CN112558112A - GNSS state domain slow-change slope fault integrity monitoring method - Google Patents

GNSS state domain slow-change slope fault integrity monitoring method Download PDF

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CN112558112A
CN112558112A CN202011288910.6A CN202011288910A CN112558112A CN 112558112 A CN112558112 A CN 112558112A CN 202011288910 A CN202011288910 A CN 202011288910A CN 112558112 A CN112558112 A CN 112558112A
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state
covariance matrix
monitoring
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slow
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CN112558112B (en
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张秋昭
余章俊
孙澳
郑南山
孟晓林
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China University of Mining and Technology CUMT
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S19/00—Satellite radio beacon positioning systems; Determining position, velocity or attitude using signals transmitted by such systems
    • G01S19/01—Satellite radio beacon positioning systems transmitting time-stamped messages, e.g. GPS [Global Positioning System], GLONASS [Global Orbiting Navigation Satellite System] or GALILEO
    • G01S19/13—Receivers
    • G01S19/20—Integrity monitoring, fault detection or fault isolation of space segment
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S19/00—Satellite radio beacon positioning systems; Determining position, velocity or attitude using signals transmitted by such systems
    • G01S19/01—Satellite radio beacon positioning systems transmitting time-stamped messages, e.g. GPS [Global Positioning System], GLONASS [Global Orbiting Navigation Satellite System] or GALILEO
    • G01S19/13—Receivers
    • G01S19/23—Testing, monitoring, correcting or calibrating of receiver elements

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Abstract

The invention discloses a method for monitoring the integrity of a GNSS state domain slow-changing slope fault, which comprises the steps of determining a recursion period by utilizing a recursion principle, obtaining state innovation, namely the difference between a priori state estimation and a posterior state estimation and a covariance matrix thereof through GNSS extended Kalman filtering, and constructing recursion monitoring statistics; determining a monitoring threshold according to actual false alarm rate requirements of different navigation positioning application fields; and comparing the monitoring statistic with a monitoring threshold value, finishing the integrity monitoring of the slow-changing slope fault in the state domain, if the monitoring statistic is larger than the monitoring threshold value, giving an alarm to a user, and if not, continuing the integrity monitoring of the next epoch. The method is directly expanded from the state domain of the GNSS, monitors the integrity of the slow-change slope fault through describing the state value of the system, can operate on line in real time, and provides a new idea for the technical field of monitoring the integrity of the slow-change slope fault from the perspective of positioning results.

Description

GNSS state domain slow-change slope fault integrity monitoring method
Technical Field
The invention relates to a GNSS state domain integrity detection method, in particular to a GNSS state domain slow-change slope fault integrity monitoring method, and belongs to the technical field of satellite monitoring.
Background
Integrity refers to the ability to alert the user in time when the GNSS system fails or the error of the positioning result exceeds a limit. With the development and perfection of navigation systems such as GPS, GLONASS, BDS, Galileo and the like, the GNSS system plays a very important role in key fields such as aviation, military and the like, and in order to meet the safety requirements of users in various professional fields, the research on the integrity of the GNSS system is crucial to the modernization of the Beidou satellite navigation system in China.
The current GNSS integrity monitoring methods are mainly classified into two categories: one is to adopt an external enhancement system such as a satellite-based enhancement system, a foundation enhancement system and the like to assist in integrity monitoring; another category is receiver autonomous integrity monitoring RAIM. The external enhancement method needs external auxiliary equipment, so the method has the defects of high cost, poor autonomy and the like, and the RAIM has the advantages of low cost, strong autonomy, simple algorithm and the like and is widely applied. The main principle of RAIM is to autonomously detect and identify faults by utilizing redundant GNSS information, the concept of RAIM is firstly proposed by Kalafus in 1987, and the maximum distance method for solution is proposed by Brown in 1988; later popularized by Pervan et al and Blanch et al to the situation of simultaneous error of multiple satellites and developed into a multi-hypothesis distance solution method; lee proposed a pseudorange comparison in 1986; parkinson proposed the least squares residual method in 1988; sturza proposed a parity vector method in 1988; under the condition that noise obeys Gaussian distribution, a pseudo-range comparison method, a least square residual method and a parity vector method have equivalence; the above method is generally called a "snapshot method" because it has a strong capability of detecting a step fault.
Although the snapshot method has a good detection effect on step faults and fast-changing faults, the slow-changing slope faults are very slow, because the monitoring statistics of the snapshot method is established through the measurement errors of the current epoch, when the measurement errors of each epoch are kept small all the time and the total errors are gradually accumulated and increased, the snapshot method is 'failed'. Therefore, many scholars at home and abroad develop researches on the slow-changing slope fault, the current mainstream slow-changing slope fault integrity monitoring algorithm is a new extrapolation method based on a measurement domain, a rate detection method developed on the basis of the new extrapolation method, and partial scholars also introduce a least square support vector machine to assist in monitoring the slow-changing slope fault integrity.
Generally, most of current slow-ramp fault integrity monitoring algorithms are developed from a measurement domain, but from the practical application perspective, a user often cares about a state value as a final positioning result rather than a measurement value as an intermediate quantity, and in the aspect of describing the integrity of the GNSS system, the measurement value is far from being straightforward with the state value, and in many cases, a fault of the measurement value does not necessarily represent a fault of the final state value, so that it is necessary to research an integrity monitoring algorithm directly developed from the state domain for the slow-ramp fault.
Disclosure of Invention
Aiming at the problems in the prior art, the invention provides a method for monitoring the integrity of the slow-change slope fault in a GNSS state domain, which can be directly expanded from the state domain of a GNSS system, and can monitor the integrity of the slow-change slope fault by describing the state value of the system, so that a user can directly and clearly see the fault of the final state value.
The invention relates to a GNSS state domain slow-change slope fault integrity monitoring method, which comprises the following steps:
s1: initialization: defining initial state value and false alarm rate P of receiverFA；
S2: obtaining an estimated value of the posterior state of the k epoch through GNSS extended Kalman filtering
Figure BDA0002783272590000021
And its covariance matrix
Figure BDA0002783272590000022
S3: determining a recurrence period m
If m is larger than or equal to k, monitoring by adopting a classical state domain integrity monitoring method;
if m is less than k, estimating the posterior state from k-m epoch
Figure BDA0002783272590000023
And its covariance matrix
Figure BDA0002783272590000024
Time is updated to k epochs, and prior state estimation in the recursion process is calculated
Figure BDA0002783272590000025
Prior state covariance matrix
Figure BDA0002783272590000026
A posteriori state covariance matrix
Figure BDA0002783272590000027
S4: calculating "State innovation"
Figure BDA0002783272590000028
I.e. recursive a priori state estimation
Figure BDA0002783272590000029
And a posteriori state estimation
Figure BDA00027832725900000210
The difference between two and the covariance matrix thereof
Figure BDA00027832725900000211
S5: constructing state domain slow-change slope fault monitoring statistic savg，k；
S6: according to the false alarm rate P defined in the step S1FACalculating the false alarm rate PFALower monitoring threshold
Figure BDA00027832725900000212
S7: monitoring statistic savg，kAnd a monitoring threshold
Figure BDA00027832725900000213
Make a comparison
If it is
Figure BDA00027832725900000214
Step S8 is executed;
if it is
Figure BDA0002783272590000031
An alarm is given to the user and the algorithm needs to be reinitialized, returning to step S1;
s8: predicting the prior state estimation value of the next epoch and the covariance matrix thereof, and returning to the step S2;
compared with the traditional innovation extrapolation method based on the measurement error, the method provided by the invention has the advantages that the completeness is monitored directly from the state domain of the GNSS system, the completeness is monitored by constructing the state innovation, namely the difference between the prior state estimation and the posterior state estimation and the covariance matrix thereof by utilizing the recursion principle, the algorithm content is straightforward, the state domain fault identification rate is high, the online real-time operation can be realized, and a new thought is provided for the technical field of slowly-varying slope fault completeness monitoring from the positioning result perspective. In addition, the invention can be used for not only a single system such as GPS, GLONASS, BDS and GALILEO, but also the combined positioning of different satellite systems and inertial systems.
Drawings
FIG. 1 is a flow chart of the present invention;
fig. 2 is a diagram of the relationship between the monitoring threshold and the false alarm rate and the dimension of the state domain.
Detailed Description
The invention will be further explained with reference to the drawings.
As shown in fig. 1, the method for monitoring integrity of a slow-changing slope fault in a GNSS state domain of the present invention specifically includes:
s1: initialization: defining the initial state value of the receiver (i.e. the initial value of the time of the receiver 0) and the false alarm rate PFAThe false alarm rate PFAPositioning the false alarm rate of a specific application field for navigation;
s2: obtaining an estimated value of the posterior state of the k epoch through GNSS extended Kalman filtering
Figure BDA0002783272590000032
And its covariance matrix
Figure BDA0002783272590000033
S3: determining a recurrence period m
If m is larger than or equal to k, monitoring by adopting a classical state domain integrity monitoring method;
if m is less than k, estimating the posterior state from k-m epoch
Figure BDA0002783272590000034
And its covariance matrix
Figure BDA0002783272590000035
Time is updated to k epochs, and prior state estimation in the recursion process is calculated
Figure BDA0002783272590000036
Prior state covariance matrix
Figure BDA0002783272590000037
A posteriori state covariance matrix
Figure BDA0002783272590000038
S4: calculating "State innovation"
Figure BDA0002783272590000039
I.e. recursive a priori state estimation
Figure BDA00027832725900000310
And a posteriori state estimation
Figure BDA00027832725900000311
The difference between two and the covariance matrix thereof
Figure BDA0002783272590000041
S5: constructing state domain slow-change slope fault monitoring statistic savg，k；
S6: according to the false alarm rate P defined in the step S1FACalculating the false alarm rate PFALower monitoring threshold
Figure BDA0002783272590000042
S7: monitoring statistic savg，kAnd a monitoring threshold
Figure BDA0002783272590000043
Make a comparison
If it is
Figure BDA0002783272590000044
Step S8 is executed;
if it is
Figure BDA0002783272590000045
An alarm is given to the user and the algorithm needs to be reinitialized, returning to step S1;
s8: and predicting the prior state estimation value of the next epoch and the covariance matrix thereof, and returning to the step S2.
The invention can be used for not only single systems such as GPS, GLONASS, BDS and GALILEO, but also combined positioning of different satellite systems and inertial systems, and the following embodiment is that the invention is applied to BDS pseudo range single-point positioning, and specifically comprises the following steps:
s1: initialization: defining the initial state value of the receiver (i.e. the initial value of the time of the receiver 0) and the false alarm rate PFAThe false alarm rate PFAPositioning the false alarm rate of a specific application field for navigation;
defining the prior state estimate of the receiver k epoch as
Figure BDA0002783272590000046
And its covariance matrix is
Figure BDA0002783272590000047
Figure BDA0002783272590000048
Figure BDA0002783272590000049
And determining the false alarm rate as P according to the specific application field of navigation positioningFA，
Wherein,
Figure BDA00027832725900000410
representing the true state value x of the k epochkObey mean value of
Figure BDA00027832725900000411
Variance of
Figure BDA00027832725900000412
Normal distribution of (2);
let k equal to 0;
s2: obtaining an estimated value of a posterior state of a k epoch through BDS pseudo range single-point positioning extended Kalman filtering
Figure BDA00027832725900000413
And its covariance matrix
Figure BDA00027832725900000414
S2.1, acquiring a BDS pseudo range observation value P and a Doppler observation value D through a pseudo range observation equation and a Doppler observation equation of the BDS system:
P＝l·dX+m·dY+n·dZ+ρ0+c·dtr-c·dts+I+T
λD＝l(vx-vX)+m(vy-vY)+n(vz-vZ)+c·dtf-c·dtf
in the formula, l, m and n are direction cosines from the receiver to the satellite; dX, dY and dZ are correction numbers of coordinates of the measuring station; rho0Is the true distance between the satellite and the receiver; c is the speed of light; dtrAnd dtsRespectively a receiver clock error and a satellite clock error; i is ionospheric delay correction; t isDelay correction for troposphere; λ is the wavelength of the carrier phase; d is a satellite Doppler observed value; v. ofx，vy，vzRepresenting the speed of movement of the receiver; v. ofX，vY，vZRepresenting the movement velocity of the satellite; dtfAnd dtfRespectively representing the rate of change of the receiver clock error and the satellite clock error;
s2.2 BDS extended Kalman filtering to obtain posterior state estimation value of k epoch
Figure BDA0002783272590000051
And its covariance matrix
Figure BDA0002783272590000052
The specific method comprises the following steps:
s2.2.1 define the state equation and measurement equation of the BDS system:
xk+1＝fk(xk)+wk
zk＝hk(xk)+vk
where k is 0, 1, 2, …, vector
Figure BDA0002783272590000053
And
Figure BDA0002783272590000054
respectively representing the true state values (including the three-dimensional coordinates, three-dimensional velocity, clock error and frequency drift of the receiver) and the measured values (including pseudo-range observations P and Doppler observations D) of the k epochs, and the state transfer function fk：
Figure BDA0002783272590000055
And a measurement relation function hk：
Figure BDA0002783272590000056
Are all known; state noise
Figure BDA0002783272590000057
Probability density function of
Figure BDA0002783272590000058
And measuring noise
Figure BDA0002783272590000059
Probability density function of
Figure BDA00027832725900000510
Figure BDA00027832725900000511
Are all known and independent of each other;
s2.2.2 finding an estimate of the posterior state
Figure BDA00027832725900000512
Probability density function p (x)k|zk) Posterior state estimation
Figure BDA00027832725900000513
The general solution of (a) is given by the Bayesian recurrence relation, and the formula is as follows:
p(xk|zk-1)＝∫p(xk|xk-1)p(xk-1|zk-1)dxk-1
Figure BDA00027832725900000514
in the formula, zk＝[z0，z1，zWave (wave)，…，zk]Represents a set of all measurements from 0-k epochs; p (x)k|zk-1) Is a predicted probability density function calculated by the Kolmogorov (Chapman-Kolmogorov) equation; p (x)k|zk) Is a filtering probability density function calculated by a Bayesian rule; p (x)k|xk-1) And p (z)k|xk) Respectively, by the BDS system state transfer function fkAnd a measurement relation function hkCalculating the obtained probability density function;
s2.2.3 extended Kalman BDSFiltering to obtain the posterior state estimation value of k epoch
Figure BDA00027832725900000515
And its covariance matrix
Figure BDA00027832725900000516
Figure BDA00027832725900000517
Denotes xkIs through zkIs found and obeys a mean value of
Figure BDA00027832725900000518
Variance of
Figure BDA00027832725900000519
Normal distribution of (a):
Figure BDA0002783272590000061
Figure BDA0002783272590000062
wherein:
Figure BDA0002783272590000063
Figure BDA0002783272590000064
Figure BDA0002783272590000065
Figure BDA0002783272590000066
in the formula,
Figure BDA0002783272590000067
is an a priori state estimate of the k epoch,
Figure BDA0002783272590000068
filter gain for k epochs, zkIs a measured value of the k epoch,
Figure BDA0002783272590000069
is a prior measurement of the k epoch,
Figure BDA00027832725900000610
is a prior state covariance matrix of k epochs,
Figure BDA00027832725900000611
is a measured covariance matrix of k epochs,
Figure BDA00027832725900000612
a state measurement covariance matrix for k epochs; h iskAs a function of the measured relation of k epochs, xkIs the true state value of the k epoch, but since the true state value is not available in reality, it is generally described by a gaussian distribution approximation,
Figure BDA00027832725900000613
obey the mean value of the true state values of k epochs
Figure BDA00027832725900000614
Variance of
Figure BDA00027832725900000615
(ii) a gaussian distribution of;
s3: determining a recursion period m according to a specific application scene
If m is larger than or equal to k, monitoring by adopting a classical state domain integrity monitoring method;
if m is less than k, estimating the posterior state from k-m epoch
Figure BDA00027832725900000616
And its covariance matrix
Figure BDA00027832725900000617
Time is updated to k epochs, and prior state estimation in the recursion process is calculated
Figure BDA00027832725900000618
Prior state covariance matrix
Figure BDA00027832725900000619
A posteriori state covariance matrix
Figure BDA00027832725900000620
Determining a recurrence starting value
Figure BDA00027832725900000621
Prior state estimation in a recursion process
Figure BDA00027832725900000622
Prior state covariance matrix
Figure BDA00027832725900000623
A posteriori state covariance matrix
Figure BDA00027832725900000624
The following formula is given:
Figure BDA00027832725900000625
Figure BDA0002783272590000071
Figure BDA0002783272590000072
wherein,
Figure BDA0002783272590000073
Figure BDA0002783272590000074
Figure BDA0002783272590000075
Figure BDA0002783272590000076
in the formula,
Figure BDA0002783272590000077
is the filter gain of the k-m + i epoch,
Figure BDA0002783272590000078
is a priori measured value of k-m + i epoch,
Figure BDA0002783272590000079
is a measured covariance matrix of k-m + i epochs,
Figure BDA00027832725900000710
a state measurement covariance matrix for the k-m + i epoch;
Figure BDA00027832725900000711
representing the true value x of the state of the k-m + i epochk-m+i-1Obey mean value of
Figure BDA00027832725900000712
Variance of
Figure BDA00027832725900000713
Normal distribution of (a), fk-m+i-1Is the state transfer function of the k-m + i epoch, hk-m+iAs a function of the measured relation of k-m + i epochs, Qk-m+i-1State noise covariance matrix, R, for k-m + i epochsk-m+iIs a measurement noise covariance matrix of k-m + i epochs, i is more than or equal to 1 and less than or equal to m.
S4: calculating "State innovation"
Figure BDA00027832725900000714
I.e. recursive a priori state estimation
Figure BDA00027832725900000715
And a posteriori state estimation
Figure BDA00027832725900000716
The difference between two and the covariance matrix thereof
Figure BDA00027832725900000717
Figure BDA00027832725900000718
Figure BDA00027832725900000719
In the formula,
Figure BDA00027832725900000720
is a prior-state covariance matrix,
Figure BDA00027832725900000721
i is more than or equal to 1 and less than or equal to m, and is a covariance matrix of the posterior state.
S5: constructing state domain slow-change slope fault monitoring statistic savg，k：
Figure BDA0002783272590000081
Wherein,
Figure BDA0002783272590000082
Figure BDA0002783272590000083
in the formula (d)avgFor a weighted average sum of "state innovation" constructed by its inverse covariance matrix,
Figure BDA0002783272590000084
for "state innovation" covariance inverse matrix summation,
Figure BDA0002783272590000085
is the state innovation of the k-m + i epoch,
Figure BDA0002783272590000086
is a state innovation covariance matrix of k-m + i epochs, and i is more than or equal to 1 and less than or equal to m.
A graph of the monitoring threshold value, the false alarm rate and the state domain dimension is shown in FIG. 2;
s6: according to the false alarm rate P defined in the step S1FACalculating the false alarm rate PFALower monitoring threshold
Figure BDA0002783272590000087
Figure BDA0002783272590000088
In the formula, PFALocating false alarm rate, s, for a particular application field of navigationkFor chi-squared distributed variables subject to dimensional freedom of the corresponding state domain, F(s)k) As a function of its distribution. A graph of the monitoring threshold value, the false alarm rate and the state domain dimension is shown in FIG. 2;
s7: monitoring statistic savg，kAnd a monitoring threshold
Figure BDA0002783272590000089
Make a comparison
If it is
Figure BDA00027832725900000810
Step S8 is executed;
if it is
Figure BDA00027832725900000811
An alarm is given to the user and the algorithm needs to be reinitialized, returning to step S1;
s8: predicting the prior state estimation value of the next epoch and the covariance matrix thereof, and returning to the step S2;
predicting the prior state estimation value of the next epoch by the following formula
Figure BDA00027832725900000812
And covariance matrix thereof
Figure BDA00027832725900000813
Figure BDA00027832725900000814
Figure BDA00027832725900000815
New predicted probability density function
Figure BDA00027832725900000816
QkIs a state noise covariance matrix of k epochs.

Claims (6)

1. A GNSS state domain slow-change slope fault integrity monitoring method is characterized by comprising the following steps:
s1: initialization: defining initial state value and false alarm rate P of receiverFA；
S2: through GNSS extended Kalman filtering to obtainPosterior state estimation value of k epoch
Figure RE-FDA0002950571450000011
And its covariance matrix
Figure RE-FDA0002950571450000012
S3: determining a recurrence period m
If m is larger than or equal to k, monitoring by adopting a classical state domain integrity monitoring method;
if m is less than k, estimating the posterior state from k-m epoch
Figure RE-FDA0002950571450000013
And its covariance matrix
Figure RE-FDA0002950571450000014
Time is updated to k epochs, and the estimated value of the prior state in the recursion process is calculated
Figure RE-FDA0002950571450000015
Prior state covariance matrix
Figure RE-FDA0002950571450000016
A posteriori state covariance matrix
Figure RE-FDA0002950571450000017
S4: calculating "State innovation"
Figure RE-FDA0002950571450000018
I.e. recursive a priori state estimation
Figure RE-FDA0002950571450000019
And a posteriori state estimation
Figure RE-FDA00029505714500000110
Both of themDifference and covariance matrix thereof
Figure RE-FDA00029505714500000111
S5: constructing state domain slow-change slope fault monitoring statistic savg，k；
S6: according to the false alarm rate P defined in the step S1FACalculating the false alarm rate PFALower monitoring threshold
Figure RE-FDA00029505714500000112
S7: monitoring statistic savg，kAnd a monitoring threshold
Figure RE-FDA00029505714500000113
Make a comparison
If it is
Figure RE-FDA00029505714500000114
Step S8 is executed;
if it is
Figure RE-FDA00029505714500000115
An alarm is given to the user and the algorithm needs to be reinitialized, returning to step S1;
s8: and predicting the prior state estimation value of the next epoch and the covariance matrix thereof, and returning to the step S2.
2. The GNSS state domain slow-changing slope fault integrity monitoring method according to claim 1, wherein the recursive initial value in step S3
Figure RE-FDA00029505714500000116
Prior state estimation in a recursion process
Figure RE-FDA00029505714500000117
Prior state covariance matrix
Figure RE-FDA00029505714500000118
A posteriori state covariance matrix
Figure RE-FDA00029505714500000119
The following formula is given:
Figure RE-FDA00029505714500000120
Figure RE-FDA0002950571450000021
wherein,
Figure RE-FDA0002950571450000022
Figure RE-FDA0002950571450000023
Figure RE-FDA0002950571450000024
Figure RE-FDA0002950571450000025
in the formula,
Figure RE-FDA0002950571450000026
is the filter gain of the k-m + i epoch,
Figure RE-FDA0002950571450000027
is a priori measured value of k-m + i epoch,
Figure RE-FDA0002950571450000028
is a measured covariance matrix of k-m + i epochs,
Figure RE-FDA0002950571450000029
a state measurement covariance matrix for the k-m + i epoch;
Figure RE-FDA00029505714500000210
representing the true value x of the state of the k-m + i epochk-m+i-1Obey mean value of
Figure RE-FDA00029505714500000211
Variance of
Figure RE-FDA00029505714500000212
Normal distribution of (a), fk-m+i-1Is the state transfer function of the k-m + i epoch, hk-m+iAs a function of the measured relation of k-m + i epochs, Qk-m+i-1State noise covariance matrix, R, for k-m + i epochsk-m+iIs a measurement noise covariance matrix of k-m + i epochs, i is more than or equal to 1 and less than or equal to m.
3. The GNSS state domain slow-changing slope fault integrity monitoring method according to claim 1, wherein the "state innovation" in step S4 "
Figure RE-FDA00029505714500000213
And covariance matrix thereof
Figure RE-FDA00029505714500000214
The following formula is given:
Figure RE-FDA00029505714500000215
Figure RE-FDA00029505714500000216
in the formula,
Figure RE-FDA0002950571450000031
is a prior-state covariance matrix,
Figure RE-FDA0002950571450000032
is a posteriori state covariance matrix.
4. The GNSS state-domain slow-ramp fault integrity monitoring method according to claim 1, wherein the state-domain slow-ramp fault monitoring statistic S in step S5avg，kThe following formula is given:
Figure RE-FDA0002950571450000033
wherein,
Figure RE-FDA0002950571450000034
Figure RE-FDA0002950571450000035
in the formula (d)avgFor a weighted average sum of "state innovation" constructed by its inverse covariance matrix,
Figure RE-FDA0002950571450000036
for "state innovation" covariance inverse matrix summation,
Figure RE-FDA0002950571450000037
is k-m + i epoch "state innovation",
Figure RE-FDA0002950571450000038
is a covariance matrix of k-m + i epoch state innovation, i is more than or equal to 1 and less than or equal to m.
5. The GNSS state domain slow-changing slope fault integrity monitoring method according to claim 1, wherein the monitoring threshold in step S6 is set as the threshold
Figure RE-FDA0002950571450000039
The following formula is given:
Figure RE-FDA00029505714500000310
in the formula, PFALocating false alarm rate, s, for a particular application field of navigationkFor chi-squared distributed variables subject to dimensional freedom of the corresponding state domain, F(s)k) As a function of its distribution.
6. The GNSS state domain slow-changing slope fault integrity monitoring method according to claim 1, wherein the estimation value of the prior state of the next epoch is predicted in step S8
Figure RE-FDA00029505714500000311
And covariance matrix thereof
Figure RE-FDA00029505714500000312
The following formula is given:
Figure RE-FDA00029505714500000313
Figure RE-FDA00029505714500000314
new predicted probability density function
Figure RE-FDA00029505714500000315
QkIs a state noise covariance matrix of k epochs.
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