A method for monitoring the autonomous integrity of a pseudo-satellite-assisted GNSS positioning receiver.

Abstract

This invention discloses a receiver autonomous integrity monitoring method for pseudo-satellite-assisted GNSS positioning. The method involves constructing pseudo-satellite observation equations; building a weighting coefficient matrix using the observation matrix and calculating the spatial position accuracy factor; determining the layout range of pseudo-satellites for assisted navigation and positioning, and optimizing pseudo-satellite positions based on a sparrow search algorithm; constructing GNSS satellite observation equations; combining the GNSS satellite and pseudo-satellite systems to complete the positioning solution of the combined system; constructing verification statistics; calculating a fault detection threshold based on the system's false alarm rate and performing a consistency check to determine the presence of a fault; calculating the combined system's protection level under the premise that the system is fault-free; and determining the availability of the RAIM system based on the relationship between the protection level and the alarm limit. This invention, employing the above-mentioned receiver autonomous integrity monitoring method for pseudo-satellite-assisted GNSS positioning, can improve satellite geometry configuration during approach and landing phases, thereby enhancing the fault detection performance and availability of RAIM.

Description

Technical Field

[0001] This invention relates to the field of satellite navigation technology, and in particular to a method for monitoring the autonomous integrity of a receiver in pseudo-satellite-assisted GNSS positioning. Background Technology

[0002] Global Navigation Satellite System (GNSS) provides real-time, high-precision, and all-weather positioning services to users worldwide. With the development of multi-frequency, multi-constellation technology, the number of visible satellites for user receivers has increased, further improving positioning accuracy. However, this also increases the probability of potential satellite and constellation failures to some extent. GNSS integrity monitoring technology measures the confidence level of the positioning results provided by the navigation system and promptly issues warnings to users when the positioning accuracy fails to meet the navigation performance requirements of a specific flight phase.

[0003] In the civil aviation sector, integrity monitoring technology is crucial and a vital means of ensuring aviation operational safety. Receiver Autonomous Integrity Monitor (RAIM) is an Aircraft-based Augmentation System (ABAS) technology that utilizes redundant satellite observations to verify the consistency of observations, enabling rapid fault detection. However, RAIM performance is dependent on the number of visible satellites; when satellite measurements are insufficient, RAIM availability and fault detection performance deteriorate sharply. During approach and landing phases, obstructions often lead to low visibility of GNSS satellites, resulting in insufficient visible satellites and poor geometries. In these situations, traditional RAIM methods cannot meet the stringent navigation performance requirements of the approach and landing phases.

[0004] As an important supplement to navigation satellites, pseudosatellites are positioning signal generators capable of emitting navigation-like signals. Pseudosatellite systems can achieve navigation and positioning in areas with significant obstructions, such as cities, canyons, and indoors where GNSS satellite navigation signals cannot be received. The placement of pseudosatellites is one of the factors affecting positioning accuracy; under the same pseudorange measurement error, a well-distributed pseudosatellite network can significantly reduce positioning error and improve accuracy. During approaches or landings when navigation satellite signal quality is poor, adding pseudosatellites can improve navigation and positioning accuracy. Furthermore, integrating these systems into RAIM can improve fault detection performance and enhance RAIM's usability in complex environments.

[0005] To address this problem, this invention proposes a receiver autonomous integrity monitoring algorithm for pseudosatellite-assisted GNSS positioning. When the number of visible satellites is insufficient, it utilizes ground-deployed pseudosatellite base stations to provide redundant information, enriching navigation measurements and improving integrity monitoring performance during approach and landing phases, thus expanding the application scope of RAIM (Rapid Access Imaging). Simultaneously, by employing a sparrow search algorithm to optimize the pseudosatellite position distribution, the positioning accuracy of the pseudosatellite independent positioning system can be improved, providing safer and more reliable navigation and positioning services for aviation life safety applications. Summary of the Invention

[0006] The purpose of this invention is to provide a receiver autonomous integrity monitoring method for pseudo-satellite assisted GNSS positioning, which can improve satellite geometry during approach and landing phases and enhance the fault detection performance and availability of RAIM.

[0007] To achieve the above objectives, this invention provides a method for monitoring the autonomous integrity of a receiver in pseudo-satellite-assisted GNSS positioning, comprising the following steps:

[0008] Construct the observation matrix of the pseudosatellite system based on the observations and the positions of the pseudosatellites;

[0009] A weighting coefficient matrix is ​​constructed using the observation matrix, and the spatial position precision factor (PDOP) is calculated based on the components of the weighting coefficient matrix.

[0010] The scope of pseudo-satellite deployment for navigation and positioning assistance is determined, and the pseudo-satellite positions are optimized based on the sparrow search algorithm.

[0011] The pseudorange observation equations for GNSS satellites are constructed based on the observations of the user receiver and the positions of visible GNSS satellites.

[0012] By combining GNSS satellites and pseudo-satellite systems, the positioning solution of the combined system is completed;

[0013] Construct test statistics for RAIM fault detection in combined systems;

[0014] Calculate the fault detection threshold based on the system's false alarm rate and perform a consistency check to determine whether a fault exists.

[0015] Perform combined system protection level calculations under the premise that the system is fault-free;

[0016] The availability of the RAIM system can be determined based on the relationship between the protection level and the alarm limit.

[0017] Preferably, the observation matrix of the pseudosatellite system is constructed based on the observations and the positions of the pseudosatellites, including

[0018] The location of the user receiver is , No. The location of the pseudo-satellite is Let n be the number of pseudo-satellites. If the clocks of all pseudo-satellites in the system are synchronized, then the observation equation can be expressed as:

[0019] (1)

[0020] In the formula, This is the difference between the pseudorange measurement and the estimated value of the pseudosatellite; This is the observation matrix for pseudosatellites; The vector representing the parameters to be estimated consists of three coordinate parameters and the receiver clock error parameters corresponding to the pseudo-satellite system. This is the pseudorange error vector;

[0021] The observation matrix of the pseudosatellite system is as follows:

[0022] (2)

[0023] In the formula, To point from the user receiver to the first i The unit vector of a satellite, and the formula for calculating the unit vector is as follows:

[0024] (3).

[0025] Preferably, a weighting coefficient matrix is ​​constructed based on the observation matrix, and the spatial location precision factor (PDOP) is calculated based on the components of the weighting coefficient matrix, including...

[0026] Using the observation matrix G, the weight coefficient matrix H is obtained as follows:

[0027] (4)

[0028] The quality of pseudosatellite geometry is evaluated using the PDOP value. The formula for calculating PDOP is as follows:

[0029] (5)

[0030] Preferably, the scope of the pseudo-satellite layout for auxiliary navigation and positioning is determined, and the pseudo-satellite positions are optimized based on a sparrow search algorithm, including...

[0031] Select a fitness function and establish an optimization problem model.

[0032] The layout area of ​​the pseudo-satellites should be delineated within an appropriate range based on the actual user environment, and a two-dimensional or three-dimensional area centered on the user's landing point should be selected.

[0033] PDOP is selected as the fitness function for the optimization problem, and the three-dimensional position coordinates of the n pseudo-satellite deployment sites are used as optimization variables. The optimal positioning accuracy is obtained by finding the optimal pseudo-satellite deployment strategy.

[0034] (6)

[0035] In the formula, For the first The three-dimensional position coordinates of the pseudo-satellite ; This represents the lower bound of the pseudosatellite deployment area. This marks the upper limit of the pseudosatellite deployment area.

[0036] Population initialization: Set the population size to [value]. The individual dimension is Maximum number of iterations Safety threshold Set the ratio and number of discoverers, followers, and early warning scouts, and group the sparrows within the population into groups. ;initialization As the discoverer, As a follower, To detect and warn, the step size of the change in the three-dimensional position of the pseudo-satellites is determined. Based on the pre-set layout range boundary of the pseudo-satellites, the three-dimensional position coordinates of the pseudo-satellites are randomly generated within the upper and lower boundaries of the range according to the step size. The positions of all pseudo-satellites are then combined to form the position of a sparrow.

[0037] Calculate the fitness function value, that is, calculate the PDOP value under different pseudosatellite configurations.

[0038] Construct a fitness function according to formula (6), substitute the pseudo-satellite position corresponding to the position of each sparrow in the population into the precision factor calculation formula (5), and obtain the corresponding PDOP value of each sparrow.

[0039] Record the location of key sparrows in the population and their corresponding fitness function values.

[0040] Record the optimal position the sparrow has reached in the current iteration. and the corresponding optimal fitness value The worst position the sparrow has ever been and the corresponding worst fitness value And update the historical best position, worst position, best fitness value and worst fitness value for all iterations;

[0041] Iterative update: Based on the fitness values, the discoverer, follower, and early warning scout in the current sparrow population are reselected. The positions of the discoverer, follower, and early warning scout are updated sequentially according to the sparrow position update formula, and the corresponding fitness function values ​​are calculated. After the sparrow position is updated, a global search strategy is added. By setting a global search probability, a global search is performed with a certain probability in each iteration.

[0042] Determine if the algorithm meets the termination condition. If it does, end the iteration to obtain the optimized position of the pseudo-satellite layout and the optimized PDOP value. Otherwise, repeat the calculation of PDOP values ​​under different pseudo-satellite layouts, the position of key sparrows in the population and their corresponding fitness function values, and iterative updates.

[0043] Preferably, the pseudorange observation equations for GNSS satellites are constructed based on the observations from the user receiver and the positions of visible GNSS satellites, including...

[0044] Based on satellite observations and ephemeris information from GNSS satellites, the positions of GNSS satellites are calculated using ephemeris data. In GNSS measurements, the linearized pseudorange observation equation is:

[0045] (7)

[0046] In the formula, This is the difference between the pseudorange measurement and the estimated value of the GNSS satellite. This is the observation matrix for GNSS satellites; The vector of parameters to be estimated consists of three coordinate parameters and the receiver clock error parameters corresponding to the GNSS satellite system. This is the pseudorange error vector.

[0047] Preferably, GNSS satellites and pseudosatellite systems are combined to complete the positioning calculation of the combined system, including...

[0048] By synchronizing the GNSS satellite system with the pseudosatellite system, and combining the observation equations of the GNSS satellites and the pseudosatellites, a linearized measurement equation for the combined system is obtained:

[0049] (8)

[0050] In the formula, , , , It consists of three coordinate parameters and the receiver clock error parameters corresponding to the satellite system;

[0051] According to the principle of least squares iteration, the least squares solution is:

[0052] (9)

[0053] Substituting equation (8) into equation (9), we obtain the approximate pseudorange as follows:

[0054] (10)

[0055] The pseudo-range residual vector is obtained by the difference between equation (8) and equation (10):

[0056] (11)

[0057] In the above formula, Let be the identity matrix, and let... Then we have:

[0058] (12).

[0059] Preferably, the test statistics for RAIM fault detection of the constructed combined system include

[0060] The residual vector contains error information from the pseudorange observations. The residual vector is used to construct the test statistic for snapshot RAIM fault detection.

[0061] (13)

[0062] Observation noise The components in the data are independent of each other, and all satellites... ,but Obeying the degree of freedom of Distribution, if the pseudorange error component contains faults, then Obeying the degree of freedom Decentralization distributed.

[0063] Preferably, a fault detection threshold is calculated based on the system's false alarm rate, and a consistency check is performed to determine whether a fault exists, including...

[0064] The false alarm rate given by the system can be calculated. Detection threshold :

[0065] (14)

[0066] in, The variance representing the pseudorange observation error. This represents the sum of squares of the pseudo-range residuals. express The probability, Describing the degrees of freedom as of The probability density function of the distribution. The false alarm rate specified by the system;

[0067] Then, based on the calculated detection threshold, the unit weight error can be obtained. The detection threshold is:

[0068] (15)

[0069] Test statistic With detection threshold In comparison, if the test statistic is greater than the detection threshold, a fault is considered detected; otherwise, no fault is considered detected. When a fault is detected, a test statistic needs to be constructed for each satellite. :

[0070] (16)

[0071] In the formula, For the first The pseudorange residuals of the satellites express The first in OK The column elements are used to calculate the detection threshold for a single satellite based on the false alarm rate. :

[0072] (17)

[0073] Detection threshold and corresponding number Inspection statistics of satellites If a comparison is made, Then it means the first One of the satellites malfunctioned.

[0074] Preferably, the combined system protection level calculation is performed under the premise that there are no system faults, including

[0075] Calculate the slope of each satellite , Defined as the slope of the linear relationship between the positioning error and the test statistic:

[0076] (18)

[0077] In the formula, , , Representation matrix The Line number List, For matrix The Line number List;

[0078] Find maximum value :

[0079] (19)

[0080] Find the minimum value of the test statistic that satisfies the false negative rate requirement:

[0081] (20)

[0082] In the formula, To meet the requirements for false alarm rate The minimum value of the non-central parameter of the distribution.

[0083] Horizontal protection level It can be determined by the following formula:

[0084] (twenty one)

[0085] Preferably, the availability of the RAIM system is determined based on the relationship between the protection level and the alarm limit, including

[0086] The calculated horizontal protection level Alarm limits required by system performance indicators In contrast, if the protection level is less than the alarm limit, that is...

[0087] (twenty two)

[0088] If the calculated protection level is greater than the alarm limit, then RAIM is considered usable; otherwise, RAIM is considered unusable.

[0089] Therefore, the present invention employs the above-mentioned receiver autonomous integrity monitoring method for pseudo-satellite-assisted GNSS positioning, and its technical effects are as follows:

[0090] (1) This invention proposes a pseudo-satellite layout method based on the sparrow search algorithm, which improves the geometric structure of pseudo-satellites, enhances navigation and positioning accuracy, and has certain engineering application value;

[0091] (2) This invention proposes a positioning method using a combination of pseudo-satellites and GNSS satellites, which can be used to perform high-precision positioning when the number of GNSS satellites is insufficient, thereby improving the positioning quality;

[0092] (3) This invention proposes a sparrow search algorithm with a global search strategy, which improves the search capability of the algorithm for the global optimal solution and avoids getting trapped in local optima;

[0093] (4) This invention proposes an autonomous integrity monitoring method for a receiver of a pseudo-satellite and GNSS satellite combined system, which can provide integrity monitoring in environments or areas with severe obstruction, ensuring aviation life safety applications;

[0094] (5) This invention provides a new calculation method for the RAIM protection level of a pseudo-satellite and GNSS satellite combined system, which can reduce the redundancy protection level and improve RAIM availability.

[0095] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0096] Figure 1 This is a flowchart of a method for monitoring the autonomous integrity of a pseudo-satellite-assisted GNSS positioning receiver;

[0097] Figure 2 This is a schematic diagram illustrating the use of satellite positioning during the approach and landing phases;

[0098] Figure 3 This is a schematic diagram of the optimized layout of pseudo-satellites. Detailed Implementation

[0099] The technical solution of the present invention will be further described below with reference to the accompanying drawings and embodiments.

[0100] Unless otherwise defined, the technical or scientific terms used in this invention shall have the ordinary meaning as understood by one of ordinary skill in the art to which this invention pertains.

[0101] Example 1

[0102] like Figure 1 As shown, this invention provides a method for monitoring the autonomous integrity of a receiver in pseudo-satellite-assisted GNSS positioning, comprising the following steps:

[0103] Step 1: Construct pseudosatellite observation equations based on pseudorange observations and pseudosatellite positions.

[0104] The positioning principle of pseudosatellites is similar to that of GNSS satellites. The positioning accuracy of the system is related to the geometric spatial distribution of the pseudosatellites. The accuracy factor is an important indicator for measuring the spatial geometric layout. Under the premise of the same pseudorange measurement error, the smaller the accuracy factor value, the better the geometric spatial layout of the pseudosatellites, and the higher the positioning accuracy.

[0105] Let the location of the user receiver be... , No. The location of the pseudo-satellite is Let n be the number of pseudo-satellites. Assuming that the clocks of all pseudo-satellites in the system are synchronized, the observation equation can be expressed as:

[0106]

[0107] In the formula, This is the difference between the pseudorange measurement and the estimated value of the pseudosatellite; This is the observation matrix for pseudosatellites; The vector representing the parameters to be estimated consists of three coordinate parameters and the receiver clock error parameters corresponding to the pseudo-satellite system. This is the pseudorange error vector.

[0108] The pseudosatellite observation matrix is ​​as follows:

[0109]

[0110] In the formula, To point from the user receiver to the first The unit vector of a satellite. The formula for calculating the unit vector is as follows:

[0111]

[0112] Step 2: Construct a weighting coefficient matrix using the observation matrix and calculate the spatial location precision factor.

[0113] Using the observation matrix G, the weight coefficient matrix H can be obtained as follows:

[0114]

[0115] Spatial position precision factor This reflects the influence of spatial position errors and can be utilized. The magnitude of the value is used to evaluate the quality of the pseudo-satellite geometry. The calculation formula is as follows:

[0116]

[0117] Step 3: Determine the scope of pseudo-satellite deployment for navigation and positioning assistance, and optimize pseudo-satellite positions based on the sparrow search algorithm.

[0118] The placement of pseudosatellites is a combinatorial optimization problem, and intelligent optimization methods have shown good results in solving such problems. The Sparrow Search Algorithm (SSA) is a swarm intelligence optimization algorithm that searches for the global optimum by simulating the foraging process of sparrows. Based on traditional search algorithms, it adds a reconnaissance and search mechanism, resulting in stronger optimization capabilities and faster convergence speed.

[0119] The basic idea of ​​the SSA algorithm is to divide the population into groups of sparrows: discoverers, followers, and scouts. During the search and optimization process, the discoverers are the explorers in the sparrow search algorithm, responsible for finding new potential solutions in the search space. Discoverers typically select points randomly within the search space, allowing for a relatively large search range. The formula for updating the discoverer's position is as follows:

[0120]

[0121] In the formula, for During the nth iteration The discoverer was in the first The position of the dimension Represents the current iteration number. Indicates the dimension of the variable; This represents the maximum number of iterations. It is a random number; It is a random number that follows a normal distribution; Represent a A matrix in which every element is 1; Indicates the warning value; Indicates a safe value. When When this indicates that no individuals in the current population have detected danger, the discoverer can conduct a broad search; when This indicates that there are predators in the foraging environment where the sparrows are currently located. Some individuals have discovered the danger and alerted other individuals in the population. At this time, all sparrows in the population need to quickly fly to other safe places to forage.

[0122] The follower's position is influenced by the discoverer's position; if the follower's energy is greater than the current discoverer's, it will replace them. The follower's position update formula is as follows:

[0123]

[0124] In the formula, for During the nth iteration The first follower in the The position of the dimension; for The optimal position of the discoverer in the next iteration. for The position of the worst global position in the next iteration; Represent a A matrix, where each element is randomly assigned the value 1 or -1; Represent a A matrix in which every element is 1; These are random numbers that follow a normal distribution. Index representing a follower individual in the population; This indicates the population size, that is, the number of individual sparrows in the population. When When, it indicates that the fitness value is poor. One of the followers was in poor condition and extremely hungry, needing to fly to other places to find food and obtain more energy.

[0125] A small number of individuals in the population act as scouts and early warning systems. When danger is detected, they immediately sound the alarm and quickly move to a safer area to gain a better position. When danger is detected, the population will protect itself by updating the positions of the scouts and early warning systems using the following formula:

[0126]

[0127] In the formula, for During the nth iteration The reconnaissance and early warning personnel in the The position of the dimension; for The global optimal position at the next iteration; The step size control parameter is used to control the position, and its value is a random number that follows a normal distribution with a mean of 0 and a variance of 1. , which is a random number within that range; This represents the fitness value of the current individual sparrow. Indicates the optimal fitness value; This represents the worst fitness value; Avoid having a denominator of 0. When This indicates that the sparrows are on the fringes of the population and extremely vulnerable to predators. This indicates that the sparrows in the middle of the group are aware of the danger and need to move closer to other sparrows to minimize their risk of being preyed upon.

[0128] Based on the search and optimization principle of the sparrow search algorithm, a pseudo-satellite layout optimization method is proposed. The main steps of the algorithm are as follows:

[0129] (1) Select the fitness function and establish the optimization problem model.

[0130] Based on the actual user environment, define the layout area of ​​the pseudo-satellite within a suitable range, and select a two-dimensional or three-dimensional area centered on the user's landing point, such as a circular or square area, with a recommended diameter or side length of not less than 100m.

[0131] Considering extreme cases, when all GNSS satellites are blocked, only pseudosatellites can be used for positioning. In this case, the number of pseudosatellites must reach the minimum number of positioning satellites. To achieve higher positioning accuracy, select... To optimize the fitness function of the problem, the three-dimensional position coordinates of the n pseudo-satellite deployment sites are used as optimization variables. The optimal positioning accuracy is obtained by finding the optimal pseudo-satellite deployment strategy.

[0132]

[0133] In the formula, For the first The three-dimensional position coordinates of the pseudo-satellite ; This represents the lower bound of the pseudosatellite deployment area. This represents the upper limit of the pseudosatellite deployment area.

[0134] (2) Population initialization

[0135] Set the population size to The individual dimension is Maximum number of iterations Safety threshold Set the ratio and number of discoverers, followers, and early warning scouts to group the sparrows within the population. .initialization As the discoverer, As a follower, For reconnaissance and early warning: Determine the step size for the change of the three-dimensional position of the pseudo-satellites. Based on the pre-set layout range boundary of the pseudo-satellites, randomly generate the three-dimensional position coordinates of the pseudo-satellites within the upper and lower boundaries of the range according to the step size, and combine the positions of all pseudo-satellites to form the position of a sparrow.

[0136] (3) Calculate the fitness function value, that is, calculate the PDOP value under different pseudo-satellite layouts.

[0137] Construct the fitness function according to formula (9), and substitute the pseudo-satellite position corresponding to the position of each sparrow in the population into the precision factor calculation formula (5) to obtain the corresponding PDOP value of each sparrow.

[0138] (4) Record the location of key sparrows in the population and their corresponding fitness function values.

[0139] Record the optimal position the sparrow has reached in the current iteration. and the corresponding optimal fitness value The worst position the sparrow has ever been and the corresponding worst fitness value It updates the historical best position, worst position, best fitness value, and worst fitness value for all iterations.

[0140] (5) Iterative update

[0141] Based on the fitness values, the discoverer, follower, and early warning scout in the current sparrow population are reselected. The positions of the discoverer, follower, and early warning scout are updated sequentially according to the sparrow position update formulas (6), (7), and (8), and the corresponding fitness function values ​​are calculated. After the sparrow position is updated, a global search strategy is added. By setting a global search probability, a global search is performed with a certain probability in each iteration.

[0142] Determine if the algorithm meets the termination condition. If it does, end the iteration and obtain the optimized position of the pseudo-satellite layout and the optimized PDOP value. Otherwise, repeat (3) to (5).

[0143] Step 4: Construct the observation equations for GNSS satellites based on the user receiver's observations and the positions of visible GNSS satellites.

[0144] Information such as satellite observations and ephemeris data from GNSS satellites is collected, and the positions of the GNSS satellites are calculated based on the ephemeris. In GNSS measurements, the linearized pseudorange observation equation is:

[0145]

[0146] In the formula, This is the difference between the pseudorange measurement and the estimated value of the GNSS satellite. This is the observation matrix for GNSS satellites; The vector of parameters to be estimated consists of three coordinate parameters and the receiver clock error parameters corresponding to the GNSS satellite system. This is the pseudorange error vector.

[0147] Step 5: Combine the GNSS satellite and pseudo-satellite systems to complete the positioning calculation of the combined system.

[0148] Assuming the GNSS satellite system and the pseudo-satellite system are time-synchronized, combining the observation equations of the GNSS satellites and the pseudo-satellites yields the linearized measurement equations for the combined system:

[0149]

[0150] In the formula, , , , It consists of three coordinate parameters and the receiver clock error parameters corresponding to the satellite system.

[0151] According to the principle of least squares iteration, the least squares solution can be obtained as follows:

[0152]

[0153] Substituting equation (12) into equation (11), we can obtain the approximate pseudorange as follows:

[0154]

[0155] The pseudorange residual vector can be obtained from the difference between equation (11) and equation (13):

[0156]

[0157] In the above formula, Let be the identity matrix. Then we have:

[0158]

[0159] Step Six: Construct the test statistic for RAIM fault detection of the combined system.

[0160] The residual vector contains error information from the pseudorange observations, and the test statistic for snapshot RAIM can be constructed using the residual vector:

[0161]

[0162] Assuming observation noise The components in the data are independent of each other, and all satellites... ,but Obeying the degree of freedom of Distribution. If the pseudorange error component contains faults, then Obeying the degree of freedom Decentralization distributed.

[0163] Step 7: Calculate the fault detection threshold based on the system's false alarm rate and perform a consistency check to determine if a fault exists.

[0164] The false alarm rate given by the system can be calculated. Detection threshold :

[0165]

[0166] in, The variance representing the pseudorange observation error. This represents the sum of squares of the pseudo-range residuals. express The probability, Describing the degrees of freedom as of The probability density function of the distribution. The false alarm rate is the system's defined rate.

[0167] Then, based on the calculated detection threshold, the unit weight error can be obtained. The detection threshold is:

[0168]

[0169] Test statistic With detection threshold In comparison, if the test statistic is greater than the detection threshold, a fault is considered to have been detected; otherwise, no fault is considered to have been detected.

[0170] When a fault is detected, a test statistic needs to be constructed for each satellite. :

[0171]

[0172] In the formula, For the first The pseudorange residuals of the satellites express The first in OK Column elements. Calculate the detection threshold for a single satellite based on the false alarm rate. :

[0173]

[0174] Detection threshold and corresponding number Inspection statistics of satellites If a comparison is made, Then it means the first One of the satellites malfunctioned.

[0175] Step 8: Perform combined system protection level calculation under the premise that there are no system faults.

[0176] (1) Calculate the slope of each satellite. , Defined as the slope of the linear relationship between the positioning error and the test statistic:

[0177]

[0178] In the formula, , , Representation matrix The Line number List, For matrix The Line number List.

[0179] (2) Find maximum value :

[0180]

[0181] (3) Find the minimum value of the test statistic that satisfies the false alarm rate requirement:

[0182]

[0183] In the formula, To meet the requirements for false alarm rate The minimum value of the non-central parameter of the distribution.

[0184] (4) Horizontal protection level It can be determined by the following formula:

[0185]

[0186] Step 9: Determine the availability of the RAIM system based on the relationship between protection level and alarm limit.

[0187] The calculated horizontal protection level Alarm limits required by system performance indicators In contrast, if the protection level is less than the alarm limit, that is...

[0188]

[0189] If the calculated protection level is greater than the alarm limit, then RAIM is considered usable. If the calculated protection level is greater than the alarm limit, then RAIM is considered unusable.

[0190] Therefore, the above-mentioned pseudo-satellite-assisted GNSS positioning receiver autonomous integrity monitoring method can improve the satellite geometry configuration during approach and landing phases, and enhance the fault detection performance and availability of RAIM.

[0191] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit them. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the technical solutions of the present invention, and these modifications or equivalent substitutions cannot cause the modified technical solutions to deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. A method for monitoring the autonomous integrity of a receiver in pseudo-satellite-assisted GNSS positioning, characterized in that, Includes the following steps: Construct the observation matrix of the pseudosatellite system based on the observations and the positions of the pseudosatellites; A weighting coefficient matrix is ​​constructed using the observation matrix, and the spatial position precision factor (PDOP) is calculated based on the components of the weighting coefficient matrix. Determine the scope of pseudo-satellite deployment for navigation and positioning assistance, and optimize pseudo-satellite positions based on the sparrow search algorithm, including: Select a fitness function and establish an optimization problem model; The layout area of ​​the pseudo-satellites should be delineated within an appropriate range based on the actual user environment, and a two-dimensional or three-dimensional area centered on the user's landing point should be selected. PDOP is selected as the fitness function for the optimization problem. The three-dimensional position coordinates of the n pseudo-satellite deployment sites are used as optimization variables. The optimal positioning accuracy is obtained by finding the optimal pseudo-satellite deployment strategy, as detailed below: （1） In the formula, For the first The three-dimensional position coordinates of the pseudo-satellite ; This represents the lower bound of the pseudosatellite deployment area. This marks the upper limit of the pseudosatellite deployment area. Population initialization: Set the population size to [value]. The individual dimension is Maximum number of iterations Safety threshold Set the ratio and number of discoverers, followers, and early warning scouts, and group the sparrows within the population into groups. ;initialization As the discoverer, As a follower, To detect and warn, the step size of the change in the three-dimensional position of the pseudo-satellites is determined. Based on the pre-set layout range boundary of the pseudo-satellites, the three-dimensional position coordinates of the pseudo-satellites are randomly generated within the upper and lower boundaries of the range according to the step size. The positions of all pseudo-satellites are then combined to form the position of a sparrow. Calculate the fitness function value, that is, calculate the PDOP value under different pseudosatellite layouts; Construct a fitness function according to formula (1), substitute the pseudosatellite position corresponding to the position of each sparrow in the population into the precision factor calculation formula, and obtain the corresponding PDOP value of each sparrow. Record the location of key sparrows in the population and their corresponding fitness function values; Record the optimal position the sparrow has reached in the current iteration. and the corresponding optimal fitness value The worst position the sparrow has ever been and the corresponding worst fitness value And update the historical best position, worst position, best fitness value and worst fitness value for all iterations; Iterative update: Based on the fitness values, the discoverer, follower, and early warning scout in the current sparrow population are reselected. The positions of the discoverer, follower, and early warning scout are updated sequentially according to the sparrow position update formula, and the corresponding fitness function values ​​are calculated. After the sparrow position is updated, a global search strategy is added. By setting a global search probability, a global search is performed with a certain probability in each iteration. Determine if the algorithm meets the termination condition. If it does, end the iteration to obtain the optimized position of the pseudo-satellite layout and the optimized PDOP value. Otherwise, repeat the calculation of PDOP value under different pseudo-satellite layouts, the position of key sparrows in the population and their corresponding fitness function values, and iterative update. The pseudorange observation equations for GNSS satellites are constructed based on the observations of the user receiver and the positions of visible GNSS satellites. By combining GNSS satellites and pseudo-satellite systems, the positioning solution of the combined system is completed; Construct test statistics for RAIM fault detection in combined systems; Calculate the fault detection threshold based on the system's false alarm rate and perform a consistency check to determine whether a fault exists. Perform combined system protection level calculations under the premise that the system is fault-free; The availability of the RAIM system can be determined based on the relationship between the protection level and the alarm limit.

2. The method for monitoring the autonomous integrity of a pseudo-satellite-assisted GNSS positioning receiver according to claim 1, characterized in that, Construct an observation matrix for the pseudosatellite system based on the observations and the pseudosatellite positions, including: The location of the user receiver is , Let be the number of pseudo-satellites. Assuming all pseudo-satellites in the system have synchronized clocks, the observation equation can be expressed as: （2） In the formula, This is the difference between the pseudorange measurement and the estimated value of the pseudosatellite; This is the observation matrix for pseudosatellites; The vector representing the parameters to be estimated consists of three coordinate parameters and the receiver clock error parameters corresponding to the pseudo-satellite system. This is the pseudorange error vector; The observation matrix of the pseudosatellite system is as follows: （3） In the formula, To point from the user receiver to the first The unit vector of a satellite, and the formula for calculating the unit vector is as follows: （4）。 3. The method for monitoring the autonomous integrity of a pseudo-satellite-assisted GNSS positioning receiver according to claim 1, characterized in that, A weighting coefficient matrix is ​​constructed based on the observation matrix, and the spatial location precision factor (PDOP) is calculated based on the components of the weighting coefficient matrix, including: Using the observation matrix G, the weight coefficient matrix H is obtained as follows: （5） The quality of pseudosatellite geometry is evaluated using the PDOP value. The formula for calculating PDOP is as follows: （6）。 4. The method for monitoring the autonomous integrity of a pseudo-satellite-assisted GNSS positioning receiver according to claim 2, characterized in that, Based on the user receiver's observations and the positions of visible GNSS satellites, a pseudorange observation equation for GNSS satellites is constructed, including: Based on satellite observations and ephemeris information from GNSS satellites, the positions of GNSS satellites are calculated using ephemeris data. In GNSS measurements, the linearized pseudorange observation equation is: （7） In the formula, This is the difference between the pseudorange measurement and the estimated value of the GNSS satellite. This is the observation matrix for GNSS satellites; The vector of parameters to be estimated consists of three coordinate parameters and the receiver clock error parameters corresponding to the GNSS satellite system. This is the pseudorange error vector.

5. The method for monitoring the autonomous integrity of a pseudo-satellite-assisted GNSS positioning receiver according to claim 4, characterized in that, Combining GNSS satellites and pseudosatellite systems to complete the positioning calculation of the combined system includes: By synchronizing the GNSS satellite system with the pseudosatellite system, and combining the observation equations of the GNSS satellites and the pseudosatellites, a linearized measurement equation for the combined system is obtained: （8） In the formula, , , , It consists of three coordinate parameters and the receiver clock error parameters corresponding to the satellite system; According to the principle of least squares iteration, the least squares solution is: （9） Substituting equation (8) into equation (9), we obtain the approximate pseudorange as follows: （10） The pseudo-range residual vector is obtained by the difference between equation (8) and equation (10): （11） In the above formula, Let be the identity matrix, and let... Then we have: （12）。 6. The method for monitoring the autonomous integrity of a pseudo-satellite-assisted GNSS positioning receiver according to claim 1, characterized in that, The test statistics for RAIM fault detection in a combined system are constructed, including: The residual vector contains error information from the pseudorange observations. The residual vector is used to construct the test statistic for snapshot RAIM fault detection. （13） Represents the pseudorange residual vector, observation noise The components in the data are independent of each other, and all satellites... ,but Obeying the degree of freedom of Distribution, if the pseudorange error component contains faults, then Obeying the degree of freedom Decentralization distributed, This represents the variance of the pseudorange observation error.

7. The method for monitoring the autonomous integrity of a pseudo-satellite-assisted GNSS positioning receiver according to claim 1, characterized in that, The system calculates the fault detection threshold based on the false alarm rate and performs a consistency check to determine whether a fault exists, including: Calculate based on the false alarm rate given by the system. Detection threshold : （14） in, The variance representing the pseudorange observation error. This represents the sum of squares of the pseudo-range residuals. express The probability, Describing the degrees of freedom as of The probability density function of the distribution. The false alarm rate specified by the system; Then, based on the calculated detection threshold, the unit weight error is obtained. The detection threshold is: （15） The standard deviation of the pseudorange observation error is represented by the test statistic. With detection threshold In comparison, if the test statistic is greater than the detection threshold, a fault is considered detected; otherwise, no fault is considered detected. When a fault is detected, a test statistic needs to be constructed for each satellite. : （16） In the formula, For the first The pseudorange residuals of the satellites express The first in OK The column elements are used to calculate the detection threshold for a single satellite based on the false alarm rate. : （17） Detection threshold and corresponding number Inspection statistics of satellites If a comparison is made, Then it means the first One of the satellites malfunctioned.

8. The method for monitoring the autonomous integrity of a pseudo-satellite-assisted GNSS positioning receiver according to claim 1, characterized in that, Perform combined system protection level calculations under the premise that the system is fault-free, including: Calculate the slope of each satellite , Defined as the slope of the linear relationship between the positioning error and the test statistic: （18） In the formula, , , Representation matrix The Line number List, For matrix The Line number List; Find maximum value : （19） Find the minimum value of the test statistic that satisfies the false negative rate requirement: （20） In the formula, To meet the requirements for false alarm rate The minimum value of the non-central parameter of the distribution; Horizontal protection level Determined by the following formula: （21） In the formula, Indicates the level of horizontal protection.

9. The method for monitoring the autonomous integrity of a pseudo-satellite-assisted GNSS positioning receiver according to claim 1, characterized in that, Determining the availability of a RAIM system based on the relationship between protection level and alarm limits includes... The calculated horizontal protection level Alarm limits required by system performance indicators In contrast, if the protection level is less than the alarm limit, that is... （22） If the calculated protection level is greater than the alarm limit, then RAIM is considered usable; otherwise, RAIM is considered unusable.

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