Faulty satellite detection method at receiver end based on non-parametric estimation

Abstract

The present invention discloses a method for detecting faulty satellites at the receiver end based on non-parametric estimation, which belongs to the technical field of satellite navigation receivers. The present invention obtains the positioning estimation solution and estimation error of the linearized pseudo-range measurement equation; establishes classification variables for fault detection based on the variance inflation theory; dynamically samples the fault-free set and the faulty set to obtain a labeled sample set; calculates the classification variable regression solution using a non-parametric estimation method; constructs a faulty satellite detection network based on the positioning estimation solution and estimation error, the classification variable, the labeled sample set and the classification variable regression solution; determines the smoothing factor in the faulty satellite detection network according to the navigation continuity requirement; and detects faulty satellites using the faulty satellite detection network. In the present invention, a faulty satellite detection network is constructed based on classification variables, dynamic sampling methods, non-parametric estimation and theoretically determined smoothing factors to improve the detection performance of faulty satellites.

Description

Technical Field

[0001] The invention relates to a non-parameter estimation receiver-side fault satellite detection method, belonging to the technical field of satellite navigation receivers. Background Art

[0002] Satellite navigation technology is the foundation of efficient and safe operation of modern civil aviation. In actual use, while users have higher requirements for navigation accuracy, they also have a growing demand for navigation safety to protect the safety of users' property and lives. Aviation safety is closely related to the integrity index of the navigation system. The integrity of the navigation system can be understood as the ability of the navigation system to promptly issue warnings to users when there are unacceptable deviations in the positioning data provided to users. Among them, receiver autonomous integrity monitoring (RAIM) uses the receiver to perform consistency checks on the received redundant observation data to complete fault detection. It has become a hot topic in the research of integrity monitoring technology due to its simple implementation, no need for external equipment assistance, and low cost.

[0003] According to different basic navigation positioning algorithms, the current RAIM algorithms are mainly divided into snapshot RAIM algorithms and filtered RAIM algorithms. The snapshot RAIM algorithms mainly include: least squares residual RAIM, pseudorange comparison method and parity vector method and other traditional methods. These methods are suitable for single-satellite fault detection. Although they have the advantages of simple model and small amount of calculation, they have the disadvantages of low detection rate, insensitivity to positioning error, and serious influence of fault mode on detection effect. Filtered RAIM has the disadvantages of serious influence of noise characteristics on detection effect or large amount of calculation. At the same time, the existing neural network-based detection methods usually introduce parameters for adjusting detection capability and give the parameters based on experience. Therefore, it is difficult to evaluate whether such methods meet the navigation continuity requirements stipulated by the Civil Aviation Administration, and thus it is difficult to meet actual use needs. Summary of the invention

[0004] The purpose of the present invention is to solve the problem that the existing receiver-side fault satellite detection method has low detection efficiency and is insufficient to protect the personal safety of users, and to provide a receiver-side fault satellite detection method based on non-parametric estimation. The method obtains the positioning estimation solution and estimation error of the linearized pseudo-range measurement equation; establishes classification variables for fault detection based on the variance inflation theory; dynamically samples the fault-free set and the faulty set to obtain a labeled sample set; calculates the classification variable regression solution using a non-parametric estimation method; constructs a fault satellite detection network based on the obtained positioning estimation solution and estimation error, classification variables, labeled sample sets and classification variable regression solutions; determines the smoothing factor in the fault satellite detection network according to the navigation continuity requirements; and detects the faulty satellite using the faulty satellite detection network. In the present invention, a faulty satellite detection network is constructed based on classification variables, dynamic sampling methods, non-parametric estimation and theoretically determined smoothing factors, which can improve the detection performance of faulty satellites and is suitable for autonomous integrity monitoring of receivers in global satellite navigation. The improved detection performance of faulty satellites includes improving the sensitivity, accuracy and efficiency of faulty satellite detection.

[0005] The objective of the present invention is achieved through the following technical solutions:

[0006] The present invention discloses a method for detecting a faulty satellite at a receiver end based on non-parametric estimation, comprising the following steps:

[0007] Step 1: Obtain the positioning estimation solution and estimation error of the linearized pseudorange measurement equation;

[0008] Step 2: Establish categorical variables for fault detection based on variance inflation theory;

[0009] Step 3: Dynamically sample the fault-free set and the faulty set to obtain a labeled sample set;

[0010] Step 4: Calculate the regression solution of categorical variables using nonparametric estimation methods;

[0011] Step 5: construct a fault satellite detection network based on the positioning estimation solution and estimation error obtained in step 1, the classification variable obtained in step 2, the labeled sample set obtained in step 3, and the classification variable regression solution obtained in step 4;

[0012] Step 6: Determine the smoothing factor in the fault satellite detection network according to the navigation continuity requirement;

[0013] Step 7: Detecting a faulty satellite using the faulty satellite detection network after determining the smoothing factor can improve the detection performance of the faulty satellite. Improving the detection performance of the faulty satellite includes improving the sensitivity, accuracy and efficiency of the faulty satellite detection.

[0014] Step 1: Obtain the positioning estimation solution and estimation error of the linearized pseudorange measurement equation;

[0015] Step 1.1: Establish the linear pseudorange measurement equation.

[0016] The linear pseudorange measurement equation in the northeast sky coordinate system is:

[0017] z=Gx+ε (1)

[0018] Where z∈R n×1 , represents the offset vector between the original pseudorange from the user to each visible satellite and the calculated pseudorange, n is the number of visible satellites; x∈R m×1 represents the state variable containing the three-dimensional position parameters and the receiver clock parameters, m is the dimension of the state variable; G∈R n×m Represents the geometric matrix that transforms the position domain information into the measurement domain; ε=[ε1,ε2,...,ε n ] T represents the measurement noise vector, and ε i (i∈{1,2,...,n}) are independent and subject to Gaussian noise, σ obs,i represents the standard deviation of the measurement noise.

[0019] Step 1.2: According to the linear pseudo-range measurement equation established in step 1.1, obtain the positioning estimation solution and the estimation error; the obtaining of the positioning estimation solution and the estimation error includes a weighted least squares method and a Kalman filter method.

[0020] When the weighted least squares method is used, the implementation method of step 1.2 is:

[0021] The weighted least squares location estimation solution of x and its estimation error are:

[0022]

[0023] Where W is a weighted matrix, which is related to the altitude angle of each satellite relative to the user and the user's ranging accuracy.

[0024] When the Kalman filter method is selected, the implementation method of step 1.2 is:

[0025] The time and state update equations for the Kalman filter are shown below:

[0026]

[0027] The subscript k of each symbol represents the current time, and the subscript k-1 represents the previous time; represents the state estimation value, and P is the covariance matrix of the state prediction value; represents the state prediction value, represents the covariance matrix of the state prediction value; K is the gain matrix; R is the measurement noise covariance matrix; Q is the covariance matrix of the system noise; A and B are system parameters, and u is the control quantity;

[0028] The positioning estimation solution and estimation error are obtained according to the time and state update equation (4) of the Kalman filter.

[0029] Step 2: Establish categorical variables for fault detection based on variance inflation theory;

[0030] Because ε i are independent of each other, so the statistical model of the measurement noise vector ε is used to calculate the celestial positioning error μ through the multiple convolution formula ver The statistical model of is shown in formula (5):

[0031]

[0032] Among them, σ ver Indicates the standard deviation of the positioning error in the celestial direction; a ver,i represents the element in the third row and the i-th column of matrix A;

[0033] Based on the variance inflation theory, if there is a faulty satellite, the positioning error μ is regarded as a random variable with the same expectation but an inflated variance, and is represented by μ f express:

[0034] μ f ~N(0,k 2 σ 2 )(6) Where k represents the variance expansion factor, σ represents the standard deviation of the positioning error;

[0035] Therefore, in order to detect faulty satellites, a categorical variable Y of the celestial direction is constructed: ver As shown in formula (7):

[0036]

[0037] When Y ver =1, there is a faulty satellite in the satellite navigation system; when Y ver =0, there is no faulty satellite in the satellite navigation system; similarly, construct the fault detection classification variable Y in the east direction east and north direction fault detection categorical variable Y north as follows:

[0038]

[0039] At this point, the categorical variables of east, north and celestial direction are obtained.

[0040] Step 3: Dynamically sample the fault-free set and the faulty set to obtain a labeled sample set;

[0041] During the navigation and positioning process, the positioning system obtains n s Position estimation solution Samples, used to estimate the corresponding positioning error samples When the satellite navigation system is fault-free, the distribution of the celestial positioning error is obtained from equation (5): s samples; the sample standard deviation S of this sample set ver It obeys the modified normal distribution, as shown in formula (10):

[0042]

[0043] Among them, γ represents the correction coefficient; H0 represents the no-fault situation.

[0044] According to formula (10), we can get n1 samples. The corresponding categorical variables for the no-fault condition are labeled as n1×1 column vectors with all zeros:

[0045] y ver,s =[0,0,K,0] T (11)

[0046] When there is a fault in the satellite navigation system, the position error expands k times and the sample standard deviation S ver It follows the following distribution:

[0047]

[0048] Among them, H1 indicates that there is a faulty satellite;

[0049] According to formula (12), we can get n2 samples. The categorical variables corresponding to the fault conditions are labeled as n2×1 column vectors with all elements set to 1:

[0050] y ver,f =[1,1,K,1] T (13)

[0051] The samples from the non-fault set and the fault set are combined with the corresponding labeled categorical variables as follows to obtain the labeled sample set:

[0052]

[0053] y0=[y ver,s ,y ver,f ] (15)

[0054] The distribution of the samples is affected by the standard deviation of the positioning error σ ver The influence of the position error standard deviation σver Determined by the geometric configuration. The geometric configuration changes dynamically, so the marked sample set is also dynamically updated.

[0055] Step 4: Calculate the regression solution of categorical variables using nonparametric estimation methods;

[0056] The conditional mean of a categorical variable is expressed as follows:

[0057]

[0058] In order to simplify the expression, the subscripts representing the east, north and celestial direction of the sample standard deviation S and the categorical variable Y in this step are omitted, and f(S,Y) is the joint probability density function of the sample standard deviation S and the categorical variable Y;

[0059] Based on the non-parametric estimation method, the joint probability density function f(S,Y) is estimated using the labeled sample set obtained in step 3. The result is shown in formula (17):

[0060]

[0061] Among them, λ is the smoothing factor of the Gaussian kernel function, and s i represents the sample from equation (14), y i It means that the corresponding s from formula (15) i A labeled categorical variable;

[0062] Substitute equation (17) into equation (16) and swap the order of integration:

[0063]

[0064] according to Simplifying and reorganizing formula (18), we get the regression solution of categorical variables, and the results are as follows:

[0065]

[0066] Among them, the numerator represents the weighted average of the labeled categorical variables; the denominator represents the weighted average from the sample standard deviation S to each sample s i The sum of the Euclidean distances.

[0067] Step 5: Based on the positioning estimation solution and estimation error obtained in step 1, the classification variable obtained in step 2, the labeled sample set obtained in step 3, and the classification variable regression solution obtained in step 4, a faulty satellite detection network is constructed;

[0068] The fault satellite detection network has five layers, namely: input layer, sampling layer, clustering layer, evaluation layer and detection layer;

[0069] Input layer: When a satellite fails, the fault deviation projected to the east, north and sky directions changes with the change of the geometric configuration from the satellite to the user receiver; therefore, the positioning data in the three directions should be detected synchronously; the input layer stores the positioning data collected from the receiver and estimates the sample standard deviation S of the positioning result. Its subscript dir represents the three directions of east, north and sky:

[0070]

[0071] Sampling layer: According to equations (14) and (15), the labeled sample sets in the east, north and sky directions are obtained respectively;

[0072] Clustering layer: Use Gaussian kernel function to evaluate the similarity between the positioning data of the input layer and the labeled sample set obtained by the sampling layer; calculate the regression solution of classification variables in three directions based on non-parametric estimation method As shown in formula (19);

[0073] Evaluation layer: Based on the regression solution of the categorical variables, the switch function is used to determine whether there is a faulty satellite in the satellite navigation system;

[0074]

[0075] Among them, R dir is the fault assessment result in the east, north or sky direction, The regression solution for the categorical variable is east, north or celestial direction;

[0076] Detection layer: Perform Boolean OR operation on the evaluation results of the east, north and sky directions obtained by the evaluation layer to obtain the final fault detection result, as shown below:

[0077] R=R ver ∨R east ∨R north (twenty two)

[0078] Step 6: Determine the smoothing factor λ in the fault satellite detection network according to the navigation continuity requirement;

[0079] False alarm rate P fa Defined as:

[0080] P fa ={R=0|H0} (23)

[0081] P fa The maximum permissible value [P fa ] is derived from the continuity requirement, and the results are as follows:

[0082]

[0083] Among them, [P fa] is the maximum allowable false alarm rate; P sat is the prior failure probability of each satellite; n is the number of visible satellites; C req Requires indicators for navigation continuity.

[0084] In order to meet the false alarm rate, for all S<T fa , the fault satellite detection network should not detect the fault, that is, it meets the following requirements:

[0085]

[0086] Among them, Φ -1 Represents the standard inverse normal cumulative distribution function.

[0087] By iteratively solving equation (25), the minimum value of the smoothing factor λ can be determined: min ; Under the premise of satisfying continuity, in order to maximize the detection capability, in actual use, the smoothing factor λ is set to λ min ;

[0088] Step 7: Using the faulty satellite detection network after determining the smoothing factor to detect the faulty satellite can improve the detection performance of the faulty satellite. Improving the detection performance of the faulty satellite includes improving the sensitivity, accuracy and efficiency of the faulty satellite detection.

[0089] The positioning estimation solution and estimation error obtained in step 1 and the smoothing factor obtained in step 6 are input into the faulty satellite detection network in step 5 to detect the faulty satellite, which can improve the detection performance of the faulty satellite. Improving the detection performance of the faulty satellite includes improving the sensitivity, accuracy and efficiency of the faulty satellite detection.

[0090] When R = 1, there is a faulty satellite in the satellite navigation system and a fault occurs;

[0091] When R = 0, there is no faulty satellite in the satellite navigation system and no fault occurs;

[0092] Beneficial effects:

[0093] 1. Compared with traditional methods such as least squares residual RAIM, the receiver-side fault satellite detection method based on non-parametric estimation disclosed in the present invention uses non-parametric estimation methods to calculate the regression solution of categorical variables, construct a fault satellite detection network, and determine the smoothing factor in the fault satellite detection network according to the navigation continuity requirements. The fault satellite detection network after the smoothing factor is determined is used to detect faulty satellites, which can improve the detection performance of faulty satellites and significantly improve the correct detection capability of the system. For different faulty satellite situations, the correct detection rate of the proposed method is generally higher than that of the traditional method. At the same time, when the fault is successfully detected at the beginning, the pseudo-range fault deviation corresponding to the proposed method is smaller, that is, the proposed method is more sensitive to satellite faults.

[0094] 2. The receiver-side fault satellite detection method based on non-parametric estimation disclosed in the present invention has better universality. In the actual use of the satellite navigation system, each satellite may fail, so fault detection should take into account all satellite failures. Among all failure modes, the probability of single satellite failure is the most significant. Compared with the traditional method, a 100% correct detection rate is achieved for all single-fault satellite modes. The minimum pseudo-range fault deviation corresponding to the receiver-side fault satellite detection method based on non-parametric estimation is smaller, and the correct detection rate is higher.

[0095] 3. Compared with the existing RAIM method based on neural network, the receiver-side fault satellite detection method based on non-parametric estimation disclosed in the present invention can directly meet the navigation continuity requirements stipulated by the Civil Aviation Administration. The existing RAIM method based on neural network usually gives key parameters for measuring detection capabilities based on experience, making it difficult to determine whether such methods meet the continuity requirements. The present invention directly determines the parameter smoothing factor according to the navigation continuity requirements, and uses the fault satellite detection network after determining the smoothing factor to detect the faulty satellite, which can fundamentally meet the navigation continuity requirements. BRIEF DESCRIPTION OF THE DRAWINGS

[0096] Figure 1 A faulty satellite detection flow chart of a receiver-side faulty satellite detection method based on non-parametric estimation;

[0097] Figure 2(a) and Figure 2(b) are fault detection result diagrams of the fault satellite detection method at the receiver end based on non-parametric estimation, where (a) is a fault detection rate curve diagram of all satellites; (b) is a partial enlarged diagram of ellipse A in (a); DETAILED DESCRIPTION

[0098] In order to better illustrate the purpose, content and advantages of the present invention, the specific implementation mode is further described in detail below in conjunction with the embodiments of the present invention and the accompanying drawings.

[0099] Example 1

[0100] The process of detecting a faulty satellite by using the receiver-side faulty satellite detection method based on non-parametric estimation proposed by the present invention is shown in Figure 1 This embodiment simulates the process of a GNSS receiver using a receiver autonomous integrity monitoring algorithm to assist in navigation and positioning of a civil aircraft and perform fault monitoring, and uses an experiment to test the fault detection performance of the proposed receiver-side fault satellite detection method based on non-parametric estimation, and compares it with the traditional least squares RAIM.

[0101] Due to the limited amount of real data, in this embodiment, the fault data is constructed by artificially injecting a pseudo-range fault deviation of 0-100m with a step size of 5m into the real observation data. Considering universality, all visible satellites are set as faulty satellites, and the fault detection rates of the receiver-side faulty satellite detection method based on non-parametric estimation and the least squares RAIM method are calculated and compared in each case.

[0102] The embodiment uses a GNSS receiver located in Beijing (116.315253°E, 39.959792°N, 58m) to collect real satellite observation data and navigation files. The collection time is 00:00:00-23:59:59 on March 28, 2021, the sampling frequency is 1Hz, and the total number of epochs is 86400.

[0103] like Figure 1 As shown, the receiver-side fault satellite detection method based on non-parametric estimation disclosed in this embodiment has the following specific implementation steps:

[0104] Step 1: Obtain the positioning estimation solution and estimation error of the linearized pseudorange measurement equation;

[0105] Step 1.1: Establish the linear pseudorange measurement equation.

[0106] The linearized pseudorange measurement equation in the northeastern sky coordinate system is:

[0107] z=Gx+ε (26)

[0108] Where z∈R n×1 , represents the offset between the original pseudorange and the calculated pseudorange from the user to each visible satellite, n is the number of visible satellites; x∈R m×1 represents the state variable containing the three-dimensional position parameters and the receiver clock parameters, m is the dimension of the state variable; G∈R n×m Represents the geometric matrix that transforms the position domain information into the measurement domain; ε=[ε1,ε2,...,ε n ] T represents the measurement noise vector, and ε i (i∈{1,2,...,n}) are independent and subject to Gaussian noise, σ obs,i represents the standard deviation of the measurement noise.

[0109] Step 1.2: According to the linear pseudo-range measurement equation established in step 1.1, obtain the positioning estimation solution and the estimation error; the obtaining of the positioning estimation solution and the estimation error includes a weighted least squares method and a Kalman filter method.

[0110] When the weighted least squares method is used, the implementation method of step 1.2 is:

[0111] The weighted least squares location estimation solution of x and its estimation error are:

[0112]

[0113] Where W is a weighted matrix, which is related to the altitude angle of each satellite relative to the user and the user's ranging accuracy;

[0114] When the Kalman filter method is selected, the implementation method of step 1.2 is:

[0115] The time and state update equations for the Kalman filter are shown below:

[0116]

[0117] The subscript t of each symbol represents the current time, and the subscript k-1 represents the previous time; represents the state estimation value, and P is the covariance matrix of the state prediction value; represents the state prediction value, represents the covariance matrix of the state prediction value; K is the gain matrix; R is the measurement noise covariance matrix; Q is the covariance matrix of the system noise; A and B are system parameters, and u is the control quantity;

[0118] Step 2: Establish categorical variables for fault detection based on variance inflation theory;

[0119] Because ε i are independent of each other, so the statistical model of the measurement noise vector ε is used to calculate the celestial positioning error μ through the multiple convolution formula ver The statistical model is as follows:

[0120]

[0121] Among them, σ ver Indicates the standard deviation of the positioning error in the celestial direction; a ver,i represents the element in the third row and the i-th column of matrix A;

[0122] Based on the variance inflation theory, if there is a faulty satellite, the positioning error μ can be regarded as a random variable with the same expectation but an inflated variance, represented by μ f express:

[0123] μ f ~N(0,k 2 σ 2 )(31)where k represents the variance expansion factor, and σ represents the standard deviation of the positioning error;

[0124] Therefore, in order to detect faulty satellites, a categorical variable Y is constructed ver As shown below:

[0125]

[0126] When Y ver =1, there is a faulty satellite in the satellite navigation system; when Y ver =0, there is no faulty satellite in the satellite navigation system; similarly, construct the fault detection classification variable Y in the east direction east and north direction fault detection categorical variable Y north as follows:

[0127]

[0128] At this point, the categorical variables of east, north and celestial direction are obtained.

[0129] Step 3: Dynamically sample the fault-free set and the faulty set to obtain a labeled sample set;

[0130] During the navigation and positioning process, the positioning system obtains n s Position estimation solution Samples, used to estimate the corresponding positioning error samples The sample standard deviation S is obtained from the distribution of the celestial positioning error shown in (30) when the satellite navigation system is fault-free. s samples; the sample standard deviation S of this sample set ver It follows a modified normal distribution as follows:

[0131]

[0132] Among them, γ represents the correction coefficient; H0 represents the no-fault situation.

[0133] According to formula (35), we can get n1 samples. The corresponding categorical variables for the no-fault condition are labeled as n1×1 column vectors with all zeros:

[0134] y ver,s =[0,0,K,0] T (36)

[0135] When there is a fault in the satellite navigation system, the position error expands k times and the sample standard deviation S ver It follows the following distribution:

[0136]

[0137] Among them, H1 indicates that there is a faulty satellite.

[0138] According to formula (37), we can get n2 samples. The categorical variables corresponding to the fault conditions are labeled as n2×1 column vectors with all elements set to 1:

[0139] y ver,f =[1,1,K,1] T (38)

[0140] The samples from the non-fault set and the fault set are combined with the corresponding labeled categorical variables as follows to obtain the labeled sample set:

[0141]

[0142] y0=[y ver,s ,y ver,f ] (40)

[0143] Step 4: Calculate the regression solution of categorical variables using nonparametric estimation methods;

[0144] The conditional mean of a categorical variable is expressed as follows:

[0145]

[0146] In order to simplify the expression, the subscripts representing the east, north and celestial direction of the sample standard deviation S and the categorical variable Y in this step are omitted, and f(S,Y) is the joint probability density function of the sample standard deviation S and the categorical variable Y;

[0147] Based on the non-parametric estimation method, the joint probability density function f(S,Y) is estimated using the labeled sample set obtained in step 3. The results are as follows:

[0148]

[0149] Among them, λ is the smoothing factor of the Gaussian kernel function, and s i represents the sample from equation (39), y i It means that the corresponding s from formula (40) i A labeled categorical variable;

[0150] Substitute equation (42) into equation (41) and swap the order of integration:

[0151]

[0152] according to Simplifying and reorganizing formula (43), we get the regression solution of categorical variables, and the results are as follows:

[0153]

[0154] Step 5: Based on the positioning estimation solution and estimation error obtained in step 1, the classification variable obtained in step 2, the labeled sample set obtained in step 3, and the classification variable regression solution obtained in step 4, a faulty satellite detection network is constructed;

[0155] The fault satellite detection network has five layers, namely: input layer, sampling layer, clustering layer, evaluation layer and detection layer;

[0156] Input layer: When a satellite fails, the fault deviation projected to the east, north and sky directions changes with the change of the geometric configuration from the satellite to the user receiver; therefore, the positioning data in the three directions should be detected synchronously; the input layer stores the positioning data collected from the receiver and estimates the sample standard deviation S of the positioning result. Its subscript dir represents the three directions of east, north and sky:

[0157]

[0158] Sampling layer: According to equations (39) and (40), the labeled sample sets in the east, north and sky directions are obtained respectively;

[0159] Clustering layer: Use Gaussian kernel function to evaluate the similarity between the positioning data of the input layer and the labeled sample set obtained by the sampling layer; calculate the regression solution of classification variables in three directions based on non-parametric estimation method As shown in formula (44).

[0160] Evaluation layer: Based on the regression solution of the categorical variables, the switch function is used to determine whether there is a faulty satellite in the satellite navigation system;

[0161]

[0162] Among them, R dir is the fault assessment result in the east, north or sky direction, The regression solution for the categorical variable is east, north or celestial direction;

[0163] Detection layer: Perform Boolean OR operation on the evaluation results of the east, north and sky directions obtained by the evaluation layer to obtain the final fault detection result, as shown below:

[0164] R=R ver ∨R east ∨R north (47)

[0165] Step 6: Determine the smoothing factor λ in the fault satellite detection network according to the navigation continuity requirement;

[0166] False alarm rate P fa Defined as:

[0167] P fa ={R=0|H0} (48)

[0168] P fa The maximum permissible value [P fa ] is derived from the continuity requirement, and the results are as follows:

[0169]

[0170] Among them, [P fa ] is the maximum allowable false alarm rate; P sat is the prior failure probability of each satellite; n is the number of visible satellites; C req It is the LPV-250 navigation continuity requirement specified by the International Civil Aviation Organization (ICAO).

[0171] In order to meet the false alarm rate, for all S<T fa , the fault satellite detection network should not detect the fault, that is, it meets the following requirements:

[0172]

[0173] Among them, Φ -1 Represents the standard inverse normal cumulative distribution function.

[0174] By iteratively solving equation (50), the minimum value of the smoothing factor λ can be determined: min Under the premise of satisfying continuity, in order to maximize the detection capability, in actual use, the smoothing factor λ is set to λ min .

[0175] Step 7: Detect the faulty satellite using the faulty satellite detection network;

[0176] The positioning estimation solution and estimation error obtained in step 1 and the smoothing factor obtained in step 6 are input into the fault satellite detection network in step 5 to obtain the final detection result;

[0177] When R = 1, there is a faulty satellite in the satellite navigation system and a fault occurs;

[0178] When R = 0, there is no faulty satellite in the satellite navigation system and no fault occurs;

[0179] The fault detection rate results of this embodiment are shown in Figure 2(a) and Figure 2(b). The correct detection rate of the proposed receiver-side fault satellite detection method based on non-parametric estimation is represented by a solid line with a triangle; the correct detection rate of the traditional least squares RAIM is represented by a dotted line with a square; the correct detection rate curves corresponding to the same faulty satellite are drawn with the same color.

[0180] As the pseudorange offset increases, the detection rates of the two methods also increase, eventually reaching 100%. The proposed receiver-side fault satellite detection method based on non-parametric estimation achieves a 100% correct detection rate of all faulty satellites with a minimum pseudorange fault deviation of no more than 35m, while the least squares RAIM requires a 55m pseudorange deviation, so the performance of this method is significantly better than the least squares RAIM.

[0181] The above specific embodiments further describe the purpose, technical solutions and beneficial effects of the invention. It should be understood that the above description is not intended to limit the patent scope of the present invention. Any equivalent transformation, modification, or application in other related technical fields made using the contents of the present invention specification and drawings is also included in the patent protection scope of the present invention.

Claims

1. A method for detecting faulty satellites at a receiver end based on non-parametric estimation, characterized in that: The following steps are included: Step 1: Obtain the positioning estimation solution and estimation error of the linearized pseudorange measurement equation; The implementation method of step one is: Step 1.1: Establish a linear pseudorange measurement equation; The linear pseudorange measurement equation in the northeast sky coordinate system is: z=Gx+ε(1) Where z∈R n×1 , represents the offset vector between the original pseudorange from the user to each visible satellite and the calculated pseudorange, n is the number of visible satellites; x∈R m×1 represents the state variable containing the three-dimensional position parameters and the receiver clock parameters, m is the dimension of the state variable; G∈R n×m Represents the geometric matrix that transforms the position domain information into the measurement domain; ε=[ε1,ε2,...,ε n ] T represents the measurement noise vector, and ε i (i∈{1,2,…,n}) are independent and subject to Gaussian noise, σ obs,i represents the standard deviation of the measurement noise; Step 1.2: According to the linear pseudo-range measurement equation established in step 1.1, obtain the positioning estimation solution and the estimation error; the obtaining of the positioning estimation solution and the estimation error includes a weighted least squares method and a Kalman filter method; When the weighted least squares method is used, the implementation method of step 1.2 is: The weighted least squares location estimation solution of x and its estimation error are: Where W is a weighted matrix, which is related to the altitude angle of each satellite relative to the user and the user's ranging accuracy; When the Kalman filter method is selected, the implementation method of step 1.2 is: The time and state update equations for the Kalman filter are shown below: The subscript t of each symbol represents the current time, and the subscript t-1 represents the previous time; represents the state estimation value, and P is the covariance matrix of the state prediction value; represents the state prediction value, represents the covariance matrix of the state prediction value; K is the gain matrix; R is the measurement noise covariance matrix; Q is the covariance matrix of the system noise; A and B are system parameters, and u is the control quantity; Obtaining a positioning estimation solution and an estimation error according to the time and state update equation (4) of the Kalman filter; Step 2: Establish categorical variables for fault detection based on variance inflation theory; The implementation method of step 2 is: Because ε i are independent of each other, so the statistical model of the measurement noise vector ε is used to calculate the celestial positioning error μ through the multiple convolution formula ver The statistical model is shown in formula (5): Among them, σ ver Indicates the standard deviation of the positioning error in the celestial direction; a ver,i represents the element in the third row and i column of matrix A; Based on the variance inflation theory, if there is a faulty satellite, the positioning error μ is regarded as a random variable with the same expectation but an inflated variance, and is represented by μ f express: m f ~N(0,k 2 s 2 )(6) Where k represents the variance expansion coefficient, σ represents the standard deviation of the positioning error; Therefore, in order to detect faulty satellites, a categorical variable Y of the celestial direction is constructed ver As shown in formula (7): When Y ver =1, there is a faulty satellite in the satellite navigation system; when Y ver =0, there is no faulty satellite in the satellite navigation system; similarly, construct the fault detection classification variable Y in the east direction east and north direction fault detection categorical variable Y north as follows: At this point, we have obtained the categorical variables of east, north, and celestial direction; Step 3: Dynamically sample the fault-free set and the faulty set to obtain a labeled sample set; Step 4: Calculate the regression solution of categorical variables using nonparametric estimation methods; Step 5: construct a fault satellite detection network based on the positioning estimation solution and estimation error obtained in step 1, the classification variable obtained in step 2, the labeled sample set obtained in step 3, and the classification variable regression solution obtained in step 4; Step 6: Determine the smoothing factor in the fault satellite detection network according to the navigation continuity requirement; Step seven: Detecting a faulty satellite using the faulty satellite detection network after determining the smoothing factor can improve the detection performance of the faulty satellite; the improved detection performance of the faulty satellite includes improving the sensitivity, accuracy and efficiency of the faulty satellite detection.

2. The method for detecting faulty satellites at a receiver end based on non-parametric estimation as claimed in claim 1, characterized in that: The implementation method of step three is: During the navigation and positioning process, the positioning system obtains n s Position estimation solution Samples, used to estimate the corresponding positioning error samples When the satellite navigation system is fault-free, the distribution of the celestial positioning error is obtained from equation (5): s samples; the sample standard deviation S of this sample set ver It obeys the modified normal distribution, as shown in formula (10): Among them, γ represents the correction coefficient; H0 represents the no-fault situation; According to formula (10), we can get n1 samples. The corresponding categorical variables for the no-fault condition are labeled as n1×1 column vectors with all zeros: y ver,s ＝[0,0,…,0] T (11) When there is a fault in the satellite navigation system, the position error expands k times and the sample standard deviation S ver It follows the following distribution: Among them, H1 indicates that there is a faulty satellite; According to formula (12), we can get n2 samples. The categorical variables corresponding to the fault conditions are labeled as n2×1 column vectors with all elements set to 1: y ver,f ＝[1,1,...,1] T (13) The samples from the non-fault set and the fault set are combined with the corresponding labeled categorical variables as follows to obtain the labeled sample set: y0=[y ver,s ,and ver,f ](15) The distribution of the samples is affected by the standard deviation of the positioning error σ ver The influence of the position error standard deviation σ ver Determined by the geometric configuration; the geometric configuration changes dynamically, so the marked sample set is also dynamically updated.

3. The method for detecting faulty satellites at a receiver end based on non-parametric estimation as claimed in claim 2, characterized in that: The implementation method of step 4 is: The conditional mean of a categorical variable is expressed as follows: In order to simplify the expression, the subscripts representing the east, north and celestial direction of the sample standard deviation S and the categorical variable Y in this step are omitted, and f(S,Y) is the joint probability density function of the sample standard deviation S and the categorical variable Y; Based on the non-parametric estimation method, the joint probability density function f(S,Y) is estimated using the labeled sample set obtained in step 3. The result is shown in formula (17): Among them, λ is the smoothing factor of the Gaussian kernel function, and s i represents the sample from equation (14), y i It means that the corresponding s from formula (15) i A labeled categorical variable; Substitute equation (17) into equation (16) and swap the order of integration: according to Simplifying and reorganizing formula (18), we get the regression solution of categorical variables, and the results are as follows: Among them, the numerator represents the weighted average of the labeled categorical variables; the denominator represents the weighted average from the sample standard deviation S to each sample s i The sum of the Euclidean distances.

4. The method for detecting faulty satellites at a receiver end based on non-parametric estimation as claimed in claim 3, characterized in that: The implementation method of step five is: The fault satellite detection network has five layers, namely: input layer, sampling layer, clustering layer, evaluation layer and detection layer; Input layer: When a satellite fails, the fault deviation projected to the east, north and sky directions changes with the change of the geometric configuration from the satellite to the user receiver; therefore, the positioning data in the three directions should be detected synchronously; the input layer stores the positioning data collected from the receiver and estimates the sample standard deviation S of the positioning result. Its subscript dir represents the three directions of east, north and sky: Sampling layer: According to equations (14) and (15), the labeled sample sets in the east, north and sky directions are obtained respectively; Clustering layer: Use Gaussian kernel function to evaluate the similarity between the positioning data of the input layer and the labeled sample set obtained by the sampling layer; calculate the regression solution of classification variables in three directions based on non-parametric estimation method As shown in formula (19); Evaluation layer: Based on the regression solution of the categorical variables, the switch function is used to determine whether there is a faulty satellite in the satellite navigation system; Among them, R dir is the fault assessment result in the east, north or sky direction, The regression solution for the categorical variable is east, north or celestial direction; Detection layer: Perform Boolean OR operation on the evaluation results of the east, north and sky directions obtained by the evaluation layer to obtain the final fault detection result, as shown below: R=R ver ∨R east ∨R north (22)。 5. The method for detecting faulty satellites at a receiver end based on non-parametric estimation as claimed in claim 4, characterized in that: The implementation method of step six is: False alarm rate P fa Defined as: P fa ={R=0|H0}(23) P fa The maximum permissible value [P fa ] is derived from the continuity requirement, and the results are as follows: Among them, [P fa ] is the maximum allowable false alarm rate; P sat is the prior failure probability of each satellite; n is the number of visible satellites; C req Requirements for navigation continuity; In order to meet the false alarm rate, for all S<T fa , the fault satellite detection network should not detect the fault, that is, it meets the following requirements: Among them, Φ -1 represents the standard normal inverse cumulative distribution function; By iteratively solving equation (25), the minimum value of the smoothing factor λ can be determined: min ; Under the premise of satisfying continuity, in order to maximize the detection capability, in actual use, the smoothing factor λ is set to λ min .

6. The method for detecting faulty satellites at a receiver end based on non-parametric estimation as claimed in claim 5, characterized in that: The implementation method of step seven is: When R = 1, there is a faulty satellite in the satellite navigation system and a fault occurs; When R=0, there is no faulty satellite in the satellite navigation system and no fault occurs.

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