CN111783233B - On-orbit backup scheme optimization design method for middle-orbit Walker navigation constellation - Google Patents
On-orbit backup scheme optimization design method for middle-orbit Walker navigation constellation Download PDFInfo
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Abstract
The application discloses an optimization design method of an on-orbit backup scheme of a medium-orbit Walker navigation constellation, which comprises an on-orbit backup satellite orbit position design method and a method for replacing a fault satellite by using an on-orbit backup satellite, and specifically comprises the following steps: determining an orbit position optimization model of an on-orbit backup star according to parameters of a navigation constellation; based on an on-orbit position optimization model of the on-orbit backup star, acquiring the on-orbit position of the on-orbit backup star by utilizing a multi-objective optimization algorithm; and determining a replacement optimization model of the on-orbit backup satellite for replacing the fault satellite by combining the orbit positions of the on-orbit backup satellite, and determining a replacement method according to the replacement optimization model. The application optimizes the on-orbit backup scheme of the navigation constellation, enhances the constellation service performance, and enhances the stability and robustness of the navigation constellation; and simultaneously, in the replacement optimization model, selecting an objective function, and comparing two alternative schemes by taking the speed increment and the replacement time into consideration, so as to obtain an optimal alternative scheme.
Description
Technical Field
The application relates to an optimization design method of an on-orbit backup scheme of a middle-orbit Walker navigation constellation, which comprises an on-orbit backup satellite-orbit position design method and a method for replacing a fault satellite by using an on-orbit backup satellite, 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 navigation constellation generally deploys a plurality of backup satellites in space, and if a satellite in the constellation fails, the satellite is replaced by orbital transfer of the backup satellite. For example, the GPS (Global Positioning System) constellation deploys the backup satellites near the satellite with the highest fault probability to form a 'satellite pair', so that when one satellite fails, the backup satellites can quickly replace the failed satellite in a short time through orbital maneuver, and the influence on users is reduced. The optimal design of the on-orbit backup scheme relates to the service performance of the whole navigation constellation in the operation period, and also relates to the problems of maintenance and utilization of space track resources and the like, so that the on-orbit backup scheme must be reasonably designed.
Disclosure of Invention
The application aims to provide an optimization design method for an on-orbit backup scheme of a middle-orbit Walker navigation constellation, which comprises an on-orbit backup satellite orbit position design method and a method for replacing a fault satellite by using an on-orbit backup satellite. The on-orbit backup scheme of the navigation constellation is optimized, so that the orbit position of the on-orbit backup star is the optimal orbit position, and meanwhile, the constellation service performance and the stability and the robustness of the navigation constellation are enhanced; meanwhile, in the replacement optimization model, the selection of the objective function considers the speed increment and the replacement time, and the two replacement schemes are compared, so that the optimal replacement scheme is obtained. The application selects the alternative proposal taking the minimum time as the objective function, and can realize the replacement of satellites with lower energy in short time.
The application discloses an optimization design method of an on-orbit backup scheme of a middle-orbit Walker navigation constellation, which comprises the following steps:
determining an orbit position optimization model of an on-orbit backup star according to parameters of a navigation constellation;
based on the track position optimization model of the on-orbit backup star, acquiring the track position of the on-orbit backup star by utilizing a multi-objective optimization algorithm;
and determining a replacement optimization model of the on-orbit backup satellite for replacing the fault satellite by combining the orbit position of the on-orbit backup satellite, and determining a replacement method according to the replacement optimization model.
Preferably, the track optimization model of the on-track backup star is determined according to the parameters of the navigation constellation, 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 orbit optimization model according to the constellation position precision attenuation factor value and the number of visible satellites in a set elevation angle range;
and taking the orbit position angle of the on-orbit backup star as a constraint condition of the orbit position optimization model.
Preferably, the track positions of the on-track backup satellites on each track surface are characterized in a code form, and the code adopts floating point number code.
Preferably, the objective function of the orbit optimization model is determined according to the constellation position accuracy attenuation factor value and the number of visible satellites in the set elevation angle range, specifically:
grid dividing the service area of the navigation constellation by adopting a grid analysis method;
acquiring constellation position precision attenuation factor values and visible satellite numbers of all grid points at each moment in a set simulation time;
acquiring an average value of the constellation position accuracy attenuation factor values and an average value of the visible satellite numbers in the service area in a set simulation time period;
and determining an objective function of the orbit optimization model according to the average value of the constellation position accuracy attenuation factor values and the average value of the visible satellite numbers.
Preferably, the objective function is:
wherein F is P (X) is the average value of the constellation position accuracy attenuation factor values, F M (X) is an average of the number of visible satellites.
Preferably, the track position of the on-track backup star is obtained by using a multi-objective optimization algorithm based on the on-track backup star track position optimization model, which specifically comprises:
and obtaining the orbit position of the on-orbit backup star by using a non-dominant sorting genetic algorithm based on the on-orbit backup star orbit position optimization model.
Preferably, in combination with the orbit position of the on-orbit backup satellite, a replacement optimization model of the on-orbit backup satellite for replacing the fault satellite is determined, and a replacement method is determined according to the replacement optimization model, specifically:
determining a replacement mode of the in-orbit backup satellite according to the relation between the phase of the fault satellite and the phase of the in-orbit backup satellite; the substitution pattern includes a phase lead substitution and a phase lag substitution;
and combining the replacement modes, determining an objective function and constraint conditions of the replacement optimization model, obtaining a replacement optimization model of the on-orbit backup satellite replacement fault satellite, and determining a replacement method according to the replacement optimization model.
Preferably, in combination with the replacement mode, determining an objective function and constraint conditions of the replacement optimization model to obtain a replacement optimization model of the on-orbit backup satellite replacement failure satellite, and determining a replacement method according to the replacement optimization model, specifically:
according to the replacement mode, determining a semi-long axis of a transition orbit when the on-orbit backup satellite replaces a fault satellite;
determining an objective function and constraint conditions of the replacement optimization model by combining the semi-long axis of the transition orbit to obtain a replacement optimization model of the on-orbit backup satellite replacement fault 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 minimum replacement time when the on-orbit backup satellite replaces the failed satellite, as determined in connection with the semi-long axis of the transition orbit.
Preferably, the constraint condition of the replacement optimization model is the semi-long axis of the transition orbit, the number of turns of the on-orbit backup satellite on the transition orbit and the number of turns of the fault satellite position on the original orbit
Compared with the prior art, the method for optimally designing the on-orbit backup scheme of the middle orbit Walker navigation constellation has the following beneficial effects: the on-orbit backup scheme of the navigation constellation is optimized, so that the orbit position of the on-orbit backup star is the optimal orbit position, the constellation service performance is enhanced, and the stability and the robustness of the navigation constellation are enhanced.
And determining a replacement scheme in a replacement optimization model of the on-orbit backup satellite for replacing the fault satellite by combining the orbit positions of the on-orbit backup satellite, and taking the speed increment and the replacement time into consideration for selecting an objective function. In the embodiment of the application, the alternative scheme taking the minimum time as the objective function is finally selected, and the replacement of the satellite can be completed with lower energy in a short time by taking the objective function as the alternative scheme, thereby providing a reference for the construction of the backup satellite of the navigation constellation.
Drawings
FIG. 1 is a flow chart of an optimization design method of an on-orbit backup scheme of a middle orbit Walker navigation constellation;
FIG. 2 is a diagram showing chromosome coding according to an embodiment of the present application;
FIG. 3 is a flowchart of NSGA-II algorithm in the present application;
FIG. 4 is an on-orbit backup star-orbit optimization result;
FIG. 5 is a schematic diagram of an on-track backup star point;
fig. 6 is a constellation PDOP value comparison;
FIG. 7 is a constellation visible satellite number comparison;
FIG. 8 is a phase advance substitution schematic;
FIG. 9 is a phase lag replacement schematic;
FIG. 10 is an optimization design result with minimum speed increment as an optimization target;
fig. 11 is an optimization design result with the minimum replacement time as an optimization target.
Detailed Description
In order to make the objects, technical solutions and advantageous effects of the present application more apparent, the present application will be further described in detail with reference to the accompanying drawings and examples. It should be noted that the specific embodiments described herein are for purposes of illustration only and are not intended to limit the scope of the application.
Fig. 1 is a flowchart of an optimization design method of an on-orbit backup scheme of a track Walker navigation constellation in the application.
The application discloses an optimization design method of an on-orbit backup scheme of a middle-orbit Walker navigation constellation, which comprises the following steps:
step 1, determining an orbit position optimization model of an on-orbit backup star according to parameters of a navigation constellation, wherein the model specifically comprises the following steps:
taking the track position of the on-track backup star on each track surface as an optimization variable of a track position optimization model; the track positions of the on-orbit backup satellites on each track surface are characterized in a coding form, and the coding adopts floating point number coding;
the objective function of the orbit optimization model determined according to the constellation position precision attenuation factor value and the number of visible satellites in the set elevation angle range is specifically:
grid dividing the service area of the navigation constellation by adopting a grid analysis method;
acquiring constellation position precision attenuation factor values and visible satellite numbers of all grid points at each moment in a set simulation time period;
acquiring an average value of the constellation position accuracy attenuation factor values and an average value of the visible satellite numbers in a service area in a set simulation time period;
determining an objective function of the orbit optimization model based on an average of the constellation position accuracy degradation factor values and an average of the number of visible satellites, wherein the objective function is preferablyWherein F is P (X) is the average value of the constellation position accuracy attenuation factor values, F M (X) is the average of the number of visible satellites; f (F) P (X) and F M (X) is a formal symbol, and X has no particular meaning.
And taking the orbit position angle of the on-orbit backup star as a constraint condition of an orbit position optimization model.
Step 2, based on an on-orbit backup star orbit position optimization model, acquiring an on-orbit backup star orbit position by utilizing a multi-objective optimization algorithm, wherein the determined orbit position is an optimal orbit position of the on-orbit backup star, and specifically comprises the following steps:
based on the on-orbit backup star orbit optimization model, the optimal orbit of the on-orbit backup star is obtained by using a non-dominant ordering genetic algorithm.
Step 3, combining the orbit positions of the on-orbit backup satellites, determining a replacement optimization model of the on-orbit backup satellites for replacing the fault satellites, and determining a replacement method according to the replacement optimization model, wherein the determined replacement method is an optimal replacement method and specifically comprises the following steps:
determining a replacement mode of the in-orbit backup satellite according to the relation between the phase of the fault satellite and the phase of the in-orbit backup satellite; the substitution pattern includes a phase lead substitution and a phase lag substitution;
combining the replacement modes, determining an objective function and constraint conditions of the replacement optimization model, and obtaining a replacement optimization model of the on-orbit backup satellite replacement fault satellite, wherein an optimal replacement method is determined according to the replacement optimization model, and specifically comprises the following steps:
according to the replacement mode, determining a semi-long axis of a transition orbit when the on-orbit backup satellite replaces a fault satellite;
determining an objective function and constraint conditions of the replacement optimization model by combining a semi-long axis of the transition orbit to obtain a replacement optimization model of the on-orbit backup satellite replacement fault satellite; the objective function of the replacement optimization model is the minimum speed increment or minimum replacement time when the on-orbit backup satellite is used for replacing the fault satellite, which is determined by combining with the semi-long axis of the transition orbit; the constraint conditions of the replacement optimization model are the semi-long axis of the transition orbit, the number of turns of the on-orbit backup satellite on the transition orbit and the number of turns of the fault satellite position on the original orbit.
And determining an optimal replacement method based on the replacement optimization model.
The present application will be described in detail with reference to specific examples.
According to the method, the condition that the in-orbit backup satellite and the working satellite provide service jointly during the constellation operation is considered, an in-orbit backup satellite orbit optimization model is established, a constellation position precision attenuation factor (PDOP) value and the number of visible satellites are selected as an orbit optimization objective function, and the influence of the in-orbit backup satellite on the service performance of the system under different orbits is analyzed by using an NSGA-II algorithm;
for example, in the embodiment of the application, a middle orbit Walker navigation constellation is taken 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 degrees, and simultaneously, two on-orbit backup satellites are respectively deployed on each orbit surface in the model:
(1) Optimizing variables
In the on-orbit backup star-orbit position optimization design, the model optimization variable is the orbit position f of the on-orbit backup star on each orbit surface i,j Where i e (1, 2, 3), j e (1, 2), i is the track plane number, and j is the on-track backup star number. E.g. f 1,2 The 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, positioning accuracy is an important index for performance evaluation, and the index is also related to geometric configuration of the constellation besides being influenced by each pseudo-range measurement value, and the configuration can be quantitatively evaluated by calculating a constellation position accuracy attenuation factor (PDOP) value. Therefore, the application selects the PDOP value as one of evaluation indexes of the backup star rail position optimization, and calculates as follows:
suppose that the user coordinates are (X 0 ,Y 0 ,Z 0 ) At this time, in the user local coordinate system, N satellite coordinates satisfying the minimum observation elevation angle α may be expressed as:
r i ＝[X i ,Y i ,Z i ],(i＝1,2,...,N) (1)
the corresponding coefficient matrix H is:
in the method, in the process of the application,(i=1, 2,., N) is the distance between the satellite and the user. The matrix Q is:
the PDOP values for the end user coordinates are:
meanwhile, the application also selects the number of the visible satellites as an evaluation index of the optimization of the other backup satellite orbit position. The number of visible satellites refers to the number of satellites which can receive satellite navigation signals in a certain elevation angle range, and the value of the number of satellites determines the accuracy of a precision factor calculation result, so that the number of satellites is an important index for measuring the performance of a navigation constellation.
To more fully evaluate the performance of navigation constellation service areasThe application adopts a grid analysis method to grid-divide the service area of the navigation constellation, counts the PDOP values and the visible satellite numbers of all grid points at each moment, finally obtains the average value of the PDOP values and the visible satellite numbers of the service area in the simulation time, and uses F respectively P (X) and F M (X) represents. The mathematical model of the on-orbit backup star-orbit position optimization design of the navigation constellation is as follows:
(3) Constraint conditions
In the optimization design of the on-orbit backup star orbit position, the constraint condition of the model is the orbit position f of the on-orbit backup star i,j ∈[0°,360°]Meanwhile, due to the existence of working satellites, the orbit position of the on-orbit backup satellite cannot be valued as the orbit position of the existing working satellite in the same orbit plane.
After each parameter of the model is determined, the optimal track position of the on-track backup star is obtained by utilizing the multi-objective optimization design of the NSGA-II algorithm.
(1) Coding mode of track position optimization variable
The on-orbit backup star-orbit optimization variable belongs to a continuous variable, and to solve the variable by using an NSGA-II algorithm, the optimization variable must be encoded. Variable coding has various coding modes, wherein the most widely applied coding mode is a binary coding mode, however, when the value range of a model optimization variable is larger, in order to ensure that the optimization variable has higher precision, the number of binary character string bits needs to be increased, which can cause overlong chromosome genes, thereby reducing the searching efficiency and influencing the convergence rate of an algorithm. Therefore, the application adopts a floating point number coding method, each gene in the chromosome represents a variable, and the coding method can effectively reduce the coding length of the chromosome, improve the operation efficiency and ensure that the variable has higher precision. After each variable is encoded, they are concatenated into one chromosome, thus completing the encoding of one individual, as shown in fig. 2.
(2) Pareto-based dominant selection mechanism
Unlike the single-objective optimization problem, since it is difficult to obtain an ideal solution that enables all objective functions to reach an optimal value during the solution, further optimization of one objective typically results in degradation of the other objective, and thus the optimal solution of the multi-objective optimization problem is a set of optimal solutions. A large number of scholars develop researches on solving the multi-objective optimization problem and put forward corresponding solving ideas, wherein the application of the method is a optimization method based on the Pareto dominant idea.
Assuming that the multi-objective optimization is to solve for the minimum of the objective function, if a solution x is possible 1 Any corresponding objective function value f k (x 1 ) Are all less than or equal to the feasible solution x 2 Corresponding objective function value f k (x 2 ) And there is an objective function value f l (x 1 ) Less than x 2 Corresponding objective function value f l (x 2 ) Then call feasible solution x 1 Compared with x 2 Take over or x 1 Dominant x 2 ：
If the feasible solution x is not dominated by any other solution, the feasible solution is called a non-dominated solution, all non-dominated solutions can be obtained through iterative evolution of an algorithm, and a non-dominated solution set is called Pareto front. A Pareto dominant selection mechanism is adopted in an NSGA-II algorithm to obtain a Pareto front, and the formula is as follows:
wherein mu is i,g As test vector, X i,g Is the target vector.
(3) Optimization flow of NSGA-II algorithm
The non-dominant ranking genetic algorithm (NSGA) is a multi-objective optimization algorithm based on Pareto preferences proposed by Srinivas and Deb in 1994. On the basis, deb et al further proposed an improved algorithm NSGA-II of NSGA in 2002, the advantages of the algorithm over the previous generation algorithm are mainly that the NSGA-II algorithm adopts a rapid non-dominant sorting method, so that complexity of searching non-dominant solutions is reduced, crowding distances are defined to calculate crowding degrees among midpoints of all layers, the use of sharing functions in the NSGA algorithm is replaced, the influence of artificial determination of sharing parameters on solution space distribution is avoided, diversity of a population is maintained, an elite strategy is introduced, non-dominant sequences are determined by layering solution spaces, superiority of solutions in the population is reserved, and sampling space is enlarged. The NSGA-II algorithm mainly comprises the steps of initialization, selection, crossing, mutation and the like, and the specific flow is shown in figure 3.
And optimally designing the on-orbit backup star rail position according to the model and the optimization algorithm, wherein the service area of the middle orbit Walker navigation constellation is a global area, and the service area is meshed according to the longitude and latitude lines 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 600s. The initial parameters of the optimization algorithm are: the population number N is 50, the maximum evolution algebra G is 50, the crossover factor is 1, and the mutation factor is 0.16. And the on-orbit backup star-orbit optimization result is shown as 4.
As can be obtained from fig. 4, the interval corresponding to the number of satellites in the optimal solution set obtained by the algorithm iteration is [10.3303, 10.3306], and the interval corresponding to the PDOP value is [1.665,1.695]. Meanwhile, for different solutions in the optimized solution set, the variation range of the visible satellite number is smaller, and in the small range, the PDOP values corresponding to the different solutions show a trend of increasing along with the increase of the visible satellite number. Finally, the non-dominant solution set, pareto class 1 in fig. 4, is screened out of the optimized solution set and arranged in ascending order according to PDOP values, as shown in table 1.
TABLE 1
Since the range of variation of the visible satellite number is small as available from the non-dominant solution set in table 1, the present application selects the solution with the smallest PDOP value in the non-dominant solution set as the optimal solution for the optimization result analysis. An on-orbit backup satellite orbit diagram of the optimal solution is shown in fig. 5, in fig. 5 (b), M11 represents a satellite numbered 1 on the 1 st orbit plane, and the other is the same.
And comparing and analyzing the navigation constellation of the orbital Walker in the global area, the PDOP value of the constellation added with the on-orbit backup satellite and the number of visible satellites according to the on-orbit backup satellite orbit position of the optimal solution, as shown in fig. 6 and 7. It can be seen that the orbital Walker navigation constellation in the global area has a maximum PDOP value of 1.8889, a minimum PDOP value of 1.8759, and an average PDOP value of 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, and the reduction amplitude is 11.4%; the average PDOP value was reduced to 1.6697 by 11.3%. Similarly, for the constellation visible satellite number, the middle orbit Walker navigation constellation has a maximum value of 8.2845, a minimum value of 8.2476, and an average value of 8.2642. The maximum value of the number of visible satellites is increased to 10.3529 after the in-orbit backup satellites are added, 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 increased 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, a corresponding on-orbit backup satellite replacement orbit maneuver model, namely a replacement optimization model, is established according to the relationship between the fault satellite phase and the on-orbit backup satellite phase, and the on-orbit backup satellite replacement scheme is analyzed and compared by taking the minimum speed increment and the minimum replacement time as optimization targets, so that a final on-orbit backup satellite replacement scheme is obtained;
for a detailed description of the method of the present application for replacing an on-orbit backup satellite with a failed satellite, the present application is described in terms of specific embodiments.
The satellite phase adjustment method can be divided into common-track phase adjustment and differential-track phase adjustment according to whether the satellite phase adjustment process involves the change of the track surface or not. Because of the large fuel consumption of out-of-plane orbit adjustment, on-orbit backup satellites typically replace only failed satellites within the same orbit plane. According to the relationship between the fault satellite phase and the on-orbit backup satellite phase, the replacement of the backup satellite common orbit surface can be divided into two situations of phase advance and phase lag.
(1) Phase advance
When the phase is advanced, the earth angle theta epsilon [180 DEG, 360 DEG ] between the on-orbit backup satellite and the fault satellite along the running direction. At this time, the on-orbit backup star can enter the high-orbit transition elliptic orbit by lifting the orbit height and applying impulse once at the initial position, and the semi-major axis a of the transition orbit needs to satisfy:
a 0 ＜a (7)
wherein a is 0 Is the original track semi-long axis.
After the on-orbit backup satellite runs on the transition orbit for a plurality of circles, the position of the fault satellite just runs to the initial position of the on-orbit backup satellite, at the moment, impulse is applied to the on-orbit backup satellite once again, so that the on-orbit backup satellite enters the original orbit from the transition orbit, and the replacement of the fault satellite can be completed, as shown in fig. 8.
(2) Phase lag
With phase lag, the earth 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-track backup star can enter the low-track transition elliptical track by reducing the track height and applying impulse once at the initial position, and the semi-major axis a of the transition track needs to satisfy:
wherein a is 0 R is the earth radius, which is the original orbit semi-major axis.
After the on-orbit backup satellite runs on the transition orbit for a plurality of circles, the position of the fault satellite just runs to the initial position of the on-orbit backup satellite, at the moment, impulse is applied to the on-orbit backup satellite once again, so that the on-orbit backup satellite enters the original orbit from the transition orbit, and the replacement of the fault satellite can be completed, as shown in fig. 9.
According to the orbit maneuver model, a mathematical model of the on-orbit backup satellite replacing the fault satellite can be obtained, wherein the on-orbit backup satellite is on the original orbitIs v 1 A speed v at the transition point on the transition track 2 Since two changes of track are made, the total energy Δv required for replacement is twice the speed increase:
ΔV＝2|v 2 -v 1 | (11)
where μ is the gravitational constant.
In the process of replacing the in-orbit backup satellite, the number of turns of the in-orbit backup satellite on the transition orbit is assumed to be n, the number of turns of the fault satellite on the original orbit is assumed to be m, and if the number of turns is less than 1, the number of turns is assumed to be 0. The time required for the on-track backup star to complete replacement is Δt, then there are:
and analyzing the replacement results of each on-orbit backup satellite on 8 working satellites on the same orbit surface by taking the minimum speed increment required by the on-orbit backup satellite to replace the fault satellite as an optimization target. Because two on-orbit backup satellites are respectively deployed on each orbit surface in the middle orbit Walker navigation constellation, the minimum speed increment required by replacing different fault satellites in each orbit surface can be obtained according to the replacement result of the two on-orbit backup satellites. The model objective function is:
F＝min(ΔV x,y,z ),x∈(1,2,3),y∈(1,2),z∈(1,2,...8) (14)
in the formula DeltaV x,y,z In the x-th track plane, the number y isThe orbital backup satellite replaces the speed increment required by the failed satellite numbered z.
Model constraint: the high-orbit phase change is adopted when the phase of the in-orbit backup star advances, the low-orbit phase change is adopted when the phase of the in-orbit backup star retards, and meanwhile, for practical situations, the number of turns n of the in-orbit backup star running on a transition orbit and the number of turns m of a fault satellite position running on an original orbit are assumed to be less than or equal to 10.
Finally, as shown in fig. 10, the result of the optimization design with the minimum speed increment as the optimization target is that (a) of fig. 10 is the minimum speed increment required for replacing different satellites on each track surface, 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 replacement is smaller, the time required for replacement is longer, 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 by the on-orbit backup satellite for replacing 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 two on-orbit backup satellites in each track plane, thereby obtaining the minimum replacement time required by replacing different fault satellites in each track plane. The model objective function is:
F＝min(ΔT x,y,z ),x∈(1,2,3),y∈(1,2),z∈(1,2,...8) (15)
in the formula DeltaT x,y,z The replacement time required for an on-orbit backup satellite numbered y to replace a failed satellite numbered z in the x-th orbital plane.
Model constraint: the high-orbit phase change is adopted when the phase of the on-orbit backup star advances, the low-orbit phase change is adopted when the phase of the on-orbit backup star delays, and meanwhile, the number of turns n of the on-orbit backup star on the transition orbit and the number of turns m of the fault satellite position on the original orbit are smaller than or equal to 10.
Finally, as shown in fig. 11, the result of the optimization design with the minimum replacement time as the optimization target is that (a) of fig. 11 is the minimum replacement time required for replacing different satellites on each track surface, and (b) of fig. 11 is the replacement speed increment corresponding to 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 replacement 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, the minimum value is 0.14km/s, and the speed increment is still at a lower level.
Based on the analysis of the two alternatives described above, a orbital maneuver with minimum speed increase as the optimization objective is available, which, although requiring less energy, requires a longer time for replacement, is suitable for constellations that mainly take into account energy savings, which is not very suitable for navigation constellations that require a fast restoration of service performance. The maximum replacement time and the minimum replacement time of the orbital maneuver scheme taking the minimum replacement time as an optimization target are respectively reduced by 86.25 percent and 93.04 percent, so that the scheme can greatly reduce the replacement time, meanwhile, the speed increment is increased compared with the alternative scheme taking the minimum speed increment as the optimization target, the maximum value of the speed increment of single maneuver of the backup star is 0.58km/s, the minimum value of the speed increment of single maneuver of the backup star is 0.07km/s, and the value of the single maneuver of the backup star is still kept at a lower level for satellite orbital maneuver, and therefore, the two alternative schemes are combined, and the alternative scheme taking the minimum replacement time as the optimization target is selected as the final scheme of on-orbit backup star replacement.
While the application has been described in terms of preferred embodiments, it will be understood by those skilled in the art that various changes and modifications can be made without departing from the scope of the application, and it is intended that the application is not limited to the specific embodiments disclosed.
Claims (7)
1. An optimization design method for an on-orbit backup scheme of a middle orbit Walker navigation constellation is characterized by comprising the following steps:
determining an orbit position optimization model of an on-orbit backup star according to parameters of a navigation constellation;
based on the track position optimization model of the on-orbit backup star, acquiring the track position of the on-orbit backup star by utilizing a multi-objective optimization algorithm;
combining the orbit positions of the on-orbit backup satellites, determining a replacement optimization model of the on-orbit backup satellites for replacing the fault satellites, and determining a replacement method according to the replacement optimization model; wherein,,
the determining the orbit position optimization model of the on-orbit backup star according to the parameters of the navigation constellation 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 positions of the on-orbit backup satellites on each track surface are characterized in a coding form, and the coding adopts floating point number coding;
determining an objective function of the orbit optimization model according to the constellation position precision attenuation factor value and the number of visible satellites in a set elevation angle range, wherein the objective function specifically comprises the following steps:
grid dividing the service area of the navigation constellation by adopting a grid analysis method;
acquiring constellation position precision attenuation factor values and visible satellite numbers of all grid points at each moment in a set simulation time;
acquiring an average value of the constellation position accuracy attenuation factor values and an average value of the visible satellite numbers in the service area in a set simulation time period;
determining an objective function of the orbit optimization model according to the average value of the constellation position accuracy attenuation factor values and the average value of the visible satellite numbers;
taking the orbit position angle of the on-orbit backup star as a constraint condition of the orbit position optimization model;
the method for determining the replacement optimization model of the on-orbit backup satellite to replace the fault satellite according to the replacement optimization model comprises the following steps of: based on the optimization result of the orbit position of the on-orbit backup satellite, a corresponding on-orbit backup satellite replacement orbit maneuver model, namely a replacement optimization model, is established according to the relationship between the fault satellite phase and the on-orbit backup satellite phase, and the on-orbit backup satellite replacement scheme is analyzed and compared by taking the minimum speed increment and the minimum replacement time as optimization targets, so that the final on-orbit backup satellite replacement scheme is obtained.
2. The method for optimally designing an on-orbit backup scheme for a middle orbit Walker navigation constellation according to claim 1, wherein the objective function is:
in the method, in the process of the application,for the average value of the constellation position accuracy attenuation factor values, +.>Is the average of the number of satellites in view.
3. The optimization design method of the on-orbit backup scheme of the middle orbit Walker navigation constellation according to any one of claims 1-2, wherein the on-orbit backup star orbit optimization model is based on, and the on-orbit backup star orbit is obtained by using a multi-objective optimization algorithm, specifically:
and obtaining the orbit position of the on-orbit backup star by using a non-dominant sorting genetic algorithm based on the on-orbit backup star orbit position optimization model.
4. The optimization design method for the on-orbit backup scheme of the medium-orbit Walker navigation constellation according to claim 3, wherein the method is characterized in that a replacement optimization model for replacing a fault satellite by the on-orbit backup satellite is determined by combining the orbit positions of the on-orbit backup satellites, and the replacement method is determined according to the replacement optimization model and specifically comprises the following steps:
determining a replacement mode of the on-orbit backup satellite according to the relation between the phase of the fault satellite and the phase of the on-orbit backup satellite; the substitution pattern includes a phase lead substitution and a phase lag substitution;
and combining the replacement modes, determining an objective function and constraint conditions of the replacement optimization model, obtaining a replacement optimization model of the on-orbit backup satellite replacement fault satellite, and determining a replacement method according to the replacement optimization model.
5. The optimization design method for the on-orbit backup scheme of the medium-orbit Walker navigation constellation according to claim 4, wherein the objective function and constraint conditions of the replacement optimization model are determined in combination with the replacement mode, so as to obtain a replacement optimization model of the on-orbit backup satellite for replacing the failed satellite, and the replacement method is determined according to the replacement optimization model, specifically:
according to the replacement mode, determining a semi-long axis of a transition orbit when the on-orbit backup satellite replaces a fault satellite;
determining an objective function and constraint conditions of the replacement optimization model by combining the semi-long axis of the transition orbit to obtain a replacement optimization model of the on-orbit backup satellite replacement fault satellite;
and determining an optimal replacement method based on the replacement optimization model.
6. The optimal design method for the on-orbit backup scheme of the middle orbit Walker navigation constellation according to claim 5, wherein the objective function of the replacement optimization model is a minimum speed increment or minimum replacement time when the on-orbit backup satellite replaces the failed satellite determined in combination with the semi-long axis of the transition orbit.
7. The optimal design method for the on-orbit backup scheme of the middle-orbit Walker navigation constellation according to claim 5, wherein the constraint conditions of the replacement optimization model are the semi-long 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 failed satellite position running on the original orbit.
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