CN115134016B - ARAIM subset optimization method based on sparrow search algorithm - Google Patents
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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 autonomous integrity monitoring of receivers. Firstly, acquiring signals transmitted by satellites, extracting visible satellites observed by a receiver, and taking the positions of the visible satellites as an input sample set; then grouping and clustering the visible satellites to obtain a plurality of populations, initializing the types of the visible satellites in the populations, and determining discoverers, followers and reconnaissance early-warning persons; the method comprises the steps of carrying out positioning calculation on visible satellites in each population, carrying out fault detection, 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 various populations; iteratively updating the positions of discoverers and followers in each population, carrying out investigation and early warning on each population, screening out investigation and early warning persons causing the population fitness value to exceed a threshold value, and eliminating, thereby realizing the optimization of the ARAIM subset.
Description
Technical Field
The invention relates to the technical field of autonomous integrity monitoring of receivers, in particular to an ARAIM subset optimization method based on a sparrow search algorithm.
Background
The performance indexes of the navigation system include: accuracy, integrity, continuity, and availability. Advanced receiver autonomous integrity monitoring (Advanced Receiver Autonomous Integrity Monitoring, ARAIM) is used as a new generation of integrity monitoring technology, and dual-frequency multi-constellation is used for fault monitoring and removal, so that the functions of receiver autonomous integrity monitoring (Receiver Autonomous Integrity Monitoring, RAIM) are expanded, and vertical navigation below 200 feet (LPV-200) is supported.
ARAIM adopts multi-hypothesis solution separation algorithm, including fault detection, fault identification, fault removal and other functions. The fault detection function obtains fault subsets by means of traversing each satellite (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, namely two single faults which occur simultaneously, needs to be monitored, all possible combinations for eliminating the two fault satellites need to be established, and the combinations are called subset solutions); then the fault subset positioning result is subtracted from the positioning results of all the visible satellites to construct a test statistic; 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 is indicated to exist, and the fault removal function is continued. To achieve the above objective, the receiver needs to consider the possibility of each satellite being out of order.
With the development of global satellite navigation systems (GNSS), the number of available satellites has increased significantly, and the combination of these constellations results in improved geometry and better positioning results. However, an increased number of satellites in view means an increased probability of failure, which means that more subsets are established to check if a failure exists and to find out the satellite/constellation that has the failure. This clearly increases the computational effort, while the receiver also requires a more expensive chip to process large amounts of data. Therefore, the algorithm needs to be optimized to reduce the number of 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 known clustering class number dividing algorithm. The method is a very typical distance-based clustering algorithm, and adopts the distance as an evaluation index of similarity, namely, the closer the distance between two objects is, the larger the similarity is. Dividing data into k groups in advance, randomly selecting k objects as initial cluster centers, calculating the distance between each object and each seed cluster center, and distributing each object to the cluster center closest to the object. The algorithm considers the population to be composed of objects that are close together, thus targeting a compact and independent population as the final goal. The algorithm is an unsupervised learning algorithm for iterative solution which is commonly used in the classical cluster analysis method at present, and is widely used for data mining and intelligent algorithm fusion.
Sparrow search algorithm: the sparrow search algorithm (sparrow search algorithm) is a swarm intelligent optimization algorithm proposed according to the sparrow's behavior of foraging and evading predators. The process of foraging of sparrow groups is mainly simulated. The sparrow group foraging process is one of the finder-follower models, and a detection and early warning mechanism is superimposed. Individuals with food searching capability in sparrow are used as discoverers, other individuals are used as followers, a certain proportion of individuals are selected from the population for investigation and early warning, and if danger is found, food is abandoned so as to ensure the safety of the population. Compared with the traditional intelligent optimization algorithms such as bat algorithm, wolf optimization algorithm, whale optimization algorithm and the like, the intelligent optimization method has obvious advantages in optimization, and is high in stability, good in optimization precision and high in convergence speed.
Fault detection: the fault detection function obtains fault subsets by means of traversing each satellite (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, namely two single faults which occur simultaneously, needs to be monitored, all possible combinations for eliminating the two fault satellites need to be established, and the combinations are called subset solutions); then the fault subset positioning result is subtracted from the positioning results of all the visible satellites to construct a test statistic; and finally, judging whether the current positioning result is reliable or not by comparing the test statistic with a monitoring threshold. If the result exceeds the detection threshold, the fault is indicated to exist, and the fault removal function is continued.
Disclosure of Invention
Aiming at the defects of the prior art, the invention provides an ARAIM subset optimization method based on a sparrow search algorithm, which realizes the optimization of the ARAIM subset.
In order to solve the technical problems, the invention adopts the following technical scheme: an ARAIM subset optimization method based on a sparrow search algorithm comprises the following steps:
step 1, acquiring data; the method comprises the steps of obtaining signals sent by satellites through a signal receiving antenna, extracting visible satellites observed by a receiver at a certain moment, and taking the positions of the visible satellites 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 a navigation message, and representing coordinate points of each satellite by X, Y, Z in a geocentric and geodetic fixed coordinate system; (2) Converting the position coordinates of the receiver into X, Y, Z values in a geocentric fixed coordinate system, and then, performing difference with satellite coordinate values to calculate the elevation angle and the azimuth angle of each satellite; (3) extracting satellites with elevation angles larger than 5 degrees as visible satellites;
step 2, initializing a population by using an input sample set; the method comprises the steps of grouping visible satellites, firstly sorting the visible satellites according to the magnitude of elevation angles, selecting the first N satellites with the largest elevation angles as clustering centers, initializing a population through each clustering center, and determining the number of the clustering centers by the number of visible satellite constellations; other visible satellites are distributed to the population where the cluster center closest to the visible satellites is located through a k-means algorithm;
step 2.1, marking the position of the input sample set, namely 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 as { mu } 1 ，μ 2 ，…μ j Using j as the initial center of the population, wherein j is the number of visible satellite constellations;
step 2.2, calculating Euclidean distance from each visible satellite to the population center, wherein the Euclidean distance is shown in the following formula:
wherein x is i Representing the ith visible satellite; mu (mu) j Representing the j-th cluster center; q=1, 2,3 represents three directional components of northeast day;
comparing the distances from each visible satellite to different clustering centers, and distributing the visible satellites to the population in which the closest clustering center is located to obtain j populations, and recording the j populations as { S } 1 ,S 2 ,…,S j }；
Step 2.3, after all satellites are distributed, calculating the center point of each population again according to the positions of all visible satellites, iterating, selecting a new cluster center, and repeating the step of initializing the population until each population reaches the maximum iteration times;
step 3, initializing visible satellite types in the population; dividing the visible satellites in each population into three elevation angle areas of low elevation angle, medium elevation angle and high elevation angle according to the elevation angle, and respectively marking the areas as an area A l ,A m ,A h 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 (A) is the follower l The visible satellite in the system is a reconnaissance early warning person;
step 4, carrying out positioning calculation on the visible satellites in each population, carrying out fault detection, 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, positioning and resolving the visible satellites in each population, and solving a visible satellite position estimation residual error of the positioning and resolving by adopting a weighted least square method;
linearizing the positioning solution result of the visible satellites in each population by a Newton iteration method, and finally obtaining a visible satellite position estimation residual error Deltax by adopting a weighted least square method, wherein the visible satellite position estimation residual error Deltax is:
Δx＝(H T W (0) H) -1 H T W (0) Δy
wherein Δy is the pseudorange residual for evaluating integrity; h is a jacobian matrix, i.e., an observation matrix for receiver positioning solution; w is a weight matrix for evaluating integrity;
step 4.2, performing fault detection on all the visible satellites in each population, and determining position estimation residual errors of all the visible satellites and a fault subset, wherein the position estimation residual errors are respectively expressed as follows:
wherein,is the position estimation residual error of the visible satellite under the fault-free condition; />Representing the position estimate residuals for visible satellites in the kth failure subset, k=1, 2, …, N fault ，N fault Is the total number of fault subsets in a population; s is S (0) ＝(H T W (0) H)H T W (0) Position estimation for visible satellites in fault-free conditionsA matrix; s is S (k) ＝(H T W (k) H)H T W (k) Representing a position estimation matrix for the visible satellites in the kth failure subset;
and 4.3, constructing test statistics for each fault subset in the population, wherein the test statistics are shown in the following formula:
wherein,for the fitness value of the kth fault subset in the population, i.e. the test statistic, T k,q A detection threshold in the q-th direction on northeast days for the kth fault subset;
if the integrity risk probability is evenly distributed to each component of the visible satellite positioning solution in each failure subset, then a threshold T is detected k,q Expressed as:
wherein K is fa,q Is a threshold for a standard normal distribution;variance of positioning differences between the visible satellites in the subset of faults and the fault-free visible satellite position solutions; p (P) FA_HOR And P FA_VERT Components of the integrity risk probability in the horizontal and vertical directions, respectively; q (Q) -1 Inverse matrix of tail probability for normal distribution of zero mean units；
Step 4.4, determining the fitness value of the population;
set n in a fault subset 1 The visible satellites, the positions of the visible satellites in the fault subset are recorded as:
then the fitness function for this subset of faults is set to:
in q-dimensional space, the visible satellite positions in a population are expressed as:
setting a traversal object as a investigation early warning person, and obtaining the number of fault subsets of the population as r, wherein r is an integer; the fitness value of the population is expressed as:
wherein f r Representing an fitness value corresponding to the r-th fault subset;
step 5, iteratively updating the positions of the discoverers and the followers in each population until the maximum iteration times set according to the user needs are reached; the location update of the finder is shown in the following formula:
wherein,the position of the finder in t+1 iterations, wherein t represents the current iteration times; ter (iter) max The set maximum iteration times; alpha epsilon(0,1]Is a random number; r is R T ∈[0,1]And S is T ∈[0.5,1]Respectively representing an early warning value and a safety value; v is a random number subject to normal distribution; l represents a 1 Xq matrix and each element in the matrix is all 1; when R is T ＜S T When no fault satellite exists in the population, the step 1 is executed again, and the satellite navigation data in the next epoch is evaluated; if R is T ≥S T Then there are faulty satellites in the population;
the location update of the follower is shown in the following formula:
wherein,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 Represents the current global optimum position, X worst Then the current global worst position is indicated; a represents a 1 Xq matrix in which each element is randomly assigned a value of 1 or-1, and A + ＝A T (AA T ) -1 The method comprises the steps of carrying out a first treatment on the surface of the L represents a 1 Xq matrix and each element in the matrix is all 1;
step 6, the population performs investigation and early warning, investigation early warning persons with the population fitness value exceeding a threshold value are screened out and removed, and the ARAIM subset is optimized;
threshold detection is carried out on the positioning solutions of each fault subset and the fault-free positioning solutions in the northeast three directions, if the detection in one direction does not meet the threshold, the fault is detected, the fault mode corresponding to the positioning solution which does not pass the detection occurs, and the outlier, namely the investigation early warning person, needs to be isolated and removed; the mathematical expression for iteratively updating the position of the investigation early warning person is as follows:
wherein,the q-th dimension position of the reconnaissance early-warning person in the t+1st iteration is X best The global optimal position in the population; beta is [0,1 ]]A step length control parameter for controlling the global optimum position; k epsilon [ -1,1]For controlling the direction and step size of movement of the satellite; f (f) g And f w The best and worst fitness values in the fitness values corresponding to all the fault subsets are respectively; to avoid a denominator of 0, a minimum constant epsilon is added.
The beneficial effects of adopting above-mentioned technical scheme to produce 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 classification speed of the population can be increased, a better grouping result is obtained, the number of fault subsets can be reduced to a certain extent through grouping the visible satellites, and the calculation redundancy is reduced. Compared with the traditional algorithm, the sparrow search algorithm has the advantages of simple structure, easiness in implementation, fewer control parameters, strong local search capability and capability of finding faults without global traversal. The performance of sparrow search on reference functions such as unimodal, multimodal and the like is superior to that of traditional algorithms such as particle swarm algorithm, ant colony algorithm and the like. The sparrow search algorithm is applied to the fault detection process of the receiver, provides a new idea for the subsequent multi-constellation integrity monitoring research, and has 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 according to an embodiment of the present invention.
Detailed Description
The following describes in further detail the embodiments of the present invention with reference to the drawings and examples. The following examples are illustrative of the invention and are not intended to limit the scope of the invention.
In this embodiment, an ARAIM subset optimization method based on sparrow search algorithm, as shown in fig. 1 and 2, includes the following steps:
step 1, acquiring data; the method comprises the steps of obtaining signals sent by satellites through a signal receiving antenna, extracting visible satellites observed by a receiver at a certain moment, and taking the positions of the visible satellites 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 a navigation message, and representing coordinate points of each satellite by X, Y, Z in a geocentric and geodetic fixed coordinate system; (2) Converting the position coordinates of the receiver into X, Y, Z values in a geocentric fixed coordinate system, and then, performing difference with satellite coordinate values to calculate the elevation angle and the azimuth angle of each satellite; (3) extracting satellites with elevation angles larger than 5 degrees as visible satellites;
step 2, initializing a population by using an input sample set; the method comprises the steps of grouping visible satellites, firstly sorting the visible satellites according to the magnitude of elevation angles, selecting the first N satellites with the largest elevation angles as clustering centers, initializing a population through each clustering center, and determining the number of the clustering centers by the number of visible satellite constellations; for example: at present, only aiming at the Beidou and GPS double-satellite seats, the visible satellites in the current full view are divided into two groups, so that 2 groups can be obtained, and the groups are recorded as: { S 1 ，S 2 }. Then other visible satellites are distributed to the population where the cluster center closest to the visible satellites is located through a k-means algorithm;
step 2.1, marking the position of the input sample set, namely 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 as { mu } 1 ，μ 2 ，…μ j Using j as the initial center of the population, wherein j is the number of visible satellite constellations; the present embodiment is directed to GNSS constellations, so set j ε [1,4 ]]And j is an integer.
Step 2.2, calculating Euclidean distance from each visible satellite to the population center, wherein the Euclidean distance is shown in the following formula:
wherein x is i Representing the ith visible satellite; mu (mu) j Representing the j-th cluster center; q=1, 2,3 represents three directional components of northeast day; in combination with the space dimension to be set, the satellite studied in this embodiment is in three dimensions, so q=1, 2,3;
comparing the distances from each visible satellite to different clustering centers, and distributing the visible satellites to the population in which the closest clustering center is located to obtain j populations, and recording the j populations as { S } 1 ,S 2 ,…,S j }；
Step 2.3, after all satellites are distributed, calculating the center point (taking average value) of each population again according to the positions of all visible satellites in each population, then iterating, selecting a new cluster center, and repeating the step of initializing the population until each population reaches the maximum iteration times;
step 3, initializing visible satellite types in the population; dividing the visible satellites in each population into three elevation angle areas of low elevation angle, medium elevation angle and high elevation angle according to the elevation angle, and respectively marking the areas as an area A l ,A m ,A h 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 (A) is the follower l The visible satellite in the system is a reconnaissance early warning person;
(1) The discoverer: i.e., the more energetic individuals in each population; the satellites in view of each population that are more azimuth are defined as the initial discoverers of that population.
(2) The following: the main responsibility is to follow the discoverer to perform the corresponding task. Visible satellites with moderate azimuth angles are defined as followers.
(3) Detecting and early warning person: these individuals are located at the edge of the population and if the population exceeds a specified threshold due to their presence, these individuals are automatically outliers, thus defining a small azimuth visible satellite as a scout precautionary.
Step 4, carrying out positioning calculation on the visible satellites in each population, carrying out fault detection as shown in fig. 3, determining position estimation residual errors of all the visible satellites and fault subsets, further constructing test statistics for each fault subset in the population, and determining fitness values of each population;
the traditional optimization algorithm firstly assumes fault satellites, obtains a fault subset in a satellite-by-satellite traversal mode, and then subtracts the positioning results of the fault subset from the positioning results of all visible satellites to construct test statistics. Compared with the traditional optimization algorithm, the optimization algorithm omits the traversing process, thereby saving the calculation cost.
Step 4.1, positioning and resolving the visible satellites in each population, and solving a visible satellite position estimation residual error of the positioning and resolving by adopting a weighted least square method;
linearizing the positioning solution result of the visible satellites in each population by a Newton iteration method, and finally obtaining a visible satellite position estimation residual error Deltax by adopting a weighted least square method, wherein the visible satellite position estimation residual error Deltax is:
Δx＝(H T W (0) H) -1 H T W (0) Δy
wherein Δy is the pseudorange residual for evaluating integrity; h is a jacobian matrix, i.e., an observation matrix for receiver positioning solution; w is a weight matrix for evaluating integrity, as the case may be. The integrity reference algorithm may be employed as given in:
wherein C is int A pseudo-range covariance matrix for evaluating integrity;the user ranging precision for the ith satellite;tropospheric delay errors and user elevation errors for the ith satellite, respectively;
interpretation of the subset of faults: there are three concepts in the ARAIM algorithm, fault events, fault modes and fault subsets. The fault event is a macroscopic concept, and satellite/constellation faults that may occur are collectively referred to as a fault event. The fault mode is a combination of fault events, namely the number of possible faults, and the number of the fault events in the fault mode is also called a fault order. The fault subsets are in one-to-one correspondence with the fault modes, and represent a set of remaining fault events after the fault events with faults are removed.
Step 4.2, performing fault detection on all the visible satellites in each population, and determining position estimation residual errors of all the visible satellites and a fault subset, wherein the position estimation residual errors are respectively expressed as follows:
wherein,is the position estimation residual error of the visible satellite under the fault-free condition; />Representing the position estimate residuals for visible satellites in the kth failure subset, k=1, 2, …, N fault ，N fault Is the total number of fault subsets in a population; s is S (0) ＝(H T W (0) H)H T W (0) A position estimation matrix for the visible satellites in a fault-free condition; s is S (k) ＝(H T W (k) H)H T W (k) Representing the position estimate moment of the visible satellites in the kth failure subsetAn array;
and 4.3, constructing test statistics for each fault subset in the population, wherein the test statistics are shown in the following formula:
wherein,for the fitness value of the kth fault subset in the population, i.e. the test statistic, T k,q A detection threshold in the q-th direction on northeast days for the kth fault subset;
if the integrity risk probability is evenly distributed to each component of the visible satellite positioning solution in each failure subset, then a threshold T is detected k,q Expressed as:
wherein K is fa,q Is a threshold for a standard normal distribution;variance of positioning differences between the visible satellites in the subset of faults and the fault-free visible satellite position solutions; p (P) FA_HOR And P FA_VERT Components of the integrity risk probability in the horizontal and vertical directions, respectively; q (Q) -1 An inverse matrix of tail probability of normal distribution of zero mean units;
step 4.4, determining the fitness value of the population;
set to a certain fault subsetIn which there is n 1 The visible satellites, the positions of the visible satellites in the fault subset are recorded as:
then the fitness function for this subset of faults is set to:
in q-dimensional space, the visible satellite positions in a population are expressed as:
setting a traversal object as a investigation early warning person, and obtaining the number of fault subsets of the population as r, wherein r is an integer; the fitness value of the population is expressed as:
wherein f r Representing an fitness value corresponding to the r-th fault subset;
step 5, iteratively updating the positions of the discoverers and the followers in each population until the maximum iteration times set according to the user needs are reached; with iterative updates over time, there may be some new satellites joining the population, to ensure that discoverers have high priority characteristics, and once a newly joining satellite perceives itself to be more energetic than the discoverer, it will replace the current discoverer's location.
The discoverer has a good fitness value and is responsible for guiding the searching range and direction for the whole population, and the position of the discoverer is updated as shown in the following formula:
wherein,the position of the finder in t+1 iterations, wherein t represents the current iteration times; ter (iter) max The set maximum iteration times; alpha epsilon (0, 1)]Is a random number; r is R T ∈[0,1]And S is T ∈[0.5,1]Respectively representing an early warning value and a safety value; v is a random number subject to normal distribution; l represents a 1 Xq matrix and each element in the matrix is all 1; when R is T ＜S T When no fault satellite exists in the population, the step 1 is executed again, and the satellite navigation data in the next epoch is evaluated; if R is T ≥S T If a fault satellite exists in the population, an alarm needs to be sent to a user;
the position updating of the follower specifically comprises the following steps:
all identities in the population are not fixed and are transformed according to the situation; the follower will replace its location once it perceives itself to have more energy than the current finder;
the location update of the follower is shown in the following formula:
wherein,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 Represents the current global optimum position, X worst Then the current global worst position is indicated; a represents a 1 Xq matrix in which each element is randomly assigned a value of 1 or-1, and A + ＝A T (AA T ) -1 The method comprises the steps of carrying out a first treatment on the surface of the L represents a 1 Xq matrix and each element in the matrix is all 1;
step 6, the population performs investigation and early warning, investigation early warning persons with the population fitness value exceeding a threshold value are screened out and removed, and the ARAIM subset is optimized;
threshold detection is carried out on the positioning solutions of each fault subset and the fault-free positioning solutions in the northeast three directions, if the detection in one direction does not meet the threshold, the fault is detected, the fault mode corresponding to the positioning solution which does not pass the detection occurs, and the outlier, namely the investigation early warning person, needs to be isolated and removed; the mathematical expression for iteratively updating the position of the investigation early warning person is as follows:
wherein,the q-th dimension position of the reconnaissance early-warning person in the t+1st iteration is X best The global optimal position in the population; beta is [0,1 ]]A step length control parameter for controlling the global optimum position; k epsilon [ -1,1]For controlling the direction and step size of movement of the satellite; f (f) g And f w The best and worst fitness values in the fitness values corresponding to all the fault subsets are respectively; to avoid a denominator of 0, a minimum constant ε is added; when f k ＞f g The kth fault subset is positioned at the alarm edge, the probability of the fault satellite in the fault subset is high, and the fault is easy to occur; when f k ＝f g Indicating that the k-th fault subset has a fault satellite, wherein the population of the fault subset is affected by the fault satellite, so that a reconnaissance early-warning person needs to be updated to execute fault rejection.
Finally, it should be noted that: the above embodiments are only for illustrating the technical solution of the present invention, and are not limiting; although the invention has been described in detail with reference to the foregoing embodiments, it will be understood by those of ordinary skill in the art that: the technical scheme described in the foregoing embodiments can be modified or some or all of the technical features thereof can be replaced with equivalents; such modifications and substitutions do not depart from the spirit of the corresponding technical solutions, which are defined by the scope of the appended claims.
Claims (3)
1. An ARAIM subset optimization method based on a sparrow search algorithm is characterized by comprising the following steps of: the method comprises the following steps:
step 1, acquiring data; the method comprises the steps of obtaining signals sent by satellites through a signal receiving antenna, extracting visible satellites observed by a receiver at a certain moment, and taking the positions of the visible satellites as an input sample set;
step 2, initializing a population by using an input sample set; the method comprises the steps of grouping visible satellites, firstly sorting the visible satellites according to the magnitude of elevation angles, selecting the first N satellites with the largest elevation angles as clustering centers, initializing a population through each clustering center, and determining the number of the clustering centers by the number of visible satellite constellations; other visible satellites are distributed to the population where the cluster center closest to the visible satellites is located through a k-means algorithm;
step 3, initializing visible satellite types in the population; dividing the visible satellites in each population into three elevation angle areas of low elevation angle, medium elevation angle and high elevation angle according to the elevation angle, and respectively marking the areas as an area A l ,A m ,A h 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 (A) is the follower l The visible satellite in the system is a reconnaissance early warning person;
step 4, carrying out positioning calculation on the visible satellites in each population, carrying out fault detection, 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, positioning and resolving the visible satellites in each population, and solving a visible satellite position estimation residual error of the positioning and resolving by adopting a weighted least square method;
linearizing the positioning solution result of the visible satellites in each population by a Newton iteration method, and finally obtaining the position estimation residual error Deltax of the visible satellites by adopting a weighted least square method, wherein the position estimation residual error Deltax of the visible satellites is:
△x＝(H T W (0) H) -1 H T W (0) △y
wherein Δy is the pseudorange residual for evaluating integrity; h is a jacobian matrix, i.e., an observation matrix for receiver positioning solution; w is a weight matrix for evaluating integrity;
step 4.2, performing fault detection on all the visible satellites in each population, and determining position estimation residual errors of all the visible satellites and a fault subset, wherein the position estimation residual errors are respectively expressed as follows:
wherein,is the position estimation residual error of the visible satellite under the fault-free condition; />Representing the position estimate residuals for visible satellites in the kth failure subset, k=1, 2, …, N fault ，N fault Is the total number of fault subsets in a population; s is S (0) ＝(H T W (0) H)H T W (0) A position estimation matrix for the visible satellites in a fault-free condition; s is S (k) ＝(H T W (k) H)H T W (k) Representing a position estimation matrix for the visible satellites in the kth failure subset;
and 4.3, constructing test statistics for each fault subset in the population, wherein the test statistics are shown in the following formula:
wherein,for the fitness value of the kth fault subset in the population, i.e. the test statistic, T k,q A detection threshold in the q-th direction on northeast days for the kth fault subset;
if the integrity risk probability is evenly distributed to each component of the visible satellite positioning solution in each failure subset, then a threshold T is detected k,q Expressed as:
wherein K is fa,q Is a threshold for a standard normal distribution;variance of positioning differences between the visible satellites in the subset of faults and the fault-free visible satellite position solutions; p (P) FA_HOR And P FA_VERT Components of the integrity risk probability in the horizontal and vertical directions, respectively; q (Q) -1 An inverse matrix of tail probability of normal distribution of zero mean units;
step 4.4, determining the fitness value of the population;
set n in a fault subset 1 The visible satellites, the positions of the visible satellites in the fault subset are recorded as:
then the fitness function for this subset of faults is set to:
in q-dimensional space, the visible satellite positions in a population are expressed as:
setting a traversal object as a investigation early warning person, and obtaining the number of fault subsets of the population as r, wherein r is an integer; the fitness value of the population is expressed as:
wherein f r Representing an fitness value corresponding to the r-th fault subset;
step 5, iteratively updating the positions of the discoverers and the followers in each population until the maximum iteration times set according to the user needs are reached;
the location update of the finder is shown in the following formula:
wherein,the position of the finder in t+1 iterations, wherein t represents the current iteration times; ter (iter) max The set maximum iteration times; alpha epsilon (0, 1)]Is a random number; r is R T ∈[0,1]And S is T ∈[0.5,1]Respectively representing an early warning value and a safety value; v is a random number subject to normal distribution; l represents a 1 Xq matrix and each element in the matrix is all 1; when R is T ＜S T When no fault satellite exists in the population, the step 1 is executed again, and the satellite navigation data in the next epoch is evaluated; if R is T ≥S T Then in the populationA faulty satellite is present;
the location update of the follower is as follows:
wherein,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 Represents the current global optimum position, X worst Then the current global worst position is indicated; a represents a 1 Xq matrix in which each element is randomly assigned a value of 1 or-1, and A + ＝A T (AA T ) -1 The method comprises the steps of carrying out a first treatment on the surface of the L represents a 1 Xq matrix and each element in the matrix is all 1;
step 6, each population performs investigation and early warning, investigation early warning persons with the population fitness value exceeding a threshold value are screened out and removed, and the ARAIM subset is optimized;
threshold detection is carried out on the positioning solutions of each fault subset and the fault-free positioning solutions in the northeast three directions, if the detection in one direction does not meet the threshold, the fault is detected, the fault mode corresponding to the positioning solution which does not pass the detection occurs, and the outlier, namely the investigation early warning person, needs to be isolated and removed;
the mathematical expression for iteratively updating the position of the investigation early warning person is as follows:
wherein,the q-th dimension position of the reconnaissance early-warning person in the t+1st iteration is X best The global optimal position in the population; beta is [0,1 ]]To controlPreparing a moving step length control parameter of the global optimal position; k epsilon [ -1,1]For controlling the direction and step size of movement of the satellite; f (f) g And f w The best and worst fitness values in the fitness values corresponding to all the fault subsets are respectively; to avoid a denominator of 0, a minimum constant epsilon is added.
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 is as follows: (1) Reading a navigation message, and representing coordinate points of each satellite by X, Y, Z in a geocentric and geodetic fixed coordinate system; (2) Converting the position coordinates of the receiver into X, Y, Z values in a geocentric fixed coordinate system, and then, performing difference with satellite coordinate values to calculate the elevation angle and the azimuth angle of each satellite; (3) extracting satellites with elevation angles larger than 5 degrees as visible satellites.
3. The ARAIM subset optimization method based on the sparrow search algorithm according to claim 2, wherein: the specific method of the step 2 is as follows:
step 2.1, marking the position of the input sample set, namely 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 as { mu } 1 ，μ 2 ，…μ j Using j as the initial center of the population, wherein j is the number of visible satellite constellations;
step 2.2, calculating Euclidean distance from each visible satellite to the population center, wherein the Euclidean distance is shown in the following formula:
wherein x is i Representing the ith visible satellite; mu (mu) j Representing the j-th cluster center; q=1, 2,3 represents three directional components of northeast day;
comparing the distances from each visible satellite to different clustering centers, and distributing the visible satellites to the positions away from the visible satellitesObtaining j populations from the populations with the nearest cluster center, and marking the j populations as { S } 1 ,S 2 ,…,S j }；
And 2.3, after all satellites are distributed, recalculating the central point of each population according to the positions of all the visible satellites, iterating, selecting a new cluster center, and repeating the step of initializing the population until each population reaches the maximum iteration times.
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