CN111596317A - Method for detecting and identifying multi-dimensional fault - Google Patents
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Abstract
The invention discloses a method for detecting and identifying multi-dimensional faults, which comprises the following steps: s1: constructing fault test statistic, and testing the fault based on chi-square test; s2: when the existence of a fault is detected, a fault set is constructed by fusing the identification results of the data detection method and the correlation coefficient method; s3: identifying and eliminating faults according to the fault set; the fault is identified and processed by fusing the two typical RAIM algorithms of the data detection method and the correlation analysis method, and the method has higher fault identification accuracy and identification efficiency compared with the method of singly adopting the two typical RAIM algorithms of the data detection method and the correlation analysis method under the condition of multi-dimensional fault, and can further improve the integrity and reliability of the satellite navigation system.
Description
Technical Field
The invention relates to the technical field of integrity monitoring of satellite navigation systems, in particular to a method for detecting and identifying multi-dimensional faults.
Background
In a global satellite navigation system, satellite signals are extremely prone to interference of surrounding environments and human factors, so that positioning accuracy and reliability are difficult to guarantee, but reliability of the navigation system in the field of safety application is very important. The integrity service may alert the user in time when the navigation system is unable to provide satisfactory navigational positioning services. Receiver autonomous integrity monitoring is a common method of providing integrity services and primarily involves the detection and identification of system failures. However, the conventional RAIM algorithm is mainly proposed under the condition of single fault assumption, and has better effect when the system has single fault; however, when a plurality of faults exist in the system at the same time, although the conventional RAIM algorithm can also detect and identify the faults, the identification accuracy and efficiency are not ideal and need to be improved.
Therefore, the multi-bit fault detection and identification method is provided for identifying and processing faults by fusing two typical RAIM algorithms of a data detection method and a correlation analysis method, has higher fault identification accuracy and identification efficiency in a multi-dimensional fault situation than a method of singly adopting two RAIM algorithms of a data detection method and a correlation analysis method, and can further improve the integrity and reliability of a satellite navigation system, and is a problem to be solved by technical personnel in the field.
Disclosure of Invention
In view of the above, the invention provides a method for detecting and identifying a so-called fault, which identifies and processes the fault by fusing two typical RAIM algorithms, namely a data detection method and a correlation analysis method, and has higher fault identification accuracy and identification efficiency in a multi-dimensional fault situation compared with the case of singly adopting the two RAIM algorithms, namely the data detection method and the correlation analysis method, and can further improve the integrity and reliability of a satellite navigation system.
In order to achieve the purpose, the invention adopts the following technical scheme:
a multi-dimensional fault detection and identification method comprises the following steps:
s1: constructing fault test statistic, and testing the fault based on chi-square test;
s2: when the existence of a fault is detected, a fault set is constructed by fusing the identification results of the data detection method and the correlation coefficient method;
s3: and identifying and eliminating the faults according to the fault set.
Preferably, in S1, the fault is detected based on a hypothesis testing method, and a fault testing statistic is constructed by using a sum of squares of least squares residuals;
wherein the hypothesis test is constructed as:
H0:r＜T，H1:r＞T (1)
in the formula, H0For the original assumption, it indicates that no fault exists, H1For alternative assumptions, indicating the presence of a fault, rT is a test threshold value;
the test statistic is constructed using the sum of squares of the least squares residuals as:
where v is the least squares residual vector, P is the equivalent weight matrix of the observed quantity, σ0Is a unit weight variance factor, χ2Expressing chi-square distribution, wherein m and n are the numbers of observed quantities and state parameters respectively;
the test threshold T is determined by the number of false alarm rates and redundant observations, i.e.
In the formula, PFAFor false alarm rate, m-n represents the number of redundant observations.
Preferably, in S2, the method for constructing the fault set by the fusion data detection method and the correlation analysis method is to determine the probability of the fault occurring in each observed quantity based on the consistency evaluation of the identification results of the two methods, and construct the fault set according to the probability; the method for constructing the fault set by fusing the data detection method and the correlation analysis method comprises the following steps:
s21: identifying the faults by adopting a data detection method and a correlation analysis method, and sequencing the identification results;
s22: determining the probability of each observed quantity being a fault according to the identification results of the two methods, and sequencing the observed quantities from large to small to obtain an observed vector f;
s23: and constructing a fault set { F } according to the observation vector F.
Preferably, in S21, a data detection method and a correlation analysis method are used to identify the fault;
the correlation analysis method is to identify the observation fault based on the degree of correlation between the measurement error and the observation residual error, and the relationship between the observation error and the observation residual error v is as follows:
where y is an observation vector, a is an observation matrix, P is a weight matrix of the observation vector, I is an identity matrix, S-I-Q is a mapping matrix, S is a weight matrix of the observation vectori＝[S1iS2i… Smi]T(i 1, 2.. said., m) is the ith column of the S matrix, representing the measurement erroriProjection vector on residual vector v, reflecting measurement erroriDegree of contribution to v, correlation analysis by evaluating residual vector v and projection vector SiThe degree of correlation between the measurement errors and the observation residual errors is reflected, and fault identification is realized;
the degree of correlation between the observed error and the observed residual is characterized by a correlation coefficient, i.e.
Wherein c (i) represents a correlation coefficient of the i-th observed quantity,
and
are respectively a vector SiAnd the mean of v; sorting the observed quantities in descending order according to the magnitude of the correlation coefficient, and obtaining a vector c ═ c (1), c (2),.., c (m)]；
The data detection method is to realize the identification of observation faults based on the assumption that observation errors obey normal distribution, and the statistic quantity is defined as
In the formula, viAnd
respectively representing the ith element of the residual vector v and its corresponding standard deviation, SiiFor the ith row and ith column element of the matrix S, w (i) represents the ith viewA measured test statistic; the observations are sorted in descending order according to the magnitude of the w (i) values, obtaining a vector w ═ w (1), w (2),.., w (m)]。
Preferably, the observation vector in S22 is constructed by arranging the observation vectors f in descending order according to the probability that each observation vector is a suspected fault; the probability calculation formula of each observed quantity as a suspicious fault is
Pi＝1-(wi+ci)/2m(i＝1,2,...,m) (7)
In the formula, wiAnd ciIndex numbers of test statistics in vectors w and c respectively representing the ith observation;
according to the probability of each observation vector as suspicious fault, sequencing the observation vectors from large to small to obtain the observation vectors
f＝[f(1),f(2),...,f(m)](8)
Preferably, in S23, the method for constructing the fault set according to the observation vector F is to sequentially select 1,2, and k-1 observations from the observation vector F to construct the fault subsets F {1}, F {2},. and F { k-1 }; arbitrarily selecting k observation constructs from observations
A subset of faults F { k }, F { k +1}, F { S }; the structure of the failure set { F } is as follows:
in the formula, k is m-n-1, which represents the maximum number of faults.
Preferably, the step of identifying and rejecting faults according to the fault set in S3 is as follows:
s31: successively selecting a fault subset F { l } ( l 1, 2.. multidot.s) from the fault set { F }, and excluding suspicious observations according to elements contained in the fault subset;
s32: updating the fault test statistic r and the test threshold value T, and judging the size between the test statistic and the test threshold value;
s33: if r > T, further judging whether all fault subsets are traversed, if not, executing S31; otherwise, failure identification fails;
s34: and if r is less than or equal to T and the number num of the eliminated suspicious observations is more than 1, further carrying out reverse inspection on the eliminated suspicious observations.
According to the technical scheme, compared with the prior art, the invention discloses the method for detecting and identifying the multi-dimensional faults, the faults are identified and processed by fusing the two typical RAIM algorithms of the data detection method and the correlation analysis method, and compared with the case of the multi-dimensional faults, the method for detecting and identifying the multi-dimensional faults has higher fault identification accuracy and identification efficiency by independently adopting the two RAIM algorithms of the data detection method and the correlation analysis method, and can further improve the integrity and reliability of a satellite navigation system.
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In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below, it is obvious that the drawings in the following description are only embodiments of the present invention, and for those skilled in the art, other drawings can be obtained according to the provided drawings without creative efforts.
Fig. 1 is a flow chart of a multi-dimensional fault detection and identification method provided by the invention.
Fig. 2 is a flow chart of fault set construction by a fusion data detection method and a correlation analysis method provided by the invention.
Fig. 3 is a flow chart of a novel fault identification and processing based on a fault set according to the present invention.
FIG. 4 is a diagram of a test result using single system GPS observation data according to the present invention.
FIG. 5 is a graph showing the results of the test using single system BDS observation data provided by the present invention.
FIG. 6 is a diagram showing the test results of the observation data of the combined GPS/BDS system provided by the present invention.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
The embodiment of the invention discloses a method for detecting and identifying multi-dimensional faults, which comprises the following steps:
s1: constructing fault test statistic, and testing the fault based on chi-square test;
s2: when the existence of a fault is detected, a fault set is constructed by fusing the identification results of the data detection method and the correlation coefficient method;
s3: and identifying and eliminating the faults according to the fault set.
The specific process of multi-dimensional fault detection and identification is as follows:
constructing fault test statistics using least squares residual sum of squares, i.e.
Where v is the least squares residual vector, P is the equivalent weight matrix of the observed quantity, σ0Is a unit weight variance factor, χ2Expressing chi-square distribution, wherein m and n are the numbers of observed quantities and state parameters respectively;
the test threshold T is determined by the number of false alarm rates and redundant observations set, i.e.
In the formula, PFAM-n represents the number of redundancy observed quantities for the false alarm rate;
the following hypothesis testing method was constructed:
H0:r＜T，H1:r＞T (3)
in the formula, H0For the original hypothesis, representAbsence of failure, H1The method comprises the following steps of (1) detecting faults based on a hypothesis test method, wherein the alternative hypothesis indicates that the faults exist, r is a test statistic, and T is a test threshold;
and identifying the observation fault based on the correlation degree between the measurement error and the observation residual error by adopting a correlation analysis method, wherein the relation between the observation error and the observation residual error v is as follows:
where y is an observation vector, a is an observation matrix, P is a weight matrix of the observation vector, I is an identity matrix, S-I-Q is a mapping matrix, S is a weight matrix of the observation vectori＝[S1iS2i… Smi]T( i 1, 2.. said., m) is the ith column of the S matrix, representing the measurement erroriProjection vector on residual vector v, reflecting measurement erroriDegree of contribution to v, correlation analysis by evaluating residual vector v and projection vector SiThe degree of correlation between the measurement errors and the observation residual errors is reflected, and fault identification is realized;
using correlation coefficients to characterize the degree of correlation between observed error and observed residual, i.e.
Wherein c (i) represents a correlation coefficient of the i-th observed quantity,
and
are respectively a vector SiAnd v, according to the correlation analysis principle, the larger the correlation coefficient is, the larger the probability of the corresponding suspicious fault is;
sequencing the observed quantities according to the magnitude of the correlation coefficient in a descending order to obtain a vector
c＝[c(1),c(2),...,c(m)](6)
The observation fault is identified by adopting a data detection method based on the assumption that the observation error obeys normal distribution, and the statistic quantity is defined as
In the formula, viAnd σviRespectively representing the ith element of the residual vector v and its corresponding standard deviation, SiiThe element of the ith row and the ith column of the matrix S is w (i), the test statistic of the ith observed quantity is represented by w (i), and according to the test of the normal distribution hypothesis, the larger the value of w (i) is, the higher the probability that the observed quantity can be failed is;
sorting the observed quantities in descending order according to the magnitude of the w (i) value, thereby obtaining a vector
w＝[w(1),w(2),...,w(m)](8)
Calculating the probability of each observed quantity as a suspicious fault:
Pi＝1-(wi+ci)/2m(i＝1,2,...,m) (9)
in the formula, wiAnd ciIndex numbers of test statistics in vectors w and c respectively representing the ith observation;
arranging according to the probability of each observed quantity being suspicious fault from big to small to obtain an observed vector f
f＝[f(1),f(2),...,f(m)](10)
Firstly, sequentially selecting 1,2, a. Then, k observation quantity structures are arbitrarily selected from the observation vectors f
A subset of faults F { k }, F { k +1}, F { S }; the structure of the failure set { F } is as follows:
in the formula, k is m-n-1 which is the maximum number of faults;
successively selecting a fault subset F { l } ( l 1, 2.. multidot.s) from the fault set { F }, and excluding suspicious observations according to elements contained in the fault subset;
updating the fault test statistic r and the test threshold value T, and judging the size between the test statistic and the test threshold value;
if r > T, further judging whether all fault subsets are traversed, if not, successively selecting a fault subset F { l } (l is 1, 2.. multidot.S) from the fault set { F }, and excluding suspicious observation according to elements contained in the fault subset; otherwise, failure identification fails;
and if r is less than or equal to T and the number num of the eliminated suspicious observations is more than 1, further carrying out reverse inspection on the eliminated suspicious observations.
Examples
In order to test the performance of the multi-dimensional fault detection and identification method, the faults are identified by simulating different numbers of fault satellites based on single-system GPS, single-system BDS and GPS/BDS combined system observation data and respectively adopting a data detection method, a correlation coefficient method and the multi-dimensional fault detection and identification method provided by the invention.
TABLE 1 Performance comparison of three failure identification methods
TABLE 1 Performance comparison of three Fault identification methods
And (3) identifying the accuracy:
as can be seen from fig. 4 and table 1, for a single system GPS, when there are 2 faulty satellites, the correct identification rate of the fault by using the method provided by the present invention is better than 99%, and the correct rate is respectively increased by 8% and 32% compared with the correlation coefficient method and the data detection method; when more than 2 fault satellites exist, the correct identification rate of the method provided by the invention is reduced but still can reach more than 90%, and the correct rate is improved by 20-50% compared with a correlation coefficient method and a data detection method.
As can be seen from fig. 5 and table 1, for the single system BDS, when there are 2 faulty satellites, the correct identification rates of the faults by the three methods are substantially equivalent and all better than 94%; when more than 2 faults exist, the fault identification accuracy of the method provided by the invention can still reach 95%, and when the correlation coefficient method and the data detection method are adopted to detect and identify the 4 faulty satellites, the correct identification rate is only 79.2% and 30.1%, and the correct identification rate is obviously reduced.
As can be seen from fig. 6 and table 1, for the combined system GPS/BDS, when the number of the failed stars is not more than 6, the correct identification rate of the failure using the method provided by the present invention is better than 98%.
Efficiency of fault identification:
according to the statistical result of the fault identification efficiency, when 2 fault satellites exist in a single system, the identification efficiency of the method provided by the invention is higher than that of a correlation coefficient method and a data detection method, and is improved by about 50%; for a combined system, when the number of the fault stars is not more than 4, the identification efficiency of the method provided by the invention is almost 2 times that of a correlation coefficient method and a data detection method.
The embodiments in the present description are described in a progressive manner, each embodiment focuses on differences from other embodiments, and the same and similar parts among the embodiments are referred to each other. The device disclosed by the embodiment corresponds to the method disclosed by the embodiment, so that the description is simple, and the relevant points can be referred to the method part for description.
The previous description of the disclosed embodiments is provided to enable any person skilled in the art to make or use the present invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the generic principles defined herein may be applied to other embodiments without departing from the spirit or scope of the invention. Thus, the present invention is not intended to be limited to the embodiments shown herein but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.
Claims (7)
1. A multi-dimensional fault detection and identification method is characterized by comprising the following steps:
s1: constructing fault test statistic, and testing the fault based on chi-square test;
s2: when the existence of a fault is detected, a fault set is constructed by fusing the identification results of the data detection method and the correlation coefficient method;
s3: and identifying and eliminating the faults according to the fault set.
2. A method for detecting and identifying multi-dimensional faults according to claim 1, wherein in S1, fault detection is realized based on a hypothesis testing method, and fault detection statistics are constructed by using the sum of squares of least squares residuals;
wherein the hypothesis test is constructed as:
H0:r＜T，H1:r＞T (1)
in the formula, H0For the original assumption, it indicates that no fault exists, H1For alternative assumptions, indicating that a fault exists, r is a test statistic, and T is a test threshold;
the test statistic is constructed using the sum of squares of the least squares residuals as:
where v is the least squares residual vector, P is the equivalent weight matrix of the observed quantity, σ0Is a unit weight variance factor, χ2Expressing chi-square distribution, wherein m and n are the numbers of observed quantities and state parameters respectively;
the test threshold T is determined by the number of false alarm rates and redundant observations, i.e.
In the formula, PFAFor false alarm rate, m-n represents the number of redundant observations.
3. The multi-dimensional fault detection and identification algorithm according to claim 1, wherein the method for constructing the fault set by fusing the data detection method and the correlation analysis method in S2 is to determine the probability of the fault of each observed quantity based on the consistency evaluation of the identification results of the two methods, and construct the fault set according to the probability; the method for constructing the fault set by fusing the data detection method and the correlation analysis method comprises the following steps:
s21: identifying the faults by adopting a data detection method and a correlation analysis method, and sequencing the identification results;
s22: determining the probability of each observed quantity being a fault according to the identification results of the two methods, and sequencing the observed quantities from large to small to obtain an observed vector f;
s23: and constructing a fault set { F } according to the observation vector F.
4. A multi-dimensional fault detection and identification algorithm according to claim 3, wherein in S21, a data detection method and a correlation analysis method are adopted to identify the fault;
the correlation analysis method is to identify the observation fault based on the degree of correlation between the measurement error and the observation residual error, and the relationship between the observation error and the observation residual error v is as follows:
where y is an observation vector, a is an observation matrix, P is a weight matrix of the observation vector, I is an identity matrix, S-I-Q is a mapping matrix, S is a weight matrix of the observation vectori＝[S1iS2i… Smi]T(i 1, 2.. said., m) is the ith column of the S matrix, representing the measurement erroriProjection vector on residual vector v, reflecting measurement erroriDegree of contribution to v, correlation analysis by evaluating residual vector v and projection vector SiThe degree of correlation between the measurement errors and the observation residual errors is reflected, and fault identification is realized;
the degree of correlation between the observed error and the observed residual is characterized by a correlation coefficient, i.e.
Wherein c (i) represents a correlation coefficient of the i-th observed quantity,
and
are respectively a vector SiAnd the mean of v; sorting the observed quantities in descending order according to the magnitude of the correlation coefficient, and obtaining a vector c ═ c (1), c (2),.., c (m)]；
The data detection method is to realize the identification of observation faults based on the assumption that observation errors obey normal distribution, and the statistic quantity is defined as
In the formula, viAnd
respectively representing the ith element of the residual vector v and its corresponding standard deviation, SiiW (i) is the ith row and ith column element of the matrix S, and represents the test statistic of the ith observed quantity; the observations are sorted in descending order according to the magnitude of the w (i) values, obtaining a vector w ═ w (1), w (2),.., w (m)]。
5. The multi-dimensional fault detection and identification algorithm according to claim 3, wherein the observation vectors in S22 are constructed by arranging the probabilities of the suspicious faults according to the observation vectors to obtain observation vectors f; the probability that each observed quantity is a suspicious fault is determined according to the identification results of the two methods
Pi＝1-(wi+ci)/2m(i＝1,2,...,m) (7)
In the formula, wiAnd ciIndividual watchIndex numbers of test statistics of the ith observation in vectors w and c;
according to the probability of each observation vector as suspicious fault, sequencing the observation vectors from large to small to obtain the observation vectors
f＝[f(1),f(2),...,f(m)]。 (8) 。
6. A multi-dimensional fault detection and identification algorithm as claimed in claim 3, wherein the method for constructing the fault set according to the observation vector f in S23 is
Sequentially selecting 1,2, a. Arbitrarily selecting k observation constructs from observations
A subset of faults F { k }, F { k +1}, F { S }; the structure of the failure set { F } is as follows:
in the formula, k is m-n-1, which represents the maximum number of faults.
7. The algorithm for detecting and identifying multi-dimensional faults according to claim 1, wherein the step of identifying and rejecting faults according to the fault set in the step S3 is as follows:
s31: successively selecting a fault subset F { l } (l 1, 2.. multidot.s) from the fault set { F }, and excluding suspicious observations according to elements contained in the fault subset;
s32: updating the fault test statistic r and the test threshold value T, and judging the size between the test statistic and the test threshold value;
s33: if r > T, further judging whether all fault subsets are traversed, if not, executing S31; otherwise, failure identification fails;
s34: and if r is less than or equal to T and the number num of the eliminated suspicious observations is more than 1, further carrying out reverse inspection on the eliminated suspicious observations.
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| QIEQIE ZHANG等: "Improved Method for Single and Multiple GNSS Faults Exclusion based on Consensus Voting", 《THE JOURNAL OF NAVIGATION》 * |
| 林国钻等: "组合Baarda数据探测法与ESD检验法探测伪距粗差的新方法", 《全球定位系统》 * |
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| CN115494527A (en) * | 2022-04-13 | 2022-12-20 | 无锡奇芯科技有限公司 | Satellite system fault elimination method based on correlation coefficient |
| CN115494527B (en) * | 2022-04-13 | 2023-10-31 | 无锡奇芯科技有限公司 | Satellite system fault removal method based on correlation coefficient |
| CN115047496A (en) * | 2022-04-14 | 2022-09-13 | 东南大学 | Synchronous multi-fault detection method for GNSS/INS combined navigation satellite |
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