WO2022198748A1 - 一种面向araim应用的低轨卫星增强系统星座配置优化方法 - Google Patents

一种面向araim应用的低轨卫星增强系统星座配置优化方法 Download PDF

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WO2022198748A1
WO2022198748A1 PCT/CN2021/090796 CN2021090796W WO2022198748A1 WO 2022198748 A1 WO2022198748 A1 WO 2022198748A1 CN 2021090796 W CN2021090796 W CN 2021090796W WO 2022198748 A1 WO2022198748 A1 WO 2022198748A1
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parameter
vpl
population
sample
parameters
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王志鹏
朱衍波
杨子仪
方堃
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北京航空航天大学
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Priority to US18/089,639 priority Critical patent/US11742935B2/en
Priority to ZA2023/03609A priority patent/ZA202303609B/en

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    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04B—TRANSMISSION
    • H04B7/00—Radio transmission systems, i.e. using radiation field
    • H04B7/14—Relay systems
    • H04B7/15—Active relay systems
    • H04B7/185—Space-based or airborne stations; Stations for satellite systems
    • H04B7/1853—Satellite systems for providing telephony service to a mobile station, i.e. mobile satellite service
    • H04B7/18563—Arrangements for interconnecting multiple systems
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/20—Design optimisation, verification or simulation
    • G06F30/27—Design optimisation, verification or simulation using machine learning, e.g. artificial intelligence, neural networks, support vector machines [SVM] or training a model
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S19/00—Satellite radio beacon positioning systems; Determining position, velocity or attitude using signals transmitted by such systems
    • G01S19/01—Satellite radio beacon positioning systems transmitting time-stamped messages, e.g. GPS [Global Positioning System], GLONASS [Global Orbiting Navigation Satellite System] or GALILEO
    • G01S19/03—Cooperating elements; Interaction or communication between different cooperating elements or between cooperating elements and receivers
    • G01S19/07—Cooperating elements; Interaction or communication between different cooperating elements or between cooperating elements and receivers providing data for correcting measured positioning data, e.g. DGPS [differential GPS] or ionosphere corrections
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04B—TRANSMISSION
    • H04B7/00—Radio transmission systems, i.e. using radiation field
    • H04B7/14—Relay systems
    • H04B7/15—Active relay systems
    • H04B7/185—Space-based or airborne stations; Stations for satellite systems
    • H04B7/18521—Systems of inter linked satellites, i.e. inter satellite service
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F2111/00—Details relating to CAD techniques
    • G06F2111/04—Constraint-based CAD
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F2111/00—Details relating to CAD techniques
    • G06F2111/06—Multi-objective optimisation, e.g. Pareto optimisation using simulated annealing [SA], ant colony algorithms or genetic algorithms [GA]
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02D—CLIMATE CHANGE MITIGATION TECHNOLOGIES IN INFORMATION AND COMMUNICATION TECHNOLOGIES [ICT], I.E. INFORMATION AND COMMUNICATION TECHNOLOGIES AIMING AT THE REDUCTION OF THEIR OWN ENERGY USE
    • Y02D30/00—Reducing energy consumption in communication networks
    • Y02D30/70—Reducing energy consumption in communication networks in wireless communication networks

Definitions

  • the invention relates to the technical field of satellite navigation, in particular to a method for optimizing constellation configuration of a low-orbit satellite augmentation system for ARAIM applications.
  • GNSS Global Navigation Satellite System
  • low-orbit satellite constellations for mobile communications appeared, typically represented by the Iridium and Globalstar constellations in the United States.
  • the second-generation iridium system completed the networking, completely replacing the first-generation iridium system.
  • the new-generation Iridium system is also equipped with a navigation enhancement payload, which can provide users with other services such as positioning tracking and broadcast automatic dependent surveillance.
  • a navigation enhancement payload can provide users with other services such as positioning tracking and broadcast automatic dependent surveillance.
  • many internationally renowned companies such as OneWeb, SpaceX, Boeing in the United States, Samsung in South Korea, China Aerospace Science and Technology Corporation and Aerospace Science and Industry Corporation have successively announced the launch and deployment of their own commercial low-orbit constellations, all to provide global Seamless and stable broadband Internet communication service.
  • Hongyan mobile communication constellation will also have mobile broadcasting functions and be equipped with on-board GNSS receivers, equipped with navigation enhancement functions.
  • Beidou-3 marks the official establishment of a meter-level navigation and positioning system comparable to GPS in my country.
  • Ran Chengqi deputy chief designer of Beidou satellite navigation system engineering, said that before 2025, it is expected to be referred to as a space-based low-orbit constellation system. , to provide centimeter-level positioning services to the world.
  • the LEO satellite navigation enhancement system has a lack of integrity monitoring. Once the LEO satellite navigation system is officially used for navigation enhancement services, it will affect the ARAIM machine. availability of the onboard receiver.
  • An object of the present invention is to provide a low-orbit satellite augmentation system constellation configuration optimization method for ARAIM applications, the method comprising the following method steps:
  • Step 1 In the case of determining the equal distribution of integrity risk and continuity risk, traverse all subset solutions and the vertical protection level after failure mode, and determine the constraints of low-orbit satellite constellation configuration parameters,
  • Step 2 Determine the objective function of the parameters x 1 , x 2 , x 3 , and x 4 of the low-orbit satellite constellation configuration, eliminate the calculated values of abnormal vertical protection levels, and filter the parameters x 1 , x 2 , x 3 , x 4 . initial population,
  • the parameter x 1 is the orbit inclination angle
  • the parameter x 2 is the orbit height
  • the parameter x 3 is the starting value of the right ascension at the ascending node
  • the parameter x 4 is the starting value of the anterior angle
  • Step 3 performing fitness calculation on the objective functions of the parameters x 1 , x 2 , x 3 , and x 4 of the low-orbit satellite constellation configuration;
  • Step 4 After screening out the initial population of parameters x 1 , x 2 , x 3 , and x 4 , starting from the second generation population, merge the parent population and the child population to form a new child population, and perform fast non-dominant sorting , calculate the crowding degree of the individuals in each non-dominated layer, randomly pair the individuals, and perform the crossover operation of the genetic algorithm between the paired individuals;
  • Step 5 After the parent population and the child population are merged to form a new child population, the optimal preservation strategy and local optimal selection are performed on the new child population, and the maximum value of the objective function is selected as the optimal child.
  • step 4 Repeat step 4 until the genetic generation is less than the maximum genetic generation.
  • the vertical relegation in step 1 is expressed as:
  • VPL q max((VPL 0 ) q ,max((VPL i ) q ), where VPL 0 is the vertical protection level under no fault condition, is the integrity and continuity risk value of the failure-free mode under the subset of fully visible stars, is the projection matrix, b int,n is the maximum nominal deviation of the nth satellite;
  • VPL i is the vertical protection level corresponding to the measured deviation of the i-th failure mode not exceeding the maximum deviation, D i,q is the detection threshold;
  • G is the geometric matrix in the pseudorange observation equation
  • W INT is the model parameter of the fixed error assumption about integrity
  • Mi is a unit matrix of size N sat *N sat
  • N sat is the number of visible satellites
  • q is the qth sample points
  • the geometric matrix G in the pseudorange observation equation contains the parameters x 1 , x 2 , x 3 , and x 4 of the low-orbit satellite constellation configuration;
  • N 0 is the number of orbital planes of the low-orbit constellation
  • N SO is the number of satellites on each orbital plane
  • N C is the phase parameter
  • ⁇ is the right ascension of the ascending node
  • M represents the mean anomaly angle
  • i represents the ith orbital plane and j represents the jth satellite.
  • the objective functions of the parameters x 1 , x 2 , x 3 , and x 4 of the low-orbit satellite constellation configuration in step 2 are expressed as:
  • F VPL (x 1 ) indicates that the vertical protection level VPL is a function of the parameter x 1
  • F VPL (x 2 ) indicates that the vertical protection level VPL is a function of the parameter x 2
  • F VPL (x 3 ) indicates that the vertical protection level VPL is A function of parameter x3
  • F VPL ( x4 ) indicates that the vertical protection level VPL is a function of parameter x4 .
  • step 2 the calculated value of the abnormal vertical protection level is eliminated by the following method:
  • ⁇ all is the mean value of the calculated value of the vertical protection level VPL corresponding to all the sample points
  • ⁇ all is the standard deviation of the calculated value of the vertical protection and VPL corresponding to all the sample points
  • initial population screening is performed by the following method:
  • For the orbital inclination parameter x 1 set the sampling interval ⁇ 1 to 0.01, a total of 158 sample points are generated, and a set of data is taken every 9 sample points as a sample of the initial population, and these 15 samples constitute the orbital inclination parameter x 1 the initial population;
  • the sampling interval ⁇ 2 For the orbit height parameter x 2 , set the sampling interval ⁇ 2 to 1, a total of 1200 sample points are generated, and a set of data is taken every 19 sample points as a sample of the initial population, and the 60 samples constitute the orbit inclination parameter x 2 the initial population;
  • the sampling interval ⁇ 3 is set to 0.001, a total of 79 sample points are generated, and a group of data is taken every 4 sample points as a sample of the initial population.
  • the 15 samples consist of The initial population of orbital inclination parameter x 3 ;
  • the sampling interval ⁇ 4 For the initial value parameter x 4 of the average near point angle, set the sampling interval ⁇ 4 to 0.01, a total of 30 sample points are generated, and a set of data is taken every 4 sample points as a sample of the initial population.
  • the samples constitute the initial population of orbital inclination parameters x 4 .
  • step 3 fitness calculation is performed on the objective functions of the parameters x 1 , x 2 , x 3 , and x 4 configured by the low-orbit satellite constellation:
  • the fitness function adopts the maximum optimization problem function:
  • C min is a preset number
  • F VPL (x) estimated so far is taken
  • F VPL (x) is the objective function, indicating that the vertical protection level VPL is the parameters x 1 , x 2 , function of x3 or x4 .
  • the objective function should also satisfy the following conditions:
  • the combined ratio of the parent population and the child population to form a new child population is:
  • X ul is the upper limit of the optimized parameter range
  • X ll is the lower limit of the optimized parameter range
  • ⁇ i is the X ul sampling interval of each parameter
  • N interval is the time when the initial population is generated. sample interval.
  • the sample local mean is introduced in step 5 perform local optimal selection
  • the local optimum test is passed, and the maximum value of the objective function is used as the optimal child; if it is less than the threshold T sel , the maximum value near the objective function is searched as the optimal child.
  • sample local mean Expressed as:
  • m represents the m-th local mean
  • the maximum value is x i represents the ith sample of the corresponding parameter, and it is stipulated that every 5 samples is taken as the local mean
  • X ul is the upper limit of the optimized parameter range
  • X ll is the lower limit of the optimized parameter range
  • ⁇ i is the X ul of each parameter sampling interval.
  • the invention proposes a constellation configuration optimization method suitable for a low-orbit satellite navigation enhancement system based on the current situation of low-orbit navigation enhancement, and combines the non-dominated sorting genetic algorithm with an elite strategy to propose a constellation configuration optimization method based on the ARAIM protection level algorithm.
  • the optimization of the ARAIM protection-level algorithm is realized from another perspective, which makes up for the lack of integrity monitoring of the low-orbit augmentation system and provides a reference for the design and networking of the low-orbit satellite navigation system in the future.
  • the invention determines the parameters to be optimized through the ARAIM protection level formula, and obtains the specific observation matrix to be optimized after evenly distributing the risk value; defines the constraint range of the optimization parameters in the observation matrix, and optimizes the objective function within the constraint range; Abnormal data detection and data sampling are used to screen the initial population. When the parent and child populations are merged, a specific ratio is used to merge them purposefully. Finally, in order to avoid local optimization, the local mean of the sample is defined, and the optimized value and the local mean are thresholded. detection, in order to achieve the purpose of global optimization.
  • FIG. 1 schematically shows the spatial schematic diagram of the low-orbit enhanced ARAIM system of the present invention.
  • Fig. 2 shows the algorithm flow chart of the constellation configuration optimization method of the LEO enhanced system for ARAIM application.
  • Figure 3 shows a schematic diagram of the initial anomaly verification of the vertical protection level.
  • ARAIM Advanced Receiver Autonomous Integrity Monitor
  • the present invention aims to improve the ARAIM availability of the Beidou satellite navigation system, and reduce its protection level by introducing the low-orbit satellite navigation system.
  • Different parameters select the optimal low-orbit constellation configuration to improve the availability of ARAIM airborne receivers.
  • the low-orbit satellite system is briefly explained first.
  • FIG. 1 the space diagram of the low-orbit enhanced ARAIM system of the present invention is shown.
  • the low-orbit satellite system is equipped with an on-board GNSS receiver, which generates a
  • the time-frequency consistent signal of the satellite navigation system is broadcast to the ground through the on-board navigation payload.
  • the ground monitoring station receives the communication and navigation signal and transmits it to the main control station.
  • the main control station calculates and determines the orbit information of the low-orbit satellite, and uploads it to the low-orbit satellite through the uplink of the injection station.
  • the low-orbit satellite can downlink the ephemeris containing the orbit information to the user terminal, and the user terminal (airborne terminal) uses the information to use the algorithm to solve the problem, and the constellation configuration of the low-orbit satellite augmentation system is carried out. optimization.
  • a low-orbit satellite augmentation system constellation configuration optimization method for ARAIM applications comprising the following method steps:
  • Step 1 Under the condition that the integrity risk and the continuity risk are equally distributed, traverse all the subset solutions and the vertical protection level after the failure mode, and determine the constraints of the configuration parameters of the low-orbit satellite constellation.
  • the satellite position information is output according to the satellite almanac, and then the user grid point position information is read, which is related to the shadowing angle. Standard contrast looks for visible stars. According to the preset error model and failure mode, the fully visible constellation solution and the subset solution under each failure mode are calculated. After the solution separation threshold value test, the horizontal/vertical protection level, effective monitoring threshold value, etc. are calculated to evaluate the state of the constellation. . In the basic MHSS ARAIM protection level calculation, the vertical protection level (vertical protection value, VPL) less than 35m is the key index to evaluate the availability, and the VPL value of the grid point is calculated by the maximum value function.
  • VPL vertical protection value
  • the vertical protection level when it is determined that the integrity risk and the continuity risk are equally distributed, the vertical protection level after traversing all subset solutions and failure modes, the vertical protection level is expressed as:
  • VPL q max((VPL 0 ) q ,max((VPL i ) q ), where VPL 0 is the vertical protection level under no fault condition, is the integrity and continuity risk value of the failure-free mode under the subset of fully visible stars, is the projection matrix, b int,n is the maximum nominal deviation of the nth satellite;
  • VPL i is the vertical protection level corresponding to the measured deviation of the i-th failure mode not exceeding the maximum deviation, D i,q is the detection threshold;
  • G is the geometric matrix in the pseudorange observation equation
  • W INT is the model parameter of the fixed error assumption about integrity
  • Mi is a unit matrix of size N sat *N sat
  • N sat is the number of visible satellites
  • q is the qth sample points
  • the geometric matrix G in the pseudorange observation equation contains the parameters x 1 , x 2 , x 3 , and x 4 of the low-orbit satellite constellation configuration, where the parameter x 1 is the orbit inclination, the parameter x 2 is the orbit height, and the parameter x 3 is The starting value of the ascending node right ascension parameter, the parameter x 4 is the starting value of the anomaly angle.
  • the present invention optimizes the low-orbit enhanced system constellation configuration, and finally optimizes the maximum VPL to achieve the purpose of reducing the protection level. Since the protection level is optimized to optimize the maximum value, it can reduce the integrity and continuity risk value or Optimize the observation matrix and error parameters to achieve the optimization of the protection level.
  • the vertical protection level VPL is a function of the low-orbit constellation configuration parameters x 1 , x 2 , x 3 , and x 4 , that is, the objective function in step 2 below. Therefore, the configuration of the Low Earth Orbit LEO should be clarified first.
  • the present invention selects the Walker configuration in two dimensional Lattice Flower Constellation (2D-LFC), which is a special case of 2D-LFC. 2D-LFC can use 9 parameters to define the orbit of a satellite, 6 of which are Kepler elements.
  • a 2D-LFC constellation configuration will satisfy the following constraints:
  • N 0 is the number of orbital planes of the low-orbit constellation
  • N SO is the number of satellites on each orbital plane
  • N C is the phase parameter
  • ⁇ is the right ascension of the ascending node
  • M represents the mean anomaly angle
  • i represents the ith orbital plane and j represents the jth satellite.
  • Step 2 Determine the objective function of the parameters x 1 , x 2 , x 3 , and x 4 of the low-orbit satellite constellation configuration, eliminate the calculated values of abnormal vertical protection levels, and filter the parameters x 1 , x 2 , x 3 , x 4 . initial population,
  • the parameter x 1 is the orbital inclination angle
  • the parameter x 2 is the orbit height
  • the parameter x 3 is the starting value of the right ascension at the ascending node
  • the parameter x 4 is the starting value of the anterior angle.
  • the present invention is a multi-objective optimization problem (MOOP), it is a multi-objective optimization problem discussed based on the pareto optimal solution.
  • MOOP multi-objective optimization problem
  • the screening of the initial population is particularly critical.
  • MOOP is transformed into a single objective optimization problem (simple objective optimization problem, SOOP), and the objective functions for the four optimization parameters are listed as follows:
  • F VPL (x 1 ) indicates that the vertical protection level VPL is a function of the parameter x 1
  • F VPL (x 2 ) indicates that the vertical protection level VPL is a function of the parameter x 2
  • F VPL (x 3 ) indicates that the vertical protection level VPL is A function of parameter x3
  • F VPL ( x4 ) indicates that the vertical protection level VPL is a function of parameter x4 .
  • the first task is to remove these outliers.
  • the calculated value of the abnormal vertical protection level is eliminated by the following method:
  • ⁇ all is the mean value of the calculated value of the vertical protection level VPL corresponding to all the sample points
  • ⁇ all is the standard deviation of the calculated value of the vertical protection and VPL corresponding to all the sample points
  • the failed data will be verified separately after the entire data process, and all abnormal causes will be traversed, such as: constellation width failure, clock ephemeris failure, signal deformation, antenna bias error, etc. If there is no match, it will be added to the initial population.
  • the selection strategy of the initial population is very important.
  • the original random construction method is based on the huge sample size.
  • the configuration parameters x 1 , x 3 and x 4 of the low-orbit constellation of the present invention only need to be accurate to two or three decimal places, and x 2 It needs to be accurate to the single digit, otherwise it will increase a lot of unnecessary computational load.
  • the present invention proposes a sampling-based data initial population screening strategy for the above four parameters.
  • initial population screening is performed by the following methods:
  • For the orbital inclination parameter x 1 set the sampling interval ⁇ 1 to 0.01, a total of 158 sample points are generated, and a set of data is taken every 9 sample points as a sample of the initial population, and these 15 samples constitute the orbital inclination parameter x 1 the initial population;
  • the sampling interval ⁇ 2 For the orbit height parameter x 2 , set the sampling interval ⁇ 2 to 1, a total of 1200 sample points are generated, and a set of data is taken every 19 sample points as a sample of the initial population, and the 60 samples constitute the orbit inclination parameter x 2 the initial population;
  • the sampling interval ⁇ 3 is set to 0.001, a total of 79 sample points are generated, and a group of data is taken every 4 sample points as a sample of the initial population.
  • the 15 samples consist of The initial population of orbital inclination parameter x 3 ;
  • the sampling interval ⁇ 4 For the initial value parameter x 4 of the average near point angle, set the sampling interval ⁇ 4 to 0.01, a total of 30 sample points are generated, and a set of data is taken every 4 sample points as a sample of the initial population.
  • the samples constitute the initial population of orbital inclination parameters x 4 .
  • Step 3 Calculating the fitness of the objective functions of the parameters x 1 , x 2 , x 3 , and x 4 of the low-orbit satellite constellation configuration.
  • the individual fitness is used to evaluate the pros and cons of the individual, so the fitness function is needed to participate in the evaluation, and the appropriate evolutionary individual selection method helps to improve the evolutionary efficiency of the population.
  • the present invention performs fitness calculation on the objective functions of the parameters x 1 , x 2 , x 3 , and x 4 of the low-orbit satellite constellation configuration by the following methods:
  • the fitness function adopts the maximum optimization problem function:
  • C min is a preset number
  • F VPL (x) estimated so far is taken
  • F VPL (x) is the objective function, indicating that the vertical protection level VPL is the parameters x 1 , x 2 , function of x3 or x4 .
  • the objective function F VPL (x) Since the value of the objective function F VPL (x) only meets the requirements of LPV-200, in addition to the above fitness function, the objective function should also meet the following conditions:
  • the requirements for the objective function should also be increased, and the fitness function calculation can be performed only after passing the limit value.
  • Step 4 After screening out the initial population of parameters x 1 , x 2 , x 3 , and x 4 , starting from the second generation population, merge the parent population and the child population to form a new child population, and perform fast non-dominant sorting , the crowding degree is calculated for the individuals in each non-dominated layer, the individuals are randomly paired, and the crossover operation of the genetic algorithm is performed between the paired individuals.
  • the parent population of the previous generation will be merged with the descendant population. Since the sample size and population size of the four parameters are different, the present invention defines that the parent population and the descendant population are merged to form a new The combined proportion of the offspring population is:
  • X ul is the upper limit of the optimized parameter range
  • X ll is the lower limit of the optimized parameter range
  • ⁇ i is the X ul sampling interval of each parameter
  • N interval is the time when the initial population is generated. sample interval.
  • fast non-dominated sorting is performed.
  • the crowding degree of the individuals in each non-dominated layer is calculated, the individuals are randomly paired, and the crossover operation is performed between the two paired individuals.
  • the crossover operator also cooperates with the mutation operator.
  • the mutation operator has a strong local search ability. The mutual cooperation of the two makes the genetic algorithm have both the global search ability and the local search ability.
  • Step 5 After the parent population and the child population are merged to form a new child population, the optimal preservation strategy selection and local optimal selection are performed on the new child population, and the maximum value of the objective function is selected as the optimal child, and repeated. Step 4, until the genetic algebra is less than the maximum genetic algebra.
  • the optimal preservation strategy commonly used in the prior art can make the individuals with the highest fitness do not participate in crossover and mutation, and use it to replace the individuals with the lowest fitness after crossover and mutation. This method retains the individuals with the highest fitness, but This method is not easy to eliminate the local optimal solution of the algorithm, which reduces the global search ability.
  • the present invention has used the sampling interval ⁇ i for sampling in the initial population selection, which avoids the local optimum to a certain extent. On this basis, the present invention introduces the local mean value of the sample. Make a local optimal selection, where,
  • m represents the m-th local mean
  • the maximum value is x i represents the ith sample of the corresponding parameter, and it is stipulated that every 5 samples is taken as the local mean
  • X ul is the upper limit of the optimized parameter range
  • X ll is the lower limit of the optimized parameter range
  • ⁇ i is the X ul of each parameter sampling interval.
  • the selection threshold T sel (determined according to the statistical average of the ARAIM protection level in practical application) is set, and after the optimal preservation strategy is selected for the new offspring population, the objective function is compared with each local mean value. do bad,
  • the local optimum test is passed, and the maximum value of the objective function is used as the optimal child; if it is less than the threshold T sel , the maximum value near the objective function is searched as the optimal child.
  • step 4 After filtering out the maximum value of the objective function as the optimal offspring, repeat step 4 and cycle until the genetic algebra meets the end condition (less than the maximum algebra, and can be adjusted at any time according to the specific simulation environment).
  • the vertical protection level reaches the minimum value
  • the corresponding optimized parameters x 1 , x 2 , x 3 , and x 4 are the constellation configurations that make the low-orbit satellite augmentation system the lowest protection level. Using this configuration can ensure availability while at the same time. Take into account economic factors.
  • the invention proposes a constellation configuration optimization method suitable for a low-orbit satellite navigation enhancement system based on the current situation of low-orbit navigation enhancement, and combines the non-dominated sorting genetic algorithm with an elite strategy to propose a constellation configuration optimization method based on the ARAIM protection level algorithm.
  • the optimization of the ARAIM protection-level algorithm is realized from another perspective, which makes up for the lack of integrity monitoring of the low-orbit augmentation system and provides a reference for the design and networking of the low-orbit satellite navigation system in the future.
  • the invention determines the parameters to be optimized through the ARAIM protection level formula, and obtains the specific observation matrix to be optimized after evenly distributing the risk value; defines the constraint range of the optimization parameters in the observation matrix, and optimizes the objective function within the constraint range; Abnormal data detection and data sampling are used to screen the initial population. When the parent and child populations are merged, a specific ratio is used to merge them purposefully. Finally, in order to avoid local optimization, the local mean of the sample is defined, and the optimized value and the local mean are thresholded. detection, in order to achieve the purpose of global optimization.

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Abstract

一种面向ARAIM应用的低轨卫星增强系统星座配置优化方法，包括：1、确定完好性风险和连续性风险均等分配的情况下，遍历所有子集解和故障模式后的垂直保护级，以及确定低轨卫星星座配置参数的约束条件，2、确定低轨卫星星座配置的参数x1、x2、x3、x4的目标函数，剔除异常的垂直保护级的计算值，筛选参数x1、x2、x3、x4的初始种群，3、对低轨卫星星座配置的参数x1、x2、x3、x4的目标函数进行适应度计算；4、从第二代种群开始，将父代种群与子代种群合并形成新子代种群；5、对新子代种群进行局部最优选择，筛选出目标函数的最大值作为最优子代，重复步骤4，直至遗传代数小于最大遗传代数。弥补了低轨增强系统的完好性监测空缺，提高了ARAIM机载接收机的可用性。

Description

一种面向ARAIM应用的低轨卫星增强系统星座配置优化方法 技术领域
本发明涉及卫星导航技术领域，特别涉及一种面向ARAIM应用的低轨卫星增强系统星座配置优化方法。
背景技术
全球卫星导航系统(Global Navigation Satellite System，GNSS)发展迅速，目前已广泛应用于各个领域。未来，全球大众用户对高精度、快收敛、高完好、高安全、高可用等都提出了一系列要求，所以在复杂环境下的高安全实时精密定位成为当前GNSS更高的目标。为了解决以上问题，各国都在积极建设自己的导航增强系统，而传统的导航增强系统均为地面测站辅助信息增强的工作体制。但由于我国领土及疆域限制，难以通过全球布设地面站来实现全球厘米级定位以及快收敛服务。所以，随着布站密度和信息速率需求的不断增长，现有的增强系统已经无法支持下一代北斗实现挑战环境下的厘米级实时定位服务。为此，需要设计新型增强系统的架构与体制，以实现三个目标：1)降低对海外建站的依赖；2)将增强服务由区域增强扩展至全球增强；3)大幅提升精密定位服务的可用性和安全性。
随着通信业务的发展，在20世纪末，出现了用于移动通信的低轨卫星星座，典型的代表是美国的铱星(Iridium)和全球星(Globalstar)星座。2019年1月，第二代铱系统完成组网，完全取代第一代铱系统。新一代铱星系统除提供原有的通信服务外，还搭载了导航增强有效载荷，可为用户提供通信以外的定位跟踪、广播式自动相关监视等其他服务。2015年以来，许多国际知名企业如美国的OneWeb、SpaceX、Boeing，韩国的Samsung，中国的航天科技集团和航天科工集团等先后宣布发射和部署各自的商用低轨星座，均是为了向全球提供无缝稳定的宽带互联网通 信服务。我国的“鸿雁”星座首发星已于2018年12月29日成功发射并进入预定轨道，整个星座计划在2024年前后部署完成。鸿雁移动通信星座除满足多领域监测数据信息传送需求外，还将具备移动广播功能并且搭载星上GNSS接收机，配置导航增强功能。
由于低轨卫星市场发展迅速，且搭载导航增强载荷实现成本低，可将其作为天基监测平台，实现“天基监测+信号增强”的导航增强新系统。北斗三号的开通，标志我国正式建成与GPS媲美的米级导航定位系统，对于北斗今后的发展，北斗卫星导航系统工程副总设计师冉承其表示，2025年前有望简称天基的低轨星座系统，向全球提供厘米级定位服务。
目前关于低轨导航增强的研究主要集中于实时精密定轨及遥感监测方面，低轨卫星导航增强系统存在完好性监测空缺，一旦低轨卫星导航系统正式用于导航增强服务，将会影响ARAIM机载接收机的可用性。
因此，为了克服现有技术中的问题，需要一种面向ARAIM应用的低轨卫星增强系统星座配置优化方法。
发明内容
本发明的一个目的在于提供一种面向ARAIM应用的低轨卫星增强系统星座配置优化方法，所述方法包括如下方法步骤：
步骤1、确定完好性风险和连续性风险均等分配的情况下，遍历所有子集解和故障模式后的垂直保护级，以及确定低轨卫星星座配置参数的约束条件，
步骤2、确定低轨卫星星座配置的参数x 1、x 2、x 3、x 4的目标函数，剔除异常的垂直保护级的计算值，筛选参数x 1、x 2、x 3、x 4的初始种群，
其中，参数x 1为轨道倾角，参数x 2为轨道高度，参数x 3为升交点赤经起始值参数，参数x 4平近点角起始值；
步骤3、对低轨卫星星座配置的参数x 1、x 2、x 3、x 4的目标函数进行适应度计算；
步骤4、经过筛选出参数x 1、x 2、x 3、x 4的初始种群后，从第二代种群开始，将父代种群与子代种群合并形成新子代种群，进行快速非支配排 序，对每个非支配层中的个体进行拥挤度计算，对个体进行随机配对，并在配对的两个个体间进行遗传算法的交叉操作；
步骤5、父代种群与子代种群合并形成新子代种群后，对新子代种群进行最优保存策略选择，以及局部最优选择，筛选出目标函数的最大值作为最优子代，
重复步骤4，直至遗传代数小于最大遗传代数。
优选地，步骤1中所述垂直保级表述为：
VPL q＝max((VPL 0) q,max((VPL i) q)，其中，VPL 0为无故障条件下垂直保护级，
Figure PCTCN2021090796-appb-000001
为全可见星子集下无故障模式的完好性和连续性风险值，
Figure PCTCN2021090796-appb-000002
为投影矩阵，b int,n为第n颗卫星的最大标称偏差；
VPL i为不超过最大偏差下第i个故障模式的测量偏差对应的垂直保护级，
Figure PCTCN2021090796-appb-000003
D i,q为检测阈值；
其中，
Figure PCTCN2021090796-appb-000004
G为伪距观测方程中的几何矩阵，W INT为有关完好性的固定误差假设模型参数，M i为一个N sat*N sat大小的单位矩阵，N sat为可见卫星数目，q是表示第q个样本点，
伪距观测方程中的几何矩阵G中包含低轨卫星星座配置的参数x 1、x 2、x 3、x 4；
所述低轨卫星星座配置参数的约束条件表述为：
Figure PCTCN2021090796-appb-000005
其中，N 0表示低轨星座的轨道面个数，N SO表示每个轨道面上卫星的个数，N C为相位参数，N C∈[1，N 0]，Ω表示升交点赤经，M表示平均近点角，其中i表示第i个轨道面，j表示第j颗卫星。
优选地，步骤2中低轨卫星星座配置的参数x 1、x 2、x 3、x 4的目标函数表述为：
Figure PCTCN2021090796-appb-000006
Figure PCTCN2021090796-appb-000007
Figure PCTCN2021090796-appb-000008
Figure PCTCN2021090796-appb-000009
其中，F VPL(x 1)表示垂直保护级VPL是参数x 1的函数，F VPL(x 2)表示垂直保护级VPL是参数x 2的函数，F VPL(x 3)表示垂直保护级VPL是参数x 3的函数，F VPL(x 4)表示垂直保护级VPL是参数x 4的函数。
优选地，步骤2中通过如下方法剔除异常的垂直保护级的计算值：
设定初始异常检测阈值
Figure PCTCN2021090796-appb-000010
定义
Figure PCTCN2021090796-appb-000011
其中，
μ all为所有样本点对应的垂直保护级VPL计算值的均值，σ all所有样本点对应的垂直保护及VPL计算值的标准差，
将每个样本点的垂直保护级VPL计算值与
Figure PCTCN2021090796-appb-000012
比较，若满足不等式
Figure PCTCN2021090796-appb-000013
则该样本点通过阈值检测，等待初始种群筛选，若不满足足不等式
Figure PCTCN2021090796-appb-000014
则该样本点未通过阈值检测，该样本点存储于异常数据模块。
优选地，步骤2中通过如下方法进行初始种群筛选：
对于轨道倾角参数x 1，将采样间隔Δτ 1设为0.01，共产生158个样本点，每隔9个样本点取一组数据作为初始种群的一个样本，该15个样本组成轨道倾角参数x 1的初始种群；
对于轨道高度参数x 2，将采样间隔Δτ 2设为1，共产生1200个样本点，每隔19个样本点取一组数据作为初始种群的一个样本，该60个样本组成轨道倾角参数x 2的初始种群；
对于升交点赤经起始值参数x 3，将采样间隔Δτ 3设为0.001，共产生79个样本点，每隔4个样本点取一组数据作为初始种群的一个样本，该15个样本组成轨道倾角参数x 3的初始种群；
对于平近点角起始值参数x 4来说，将采样间隔Δτ 4设为0.01，共产生30个样本点，每隔4个样本点取一组数据作为初始种群的一个样本，该6个样本组成轨道倾角参数x 4的初始种群。
优选地，步骤3中通过如下方法对低轨卫星星座配置的参数x 1、x 2、x 3、x 4的目标函数进行适应度计算：
适应度函数采用最大最优化问题函数：
Figure PCTCN2021090796-appb-000015
其中，C min是预先设定的数，取目前为止估计的目标函数F VPL(x)的最小函数值，F VPL(x)为目标函数，表示垂直保护级VPL是参数x 1、x 2、x 3或者x 4的函数。
优选地，目标函数还应当满足如下条件：
目标函数F VPL(x)的值≤35m。
优选地，父代种群与子代种群合并形成新子代种群的合并比例为：
Figure PCTCN2021090796-appb-000016
i＝1,2,3,4，其中，X ul为优化参数范围的上限，X ll为优化参数范围的下限，Δτ i为每个参数的X ul采样间隔，N interval为生成初始种群时的样本间隔。
优选地，步骤5中引入样本局部均值
Figure PCTCN2021090796-appb-000017
进行局部最优选择，
设定选择阈值T sel，对新子代种群进行最优保存策略选择后，将目标函数与每个局部均值
Figure PCTCN2021090796-appb-000018
做差，
若大于选择阈值T sel，则通过该局部最优检验，目标函数的最大值作为最优子代；若小于阈值T sel，将搜索该目标函数附近的最大值作为最优子代。
优选地，样本局部均值
Figure PCTCN2021090796-appb-000019
表述为：
Figure PCTCN2021090796-appb-000020
其中，
m表示第m个局部均值，最大值为
Figure PCTCN2021090796-appb-000021
x i表示对应参数的第i个样本，规定每5个样本取一次均值作为局部均值，X ul为优化参数范围的上限，X ll为优化参数范围的下限，Δτ i为每个参数的X ul采样间隔。
本发明基于低轨导航增强现状提出了一种适用于低轨卫星导航增强 系统的星座配置优化方法，并结合带精英策略的非支配排序遗传算法提出了基于ARAIM保护级算法的星座配置优化方法，通过异常数据剔除、参数采样等操作从另一角度实现了ARAIM保护级算法优化，弥补了低轨增强系统的完好性监测空缺，为今后低轨卫星导航系统设计及组网提供参考。
本发明通过ARAIM保护级公式确定待优化参数，将风险值平均分配后得出具体待优化观测矩阵；定义观测矩阵中优化参数的约束范围，在约束范围内进行目标函数的优化；优化前先进行异常数据检测及数据采样以筛选初始种群，在父代子代种群合并时采用特定比例有目的性地进行合并；最后，为避免局部最优，定义样本局部均值，将优化值与局部均值进行阈值检测，以达到全局最优的目的。
应当理解，前述大体的描述和后续详尽的描述均为示例性说明和解释，并不应当用作对本发明所要求保护内容的限制。
附图说明
参考随附的附图，本发明更多的目的、功能和优点将通过本发明实施方式的如下描述得以阐明，其中：
图1示意性示出了本发明低轨增强的ARAIM系统空间示意图。
图2示出了面向ARAIM应用的低轨增强系统星座配置优化方法算法流程图。
图3示出了垂直保护级的初始异常验证示意图。
具体实施方式
通过参考示范性实施例，本发明的目的和功能以及用于实现这些目的和功能的方法将得以阐明。然而，本发明并不受限于以下所公开的示范性实施例；可以通过不同形式来对其加以实现。说明书的实质仅仅是帮助相关领域技术人员综合理解本发明的具体细节。
在下文中，将参考附图描述本发明的实施例。在附图中，相同的附图标记代表相同或类似的部件，或者相同或类似的步骤。
高级接收机自主完好性监测(Advanced Receiver Autonomous  Integrity Monitor，ARAIM)是卫星导航完好性监测中的重要技术，在机载端执行算法后如有故障可及时向用户告警，无需大量建设地面基础设施，应用方便快捷，可迅速普及。
为了解决现有技术中存在的问题，本发明旨在完善北斗卫星导航系统的ARAIM可用性，通过引入低轨卫星导航系统降低其保护级水平，本发明通过使用带精英策略的非支配排序遗传算法针对不同参数选取最优的低轨星座配置，以提高ARAIM机载接收机的可用性。
为了使本发明得以更加清晰的说明，首先对低轨卫星系统进行简要阐述，如图1所示本发明低轨增强的ARAIM系统空间示意图，低轨卫星系统搭载星上GNSS接收机，生成与北斗卫星导航系统时频一致的信号，并通过星上导航载荷向地面播发。地面监测站接收到通信导航信号后传至主控站，主控站解算后确定低轨卫星轨道信息，并通过注入站的上行链路上传至低轨卫星。此时，低轨卫星可通过下行链路将包含轨道信息的星历下传至用户端，用户端(机载端)通过利用这些信息使用算法进行解算，对低轨卫星增强系统星座配置进行优化。
图2所示本发明面向ARAIM应用的低轨增强系统星座配置优化方法算法流程图，根据本发明的实施例，一种面向ARAIM应用的低轨卫星增强系统星座配置优化方法，包括如下方法步骤：
步骤1、确定完好性风险和连续性风险均等分配的情况下，遍历所有子集解和故障模式后的垂直保护级，以及确定低轨卫星星座配置参数的约束条件。
低轨卫星及北斗导航卫星星历数据数据输入ARAIM多假设解分离(Multiple Hypothesis Solution Separation，MHSS)用户算法中后，根据卫星历书输出卫星位置信息，接着读取用户格网点位置信息，与遮蔽角标准对比寻找可见星。根据预设的误差模型及故障模式计算出全可见星解以及各个故障模式下的子集解，经过解分离阈值检验后计算水平/垂直保护级、有效监测阈值等，以此来评估星座的状态。在基本MHSS ARAIM保护级计算中，垂直保护级(vertical protection value，VPL)小于35m是评价可用性的关键指标，而该格网点的VPL值是通过最大值函数计 算而来的。
根据本发明的实施例，确定完好性风险和连续性风险均等分配的情况下，遍历所有子集解和故障模式后的垂直保护级，垂直保级表述为：
VPL q＝max((VPL 0) q,max((VPL i) q)，其中，VPL 0为无故障条件下垂直保护级，
Figure PCTCN2021090796-appb-000022
为全可见星子集下无故障模式的完好性和连续性风险值，
Figure PCTCN2021090796-appb-000023
为投影矩阵，b int,n为第n颗卫星的最大标称偏差；
VPL i为不超过最大偏差下第i个故障模式的测量偏差对应的垂直保护级，
Figure PCTCN2021090796-appb-000024
D i,q为检测阈值；
其中，
Figure PCTCN2021090796-appb-000025
G为伪距观测方程中的几何矩阵，W INT为有关完好性的固定误差假设模型参数，M i为一个N sat*N sat大小的单位矩阵，N sat为可见卫星数目，q是表示第q个样本点，
伪距观测方程中的几何矩阵G中包含低轨卫星星座配置的参数x 1、x 2、x 3、x 4，其中，参数x 1为轨道倾角，参数x 2为轨道高度，参数x 3为升交点赤经起始值参数，参数x 4平近点角起始值。
本发明的对低轨增强系统星座配置进行优化，最终是优化最大的VPL达到减小保护级的目的，由于保护级优化为优化最大值的问题，所以通过减小完好性及连续性风险值或优化观测矩阵和误差参数实现保护级的优化。
在优化过程中，垂直保护级VPL是低轨星座配置参数x 1、x 2、x 3、x 4的函数，即下文中步骤2中的目标函数。因此首先应明确低轨星座(Low Earth Orbit LEO)的配置。结合实际发射成本问题，本发明选取two dimensional Lattice Flower Constellation(2D-LFC)中的Walker构型，该构型为2D-LFC的特例。2D-LFC可用9个参数来定义一颗卫星的轨道，其中6个参数为开普勒元素。
根据本发明，确定低轨卫星星座配置参数的约束条件，一个2D-LFC星座配置将满足以下约束：
Figure PCTCN2021090796-appb-000026
其中，N 0表示低轨星座的轨道面个数，N SO表示每个轨道面上卫星的个数，N C为相位参数，N C∈[1，N 0]， Ω表示升交点赤经，M表示平均近点角，其中i表示第i个轨道面，j表示第j颗卫星。
考虑到外部约束条件，四个参数应被约束在一定范围内，如表1所示。
表1 LEO星座优化参数
参数 范围
x 1轨道倾角(rad) 0～π/2
x 2轨道高度(km) 800～2000
x 3升交点赤经起始值(rad) 0～0.782
x 4平近点角起始值(rad) 0～0.3
步骤2、确定低轨卫星星座配置的参数x 1、x 2、x 3、x 4的目标函数，剔除异常的垂直保护级的计算值，筛选参数x 1、x 2、x 3、x 4的初始种群，
其中，参数x 1为轨道倾角，参数x 2为轨道高度，参数x 3为升交点赤经起始值参数，参数x 4平近点角起始值。
确定目标函数
由于本发明为多目标最优化问题(multiple objective optimization problem，MOOP)，是基于pareto最优解讨论的多目标优化问题，在使用带精英策略的非支配排序遗传算法(Elitist Nondominated Sorting Genetic Algorithm，NSGA-II)方法中，初始种群的筛选尤为关键。
首先将MOOP转化为单目标最优化问题(simple objective optimization problem，SOOP)，对四个优化参数分别列出目标函数如下：
Figure PCTCN2021090796-appb-000027
Figure PCTCN2021090796-appb-000028
Figure PCTCN2021090796-appb-000029
Figure PCTCN2021090796-appb-000030
在数学处理中，最大值的最小化也就是min(max((VPL 0) q,max((VPL i) q)))，由于不便于数学计算，因此将式子取两个负号，原优化目标变形为：
Figure PCTCN2021090796-appb-000031
则低轨卫星星座配置的四个参数x 1、x 2、x 3、x 4对应的目标函数描述为：
Figure PCTCN2021090796-appb-000032
Figure PCTCN2021090796-appb-000033
Figure PCTCN2021090796-appb-000034
Figure PCTCN2021090796-appb-000035
其中，F VPL(x 1)表示垂直保护级VPL是参数x 1的函数，F VPL(x 2)表示垂直保护级VPL是参数x 2的函数，F VPL(x 3)表示垂直保护级VPL是参数x 3的函数，F VPL(x 4)表示垂直保护级VPL是参数x 4的函数。
剔除异常垂直保护级的计算值
由于卫星中断、星历计算错误、漏警虚警等原因有可能出现个别VPL计算值与真实值相差较大，这样的VPL值无法正常参与最优化计算。所以，首要任务是剔除这些异常值。
根据本发明的实施例，如图3所示垂直保护级的初始异常验证示意图，通过如下方法剔除异常的垂直保护级的计算值：
根据VPL设定初始异常检测阈值
Figure PCTCN2021090796-appb-000036
定义
Figure PCTCN2021090796-appb-000037
Figure PCTCN2021090796-appb-000038
其中，
μ all为所有样本点对应的垂直保护级VPL计算值的均值，σ all所有样本点对应的垂直保护及VPL计算值的标准差，
将每个样本点的垂直保护级VPL计算值与
Figure PCTCN2021090796-appb-000039
比较，若满足不等式
Figure PCTCN2021090796-appb-000040
则该样本点通过阈值检测，进入轨道参数编码模块，等待初始种群筛选，若不满足足不等式
Figure PCTCN2021090796-appb-000041
则该样本点未通 过阈值检测，该样本点存储于异常数据模块。
未通过的数据将在整个数据流程进行之后单独验证，遍历所有异常原因，如：星座宽故障、时钟星历故障、信号变形、天线偏置误差等，若无匹配，再加入初始种群中。
筛选初始种群
由于初始种群的选择是遗传算法的基础，所以初始种群的选择策略至关重要。原始的随机构造方式是建立在样本量巨大的基础上的，然而本发明的低轨星座的配置参数x 1、x 3、x 4只需精确到小数点后两位或后三位，x 2只需精确到个位，否则将增加许多不必要的计算负荷。针对此背景，本发明提出一种针对上述四种参数的基于采样的数据初始种群筛选策略。
根据本发明的实施例，通过如下方法进行初始种群筛选：
对于轨道倾角参数x 1，将采样间隔Δτ 1设为0.01，共产生158个样本点，每隔9个样本点取一组数据作为初始种群的一个样本，该15个样本组成轨道倾角参数x 1的初始种群；
对于轨道高度参数x 2，将采样间隔Δτ 2设为1，共产生1200个样本点，每隔19个样本点取一组数据作为初始种群的一个样本，该60个样本组成轨道倾角参数x 2的初始种群；
对于升交点赤经起始值参数x 3，将采样间隔Δτ 3设为0.001，共产生79个样本点，每隔4个样本点取一组数据作为初始种群的一个样本，该15个样本组成轨道倾角参数x 3的初始种群；
对于平近点角起始值参数x 4来说，将采样间隔Δτ 4设为0.01，共产生30个样本点，每隔4个样本点取一组数据作为初始种群的一个样本，该6个样本组成轨道倾角参数x 4的初始种群。
步骤3、对低轨卫星星座配置的参数x 1、x 2、x 3、x 4的目标函数进行适应度计算。
经过筛选和采样后产生了规模为N的初始种群，接着进行快速非支配排序以及选择、交叉、变异等操作。执行的算法是一个类似进化理论的优胜劣汰的过程，整个过程也是对个体适应度大小的评价过程。
遗传算法中用个体适应度的大小来评估个体的优劣程度，所以需要适应度函数来参与评价，合适的进化个体选择方法有助于提高种群进化效率。
本发明通过如下方法对低轨卫星星座配置的参数x 1、x 2、x 3、x 4的目标函数进行适应度计算：
适应度函数采用最大最优化问题函数：
Figure PCTCN2021090796-appb-000042
其中，C min是预先设定的数，取目前为止估计的目标函数F VPL(x)的最小函数值，F VPL(x)为目标函数，表示垂直保护级VPL是参数x 1、x 2、x 3或者x 4的函数。
由于目标函数F VPL(x)的值在LPV-200的要求下才符合要求，所以除上述适应度函数外，目标函数还应当满足如下条件：
目标函数F VPL(x)的值≤35m。
在检查适应度函数前，还应增加对于目标函数的要求，通过限值后才可进行适应度函数计算。
步骤4、经过筛选出参数x 1、x 2、x 3、x 4的初始种群后，从第二代种群开始，将父代种群与子代种群合并形成新子代种群，进行快速非支配排序，对每个非支配层中的个体进行拥挤度计算，对个体进行随机配对，并在配对的两个个体间进行遗传算法的交叉操作。
根据本发明的实施例，从第二代开始，上一代父代种群将与子代种群合并，由于4个参数的样本量及种群数量不同，本发明定义父代种群与子代种群合并形成新子代种群的合并比例为：
Figure PCTCN2021090796-appb-000043
i＝1,2,3,4，其中，X ul为优化参数范围的上限，X ll为优化参数范围的下限，Δτ i为每个参数的X ul采样间隔，N interval为生成初始种群时的样本间隔。
根据不同比例合并后再进行快速非支配排序，同时对每个非支配层中的个体进行拥挤度计算，对个体进行随机配对，并在配对的两个个体间进行交叉操作。通常，交叉算子还与变异算子相互配合，变异算子局 部搜索能力强，两者相互配合使得遗传算法既具备全局搜索的能力，也具备局部搜索能力。
步骤5、父代种群与子代种群合并形成新子代种群后，对新子代种群进行最优保存策略选择，以及局部最优选择，筛选出目标函数的最大值作为最优子代，重复步骤4，直至遗传代数小于最大遗传代数。
在遗传算法的进化过程中，只有适应度高的个体才有机会遗传到下一代，适应度低的个体遗传到下一代的概率较小，这种优胜劣汰的过程通过选择算子来实现。结合精英策略，父代中的优良个体才能进入子代继续遗传，以防止帕累托最优解地丢失。
现有技术中常用的最优保存策略可以使适应度最高的个体不参与交叉和变异，并用它替换掉交叉、变异后适应度最低的个体，通过这种方法保留了适应度最高的个体，但是这种方法不容易淘汰算法的局部最优解，使全局搜索能力下降。
本发明在初始种群挑选中已经使用采样间隔Δτ i进行采样，在一定程度上避免了局部最优，在此基础上，本发明引入样本局部均值
Figure PCTCN2021090796-appb-000044
进行局部最优选择，其中，
样本局部均值
Figure PCTCN2021090796-appb-000045
表述为：
Figure PCTCN2021090796-appb-000046
其中，
m表示第m个局部均值，最大值为
Figure PCTCN2021090796-appb-000047
x i表示对应参数的第i个样本，规定每5个样本取一次均值作为局部均值，X ul为优化参数范围的上限，X ll为优化参数范围的下限，Δτ i为每个参数的X ul采样间隔。
根据本发明，设定选择阈值T sel(根据实际应用中ARAIM保护级的统计平均确定)，对新子代种群进行最优保存策略选择后，将目标函数与每个局部均值
Figure PCTCN2021090796-appb-000048
做差，
若大于选择阈值T sel，则通过该局部最优检验，目标函数的最大值作 为最优子代；若小于阈值T sel，将搜索该目标函数附近的最大值作为最优子代。
通过局部最优选择，筛选出目标函数的最大值作为最优子代后，重复步骤4，并循环，直至遗传代数满足结束条件(小于最大代数，根据具体仿真环境随时调整)。此时，垂直保护级达到最小值，相应的优化参数x 1、x 2、x 3、x 4的值即为使低轨卫星增强系统保护级最低的星座配置，使用该配置在保证可用性的同时兼顾经济因素。
本发明基于低轨导航增强现状提出了一种适用于低轨卫星导航增强系统的星座配置优化方法，并结合带精英策略的非支配排序遗传算法提出了基于ARAIM保护级算法的星座配置优化方法，通过异常数据剔除、参数采样等操作从另一角度实现了ARAIM保护级算法优化，弥补了低轨增强系统的完好性监测空缺，为今后低轨卫星导航系统设计及组网提供参考。
本发明通过ARAIM保护级公式确定待优化参数，将风险值平均分配后得出具体待优化观测矩阵；定义观测矩阵中优化参数的约束范围，在约束范围内进行目标函数的优化；优化前先进行异常数据检测及数据采样以筛选初始种群，在父代子代种群合并时采用特定比例有目的性地进行合并；最后，为避免局部最优，定义样本局部均值，将优化值与局部均值进行阈值检测，以达到全局最优的目的。
结合这里披露的本发明的说明和实践，本发明的其他实施例对于本领域技术人员都是易于想到和理解的。说明和实施例仅被认为是示例性的，本发明的真正范围和主旨均由权利要求所限定。

Claims (10)

  1. 一种面向ARAIM应用的低轨卫星增强系统星座配置优化方法，其特征在于，所述方法包括如下方法步骤：
    步骤1、确定完好性风险和连续性风险均等分配的情况下，遍历所有子集解和故障模式后的垂直保护级，以及确定低轨卫星星座配置参数的约束条件，
    步骤2、确定低轨卫星星座配置的参数x 1、x 2、x 3、x 4的目标函数，剔除异常的垂直保护级的计算值，筛选参数x 1、x 2、x 3、x 4的初始种群，
    其中，参数x 1为轨道倾角，参数x 2为轨道高度，参数x 3为升交点赤经起始值参数，参数x 4平近点角起始值；
    步骤3、对低轨卫星星座配置的参数x 1、x 2、x 3、x 4的目标函数进行适应度计算；
    步骤4、经过筛选出参数x 1、x 2、x 3、x 4的初始种群后，从第二代种群开始，将父代种群与子代种群合并形成新子代种群，进行快速非支配排序，对每个非支配层中的个体进行拥挤度计算，对个体进行随机配对，并在配对的两个个体间进行遗传算法的交叉操作；
    步骤5、父代种群与子代种群合并形成新子代种群后，对新子代种群进行最优保存策略选择，以及局部最优选择，筛选出目标函数的最大值作为最优子代，
    重复步骤4，直至遗传代数小于最大遗传代数。
  2. 根据权利要求1所述的方法，其特征在于，步骤1中所述垂直保级表述为：
    VPL q＝max((VPL 0) q,max((VPL i) q)，其中，VPL 0为无故障条件下垂直保护级，
    Figure PCTCN2021090796-appb-100001
    为全可见星子集下无故障模式的完好性和连续性风险值，
    Figure PCTCN2021090796-appb-100002
    为投影矩阵，b int,n为第n颗卫星的最大标称偏差；
    VPL i为不超过最大偏差下第i个故障模式的测量偏差对应的垂直保护级，
    Figure PCTCN2021090796-appb-100003
    D i,q为检测阈值；
    其中，
    Figure PCTCN2021090796-appb-100004
    G为伪距观测方程中的几何矩阵，W INT为有关完好性的固定误差假设模型参数，M i为一个N sat*N sat大小的单位矩阵，N sat为可见卫星数目，q是表示第q个样本点，
    伪距观测方程中的几何矩阵G中包含低轨卫星星座配置的参数x 1、x 2、x 3、x 4；
    所述低轨卫星星座配置参数的约束条件表述为：
    Figure PCTCN2021090796-appb-100005
    其中，N 0表示低轨星座的轨道面个数，N SO表示每个轨道面上卫星的个数，N C为相位参数，N C∈[1，N 0]，Ω表示升交点赤经，M表示平均近点角，其中i表示第i个轨道面，j表示第j颗卫星。
  3. 根据权利要求1所述的方法，其特征在于，步骤2中低轨卫星星座配置的参数x 1、x 2、x 3、x 4的目标函数表述为：
    Figure PCTCN2021090796-appb-100006
    Figure PCTCN2021090796-appb-100007
    Figure PCTCN2021090796-appb-100008
    Figure PCTCN2021090796-appb-100009
    其中，F VPL(x 1)表示垂直保护级VPL是参数x 1的函数，F VPL(x 2)表示垂直保护级VPL是参数x 2的函数，F VPL(x 3)表示垂直保护级VPL是参数x 3的函数，F VPL(x 4)表示垂直保护级VPL是参数x 4的函数。
  4. 根据权利要求1所述的方法，其特征在于，步骤2中通过如下方法剔除异常的垂直保护级的计算值：
    设定初始异常检测阈值
    Figure PCTCN2021090796-appb-100010
    定义
    Figure PCTCN2021090796-appb-100011
    其中，
    μ all为所有样本点对应的垂直保护级VPL计算值的均值，σ all所有样本点对应的垂直保护及VPL计算值的标准差，
    将每个样本点的垂直保护级VPL计算值与
    Figure PCTCN2021090796-appb-100012
    比较，若满足不 等式
    Figure PCTCN2021090796-appb-100013
    则该样本点通过阈值检测，等待初始种群筛选，若不满足足不等式
    Figure PCTCN2021090796-appb-100014
    则该样本点未通过阈值检测，该样本点存储于异常数据模块。
  5. 根据权利要求1所述的方法，其特征在于，步骤2中通过如下方法进行初始种群筛选：
    对于轨道倾角参数x 1，将采样间隔Δτ 1设为0.01，共产生158个样本点，每隔9个样本点取一组数据作为初始种群的一个样本，该15个样本组成轨道倾角参数x 1的初始种群；
    对于轨道高度参数x 2，将采样间隔Δτ 2设为1，共产生1200个样本点，每隔19个样本点取一组数据作为初始种群的一个样本，该60个样本组成轨道倾角参数x 2的初始种群；
    对于升交点赤经起始值参数x 3，将采样间隔Δτ 3设为0.001，共产生79个样本点，每隔4个样本点取一组数据作为初始种群的一个样本，该15个样本组成轨道倾角参数x 3的初始种群；
    对于平近点角起始值参数x 4来说，将采样间隔Δτ 4设为0.01，共产生30个样本点，每隔4个样本点取一组数据作为初始种群的一个样本，该6个样本组成轨道倾角参数x 4的初始种群。
  6. 根据权利要求1所述的方法，其特征在于，步骤3中通过如下方法对低轨卫星星座配置的参数x 1、x 2、x 3、x 4的目标函数进行适应度计算：
    适应度函数采用最大最优化问题函数：
    Figure PCTCN2021090796-appb-100015
    其中，C min是预先设定的数，取目前为止估计的目标函数F VPL(x)的最小函数值，F VPL(x)为目标函数，表示垂直保护级VPL是参数x 1、x 2、x 3或者x 4的函数。
  7. 根据权利要求6所述的方法，其特征在于，目标函数还应当满足如下条件：
    目标函数F VPL(x)的值≤35m。
  8. 根据权利要求1所述的方法，其特征在于，父代种群与子代种群合并形成新子代种群的合并比例为：
    Figure PCTCN2021090796-appb-100016
    其中，X ul为优化参数范围的上限，X ll为优化参数范围的下限，Δτ i为每个参数的X ul采样间隔，N interval为生成初始种群时的样本间隔。
  9. 根据权利要求1所述的方法，其特征在于，步骤5中引入样本局部均值
    Figure PCTCN2021090796-appb-100017
    进行局部最优选择，
    设定选择阈值T sel，对新子代种群进行最优保存策略选择后，将目标函数与每个局部均值
    Figure PCTCN2021090796-appb-100018
    做差，
    若大于选择阈值T sel，则通过该局部最优检验，目标函数的最大值作为最优子代；若小于阈值T sel，将搜索该目标函数附近的最大值作为最优子代。
  10. 根据权利要求9所述的方法，其特征在于，样本局部均值
    Figure PCTCN2021090796-appb-100019
    表述为：
    Figure PCTCN2021090796-appb-100020
    其中，
    m表示第m个局部均值，最大值为
    Figure PCTCN2021090796-appb-100021
    x i表示对应参数的第i个样本，规定每5个样本取一次均值作为局部均值，X ul为优化参数范围的上限，X ll为优化参数范围的下限，Δτ i为每个参数的X ul采样间隔。
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Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN115758704A (zh) * 2022-11-10 2023-03-07 北京航天驭星科技有限公司 卫星南北保持策略模型的建模方法、模型、获取方法
CN116070528A (zh) * 2023-03-07 2023-05-05 中国人民解放军战略支援部队航天工程大学 一种异构低轨导航星座设计优化方法及系统

Families Citing this family (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN115134016B (zh) * 2022-06-29 2024-01-19 沈阳航空航天大学 一种基于麻雀搜索算法的araim子集优化方法
CN116520711B (zh) * 2023-07-03 2023-10-13 中国西安卫星测控中心 一种电推卫星walker星座组网控制筹划方法
CN116633424B (zh) * 2023-07-25 2023-09-26 中国人民解放军战略支援部队航天工程大学 一种规避大规模星座下行链路干扰的Walker星座构型设计方法
CN117252113B (zh) * 2023-11-17 2024-02-23 中国人民解放军战略支援部队航天工程大学 面向中轨导航星座卫星失效的低轨混合星座优化设计方法

Citations (6)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN107329146A (zh) * 2017-07-05 2017-11-07 中国人民解放军装备学院 一种导航卫星低轨监测星座的优化设计方法
CN107798187A (zh) * 2017-10-24 2018-03-13 北京理工大学 一种高效卫星星座多目标优化方法
CN109061683A (zh) * 2018-06-29 2018-12-21 北京航空航天大学 一种优化水平保护级的h-araim系统
CN109635332A (zh) * 2018-11-08 2019-04-16 北京航空航天大学 一种基于遗传算法的变步长星座轨道优化方法及装置
CN111708054A (zh) * 2020-06-16 2020-09-25 沈阳航空航天大学 基于粒子群优化算法的araim垂直保护级优化方法
US20200348422A1 (en) * 2019-05-01 2020-11-05 Swift Navigation, Inc. Systems and methods for high-integrity satellite positioning

Family Cites Families (14)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US6281836B1 (en) * 1999-05-21 2001-08-28 Trimble Navigation Ltd Horizontal/vertical protection level adjustment scheme for RAIM with baro measurements
US8131463B2 (en) * 2003-12-02 2012-03-06 Gmv Aerospace And Defence, S.A. GNSS navigation solution integrity in non-controlled environments
US8712321B1 (en) * 2013-01-07 2014-04-29 Viasat, Inc. Satellite fleet deployment
US9547086B2 (en) * 2013-03-26 2017-01-17 Honeywell International Inc. Selected aspects of advanced receiver autonomous integrity monitoring application to kalman filter based navigation filter
US9784844B2 (en) * 2013-11-27 2017-10-10 Honeywell International Inc. Architectures for high integrity multi-constellation solution separation
CN106249253B (zh) * 2016-07-20 2018-09-25 中国人民解放军战略支援部队航天工程大学 低轨通信和导航增强混合星座的优化设计方法
CN107238848B (zh) * 2017-07-07 2019-09-27 北京航空航天大学 卫星导航系统可用性的评估方法及装置
CN109001763B (zh) * 2018-06-04 2020-06-30 北京未来导航科技有限公司 一种基于低轨星座的导航增强方法及系统
US10197678B1 (en) * 2018-07-17 2019-02-05 Beihang University H-ARAIM system of optimizing a horizontal protection level
US11226416B1 (en) * 2018-09-25 2022-01-18 Globalstar, Inc. System and method to reduce PPP filter convergence time using LEO frequency band signals
CN109581445B (zh) * 2018-11-01 2021-03-19 北京航空航天大学 一种基于北斗星座的araim子集选择方法及系统
CN110068840B (zh) * 2019-05-15 2020-12-29 北京航空航天大学 一种基于伪距测量特征值提取的araim故障检测方法
EP3792665A1 (en) * 2019-09-10 2021-03-17 Trimble Inc. Protection level generation methods and systems for applications using navigation satellite system (nss) observations
US11555930B2 (en) * 2020-06-24 2023-01-17 Honeywell Aerospace Sas Split vertical advanced receiver autonomous integrity monitoring

Patent Citations (6)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN107329146A (zh) * 2017-07-05 2017-11-07 中国人民解放军装备学院 一种导航卫星低轨监测星座的优化设计方法
CN107798187A (zh) * 2017-10-24 2018-03-13 北京理工大学 一种高效卫星星座多目标优化方法
CN109061683A (zh) * 2018-06-29 2018-12-21 北京航空航天大学 一种优化水平保护级的h-araim系统
CN109635332A (zh) * 2018-11-08 2019-04-16 北京航空航天大学 一种基于遗传算法的变步长星座轨道优化方法及装置
US20200348422A1 (en) * 2019-05-01 2020-11-05 Swift Navigation, Inc. Systems and methods for high-integrity satellite positioning
CN111708054A (zh) * 2020-06-16 2020-09-25 沈阳航空航天大学 基于粒子群优化算法的araim垂直保护级优化方法

Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN115758704A (zh) * 2022-11-10 2023-03-07 北京航天驭星科技有限公司 卫星南北保持策略模型的建模方法、模型、获取方法
CN116070528A (zh) * 2023-03-07 2023-05-05 中国人民解放军战略支援部队航天工程大学 一种异构低轨导航星座设计优化方法及系统

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