A method for integrity monitoring of a navigation constellation at the Earth-Moon libration points

Abstract

The present invention relates to a method for integrity monitoring of a navigation constellation at the Earth-Moon libration points, and particularly to a method for integrity monitoring of a navigation constellation at the Earth-Moon libration points based on multi-hypothesis solution separation, belonging to the field of satellite navigation technology. The method for integrity monitoring of a navigation constellation at the Earth-Moon libration points refers to the ability to autonomously detect and troubleshoot faults when an inter-satellite link of the navigation constellation at the Earth-Moon libration points fails. This method is applied to the integrity monitoring of the libration point navigation constellation. When there is a constant deviation in the inter-satellite ranging information of an inter-satellite link, the algorithm can autonomously detect and eliminate the fault, ensuring that the navigation constellation can continue to complete autonomous orbit determination, and further providing navigation satellite orbit data for lunar probes to complete navigation tasks.

Description

Technical Field

[0001] The present invention relates to a method for integrity monitoring of a navigation constellation at the Earth-Moon libration points, and particularly to a method for integrity monitoring of a navigation constellation at the Earth-Moon libration points based on multi-hypothesis solution separation, belonging to the technical field of satellite navigation. The method for integrity monitoring of a navigation constellation at the Earth-Moon libration points refers to the ability to autonomously detect and troubleshoot faults when inter-satellite links of the navigation constellation at the Earth-Moon libration points fail. Background Art

[0002] Deep space exploration missions require that the navigation system should have autonomy and a certain accuracy, and higher positioning accuracy is also required for specific missions. High-precision autonomous orbit determination of satellites in the Earth-Moon space can be achieved by using the gravitational asymmetry of the three-body system. There are some periodic orbits near the libration points in the three-body system, and their shapes and sizes are unique. Other satellites can determine their positions by observing the distances to the libration point satellites. Among them, L 1 、L 2 and L 3 are collinear libration points, and there are three types of periodic orbits near them, namely Halo orbit (H), Plane Lyapunov orbit (PL), and Vertical Lyapunov orbit (VL); L 4 and L 5 are triangular libration points, and there are also three types of periodic orbits near them, namely Plane short period orbit (SP), Plane long period orbit (LP), and Vertical period orbit (VP). Therefore, satellites can be deployed on these periodic orbits to form a navigation constellation. This type of libration point navigation constellation first completes the autonomous orbit determination of navigation satellites, and then uses the orbit determination data of navigation satellites to provide navigation services for lunar probes. The deep space has a complex electromagnetic environment, and a tiny particle may damage sensitive components. If the component belongs to the measurement unit, measurement deviation or even inability to complete the measurement task will occur. This will lead to deviation in the orbit determination data of the navigation constellation, and further affect the navigation performance. Therefore, the navigation constellation should have the ability to detect and troubleshoot faults.

[0003] Multi-hypothesis solution separation can be used in integrity algorithms. By using different combinations of redundant information to construct several subsets of positioning solutions, the difference between the global positioning solution obtained from all measurement information and the subset solutions is used to construct a test statistic to achieve fault detection and exclusion. For the Global Navigation Satellite System (GNSS), when the system fails, it is usually considered that a satellite has failed, while the fault forms of the libration point navigation constellation are different from and similar to those of GNSS. For the libration point navigation constellation of the Earth-Moon system, first, inter-satellite links are used to complete measurements and achieve autonomous orbit determination, and then the orbit determination data is used to provide navigation services for lunar probes. In the navigation stage, the fault forms are the same as those of GNSS. At the navigation system end, due to the particularity of the orbit determination principle of the libration point constellation, the fault forms in the orbit determination stage are different from those of GNSS. Its particularity lies in that the navigation satellites in the constellation belong to both the navigation system and the carrier. Therefore, the fault forms can be divided into two types: one is that a single satellite fails, resulting in the failure of all associated inter-satellite links; the other is that a single satellite fails, resulting in the failure of one of the associated inter-satellite links. Summary of the Invention

[0004] The technical problem to be solved by the present invention is to overcome the deficiencies of the prior art and propose a method for monitoring the integrity of the libration point navigation constellation of the Earth-Moon system, aiming to solve the problem that there is no integrity monitoring technology for the libration point navigation constellation of the Earth-Moon system.

[0005] The technical solution of the present invention is:

[0006] A method for monitoring the integrity of the libration point navigation constellation of the Earth-Moon system, which constructs an extended Kalman filter orbit determination model under the actual force model; determines the multi-hypothesis test problem of the inter-satellite link fault mode according to the multi-hypothesis solution separation method; calculates the solution separation and solution separation variance according to the solution separation method; excludes faults according to the multi-hypothesis solution separation, and calculates the protection level. The key points and points to be protected by the present invention are the idea of constructing an extended Kalman filter orbit determination model under the actual force model, the idea of applying the multi-hypothesis solution separation method to the integrity monitoring of the libration point navigation constellation of the Earth-Moon system, and the integrity monitoring algorithm of the libration point navigation constellation of the Earth-Moon system based on the multi-hypothesis solution separation. The present invention only involves the scenario where a single inter-satellite link fails in the orbit determination stage. The steps of this method include:

[0007] Step 1, construct an extended Kalman filter orbit determination model under the actual force model;

[0008] Step 2, determine the multi-hypothesis test problem of the inter-satellite link fault mode according to the multi-hypothesis solution separation method;

[0009] Step 3, calculate the solution separation and solution separation variance of the satellite orbit according to the multi-hypothesis test problem in Step 2 and the orbit determination model constructed in Step 1;

[0010] Step 4: Set the fault detection and troubleshooting trigger conditions according to the solution separation and solution separation variance obtained in Step 3;

[0011] Step 5: Calculate the protection level according to the solution separation variance obtained in Step 3 to complete the integrity monitoring of the navigation constellation.

[0012] In the above Step 1, the method for constructing the extended Kalman filter orbit determination model under the actual force model is as follows:

[0013] If only considering the solar gravity, the dynamic equation of the navigation satellite in the Earth J2000 inertial coordinate system is:

[0014]

[0015] where: μ e , μ m and μ s are the gravitational constants of the Earth, the Moon and the Sun respectively; r is the satellite position vector, r m,sat is the vector from the Moon to the satellite, r e,m is the Moon position vector, r s,sat is the vector from the Sun to the satellite, r e,s is the Sun position vector. The position vectors of the Sun and the Moon can be obtained from the JPL DE430 table;

[0016] The position and velocity of each satellite in the Earth J2000 inertial system are expressed as:

[0017]

[0018] Then the quantities to be estimated for n satellites are:

[0019] X 6n×1 = [x 1 x 2 ...x n T (3)

[0020] where n is the number of navigation satellites and n ≥ 4, s = 1, 2,..., n;

[0021] Let the state equation of the Kalman filter be:

[0022]

[0023] where is constructed from Equation (1), and the inter-satellite distance calculation formula is:

[0024]

[0025] where: v is a zero-mean Gaussian white noise, obtained by measuring every two satellites For the observed quantity, the observation equation is:

[0026] Y N×1 = H(X, t) + v (6)

[0027] Denote the reference solution of X at time t k as X * , and the reference solution of Y as Y * . Substitute X * into Equation (6) to obtain. Denote the state deviation and the observation deviation as

[0028] From time t k to time t k+1 , the state transition matrix Φ(t k+1 , t k ) is obtained by numerical integration together with the state equation. The calculation formula is as follows:

[0029]

[0030] The Jacobian matrix of the observation equation is:

[0031]

[0032] The EKF filtering equation is:

[0033]

[0034] In the formula, P k-1 is the estimated error variance matrix at time t k-1 , P k|k-1 is the predicted error variance matrix at time t k , P k is the estimated error variance matrix at time t k , Q k is the system noise variance, R k is the observation noise variance, K k is the Kalman filter gain, and I is the identity matrix.

[0035] In the second step described above, according to the multi-hypothesis solution separation method, the method for determining the multi-hypothesis test problem of the inter-satellite link fault mode is:

[0036] If there are a total of N inter-satellite links in the navigation constellation, corresponding to N pieces of observation information, when a fault occurs in the libration point constellation, it can be assumed that a fault occurs in the inter-satellite link. Assume that the fault modes to be monitored for the inter-satellite link are N + 1 kinds. Then the multi-hypothesis test problem is:

[0037]

[0038] For the fault mode of H 0 , the set S0 Containing the measurement information of N inter-satellite links, S 0 is called the complete set; for H i of the failure mode, the set S i contains the measurement information of the remaining N - 1 inter-satellite links except for the measurement information of the i-th inter-satellite link, S i is called a subset. The state estimator obtained from the complete set is called the complete set solution, and the state estimator obtained from the subset is called the subset solution;

[0039] In the third step described above, according to the multiple hypothesis testing problem and the orbit determination model, the method for calculating the solution separation and solution separation variance of the satellite orbit is as follows:

[0040] The solution separation is the difference between the complete set solution and the subset solution, and can be expressed as:

[0041]

[0042] In the formula: is the complete set positioning solution of the s-th satellite in the d direction; is the subset positioning solution of the s-th satellite in the d direction; d can be set to the x, y, or z direction. The corresponding solution separation variance of the s-th satellite in the d direction is:

[0043]

[0044] In the formula: is the error variance of the s-th satellite in the d direction of the complete set, which can be obtained from the variance of the estimated solution in the complete set filtering; is the error variance of the s-th satellite in the d direction of the subset, which can be obtained from the estimated solution variance in the subset filtering; is the covariance P 0i,k between the complete set solution and the subset solution of the s-th satellite in the d direction, which can be obtained from the following formula:

[0045]

[0046] In the formula: the first position of the subscript of the variable represents the subordination relationship of the variable, 0 represents the parameter in the complete set filtering, i represents the parameter in the subset filtering, and 0i represents the parameter between the complete set filtering and the subset filtering; the second position represents the time.

[0047] In the fourth step described above, the method for setting the fault detection and fault exclusion trigger conditions according to the solution separation and solution separation variance is as follows:

[0048] Allocate the continuity risk to each failure mode and calculate the detection threshold. The calculation formula is:

[0049]

[0050] In the formula: T i represents the detection threshold, Creq Represents the continuity risk, P(H 0 ) represents the probability of no failure, Q -1 represents the inverse function of the standard normal distribution tail function.

[0051] When it is considered that there is a failure in the inter-satellite link. At this time, the sum of squares of the posterior residuals SSE is calculated. The subset with the smallest SSE is most likely to be the fault-free subset, that is, this subset does not contain the measurement information of the faulty inter-satellite link. The calculation formula of SSE is:

[0052]

[0053] If it is necessary to exclude the faulty inter-satellite link, it is also necessary to perform a disconnection on the subset based on each subset. If in the subset with the smallest SSE, the disconnection of any sub-subset is less than the detection threshold, the excluded inter-satellite link is the faulty inter-satellite link.

[0054] In the fifth step described above, the method for calculating the protection level according to the disconnection variance is:

[0055] The approximate calculation formula of the protection level in Gaussian white noise is:

[0056]

[0057] In the formula, represents the protection level in the d direction of the s-th satellite, P(H i ) is the probability that the i-th inter-satellite link fails while other inter-satellite links do not fail, I req represents the integrity risk requirement value. Equation (16) has only as the unknown, and the bisection method can be used to solve it. The fault mode probability in the formula is:

[0058]

[0059] In the formula, P sat_link is the probability of failure of each inter-satellite link.

[0060] Beneficial effects

[0061] (1) The present invention first proposes a method for monitoring the integrity of a navigation constellation at the Earth-Moon libration points, solving the problem of the lack of integrity monitoring technology for this type of navigation constellation.

[0062] (2) The existing orbit determination model for the libration point navigation constellation in the Earth-Moon system is constructed based on the circular restricted three-body problem. Whether the extended Kalman filter converges depends on whether the system noise variance is appropriate. The appropriate system noise variance needs to be determined through a large number of trials and errors, and the orbit determination model depends on the system noise variance. However, the extended Kalman filter orbit determination model under the actual force model constructed in the present invention can avoid the problem that the model depends on the system noise variance.

[0063] (3) According to the multi-hypothesis solution separation method, the present invention first gives a construction method for the position solution separation of the libration point navigation constellation in the Earth-Moon system. The number of solution separations is three times the number of navigation satellites, and the number of candidate solution separations is sufficient. When a certain solution separation has poor integrity monitoring, there are still multiple solution separations available for selection.

[0064] (4) A method for integrity monitoring of the libration point navigation constellation in the Earth-Moon system based on multi-hypothesis solution separation proposed by the present invention can be applied to the integrity monitoring of the libration point navigation constellation. When there is a constant deviation in the inter-satellite ranging information of an inter-satellite link, the algorithm can autonomously detect and eliminate the fault, ensuring that the navigation constellation can continue to complete autonomous orbit determination, and then providing navigation satellite orbit data for the lunar probe to complete the navigation task.

[0065] (5) In actual situations, each inter-satellite link may fail, and it is impossible to know which inter-satellite link has failed. Therefore, this method should consider the fault exclusion rate when each inter-satellite link fails alone. Through Monte Carlo simulation experiments, it is found that the fault exclusion rate can reach 100% when each inter-satellite link fails while other inter-satellite links do not fail.

[0066] (6) The present invention first gives a method for calculating the protection level in the integrity monitoring of the libration point navigation constellation in the Earth-Moon system based on multi-hypothesis solution separation. When the navigation constellation has no fault, the protection level can envelope the error curve. Description of the Drawings

[0067] Figure 1 is the protection level when there is no fault;

[0068] Figure 2 is the fault exclusion rate;

[0069] Figure 3 is the number of epochs required to exclude the fault. Detailed Embodiment

[0070] To better illustrate the purpose, content, and advantages of the present invention, the following further elaborates on the detailed embodiment in combination with the embodiments and drawings of the present invention.

[0071] Embodiment 1

[0072] There are many configurations of the Earth-Moon system libration point navigation constellations. The present invention will adopt the 1 H 2 SP 4 LP 5 four-star constellation. The orbits of the four navigation satellites in this constellation are the L 1 -point Halo orbit, L 2 -point Halo orbit, L 4 -point Plane short period orbit and L 5 -point Plane long period orbit, with an orbital amplitude of 10,000 km for all and an initial phase of 0°. The above four navigation satellites are sequentially coded as: 1, 2, 3, 4. The troubleshooting performance of the integrity monitoring method for the Earth-Moon system libration point navigation constellation based on multi-hypothesis solution separation is evaluated through simulation experiments.

[0073] Step 1: Construct an extended Kalman filter orbit determination model under the actual force model, and the method is as follows:

[0074] If only considering the solar gravity, the dynamic equation of the navigation satellite in the Earth J2000 inertial coordinate system is:

[0075]

[0076] In the formula: μ e , μ m and μ s are the gravitational constants of the Earth, the Moon and the Sun respectively; r is the satellite position vector, r m,sat is the vector from the Moon to the satellite, r e,m is the Moon position vector, r s,sat is the vector from the Sun to the satellite, r e,s is the Sun position vector. The position vectors of the Sun and the Moon can be obtained from the JPL DE430 table.

[0077] The position and velocity of each satellite in the Earth J2000 inertial system can be expressed as:

[0078]

[0079] In the formula, s represents the satellite number, and the quantities to be estimated for n satellites are:

[0080] X 6n×1 = [x 1 x 2 ...x n T (20)

[0081] In the formula, n is the number of navigation satellites, s = 1, 2,..., n. In this embodiment, n = 4.

[0082] Let the state equation of the Kalman filter be:

[0083]

[0084] where can be constructed from Equation (18), and the formula for the inter-satellite distance is:

[0085]

[0086] where: v is zero-mean Gaussian white noise. One measurement is made for every two satellites to obtain observation quantities. In this embodiment, N = 6, and the observation equation is:

[0087] Y N×1 = H(X, t) + v (23)

[0088] Denote the reference solution of X at time t k as X * , and the reference solution of Y as Y * . X * can be substituted into Equation (6) to obtain. Denote the state deviation and the observation deviation

[0089] From time t k to time t k+1 , the state transition matrix Φ(t k+1 , t k ) can be numerically integrated together with the state equation, and the calculation formula is as follows:

[0090]

[0091] The Jacobian matrix of the observation equation is:

[0092]

[0093] The EKF filtering equation is:

[0094]

[0095] where P k-1 is the estimated error variance matrix at time t k-1 , P k|k-1 is the predicted error variance matrix at time t k , P k is the estimated error variance matrix at time t k , Q k is the system noise variance, R k is the observation noise variance, K k is the Kalman filter gain, and I is the identity matrix.

[0096] Step 2: According to the multi-hypothesis solution separation method, determine the multi-hypothesis testing problem of the inter-satellite link failure mode. The method is as follows:

[0097] If there are N inter-satellite links in the navigation constellation, corresponding to N pieces of observation information. When a failure occurs in the libration point constellation, it can be assumed that a failure occurs in the inter-satellite link. Assuming that the number of failure modes to be monitored for the inter-satellite link is N + 1, then the multi-hypothesis testing problem is:

[0098]

[0099] For the failure mode of H 0 the set S 0 contains the measurement information of N inter-satellite links, and S 0 is called the universal set; for the failure mode of H i the set S i contains the measurement information of the remaining N - 1 inter-satellite links except for the measurement information of the i-th inter-satellite link, and S i is called the subset. The state estimator obtained from the universal set is called the universal set solution, and the state estimator obtained from the subset is called the subset solution.

[0100] Step 3: According to the multi-hypothesis testing problem in Step 2 and the orbit determination model constructed in Step 1, calculate the solution separation and solution separation variance of the satellite orbit. The method is as follows:

[0101] The solution separation is the difference between the universal set solution and the subset solution, and can be expressed as:

[0102]

[0103] In the formula: is the universal set positioning solution of the s-th satellite in the d direction; is the subset positioning solution of the s-th satellite in the d direction; d can be set to the x, y or z direction. The corresponding solution separation variance of the s-th satellite in the d direction is:

[0104]

[0105] In the formula: is the error variance of the s-th satellite in the d direction of the universal set, which can be obtained from the variance of the estimated solution in the universal set filtering; is the error variance of the s-th satellite in the d direction of the subset, which can be obtained from the variance of the estimated solution in the subset filtering; is the covariance between the universal set solution and the subset solution of the s-th satellite in the d direction, which can be obtained from the following formula:

[0106]

[0107] In the formula: the first position of the subscript of the variable represents the subordination relationship of the variable, 0 represents the parameter in the global filtering, i represents the parameter in the subset filtering, and 0i represents the parameter between the global filtering and the subset filtering; the second position represents the time instant.

[0108] In this embodiment, let s = 1, d be x, and it means to take L 1 The separation of the x-direction of the Halo orbit navigation satellite at point H.

[0109] Step 4, set the fault detection and troubleshooting trigger conditions according to the separation and separation variance obtained in Step 3. The method is as follows:

[0110] Allocate the continuity risk to each fault mode and calculate the detection threshold. The calculation formula is:

[0111]

[0112] In the formula: T i represents the detection threshold, C req represents the continuity risk, P(H 0 ) represents the probability of no fault, Q -1 represents the inverse function of the standard normal distribution tail function.

[0113] When it is considered that there is a fault in the inter-satellite link. At this time, calculate the sum of squares of the posterior residuals SSE. The subset with the smallest SSE is most likely the fault-free subset, that is, this subset does not contain the measurement information of the faulty inter-satellite link. The calculation formula of SSE is:

[0114]

[0115] If it is necessary to exclude the faulty inter-satellite link, it is also necessary to perform a separation on the subset again based on each subset. If, in the subset with the smallest SSE, the separation of any sub-subset is less than the detection threshold, the excluded inter-satellite link is the faulty inter-satellite link.

[0116] Step 5, calculate the protection level according to the separation variance obtained in Step 3 to complete the integrity monitoring of the navigation constellation. The method is as follows:

[0117] The approximate calculation formula of the protection level in Gaussian white noise is:

[0118]

[0119] In the formula: represents the protection level of the s-th satellite in the d direction, P(H i ) is the probability that the i-th inter-satellite link fails while other inter-satellite links do not fail, I req represents the integrity risk requirement value. Equation (33) is only is an unknown number and can be solved by the bisection method. The probability of the fault mode in the formula is:

[0120]

[0121] where P sat_link is the probability of a fault occurring in each inter-satellite link.

[0122] In this embodiment, the observation information is calculated from the nominal orbit and zero-mean Gaussian white noise is added. The EKF filtering parameters are shown in Table 1. A constant bias is added to each inter-satellite distance observation value, and 200 Monte Carlo experiments are carried out to test the effectiveness of the multi-hypothesis solution separation integrity monitoring.

[0123] Table 1 EKF parameters

[0124]

[0125]

[0126] Since there are no relevant parameters for the integrity of the Earth-Moon libration point navigation constellation for the time being, the relevant parameters of GNSS integrity are temporarily adopted. The integrity parameters are shown in Table 2.

[0127] Table 2 Values of integrity-related parameters

[0128] Parameter <![CDATA[P sat_link > <![CDATA[I req > <![CDATA[C req > Value <![CDATA[10 -5 > <![CDATA[10 -7 > <![CDATA[4×10 -6 >

[0129] Figure 1 is the position error and protection level within one day after the subset filtering starts to work. The positioning error curve is below the protection level curve. Figure 2 is the fault exclusion rate. When faults occur in each of the six inter-satellite links respectively, the integrity monitoring method using multi-hypothesis solution separation can achieve a 100% fault exclusion rate. Figure 3 is the number of epochs required for fault exclusion. The six curves corresponding to the occurrence of faults in each inter-satellite link almost coincide. When the inter-satellite ranging information has a constant bias exceeding 20σ, the number of epochs required drops below 6. In summary, the present invention can achieve the integrity monitoring of the Earth-Moon libration point navigation constellation.

[0130] The above specific description further details the purpose, technical solution and beneficial effects of the invention. It should be understood that the above is only a specific embodiment of the present invention and is not used to limit the protection scope of the present invention. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A method for integrity monitoring of a navigation constellation at the Earth-Moon libration points, characterized in that the steps of this method include: Step 1, construct an extended Kalman filter orbit determination model under the actual force model; Step 2, determine the multi-hypothesis testing problem of the inter-satellite link fault mode according to the multi-hypothesis solution separation method; Step 3, calculate the solution separation and solution separation variance of the satellite orbit according to the multi-hypothesis testing problem in Step 2 and the orbit determination model constructed in Step 1; Step 4, set the fault detection and fault exclusion trigger conditions according to the solution separation and solution separation variance obtained in Step 3; Step 5, calculate the protection level according to the solution separation variance obtained in Step 3 to complete the integrity monitoring of the navigation constellation; In the said Step 1, the method for constructing the extended Kalman filter orbit determination model under the actual force model is: The dynamic equation of the navigation satellite in the Earth J2000 inertial coordinate system is: where: μ e , μ m and μ s are the gravitational constants of the Earth, the Moon, and the Sun, respectively; r is the satellite position vector, r m,sat is the vector from the Moon to the satellite, r e,m is the Moon position vector, r s,sat is the vector from the Sun to the satellite, r e,s is the Sun position vector; The position and velocity of each satellite in the Earth J2000 inertial system are expressed as: Then the quantities to be estimated for n satellites are: X 6n×1 = [x 1 x 2 ...x n T (3)​ where n is the number of navigation satellites and n≥4, s = 1, 2, …, n; Let the state equation of the Kalman filter be: In the formula Constructed from Equation (1), the formula for calculating the inter-satellite distance is as follows: where: v is zero-mean Gaussian white noise, and one measurement is obtained for every two satellites. observations are available, and the observation equation is: Let \(t\) be k The reference solution for \(X\) at time \(X\) is \(X\) * , and the reference solution for \(Y\) is \(Y\) * , \(X\) can be * Substituting into Equation (6), let the state deviation and the observation deviation be From time t k to time t k+1 The state transition matrix Φ(t k+1 , t k ) is obtained by numerical integration together with the state equation, and the calculation formula is as follows: The Jacobian matrix of the observation equation is: The EKF filtering equation is: where P k-1 is the variance matrix of the estimation error at time t k-1 , P k|k-1 is the variance matrix of the prediction error at time t k , P k is the variance matrix of the estimation error at time t k , Q k is the system noise variance, R k is the observation noise variance, K k is the Kalman filter gain, and I is the identity matrix; In the said Step 2, the method for determining the multi-hypothesis testing problem of the inter-satellite link fault mode according to the multi-hypothesis solution separation method is: If there are N inter-satellite links in total in the navigation constellation, corresponding to N pieces of observation information, when a fault occurs in the libration point constellation, assuming that a fault occurs in the inter-satellite link, and assuming that the fault modes to be monitored for the inter-satellite link are N + 1 kinds, then the multi-hypothesis testing problem is: For H 0 in the failure mode, the set S 0 contains the measurement information of N inter-satellite links, and S 0 is called the universal set; For H i 's failure mode, the set S i contains the measurement information of the remaining N - 1 inter - satellite links except for the measurement information of the i - th inter - satellite link. S i is called a subset; The state estimator obtained from the complete set is called the complete set solution, and the state estimator obtained from the subset is called the subset solution; In the said Step 3, the method for calculating the solution separation and solution separation variance of the satellite orbit according to the multi-hypothesis testing problem and the orbit determination model is: The solution separation is the difference between the complete set solution and the subset solution, expressed as: Where: is the full set positioning solution of the s-th satellite in the d direction; is the subset positioning solution of the s-th satellite in the d direction; d can be set as the x, y or z direction, and the separation variance of the d-direction solution of the s-th satellite is: Wherein: is the variance of the d-direction error of the s-th satellite in the full set, obtained from the variance of the estimated solution in the full set filtering; is the variance of the d-direction error of the s-th satellite in the subset, obtained from the variance of the estimated solution in the subset filtering; is the covariance P between the full set solution and the subset solution of the d-direction of the s-th satellite 0i,k , obtained by the following formula: where: the first position of the subscript of the variable represents the subordination relationship of the variable, 0 represents the parameter in the complete set filtering, i represents the parameter in the subset filtering, and 0i represents the parameter between the complete set filtering and the subset filtering; the second position represents the time.

2. A method for integrity monitoring of a navigation constellation at the Earth-Moon libration points according to claim 1, characterized in that: In the said Step 4, the method for setting the fault detection and fault exclusion trigger conditions according to the solution separation and solution separation variance is: Allocate the continuity risk to each fault mode and calculate the detection threshold, and the calculation formula is: Where: T i represents the detection threshold, C req represents the continuity risk, P(H 0 ) represents the probability of no failure, Q -1 represents the inverse function of the standard normal distribution tail function.

3. A method for integrity monitoring of a navigation constellation at the Earth-Moon libration points according to claim 2, characterized in that: When an inter-satellite link fails, the sum of squares of the posterior residuals SSE is calculated at this time. The subset with the smallest SSE is most likely the fault-free subset, that is, this subset does not contain the measurement information of the faulty inter-satellite link. The calculation formula of SSE is as follows:

4. A method for integrity monitoring of a navigation constellation at the Earth-Moon libration points according to claim 3, characterized in that: When excluding the faulty inter-satellite link, perform a solution separation on the subset again on the basis of each subset. If, in the subset with the smallest SSE, the solution separation of any sub-subset is less than the detection threshold, then the excluded inter-satellite link is the faulty inter-satellite link.

5. A method for integrity monitoring of a navigation constellation at the Earth-Moon libration points according to claim 4, characterized in that: In the said Step 5, the method for calculating the protection level according to the solution separation variance is: The approximate calculation formula for the protection level in Gaussian white noise is: where, PL xs,d represents the protection level in the d direction of the s-th satellite, and P(H i ) is the probability that the i-th inter-satellite link fails while other inter-satellite links do not fail. I req represents the integrity risk requirement value.

6. A method for integrity monitoring of a navigation constellation at the Earth-Moon libration point according to claim 5, characterized in that: PL in Equation (16) xs,d is an unknown, and the bisection method is used to solve it. The probability of the failure mode in the equation is as follows: where P sat_link is the probability of a fault occurring in each inter-satellite link.

Images