CN116070528B - Heterogeneous low-orbit navigation constellation design optimization method and system - Google Patents
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Abstract
The invention discloses a heterogeneous low-orbit navigation constellation design optimization method and system, comprising the following steps: step S1: setting track height and track surface number, and calculating a track inclination angle of the first sub-constellation according to the minimum observation elevation angle at the pole; step S2: calculating the track inclination angle of the second sub-constellation according to the minimum geometric accuracy dilution factor criterion; step S3: the number of sub-constellations and the phase factor values of adjacent satellites on adjacent track surfaces are arranged and combined to form a sample set; step S4: based on the sample set, calculating satellite coverage layer numbers and position accuracy dilution factors of different sub-constellation configurations, performing primary optimization on the satellite coverage layer numbers and the position accuracy dilution factors through an NSGA-II algorithm, and screening all sub-constellation configurations meeting a first constraint condition; step S5: and carrying out secondary optimization on the selected sub-constellation configuration based on a genetic algorithm, finding out the sub-constellation configuration with the minimum satellite number as the optimal constellation configuration, and determining a constellation design scheme.
Description
Technical Field
The invention relates to the field of satellite constellation design, in particular to a heterogeneous low-orbit navigation constellation design optimization method and system.
Background
With the increasing importance of various countries in the satellite navigation field, the development of the satellite navigation system is more and more vigorous. However, since navigation satellites are susceptible to interference and shielding, backup means are actively studied in various countries to make up for the shortage of global satellite navigation systems (Global Navigation Satellite System, GNSS) in positioning. Among them, the low-rail-opportunistic signal-based positioning is a very effective auxiliary method. In studying the positioning algorithm of the low-rail opportunistic signal, a reliable cooperative constellation is first required. However, there is no established constellation at home, and many pieces of information of the existing constellation are difficult to obtain, so it is a very important link to establish a reliable cooperative constellation.
In the process of constructing a low orbit navigation constellation, the factors such as the number of satellites, orbit height, orbit inclination angle and constellation configuration need to be comprehensively considered. However, the performance index and the transmission cost are often restricted, for example, as the number of satellites and the orbit height are increased, the navigation performance is improved, and higher transmission cost is also often brought. It is therefore necessary to find an optimal solution under given conditions by means of an optimization algorithm.
The low-orbit constellation optimization design is used as a current research hot spot, and attracts the eyes of many scholars. According to the prior literature, constellation optimization design technology based on various optimization algorithms including particle swarm, genetic, simulated annealing and the like exists.
The mixed constellation optimization design method based on the improved particle swarm algorithm is relatively simple to realize, but the particle swarm algorithm is not a good choice for the discrete problems of constellation optimization design, and in addition, the mixed constellation formed by combining two different configurations of a low orbit and an elliptical orbit contains relatively more characteristic parameters, so that the computational complexity is improved.
The low orbit navigation constellation configuration optimization design based on the genetic algorithm takes the total number of satellites as a primary target, reduces the orbit number of the satellites as much as possible on the basis, can better promote the constellation coverage layer number and reduce the PDOP value. However, the method is designed only for a constellation with a single configuration, the function is relatively simple, and the considered constraint conditions are not perfect.
The low-orbit communication constellation optimization based on the simulated annealing algorithm is a method designed for a large-scale communication constellation, converts the constellation design problem into a multi-objective optimization problem, takes the coverage duration and the coverage weight as objective functions, mainly focuses on the global coverage capability of the constellation, and does not focus on the navigation performance of the constellation.
The present invention is specifically proposed for the above-mentioned problems, as well as with reference to literature and existing constellation systems of other scholars.
Disclosure of Invention
The invention provides a heterogeneous low-orbit navigation constellation design optimization method and system, which takes a heterogeneous low-orbit navigation constellation consisting of two sub-constellations as a research object, adopts Walker-delta configuration, designs a combination-discretization coding method, focuses on a plurality of key factors such as covering capacity, navigation performance and construction cost of the constellation by combining NSGA-II with a genetic algorithm, optimizes the constellation design step by step, and can reduce the cost of constellation construction while guaranteeing the navigation performance in the global scope.
The invention adopts the technical scheme that: a heterogeneous low-orbit navigation constellation design optimization method, the heterogeneous low-orbit navigation constellation comprising a first sub-constellation and a second sub-constellation, the method comprising the steps of:
step S1: setting track height and track surface number, and calculating the track inclination angle of the first sub-constellation according to the minimum observation elevation angle at the pole;
step S2: calculating the orbital tilt angles of the second sub-constellation under the condition of different satellite numbers according to a minimum geometric accuracy dilution factor criterion;
step S3: the number of sub-constellations and the phase factor values of adjacent satellites on adjacent track surfaces are arranged and combined to form a sample set;
step S4: based on the sample set, calculating satellite coverage layer numbers and position accuracy dilution factors of different sub-constellation configurations, performing primary optimization on the satellite coverage layer numbers and the position accuracy dilution factors through an NSGA-II algorithm, and screening all sub-constellation configurations meeting a first constraint condition;
step S5: and (3) performing secondary optimization on the sub-constellation configurations screened in the step (S4) based on a genetic algorithm, finding out the sub-constellation configuration with the minimum satellite number as an optimal constellation configuration, and determining constellation design schemes of the first sub-constellation and the second sub-constellation.
Further, the first sub-constellation and the second sub-constellation are designed by adopting a Walker-delta configuration.
Further, the step S1 further includes: the orbital altitude is set based on the satellite vision area and the user's lowest observation elevation angle.
Further, the step S1 further includes: and determining the value range of the phase factors of the adjacent satellites on the adjacent track surfaces to be [0 ] and the track surface number to be-1 ] according to the track surface number.
Further, the step S3 further includes: the sample set is binary coded.
Further, the step S5 further includes: and (3) performing secondary coding on the constellation configuration screened in the step (S4), and performing secondary optimization based on the constellation configuration subjected to secondary coding.
Further, the first constraint condition is that the following two conditions are satisfied at the same time:
(1) The average value of satellite coverage layers is more than or equal to 3 between latitude [ -70 degrees and 70 degrees ];
(2) The average value of the dilution factors of the position accuracy is less than or equal to 10.
Further, in the step S1, at different track heights, the minimum observation elevation angle at the pole and the track inclination angle of the first sub-constellation should satisfy:
wherein (1)>
For the minimum observation elevation of the satellite at the pole, < >>
For the orbital tilt of the first sub-constellation,r e for the radius of the earth,has a satellite orbit height, the satellite orbit height,γrepresenting the tangential angle at which the satellite and its visible spherical cap boundary are at that time.
Further, in the step S2, the condition that the geometric dilution factor takes the minimum value is:
wherein,,N j represent the firstjThe total number of satellites in the sub-constellation configuration,Krepresenting the number of sub-constellations +.>
Represents the firstjTrack tilt of sub-constellation configuration.
The invention also provides a heterogeneous low-orbit navigation constellation design optimization system, wherein the heterogeneous low-orbit navigation constellation comprises a first sub-constellation and a second sub-constellation, and the system comprises:
the sub-constellation orbit inclination angle calculation module is used for calculating the orbit inclination angle of the first sub-constellation according to the minimum observation elevation angle at the pole position based on the set orbit height and orbit surface number; calculating the orbital tilt angles of the second sub-constellation under the condition of different satellite numbers according to a minimum geometric accuracy dilution factor criterion;
the sample set construction module is used for arranging and combining the number of sub-constellations and the phase factor values of adjacent satellites on adjacent track surfaces to form a sample set;
the first-level optimization module is used for calculating satellite coverage layer numbers and position accuracy dilution factors of different sub-constellation configurations based on the sample set, carrying out first-level optimization on the satellite coverage layer numbers and the position accuracy dilution factors through an NSGA-II algorithm, and screening all the sub-constellation configurations meeting a first constraint condition;
the secondary optimization module is used for performing secondary optimization on the sub-constellation configurations screened by the primary optimization module based on a genetic algorithm, finding out the sub-constellation configuration with the minimum satellite number as an optimal constellation configuration, and determining constellation design schemes of the first sub-constellation and the second sub-constellation.
The beneficial effects of the invention are as follows:
aiming at the problem of optimal design of heterogeneous low-orbit navigation constellations, the invention specifically analyzes influence factors, takes the number of satellites, the coverage capacity and the navigation capacity which are three key indexes as optimization targets, and proposes a mode of combining NSGA-II with a genetic algorithm to optimize the design of the low-orbit constellations step by step. For an important link in the optimization process, namely coding, a 'combination-discretization' coding method is designed, so that the correlation between characteristic parameters is considered, and the whole optimization process is simplified.
The invention is the application of the optimization algorithm in the field of constellation design, aims at reducing constellation construction cost while ensuring navigation performance, and provides a good idea for subsequent simulation experiments and engineering application.
Drawings
FIG. 1 is a schematic view of a satellite visible spherical cap;
FIG. 2 is a schematic diagram of the relationship between satellite altitude, minimum elevation angle, and coverage;
FIG. 3 is a plot of number of spacecraft versus altitude;
FIG. 4 is a schematic diagram of a range Allen radiation band;
FIG. 5 is a schematic diagram of the relationship between the minimum elevation angle of observation at the pole and the track tilt angle at different track heights;
FIG. 6 is a schematic view of satellite observations at poles;
FIG. 7 is a basic flowchart of a genetic algorithm;
FIG. 8 is a basic flow chart of NSGA-II algorithm;
FIG. 9 is a schematic diagram of a "combined-discretized" encoding process;
FIG. 10 is a schematic diagram of a step-wise optimization process.
Detailed Description
The following description is presented to enable any person skilled in the art to make and use the invention. The preferred embodiments in the following description are by way of example only and other obvious variations will occur to those skilled in the art. The basic principles of the invention defined in the following description may be applied to other embodiments, variations, modifications, equivalents, and other technical solutions without departing from the spirit and scope of the invention.
It will be understood that the terms "a" and "an" should be interpreted as referring to "at least one" or "one or more," i.e., in one embodiment, the number of elements may be one, while in another embodiment, the number of elements may be plural, and the term "a" should not be interpreted as limiting the number.
The terminology used herein is for the purpose of describing various embodiments only and is not intended to be limiting. As used herein, the singular is intended to include the plural as well, unless the context clearly indicates otherwise. It will be further understood that the terms "comprises" and/or "comprising," when used in this specification, specify the presence of stated features, integers, steps, operations, elements, or groups thereof, but do not preclude the presence or addition of one or more other features, integers, steps, operations, elements, or groups thereof.
The specific embodiment of the invention mainly comprises the following parts:
(1) Specifically analyzing influencing factors of constellation design, determining partial parameters, and constructing a determined parameter set;
(2) Calculating the inclination angles corresponding to the sub-constellations of different satellite numbers according to the pole observation requirement and the minimum GDOP criterion;
(3) Interconnecting MATLAB and STK, obtaining satellite cover layer number average values and PDOP average values of certain grid points in different configurations within a 24-hour time range, and screening all configurations meeting certain constraint conditions through NSGA-II algorithm;
(4) And (3) performing secondary coding on the configuration screened in the step (3), searching out the optimal configuration based on a genetic algorithm, and finally determining a constellation design scheme.
The constellation design flow, the minimum GDOP construction criterion and the optimization algorithm will be specifically described one by one.
1. Constellation design flow:
1. constellation design principle
(1) Adopting a mixing configuration to ensure uniform global distribution;
(2) The complexity of the mixing configuration and the number of satellites are reduced as much as possible;
(3) For densely populated areas, at least three satellites are visible at any moment to meet the requirement of independent positioning;
2. influence factor analysis
(1) Constellation configuration
In the existing GNSS system, the main body MEO part adopts Walker-delta configuration, which is beneficial to obtaining good observation effect. The constellation designed by the invention also adopts Walker-delta configuration. Generally adoptN/P/FThe description is made to describe this configuration,Nrepresenting the total number of satellites,Prepresenting the number of track facets of the constellation,F（F∈[0, P-1]) Representing the phase factors of adjacent satellites on adjacent orbit surfaces.
(2) Track height
Fig. 1 shows a schematic view of a satellite visual spherical cap. For low orbit satellites, the impact of orbit height on its coverage is very pronounced, so careful selection of orbit height is required when designing the constellation. Radius of earthr e The satellite orbit height ishSatellite visibility regionCThe lowest elevation angle of the spherical crown edge ground user is as the center
Then according to the sine theorem, the corresponding center-of-gravity half-center angle (also called the visual angle)
Fig. 2 shows the relationship between satellite altitude, minimum elevation angle and coverage.
The satellite height is set to have a range of 500 km-1500 km, and the user's minimum observation elevation angle is set to have a range of 5 DEG-50 deg. As can be seen from fig. 2, the coverage of the satellite is expanding as the orbit height increases. In designing LEO constellation, generally take
。
The choice of orbit altitude also requires consideration of factors such as spacecraft, van allen radiation, ionospheric delay, etc.
1) Spacecraft
Fig. 3 shows a spacecraft number versus altitude profile. As shown in fig. 3, most space vehicles are currently concentrated at a altitude of 500-1000 km in a region of low earth orbit according to SSN statistics. Therefore, for safety reasons, the constellation track height designed herein should be chosen to be above 1000 km.
2) Van Allen radiation
Van Allen radiation band refers to a high-energy particle radiation band near the earth, wherein high-energy particles have extremely strong penetrability and can cause damage to satellites and other devices.
Fig. 4 is a schematic diagram of a range allen radiation band. The latitude range of the Van Allen radiation band is generally considered to be 40-50 degrees in North and south latitude, and the Van Allen radiation band is divided into an inner band and an outer band, wherein the range of the inner band is approximately 1500-5000 km above the ground surface, and the outer band is 13000-20000 km. The above-mentioned areas should be avoided when designing the constellation. Therefore, the orbit height of the low-orbit satellite should not exceed 1500km.
3) Ionospheric delay
The ionosphere is generally located in a space range of about 50km to 1000km from the earth's surface, where a large number of free electrons and ions are present, which can affect the propagation of electromagnetic waves. The low-orbit constellation is considered to be not only used as an auxiliary means for independent positioning, but also can enhance GNSS positioning. In order to play a good role of a "space-based monitoring station" and reduce the bias generated when receiving GNSS signals, it is necessary to set the height of the low-orbit constellation above 1000 km.
(3) Track inclination angle
Fig. 5 shows the relationship between the minimum observed elevation angle at the pole and the track tilt angle at different track heights. The track inclination angle has decisive influence on the uniform distribution of the navigation performance of the LEO constellation, the sub-constellation with low inclination angle can better cover the middle-low latitude area, and the sub-constellation with high inclination angle ensures the navigation effect on the high latitude area, especially the dipolar area. In the two-pole region, under different track heights, the minimum observation elevation angle at the pole and the corresponding track inclination angle should satisfy:
wherein,,r e for the earth radius>
For the inclination angle of the track,has a satellite orbit height, the satellite orbit height,
representing the minimum observation elevation angle of the satellite at the pole, namely, the observation elevation angle near the pole when the satellite runs to the position with the maximum latitude of the point below the satellite;γrepresenting the tangential angle at which the satellite and its visible spherical cap boundary are at that time.
Fig. 6 shows a schematic view of satellite observations at poles. To ensure good visibility at the poles, a minimum observation elevation angle of the satellite at the poles is set
。
2. Minimum GDOP construction criteria
The dilution of precision (Dilution of Precision, DOP) is an important index describing the navigation performance of the constellation, and mainly includes a position dilution of precision (Position Dilution of Precision, PDOP), a geometric dilution of precision (Geometric Dilution of Precision, GDOP), and the like.
The present invention is primarily directed to the optimal design of navigation constellations, and therefore requires minimum geometric dilution of precision (GDOP) criteria based in this process. According to the literature, when the GDOP value of the mass center of the earth is minimum, the distribution of the GDOP of the earth surface is correspondingly uniform.
For a single Walker constellation, the condition for the GDOP to be at its minimum is:
in the method, in the process of the invention,Prepresenting the number of track surfaces to be tracked,nrepresenting the number of satellites per orbital plane, < > j->
Representing the track pitch angle. When->
When the GDOP takes a minimum value.
For the combined Walker constellation, the condition that the GDOP takes the extremum is:
in->
Represents the firstjThe total number of satellites in the Walker configuration,Krepresenting the number of sub-constellations in a heterogeneous constellation, +.>
Represents the firstjThe track inclination angles of the Walker configurations can be obtained by simplifying the following steps:
in the present invention, only the heterogeneous low-orbit navigation constellation design comprising two sub-constellations is studied, i.eKCase=2.
3. Optimization algorithm:
1. genetic algorithm
Genetic algorithm is derived from the species evolution theory of darwiny, i.e. "object bid, survival of the right, and mainly comprises the processes of coding, selection, crossing and mutation. Each chromosome in the genetic algorithm corresponds to a solution to the problem, and the performance of the method can be evaluated by using an adaptability function. The genetic algorithm achieves the purpose of evolution by continuously updating iteration, and finally, the optimal solution is found out from the multi-element problem. The specific flow is shown in fig. 7.
2. Non-dominant ranking genetic algorithm
The Non-dominant ranking genetic algorithm (Non-dominated Sorting Genetic Algorithms, NSGA) is a multi-objective optimization algorithm, which is similar to the genetic algorithm and mainly comprises links of population initialization, crossing, mutation, selection and the like, and is mainly different in that the NSGA layers the dominant relationship of individuals before executing a selection operator. Wherein NSGA-II is an improvement over basic NSGA, and is mainly characterized in the "selection" layer: through rapid non-dominant sequencing and individual crowding degree calculation, the sample diversity is ensured while the calculation complexity is reduced, and an elite selection strategy is introduced, so that the sampling space is enlarged. The NSGA-II algorithm has good application in the multi-objective (mainly two-objective) problem. The specific flow is shown in fig. 8.
4. Description of specific embodiments:
the implementation of the present invention will be described in detail below in connection with specific embodiments.
Because a plurality of parameters are involved in the constellation design, if the parameters are used as isolated characteristic variables in an optimization algorithm, huge calculation complexity is brought, and meanwhile, the correlation between the parameters is ignored. Therefore, the invention firstly analyzes and processes the characteristic parameters related to the constellation design, determines the values of partial parameters according to the actual requirements, and then establishes a set of 'combination-discretization' binary coding mechanism, thereby facilitating the genetic operation of the subsequent algorithm.
1. Data preparation phase
The heterogeneous constellation in the embodiment of the invention comprises two sub-constellations, namely a first sub-constellation and a second sub-constellation, wherein the first sub-constellation and the second sub-constellation are designed by adopting Walker-delta configuration.
Step S1: and setting track height and track surface number, and calculating the track inclination angle of the first sub-constellation according to the minimum observation elevation angle at the pole.
Firstly, selecting the track height according to the analysis of the selection of the track height; in particular, the orbital altitude is set based on the satellite visibility region and the user's lowest observation elevation angle, while taking into account factors such as spacecraft, van allen radiation, ionospheric delay, etc. For example, the track height may be set to 1100km in the present embodiment;
then, according to the minimum observation angle at the pole, calculating the track inclination angle of the first sub-constellation; at different track heights, the minimum observation elevation angle at the pole and the corresponding track inclination angle should satisfy the following conditions:
wherein,,r e for the earth radius>
For the inclination angle of the track,hfor satellite orbit altitude, +.>
Representing the minimum observation elevation angle of the satellite at the pole, namely, the observation elevation angle near the pole when the satellite runs to the position with the maximum latitude of the point below the satellite;γrepresenting the tangential angle at which the satellite and its visible spherical cap boundary are at that time.
In this embodiment, to ensure good visibility at the poles, a minimum observation elevation angle of the satellite at the poles is set
. When the satellite orbit height is set to 1100km, the orbit inclination +.>
The range of the values of (a) is [77.6 degrees, 90 degrees),
the number of track surfaces is set, and the value range of the phase factor of the adjacent satellite on the adjacent track surface is determined to be [0 ] according to the number of track surfaces, and the number of track surfaces is-1 ] (an integer).
Step S2: and calculating the orbital tilt angles of the second sub-constellation under the condition of different satellite numbers according to a minimum geometric dilution of precision (GDOP) criterion.
For the combined Walker constellation of the present invention, the geometric dilution of precision factor GDOP takes the extreme value as follows:
wherein,,N j represent the firstjThe total number of satellites in the sub-constellation configuration,Krepresenting the number of sub-constellations,
represents the firstjTrack tilt of sub-constellation configuration. In an embodiment of the present invention, in the present invention,K=2。
in practical design, there are also some constraints to set an upper limit on the total number of satellites in the constellation and an upper limit on the number of satellites in each sub-constellation.
Step S3: and (3) arranging and combining the number of sub-constellations and the phase factor values of adjacent satellites on adjacent track surfaces to form a sample set.
FIG. 9 is a schematic diagram showing the process of data preparation, sample set formation and binary encoding according to an embodiment of the present invention, wherein the input set of determined parameters 1 is
，hFor satellite orbit altitude, +.>
For the orbital tilt angle of the first sub-constellation configuration,K=2。
the invention adopts the idea of controlling variables, the number of sub-constellations and the phase factors are arranged and combined, each combination mode is regarded as an individual, and the sub-constellations are orderly sequenced; how many permutation and combination modes are, which indicates how many discrete individuals are (because the track inclination angle of the second sub-constellation is uniquely determined after the number is determined, only an index matrix is needed in the code implementation process, and the permutation and combination process is not needed to be participated).
It should be noted that the constellation design problem in the present invention is a discrete optimization problem, and cannot be given a certain meaning to each binary code like a continuous problem. Thus, the new chromosome obtained after the crossover or mutation operation is decimal, and the total amount of the sample may be exceeded. To address this problem, the processing mode is to randomly give a meaningful value, so that errors can be avoided, and randomness is increased.
Illustrating: assuming a total of 720 sets of samples, 10 bits binary encoding (720 < 210) is required. The binary code of each 10 bits is denoted as X bin When X is bin Turning to decimal X dec Thereafter, if X dec > 720, then randomly designate X dec Is a certain number between 1 and 720.
Step S4: based on the binary coded sample set, calculating satellite coverage layer numbers and position accuracy dilution factors of different sub-constellation configurations, performing primary optimization on the satellite coverage layer numbers and the position accuracy dilution factors through an NSGA-II algorithm, and screening all the sub-constellation configurations meeting a first constraint condition.
There are several metrics to evaluate the performance of a navigation constellation, the most important of which is constellation coverage, navigation capability and satellite number. The constellation coverage capability and the navigation capability are generally positively correlated with the constellation construction cost, and the satellite number and the constellation construction cost are negatively correlated, so that the evaluation indexes are mutually restricted, comprehensive consideration is needed in the design process, and the number of satellites is reduced as much as possible while the good coverage capability and the navigation capability are met, so that the cost is reduced.
In the optimization process, it is often difficult to establish a suitable objective function while considering these three factors, and the final goal is to reduce the number of satellites as much as possible. Therefore, the invention considers the adoption of a step-by-step optimization strategy, sets the satellite coverage layer number and the position accuracy dilution factor DOP value as a primary optimization target, and sets the satellite number as a secondary optimization target. As shown in fig. 10, the NSGA-ii algorithm is first used to perform a first level optimization on the satellite coverage layer number and the position accuracy dilution factor PDOP value, and then the genetic algorithm is used to perform a second level optimization on the satellite number.
And interconnecting MATLAB and STK through a COM interface, and respectively calculating satellite cover layer number average values and PDOP average values of constellations of different configurations.
In the primary optimization stage, since there are two optimization targets in the primary optimization, namely the satellite coverage layer number and the PDOP value, the objective function is expressed as the following two formulas:
wherein,,NAsset ave the average value of the number of satellite coverage layers is represented,PDOP ave the average value of the position accuracy dilution factor is shown. Different combinations are grouped according to the number of track surfaces, the design with the same number of track surfaces is regarded as a group, and the configuration for screening out all the configurations meeting the following two conditions simultaneously is found out in each group:
(1) The average value of satellite coverage layers is more than or equal to 3 between latitude [ -70 degrees and 70 degrees ];
(2) The average value of the position accuracy dilution factors PDOP is less than or equal to 10.
Step S5: and (3) performing secondary optimization on the sub-constellation configurations screened in the step (S4) based on a genetic algorithm, finding out the sub-constellation configuration with the minimum satellite number as an optimal constellation configuration, and determining constellation design schemes of the first sub-constellation and the second sub-constellation.
Step S5 further includes: and (3) performing secondary coding on the sub-constellation configuration screened in the step (S4), performing secondary optimization based on the constellation configuration after the secondary coding, finding out the optimal sub-constellation configuration, and determining the optimal sub-constellation configuration as a final constellation design scheme.
The sub-constellation configurations screened in the step S4 are reordered and used as individuals in secondary optimization, and the secondary optimization aims at minimizing the number of satellites and is expressed as follows:
wherein,,N i represent the firstiTotal number of satellites in a sub-constellation configuration.
In another embodiment, based on the above method for optimizing heterogeneous low-orbit navigation constellation design, the invention further provides a heterogeneous low-orbit navigation constellation design optimization system, wherein the heterogeneous low-orbit navigation constellation comprises a first sub-constellation and a second sub-constellation, and the optimization system comprises:
the sub-constellation orbit inclination angle calculation module is used for calculating the orbit inclination angle of the first sub-constellation according to the minimum observation elevation angle at the pole position based on the set orbit height and orbit surface number; calculating the orbital tilt angles of the second sub-constellation under the condition of different satellite numbers according to a minimum geometric accuracy dilution factor criterion;
the sample set construction module is used for arranging and combining the number of sub-constellations and the phase factor values of adjacent satellites on adjacent track surfaces to form a sample set;
the first-level optimization module is used for calculating satellite coverage layer numbers and position accuracy dilution factors of different sub-constellation configurations based on the sample set, carrying out first-level optimization on the satellite coverage layer numbers and the position accuracy dilution factors through an NSGA-II algorithm, and screening all the sub-constellation configurations meeting a first constraint condition;
the secondary optimization module is used for performing secondary optimization on the sub-constellation configurations screened by the primary optimization module based on a genetic algorithm, finding out the sub-constellation configuration with the minimum satellite number as an optimal constellation configuration, and determining constellation design schemes of the first sub-constellation and the second sub-constellation.
In summary, the invention aims at the problem of optimal design of heterogeneous low-orbit navigation constellation, specifically analyzes influencing factors, and proposes a mode of combining NSGA-II and genetic algorithm to step-by-step optimize the design of the low-orbit constellation by taking the three key indexes, namely satellite number, coverage capability and navigation capability, as optimization targets. For an important link in the optimization process, namely coding, a 'combination-discretization' coding method is designed, so that the correlation between characteristic parameters is considered, and the whole optimization process is simplified.
The invention is the application of the optimization algorithm in the field of constellation design, aims at reducing constellation construction cost while ensuring navigation performance, and provides a good idea for subsequent simulation experiments and engineering application.
In the description of the present specification, a description referring to the terms "one embodiment," "some embodiments," "examples," or "some examples," etc., means that a particular feature, structure, material, or characteristic described in connection with the embodiment or example is included in at least one embodiment or example of the invention. In this specification, schematic representations of the above terms are not necessarily directed to the same embodiment or example. Furthermore, the particular features, structures, materials, or characteristics described may be combined in any suitable manner in any one or more embodiments or examples. Furthermore, the different embodiments or examples described in this specification and the features of the different embodiments or examples may be combined and combined by those skilled in the art without contradiction. It is to be noted that the flowcharts and block diagrams in the figures illustrate the architecture, functionality, and operation of possible implementations of systems, methods and computer program products according to various embodiments of the present invention. In this regard, each block in the flowchart or block diagrams may represent a module, segment, or portion of code, which comprises one or more executable instructions for implementing the specified logical function(s). It should also be noted that, in some alternative implementations, the functions noted in the block may occur out of the order noted in the figures. For example, two blocks shown in succession may, in fact, be executed substantially concurrently, or the blocks may sometimes be executed in the reverse order, depending upon the functionality involved. It will also be noted that each block of the block diagrams and/or flowchart illustration, and combinations of blocks in the block diagrams and/or flowchart illustration, can be implemented by special purpose hardware-based systems which perform the specified functions or acts, or combinations of special purpose hardware and machine instruction.
It will be clear to those skilled in the art that, for convenience and brevity of description, specific working procedures of the above-described systems, apparatuses and units may refer to corresponding procedures in the foregoing method embodiments, and are not repeated herein.
In the several embodiments provided in this application, it should be understood that the disclosed systems, devices, and methods may be implemented in other manners. The above-described apparatus embodiments are merely illustrative, for example, the division of the units is merely a logical function division, and there may be other manners of division in actual implementation, and for example, multiple units or components may be combined or integrated into another system, or some features may be omitted, or not performed.
The units described as separate units may or may not be physically separate, and units shown as units may or may not be physical units, may be located in one place, or may be distributed on a plurality of network units. Some or all of the units may be selected according to actual needs to achieve the purpose of the solution of this embodiment.
In addition, each functional unit in the embodiments of the present invention may be integrated in one processing unit, or each unit may exist alone physically, or two or more units may be integrated in one unit. The functions, if implemented in the form of software functional units and sold or used as a stand-alone product, may be stored in an acquisition machine readable storage medium. Based on this understanding, the technical solution of the present invention may be embodied essentially or in a part contributing to the prior art or in a part of the technical solution in the form of a software product stored in a storage medium, comprising several instructions for causing an obtaining machine (which may be a personal obtaining machine, a server, a network machine, etc.) to perform all or part of the steps of the method according to the embodiments of the present invention. And the aforementioned storage medium includes: a U-disk, a removable hard disk, a Read-Only Memory (ROM), a random access Memory (RAM, random Access Memory), a magnetic disk, or an optical disk, or other various media capable of storing program codes.
Finally, it should be noted that: the above embodiments are only for illustrating the technical solution of the present invention, and not for limiting the same; although the invention has been described in detail with reference to the foregoing embodiments, it will be understood by those of ordinary skill in the art that: the technical scheme described in the foregoing embodiments can be modified or some or all of the technical features thereof can be replaced by equivalents; such modifications and substitutions do not depart from the spirit of the invention, and are intended to be included within the scope of the appended claims and description.
Claims (8)
1. A heterogeneous low-orbit navigation constellation design optimization method, the heterogeneous low-orbit navigation constellation comprising a first sub-constellation and a second sub-constellation, the method comprising the steps of:
step S1: setting the orbit height of a satellite and the orbit surface number of a first sub-constellation, and calculating the orbit inclination angle of the first sub-constellation according to the minimum observation elevation angle of the satellite at a pole;
step S2: calculating the orbital tilt angle of the second sub-constellation under the condition of different satellite numbers according to the condition that the geometric accuracy dilution factor takes the minimum value; the condition that the geometric accuracy dilution factor takes the minimum value is as follows:
wherein,,N j represent the firstjThe total number of satellites in the sub-constellation configuration,Krepresenting the number of sub-constellations,α j represents the firstjTrack tilt of sub-constellation configuration;
step S3: the number of the sub-constellations and the value of the phase factor are arranged and combined to form a sample set;
step S4: based on the sample set, calculating satellite coverage layer numbers and position accuracy dilution factors of different sub-constellation configurations, performing primary optimization on the satellite coverage layer numbers and the position accuracy dilution factors through an NSGA-II algorithm, and screening all sub-constellation configurations meeting a first constraint condition;
step S5: and (3) performing secondary optimization on the sub-constellation configurations screened in the step (S4) based on a genetic algorithm, finding out the sub-constellation configuration with the minimum satellite number as an optimal constellation configuration, and determining constellation design schemes of the first sub-constellation and the second sub-constellation.
2. The heterogeneous low-orbit navigation constellation design optimization method according to claim 1, wherein the first sub-constellation and the second sub-constellation are designed in a Walker-delta configuration.
3. The heterogeneous low-orbit navigation constellation design optimization method according to claim 1, wherein said step S1 further comprises: the satellite orbit height is set based on the satellite vision area and the user's lowest observation elevation angle.
4. The heterogeneous low-orbit navigation constellation design optimization method according to claim 1, wherein said step S3 further comprises: the sample set is binary coded.
5. The heterogeneous low-orbit navigation constellation design optimization method according to claim 4, wherein said step S5 further comprises: and (3) performing secondary coding on all the sub-constellation configurations which meet the first constraint condition and are screened in the step (S4), and performing secondary optimization based on the sub-constellation configurations after secondary coding.
6. The heterogeneous low-rail navigation constellation design optimization method of claim 1, wherein said first constraint condition is that both of the following conditions are satisfied:
(1) The average value of satellite coverage layers is more than or equal to 3 between latitude [ -70 degrees and 70 degrees ];
(2) The average value of the dilution factors of the position accuracy is less than or equal to 10.
7. The heterogeneous low-orbit navigation constellation design optimization method according to claim 1, wherein in said step S1, at different satellite orbit heights, the minimum observation elevation angle at the pole and the orbit inclination angle of said first sub-constellation should be satisfied:
wherein,,φfor the minimum observation elevation angle of the satellite at the pole,αfor the orbital tilt of the first sub-constellation,r e for the radius of the earth,has a satellite orbit height, the satellite orbit height,γis the tangential angle at the boundary of the satellite and its visible spherical cap.
8. A heterogeneous low-orbit navigation constellation design optimization system, the heterogeneous low-orbit navigation constellation comprising a first sub-constellation and a second sub-constellation, the system comprising:
the sub-constellation orbit inclination angle calculation module is used for calculating the orbit inclination angle of the first sub-constellation according to the minimum observation elevation angle of the satellite at the pole position based on the set satellite orbit height and the orbit surface number of the first sub-constellation; calculating the orbit inclination angle of the second sub-constellation under the condition of different satellite numbers according to the condition that the geometric accuracy dilution factor takes the minimum value; the condition that the geometric accuracy dilution factor takes the minimum value is as follows:
wherein,,N j represent the firstjThe total number of satellites in the sub-constellation configuration,Krepresenting the number of sub-constellations,α j represents the firstjTrack tilt of sub-constellation configuration;
the sample set construction module is used for arranging and combining the number of sub-constellations and the value of the phase factor to form a sample set;
the first-level optimization module is used for calculating satellite coverage layer numbers and position accuracy dilution factors of different sub-constellation configurations based on the sample set, carrying out first-level optimization on the satellite coverage layer numbers and the position accuracy dilution factors through an NSGA-II algorithm, and screening all the sub-constellation configurations meeting a first constraint condition;
the secondary optimization module is used for performing secondary optimization on the sub-constellation configurations screened by the primary optimization module based on a genetic algorithm, finding out the sub-constellation configuration with the minimum satellite number as an optimal constellation configuration, and determining constellation design schemes of the first sub-constellation and the second sub-constellation.
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