CN115242288A - Inter-satellite link topology determination method for global satellite navigation system - Google Patents
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Abstract
The invention discloses a method for determining inter-satellite link topology for a global satellite navigation system, which comprises the steps of taking inter-satellite links among all satellites in a single observation period in the system as an individual, combining the individuals corresponding to a plurality of observation periods together to be regarded as a population, carrying out constraint processing on the population to obtain a constraint population, carrying out hierarchical processing on the constraint population to be regarded as a generation population, carrying out iterative optimization on the generation population based on genetic evolution processing and a preset filling rule, finishing evolution of the generation population after preset iteration times, and determining the inter-satellite link topology according to the generation population finished by iteration.
Description
Technical Field
The invention belongs to the technical field of satellite navigation, and particularly relates to a method for determining inter-satellite link topology for a global satellite navigation system.
Background
The global satellite navigation system is a space-based radio navigation positioning system that can provide users with all-weather 3-dimensional coordinates and velocity and time information at any location on the earth's surface or in near-earth space.
When a Beidou third-generation global satellite navigation system is established, a large number of base stations cannot be established in the global range, information transmission among inter-satellite links becomes an important component of the Beidou navigation system, the inter-satellite links are communication links between satellites and between the ground, and the inter-satellite links have a bidirectional pseudo-range ranging function.
Therefore, how to further improve the positioning accuracy of the beidou navigation system three and improve the network topology structure in the inter-satellite link, thereby improving the performance of the beidou navigation system, is a technical problem to be solved by technical personnel in the field.
Disclosure of Invention
The invention aims to solve the technical problems of simple structure and low positioning precision of an inter-satellite link of the existing global satellite navigation system, and provides a method for determining the topology of the inter-satellite link of the global satellite navigation system.
The technical scheme of the invention is as follows: a method for determining the topology of an inter-satellite link for a global satellite navigation system comprises the following steps:
s1, taking inter-satellite links among all satellites in a single observation period in the global satellite navigation system as an individual, combining the individuals corresponding to the plurality of observation periods together to be regarded as a population, and initializing the population to obtain an initial population, wherein one observation period comprises a plurality of time slots;
s2, carrying out constraint processing on the initial population to obtain a constrained population;
s3, carrying out grading treatment on the constrained population to serve as a first generation population, carrying out genetic evolution treatment on the first generation population to obtain a second generation population, combining the first generation population and the second generation population to form a new generation population, carrying out grading treatment on the new generation population to obtain a new generation graded population, filling the new generation graded population into the first generation population according to a preset filling rule, and carrying out iteration execution on the step according to preset iteration times;
and S4, determining the inter-satellite link topological structure according to the generation population after iteration.
Further, initializing the population in the step S1 to obtain an initial population, specifically including the following steps:
s11, numbering each satellite in the global satellite navigation system;
s12, taking all forward inter-satellite links in a single time slot in a single observation period as a gene, and determining a gene coding vector corresponding to the single time slot according to the number and the number of the inter-satellite links in the single time slot;
s13, determining the gene coding vectors corresponding to all the time slots in a single observation period, combining the gene coding vectors into a coding matrix and regarding the coding matrix as a chromosome;
and S14, determining the chromosomes corresponding to all the observation periods so as to finish the initialization of the population.
Further, the constraint processing in step S2 specifically includes:
constraining the initial population by the geometric visibility constraint, the antenna visibility constraint and the inter-satellite distance constraint to obtain a constrained population;
the geometric visibility constraint may be specifically constrained by the following equation:
the antenna visibility constraint may be specifically constrained by the following equation:
the inter-satellite distance constraint may be specifically constrained by the following formula:
a, B is the global satellite navigation system to be established chain satellite, theta A Is the included angle theta between the single inter-satellite link between the AB satellites and the A satellite-geocentric connecting line on the single inter-satellite link B Is the included angle between the single inter-satellite link between the AB satellites and the earth center connecting line between the B satellite on the single inter-satellite link, R is the radius of the earth, h is the thickness of the atmosphere, d A For the A satellite orbital altitude, d B Taking the earth mass center as the sphere center, adding R and h into a radius to form a sphere, wherein the tangent of the spherical surface passing through the satellite A is a first tangent, the tangent of the spherical surface passing through the satellite B is a second tangent, and beta is beta A Is the angle between the first tangent and the line connecting the A satellite and the earth center, beta B Is the included angle between the second tangent and the connecting line from the B satellite to the geocentric, alpha max Is the maximum scan angle of the satellite antenna,/ AB Is the actual inter-satellite distance, L, between the A satellite and the B satellite Amin Is said theta A And said alpha max When the distances between the A satellite and the earth center to the single inter-satellite link vertical point between the AB satellites are equal, L Bmin Is said theta B And said alpha max When the distance between the B satellite and the earth center to the single inter-satellite link vertical point between the AB satellites is equal, L Amax Is that it isA distance between the satellite and the tangent point of the first tangent line, L Bmax The distance between the B satellite and the second tangent point is obtained.
Further, the step S3 includes pareto classification processing and congestion degree processing, and the classification processing specifically includes the steps of:
s31, establishing a plurality of objective functions based on the number of idle satellites, the inter-satellite distance of the established-link satellites and the PDOP value of the whole satellite
S32, based on a plurality of objective functions, performing fast non-dominated sorting on corresponding populations to perform pareto grading processing on the corresponding populations to obtain corresponding graded populations, wherein the corresponding graded populations comprise a plurality of graded populations, each graded population corresponds to one pareto grade, and the corresponding graded populations are arranged in the corresponding graded populations according to the sequence from low to high of the pareto grades, wherein the corresponding populations are specifically the constraint population and the new generation population, and the corresponding graded populations are specifically the first generation population and the new generation graded population;
s33, determining the crowding degrees corresponding to all the individuals except two boundary individuals in each level population in the corresponding level population, and arranging the corresponding individuals in each level population according to the sequence of the crowding degrees from large to small.
Further, the plurality of objective functions in step S31 specifically include:
objective function f of the number of idle satellites 1 Comprises the following steps:
f 1 ＝max(Num 1 ,Num 2 ,…,Num TimeslotNum )-min(Num 1 ,Num 2 ,…,Num TimeslotNum ) (ii) a Target function f of distance between satellites of the building link satellite 2 Comprises the following steps:
an objective function f of the global satellite PDOP value 3 Comprises the following steps:
wherein, num i Representing the number of the inter-satellite links in the ith time slot, timeslotNum representing the number of the time slots in one observation period, m being the number of the inter-satellite links in one time slot, D ij Is the inter-satellite distance of the j inter-satellite link in the ith time slot, PDOP i Indicating the PDOP value for the ith satellite with the current inter-satellite link network structure.
Further, the preset filling rule in step S3 is specifically:
and sequentially placing the corresponding grade populations in the grading populations into the generation populations according to the sequence of the pareto grades from low to high until a certain grade population cannot be placed into the generation populations, and sequentially placing individuals in the certain grade population into the generation populations according to the sequence of the crowdedness from high to low until the generation populations are filled.
Further, the step S4 specifically includes the following steps:
s41, determining a plurality of objective function values of the generation population after iteration is completed, and comparing the values with a preset result threshold value;
s42, judging whether a plurality of objective function values of the generation population are smaller than the preset result threshold value, if so, determining the inter-satellite link topological structure according to the generation population and the coordinates of all satellites, and if not, continuously iterating the generation population for preset iteration times.
Further, the genetic evolution process specifically includes a selection process, a crossover process and a mutation process.
Compared with the prior art, the invention has the beneficial effects that:
(1) According to the invention, inter-satellite links among all satellites in a single observation period in the global satellite navigation system are taken as an individual, the individuals corresponding to a plurality of observation periods are combined together to be taken as a population, the population is subjected to iterative evolution to form a population with an optimal grade through genetic evolution, and the inter-satellite links of the global satellite navigation system are subjected to topology according to the population with the optimal grade and the coordinates of all satellites, so that the autonomous navigation positioning precision of the current inter-satellite links is improved, the network topology structure is enriched, the performance of the global satellite navigation system is improved, and the autonomous navigation task is better completed.
(2) The invention fills the graded population into the first generation population for iteration through the preset filling rule, thereby ensuring the comprehensiveness and the accuracy of the iterative evolution process, ensuring that the iteration is carried out towards the optimal direction, and ensuring that the corresponding population is the optimal population when the inter-satellite link topology is carried out.
(3) By setting reasonable iteration times, the invention avoids the problems that the optimal scheme cannot be obtained or the calculation space is wasted due to incomplete evolution or over-evolution, and reduces the calculation complexity on the premise of ensuring the evolution quality.
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Fig. 1 is a schematic flowchart illustrating a method for determining inter-satellite link topology for a global satellite navigation system according to an embodiment of the present invention;
fig. 2 is a schematic flowchart illustrating a method for determining an inter-satellite link topology for a global navigation satellite system according to another embodiment of the present invention.
Detailed Description
The technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the drawings in the embodiments of the present application, and it is obvious that the described embodiments are only a part of the embodiments of the present application, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present application.
As described in the background art, the inter-satellite link topology of the existing global satellite navigation system is mostly a mesh topology, which is relatively simple and fixed, and limits the performance of the network, and meanwhile, the positioning accuracy cannot meet the requirement.
Therefore, the application provides a method for determining the inter-satellite link topology for the global satellite navigation system, which is used for solving the technical problems of single topology structure and low positioning accuracy of the existing inter-satellite link.
Fig. 1 is a schematic flow chart of a method for determining an inter-satellite link topology for a global satellite navigation system according to an embodiment of the present invention, where the method includes the following steps:
step S1, inter-satellite links among all satellites in a single observation period in the global satellite navigation system are taken as an individual, the individuals corresponding to the observation periods are combined together to be taken as a population, the population is initialized to obtain an initial population, and one observation period comprises a plurality of time slots.
Specifically, the scheme of the application mainly includes that inter-satellite links among all satellites in the global satellite navigation system are evolved by combining a multi-target genetic optimization method to determine the inter-satellite link network topology of the optimal level, so that the inter-satellite links among all satellites in a single observation period in the system are taken as an individual, the individuals corresponding to the plurality of observation periods are combined together to be taken as a group, and the group is initialized so as to determine the inter-satellite link network topology of the optimal level in the subsequent process.
In order to facilitate the evolution of the inter-satellite link network topology structure with the optimal level, in step S1 of the present application, the method for initializing the population to obtain an initial population specifically includes the following steps:
s11, numbering each satellite in the global satellite navigation system;
s12, taking all forward inter-satellite links in a single time slot in a single observation period as a gene, and determining a gene coding vector corresponding to the single time slot according to the number and the number of the inter-satellite links in the single time slot;
s13, determining the gene coding vectors corresponding to all the time slots in a single observation period, combining the gene coding vectors into a coding matrix and regarding the coding matrix as a chromosome;
and S14, determining the chromosomes corresponding to all the observation periods so as to finish the initialization of the population.
The existing global satellite navigation system such as the Beidou satellite navigation system III generally adopts a Ka-band narrow-beam inter-satellite link, the narrow-beam inter-satellite link has the advantages of flexible directional switching, high ranging accuracy, high communication rate, good anti-interference performance, low power consumption and the like, the narrow-beam inter-satellite link establishes a dynamic switching link in a point-to-point mode, in the link mode, a time slice in an observation period is divided into a plurality of time slots, each time slot is 3s, a forward inter-satellite link is established in the first 1.5s, a reverse inter-satellite link is established in the second 1.5s to ensure that a bidirectional link is formed, a plurality of links can be established in each time slot, but each satellite can only establish a link with one satellite at the same time.
First, each satellite in the system is labeled or numbered, for example, the beidou three-numbered gnss includes 30 satellites, which are numbered from 1 to 30.
All the inter-satellite links in each time slot are bidirectional, when all the forward links are determined, the reverse link can be uniquely determined, all the forward inter-satellite links in a single time slot can be used as a gene, the gene can be represented by a gene coding vector, the gene coding can be determined according to the number and the number of the inter-satellite links in a single time slot, the single inter-satellite link between two chain-building satellites can combine the number of a transmitting satellite and the number of a receiving satellite, and the specific expression of the gene coding vector is as follows:
wherein CrossNum is the number of links between satellites in a single time slot, s is the number of satellites, trID is the number of transmitting satellites, and RevID is the number of receiving satellites.
The combination of the gene coding vectors corresponding to all time slots in a single observation period is a coding matrix, and the coding matrix is regarded as a chromosome and is used as a chromosome
Specific body surfaceThe expression is as follows:
wherein, the TimeslotNum is the number of time slots in a single observation period, and s is the number of satellites.
And determining all chromosomes corresponding to the multiple observation periods so as to complete population initialization, wherein the multiple observation periods are determined according to the population scale preset by the complexity, and how many observation periods, namely many chromosomes, exist in the population scale.
It should be noted that, a person skilled in the art may flexibly select the method for initializing the population according to actual situations, which does not affect the scope of the present application.
And S2, carrying out constraint processing on the initial population to obtain a constrained population.
In a global satellite navigation system, two satellites are not visible at any time, so that an initial population needs to be constrained, the satellites needing to establish an inter-satellite link are reserved, codes which do not meet constraint conditions are reset to zero, the constraint conditions are constraint processing, and the constraint processing specifically comprises geometric visibility constraint, astronomical visibility constraint and inter-satellite distance constraint.
In order to accurately constrain individuals in the initial population, in this embodiment of the present application, the constraint processing in step S2 specifically includes:
constraining the initial population by the geometric visibility constraint, the antenna visibility constraint and the inter-satellite distance constraint to obtain a constrained population;
the geometric visibility constraint may specifically be constrained by the following formula:
the antenna visibility constraint may be specifically constrained by the following equation:
the inter-satellite distance constraint may be specifically constrained by the following formula:
a, B is the global satellite navigation system to be established chain satellite, theta A Is the included angle theta between the single inter-satellite link between the AB satellites and the earth center connecting line of the A satellite on the single inter-satellite link B Is the included angle between the single inter-satellite link between the AB satellites and the earth center connecting line between the B satellite on the single inter-satellite link, R is the radius of the earth, h is the thickness of the atmosphere, d A For the A satellite orbital altitude, d B Taking the earth mass center as the sphere center, adding R and h into a radius to form a sphere, wherein the tangent of the spherical surface passing through the satellite A is a first tangent, the tangent of the spherical surface passing through the satellite B is a second tangent, and beta is beta A Is the angle between the first tangent and the line connecting the A satellite and the earth center, beta B Is the included angle between the second tangent and the connecting line from the B satellite to the geocentric, alpha max Is the maximum scan angle of the satellite antenna,/ AB Is the actual inter-satellite distance, L, between the A satellite and the B satellite Amin Is said theta A And said alpha max When the distances between the A satellite and the earth center to the single inter-satellite link vertical point between the AB satellites are equal, L Bmin Is said theta B And said alpha max When the distance between the B satellite and the earth center to the single inter-satellite link vertical point between the AB satellites is equal, L Amax Is the distance, L, from the A satellite to the first tangent point Bmax The distance between the B satellite and the second tangent point is obtained.
The method is characterized in that individuals in a population are constrained, satellites in a global satellite navigation system are substantially constrained, codes needing to establish inter-satellite links are judged, namely every two satellites needing to establish inter-satellite links, and the codes can be comprehensively and accurately constrained through the three constraint conditions, so that the codes needing to establish the inter-satellite links are determined.
It should be noted that the constraint condition in the above scheme is only a specific implementation scheme in the embodiment of the present application, and any other manner that can constrain the initial population to determine which two satellites need to establish an inter-satellite link belongs to the protection scope of the present application.
And S3, performing hierarchical processing on the constrained population to serve as a generation population, performing genetic evolution processing on the generation population to obtain a second generation population, combining the generation population and the second generation population to form a new generation population, performing the hierarchical processing on the new generation population to obtain a hierarchical population, filling the hierarchical population into the generation population according to a preset filling rule, and performing iteration according to preset iteration times.
Specifically, the scheme of the application is a technical scheme combining a multi-target genetic method, an optimal population, namely an optimal intersatellite link topological structure, is determined through population evolution iteration, a first generation population is obtained by carrying out classification processing on a constrained population subjected to constraint processing in the application, the first generation population is also a parent population, a second generation population is obtained through genetic evolution processing including selection processing, cross processing and variation processing on the first generation population, the first generation population and the second generation population are combined to form a new generation population, meanwhile, classification processing is carried out on the new generation population again to obtain a classification population, finally, the classification population is filled into the first generation population according to a preset filling rule, the step is used as a complete iteration process, the iteration process is actually an optimization process, individuals in the new generation population are classified through the classification processing, then, the classification population is filled into the first generation population according to the preset filling rule, namely, the individuals in the classification population are preferably filled into the first generation population, the first generation population after iteration is ensured to be the optimal population through the preset iteration number, meanwhile, the calculation complexity of the cross processing and the classification processing are reduced, and the specific classification processing and the classification processing are referred to be the classification processing, and the classification processing.
In order to implement the classification processing more accurately, in the embodiment of the present application, the classification processing in step S3 includes pareto classification processing and congestion degree processing, and the classification processing specifically includes the following steps:
s31, establishing a plurality of objective functions based on the number of idle satellites, the inter-satellite distance of the established-link satellites and the PDOP value of the whole satellite
S32, performing fast non-dominated sorting on corresponding populations based on a plurality of objective functions so as to perform pareto grading processing on the corresponding populations to obtain corresponding graded populations, wherein the corresponding graded populations comprise a plurality of graded populations, each graded population corresponds to one pareto grade, and the corresponding graded populations are arranged in the corresponding graded populations according to the sequence of the pareto grades from low to high, wherein the corresponding populations are specifically the constraint population and the new generation population, and the corresponding graded populations are specifically the generation population and the new generation graded population;
s33, determining the crowding degrees corresponding to all the individuals except two boundary individuals in each level population in the corresponding level population, and arranging the corresponding individuals in each level population according to the sequence of the crowding degrees from large to small.
The classification processing is actually pareto classification processing and congestion degree processing, and before pareto classification processing, corresponding populations need to be subjected to fast non-dominated sorting according to three objective functions, wherein the three objective functions are as follows:
objective function f of the number of idle satellites 1 Comprises the following steps:
f 1 ＝max(Num 1 ,Num 2 ,…,Num TimeslotNum )-min(Num 1 ,Num 2 ,…,Num TimeslotNum ) (ii) a Target function f of distance between satellites of the building link satellite 2 Comprises the following steps:
an objective function f of the global satellite PDOP value 3 Comprises the following steps:
wherein, num i Representing the number of the inter-satellite links in the ith time slot, the TimeslotNum representing the number of the time slots in one observation period, m being the number of the inter-satellite links in one time slot, D ij Is the inter-satellite distance of the j inter-satellite link in the ith time slot, PDOP i Indicating the PDOP value for the ith satellite with the current inter-satellite link network structure.
And (3) a Position Precision of Precision (PDOP) value of the whole satellite, wherein the PDOP value is a space geometric intensity factor of satellite distribution, and after the fast non-dominated sorting is carried out, pareto classification is carried out on the corresponding population.
Pareto, that is, pareto Optimality (Pareto Optimality), is an ideal state of resource allocation, when Pareto hierarchical processing is performed, a Pareto domination relation is determined first, and for a minimization multi-objective optimization problem, for 3 target components f i (x) I =1,2,3, any given two decision variables (topology) Chromo a ，Chromo b If the following two conditions are satisfied, it is called Chromo a Dominating Chromo b 。
(1) For the
All have f i (Chromo a )≤f i (Chromo b ) This is true.
(2)
So that f i (Chromo a )<f i (Chromo b ) This is true.
If for a decision variable there are no other decision variables that can dominate it, then the decision variable is said to be a non-dominated solution.
Pareto grade: in a set of solutions, the pareto rating of the non-dominant solution is defined as 1, the non-dominant solution is deleted from the set of solutions, the pareto rating of the remaining solutions is defined as 2, and so on, the pareto ratings of all solutions in the set of solutions can be obtained.
The crowding degree is determined so that the obtained solution is more uniform in the target space, that is, so that the satellite is more uniform in space, and the crowding degree n is calculated for the individuals in each level of population a 。
Firstly, the individuals in the hierarchical population are sorted according to each objective function and recorded
For individual objective function value f m The maximum value of (a) is,
for individual objective function value f m The congestion degree for the sorted two boundaries is set to infinity ∞.
The crowdedness of all the individuals except two boundaries in the level population is determined,
wherein f is m (i + 1) is the value of the objective function one bit after the individual is sorted.
In order to iterate out an optimal population, in this embodiment of the application, the preset filling rule in step S3 specifically includes:
and sequentially placing the corresponding grade populations in the grading populations into the generation populations according to the sequence of the pareto grades from low to high until a certain grade population cannot be placed into the generation populations, and sequentially placing individuals in the certain grade population into the generation populations according to the sequence of the crowdedness from high to low until the generation populations are filled.
By this step, it can be ensured that the iterative process is iterative towards the optimization direction.
It should be noted that the above scheme for classifying the corresponding population is only one specific implementation manner in the embodiment of the present application, and a person skilled in the art may flexibly set different classification manners according to actual situations, which does not affect the protection scope of the present application.
And S4, determining the inter-satellite link topological structure according to the generation of population after iteration is completed.
The first generation population forms an optimal population after iteration is completed, and at the moment, the topological structure of the inter-satellite link can be set according to the first generation population after iteration is completed.
In order to determine the inter-satellite link topology more accurately, in this embodiment of the present application, the step S4 specifically includes the following steps:
s41, determining a plurality of objective function values of the generation population after iteration is completed, and comparing the values with a preset result threshold value;
s42, judging whether a plurality of objective function values of the first generation population are smaller than the preset result threshold value, if so, determining the inter-satellite link topological structure according to the first generation population and the coordinates of all satellites, and if not, continuously iterating the first generation population for preset iteration times.
Specifically, after the preset iteration times are completed, a plurality of objective function values of a generation of population after the iteration is completed are compared with a preset result value, if the plurality of objective function values are smaller than a preset result threshold value, the evolution is completed, an inter-Satellite link topological structure can be determined according to the generation of population and a Satellite coordinate, the Satellite coordinate can be determined by an STK (Satellite Tool Kit), and the inter-Satellite distance can be calculated based on the STK.
The invention discloses an intersatellite link topology method for global satellites, which comprises the steps of using intersatellite links among all satellites in a single observation period in a global satellite navigation system as an individual, combining the individuals corresponding to the observation periods together to be regarded as a population, initializing the population to obtain an initial population, carrying out constraint processing on the initial population to obtain a constrained population, carrying out constraint processing including geometric visibility constraint, antenna visibility constraint and inter-satellite distance constraint, carrying out hierarchical processing on the constrained population to be used as a first generation population, carrying out genetic evolution processing on the first generation population to obtain a second generation population, combining the first generation population and the second generation population to form a new generation population, carrying out hierarchical processing on the new generation population to obtain a new generation hierarchical population, filling the new generation hierarchical population into the first generation population according to a preset filling rule, carrying out iteration execution according to a preset number of times, wherein the genetic evolution processing specifically comprises selection processing, cross processing and variation processing, the hierarchical processing specifically comprises pareto processing and degree processing, finally determining an optimal iterative link topology structure among the first generation, and determining the intersatellite links, and improving the network topology structure of the intersatellite navigation links, thereby improving the satellite navigation network topology.
Referring to fig. 2, another embodiment of the present application provides a method for determining an inter-satellite link topology for a global satellite navigation system, the method including:
and S51, initializing the population.
Specifically, in this embodiment, the third beidou is taken as an example, first, 30 beidou satellites are numbered, the 24 MEO satellites are numbered as 1-24,3 GEO satellites are numbered as 25-27,3 IGSO satellites are numbered as 28-30, then inter-satellite links among all satellites in a single observation period in the global satellite navigation system are taken as an individual, the individuals corresponding to the plurality of observation periods are combined together to be taken as a population,
the Beidou third-generation global satellite navigation system adopts a Ka-band narrow-beam inter-satellite link, the narrow-beam inter-satellite link has the advantages of flexible directional switching, high ranging precision, high communication rate, good anti-interference performance, low power consumption and the like, the narrow-beam inter-satellite link establishes a dynamic switching link in a point-to-point mode, in the link mode, a time slice in an observation period is divided into a plurality of time slots, each time slot is 3s, a forward inter-satellite link is established in the first 1.5s, a reverse inter-satellite link is established in the second 1.5s to ensure that a bidirectional link is formed, a plurality of links can be established in each time slot, but each satellite can only establish a link with one satellite at the same time.
All the inter-satellite links in each time slot are bidirectional, when all the forward links are determined, the reverse links can be uniquely determined, all the forward inter-satellite links in a single time slot can be used as a gene, the gene can be represented by a gene coding vector, the gene coding can be determined according to the number and the number of the inter-satellite links in the single time slot, and the specific expression of the gene coding vector is as follows:
wherein CrossNum is the number of links between satellites in a single time slot, s is the number of satellites, trID is the number of transmitting satellites, and RevID is the number of receiving satellites.
The combination of the gene coding vectors corresponding to all time slots in a single observation period is a coding matrix, and the coding matrix is regarded as a chromosome and is used as a chromosome
The specific expression is as follows:
wherein, the TimeslotNum is the number of time slots in a single observation period, and s is the number of satellites.
And determining all chromosomes corresponding to the plurality of observation periods, thereby completing the initialization of the population.
That is, with the known constellation geometry, the total constellation satellite number s and the total time slot number TimeslotNum for one observation period are both known. For a single gene, the inter-satellite link number CrossNum in the time slot is randomly generated in the range of [0,s ]. Then, randomly generating the serial numbers of the transmitting star and the receiving star of each link element in the gene vector in a [1,s ] interval respectively to form a gene vector; timeslotNum genes are generated according to the mode, and are combined into a chromosome, and the initial population is obtained through the initialization.
And S52, carrying out constraint processing on the initial population to obtain a constrained population.
In practical situations, since every two satellites are not visible at any time, a constrained population is obtained by constraining an initial population, and can be processed through three constraint conditions, wherein the constraint treatment specifically includes geometric visibility constraint, antenna visibility constraint and inter-satellite distance constraint, and a code which does not conform to the constraint conditions is reset to 0.
The geometric visibility constraint may be specifically constrained by the following equation:
the antenna visibility constraint may be specifically constrained by the following equation:
the inter-satellite distance constraint may be specifically constrained by the following formula:
a, B is a satellite to be linked in the global satellite navigation system, θ A Is the included angle theta between the single inter-satellite link between the AB satellites and the earth center connecting line of the A satellite on the single inter-satellite link B Is the included angle between the single inter-satellite link between the AB satellites and the earth center connecting line between the B satellites on the single inter-satellite link, R is the earth radius, h is the atmospheric thickness, d A Is the A satellite orbit altitude, d B Taking the earth mass center as the sphere center, adding R and h into a radius to form a sphere, wherein the tangent of the spherical surface passing through the satellite A is a first tangent, the tangent of the spherical surface passing through the satellite B is a second tangent, and beta is beta A Is the angle between the first tangent and the line connecting the satellite A to the geocentric, beta B Is the included angle between the second tangent and the connecting line from the B satellite to the geocentric, alpha max Is the maximum scan angle of the satellite antenna,/ AB Is the actual inter-satellite distance, L, between the A satellite and the B satellite Amin Is said theta A And said a max When the distances between the A satellite and the earth center to the single inter-satellite link vertical point between the AB satellites are equal, L Bmin Is said theta B And said alpha max When the distance between the B satellite and the earth center to the single inter-satellite link vertical point between the AB satellites is equal, L Amax Is the distance between the A satellite and the tangent point of the first tangent line, L Bmax The distance between the B satellite and the second tangent point is obtained.
And S53, carrying out grading treatment on the constrained population.
The grading treatment comprises pareto grading treatment and crowding degree treatment, the corresponding population needs to be subjected to rapid non-dominated sorting according to three objective functions before pareto grading treatment is carried out, and the three objective functions are respectively
Objective function f of the number of idle satellites 1 Comprises the following steps:
f 1 ＝max(Num 1 ,Num 2 ,…,Num TimeslotNum )-min(Num 1 ,Num 2 ,…,Num TimeslotNum ) (ii) a Target function f of distance between satellites of the building link satellite 2 Comprises the following steps:
an objective function f of the global satellite PDOP value 3 Comprises the following steps:
wherein, num i Representing the number of the inter-satellite links in the ith time slot, the TimeslotNum representing the number of the time slots in one observation period, m being the number of the inter-satellite links in one time slot, D ij Is the inter-satellite distance of the j inter-satellite link in the ith time slot, PDOP i Indicating the PDOP value for the ith satellite with the current inter-satellite link network structure.
And after the rapid non-dominant sorting is carried out, carrying out pareto grading on the corresponding population.
When carrying out pareto grading processing, determining pareto domination relation firstly, and for the minimization multi-objective optimization problem, for 3 objective components f i (x) I =1,2,3, any given two decision variables (topology scheme) Chromo a ，Chromo b Chromo is called if the following two conditions are satisfied a Dominating Chromo b 。
(1) For the
All have f i (Chromo a )≤f i (Chromo b ) This is true.
(2)
So that f i (Chromo a )<f i (Chromo b ) This is true.
If for a decision variable, there are no other decision variables that can dominate it, then the decision variable is said to be a non-dominated solution.
Pareto grade: in a set of solutions, the pareto rating of the non-dominant solution is defined as 1, the non-dominant solution is deleted from the set of solutions, the pareto rating of the remaining solutions is defined as 2, and so on, the pareto ratings of all solutions in the set of solutions can be obtained.
The crowdedness is determined to make the obtained solution more uniform in the target space, i.e. to make the satellite more uniform in spaceCalculating crowdedness n of individuals in each level of population d 。
Firstly, the individuals in the hierarchical population are sorted according to each objective function and recorded
For individual objective function value f m The maximum value of (a) is,
for individual objective function value f m The congestion degree for the sorted two boundaries is set to infinity ∞.
The crowdedness of all the individuals except two boundaries in the level population is determined,
wherein, f m (i + 1) is the value of the objective function one bit after the individual is sorted.
After the individual crowding degree is determined, the individuals are arranged in each level of population according to the sequence of the crowding degree from large to small.
And S54, taking the constraint population after the grading treatment as a generation population and performing iteration.
In this step, the constrained population after the classification processing is used as a generation population, and iteration is performed on the generation population, wherein the iteration process specifically comprises: taking a first-generation population as a parent, obtaining a second-generation population through genetic evolution treatment, wherein the genetic evolution treatment specifically comprises selection treatment, cross treatment and variation treatment, the first-generation population and the second-generation population are put together to form a new-generation population, the new-generation population is subjected to grading treatment to obtain a new-generation graded population, the new-generation graded population comprises a plurality of graded populations, each graded population corresponds to a pareto grade, then the graded populations are put into the first-generation population according to the sequence of the pareto grades from low to high until a certain graded population cannot be completely put into the first-generation population, and then individuals in the graded populations are put into the first-generation population once according to the sequence of the congestion degrees from high to low until the first-generation population is filled.
The iteration times are preset iteration times, so that incomplete or excessive population evolution is avoided.
And S55, determining an inter-satellite link topological structure according to the first generation of population after iteration is finished.
Determining a plurality of objective function values of a generation population after iteration is finished, comparing the multi-objective function values with a preset result threshold, if the objective function values are smaller than the preset result threshold, finishing the evolution and determining an inter-satellite link topological structure according to the generation population, if the objective function values are not smaller than the preset result threshold, incomplete the evolution, and iterating again according to the preset iteration times.
According to the scheme, inter-satellite links among all satellites in a single observation period in the global satellite navigation system are taken as an individual, the individuals corresponding to the plurality of observation periods are combined together to be regarded as a group, the group is initialized to obtain an initial group, the optimal topological structure of the inter-satellite links is convenient to determine, and meanwhile, a grading treatment and a preset filling rule are set, so that the initial group can be evolved into the optimal-level group in the iteration process, the coverage range of the global satellite navigation system is expanded, the transmission delay is reduced, the performance of the system is effectively improved, and the autonomous navigation task is better completed.
It will be appreciated by those of ordinary skill in the art that the embodiments described herein are intended to assist the reader in understanding the principles of the invention and are to be construed as being without limitation to such specifically recited embodiments and examples. Those skilled in the art, having the benefit of this disclosure, may effect numerous modifications thereto and changes may be made without departing from the scope of the invention in its aspects.
Claims (8)
1. A method for determining inter-satellite link topology for a global satellite navigation system, comprising the steps of:
s1, taking inter-satellite links among all satellites in a single observation period in the global satellite navigation system as an individual, combining the individuals corresponding to the plurality of observation periods together to be regarded as a population, and initializing the population to obtain an initial population, wherein one observation period comprises a plurality of time slots;
s2, carrying out constraint processing on the initial population to obtain a constrained population;
s3, performing grading treatment on the constrained population to serve as a generation population, performing genetic evolution treatment on the generation population to obtain a second generation population, combining the generation population and the second generation population to form a new generation population, performing the grading treatment on the new generation population to obtain a new generation graded population, filling the new generation graded population into the generation population according to a preset filling rule, and performing iteration according to preset iteration times;
and S4, determining the inter-satellite link topological structure according to the generation population after iteration.
2. The method according to claim 1, wherein the initializing the population in step S1 to obtain an initial population specifically includes the following steps:
s11, numbering each satellite in the global satellite navigation system;
s12, taking all forward inter-satellite links in a single time slot in a single observation period as a gene, and determining a gene coding vector corresponding to the single time slot according to the number and the number of the inter-satellite links in the single time slot;
s13, determining the gene coding vectors corresponding to all the time slots in a single observation period, combining the gene coding vectors into a coding matrix and regarding the coding matrix as a chromosome;
s14, determining the chromosomes corresponding to all the observation periods so as to complete initialization of the population.
3. The method for determining the inter-satellite link topology for the global navigation satellite system according to claim 1, wherein the constraint processing in the step S2 specifically comprises:
constraining the initial population by geometric visibility constraint, antenna visibility constraint and inter-satellite distance constraint to obtain a constrained population;
the geometric visibility constraint may be specifically constrained by the following equation:
the antenna visibility constraint may be specifically constrained by the following equation:
the inter-satellite distance constraint may be specifically constrained by the following formula:
a, B is a satellite to be linked in the global satellite navigation system, θ A Is the included angle theta between the single inter-satellite link between the AB satellites and the earth center connecting line of the A satellite on the single inter-satellite link B Is the included angle between the single inter-satellite link between the AB satellites and the earth center connecting line between the B satellite on the single inter-satellite link, R is the radius of the earth, h is the thickness of the atmosphere, d A Is the A satellite orbit altitude, d B Taking the earth mass center as the sphere center, adding R and h into a radius to form a sphere, wherein the tangent of the spherical surface passing through the satellite A is a first tangent, the tangent of the spherical surface passing through the satellite B is a second tangent, and beta is beta A Is the angle between the first tangent and the line connecting the satellite A to the geocentric, beta B Is the included angle between the second tangent and the connecting line from the B satellite to the geocentric, alpha max Is the maximum scan angle of the satellite antenna,/ AB Is the actual inter-satellite distance, L, between the A satellite and the B satellite Amin Is said theta A And said alpha max When the distances between the A satellite and the earth center to the single inter-satellite link vertical point between the AB satellites are equal, L Bmin Is said θ B And said alpha max When the distance between the B satellite and the earth center to the single inter-satellite link vertical point between the AB satellites is equal, L Amax Is the distance, L, from the A satellite to the first tangent point Bmax The distance between the B satellite and the second tangent point is obtained.
4. The method according to claim 1, wherein the classification process in step S3 includes a pareto classification process and a congestion degree process, and the classification process includes the following specific steps:
s31, establishing a plurality of objective functions based on the number of idle satellites, the inter-satellite distance of the established-link satellites and the PDOP value of the whole satellite
S32, based on a plurality of objective functions, performing fast non-dominated sorting on corresponding populations to perform pareto grading processing on the corresponding populations to obtain corresponding graded populations, wherein the corresponding graded populations comprise a plurality of graded populations, each graded population corresponds to one pareto grade, and the corresponding graded populations are arranged in the corresponding graded populations according to the sequence from low to high of the pareto grades, wherein the corresponding populations are specifically the constraint population and the new generation population, and the corresponding graded populations are specifically the first generation population and the new generation graded population;
s33, determining the crowding degrees corresponding to all the individuals except two boundary individuals in each level population in the corresponding level population, and arranging the corresponding individuals in each level population according to the sequence of the crowding degrees from large to small.
5. The method for determining the inter-satellite link topology for the global navigation satellite system according to claim 4, wherein the plurality of objective functions in step S31 specifically include:
objective function f of the number of idle satellites 1 Comprises the following steps:
f 1 ＝max(Num 1 ,Num 2 ,…,Num TimeslotNum )-min(Num 1 ,Num 2 ,…,Num TimeslotNum )；
target function f of distance between satellites of the building link satellite 2 Comprises the following steps:
an objective function f of the global satellite PDOP value 3 Comprises the following steps:
wherein, num i Representing the number of the inter-satellite links in the ith time slot, the TimeslotNum representing the number of the time slots in one observation period, m being the number of the inter-satellite links in one time slot, D ij Is the inter-satellite distance of the j inter-satellite link in the ith time slot, PDOP i Indicating the PDOP value for the ith satellite with the current inter-satellite link network structure.
6. The method according to claim 4, wherein the preset filling rule in step S3 is specifically:
and sequentially placing the corresponding grade populations in the grading populations into the generation populations according to the sequence of the pareto grades from low to high until all the grade populations cannot be placed into the generation populations, and sequentially placing the individuals in the grade populations into the generation populations according to the sequence of the crowdedness from high to low until the generation populations are full.
7. The method according to claim 1, wherein the step S4 specifically includes the steps of:
s41, determining a plurality of objective function values of the generation population after iteration is completed, and comparing the values with a preset result threshold value;
s42, judging whether a plurality of objective function values of the first generation population are smaller than the preset result threshold value, if so, determining the inter-satellite link topological structure according to the first generation population and the coordinates of all satellites, and if not, continuously iterating the first generation population for preset iteration times.
8. The method of claim 1, wherein the genetic evolution process comprises a selection process, a crossover process, and a mutation process.
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