LU503692B1

LU503692B1 - Constellation configuration optimization method for araim-application-oriented low earth orbit satellite enhancement system

Info

Publication number: LU503692B1
Application number: LU503692A
Authority: LU
Inventors: Kun Fang; Ziyi Yang; Yanbo Zhu; Zhipeng Wang
Original assignee: Univ Beihang
Priority date: 2023-03-20
Filing date: 2023-03-20
Publication date: 2023-09-25

Abstract

Disclosed is a constellation configuration optimization method for an ARAIM-application-oriented low earth orbit satellite enhancement system. The method includes: 1. traversing all subset solutions and post-fault-mode vertical protection levels, and determining constraint conditions for low earth orbit satellite constellation configuration parameters; 2. determining objective functions of the low earth orbit satellite constellation configuration parameters x1、x2、x3、x4 , eliminating abnormal calculated values of the vertical protection levels, and screening initial populations of x1、x2、x3、x4 the parameters performing fitness calculation on the objective x1、x2、x3、x4 functions of ; starting from a second-generation population, combining a parent population and offspring populations, so as to generate new child populations; and 5. performing local optimal selection on the new child populations, screening out maximum values of the objective functions as optimal children, and repeating step 4 until the number of genetic generations is less than the maximum number of genetic generations.

Description

BL-5627

CONSTELLATION CONFIGURATION OPTIMIZATION METHOD FOR LUs03692

ARAIM-APPLICATION-ORIENTED LOW EARTH ORBIT SATELLITE

ENHANCEMENT SYSTEM

TECHNICAL FIELD

[01] The present invention relates to the technical field of satellite navigation, and in particular to a constellation configuration optimization method for an advanced receiver autonomous integrity monitor (ARAIM)-application-oriented low earth orbit satellite enhancement system.

BACKGROUND ART

[02] The global navigation satellite system (GNSS) has developed rapidly and has been widely used in various fields. In the future, global mass users put forward a series of requirements for high accuracy, fast convergence, high integrity, high security and high availability, so high-security real-time precise positioning in a complex environment becomes a higher target of the current GNSS. In order to solve the above problems, nations are actively building their own navigation enhancement system, while the traditional navigation enhancement systems are all ground station assisted information enhancement working systems. However, due to territorial and regional constraints in China, it is difficult to achieve global centimeter-level positioning and fast convergence services through global deployment of ground stations. Therefore, with the increasing demand for station density and information rate, existing enhancement systems have failed to support the next generation of Beidou to achieve centimeter-level real-time positioning services in challenging environments. To this end, the architecture and system of the new enhancement system needs to be designed to achieve three objectives: 1) reducing the dependence on overseas stations; 2) extending the enhanced services from regional enhancement to global enhancement; and 3) significantly improving the availability and safety of precision positioning services.

[03] With the development of communication services, at the end of the 20" century, a low earth orbit satellite constellation for mobile communication appeared, typically represented by the Iridium and Globalstar constellations of the United States. In January 2019, the second generation Iridium system completed networking and completely replaced the first generation Iridium system. Besides providing the original communication services, the new generation of Iridium system further has a navigation enhanced payload, which can provide users with other services of positioning and tracking, broadcast-type automatic related monitoring, etc. besides communication.

Since 2015, many well-known international enterprises such as OneWeb, SpaceX,

Boeing in the United States, Samsung in Korea, China Aerospace Science and

Technology Corporation and China Aerospace Science And Industrial Corporation have announced launching and deploying their respective commercial low earth orbit constellations, to provide seamless and stable broadband Internet communication services for the world. The first satellite of the “Hongyan” constellation in China has been launched successfully on December 29, 2018 and entered the intended orbit, and the whole constellation plan is designed to be deployed around 2024. The Hongyan 1

BL-5627 . RUE . . . . oo LU503692 mobile communication constellation satisfies the needs of multi-domain monitoring data transmission, and further has a mobile broadcast function and an onboard GNSS receiver, and is equipped with navigation enhancement function.

[04] Because of the rapid development of the low earth orbit satellite market and the low cost of carrying navigation enhancement load, it can be used as a space-based monitoring platform to realize the new navigation enhancement system of “space-based monitoring + signal enhancement”. Opening of Beidou No. 3 symbolizes that China has formally built a meter-level navigation and positioning system comparable to GPS. For the future development of Beidou, the deputy general designer of Beidou satellite navigation system engineering Ran chengqi has noted that it is expected to build a space-based low earth orbit constellation system and provide centimeter-level positioning services to the world before 2025.

[05] The research on low earth orbit navigation enhancement mainly focuses on real-time precise orbit determination and remote sensing monitoring. The low earth orbit satellite navigation enhancement system has an integrity monitoring gap. Once the low earth orbit satellite navigation system is formally used for the navigation enhancement service, it will affect the availability of an advanced receiver autonomous integrity monitor (ARAIM) airborne receiver.

[06] Therefore, in order to solve the problems in the prior art, there is a need for a constellation configuration optimization method for an ARAIM-application-oriented low earth orbit satellite enhancement system.

SUMMARY

[07] An objective of the present invention is to provide a constellation configuration optimization method for an advanced receiver autonomous integrity monitor (ARAIM)-application-oriented low earth orbit satellite enhancement system. The method includes:

[08] step 1, when it is determined that integrity risks and continuity risks are equally distributed, traversing all subset solutions and post-fault-mode vertical protection levels, and determining constraint conditions for low earth orbit satellite constellation configuration parameters;

[09] step 2, determining objective functions of the low earth orbit satellite constellation configuration parameters Xp Xr Aa da, eliminating abnormal calculated values of the vertical protection levels, and screening initial populations of the parameters Np on Xe da

[10] where parameter *! is a track inclination angle, parameter * is a track height, parameter X is an initial value parameter of a right ascension of ascending node, and parameter 4 is an initial value of a mean anomaly;

[11] step 3, performing fitness calculation on the objective functions of the low 2

BL-5627

LU503692 earth orbit satellite constellation configuration parameters Np tas Aa Ma,

[12] step 4, after screening out the initial populations of the parameters

Xp Xn Xn X . . . . 1 72° *3° “4, starting from a second-generation population, combining a parent population and offspring populations, so as to generate new offspring populations, performing rapid nondominated sorting, calculating a crowding degree of individuals in each nondominated layer, randomly pairing the individuals, and performing a genetic algorithm crossover-operation between the paired two individuals; and

[13] step 5, after combining the parent population and the offspring populations, so as to generate the new offspring populations, performing elitist strategy selection and local optimal selection on the new offspring populations, screening out maximum values of the objective functions as optimal offspring, and

[14] repeating step 4 until the number of genetic generations is less than the maximum number of genetic generations.

[15] Preferably, in step 1, the vertical protection level is expressed as:

PL, = PL PL, . . .

[16] VPL, = Max((VPLo) 4 max(VPL,), ). where VPLy is the vertical protection

Nsat _. VPLy), = Kine Co, + SO bn Kop level under fault-free conditions, (PL), = Kip 904 + 2, | oo mtn MD4 js an integrity and continuity risk value of the fault-free mode under the fully visible satellite

SY. oo . bin : . . 2 subset, 7” is a projection matrix, and ”“” is a maximum nominal deviation of the n't satellite;

VPL . . . 2

[17] i is the vertical protection level corresponding to a measurement deviation of an ih fault mode under a maximum deviation, i Nsat i

VPL;), =K,, 0, + S |b. + D, 5 . (PL), = King Oi Ds] a mtn M and Dia is a detection threshold; 5, = GW 0 = SEM Wa . .

[18] where *4 Wir a , ( Moa aa , G is a geometric matrix in a pseudorange observation equation, Wir is a fixed error assumption model parameter on the integrity, M, is an identity matrix of size Na “Noa Na is the number of visible satellites, q represents a q sample point, and

[19] the geometric matrix G in the pseudorange observation equation contains the low earth orbit satellite constellation configuration parameters Xp or XY and

[20] a constraint condition of the low earth orbit satellite constellation configuration parameters is expressed as:

N, 0 18, 8 i —l

X N Io MM. |=

N À —l

[21] C 50 ÿ H J , where Ny represents the number 3

BL-5627

LU503692 of orbital planes of the low earth orbit constellation, No represents the number of satellites on each orbital plane, Ne is a phase parameter, Nee Dr N,] , Q represents a right ascension of ascending node, M represents the mean anomaly, i represents the i orbital plane, and j represents the j satellite.

[22] Preferably, in step 2, the objective functions of the low earth orbit satellite constellation configuration parameters ro YY are expressed as: min [- For, (x)] st0<x< z

[23] 2, [- Fp (x,)]

[24] s.1.800 < x, < 2000 , mn [- For (x;)]

[25] 51.0<x,<0.782 [- For (x,)]

[26] s10 8 x, 503 , Where Fp C9) represents that the vertical protection level (VPL) is a function of parameter “1, Fp C2) represents that the vertical protection level (VPL) is a function of parameter 2, Fry (x3) represents that the vertical . . . x EF (x) protection level (VPL) is a function of the parameter “3, and ~ "7L “+” represents that the vertical protection level (VPL) is a function of the parameter *4.

[27] Preferably, in step 2, eliminating abnormal calculated values of the vertical protection levels is performed by:

[28] setting initial abnormality detection threshold Lis and Lis , defining

T et = Uy +20, and T first = Hu 20 an where

[29] Hall is a mean value of the calculated values of the vertical protection levels (VPL) corresponding to all sample points, and Cal is a standard deviation of the calculated values of the vertical protection levels (VPL) corresponding to all sample points,

[30] comparing the calculated value of the vertical protection level (VPL) of each sample point with Lis and Lis , under the condition that an inequation 4

BL-5627 7+ UPL <T- LU503692 < < . . . ; ; first = - ft is satisfied, making the sample point pass the threshold detection and wait for initial population screening, and under the condition that the inequation iy < <T.. .

List SVPL SL gr is unsatisfied, making the sample point not pass the threshold detection, and stored in an abnormal data module.

[31] Preferably, in step 2, screening the initial populations is performed by:

[32] as for the track inclination angle parameter “1, setting a sampling interval

ÂT as 0.01, to generate a total of 158 sample points, taking a set of data every 9 sample points as a sample of the initial population, where the 15 samples constitute the initial population of the track inclination angle parameter “1;

[33] as for the track height parameter *2, setting a sampling interval AT, as 1, to generate a total of 1200 sample points, taking a set of data every 19 sample points as a sample of the initial population, where the 60 samples constitute the initial population of the track height parameter “2;

[34] as for the initial value parameter % ofa right ascension of ascending node, setting a sampling interval Az; as 0.001, to generate a total of 79 sample points, taking a set of data every 4 sample points as a sample of the initial population, where the 15 samples constitute the initial population of the initial value parameter % ofa right ascension of ascending node; and

[35] as for the initial value parameter “+ of a mean anomaly, setting a sampling interval 274 as 0.01, to generate a total of 30 sample points, taking a set of data every 4 sample points as a sample of the initial population, where the 6 samples constitute the initial population of the initial value *4 of a mean anomaly.

[36] Preferably, in step 3, fitness calculation on the objective functions of the low earth orbit satellite constellation configuration parameters Np or Xp gg performed by:

[37] using a maximum optimization problem function for a fitness function:

F, (x) + Coin > Cin + F, (x)>0

Fitness(F,p, (x)) = hs Fo (x)<0 i. c , + x) < 5

[38] min VPE , where "in is a preset number that is a minimum function value of the objective function Fr (5) estimated

BL-5627

LU503692 so far, and Fp (x) is the objective function, and represents that the vertical protection level (VPL) is a function of the parameter “1, *2, X or Ya,

[39] Preferably, the objective function further satisfies the following condition:

[40] a value of the objective function * PL is < 35 m.

[41] Preferably, a combination proportion of combining the parent population and the offspring populations to form the new offspring populations 1s:

Xu =X

Ar, pro, =——————=

[42] UN, int erval +1) , i = 1, 2, 3, 4, where Xu is an upper limit of an optimization parameter range, Xo is a lower limit of the optimization parameter range,

Az, isa Xu sampling interval for each parameter, and Nera is a sample interval when the initial populations are generated.

[43] Preferably, in step 5, a sample local mean A, is introduced for local optimal selection,

[44] a selection threshold Ta is set, after elitist strategy selection is performed on the new offspring populations, a difference is made between the objective function and

A” each local mean ‘”, and

[45] under the condition that the difference is greater than the selection threshold

Ta a maximum value of the objective function is taken as the optimal offspring by means of local optimal test; and under the condition that the difference is less than the threshold Te , a maximum value around the objective function is searched as the optimal offspring.

[46] Preferably, the sample local mean A, is expressed as: so Xu =X) dx AT,

Ar = Sn Un =0,123,...5 m=123,.. =— k 5

[47] , Where, 6

BL-5627

LU503692

Xu X

Ar,

[48] m represents the m“ local mean, a maximum value is ‚X represents the ‘“ sample of the corresponding parameter, it is specified to take a mean once every 5 samples as the local mean, Xu is an upper limit of an optimization parameter range, Xo is a lower limit of the optimization parameter range, and Az, is a Xu sampling interval for each parameter.

[49] The present invention proposes a constellation configuration optimization method suitable for a low earth orbit satellite navigation enhancement system based on a current situation of low earth orbit navigation enhancement, and proposes a constellation configuration optimization method based on an ARAIM protection level algorithm in combination with the elitist nondominated sorting genetic algorithm. The

ARAIM protection level algorithm is optimized from another perspective by means of operations of abnormal data elimination, parameter sampling, etc., so as to fill a gap in integrity monitoring of the low earth orbit enhancement system, and provide a reference for future low earth orbit satellite navigation system design and networking.

[50] In the present invention, parameters to be optimized are determined by means of an ARAIM protection level formula, and a particular observation matrix to be optimized is obtained after risk values are evenly distributed; a constraint range of the optimization parameters in the observation matrix is defined, and the objective functions are optimized in the constraint range; the initial populations are screened by abnormal data detection and data sampling before optimization, and the parent population and the offspring populations are combined purposely in a particular proportion; and finally, in order to avoid local optimization, the sample local mean is defined, and the optimized value and the local mean are detected by threshold to achieve the goal of global optimization.

[51] It is to be understood that both the foregoing general description and the following detailed description are illustrative and explanatory and are not restrictive of the protect content claimed by the present invention.

BRIEF DESCRIPTION OF THE DRAWINGS

[52] Further objectives, functions and advantages of the present invention will be elucidated by means of the following description of embodiments of the present invention with reference to the accompanying drawings, where:

[53] FIG 1 schematically shows a schematic spatial diagram of a low-earth-orbit enhanced advanced receiver autonomous integrity monitor (ARAIM) system of the present invention.

[54] FIG 2 is a flowchart of an algorithm of a constellation configuration 7

BL-5627 optimization method for an ARAIM-application-oriented low earth orbit enhancement LU503692 system.

[55] FIG 3 is a schematic diagram of initial abnormality verification for a vertical protection level.

DETAILED DESCRIPTION OF THE EMBODIMENTS

[56] The objectives and functions of the present invention and methods for accomplishing the objectives and functions will be elucidated with reference to illustrative examples. However, the present invention is not limited to the illustrative examples disclosed below; and it can be implemented in different forms. The essence of the specification is merely intended to facilitate a comprehensive understanding of the present invention by those skilled in the relevant art.

[57] Examples of the present invention will be described below with reference to the accompanying drawings. In the accompanying drawings, the identical reference numerals denote the identical or similar parts, or the identical or similar steps.

[58] An advanced receiver autonomous integrity monitor (ARAIM) is an important technology in satellite navigation integrity monitoring. After an algorithm is implemented on an airborne side, a user may be alerted in time under the condition that there is any fault, it does not need to build a large number of ground infrastructure, application is convenient and rapid, and it can be rapidly popularized.

[59] In order to solve the problems in the prior art, the present invention aims to improve the ARAIM availability of the Beidou satellite navigation system, a protection level is reduced by introducing a low earth orbit satellite navigation system, and an elitist nondominated sorting genetic algorithm is used for selecting optimal low earth orbit constellation configurations for different parameters, so as to improve the availability of the ARAIM airborne receiver.

[60] In order to make the description of the present invention clearer, a brief description of a low earth orbit satellite system is firstly provided. FIG 1 is a schematic spatial diagram of a low earth orbit enhanced ARAIM system according to the present invention. The low earth orbit satellite system is equipped with an onboard global navigation satellite system (GNSS) receiver, generates a signal having a time frequency consistent with a Beidou satellite navigation system, and broadcasts same to the ground by means of an onboard navigation load. After receiving a communication navigation signal, a ground monitoring station transmits the signal to a main control station, and after solving, the main control station determines orbit information about the low earth orbit satellite, and uploads the orbit information to the low earth orbit satellite by means of an uplink of an injection station. In this case, the low earth orbit satellite may transmit an ephemeris containing the orbit information to a user side by means of a downlink, and the user side (airborne side) uses these information for calculation by means of the algorithm, to optimize the constellation configuration of the low earth orbit satellite enhancement system.

[61] FIG 2 is a flowchart of an algorithm of a constellation configuration optimization method for an ARAIM-application-oriented low earth orbit enhancement system according to the present invention. According to an example of the present 8

BL-5627 invention, the constellation configuration optimization method for an LU503692

ARAIM-application-oriented low earth orbit satellite enhancement system includes:

[62] Step 1, when it is determined that integrity risks and continuity risks are equally distributed, traverse all subset solutions and post-fault-mode vertical protection levels, and determine constraint conditions for low earth orbit satellite constellation configuration parameters

[63] After inputting ephemeris data of the low earth orbit satellites and Beidou navigation satellites into an ARAIM multiple hypothesis solution separation (MHSS) user algorithm, position information of the satellites is output according to the satellite ephemerides, and then position information of a user grid point is read and is compared with a shielding angle standard to search for visible satellites. According to a preset error model and a fault mode, fully visible satellite solutions and subset solutions under each fault mode are calculated, and horizontal/vertical protection levels and effective monitoring thresholds are calculated after a threshold test of solution separation, so as to evaluate a state of the constellation. In the basic MHSS ARAIM protection level calculation, the vertical protection level (VPL) being less than 35 m is a key index to evaluate the availability, and a VPL value of the grid point is calculated by means of a maximum function.

[64] According to the example of the present invention, when it is determined that integrity risks and continuity risks are equally distributed, all subset solutions and post-fault-mode vertical protection levels are traversed, and the vertical protection level is expressed as:

PL, = PL PL, . . .

[65] PPL, = max((FPLy),, max((VPL,), ). where VPLy is the vertical protection

Nsat _. VPLy), = Kine Co, + SO bn Kop level under fault-free conditions, PLo)y = Kara" og En | oo] mtn MD.g ig an integrity and continuity risk value of the fault-free mode under the fully visible satellite

SY. oo . bin : . . 2 subset, 7” is a projection matrix, and ”“” is a maximum nominal deviation of the n satellite;

VPL . . .

[66] i 1s the vertical protection level corresponding to a measurement deviation of an i" fault mode under a maximum deviation, i Nsat ;

VPL;), =K,, 0, + S |b. + D, 5 . (PL), = King Oi En | a mtn 744 and Dia is a detection threshold;

Goo = VW 0 = JCM Wy GT)! . .

[67] where 4 GW aa , TA ( Wir Dag , G is a geometric matrix in a pseudorange observation equation, Wir is a fixed error assumption model parameter on the integrity, M, is an identity matrix of size Noa “Noa Noa is the number of visible satellites, q represents a q sample point, and

[68] the geometric matrix G in the pseudorange observation equation contains the low earth orbit satellite constellation configuration parameters Xi Xo Xe X4 where 9

BL-5627

LU503692 parameter *! is a track inclination angle, parameter * is a track height, parameter

X is an initial value parameter of a right ascension of ascending node, and parameter *4 is an initial value of a mean anomaly.

[69] The present invention optimizes the constellation configuration of a low earth orbit enhancement system, and finally optimizes the maximum VPL to reduce the protection level. Since the protection level optimization is the problem of maximum value optimization, the protection level optimization is achieved by reducing the integrity and continuity risk values or optimizing the observation matrix and error parameters.

[70] In an optimization process, the vertical protection level (VPL) is a function of the low earth orbit constellation configuration parameters X> Xo Xo X4 that is, the objective functions in step 2 below. The configuration of the low earth orbit (LEO) constellation should therefore be defined first. In combination with the problem of an actual launch cost, the present invention selects a Walker configuration in a two dimensional lattice flower constellation (2D-LFC), which is a special case of 2D-LFC.

The 2D-LFC may define an orbit of a satellite with 9 parameters, of which 6 are Kepler elements.

[71] According to the present invention, a constraint condition for determining the low earth orbit satellite constellation configuration parameters is determined, and a 2D-LFC constellation configuration satisfies the following constraint:

Fa [2 Qu ai =

N. No |M, M j 1

[72] C Sod H J , where Ny represents the number of orbital planes of the low earth orbit constellation, Nso represents the number of satellites on each orbital plane, Ne is a phase parameter, Nee Dr No], Q represents a right ascension of ascending node, M represents the mean anomaly, i represents the i orbital plane, and j represents the j satellite.

[73] Considering external constraint conditions, the four parameters should be constrained in certain ranges, as shown in Table 1.

[74] Table 1 LEO constellation optimization parameters

X Track height (km) 800-2000 % initial value of right ascension of 0-0.782 ascending node (rad)

BL-5627

LU503692

[75] Step 2, determine objective functions of the low earth orbit satellite constellation configuration parameters Xp Xr X» X4 eliminate abnormal calculated values of the vertical protection levels, and screen initial populations of the parameters

Xp Xn Xp X,

[76] where parameter “1 is a track inclination angle, parameter *2 is a track height, parameter X is an initial value parameter of a right ascension of ascending node, and parameter * is an initial value of a mean anomaly

[77] Objective function determination

[78] Since the present invention is a multiple objective optimization problem (MOOP), which is a multiple objective optimization problem based on the discussion of a pareto optimal solution, and screening of the initial populations is particularly critical in the elitist nondominated sorting genetic algorithm (NSGA-IT) method.

[79] Firstly, the MOOP is transformed into a single objective optimization problem (SOOP), and the objective functions are respectively listed for four optimization parameters as follows: min [- For, (x)] st0<x< z

[80] 2, [- For (x,)] <x, <

[81] s.1.800 < x, < 2000 , mn [- For (x;)] <x, <

[82] st0< x, <0.782 , (m [- For (x,)] <x, <

[83] 5£0<x,<03

[84] In mathematical processing, the minimization of the maximum value is min (max((YPL, ),, max((VPL,), ))) , due to the inconvenience of mathematical calculation, two negative signs are taken for the formula, and an original optimization objective is transformed into: asp min [ max(OPL,), max((PL), ))

[86] The objective functions corresponding to the four low earth orbit satellite constellation configuration parameters ro YY are expressed as: 11

BL-5627 . LU503692 min [- For, (x)] st0<x< z

[87] 2, [- For (x,)] <x, <

[88] s.1.800 < x, < 2000 , min [- For (x;)]

[89] 51.0<x,<0.782 [- vez (x,)] <x, < . .

[90] s10 8 x, 503 , where Fp C9) represents that the vertical protection level (VPL) is a function of parameter “1, Fp C2) represents that the vertical protection level (VPL) is a function of parameter 2, Fry (x3) represents that the vertical . . . x EF (x) protection level (VPL) is a function of the parameter “3, and ~ "7L “+” represents that the vertical protection level (VPL) is a function of the parameter *4.

[91] Elimination of abnormal calculated values of vertical protection levels

[92] Due to satellite interruption, ephemeris calculation errors, miss alarm, false alarm and other reasons, there may be a large difference between individual VPL calculation values and a real value, and such VPL values cannot normally participate in optimization calculation. Therefore, the first task is to eliminate these outliers.

[93] According to the example of the present invention, FIG 3 is a schematic diagram of initial abnormality verification for a vertical protection level. The abnormal calculated values of the vertical protection levels are eliminated by:

[94] set initial abnormality detection threshold Lis and Lis according to VPL, define Ts = Uy +20, ‚and Th = Uy 20 an _ where

[95] Hall is a mean value of the calculated values of the vertical protection levels (VPL) corresponding to all sample points, and Par is a standard deviation of the calculated values of the vertical protection levels (VPL) corresponding to all sample points,

[96] compare the calculated value of the vertical protection level (VPL) of each sample point with Lis and Lis , under the condition that an inequation st < <T.. .

List SVPL SL gr is satisfied, make the sample point pass the threshold detection, enter 12

BL-5627 . . . 2, . . LU503692 an orbit parameter coding module, and wait for initial population screening, and under 2 . . IT, <VPL<T,, . . the condition that the inequation “/"" ' fist is unsatisfied, make the sample point not pass the threshold detection, and stored in an abnormal data module.

[97] Failed data is verified separately after the entire data flow, all abnormal causes are traversed, such as: a constellation width fault, a clock ephemeris fault, a signal distortion, an antenna offset error, etc. under the condition that there is no match, then the failed data is added to the initial populations.

[98] Initial population screening

[99] Since the screening of the initial populations is the basis of the genetic algorithm, a selection strategy for the initial populations is crucial. An original random construction mode is based on a large sample size. However, the low earth orbit constellation configuration parameters Xr %> % of the present invention only need to be accurate to two or three decimal places, and *2 only needs to be accurate to one place, otherwise a lot of unnecessary computational load will be added. For this background, the present invention proposes a sample-data-based initial population screening strategy for the four parameters described above.

[100] According to the example of the present invention, screening the initial populations is performed by:

[101] as for the track inclination angle parameter “1, set a sampling interval Az, as 0.01, to generate a total of 158 sample points, take a set of data every 9 sample points as a sample of the initial population, where the 15 samples constitute the initial population of the track inclination angle parameter “1;

[102] as for the track height parameter *2, set a sampling interval AT, as 1, to generate a total of 1200 sample points, take a set of data every 19 sample points as a sample of the initial population, where the 60 samples constitute the initial population of the track height parameter “2;

[103] as for the initial value parameter % ofa right ascension of ascending node, set a sampling interval Az; as 0.001, to generate a total of 79 sample points, take a set of data every 4 sample points as a sample of the initial population, where the 15 samples constitute the initial population of the initial value parameter % ofa right ascension of ascending node; and

[104] as for the initial value “4 of a mean anomaly, set a sampling interval AT, as 0.01, to generate a total of 30 sample points, take a set of data every 4 sample points as 13

BL-5627 . . ee . LU503692 a sample of the initial population, where the 6 samples constitute the initial population of the initial value ** of a mean anomaly.

[105] Step 3, performing fitness calculation on the objective functions of the low . . . . Xp Xp X X earth orbit satellite constellation configuration parameters “1° “2% 73% 74

[106] After screening and sampling, an initial population of size N is produced, the rapid nondominated sorting, and selection, crossover, mutation, etc are performed. The algorithm executed is a fittest survival process similar to the evolutionary theory, and the entire process is also an assessment of the magnitude of the fitness of an individual.

[107] The magnitude of the fitness of an individual is used in the genetic algorithm to assess the quality of an individual, such that a fitness function is needed to participate in the evaluation, and a suitable evolutionary individual selection method helps to improve population evolution efficiency.

[108] In the present invention, fitness calculation on the objective functions of the . . . . Xp Xp Xn Xp 5; low earth orbit satellite constellation configuration parameters 1 72° 73% 74 js performed by:

[109] use a maximum optimization problem function for a fitness function:

F, (x) + Coin > Cin + F, (x)>0

Fitness(Fıp, (x)) = hs Far (x)<0 a C , + x) < oo

[110] min VPE , where “min is a preset number that is a minimum function value of the objective function Fp (x) estimated so far, and Fp (x) is the objective function, and represents that the vertical protection level (VPL) is a function of the parameter “1, *2, X or Ya,

[111] Since the value of the objective function Fin (x) only satisfies the requirements of LPV-200, besides the above fitness function, the objective function should also satisfy the following condition: es . For (x) .

[112] a value of the objective function is < 35 m.

[113] Before checking the fitness function, the requirements for the objective function should also be added, and fitness function calculation may be performed after passing the limit value.

[114] Step 4, after screening out the initial populations of the parameters

Xp Xp Xp X . . .

IM 72 73° “4, start from a second-generation population, combine a parent population and offspring populations, so as to generate new offspring populations, perform rapid nondominated sorting, calculate a crowding degree of individuals in each nondominated layer, randomly pair the individuals, and perform a genetic algorithm crossover-operation between the paired two individuals. 14

BL-5627

[115] According to the example of the present invention, starting from the second LU503692 generation, the parent population of the previous generation is combined with the offspring populations, and since the sample size and the population number of the 4 parameters are different, the present invention defines a combination proportion of combining the parent population and the offspring populations to form the new offspring populations as: x ul _ X Il pro = AT

[116] ‘ UNiwerar +1). i = 1, 2, 3, 4, where Xu is an upper limit of an optimization parameter range, Xo is a lower limit of the optimization parameter range,

[117] After combination is performed in different proportions, rapid nondominated sorting is performed, a crowding degree of individuals in each nondominated layer is further calculated, the individuals are randomly paired, and a crossover-operation is performed between the paired two individuals. In general, a crossover operator and a mutation operator cooperate with each other, and the mutation operator has strong local search ability, such that the genetic algorithm has both global search ability and local search ability by means of the cooperation of the two.

[118] Step 5, after combining the parent population and the offspring populations, so as to generate the new offspring populations, perform elitist strategy selection and local optimal selection on the new offspring populations, screen out maximum values of the objective functions as optimal offspring, and repeat step 4 until the number of genetic generations is less than the maximum number of genetic generations

[119] In an evolution process of the genetic algorithm, only individuals with high fitness have a chance to be inherited to the next generation, and individuals with low fitness have a smaller probability to be inherited to the next generation. This fittest survival process is achieved by a selection operator. In combination with an elitist strategy, the elitist individuals in parents may enter the offspring to continue inheritance, so as to prevent a loss of a Pareto optimal solution.

[120] An elitist strategy commonly used in the prior art may make the individual with the highest fitness not participate in crossover and mutation, and replace the individual with the lowest fitness after crossover and mutations with the individual with the highest fitness. The individual with the highest fitness remains through this method, but this method cannot easily eliminate a local optimal solution of the algorithm, such that the global search capability is reduced.

[121] In the present invention, the sampling interval Az, has been used for sampling in the initial population selection, so as to avoid a local optimum to a certain extent, and on this basis, the present invention introduces a sample local mean 4, for

BL-5627 local optimum selection, where LU503692

[122] the sample local mean A, is expressed as: xX, X

TE ae

Ar == n=0,123,...5 m=123,..4 + k 5

[123] , Where,

Xu =X

Ar,

[124] m represents the m™ local mean, a maximum value is , 4 represents the ‘“ sample of the corresponding parameter, it is specified to take a mean once every 5 samples as the local mean, Xu is an upper limit of an optimization

X û : . Co. Art. . parameter range, is a lower limit of the optimization parameter range, and ~ 7 is

X Lo a “= sampling interval for each parameter.

[125] According to the present invention, a selection threshold Te (determined according to a statistical average of the ARAIM protection level in the actual application) is set, after elitist strategy selection is performed on the new offspring populations, a difference is made between the objective function and each local mean 4, , and

[126] under the condition that the difference is greater than the selection threshold

Ta a maximum value of the objective function is taken as the optimal offspring by means of local optimal test; and under the condition that the difference is less than the threshold To a maximum value around the objective function is searched as the optimal offspring.

[127] After screening out the maximum values of the objective functions as the optimal offspring by means of local optimal selection, step 4 is repeated, loop is performed until the number of genetic generations satisfies an end condition (which is less than the maximum number of genetic generations, and is adjusted at any time according to a particular simulation environment). In this case, the vertical protection level reaches a minimum value, and a value of the corresponding optimization

Xp Xn Xp X, : . . parameter 7!” 72° “3° %4 1s the constellation configuration of the low earth orbit 16

BL-5627 satellite enhancement system with the lowest protection level, and the configuration LU503692 may ensure the availability while taking into account economic factors.

[128] The present invention proposes a constellation configuration optimization method suitable for a low earth orbit satellite navigation enhancement system based on a current situation of low earth orbit navigation enhancement, and proposes a constellation configuration optimization method based on an ARAIM protection level algorithm in combination with the elitist nondominated sorting genetic algorithm. The

[129] In the present invention, parameters to be optimized are determined by means of an ARAIM protection level formula, and a particular observation matrix to be optimized is obtained after risk values are evenly distributed; a constraint range of the optimization parameters in the observation matrix is defined, and the objective functions are optimized in the constraint range; the initial populations are screened by abnormal data detection and data sampling before optimization, and the parent population and the offspring populations are combined purposely in a particular proportion; and finally, in order to avoid local optimization, the sample local mean is defined, and the optimized value and the local mean are detected by threshold to achieve the goal of global optimization.

[130] Other examples of the present invention will be apparent to and understood by those skilled in the art from consideration of the specification and practice of the present invention disclosed herein. It is intended that the specification and examples be considered as illustrative only, with a true scope and purpose of the present invention being indicated by the claims. 17

Claims

BL-5627 CLAIMS: LU503692

1. À constellation configuration optimization method for an advanced receiver autonomous integrity monitor (ARAIM)-application-oriented low earth orbit satellite enhancement system, comprising: step 1, when it is determined that integrity risks and continuity risks are equally distributed, traversing all subset solutions and post-fault-mode vertical protection levels, and determining constraint conditions for low earth orbit satellite constellation configuration parameters; step 2, determining objective functions of the low earth orbit satellite constellation configuration parameters Xp Aa Aa da, eliminating abnormal calculated values of the vertical protection levels, and screening initial populations of the parameters Xp Xp Xn X, wherein parameter “! is a track inclination angle, parameter * is a track height, parameter X is an initial value parameter of a right ascension of ascending node, and parameter *4 is an initial value of a mean anomaly; step 3, performing fitness calculation on the objective functions of the low earth

. . . . Xp Xp X X orbit satellite constellation configuration parameters “1° 72° 73% 74: . CL . Xp Xp X X step 4, after screening out the initial populations of the parameters 1 “2° 73% "4, starting from a second-generation population, combining a parent population and offspring populations, so as to generate new offspring populations, performing rapid nondominated sorting, calculating a crowding degree of individuals in each nondominated layer, randomly pairing the individuals, and performing a genetic algorithm crossover-operation between the paired two individuals; and step 5, after combining the parent population and the offspring populations, so as to generate the new offspring populations, performing elitist strategy selection and local optimal selection on the new offspring populations, screening out maximum values of the objective functions as optimal offspring, and repeating step 4 until the number of genetic generations is less than the maximum number of genetic generations.

2. The method according to claim 1, wherein in step 1, the vertical protection level is expressed as: VPL, = max((VPL,),, max((VPL, . . . . 1 X((VPLy ),, max((VPL,),) , Wherein VPLy is the vertical protection level Nsat

_. VPLy), = Kine Co, + Son bh, Va under fault-free conditions, (PL), = Kia" 904 + 2, | oo mtn Ka. is an integrity and continuity risk value of the fault-free mode under the fully visible satellite 18

BL-5627 s° b LU503692 subset, 7” is a projection matrix, and ”“” is a maximum nominal deviation of the n satellite: VPL, . . . . 2 i is the vertical protection level corresponding to a measurement deviation of an it fault mode under a maximum deviation, i Nsat ; VPL,), = K\ma'Tiat+ S |b. + D, D, . . (PL), = King Oi En | a mtn 744 and 44 is a detection threshold; 004 = GW GY 0,5 = (GTM, GT . . wherein a a ! 4 G is a geometric matrix in a pseudorange observation equation, Wir is a fixed error assumption model parameter on the integrity, M, is an identity matrix of size Noa “Noa Noa is the number of visible satellites, q represents a q sample point, and the geometric matrix G in the pseudorange observation equation contains the low

. . . . Xp Xp X X earth orbit satellite constellation configuration parameters “1” “2° 3° “4: and a constraint condition of the low earth orbit satellite constellation configuration parameters is expressed as: N, 0 18 Q i —l X N Io MM. |= N I —l ; C Sod H J , wherein Ny represents the number of orbital planes of the low earth orbit constellation, Nso represents the number of satellites on each orbital plane, Ne is a phase parameter, Nee Dr N,] , Q represents a right ascension of ascending node, M represents the mean anomaly, i represents the i orbital plane, and j represents the j satellite.

3. The method according to claim 1, wherein in step 2, the objective functions of . . . . Xp Xp X X the low earth orbit satellite constellation configuration parameters 7!” 72° “3 74 are expressed as: min [- For, (x)] x st0<xy<— 2 min [- For (x,)]

s.1.800 < x, < 2000 min [- For (x;)]

51.0<x,<0.782 19

BL-5627 . LU503692 ma [- For (x,)] <x, < . . ;

5.105 x, 503 , wherein Fp C9) represents that the vertical protection level (VPL) is a function of parameter “1, Fp C2) represents that the vertical protection level (VPL) is a function of parameter 2, Fry (x3) represents that the vertical ; ; ; X3 Fp (xy) protection level (VPL) is a function of the parameter “3, and represents that the vertical protection level (VPL) is a function of the parameter *4.

4. The method according to claim 1, wherein in step 2, eliminating abnormal calculated values of the vertical protection levels is performed by: . ee . . T fs T fs . setting initial abnormality detection threshold ”“ and ~/ | defining T et = Uy +20, ‚and T first = Hu 20 an , wherein Fall is a mean value of the calculated values of the vertical protection levels (VPL) corresponding to all sample points, and Pan is a standard deviation of the calculated values of the vertical protection levels (VPL) corresponding to all sample points, comparing the calculated value of the vertical protection level (VPL) of each 0 un The Th, y sample point with ~/# and ~/ under the condition that an inequation T,,<VPL<T,., . cute frs SV frst is satisfied, making the sample point pass the threshold detection and wait for initial population screening, and under the condition that the inequation T,,<VPL<T,, . frs SV frst is unsatisfied, making the sample point not pass the threshold detection, and stored in an abnormal data module.

5. The method according to claim 1, wherein in step 2, screening the initial populations is performed by: as for the track inclination angle parameter “1, setting a sampling interval ÂT as

0.01, to generate a total of 158 sample points, taking a set of data every 9 sample points as a sample of the initial population, wherein the 15 samples constitute the initial population of the track inclination angle parameter *1; as for the track height parameter *2, setting a sampling interval AT, as 1, to generate a total of 1200 sample points, taking a set of data every 19 sample points as a sample of the initial population, wherein the 60 samples constitute the initial population of the track height parameter “2;

BL-5627 LU503692 as for the initial value parameter % oof a right ascension of ascending node, setting a sampling interval Az; as 0.001, to generate a total of 79 sample points, taking a set of data every 4 sample points as a sample of the initial population, wherein the 15 samples constitute the initial population of the initial value parameter % ofa right ascension of ascending node; and as for the initial value parameter *4 of a mean anomaly, setting a sampling interval 274 as 0.01, to generate a total of 30 sample points, taking a set of data every 4 sample points as a sample of the initial population, wherein the 6 samples constitute the initial population of the initial value ** of a mean anomaly.

6. The method according to claim 1, wherein in step 3, fitness calculation on the objective functions of the low earth orbit satellite constellation configuration parameters Xp ox Xe Ny js performed by: using a maximum optimization problem function for a fitness function: F, (x) + Coin > Cin + F, (x)>0 Fitness(F,p, (x)) = hs Fo (x)<0 i. c , + X)s . ; . min VPE , wherein ””" is a preset number that is a minimum function value of the objective function Fr (5) estimated so far, and Fp (x) is the objective function, and represents that the vertical protection level (VPL) is a function of the parameter “1, *2, X or Ya,

7. The method according to claim 6, wherein the objective function also satisfies the following condition: a value of the objective function Fin (x) is < 35 m.

8. The method according to claim 1, wherein a combination proportion of combining the parent population and the offspring populations to form the new offspring populations is: Xu =X Ar, pro, =——————= UN mort +1) , i = 1, 2, 3, 4, wherein Xu is an upper limit of an optimization parameter range, Xo is a lower limit of the optimization parameter range, Az, isa Xu sampling interval for each parameter, and Nera is a sample interval 21

BL-5627 when the initial populations are generated. LU503692

9. The method according to claim 1, wherein in step 5, a sample local mean A, is introduced for local optimal selection, a selection threshold Te is set, after elitist strategy selection is performed on the new offspring populations, a difference is made between the objective function and each local mean An, and under the condition that the difference is greater than the selection threshold La ‚a maximum value of the objective function is taken as the optimal offspring by means of local optimal test; and under the condition that the difference is less than the threshold Ta , a maximum value around the objective function is searched as the optimal offspring.

10. The method according to claim 9, wherein the sample local mean A, is expressed as: 5(n+1) Kur An n > Li Ar, Ar == TU 20123, M=1,2,3,...) =— k 5 , wherein, Xu =X Ar, m represents the m“® local mean, a maximum value is , represents the ‘“ sample of the corresponding parameter, it is specified to take a mean once every 5 samples as the local mean, Xu is an upper limit of an optimization X û : . Co. Art. . parameter range, is a lower limit of the optimization parameter range, and ~ 7 is X ; Lo. a “= sampling interval for each parameter. 22