KR100543373B1 - Integrity Monitoring Method by Multiple Failures of Satellite Navigation System - Google Patents

Abstract

According to the present invention, when a GPS (Global Positioning System) sends wrong navigation information due to a malfunction of a component, ground users using the navigation system recognize the wrong information as a true value, and when the navigation system is used in a navigation system, the accuracy is lowered and an accident may occur during precise navigation. The present invention relates to a method for detecting a GPS failure in which a satellite navigation system detects a failure signal more quickly even in the case of multiple failures.

Aeronautical navigation requires integrity monitoring as well as navigation accuracy to ensure the safety of the aircraft when using GPS. Integrity monitoring is performed as a function to check this. The integrity monitoring checks whether satellite navigation solutions are maintained. When a GPS system breaks down due to work, the ground-based user system detects this and alerts the user within a reasonable time so that the user can cope with it.

Implementing such integrity monitoring is largely performed by the GPS receiver itself or using other navigation-related equipment mounted on the ground compensation system or aircraft, and RAIM (Receiver Autonomous Integrity Monitoring) is one of the above methods. As a method of monitoring the integrity on its own, a method of detecting and identifying a failure under the assumption that one satellite has failed in the RAIM technique has been announced, but occurs when two or more satellites have failed at the same time. Under the assumption of low probability, there are few studies because of the difficulty of identification due to the mutual attenuation effect of bias signal.

In the present invention, by avoiding the interference of the parity vector through the regeneration of the parity vector by the vertical transformation in the parity space, the problem that is difficult to accurately identify due to the interference of the error factors in the case of GPS multi-fault that can occur in actual application To achieve identification of multiple faults.

Aviation Navigation, GPS, RAIM, Integrity Monitoring, Multi-Fault Diagnosis

Description

Integrity Monitoring Method by Multiple Failures of Satellite Navigation System {omitted}

1 is a flow chart for troubleshooting pretreatment by the existing method

2 is a flow chart of fault diagnosis preprocessing in the parity space of the present invention.

3 is a flowchart of troubleshooting of the present invention.

4 is a table showing the number of cases required for calculation

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a satellite navigation system (GPS) integrity monitoring (GPS) Integrity Monitoring, and more particularly, to GPS Receiver Autonomous Integrity Monitoring where integrity monitoring is performed in the GPS receiver itself.

In the case of aeronautical navigation using GPS, a single fault of a GPS satellite among existing aeronautical GPS receivers including integrity monitoring is required in order to monitor whether a GPS satellite signal is a defect-free signal from a reliability point of view. However, the present invention can detect and identify a GPS satellite failure even in the case of multiple failures, and can quickly process at a calculation speed, thereby increasing the performance of GPS failure diagnosis performance in performing integrity monitoring of aeronautical navigation. will be.

The research on RAIM has been conducted since the late 1980's to find out the fault detection and fault identification to determine whether a navigation satellite is included in the navigation solution and to identify the failure satellite and exclude it from the navigation solution.

As a study on fault detection, Lee, YC, "Analysis of Range and Position Comparison Methods as a Means to Provide GPS Integrity in the User Receiver," Proceeding of the Annual Meeting of the ION, June 24-26, 1986. pp.1 From (4) to (n-4) pseudoranges were estimated using the navigation solution from four satellites of n visible satellites, the difference between this estimate and the actual measurement was calculated as a surplus, and compared with the threshold. McBurney is a (n-1) satellite deployment group that excludes one satellite from n visible satellites in "Self-contained GPS failure Detection: The Kalman Filter Approach," Proceedings of the ION Satellite Division Technical Meeting, 1987. As the navigation solutions were obtained and the navigation transitions increased over time in satellite groups including fault satellites, the maximum distance between navigation solutions due to the transition was compared with the threshold.

Parkinson and Axelrad report "Autonomous GPS Integrity Monitoring Using the Pseudorange Residual," Navigation , Vol. 35, No. 2, 1988, pp. From 255 to 274., the difference between the pseudorange estimate and the measured value obtained by the least-squares method for n visible satellites was obtained as a surplus and compared with the threshold. Sturza and Brown wrote "Comparision of Fixed and Variable Threshold," In GPS-90, Sep 19-20, we calculated the parity vector in the parity space for (n-4) surplus measurements and compared the magnitude of the parity vector with the threshold.

A study on the failure to identify Sturza and Brown "The Effect of Geometry on Integrity Monitoring Performance," Proceedings of the Institute of Navigation Annual Meeting, June 1990. In HDOP HDOP _i for the entire satellite for each of the n satellites The satellite with the largest difference of δH _max was identified as the fault satellite, and the visible satellite whose feature vector most closely matches the parity vector in the parity space was identified as the fault satellite using the direction of the parity vector. Brown [8] calculated the rate of change of horizontal position error with respect to the GPS pseudorange for the visible satellites in "Update on GPS Integrity Requirements of the RTCA MOPS", ION GPS-91, and SEP 11-13. The satellite with SLOP _max ) was identified as fault.

Among these techniques, the pseudo distance comparison method, least square method, and parity vector method have the same result of calculating the Test Statistic, and the method of comparing the interval of the maximum navigation solution is similar to the failure diagnosis and exclusion method. Difficult to express mathematically. The least-squares method is easy to interpret because the mathematical expression is clear, but the calculation of numerical parameters according to the noncentral x ² distribution is required, and the parity vector method has Gaussian distribution, and it is possible to set the threshold analytically, Failure identification can be done, but it is not easy to determine the parity vector.

)을 구함으로써 2개 고장의 경우 식별 가능성을 제시하였다.In the RAIM technique, algorithms for fault detection and identification have been proposed under the assumption that one satellite has failed, and experimental results have been published. Difficulties in identification have resulted in limited research. Brown says, "Solution of the Two-Failure GPS RAIM Problem Under Worst-Case Bias Conditions: Parity Space Approach, Journal of The ION , Vol. 44, No. 4, Winter 1997-1998, pp. 425-431. Maximum value of the rate of change of position error with respect to the GPS pseudorange in

) Gives the possibility of identification in case of two failures.

The basic principle of RAIM is to use the distance measurement available in the direction of the signal received at a given time and then use the following equation, linearized from the nominal navigation solution.

Where y is the (n × 1) vector as the difference between the actual and estimated pseudoranges, x is the (4 × 1) vector as the positional change and the change in the receiver's clock error, and H is the (n × 4) matrix as the observation matrix. and ε are measurement errors.

In Eq. (1), the navigation solution by least squares estimation is

The measurement residual is as follows.

분포를 가진다.The test statistic for fault diagnosis using the residual size of equation (3) is defined as follows and the probability distribution for this is

Has a distribution.

분포 확률밀도함수에 적용함으로써 계산할 수 있다.The threshold that compares to the judged value for the determination of failure is based on the maximum false alarm rate proposed by RTCA SC-159.

It can be calculated by applying to the distribution probability density function.

Let's perform fault identification as well as fault detection.

The size of the residual is calculated for the number of _n C _k cases from (nk) satellite data excluding k measurements from n measurements.

는 k번째 위성을 배제한 위성군의 잔차이다.here

Is the residual of the satellite group excluding the k-th satellite.

The determination value of Equation (5) has the smallest residual value in the case of the satellite group that does not include the failure, and identifies the excluded satellite as the failure.

In this method, as shown in FIG. 1, when _n is the number of visible satellites and k is the number of fault satellites, _n C _k is required. Similarly, the number of cases increases, so the computational amount increases, and as a result, real-time calculation becomes difficult, so that it cannot be applied to the actual GPS receiver.

In (1), by introducing (n-4) × n matrix p as equation (6) as the vertical transformation matrix of the observation matrix _H , it is possible to define a parity vector for performing troubleshooting in the parity space.

Through this, as shown in equation (7), the parity vector can be expressed by only an error including a failure regardless of the state variable.

The parity transformation matrix p has the relation of equation (8).

The parity transformation matrix p generally uses the QR matrix separation technique of Q ^T H = R , which multiplies the observation matrix H in equation (1) by the vertical transformation matrix Q to form a matrix R of upper and lower triangular matrices. have.

The magnitude of the parity vector of equation (7) is used as a judgment value for fault detection and has a Gaussian probability distribution. Therefore, the threshold for comparing the judgment value can be obtained through Gaussian probability distribution density function.

Likewise, when the parity vector is extended to perform fault identification, it is as follows. Distinguish the parity conversion matrix P into a column P ₁ without faults and a column P ₂ with faults.

Here, when the number of satellites is n, P is a (n-4) × n matrix, P ₁ is (n-4) × (n-2), and P ₂ is a (n-4) × 2 matrix.

Further, another transformation matrix G (n-6) × (n-4) perpendicular to P ₂ is defined as follows.

Equation (11) gives the following relation as in the parity space.

를 정의하면 다음과 같다.New Parity Vector Using the Transformation Matrix G Above

If is defined as:

Where ε ₁ and ε ₂ are measurement errors.

는 고장위성을 제외한 경우에 유도된 페러티 벡터이므로 페러티 벡터의 크기는 가장 작은 값을 가진다. n개의 가시위성의 경우 k개의 위성을 고장으로 가정하면 (n-4)×k행렬의 P ₂를 정의하고 _nC_k, 경우의 수에 대한

(k = 1,2,…_nC_k)를 각각 계산한 다음 min

인 경우의 P ₂행렬에 포함된 k개 위성을 고장으로 식별한다.

Since is a derived parity vector excluding the fault satellite, the size of the parity vector has the smallest value. For n visible satellites, assuming that k satellites are faulty, we define P ₂ of (n-4) × k matrices and _n C _k ,

Calculate ( k = 1,2,… _n C _k ) respectively and then min

We identify k satellites included in the P ₂ matrix in case of a failure.

This fault diagnosis preprocessing flowchart is shown in FIG.

각각 두가지 위성군으로 구별할 때 H ₁에 대한 측정식과 페러티 벡터 표현은 다음과 같다.

For each of the two satellite groups, the measurement equation for H ₁ and the representation of the parity vector are as follows.

The parity transformation matrix for equation (14) has the following relationship.

과 앞에서 정의한 관측행렬 H에 대한 페러티 변환행렬

간에 다음의 관계식이 성립한다.These parity transformation matrices

Parity transformation matrix for and observation matrix H defined above

However, the following relation holds.

From the equations (10), (11) and (16), the following relational expression can be obtained.

에서 GP ₂=0가 되도록 하여 재생성된 페러티 백터

는 관측행렬

와 측정오차

에서 H ₁로부터 구한 페러티 변환행렬

과 측정오차 ε₁에 의해 구한 페러티 벡터와 동일하며,

의 크기는 최소자승기법에서 의사거리 측정치 y ₁에 대한 잔차의 크기와 같다.That is, the parity transformation matrix

Parity vector regenerated with GP ₂ = 0 in

Is the observation matrix

And measurement error

Transformation matrix obtained from H ₁

Is the same as the parity vector found by and the measurement error ε ₁ ,

The magnitude of is equal to the magnitude of the residual for the pseudorange measurement y ₁ in the least-squares method.

Has similarities between how a reconfigure Ferrer tea transformation matrix from simple Ferrer T vector technique in Ferrer tee area and a doctor method that generated the Ferrer T vector to reconstruct the measurement in the distance space such similarities reconverted to Ferrer tea transformation matrix G It is done by

However, in terms of computation speed for real-time implementation, the method of reconstructing the parity transform matrix from the simple parity vector technique is more efficient.

로 분리하고 H ₁에 대한 최소자승 추정치 계산을 한 후에 페러티 벡터 또는 측정 잔차를 구해야 하므로 _nC_k, 경우의 수마다 H를 재분리하고 각각에 대하여 최소자승 추정연산을 해야 한다.By reconfiguring the measurement value as shown in Figure 1 in a method for generating a first vector T Ferrer H

Since we need to calculate the least squares estimate for H ₁ and calculate the residual vector or _n C _k , we need to re-separate H for each number of cases and perform the least-squares estimate for each.

에 대하여 _nC_k 경우의 수만큼 P를 재분리 후 각각에 대하여 페러티 벡터 또는 측정 잔차를 계산하면 되므로 경우의 수마다 최소자승 추정을 할 필요가 없다.On the other hand, in a reconstruction method to Ferrer transformation matrix T as it is shown in FIG. 2 Ferrer tea obtained through a least squares estimate from a single transformation matrix H

After re-separating P by the number of cases of _n C _k , we need to calculate the parity vector or the residual for each, so there is no need to estimate the least-squares for each case.

As a result, the method of diagnosing satellite k excluded from the satellite group having the smallest value by comparing the magnitude of the residual or the parity vector with respect to the _n C _k satellite group excluding the k-th satellite from the measured value results in multiple faults as well as single failures. The same applies in case of failure.

The parity vector reconstructed from the simple parity vector through the reconstruction of the parity matrix provides the discriminant for fault detection and identification even in the case of multiple faults, and compared to the method of searching for satellite groups from pseudorange measurements in real time. More efficient.

Claims (2)

Raw data from the GPS receiver (

) After receiving (step 1), the receiver position value (

) And the measurement matrix (

), The third step, and the pseudorange measurement change (

) (Step 4), and measure the change in receiver position (

(Step 5), and improve the receiver position (

(Step 6), and compare the receiver position change amount with the error value (

) To the receiver position (

), Estimate the navigation solution (step 7), generate the residual or parity vector ( p ) (step 8), generate the discriminant value TS | _k , and compare it with the threshold to see if there is a failure. In performing the troubleshooting (step 9) to find out, A parity transformation matrix for the parity vector p generated in the eighth process

Reconstructing), but classifying the parity transformation matrix P into a column without a fault satellite ( P ₁ ) and a column ( P ₂ ) including a fault satellite; And A new parity vector reconstructed from the transformation matrix G for the parity vector p

And an eleventh process of performing fault diagnosis of the ninth process. Where P is a (n-4) × n matrix, P ₁ is a (n-4) × (n-2) matrix, P ₂ is a (n-4) × 2 matrix, and a new parity vector (

)

(ε ₁ , ε ₂ is measurement error), G is

Defined as. The method of claim 1, In a ninth process of performing the troubleshooting, Min when the number of fault satellites k = 1 without knowing the number of fault satellites

( k = 1,2,… _n C _k ), After eliminating k satellites, the determination value TS | _k is calculated and compared with a threshold value. When the determination value TS | _k is smaller than the threshold value, the fault satellite P ₂ is excluded. Occation(

), So until it finds such a case, increasing the number of satellite failures k value by 1 min

Calculate and calculate the determination value TS | _k and compare it with a threshold, and repeat the process. If the determination value TS | _k is smaller than the threshold, when the fault satellite is one ( k = 1), the determination value TS for the entire satellite group is calculated and then compared with the threshold. If the determination value TS is less than the threshold, it is determined that there is no failure satellite. If the determination value TS of the entire satellite group is larger than the threshold, one failure satellite exists. A method for monitoring integrity of multiple satellite navigation systems, characterized in that if one or more fault satellites ( k> 1), the satellites defined as P ₂ are identified as fault satellites as k fault satellites.

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