CN115134016A - ARAIM subset optimization method based on sparrow search algorithm - Google Patents

ARAIM subset optimization method based on sparrow search algorithm Download PDF

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CN115134016A
CN115134016A CN202210748214.1A CN202210748214A CN115134016A CN 115134016 A CN115134016 A CN 115134016A CN 202210748214 A CN202210748214 A CN 202210748214A CN 115134016 A CN115134016 A CN 115134016A
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王尔申
王欢
高兢
佟刚
张汉茹
李兴广
曲萍萍
陈昌龙
管祥民
曾洪正
徐开俊
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Abstract

The invention provides an ARAIM subset optimization method based on a sparrow search algorithm, and relates to the technical field of receiver autonomous integrity monitoring. Firstly, acquiring a signal transmitted by a satellite, extracting a visible satellite observed by a receiver, and taking the position of the visible satellite as an input sample set; grouping and clustering visible satellites to obtain a plurality of populations, initializing visible satellite types in the populations, and determining discoverers, followers and reconnaissance early-warning persons; positioning and resolving the visible satellites in each population, detecting faults, determining position estimation residual errors of all the visible satellites and fault subsets, further constructing test statistics aiming at each fault subset in the population, and determining a fitness value of each population; iteratively updating the positions of the finder and the follower in each population, carrying out detection early warning on each population, screening out the detection early warning persons causing the population fitness value to exceed the threshold value, and removing the detection early warning persons, thereby realizing the optimization of the ARAIM subset.

Description

ARAIM subset optimization method based on sparrow search algorithm
Technical Field
The invention relates to the technical field of receiver autonomous integrity monitoring, in particular to an ARAIM subset optimization method based on a sparrow search algorithm.
Background
The performance indexes of the navigation system comprise: accuracy, integrity, continuity, and availability. Advanced Receiver Autonomous Integrity Monitoring (ARAIM) is used as a new generation of Integrity Monitoring technology, double-frequency multi-constellation is adopted to complete fault Monitoring and elimination, the function of Receiver Autonomous Integrity Monitoring (RAIM) is expanded, and vertical navigation of less than 200 feet (LPV-200) is supported.
ARAIM adopts a multi-hypothesis solution separation algorithm, and comprises functions of fault detection, fault identification, fault elimination and the like. The fault detection function obtains a fault subset by means of satellite-by-satellite traversal (for each fault to be monitored, a subset solution which does not contain the fault needs to be established, for example, if a second-order fault needs to be monitored, namely two single faults which occur simultaneously, all possible combinations for eliminating the two faulty satellites are created, and the combinations are called subset solutions); subtracting the positioning results of the fault subset and the positioning results of all visible satellites to construct test statistics; and finally, judging whether the current positioning result is reliable or not by comparing the test statistic with a detection threshold. If the result exceeds the detection threshold, the fault exists, and the fault elimination function is continuously executed. To achieve this, the receiver needs to take into account the possibility of each satellite failing.
With the development of Global Navigation Satellite Systems (GNSS), the number of available satellites has increased significantly, and the combination of these constellations leads to improved geometry and hence better positioning results. However, it can be seen that the increased number of satellites means that the probability of failure increases, and the increased probability of failure means that more subsets are built to check whether there is a failure and find out the satellite/constellation in which there is a failure. This certainly results in a significant increase in the amount of computation, while the receiver also requires a more expensive chip to process a large amount of data. Therefore, the algorithm needs to be optimized to reduce the number of the fault subsets, improve the execution efficiency of the algorithm, and reduce the cost of the receiver. A fast and efficient fault subset optimization algorithm is needed at this point.
k-means clustering algorithm: the k-means clustering algorithm is a basic partitioning algorithm of known clustering class numbers. The method is a very typical clustering algorithm based on distance, and the distance is used as an evaluation index of similarity, namely, the closer the distance between two objects is, the greater the similarity of the two objects is. Dividing data into k groups in advance, randomly selecting k objects as initial clustering centers, calculating the distance between each object and each seed clustering center, and allocating each object to the nearest clustering center. The algorithm considers that the population is composed of objects that are close in distance, and therefore a compact and independent population is obtained as a final target. The algorithm is an unsupervised learning algorithm for iterative solution, which is commonly used in the current classical cluster analysis method, and is widely used for the fusion of data mining and intelligent algorithms.
Sparrow search algorithm: the sparrow search algorithm (sparrow search algorithm) is a group intelligence optimization algorithm proposed based on the behavior of sparrows to forage for food and evade predators. Mainly simulates the process of sparrow group foraging. The sparrow foraging process is one of finder-follower models, and a detection early warning mechanism is also superposed. The sparrows have the ability of searching food as discoverers and other individuals as followers, and meanwhile, a certain proportion of individuals in the population are selected for detection and early warning, and if danger is found, food is abandoned, so that the safety of the population is ensured. Compared with the traditional intelligent optimization algorithms such as a bat algorithm, a wolf optimization algorithm, a whale optimization algorithm and the like, the optimization problem has obvious advantages of high stability, good optimization precision and high convergence rate.
Fault detection: the fault detection function obtains a fault subset by means of satellite-by-satellite traversal (for each fault to be monitored, a subset solution which does not contain the fault needs to be established, for example, if a second-order fault needs to be monitored, namely two single faults which occur simultaneously, all possible combinations for eliminating the two faulty satellites are created, and the combinations are called subset solutions); subtracting the positioning results of the fault subset and the positioning results of all visible satellites to construct test statistics; and finally, judging whether the current positioning result is reliable or not by comparing the test statistic with the monitoring threshold. If the result exceeds the detection threshold, the fault exists, and the fault elimination function is continuously executed.
Disclosure of Invention
The technical problem to be solved by the present invention is to provide an ARAIM subset optimization method based on a sparrow search algorithm to realize the optimization of ARAIM subsets, aiming at the defects of the prior art.
In order to solve the technical problems, the technical scheme adopted by the invention is as follows: an ARAIM subset optimization method based on a sparrow search algorithm comprises the following steps:
step 1, acquiring data; acquiring a signal transmitted by a satellite through a signal receiving antenna, extracting a visible satellite observed by a receiver at a certain moment, and taking the position of the visible satellite as an input sample set;
the specific method for extracting the visible satellite observed by the receiver at a certain moment comprises the following steps: (1) reading navigation messages, and representing the coordinate point of each satellite by X, Y, Z in a geocentric coordinate system; (2) converting the position coordinates of the receiver into X, Y, Z values in a geocentric geostationary coordinate system, and then calculating the elevation angle and azimuth angle of each satellite by making a difference with the coordinate values of the satellites; (3) extracting satellites with elevation angles larger than 5 degrees as visible satellites;
step 2, initializing a population by using an input sample set; grouping visible satellites, firstly sorting the visible satellites according to the size of an elevation angle, selecting the first N satellites with the largest elevation angle as clustering centers, initializing a cluster through each clustering center, and determining the number of the clustering centers by the number of visible satellite constellations; distributing other visible satellites to a population where a clustering center closest to the visible satellites is located through a k-means algorithm;
step 2.1, recording an input sample set, namely the position of the visible satellite at the current moment as: x ═ X 1 ,x 2 …x n ]Selecting j visible satellites with the largest azimuth angle from X and recording the j visible satellites as mu 1 ，μ 2 ，…μ j Taking j as the initial center of the population, wherein j is the number of visible satellite constellations;
step 2.2, calculating the Euclidean distance from each visible satellite to the center of the population, wherein the Euclidean distance is shown in the following formula:
Figure BDA0003720214360000031
wherein x is i Represents the ith visible satellite; mu.s j Representing the jth cluster center; q is 1,2,3 represents three directional components in northeast;
comparing the distance from each visible satellite to different clustering centers, distributing the visible satellites to the population where the clustering center closest to the visible satellite is located to obtain j populations, and marking as { S 1 ,S 2 ,…,S j }；
Step 2.3, after all the satellites are distributed, calculating the central point of each population again according to the positions of all the visible satellites in each population, then iterating, selecting a new clustering center, and repeating the step of initializing the population until each population reaches the maximum iteration times;
step 3, initializing the visible satellite type in the population; dividing visible satellites in each population into three elevation angle areas of low elevation angle, medium elevation angle and high elevation angle, and respectively recording the three elevation angle areas as an area A l ,A m ,A h Then counting the number of satellites in three elevation angle areas in a certain time period; initialization A h The visible satellite in (1) is the finder, A m The visible satellite in (A) is the follower l The visible satellite in the system is a reconnaissance early-warning person;
step 4, positioning and resolving the visible satellites in each population, detecting faults, determining position estimation residual errors of all the visible satellites and fault subsets, further constructing test statistics aiming at each fault subset in the population, and determining fitness values of each population;
step 4.1, performing positioning calculation on the visible satellites in each population, and solving a visible satellite position estimation residual error of the positioning calculation by adopting a weighted least square method;
linearizing the positioning calculation result of the visible satellite in each population by a Newton iteration method, and finally obtaining the position estimation residual error delta x of the visible satellite by adopting a weighted least square method as follows:
Δx＝(H T W (0) H) -1 H T W (0) Δy
wherein, Δ y is a pseudo-range residual error of the integrity evaluation; h is a Jacobian matrix, namely an observation matrix for positioning calculation of the receiver; w is a weight matrix for assessing integrity;
step 4.2, performing fault detection on all visible satellites in each population, and determining position estimation residual errors of all visible satellites and the fault subset, wherein the position estimation residual errors are respectively expressed as:
Figure BDA0003720214360000032
Figure BDA0003720214360000033
wherein, the first and the second end of the pipe are connected with each other,
Figure BDA0003720214360000034
is the position estimation residual error of the visible satellite under the fault-free condition;
Figure BDA0003720214360000035
represents the position estimate residual for the satellites in view in the kth subset of faults, k 1,2, …, N fault ，N fault Is the total number of fault subsets in a population; s (0) ＝(H T W (0) H)H T W (0) Estimating a matrix for the position of a visible satellite under fault-free conditions; s (k) ＝(H T W (k) H)H T W (k) A position estimate matrix representing satellites in view in the kth subset of faults;
and 4.3, constructing test statistics aiming at each fault subset in the population, wherein the test statistics are shown in the following formula:
Figure BDA0003720214360000041
wherein the content of the first and second substances,
Figure BDA0003720214360000042
fitness value, i.e. test statistic, T for the kth fault subset in the population k,q A detection threshold for the kth fault subset in the qth direction of the northeast;
detecting a threshold T if the integrity risk probability is evenly distributed over each component of the visible satellite positioning solution in each failure subset k,q Expressed as:
Figure BDA0003720214360000043
Figure BDA0003720214360000044
Figure BDA0003720214360000045
wherein, K fa,q Is a threshold of a standard normal distribution;
Figure BDA0003720214360000046
a variance of the positioning difference between the position solutions of the visible satellites and the non-fault visible satellites in the fault subset; p is FA_HOR And P FA_VERT Components of the integrity risk probability in the horizontal and vertical directions, respectively; q -1 The inverse matrix is the tail probability of the zero-mean unit normal distribution;
4.4, determining the fitness value of the population;
set n in a fault subset 1 Visible satellites, and the positions of the visible satellites in the fault subset are recorded as:
Figure BDA0003720214360000047
then, the fitness function for the subset of faults is set to:
Figure BDA0003720214360000048
in q-dimensional space, the positions of visible satellites in a certain population are represented as:
Figure BDA0003720214360000049
setting a traversal object as a detection and early warning person, obtaining that the number of fault subsets of the population is r, and taking r as an integer; the fitness value of the population is expressed as:
Figure BDA0003720214360000051
wherein, f r Representing a fitness value corresponding to the r-th subset of faults;
step 5, iteratively updating the positions of the finder and the follower in each population until the maximum iteration times set according to the user needs are reached; the location update of the discoverer is shown in the following formula:
Figure BDA0003720214360000052
wherein the content of the first and second substances,
Figure BDA0003720214360000053
the position of the finder in t +1 iterations, wherein t represents the current iteration number; iter max Is the set maximum iteration number; alpha epsilon (0, 1)]Is a random number; r T ∈[0,1]And S T ∈[0.5,1]Respectively representing an early warning value and a safety value; v is a random number following a normal distribution; l represents a 1 × q matrix and each element in the matrix is 1 in total; when R is T ＜S T When no fault satellite exists in the population, the step 1 is executed again, and satellite navigation data in the next epoch are evaluated; if R is T ≥S T If so, a fault satellite exists in the population;
the follower's location update is shown in the following equation:
Figure BDA0003720214360000054
wherein, the first and the second end of the pipe are connected with each other,
Figure BDA0003720214360000055
the position of the follower at t +1 iterations; m represents the number of followers in the population, n represents the number of visible satellites in the population, X p Representing the current global optimum position, X worst Then the current global worst position is indicated; a represents a 1 × q matrix in which each elementRandomly assigned a value of 1 or-1, and A + ＝A T (AA T ) -1 (ii) a L represents a 1 × q matrix and each element in the matrix is 1 in total;
step 6, carrying out detection early warning on the population, screening out detection early warning persons causing the population fitness value to exceed a threshold value, and removing the detection early warning persons to realize optimization of an ARAIM subset;
performing threshold detection on the positioning solution and the non-fault positioning solution of each fault subset in the northeast direction, wherein if the detection in one direction does not meet the threshold, the detection means that a fault is detected, and a fault mode corresponding to the positioning solution which does not pass the detection occurs, and the outlier, namely, a reconnaissance early-warning person needs to be isolated and eliminated; the mathematical expression for the iterative update of the positions of the investigation early-warning persons is as follows:
Figure BDA0003720214360000061
wherein, the first and the second end of the pipe are connected with each other,
Figure BDA0003720214360000062
is the q-dimension position, X, of the scouting forewarner in the t +1 iteration best The global optimal position in the population is obtained; beta to [0,1 ]]A movement step control parameter for controlling the global optimum position; k ∈ [ -1,1]The device is used for controlling the moving direction and the step length of the satellite; f. of g And f w Respectively the best and worst fitness value in the fitness values corresponding to all fault subsets; to avoid a denominator of 0, a minimum constant epsilon is added.
Adopt the produced beneficial effect of above-mentioned technical scheme to lie in: according to the ARAIM subset optimization method based on the sparrow search algorithm, the k-means algorithm is introduced into the population grouping process, the population classification speed can be increased, a better grouping result is obtained, the number of fault subsets can be reduced to a certain extent by grouping visible satellites, and the calculation redundancy is reduced. Compared with the traditional algorithm, the sparrow search algorithm is simple in structure, easy to implement, less in control parameters, strong in local search capability and capable of finding faults without global traversal. The performance of sparrow search on the basis functions of single peak, multiple peaks and the like is superior to that of traditional algorithms such as a particle swarm algorithm and an ant colony algorithm. The sparrow search algorithm is applied to the fault detection process of the receiver, a new idea is provided for the subsequent multi-constellation integrity monitoring research, and the method has a practical reference value.
Drawings
Fig. 1 is a frame diagram of an ARAIM subset optimization method based on a sparrow search algorithm according to an embodiment of the present invention;
fig. 2 is a flowchart of an ARAIM subset optimization method based on a sparrow search algorithm according to an embodiment of the present invention;
fig. 3 is a schematic diagram of a fault detection process provided in an embodiment of the present invention.
Detailed Description
The following detailed description of embodiments of the present invention is provided in connection with the accompanying drawings and examples. The following examples are intended to illustrate the invention but are not intended to limit the scope of the invention.
In this embodiment, an ARAIM subset optimization method based on a sparrow search algorithm, as shown in fig. 1 and 2, includes the following steps:
step 1, acquiring data; acquiring a signal transmitted by a satellite through a signal receiving antenna, extracting a visible satellite observed by a receiver at a certain moment, and taking the position of the visible satellite as an input sample set;
the specific method for extracting the visible satellite observed by the receiver at a certain moment comprises the following steps: (1) reading navigation messages, and representing the coordinate point of each satellite by X, Y, Z in a geocentric coordinate system; (2) converting the position coordinates of the receiver into X, Y, Z values in a geocentric coordinate system, and calculating the elevation angle and the azimuth angle of each satellite by making a difference with the coordinate values of the satellites; (3) extracting satellites with elevation angles larger than 5 degrees as visible satellites;
step 2, initializing a population by using an input sample set; grouping visible satellites, firstly sequencing the visible satellites according to the size of an elevation angle, selecting the first N satellites with the largest elevation angle as clustering centers, initializing a group through each clustering center, wherein the number of the clustering centers is determined by the visible satellitesDetermining the number of constellations; for example: only aim at big dipper and two stars of GPS at present, just so divide into two sets of with the visible satellite of current full view, can obtain 2 colonies, note: { S 1 ，S 2 }. Distributing other visible satellites to a population where a clustering center closest to the visible satellites is located through a k-means algorithm;
step 2.1, recording an input sample set, namely the position of the visible satellite at the current moment as: x ═ X 1 ,x 2 …x n ]Selecting j visible satellites with the largest azimuth angle from X and recording the j visible satellites as [ mu ] 1 ，μ 2 ，…μ j Taking j as the initial center of the population, and taking the number of visible satellite constellations as j; the present embodiment is for a GNSS constellation, so set j ∈ [1,4 ]]And j is an integer.
Step 2.2, calculating the Euclidean distance from each visible satellite to the center of the population, wherein the Euclidean distance is shown in the following formula:
Figure BDA0003720214360000071
wherein x is i Represents the ith visible satellite; mu.s j Represents the jth cluster center; q is 1,2,3 represents three directional components in northeast; in combination with the need to set spatial dimensions, the satellite under study in this embodiment is in three-dimensional space, so q is 1,2, 3;
comparing the distance from each visible satellite to different clustering centers, distributing the visible satellites to the clusters where the clustering centers closest to the visible satellites are located to obtain j clusters, and marking as { S 1 ,S 2 ,…,S j }；
Step 2.3, after all the satellites are distributed, the central point (average value) of each population is recalculated according to the positions of all the visible satellites in each population, then iteration is carried out, a new clustering center is selected, and the step of initializing the population is repeated until each population reaches the maximum iteration times;
step 3, initializing the visible satellite type in the population; dividing the visible satellites in each population into a low elevation angle area, a middle elevation angle area and a high elevation angle area according to the elevation angle size,are respectively marked as an area A l ,A m ,A h Then counting the number of satellites in three elevation angle areas in a certain time period; initialization A h The visible satellite in (A) is the finder m The visible satellite in (1) is the follower, A l The visible satellite in the system is a reconnaissance early-warning person;
(1) the discoverer: i.e. individuals with higher energy in each population; the visible satellites with larger azimuth angles in each population are defined as the initial discoverers of the population.
(2) Following the person: the main responsibility is to follow the discoverer to perform the corresponding task. Satellites in view with moderate azimuth are defined as followers.
(3) Investigation of the early-warning person: the individuals are located at the edge of the population, and if the population exceeds a specified threshold value due to the existence of the individuals, the individuals can automatically depart from the population, so that the visible satellites with small azimuth angles are defined as reconnaissance forewarners.
Step 4, positioning and resolving the visible satellites in each population, performing fault detection as shown in fig. 3, determining position estimation residual errors of all visible satellites and fault subsets, further constructing test statistics for each fault subset in the population, and determining fitness values of each population;
in the traditional optimization algorithm, a fault satellite is assumed, a fault subset is obtained in a satellite-by-satellite traversal mode, and then the positioning result of the fault subset and the positioning results of all visible satellites are subtracted to construct test statistic. Compared with the traditional optimization algorithm, the optimization algorithm of the invention saves the traversal process, thereby saving the calculation cost.
Step 4.1, performing positioning calculation on the visible satellites in each population, and solving a visible satellite position estimation residual error of the positioning calculation by adopting a weighted least square method;
linearizing the positioning calculation result of the visible satellite in each population by a Newton iteration method, and finally obtaining the position estimation residual error delta x of the visible satellite by adopting a weighted least square method as follows:
Δx＝(H T W (0) H) -1 H T W (0) Δy
wherein, Δ y is a pseudo-range residual error of the integrity evaluation; h is a Jacobian matrix, namely an observation matrix for positioning calculation of the receiver; w is a weight matrix used to assess integrity, as the case may be. The method can adopt the following steps given in the integrity benchmark algorithm:
Figure BDA0003720214360000081
Figure BDA0003720214360000082
wherein, C int A pseudorange covariance matrix for evaluating integrity;
Figure BDA0003720214360000083
ranging accuracy for the user of the ith satellite;
Figure BDA0003720214360000084
troposphere delay errors and user elevation errors of the ith satellite are respectively obtained;
interpretation of the failure subset: there are three concepts in the ARAIM algorithm, failure event, failure mode, and failure subset. Failure events are macroscopic concepts, collectively referred to as failure events, which may occur for a satellite/constellation failure. The failure mode is a combination of failure events, i.e. the number of possible failures, and the number of events having failures in the failure mode is also called the failure order. The failure subsets correspond to the failure modes one by one and represent a set of residual failure events after the failure events which have failed are eliminated.
Step 4.2, performing fault detection on all visible satellites in each population, and determining position estimation residuals of all visible satellites and a fault subset, wherein the position estimation residuals are respectively expressed as:
Figure BDA0003720214360000085
Figure BDA0003720214360000086
wherein the content of the first and second substances,
Figure BDA0003720214360000087
is the position estimation residual error of the visible satellite under the fault-free condition;
Figure BDA0003720214360000088
represents the position estimate residual for the satellites in view in the kth subset of faults, k 1,2, …, N fault ，N fault Is the total number of fault subsets in a population; s (0) ＝(H T W (0) H)H T W (0) Estimating a matrix for the position of a visible satellite under fault-free conditions; s (k) ＝(H T W (k) H)H T W (k) A position estimate matrix representing satellites in view in the kth subset of faults;
and 4.3, constructing test statistics aiming at each fault subset in the population, wherein the test statistics are shown in the following formula:
Figure BDA0003720214360000091
wherein the content of the first and second substances,
Figure BDA0003720214360000092
fitness value, i.e. test statistic, T for the kth fault subset in the population k,q A detection threshold for the kth fault subset in the qth direction of the northeast;
detecting a threshold T if the integrity risk probability is evenly distributed over each component of the visible satellite positioning solution in each failure subset k,q Expressed as:
Figure BDA0003720214360000093
Figure BDA0003720214360000094
Figure BDA0003720214360000095
wherein, K fa,q Is a threshold of a standard normal distribution;
Figure BDA0003720214360000096
a variance of the positioning difference between the position solutions of the visible satellites and the non-fault visible satellites in the fault subset; p FA_HOR And P FA_VERT Components of the integrity risk probability in the horizontal and vertical directions, respectively; q -1 The inverse matrix is the tail probability of the zero-mean unit normal distribution;
step 4.4, determining the fitness value of the population;
set n in a fault subset 1 Visible satellites, and the positions of the visible satellites in the fault subset are recorded as:
Figure BDA0003720214360000097
then, the fitness function for the subset of faults is set to:
Figure BDA0003720214360000098
in q-dimensional space, the positions of visible satellites in a certain population are represented as:
Figure BDA0003720214360000099
setting a traversal object as a detection early-warning person, obtaining the number of fault subsets of the population as r, and taking an integer from r; the fitness value of the population is expressed as:
Figure BDA00037202143600000910
wherein f is r Representing a fitness value corresponding to the r-th subset of faults;
step 5, iteratively updating the positions of the finder and the follower in each population until the maximum iteration times set according to the user needs are reached; with the iterative update of time, some new satellites may join the population, and in order to ensure that the discoverer has the characteristic of high priority, once the newly joined satellites detect that the energy of the newly joined satellites is larger than that of the discoverer, the newly joined satellites replace the position of the current discoverer.
The finder has a better fitness value and is responsible for directing the search range and direction for the whole population, and the location of the finder is updated as shown in the following formula:
Figure BDA0003720214360000101
wherein, the first and the second end of the pipe are connected with each other,
Figure BDA0003720214360000102
the position of the finder in t +1 iterations, wherein t represents the current iteration number; iter (R) max Is the set maximum iteration number; alpha epsilon (0, 1)]Is a random number; r T ∈[0,1]And S T ∈[0.5,1]Respectively representing an early warning value and a safety value; v is a random number following a normal distribution; l represents a 1 × q matrix and each element in the matrix is 1 in total; when R is T ＜S T When no fault satellite exists in the population, the step 1 is executed again, and satellite navigation data in the next epoch are evaluated; if R is T ≥S T If the satellite is a fault satellite in the population, an alarm needs to be sent to a user;
the position updating of the follower comprises the following specific steps:
all identities in the population are not fixed and are changed according to conditions; once the follower perceives that the energy of the follower is larger than that of the current finder, the follower replaces the position of the follower;
the follower's location update is shown in the following equation:
Figure BDA0003720214360000103
wherein the content of the first and second substances,
Figure BDA0003720214360000104
the position of the follower at t +1 iterations; m represents the number of followers in the population, n represents the number of visible satellites in the population, X p Representing the current global optimum position, X worst Then the current global worst position is indicated; a represents a 1 × q matrix in which each element is randomly assigned a value of 1 or-1, and A + ＝A T (AA T ) -1 (ii) a L represents a 1 × q matrix and each element in the matrix is 1 in total;
step 6, carrying out detection early warning on the population, screening out detection early warning persons causing the population fitness value to exceed a threshold value, and removing the detection early warning persons to realize optimization of ARAIM subsets;
performing threshold detection on the positioning solution and the non-fault positioning solution of each fault subset in the northeast direction, wherein if the detection in one direction does not meet the threshold, the detection means that a fault is detected, and a fault mode corresponding to the positioning solution which does not pass the detection occurs, and the outlier, namely, a reconnaissance early-warning person needs to be isolated and eliminated; the mathematical expression for the iterative update of the positions of the investigation early-warning persons is as follows:
Figure BDA0003720214360000111
wherein the content of the first and second substances,
Figure BDA0003720214360000112
is the q-dimension position, X, of the scouting forewarner in the t +1 iteration best The global optimal position in the population is obtained; beta to [0,1 ]]Controlling parameters for controlling the moving step length of the global optimal position; k ∈ [ -1,1]The device is used for controlling the moving direction and the step length of the satellite; f. of g And f w Respectively the best and worst fitness value in the fitness values corresponding to all fault subsets; to avoid a denominator of 0, a minimum constant ε is added; when f is k ＞f g Is shown byThe kth fault subset is located at the alarm edge, and the probability of fault satellites in the fault subset is high, so that faults are easy to occur; when f is k ＝f g And indicating that the fault satellite exists in the kth fault subset, wherein the population in which the fault subset is located is influenced by the fault satellite, so that the reconnaissance early-warning personnel needs to be updated to execute fault elimination.
Finally, it should be noted that: the above examples are only intended to illustrate the technical solution of the present invention, but not to limit it; although the present invention has been described in detail with reference to the foregoing embodiments, it will be understood by those of ordinary skill in the art that: the technical solutions described in the foregoing embodiments may still be modified, or some or all of the technical features may be equivalently replaced; such modifications and substitutions do not depart from the spirit of the corresponding technical solutions and scope of the present invention as defined in the appended claims.

Claims (6)

1. An ARAIM subset optimization method based on a sparrow search algorithm is characterized by comprising the following steps: the method comprises the following steps:
step 1, acquiring data; acquiring a signal transmitted by a satellite through a signal receiving antenna, extracting a visible satellite observed by a receiver at a certain moment, and taking the position of the visible satellite as an input sample set;
step 2, initializing a population by using an input sample set; grouping visible satellites, firstly sorting the visible satellites according to the size of an elevation angle, selecting the first N satellites with the largest elevation angle as clustering centers, initializing a cluster through each clustering center, and determining the number of the clustering centers by the number of visible satellite constellations; distributing other visible satellites to a population where a cluster center nearest to the visible satellites is located through a k-means algorithm;
step 3, initializing the visible satellite type in the population; dividing visible satellites in each population into three elevation angle areas of low elevation angle, medium elevation angle and high elevation angle, and respectively recording the three elevation angle areas as an area A l ,A m ,A h Then counting the number of satellites in three elevation angle areas in a certain time period; initialization A h The visible satellite in (A) is the finder m In (1) visible satellitesFor following, A l The visible satellite in the satellite system is a reconnaissance early-warning person;
step 4, positioning and resolving the visible satellites in each population, detecting faults, determining position estimation residual errors of all the visible satellites and fault subsets, further constructing test statistics aiming at each fault subset in the population, and determining fitness values of each population;
step 5, iteratively updating the positions of the finder and the follower in each population until the maximum iteration times set according to the user needs are reached;
and 6, carrying out detection early warning on each population, screening out detection early warning persons causing the population fitness value to exceed a threshold value, and removing the detection early warning persons to realize optimization of the ARAIM subset.
2. The ARAIM subset optimization method based on the sparrow search algorithm, as claimed in claim 1, wherein: the specific method for extracting the visible satellite observed by the receiver at a certain moment in the step 1 comprises the following steps: (1) reading navigation messages, and representing the coordinate point of each satellite by X, Y, Z in a geocentric coordinate system; (2) converting the position coordinates of the receiver into X, Y, Z values in a geocentric coordinate system, and calculating the elevation angle and the azimuth angle of each satellite by making a difference with the coordinate values of the satellites; (3) and extracting the satellite with the elevation angle larger than 5 degrees as a visible satellite.
3. The ARAIM subset optimization method based on the sparrow search algorithm as claimed in claim 2, wherein: the specific method of the step 2 comprises the following steps:
step 2.1, recording an input sample set, namely the position of the visible satellite at the current moment as: x ═ X 1 ,x 2 …x n ]Selecting j visible satellites with the largest azimuth angle from X and recording the j visible satellites as [ mu ] 1 ，μ 2 ，…μ j Taking j as the initial center of the population, and taking the number of visible satellite constellations as j;
step 2.2, calculating the Euclidean distance from each visible satellite to the center of the population, wherein the Euclidean distance is shown in the following formula:
Figure FDA0003720214350000021
wherein x is i Represents the ith visible satellite; mu.s j Representing the jth cluster center; q is 1,2,3 represents three directional components in northeast;
comparing the distance from each visible satellite to different clustering centers, distributing the visible satellites to the population where the clustering center closest to the visible satellite is located to obtain j populations, and marking as { S 1 ,S 2 ,…,S j }；
And 2.3, after all the satellites are distributed, recalculating the central point of each population according to the positions of all the visible satellites in each population, then performing iteration, selecting a new clustering center, and repeating the step of initializing the population until each population reaches the maximum iteration times.
4. The ARAIM subset optimization method based on the sparrow search algorithm as claimed in claim 3, wherein: the specific method of the step 4 comprises the following steps:
step 4.1, performing positioning calculation on the visible satellites in each population, and solving a visible satellite position estimation residual error of the positioning calculation by adopting a weighted least square method;
linearizing the positioning calculation result of the visible satellite in each population by a Newton iteration method, and finally obtaining the position estimation residual error delta x of the visible satellite by adopting a weighted least square method as follows:
Δx＝(H T W (0) H) -1 H T W (0) Δy
wherein, Δ y is a pseudo-range residual error of the integrity evaluation; h is a Jacobian matrix, namely an observation matrix for positioning and resolving the receiver; w is a weight matrix for assessing integrity;
step 4.2, performing fault detection on all visible satellites in each population, and determining position estimation residuals of all visible satellites and a fault subset, wherein the position estimation residuals are respectively expressed as:
Figure FDA0003720214350000022
Figure FDA0003720214350000023
wherein the content of the first and second substances,
Figure FDA0003720214350000024
is the position estimation residual error of the visible satellite under the fault-free condition;
Figure FDA0003720214350000025
represents the position estimate residual for the satellites in view in the kth subset of faults, k 1,2, …, N fault ，N fault Is the total number of fault subsets in a population; s. the (0) ＝(H T W (0) H)H T W (0) Estimating a matrix for the position of a visible satellite under fault-free conditions; s (k) ＝(H T W (k) H)H T W (k) A position estimate matrix representing satellites in view in the kth subset of faults;
and 4.3, constructing test statistics aiming at each fault subset in the population, wherein the test statistics are shown in the following formula:
Figure FDA0003720214350000026
wherein the content of the first and second substances,
Figure FDA0003720214350000027
fitness value, i.e. test statistic, T for the kth fault subset in the population k,q A detection threshold for the kth fault subset in the qth direction of the northeast;
detecting a threshold T if the integrity risk probability is evenly distributed over each component of the visible satellite positioning solution in each failure subset k,q Expressed as:
Figure FDA0003720214350000031
Figure FDA0003720214350000032
Figure FDA0003720214350000033
wherein, K fa,q Is a threshold of a standard normal distribution;
Figure FDA0003720214350000034
a variance of the positioning difference between the position solutions of the visible satellites and the non-fault visible satellites in the fault subset; p is FA_HOR And P FA_VERT Components of the integrity risk probability in the horizontal and vertical directions, respectively; q -1 The inverse matrix is the tail probability of the zero-mean unit normal distribution;
step 4.4, determining the fitness value of the population;
set n in a fault subset 1 Visible satellites, and the positions of the visible satellites in the fault subset are recorded as:
Figure FDA0003720214350000035
then, the fitness function for the subset of faults is set to:
Figure FDA0003720214350000036
in q-dimensional space, the positions of visible satellites in a certain population are represented as:
Figure FDA0003720214350000037
setting a traversal object as a detection and early warning person, obtaining that the number of fault subsets of the population is r, and taking r as an integer; the fitness value of the population is expressed as:
Figure FDA0003720214350000038
wherein f is r Representing the fitness value corresponding to the r-th subset of faults.
5. The ARAIM subset optimization method based on the sparrow search algorithm, according to claim 4, is characterized in that: step 5, the location update of the discoverer is shown as the following formula:
Figure FDA0003720214350000041
wherein the content of the first and second substances,
Figure FDA0003720214350000042
the position of the finder in t +1 iterations, wherein t represents the current iteration number; iter (R) max Is the set maximum iteration number; alpha epsilon (0, 1)]Is a random number; r T ∈[0,1]And S T ∈[0.5,1]Respectively representing an early warning value and a safety value; v is a random number following a normal distribution; l represents a 1 × q matrix and each element in the matrix is 1 in total; when R is T ＜S T When no fault satellite exists in the population, the step 1 is executed again, and satellite navigation data in the next epoch are evaluated; if R is T ≥S T If so, a fault satellite exists in the population;
the follower's location update is shown in the following equation:
Figure FDA0003720214350000043
wherein, the first and the second end of the pipe are connected with each other,
Figure FDA0003720214350000044
the position of the follower at t +1 iterations; m represents the number of followers in the population, n represents the number of visible satellites in the population, X p Representing the current global optimum position, X worst Then the current global worst position is indicated; a represents a 1 × q matrix in which each element is randomly assigned a value of 1 or-1, and A + ＝A T (AA T ) -1 (ii) a L represents a 1 × q matrix and each element in the matrix is all 1.
6. The ARAIM subset optimization method based on the sparrow search algorithm as claimed in claim 5, wherein: the specific method of the step 6 comprises the following steps:
performing threshold detection on the positioning solution and the non-fault positioning solution of each fault subset in the northeast direction, wherein if the detection in one direction does not meet the threshold, the detection means that a fault is detected, and a fault mode corresponding to the positioning solution which does not pass the detection occurs, and the outlier, namely, a reconnaissance early-warning person needs to be isolated and eliminated;
the mathematical expression for iteratively updating the position of the detection forewarner is as follows:
Figure FDA0003720214350000045
wherein the content of the first and second substances,
Figure FDA0003720214350000046
is the q-dimension position, X, of the scouting forewarner in the t +1 iteration best Is a global optimal position in the population; beta to [0,1 ]]Controlling parameters for controlling the moving step length of the global optimal position; k ∈ [ -1,1]The device is used for controlling the moving direction and the step length of the satellite; f. of g And f w Respectively the best and worst fitness value in the fitness values corresponding to all fault subsets; to avoid a denominator of 0, a minimum constant epsilon is added.
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* Cited by examiner, † Cited by third party
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CN111708054A (en) * 2020-06-16 2020-09-25 沈阳航空航天大学 ARAIM vertical protection level optimization method based on particle swarm optimization algorithm
CN113515881A (en) * 2021-03-23 2021-10-19 北京航空航天大学 ARAIM application-oriented low-orbit satellite augmentation system constellation configuration optimization method

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