A method for predicting faulty satellites that lead to high RAIM missed detection rate

Abstract

The present application relates to a method for predicting faulty satellites that cause a high RAIM miss detection rate. The method comprises: deriving a detection statistic based on an observation equation for a satellite containing a fault bias to obtain a derived detection statistic; determining from the detection statistic that the detection statistic and the fault bias are linearly related, with the slope value being related to the satellite geometry; and determining the faulty satellite based on the detection statistic when the fault bias is fixed. The faulty detection statistic is normalized by the pseudorange noise variance, and an expression for the fault miss detection rate is constructed using the normalized fault detection statistic and a non-centralized parameter. The expression for the fault miss detection rate is derived by solving the expression for the non-centralized parameter to obtain a definition of the miss detection rate as a function of the satellite geometry, and prediction of faulty satellites that cause a high RAIM miss detection rate is achieved based on the definition. This method can predict faulty satellites that cause a high RAIM miss detection rate.

Description

Technical Field

[0001] The present application relates to the technical field of satellite fault detection, and in particular to a method for predicting faulty satellites that result in a high RAIM missed detection rate. Background Art

[0002] With the official launch of the Beidou satellite navigation system, the navigation accuracy of global navigation satellite systems (GNSS) users has been further improved. In civil aviation, while users' requirements for navigation accuracy are increasing, their demands for integrity, which is related to the safety of users' lives and property, are also growing. Integrity generally refers to the system's ability to promptly alert users when a satellite navigation system malfunctions and the navigation information provided cannot be used for correct navigation. Integrity is the user's confidence in the information provided by the navigation system and is an important performance indicator for ensuring user safety. Receiver autonomous integrity monitoring (RAIM) is a method in which the receiver uses redundant observation information to monitor the receiver's positioning results. It is a key component of integrity monitoring. This algorithm is simple to implement and widely used, but in practice, it can only detect large pseudorange fault deviations, limiting its effectiveness.

[0003] Traditional RAIM can only be used for integrity monitoring during the non-precision approach phase and requires high satellite geometry. RAIM monitoring under poor satellite geometry is prone to missed detections and false detections. Summary of the Invention

[0004] Based on this, it is necessary to provide a faulty satellite prediction method that can predict the faulty satellites that cause a high RAIM missed detection rate and the faulty satellite detection probability to address the above technical problems.

[0005] A method for predicting a faulty satellite that causes a high RAIM missed detection rate, the method comprising:

[0006] Obtain the number of satellites and the satellite observation equation of the navigation system at the observation time and construct the detection statistics according to the RAIM detection method;

[0007] The detection statistic is derived based on the observation equation of the satellite containing the fault deviation, and the derived detection statistic is obtained. From the detection statistic, it can be seen that the detection statistic and the fault deviation are linearly related. The expression of the slope value shows that the slope value is related to the satellite geometry. When the fault deviation is fixed, the smaller the slope value in the detection statistic, the smaller the detection statistic. The faulty satellite can be determined based on the detection statistic.

[0008] Calculating the fault detection statistic of the faulty satellite; normalizing the fault detection statistic with respect to the pseudorange noise variance to obtain the normalized fault detection statistic;

[0009] The detection threshold is determined according to the preset false alarm rate, and the expression for the fault missed detection rate is constructed using the detection threshold, the normalized fault detection statistics, and the non-centralized parameter. The expression for the fault missed detection rate is derived by solving the expression of the non-centralized parameter, and the definition of the missed detection rate related to the satellite geometric configuration is obtained. Based on the definition, the faulty satellites that cause a high RAIM missed detection rate are predicted.

[0010] The above-mentioned method for predicting a faulty satellite that causes a high RAIM missed detection rate, the present application derives a detection statistic constructed using a RAIM detection method based on an observation equation of a satellite containing a fault deviation, and obtains a derived detection statistic; from the detection statistic, it can be seen that the detection statistic and the fault deviation are linearly related, and from the expression of the slope value, it can be seen that the slope value is related to the satellite geometric configuration. When the fault deviation is fixed, the smaller the slope value in the detection statistic, the smaller the detection statistic, and the faulty satellite is judged based on the detection statistic; the fault detection statistic of the faulty satellite is calculated; the fault detection statistic is normalized by the pseudorange noise variance to obtain the normalized fault detection statistic. The invention relates to a method for detecting a satellite with a high RAIM miss detection rate and a method for detecting a satellite with a high miss detection rate. The invention relates to a method for detecting a satellite with a high ... BRIEF DESCRIPTION OF THE DRAWINGS

[0011] Figure 1 1 is a flow chart of a method for predicting a faulty satellite that causes a high RAIM missed detection rate in one embodiment;

[0012] Figure 2 is a characteristic slope diagram of a geometric configuration in one embodiment;

[0013] Figure 3Schematic diagram of a characteristic curve diagram at the 91st observation time in one embodiment;

[0014] Figure 4 Schematic diagram of the slope of satellite 7 at different observation times in another embodiment;

[0015] Figure 5 is a graph of fault deviation and detection probability at the 91st observation time in one embodiment;

[0016] Figure 6 1 is a graph showing the relationship between the detection probability and pseudorange deviation of satellite 7 in the 86th to 91st observation results in one embodiment;

[0017] Figure 7 Graph showing the relationship between different satellite detection probabilities and pseudorange deviations under the 91st observation result in one embodiment. DETAILED DESCRIPTION

[0018] In order to make the purpose, technical solutions and advantages of this application more clear, the following further describes this application in detail with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain this application and are not intended to limit this application.

[0019] In one embodiment, Figure 1 As shown, a method for predicting a faulty satellite that causes a high RAIM missed detection rate is provided, comprising the following steps:

[0020] Step 102: Obtain the number of satellites and the satellite observation equations of the navigation system at the observation time and construct detection statistics according to the RAIM detection method.

[0021] Assuming that the number of visible satellites of the navigation system at a certain moment is n, the linearized pseudo-range observation equation is expressed as follows:

[0022] y=H·x+ε

[0023] When a fault occurs, the fault deviation is added and the pseudorange observation equation is:

[0024] y=H·x+γ+ε

[0025] Where H is the coefficient matrix.

[0026] Assume that only satellite j has fault bias in the current observation, and other satellites do not contain fault bias and any noise. Then the ε vector in the pseudorange observation equation is

[0027] In step 104, the detection statistic is derived based on the observation equation of the satellite containing the fault deviation to obtain the derived detection statistic. From the detection statistic, it can be seen that the detection statistic and the fault deviation are linearly related. From the expression of the slope value, it can be seen that the slope value is related to the satellite geometric configuration. When the fault deviation is fixed, the smaller the slope value in the detection statistic, the smaller the detection statistic. The faulty satellite is determined based on the detection statistic.

[0028] The detection statistic is derived based on the observation equation of the satellite containing the fault deviation, and the derived detection statistic is

[0029] Where S = Q p T Q p , S j,j is the element in the j-th row and j-th column of the matrix. Deviation from added fault |b j It is a linear relationship, and its slope is And by The expression shows that its value is the same as Q p Related to the satellite geometry. j |Fixed, The smaller the value of The smaller the value, the less sensitive the satellite is to RAIM detection.

[0030] Step 106, calculate the fault detection statistic of the faulty satellite; normalize the fault detection statistic with respect to the pseudorange noise variance to obtain the normalized fault detection statistic; determine the detection threshold based on the preset false alarm rate, and construct an expression for the fault missed detection rate using the detection threshold, the normalized fault detection statistic, and the non-centralized parameter; derive the expression for the fault missed detection rate by solving the expression for the non-centralized parameter, and obtain a definition of the missed detection rate as a function of the satellite geometric configuration. Based on the definition, the pseudorange noise variance of the faulty satellite that causes the high RAIM missed detection rate is predicted.

[0031] Then calculate the fault detection statistics of the faulty satellite:

[0032]

[0033] Among them, p k is the kth element in the odd-even space vector. For the convenience of analysis, the detection quantity is normalized to the pseudo-range noise variance:

[0034] z=WSSE / σ 2

[0035] With a pre-set false alarm rate, the detection threshold can be determined, allowing the relationship between fault deviation and detection probability to be derived. The detection threshold, normalized fault detection statistics, and non-centralized parameters are used to construct an expression for the fault missed detection rate. The expression for the fault missed detection rate is derived by solving the expression for the non-centralized parameter. The relevant formula is as follows.

[0036]

[0037] From the above formula, we can know that the fault missed detection rate P m It is only related to the non-centralized parameter λ; and λ is related to Q p The missed detection rate is related to the satellite geometry.

[0038] The above-mentioned method for predicting a faulty satellite that causes a high RAIM missed detection rate, the present application derives a detection statistic constructed using a RAIM detection method based on an observation equation of a satellite containing a fault deviation, and obtains a derived detection statistic; from the detection statistic, it can be seen that the detection statistic and the fault deviation are linearly related, and from the expression of the slope value, it can be seen that the slope value is related to the satellite geometric configuration. When the fault deviation is fixed, the smaller the slope value in the detection statistic, the smaller the detection statistic, and the faulty satellite is judged based on the detection statistic; the fault detection statistic of the faulty satellite is calculated; the fault detection statistic is normalized by the pseudorange noise variance to obtain the normalized fault detection statistic. The invention relates to a method for detecting a satellite with a high RAIM miss detection rate and a method for detecting a satellite with a high miss detection rate. The invention relates to a method for detecting a satellite with a high ...

[0039] In one embodiment, the observation equation for a satellite including fault bias is

[0040] y=H·x+ε

[0041] Where H is the coefficient matrix, ε represents the fault deviation vector, b j represents the fault deviation of satellite j.

[0042] In one embodiment, the detection statistic is constructed as

[0043]

[0044] Where p represents an even-odd space vector, and the superscript T represents a transpose operation.

[0045] In one embodiment, the detection statistic is derived according to the observation equation of the satellite including the fault bias to obtain the derived detection statistic, including:

[0046] Perform QR decomposition on the coefficient matrix in the observation equation to obtain the orthogonal matrix and the upper triangular matrix;

[0047] Perform a transpose operation on the orthogonal matrix to obtain a transposed matrix; take the (n-4) rows after the transposition to obtain an even-odd space matrix; where n represents the number of visible satellites;

[0048] The detection statistics are derived based on the parity space matrix and the fault deviation vector, and the derived detection statistics are:

[0049]

[0050] Where ε represents the fault deviation vector, Q p represents the parity space matrix, b j represents the fault deviation of satellite j, and the superscript T represents the transposition operation. Indicates the slope value.

[0051] In one embodiment, the smaller the detection statistic, the less sensitive the satellite is to RAIM detection.

[0052] In one embodiment, calculating a fault detection statistic for a faulty satellite includes:

[0053] The fault detection statistics of the faulty satellite are calculated as

[0054]

[0055] in, represents the parity space vector, Q represents the orthogonal matrix, ε represents the fault deviation vector, Q :,s represents the sth column element of the orthogonal matrix Q, L s Indicates fault deviation, H0 indicates the case without fault, H1 indicates the case with fault, p k Represents the kth element in the parity space vector.

[0056] In one embodiment, the fault detection statistic is normalized by the pseudorange noise variance to obtain the normalized fault detection statistic:

[0057] z=WSSE / σ 2

[0058] Among them, σ 2 represents the pseudorange noise variance.

[0059] In one embodiment, a fault missed detection rate expression is constructed using a detection threshold, a normalized fault detection statistic, and a non-centralized parameter, including:

[0060] The fault missed detection rate expression is constructed using the detection threshold, normalized fault detection statistics and non-centralized parameters:

[0061]

[0062] Among them, T(P f ) represents the fault detection threshold, n represents the number of visible satellites, and z represents the normalized fault detection statistic.

[0063] In one embodiment, the expression for solving the non-centralized parameter is

[0064]

[0065] Among them, σ 2 represents the pseudorange noise variance, Q :,s represents the sth column element of the orthogonal matrix Q, L s Indicates fault deviation, and H1 indicates a fault condition.

[0066] In this specific example, to screen for satellites with a high missed detection rate, we selected GPS constellation data from 04:44 on June 26, 2024, to 04:44 on June 27, 2024, with a minimum elevation angle of 15° relative to Changsha, and observed every 10 minutes. The pseudorange noise added was Gaussian white noise with a variance of 9 and a mean of 0.

[0067] The experiment generated a total of 144 observation results. The slope value was calculated from the data from observation time 86 to observation time 91, that is, from 19:04 to 20:04 on June 26, 2024. The results are as follows: Figure 2As shown. Furthermore, among the high missed detection rate satellites generated by each observation result, find the satellite with the lowest slope value. The simulation results show that the satellite with the lowest slope value in the entire data is the second satellite in the 91st observation, that is, satellite No. 7 in the GPS constellation. Its slope value is 0.006597, which is the minimum slope value of the high missed detection rate satellites at all observation times. The PRN numbers of the satellite combination at the 91st observation time are: 6; 7; 14; 24; 25; 29, corresponding to Figure 5 and Figure 7 For this observation, the slope characteristic curves of different satellites were simulated, and the results are as follows: Figure 3 shown.

[0068] In addition, the data shows that there were no satellites entering or leaving the observation array during the observation period of nearly 1 hour, that is, from observation time 86 to 91. Moreover, satellite 7 was always the second satellite at each observation time. Based on this, the slope value change of the satellite with the minimum slope value over a period of time in the same satellite combination was simulated, and the results are as follows: Figure 4 The simulation results show that from observation times 86 to 91, the slope value for satellite 7 is the smallest and gradually decreases (0.0727; 0.0538; 0.0369; 0.0231; 0.0129; 0.0065). This indicates that satellite 7 has the lowest sensitivity to RAIM detection and becomes increasingly less sensitive during the 1-hour existence of this satellite combination.

[0069] In order to explore the difference between the satellite with high missed detection rate and other satellites with the same geometric configuration, the following simulation experiments are conducted. (1) The same pseudorange deviation is added to the satellite at the 91st observation time to compare its detection probability; (2) The maximum pseudorange deviation that can be added to different satellites under the same detection probability is explored. The maximum pseudorange deviation that can be added to satellite 7 at different observation times is explored. Figure 5 As shown in the figure, the simulation results show that as the added pseudorange deviation Ls increases, the detection probability of the remaining satellites almost shows a jumping trend, while the change of satellite 7 is very slow, and even begins to show slight changes when the added Ls is close to 100m.

[0070] like Figure 6 and Figure 7 As shown, it can be concluded that: (1) As the detection probability p increases, the pseudorange bias Ls that can be added also increases, and the step size of L2's increase is larger than that of the other five satellites. (2) Compared with the other five satellites, under the same detection probability, the pseudorange bias that can be added to L2 is significantly larger, indicating that it has the lowest sensitivity to RAIM detection. (3) Among the different observation times, satellite 7 at the 91st observation time has the lowest sensitivity to RAIM detection and the largest pseudorange bias that can be added under the same detection probability, which is consistent with the result that the lowest slope value of the characteristic slope graph is the 91st observation.

[0071] It should be understood that although Figure 1 The steps in the flowchart are shown in sequence as indicated by the arrows, but these steps are not necessarily executed in the order indicated by the arrows. Unless otherwise specified in this document, there is no strict order restriction for the execution of these steps, and these steps can be executed in other orders. In addition, Figure 1 At least part of the steps may include multiple sub-steps or multiple stages. These sub-steps or stages are not necessarily executed at the same time, but can be executed at different times. The execution order of these sub-steps or stages is not necessarily sequential, but can be executed in turn or alternately with other steps or at least part of the sub-steps or stages of other steps.

[0072] The technical features of the above embodiments can be combined arbitrarily. To make the description concise, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0073] The above-described embodiments merely represent several implementation methods of the present application. While the descriptions are relatively specific and detailed, they should not be construed as limiting the scope of the present invention. It should be noted that a person skilled in the art could make various modifications and improvements without departing from the spirit of the present application, all of which fall within the scope of protection of the present application. Therefore, the scope of protection of the present patent application shall be determined by the appended claims.

Claims

1. A method for predicting faulty satellites that result in a high RAIM missed detection rate, characterized in that: The method comprises: Obtain the number of satellites and the satellite observation equation of the navigation system at the observation time and construct the detection statistics according to the RAIM detection method; The detection statistic is derived according to an observation equation of a satellite including a fault deviation to obtain a derived detection statistic; from the detection statistic, it can be seen that the detection statistic and the fault deviation are linearly related, and from an expression of the slope value, it can be seen that the slope value is related to the satellite geometric configuration. When the fault deviation is fixed, the smaller the slope value in the detection statistic, the smaller the detection statistic, and the faulty satellite is determined based on the detection statistic; Calculating a fault detection statistic of the faulty satellite; normalizing the fault detection statistic with respect to the pseudorange noise variance to obtain a normalized fault detection statistic; A detection threshold is determined based on a preset false alarm rate, and an expression for a fault missed detection rate is constructed using the detection threshold, a normalized fault detection statistic, and a non-centralized parameter. The expression for the fault missed detection rate is derived by solving the expression for the non-centralized parameter, thereby obtaining a definition of the missed detection rate as related to the satellite geometry. Based on this definition, faulty satellites that cause a high RAIM missed detection rate are predicted.

2. The method according to claim 1, characterized in that The observation equation of the satellite containing the fault deviation is y=H·x+ε Where H is the coefficient matrix, ε represents the fault deviation vector, b j represents the fault deviation of satellite j.

3. The method according to claim 1, characterized in that Construct the test statistic as Where p represents an even-odd space vector, and the superscript T represents a transpose operation.

4. The method according to claim 1, wherein The detection statistic is derived according to the observation equation of the satellite including the fault deviation to obtain the derived detection statistic, including: Performing QR decomposition on the coefficient matrix in the observation equation to obtain an orthogonal matrix and an upper triangular matrix; Performing a transpose operation on the orthogonal matrix to obtain a transposed matrix; taking the last (n-4) rows of the transposed matrix to obtain an even-odd space matrix; wherein n represents the number of visible satellites; The detection statistic is derived according to the parity space matrix and the fault deviation vector, and the derived detection statistic is obtained as follows: Where ε represents the fault deviation vector, Q p represents the parity space matrix, b j represents the fault deviation of satellite j, and the superscript T represents the transposition operation. Indicates the slope value.

5. The method according to claim 1, characterized in that The smaller the detection statistic, the less sensitive the satellite is to RAIM detection.

6. The method according to claim 1, characterized in that Calculating a fault detection statistic of the faulty satellite includes: The fault detection statistic of the faulty satellite is calculated as in, represents the parity space vector, Q represents the orthogonal matrix, ε represents the fault deviation vector, Q :,s represents the sth column element of the orthogonal matrix Q, L s Indicates fault deviation, H0 indicates the case without fault, H1 indicates the case with fault, p k Represents the kth element in the parity space vector.

7. The method according to claim 6, characterized in that The fault detection statistic is normalized to the pseudorange noise variance to obtain the normalized fault detection statistic: z=WSSE / σ 2 Among them, σ 2 represents the pseudorange noise variance.

8. The method according to claim 1, characterized in that The fault missed detection rate expression is constructed using the detection threshold, the normalized fault detection statistics, and the non-centralized parameter, including: The fault missed detection rate expression is constructed using the detection threshold, normalized fault detection statistics and non-centralized parameters: Among them, T(P f ) represents the fault detection threshold, n represents the number of visible satellites, and z represents the normalized fault detection statistic.

9. The method according to claim 1, characterized in that The expression for solving the non-centralized parameter is Among them, σ 2 represents the pseudorange noise variance, Q :,s represents the sth column element of the orthogonal matrix Q, L s Indicates fault deviation, and H1 indicates a fault condition.

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