CN102135621A - Fault recognition method for multi-constellation integrated navigation system - Google Patents

Abstract

The invention discloses a fault recognition method for a multi-constellation integrated navigation system. The method comprises the following steps of: unifying time and space coordinates of the multi-constellation system; determining fault detection usability; determining a fault; recognizing and removing faulty satellites and the like. Faults of various satellites can be monitored and recognized simultaneously, the success rate of recognizing and removing the faulty satellites is greatly improved due to unification of the time and space coordinates of the multi-constellation system and repeated detection and judgment, and the navigation positioning accuracy, positioning performance and reliability of the multi-constellation integrated navigation system are improved; therefore, the navigation service performance is improved.

Description

A kind of fault recognition method of many constellation combination navigational system

Technical field

The present invention relates to a kind of fault recognition method of navigational system, especially relate to a kind of fault recognition method of many constellation combination navigational system.

Background technology

Gps system (GPS (Global Position System)) has obtained using widely in the world, in gps system, many constellation combination navigational system has higher navigation and positioning accuracy and good positioning performance and reliability, makes its navigation Service that provides can reach the level that originally must use enhanced system just can have.

Yet, when existing a variety of causes such as fault satellites or for a long time false lock to cause the error of system to surpass the limit that allows when many constellation combination navigational system, with not competent navigation work.Cause the reason that breaks down in the satellite navigation system location to mainly contain following several at present:

1) bearing accuracy of satellite navigation is subjected to the influence of number of satellite and geometric distributions thereof, and there is the few and bad area of geometric distributions, location of number of satellite in gps system, and performance will worsen;

2) satellite navigation system is huge and complicated, and soft, the hardware fault of system also can make the satellite navigation positioning error increase, so that influences aircraft flight safety;

3) gps system have the national security interests of state for oneself, once taked the measure of some restriction bearing accuracies, under the situation that military conflict and war take place from now on, very difficult assurance has state and does not adopt similar measure for military interests;

4) electromagnetic wave in the external environment, ionosphere variation reach with natural disturbance, artificial interference, and particularly hostility is disturbed the reliability that also can influence satellite navigation.

To the identification of fault and the enhancing of integrity mainly is to adopt monitoring technology, and the Realtime Alerts ability is provided.The method that realizes system health can be divided into two classes, and a class is an internalist methodology, and another kind of is externalist methodology.Internalist methodology is to realize integrity monitoring with receiver internal sensor information, i.e. RAIM.

Application number is that the application for a patent for invention of CN 200610165465.8 discloses a kind of GNSS receiver autonomous integrity monitoring method based on many stars Fault Identification, and following steps are arranged: a. carries out the usability analyses of autonomous integrity; B. carry out single star, many stars fault judgement: detection statistic and single star or many stars detection threshold are compared,, show current non-fault, continue monitoring as not surpassing any thresholding; As surpassing thresholding, decision enters corresponding Fault Identification step; C. carry out single star, many stars Fault Identification: carry out Fault Identification with feature deviation collimation method during single star, carry out Fault Identification with hypothesis testing approach during many stars; D. get rid of checking: weed out fault satellites in the combinations of satellites, repeating step a, step b selecting; As do not find that fault shows that then step c is correct, the satellite of having fixed a breakdown; As find that new fault then shows step c failure, needs concrete condition is analyzed: failure when single in this way star fault is got rid of then may be many stars fault; Failure when many stars fault is got rid of in this way thinks that then the current time measurement data can't finish the integrality monitoring.The GNSS receiver autonomous integrity monitoring method that possesses above-mentioned steps based on many stars Fault Identification, the low major defect of success ratio of the existence identification and the satellite of fixing a breakdown.

Summary of the invention

Purpose of the present invention overcomes deficiency of the prior art exactly, the fault recognition method of a kind of many constellation combination navigational system that the success ratio of the satellite that a kind of dependable performance is provided, discerns and fixes a breakdown is high.

For solving the problems of the prior art, the fault recognition method of a kind of many constellation combination navigational system of the present invention may further comprise the steps:

When 1) carrying out many constellation systems and the unification of volume coordinate

1.1) unification when carrying out many constellation systems: during according to the system of each constellation and the fixed conversion relation that exists between the UTC (world's unified time), carry out rough resolving, the system time of unified all constellation systems during with the system of various constellations; During the system of each constellation and the clock correction between the UTC

Obtain by following pseudorange observation equation:

${\mathrm{\ρ}}_i^g=[{(x-X_i^g)}^2+{(y-Y_i^g)}^2+{{(z-Z_i^g)}^2]}^{1/2}+\mathrm{c\δ}{T}_r^g$

$\mathrm{\δ}{T}_r^g=[{[{(x-X_i^g)}^2+{(y-Y_i^g)}^2+{(z-Z_i^g)}^2]}^{1/2}-{\mathrm{\ρ}}_i^g]/c$

Wherein, subscript g represents system's sequence number, and i is observed reading sequence number (i=1,2,3,4,5); (x, y z) are the coordinate of receiver under selected coordinate system, (X ^g, Y ^g, Z ^g) observation satellite in each constellation is transformed into the coordinate of selecting under the coordinate system for utilizing the coordinate conversion formula;

For the clock correction between receiver and each constellation (r=1,2...N),

Be the pseudorange observed reading of every satellites in view, c is the light velocity;

For N constellation, the unknown quantity that receiver has N+3 needs to measure needs N+3 pseudorange observation equation to find the solution, when obtaining the system of each constellation and the clock correction between the UTC

1.2) carry out the unification of many constellation space coordinate

The unified of volume coordinate adopts following coordinate conversion formula to finish:

${\left[\begin{array}{c}x\\ y\\ z\end{array}\right]}_{\mathrm{sys}1}=\left[\begin{array}{c}\mathrm{\Δx}\\ \mathrm{\Δy}\\ \mathrm{\Δz}\end{array}\right]+(1+m)\left[\begin{array}{ccc}1& -{\mathrm{\θ}}_z& {\mathrm{\θ}}_y\\ {\mathrm{\θ}}_z& 1& -{\mathrm{\θ}}_x\\ -{\mathrm{\θ}}_y& {\mathrm{\θ}}_x& 1\end{array}\right]{\left[\begin{array}{c}x\\ y\\ z\end{array}\right]}_{\mathrm{sys}}$

Wherein, (Δ x, Δ y, Δ z) is earth center offset, θ _x, θ _y, θ _zThe coordinate axis rotation angle, m is a scale factor, (x, y, z) _SysBe the coordinate in the coordinate system to be converted, (x, y, z) _Sys1Coordinate for target-based coordinate system;

2) fault detect availability is judged

2.1) judge the satellites in view number, if satellites in view number＜N+3 illustrate that fault detect can't carry out, system carries out integrity and reports to the police, otherwise continuation;

2.2) the availability judgement:

At first obtain fault detect threshold value σ _T, formula is as follows:

${\mathrm{\σ}}_T={\mathrm{\σ}}_0\×T/\sqrt{n-4}$

Wherein, σ ₀Variance yields for the pseudo range measurement error; N is the number of satellites in view; Threshold T is determined by following formula:

$\mathrm{Pr}(\mathrm{SSE}/{\mathrm{\&sigma;}}_0^2<T^2)={\&Integral;}_0^{T^2}{f}_{{\mathrm{\&chi;}}_{(n-4,\mathrm{\&lambda;})}^2}\left(x\right)\mathrm{dx}=1-P_{\mathrm{FA}}$

Wherein, P _FABe tolerable false-alarm probability;

(x) for degree of freedom be the χ of n-4 ²The probability density function that distributes;

Be the statistical probability of residual error statistics quadratic sum less than threshold T;

In the formula:

$\mathrm{SSE}=v^T\mathrm{Wv}/{\mathrm{\&sigma;}}_0^2$

v＝(I-G(G ^TWG) ^-1G ^TW)ε

Wherein, G is the linearization matrix that is made of each satellite to the direction cosine vector of receiver, and ε is the pseudorange error vector, and W is n * n dimension observation pseudorange weight matrix, and I is a unit matrix;

Suppose that there is fault in i satellite, its deviation is b _i, SSE then obeys the decentralization χ that degree of freedom is n-4 ²Distribute, non-centrality parameter λ can be obtained by following formula:

$\mathrm{\&lambda;}=E\left(v^T\mathrm{Wv}\right)/{\mathrm{\&sigma;}}_0^2={\mathrm{RPE}}_i^2/{\mathrm{\&sigma;}}_0^2{\mathrm{\&delta;HDOP}}_i^2$

Wherein,

${\mathrm{RPE}}_i=(A_{1i}^2+A_{2i}^2)W_{\mathrm{ii}}^2{b}_i$

$\mathrm{\&delta;}{\mathrm{HDOP}}_i={\mathrm{HDOP}}_i-\mathrm{HDOP}=\frac{A_{1i}^2+A_{2i}^2}{Q_{v_{\mathrm{ii}}}}$

A＝(G ^TWG) ^-1G ^T

Q _v＝W ^-1-G(G ^TWG) ^-1G ^T

HDOP represents the horizontal location dilution of precision of all observation satellites, HDOP _iI the horizontal location dilution of precision behind the satellite removed in expression;

Calculate δ HDOP _Max

Before the syndrome check, the HDOP that just calculates each satellite correspondence in real time _i, go and the maximal value of getting wherein is δ HDOP _Max

Calculated level positioning error protection limit value HPL, formula is as follows;

$\mathrm{HPL}={\mathrm{\&delta;HDOP}}_{\max }\&times;{\mathrm{\&sigma;}}_0\&times;\sqrt{\mathrm{\&lambda;}}$

HPL and lateral error protection limit value HAL are compared, if transfinite, then fault detect is unavailable, and system carries out integrity and reports to the police, otherwise continues;

3) fault verification

Variance with the error of actual observation pseudorange

With step 2) in the fault detect threshold value σ that tries to achieve _TCompare, if

Then expression detects fault, and work continues, otherwise end-of-job;

4) identification and eliminating fault satellites

4.1) judge the satellites in view number, if satellites in view number＜N+4, Fault Identification can't be carried out, system carries out integrity and reports to the police, otherwise continues;

4.2) the identification fault satellites: characteristic curve deviation collimation method is adopted in the identification of fault satellites, at first observed differential matrix G is carried out QR and decomposes, and obtains matrix Q ^T:

$Q^T=\left[\begin{array}{c}{Q}_X\\ Q_P\end{array}\right]$

Wherein, Q _XBe Q ^TPreceding 4 row, Q _PBe Q ^TRemaining n-4 is capable;

Odd even residual error vector p is p=Q _PY=Q _P(Gx+ ε)=Q _Pε

Calculate the feature deviation line K of every satellite _Cha:

$K_{\mathrm{cha}}=\frac{Q_p(1,i)}{Q_p(2,i)}$

Calculate the feature deviation slope K of odd even space vector _p:

K _p＝p ₁/p ₂

Wherein, p ₁With p ₂Be the element of odd even vector p, if the K of i satellite _ChaWith K _pVery approaching, then i satellite is identified as fault satellites;

4.3) satellite of fixing a breakdown: will be step by step 4.2) in the fault satellites of identification get rid of;

5) repeating step 1) to step 4);

6) repeating step 2) and step 3), if there is not fault, the proof satellite of successfully having fixed a breakdown then, end-of-job, otherwise think that this measurement data can't finish autonomous integrity test, system carries out integrity and reports to the police.

The fault recognition method of a kind of many constellation combination navigational system of the present invention, can break down simultaneously to multi-satellite and monitor and discern, by to many constellation systems the time and unification and the repeated detection and the judgement of volume coordinate, improved the success ratio of the identification and the satellite of fixing a breakdown greatly, strengthen many constellation combination navigational system navigation and positioning accuracy, positioning performance and reliability, thereby improved the navigation Service performance.

Description of drawings

Fig. 1 is the overview flow chart of the fault recognition method of a kind of many constellation combination navigational system of the present invention.

Embodiment

Fig. 1 is the overview flow chart of the fault recognition method of a kind of many constellation combination navigational system of the present invention

As shown in Figure 1, this method may further comprise the steps:

Step S1, when carrying out many constellation systems and the unification of volume coordinate, for observation data, in the time of need at first carrying out many constellation systems and the unification of volume coordinate from a plurality of various constellations, with the accuracy that the assurance system is resolved data, guaranteed the success ratio of the identification and the satellite of fixing a breakdown simultaneously.This step is finished step by step by following two:

S1.1 step by step, the unification when carrying out many constellation systems during according to the system of each constellation and the fixed conversion relation that exists between the UTC, is carried out rough resolving, the system time of unified all constellation systems during with the system of various constellations.

During the system of each constellation and the clock correction between the UTC

Obtain by following pseudorange observation equation:

${\mathrm{\&rho;}}_i^g=[{(x-X_i^g)}^2+{(y-Y_i^g)}^2+{{(z-Z_i^g)}^2]}^{1/2}+\mathrm{c\&delta;}{T}_r^g$

$\mathrm{\&delta;}{T}_r^g=[{[{(x-X_i^g)}^2+{(y-Y_i^g)}^2+{(z-Z_i^g)}^2]}^{1/2}-{\mathrm{\&rho;}}_i^g]/c$

Wherein, subscript g represents system's sequence number, and i is observed reading sequence number (i=1,2,3,4,5); (x, y z) are the coordinate of receiver under selected coordinate system, (X ^g, Y ^g, Z ^g) observation satellite in each constellation is transformed into the coordinate of selecting under the coordinate system for utilizing the coordinate conversion formula;

For the clock correction between receiver and each constellation (r=1,2...N), Be the pseudorange observed reading of every satellites in view, c is the light velocity;

For N constellation, the unknown quantity that receiver has N+3 needs to measure needs N+3 pseudorange observation equation to find the solution, when obtaining the system of each constellation and the clock correction between the UTC

S1.2 carries out the unification of many constellation space coordinate step by step, in order to handle the observation data of various constellations simultaneously, needs a unified coordinate system.The coordinate of all constellations is unified under the coordinate system, need carries out coordinate conversion, in the present embodiment, coordinate conversion adopts classical Bursa-Wolf model, and formula is as follows:

${\left[\begin{array}{c}x\\ y\\ z\end{array}\right]}_{\mathrm{sys}1}=\left[\begin{array}{c}\mathrm{\&Delta;x}\\ \mathrm{\&Delta;y}\\ \mathrm{\&Delta;z}\end{array}\right]+(1+m)\left[\begin{array}{ccc}1& -{\mathrm{\&theta;}}_z& {\mathrm{\&theta;}}_y\\ {\mathrm{\&theta;}}_z& 1& -{\mathrm{\&theta;}}_x\\ -{\mathrm{\&theta;}}_y& {\mathrm{\&theta;}}_x& 1\end{array}\right]{\left[\begin{array}{c}x\\ y\\ z\end{array}\right]}_{\mathrm{sys}}$

Wherein, (Δ x, Δ y, Δ z) is earth center offset, θ _x, θ _y, θ _zThe coordinate axis rotation angle, m is a scale factor, (x, y, z) _SysBe the coordinate in the coordinate system to be converted, (x, y, z) _Sys1Coordinate for target-based coordinate system.

By this step S1, can all observation datas is unified under same time and space coordinates, realized shielding to a plurality of constellation differences.

Step S2, the fault detect availability judges, when the system of completing steps S1 and volume coordinate after reunification, the fault detect availability that need carry out before the fault judgement judges, comprise altogether following two step by step:

S2.1 at first judges the satellites in view number step by step, if satellites in view number＜N+3 illustrates that fault detect can't carry out, system carries out integrity and reports to the police, if the number 〉=N+3 of satellites in view then continue to carry out S2.2 step by step;

S2.2 step by step, availability is judged, carries out the fault detect availability and judges, at first obtains fault detect threshold value σ _T, formula is as follows:

${\mathrm{\&sigma;}}_T={\mathrm{\&sigma;}}_0\&times;T/\sqrt{n-4}$

Wherein, σ ₀Variance yields for the pseudo range measurement error; N is the number of satellites in view; Threshold T is determined by following formula:

$\mathrm{Pr}(\mathrm{SSE}/{\mathrm{\&sigma;}}_0^2<T^2)={\&Integral;}_0^{T^2}{f}_{{\mathrm{\&chi;}}_{(n-4,\mathrm{\&lambda;})}^2}\left(x\right)\mathrm{dx}=1-P_{\mathrm{FA}}$

Wherein, P _FABe tolerable false-alarm probability;

For degree of freedom is the χ of n-4 ²The probability density function that distributes;

Be the statistical probability of residual error statistics quadratic sum less than threshold T.

In the formula:

$\mathrm{SSE}=v^T\mathrm{Wv}/{\mathrm{\&sigma;}}_0^2$

v＝(I-G(G ^TWG) ^-1G ^TW)ε

Wherein, G is the linearization matrix that is made of each satellite to the direction cosine vector of receiver, and ε is the pseudorange error vector, and W is n * n dimension observation pseudorange weight matrix, and I is a unit matrix.

Suppose that there is fault in i satellite, its deviation is b _i, SSE then obeys the decentralization χ that degree of freedom is n-4 ²Distribute, non-centrality parameter λ can be obtained by following formula:

$\mathrm{\&lambda;}=E\left(v^T\mathrm{Wv}\right)/{\mathrm{\&sigma;}}_0^2={\mathrm{RPE}}_i^2/{\mathrm{\&sigma;}}_0^2{\mathrm{\&delta;HDOP}}_i^2$

Wherein,

${\mathrm{RPE}}_i=(A_{1i}^2+A_{2i}^2)W_{\mathrm{ii}}^2{b}_i$

$\mathrm{\&delta;}{\mathrm{HDOP}}_i={\mathrm{HDOP}}_i-\mathrm{HDOP}=\frac{A_{1i}^2+A_{2i}^2}{Q_{v_{\mathrm{ii}}}}$

A＝(G ^TWG) ^-1G ^T

Q _v＝W ^-1-G(G ^TWG) ^-1G ^T

HDOP represents the horizontal location dilution of precision of all observation satellites, HDOP _iI the horizontal location dilution of precision behind the satellite removed in expression.

Calculate δ HDOP _Max

Before the syndrome check, the HDOP that just calculates each satellite correspondence in real time _i, go and the maximal value of getting wherein is δ HDOP _Max

Calculated level positioning error protection limit value HPL, formula is as follows;

$\mathrm{HPL}={\mathrm{\&delta;HDOP}}_{\max }\&times;{\mathrm{\&sigma;}}_0\&times;\sqrt{\mathrm{\&lambda;}}$

Horizon location error is protected limit value HPL and lateral error protection limit value HAL relatively, if transfinite, then fault detect is unavailable, and system carries out integrity and reports to the police, otherwise continues execution in step S3.

Step S3, fault verification is with the variance of the error of actual observation pseudorange

Carry out σ with the fault detect threshold value of trying to achieve among the step S2 _TCompare, if

Then expression detects fault, continues execution in step S4, otherwise end-of-job.

Step S4, fault satellites is also got rid of in identification, detects the existence of fault satellites in step S3, then will carry out identification and eliminating to fault satellites, comprise altogether following 3 step by step:

S4.1 at first will judge the satellites in view number step by step, if satellites in view number＜N+4, Fault Identification can't be carried out, and system carries out integrity and reports to the police, if the number 〉=N+4 of satellites in view then continues to carry out S4.2 step by step.

S4.2 discerns fault satellites step by step, and characteristic curve deviation collimation method is adopted in the identification of fault satellites, at first observed differential matrix G is carried out QR and decomposes, and obtains matrix Q ^T:

$Q^T=\left[\begin{array}{c}{Q}_X\\ Q_P\end{array}\right]$

Wherein, Q _XBe Q ^TPreceding 4 row, Q _PBe Q ^TRemaining n-4 is capable;

Odd even residual error vector p is p=Q _PY=Q _P(Gx+ ε)=Q _Pε

Calculate the feature deviation line K of every satellite _Cha:

$K_{\mathrm{cha}}=\frac{Q_p(1,i)}{Q_p(2,i)}$

Calculate the feature deviation slope K of odd even space vector _p:

K _p＝p ₁/p ₂

Wherein, p ₁With p ₂Be the element of odd even vector p, if the K of i satellite _ChaWith K _pVery approaching, then i satellite is identified as fault satellites.

S4.3 step by step, the satellite of fixing a breakdown: the fault satellites of discerning among the S4.2 is got rid of step by step.

For the identification of the fault recognition method that guarantees a kind of many constellation combination navigational system of the present invention and the success ratio of the satellite of fixing a breakdown, get rid of many fault satellites, need many identifications and judge.

Step S5, repeating step S1 are to step S4, and identification and eliminating be the fault satellites of existence still.Repeating step S1 be when preventing the system of each constellation and UTC between clock correction

New variation is arranged, the observation data of each constellation of reading once more is unified under new identical time and space coordinates, realize shielding once more to a plurality of constellations differences.

Do not have fault if repeating step S2 and step S3 judge, then prove the star of successfully having fixed a breakdown, end-of-job; If fault is still arranged, then continue execution in step S4, with identification and the eliminating of carrying out fault satellites.

Step S6, repeating step S2 and step S3, there is not fault if judge, then prove the satellite of successfully having fixed a breakdown, end-of-job, otherwise, because the restriction of prior art level, therefore the satellite of can not fixing a breakdown once more thinks that this measurement data can't finish autonomous integrity test, and system carries out integrity and reports to the police.

In a word, what embodiments of the invention were announced is its preferred implementation, but is not limited to this.Those of ordinary skill in the art understands spirit of the present invention very easily according to the foregoing description, and makes different amplifications and variation, but only otherwise break away from spirit of the present invention, all within protection scope of the present invention.

Claims (1)

1. the fault recognition method of constellation combination navigational system more than a kind is characterized in that, may further comprise the steps:

When 1) carrying out many constellation systems and the unification of volume coordinate

1.1) unification when carrying out many constellation systems: during according to the system of each constellation and the fixed conversion relation that exists between the UTC, carry out rough resolving, the system time of unified all constellation systems during with the system of various constellations;

During the system of each constellation and the clock correction between the UTC

Obtain by following pseudorange observation equation:

${\mathrm{\&rho;}}_i^g=[{(x-X_i^g)}^2+{(y-Y_i^g)}^2+{{(z-Z_i^g)}^2]}^{1/2}+\mathrm{c\&delta;}{T}_r^g$

$\mathrm{\&delta;}{T}_r^g=[{[{(x-X_i^g)}^2+{(y-Y_i^g)}^2+{(z-Z_i^g)}^2]}^{1/2}-{\mathrm{\&rho;}}_i^g]/c$

Wherein, subscript g represents system's sequence number, and i is observed reading sequence number (i=1,2,3,4,5); (x, y z) are the coordinate of receiver under selected coordinate system, (X ^g, Y ^g, Z ^g) observation satellite in each constellation is transformed into the coordinate of selecting under the coordinate system for utilizing the coordinate conversion formula;

For the clock correction between receiver and each constellation (r=1,2...N),

Be the pseudorange observed reading of every satellites in view, c is the light velocity;

For N constellation, the unknown quantity that receiver has N+3 needs to measure needs N+3 pseudorange observation equation to find the solution, when obtaining the system of each constellation and the clock correction between the UTC

1.2) carry out the unification of many constellation space coordinate

The unified of volume coordinate adopts following coordinate conversion formula to finish:

${\left[\begin{array}{c}x\\ y\\ z\end{array}\right]}_{\mathrm{sys}1}=\left[\begin{array}{c}\mathrm{\&Delta;x}\\ \mathrm{\&Delta;y}\\ \mathrm{\&Delta;z}\end{array}\right]+(1+m)\left[\begin{array}{ccc}1& -{\mathrm{\&theta;}}_z& {\mathrm{\&theta;}}_y\\ {\mathrm{\&theta;}}_z& 1& -{\mathrm{\&theta;}}_x\\ -{\mathrm{\&theta;}}_y& {\mathrm{\&theta;}}_x& 1\end{array}\right]{\left[\begin{array}{c}x\\ y\\ z\end{array}\right]}_{\mathrm{sys}}$

Wherein, (Δ x, Δ y, Δ z) is earth center offset, θ _x, θ _y, θ _zThe coordinate axis rotation angle, m is a scale factor, (x, y, z) _SysBe the coordinate in the coordinate system to be converted, (x, y, z) _Sys1Coordinate for target-based coordinate system;

2) fault detect availability is judged

2.1) judge the satellites in view number, if satellites in view number＜N+3 illustrate that fault detect can't carry out, system carries out integrity and reports to the police, otherwise continuation;

2.2) the availability judgement:

At first obtain fault detect threshold value σ _T, formula is as follows:

${\mathrm{\&sigma;}}_T={\mathrm{\&sigma;}}_0\&times;T/\sqrt{n-4}$

Wherein, σ ₀Variance yields for the pseudo range measurement error; N is the number of satellites in view; Threshold T is determined by following formula:

$\mathrm{Pr}(\mathrm{SSE}/{\mathrm{\&sigma;}}_0^2<T^2)={\&Integral;}_0^{T^2}{f}_{{\mathrm{\&chi;}}_{(n-4,\mathrm{\&lambda;})}^2}\left(x\right)\mathrm{dx}=1-P_{\mathrm{FA}}$

Wherein, P _FABe tolerable false-alarm probability;

For degree of freedom is the χ of n-4 ²The probability density function that distributes;

Be the statistical probability of residual error statistics quadratic sum less than threshold T;

In the formula:

$\mathrm{SSE}=v^T\mathrm{Wv}/{\mathrm{\&sigma;}}_0^2$

v＝(I-G(G ^TWG) ^-1G ^TW)ε

Wherein, G is the linearization matrix that is made of each satellite to the direction cosine vector of receiver, and ε is the pseudorange error vector, and W is n * n dimension observation pseudorange weight matrix, and I is a unit matrix;

Suppose that there is fault in i satellite, its deviation is b _i, SSE then obeys the decentralization χ that degree of freedom is n-4 ²Distribute, non-centrality parameter λ can be obtained by following formula:

$\mathrm{\&lambda;}=E\left(v^T\mathrm{Wv}\right)/{\mathrm{\&sigma;}}_0^2={\mathrm{RPE}}_i^2/{\mathrm{\&sigma;}}_0^2{\mathrm{\&delta;HDOP}}_i^2$

Wherein,

${\mathrm{RPE}}_i=(A_{1i}^2+A_{2i}^2)W_{\mathrm{ii}}^2{b}_i$

$\mathrm{\&delta;}{\mathrm{HDOP}}_i={\mathrm{HDOP}}_i-\mathrm{HDOP}=\frac{A_{1i}^2+A_{2i}^2}{Q_{v_{\mathrm{ii}}}}$

A＝(G ^TWG) ^-1G ^T

Q _v＝W ^-1-G(G ^TWG) ^-1G ^T

HDOP represents the horizontal location dilution of precision of all observation satellites, HDOP _iI the horizontal location dilution of precision behind the satellite removed in expression;

Calculate δ HDOP _Max

Before the syndrome check, the HDOP that just calculates each satellite correspondence in real time _i, go and the maximal value of getting wherein is δ HDOP _Max

Calculated level positioning error protection limit value HPL, formula is as follows;

$\mathrm{HPL}={\mathrm{\&delta;HDOP}}_{\max }\&times;{\mathrm{\&sigma;}}_0\&times;\sqrt{\mathrm{\&lambda;}}$

HPL and lateral error protection limit value HAL are compared, if transfinite, then fault detect is unavailable, and system carries out integrity and reports to the police, otherwise continues;

3) fault verification

Variance with the error of actual observation pseudorange

With step 2) in the fault detect threshold value σ that tries to achieve _TCompare, if

Then expression detects fault, and work continues, otherwise end-of-job;

4) identification and eliminating fault satellites

4.1) judge the satellites in view number, if satellites in view number＜N+4, Fault Identification can't be carried out, system carries out integrity and reports to the police, otherwise continues;

4.2) the identification fault satellites: characteristic curve deviation collimation method is adopted in the identification of fault satellites, at first observed differential matrix G is carried out QR and decomposes, and obtains matrix Q ^T:

$Q^T=\left[\begin{array}{c}{Q}_X\\ Q_P\end{array}\right]$

Wherein, Q _XBe Q ^TPreceding 4 row, Q _PBe Q ^TRemaining n-4 is capable;

Odd even residual error vector p is p=Q _PY=Q _P(Gx+ ε)=Q _Pε

Calculate the feature deviation line K of every satellite _Cha:

$K_{\mathrm{cha}}=\frac{Q_p(1,i)}{Q_p(2,i)}$

Calculate the feature deviation slope K of odd even space vector _p:

K _p＝p ₁/p ₂

Wherein, p ₁With p ₂Be the element of odd even vector p, if the K of i satellite _ChaWith K _pVery approaching, then i satellite is identified as fault satellites;

4.3) satellite of fixing a breakdown: will be step by step 4.2) in the fault satellites of identification get rid of;

5) repeating step 1) to step 4);

6) repeating step 2) and step 3), if there is not fault, the proof satellite of successfully having fixed a breakdown then, end-of-job, otherwise think that this measurement data can't finish autonomous integrity test, system carries out integrity and reports to the police.