Based on the above analysis of the two alternatives, it is possible to obtain an orbital maneuver solution with minimum speed increment as the optimization goal, although less energy is required, but the time required for the replacement is longer, which is suitable for the constellation mainly considering energy saving, and which is not very suitable for the navigation constellation requiring fast service performance recovery. The longest replacement time and the shortest replacement time of the orbital maneuver scheme with the minimum replacement time as the optimization target are respectively reduced by 86.25 percent and 93.04 percent, so the scheme can greatly reduce the replacement time, meanwhile, the speed increment is increased compared with the replacement scheme with the minimum replacement time as the optimization target, the maximum value of the speed increment of the single maneuver of the backup satellite is 0.58km/s, the minimum value of the speed increment of the single maneuver of the backup satellite is 0.07km/s, and the value of the speed increment is still kept at a lower level for the orbital maneuver of the satellite, so the two replacement schemes are combined, and the replacement scheme with the minimum replacement time as the optimization target is selected as the final scheme for the replacement of the on-orbit backup satellite.
Although the present application has been described with reference to a few embodiments, it should be understood that various changes, substitutions and alterations can be made herein without departing from the spirit and scope of the application as defined by the appended claims.
Claims (9)
1. An on-orbit backup scheme optimization design method for a navigation constellation is characterized by comprising the following steps:
determining an optimization variable, an objective function and a constraint condition of a track position optimization model of the on-track backup satellite according to the parameters of the navigation constellation;
based on the track position optimization model of the on-track backup satellite, obtaining the optimal track position of the on-track backup satellite by using a multi-objective optimization algorithm;
and determining a replacement optimization model for replacing the fault satellite by the on-orbit backup satellite by combining the optimal orbit position of the on-orbit backup satellite, and determining an optimal replacement method according to the replacement optimization model.
2. The optimal design method for the on-orbit backup scheme of the navigation constellation according to claim 1, wherein the optimization variables, the objective function and the constraint conditions of the on-orbit backup star orbit bit optimization model are determined according to the parameters of the navigation constellation, and specifically comprise:
taking the track position of the on-track backup star on each track surface as an optimization variable of the track position optimization model;
determining an objective function of the rail position optimization model according to the precision attenuation factor value of the constellation position and the number of visible satellites in a set elevation angle range;
and taking the track position angle of the on-track backup star as a constraint condition of the track position optimization model.
3. The optimal design method for the on-orbit backup scheme of the navigation constellation according to claim 2, wherein the orbit bits of the on-orbit backup star on each orbit surface are represented in a coding form, and the coding adopts floating point number coding.
4. The method for optimally designing the on-orbit backup scheme of the navigation constellation according to claim 2, wherein the objective function of the orbit optimization model determined according to the precision attenuation factor value of the constellation position and the number of visible satellites in the set elevation angle range is specifically as follows:
carrying out grid division on the service area of the navigation constellation by adopting a grid analysis method;
acquiring the constellation position precision attenuation factor values and the number of visible satellites of all grid points at each moment;
acquiring an average value of the constellation position precision attenuation factor values and an average value of the number of visible satellites in a set simulation time period;
and determining an objective function of the orbit optimization model according to the average value of the precision attenuation factor values of the constellation positions and the average value of the number of the visible satellites.
5. The optimal design method for the on-orbit backup scheme of the navigation constellation according to claim 1, wherein the optimal orbit position of the on-orbit backup star is obtained by using a multi-objective optimization algorithm based on the on-orbit backup star-orbit position optimization model, and specifically comprises the following steps:
and obtaining the optimal track position of the on-orbit backup star by using a non-dominated sorting genetic algorithm based on the on-orbit backup star track position optimization model.
6. The optimal design method for the on-orbit backup scheme of the navigation constellation according to claim 1, wherein a replacement optimization model for replacing the failed satellite by the on-orbit backup satellite is determined in combination with the optimal orbit position of the on-orbit backup satellite, and an optimal replacement method is determined according to the replacement optimization model, specifically:
determining a replacement mode of the in-orbit backup satellite according to the relationship between the phase of the fault satellite and the phase of the in-orbit backup satellite; the replacement mode comprises a phase lead replacement and a phase lag replacement;
and determining an objective function and constraint conditions of the replacement optimization model by combining the replacement mode to obtain a replacement optimization model for replacing the fault satellite by the on-orbit backup satellite, and determining an optimal replacement method according to the replacement optimization model.
7. The optimal design method for the navigation constellation in-orbit backup scheme according to claim 6, wherein an objective function and a constraint condition of a replacement optimization model are determined in combination with the replacement mode to obtain a replacement optimization model for replacing a failed satellite with an in-orbit backup satellite, and an optimal replacement method is determined according to the replacement optimization model, specifically:
determining a semi-major axis of a transition orbit when the on-orbit backup satellite replaces the fault satellite according to the replacement mode;
determining an objective function and constraint conditions of a replacement optimization model by combining the semi-major axis of the transition orbit to obtain a replacement optimization model for replacing the fault satellite by the on-orbit backup satellite;
and determining an optimal replacement method based on the replacement optimization model.
8. The optimal design method for the on-orbit backup scheme of the navigation constellation according to claim 7, wherein the objective function of the replacement optimization model is the minimum speed increment or the minimum replacement time when the on-orbit backup satellite replaces the failed satellite, which is determined by combining the semimajor axis of the transition orbit.
9. The optimal design method for the on-orbit backup scheme of the navigation constellation according to claim 7, wherein the constraint conditions of the replacement optimization model are a semi-major axis of the transition orbit, the number of turns of the on-orbit backup satellite running on the transition orbit and the number of turns of the failure satellite position running on the original orbit.
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| CN117252113A (en) * | 2023-11-17 | 2023-12-19 | 中国人民解放军战略支援部队航天工程大学 | Low-orbit hybrid constellation optimization design method for medium-orbit navigation constellation satellite failure |
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| CN117040607B (en) * | 2023-10-10 | 2024-03-26 | 中国人民解放军战略支援部队航天工程大学 | Design method of low-orbit communication satellite constellation |
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| CN117252113A (en) * | 2023-11-17 | 2023-12-19 | 中国人民解放军战略支援部队航天工程大学 | Low-orbit hybrid constellation optimization design method for medium-orbit navigation constellation satellite failure |
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