Navigation integrity assessment method and system integrating multiple factors

Abstract

The present application relates to a kind of navigation integrity evaluation method and system of comprehensive multi-factor influence, belong to satellite navigation integrity monitoring technical field, solve the problem that focusing single rough error processing risk in prior art, lack multi-factor collaborative influence analysis, cannot truly reflect the problem of positioning uncertainty.Method includes: obtaining observation dataset, ephemeris data and receiver approximate three-dimensional coordinates, constructs function model, calculates final correction number approximation, determines final posterior standard deviation;Based on all rough error containing observation value, calculate the maximum rough error clustering number, determine multi-rough error processing risk;Based on observation dataset, calculate single-system positioning result, determine ambiguity fixing error risk;According to final correction number approximation, final posterior standard deviation, multi-rough error processing risk and ambiguity fixing error risk, determine navigation integrity evaluation result.The present application realizes navigation integrity evaluation under the influence of multi-factor, improves the quantitative accuracy of the uncertainty of positioning result.

Description

Technical Field

[0001] This invention relates to the field of satellite navigation integrity monitoring technology, and in particular to a navigation integrity assessment method and system that integrates the influence of multiple factors. Background Technology

[0002] GNSS (Global Navigation Satellite System) is the spatiotemporal cornerstone of modern information society, providing indispensable high-precision positioning, navigation, and timing services for key sectors such as transportation, communication, energy, defense, and unmanned intelligent systems. However, with the accelerated deployment of highly autonomous systems such as autonomous driving and embodied intelligent robots, navigation systems not only need to provide high-precision location information but also must possess the ability to assess their own performance reliability in real time—that is, integrity. Integrity research aims to quantify the uncertainty of positioning results, provide timely warnings when navigation system malfunctions, and ensure that safety mechanisms are triggered promptly when dangerous deviations occur, preventing accidents caused by navigation and positioning errors. Especially in challenging scenarios such as urban canyons, tunnel entrances and exits, and complex electromagnetic environments, traditional accuracy indicators can no longer reflect real risks. Only through rigorous integrity mechanisms and accurate assessment of navigation and positioning deviations can the leap from "being able to locate" to "being able to rely on" be achieved. Therefore, conducting research on navigation and positioning integrity is not only a core technological support for improving the resilience of PNT (high-precision positioning, navigation and timing) systems, but also a strategic cornerstone for promoting the safe, reliable and large-scale application of intelligent transportation, unmanned systems and future aerospace infrastructure.

[0003] Existing navigation integrity assessment methods mostly focus on handling risks associated with single gross errors, with insufficient research on robustness handling in scenarios with multiple gross errors, reliability verification of ambiguity fixation, and the synergistic effects of system errors (such as multipath errors). In complex urban, canyon, forest, or electromagnetic interference environments, residual gross errors and ambiguity fixation errors are unavoidable. The posterior standard deviation of traditional filter outputs often underestimates the true error, leading to system overconfidence and an inability to accurately reflect positioning uncertainty.

[0004] Therefore, there is an urgent need for a comprehensive navigation integrity assessment method and system that takes into account multiple factors, including the risks of handling gross errors, the risk of ambiguity fixation errors, and the impact of post-test standard deviation, to assess the integrity of positioning results and solve the problem of unreasonable integrity assessment of GNSS navigation and positioning results in complex environments. Summary of the Invention

[0005] Based on the above analysis, the embodiments of the present invention aim to provide a navigation integrity assessment method and system that integrates the influence of multiple factors, in order to solve the problems of the prior art that focus on handling risks of single gross errors, lack multi-factor synergistic influence analysis, and cannot truly reflect positioning uncertainty, thereby realizing navigation integrity assessment under the influence of multiple factors and improving the quantitative accuracy of positioning uncertainty.

[0006] On one hand, embodiments of the present invention provide a navigation integrity assessment method that integrates the influence of multiple factors, including: Acquire observation datasets, ephemeris data, and approximate three-dimensional coordinates of the receiver to construct a function model; wherein, the observation datasets include observation values ​​from multiple navigation systems; Using the observed dataset, calculate the final correction approximation of the parameters to be estimated in the function model, and determine the final posterior standard deviation; Based on the final correction approximation and the final posterior standard deviation, the observations containing gross errors are extracted from the observation dataset; based on all the observations containing gross errors, the maximum number of gross error clusters is calculated to determine the risk of multiple gross error processing. Based on the observation dataset and the approximate final correction value, calculate the single-system positioning result for each navigation system and determine the risk of ambiguity fixation error. Based on the observed dataset and the corresponding final posterior standard deviation, the risk of multiple gross errors, and the risk of ambiguity fixation error, the navigation integrity assessment result is determined.

[0007] Furthermore, using the observed dataset, the final correction approximation of the parameters to be estimated in the function model is calculated, and the final a posteriori standard deviation is determined, including: Multiple minimum observation subsets are extracted from the observation dataset. Based on the function model, the correction approximation value of the parameter to be estimated corresponding to each minimum observation subset is calculated. The best correction approximation value is determined from all the correction approximation values. Based on the optimal correction approximation, the observation dataset, and the function model, calculate the final correction approximation and the final a posteriori standard deviation.

[0008] Further, multiple minimum observation subsets are extracted from the observation dataset. Based on the function model, the approximate correction value of the parameter to be estimated corresponding to each minimum observation subset is calculated. The optimal correction approximate value is determined from all the correction approximate values, including: Step a: Extract the minimum observation subset from the observation dataset, and calculate the approximate value of the correction and the post-hoc residual matrix corresponding to the minimum observation subset based on the function model; Step b: Based on the post-hoc residual matrix and gross error threshold, calculate the inlier rate corresponding to the minimum observation subset; Step c: Update the current maximum interior rate based on the interior rate and the current maximum interior rate; Step d: Based on the updated current maximum inlier rate, determine whether the subset extraction stopping condition has been met. If the subset extraction stopping condition has been met, determine the optimal correction approximation value based on the correction approximation value corresponding to the updated current maximum inlier rate. If the subset extraction stopping condition has not been met, return to step a.

[0009] Further, based on the final correction approximation, the final posterior standard deviation, and the function model, the observations containing outliers are extracted from the observation dataset; based on all the observations containing outliers, the maximum outlier cluster number is calculated to determine the risk of handling multiple outliers, including: Based on the observation dataset, the final correction approximation, and the function model, calculate the final a posteriori residual corresponding to each observation value; Based on the final a posteriori residual of each observation and the gross error threshold, extract the observations containing gross errors from the observation dataset; Based on all the observations containing gross errors, the final correction approximation, and the final a posteriori standard deviation, the maximum number of gross error clusters is calculated to determine the risk of multiple gross error handling.

[0010] Furthermore, based on all the observations containing outliers, the final correction approximation, and the final a posteriori standard deviation, the maximum outlier cluster number is calculated to determine the risk of handling multiple outliers, including: Based on the final posterior standard deviation, the clustering distance threshold is determined; The maximum number of outlier clusters is calculated based on the final a posteriori residuals corresponding to all the observations containing outliers and the clustering distance threshold. The multi-gross handling risk is calculated based on the number of all observations containing gross errors and the number of the largest gross error cluster.

[0011] Furthermore, the risk of handling multiple gross errors is calculated using the following formula: In the formula, This indicates the risk of handling multiple gross errors; This represents the probability of gross error handling failure. ,in, This represents the maximum number of gross clusters. This indicates the number of all observations containing gross errors; , This represents the risk assessment coefficient.

[0012] Furthermore, based on the observation dataset and the final correction approximation, the single-system positioning result corresponding to each navigation system is calculated to determine the ambiguity fixation error risk, including: Based on the approximate final correction value and the function model, gross errors are removed from the observation dataset to obtain the corrected observation dataset; The ambiguity of the corrected observation dataset is solved to determine the fixed ambiguity; For each observation value of the navigation system in the corrected observation dataset, the corresponding single-system positioning result is calculated based on the final correction approximation and the fixed ambiguity. Based on the positioning results of each single system, the risk of ambiguity fixation error is calculated.

[0013] Further, ambiguity is solved on the corrected observation dataset to determine fixed ambiguities, including: The ambiguity of the corrected observation dataset is solved to determine the optimal ambiguity and the second-best ambiguity, and to determine whether the optimal ambiguity is reliable. If the optimal ambiguity is reliable, then the optimal ambiguity is determined as the fixed ambiguity.

[0014] Furthermore, the navigation integrity assessment results include the protection level in different spatial directions; Based on the observed dataset and the corresponding final posterior standard deviation, the risk of multiple gross errors, and the risk of ambiguity fixation error, the navigation integrity assessment result is determined, including: Extract the corresponding three-dimensional coefficient matrix and variance matrix from the observation dataset; Based on the three-dimensional coefficient matrix, the variance matrix, and the final posterior standard deviation, the final posterior variance for different spatial directions is determined. The protection level for different spatial orientations is determined based on each of the final posterior variances, the multiple gross error handling risk, and the ambiguity fixation error risk.

[0015] On the other hand, embodiments of the present invention provide a navigation integrity assessment system that integrates the influence of multiple factors, including: An observation acquisition module is used to acquire an observation dataset and approximate three-dimensional coordinates of a receiver; wherein, the observation dataset includes observations from multiple navigation systems; The gross error processing module is used to calculate the final correction approximation and the final a posteriori standard deviation of the parameter to be estimated based on the observation dataset. The gross error processing module is further configured to extract the observations containing gross errors from the observation dataset based on the final correction approximation and the final posterior standard deviation; and to calculate the maximum gross error cluster number based on all the observations containing gross errors to determine the risk of multiple gross error processing. The ambiguity fixing module is used to observe the dataset and the approximate value of the final correction, calculate the single-system positioning result for each navigation system, and determine the risk of ambiguity fixing errors. The integrity assessment module is used to determine the navigation integrity assessment result based on the final correction approximation, the final posterior standard deviation, the multiple gross error handling risk, and the ambiguity fixation error risk.

[0016] Compared with the prior art, the present invention can achieve at least one of the following beneficial effects: By using the observation dataset and receiver approximate three-dimensional coordinates, the approximate final correction value and final posterior standard deviation of the parameters to be estimated are calculated, thereby achieving a quantitative assessment of the impact of the posterior standard deviation on navigation integrity. This is then used to extract the observations containing gross errors, calculate the maximum number of gross error clusters, determine the risk of handling multiple gross errors, and quantify the impact of environmentally generated gross errors on navigation integrity. The observation dataset and the approximate final correction value are used to determine the risk of ambiguity fixing errors, quantifying the impact of observation ambiguity on navigation integrity. Finally, the navigation integrity assessment results under the influence of multiple factors are determined, improving the quantitative accuracy of the uncertainty in the positioning results.

[0017] In this invention, the above-described technical solutions can be combined with each other to achieve more preferred combinations. Other features and advantages of this invention will be set forth in the following description, and some advantages may become apparent from the description or be learned by practicing the invention. The objects and other advantages of this invention can be realized and obtained from what is particularly pointed out in the description and drawings. Attached Figure Description

[0018] The accompanying drawings are for illustrative purposes only and are not intended to limit the invention. Throughout the drawings, the same reference numerals denote the same parts. Figure 1 This is a flowchart illustrating a navigation integrity assessment method that integrates the influence of multiple factors, as described in an embodiment of the present invention. Figure 2 This is a schematic diagram of the protection level and positioning deviation in an open environment provided by an embodiment of the present invention; Figure 3 This is a schematic diagram of the protection level and positioning deviation in the forest environment provided in an embodiment of the present invention; Figure 4 This is a schematic diagram of the main modules of a navigation integrity assessment system that integrates the influence of multiple factors in an embodiment of the present invention. Detailed Implementation

[0019] Preferred embodiments of the present invention will now be described in detail with reference to the accompanying drawings, which form part of this application and are used together with the embodiments of the present invention to illustrate the principles of the present invention, but are not intended to limit the scope of the present invention.

[0020] A specific embodiment of the present invention discloses a navigation integrity assessment method that integrates the influence of multiple factors, such as... Figure 1 As shown, it includes: Step S1: Obtain the observation dataset, ephemeris data, and approximate three-dimensional coordinates of the receiver, and construct a function model; wherein, the observation dataset includes observation values ​​from multiple navigation systems.

[0021] The process involves acquiring observation datasets, ephemeris data, and approximate three-dimensional coordinates of the receiver, and constructing a function model, including steps S11-S12.

[0022] Step S11: Obtain the observation dataset, ephemeris data, and approximate three-dimensional coordinates of the receiver.

[0023] (1) Observation dataset In this embodiment, the observation dataset includes observations from multiple navigation systems, which can be obtained through data interfaces with these systems. The navigation systems include GPS navigation coefficients and the BeiDou Navigation Satellite System, each comprising multiple satellites and a receiver. In other embodiments, the navigation systems include at least two of the following: GPS navigation coefficients, BeiDou Navigation Satellite System, GLONASS Navigation Satellite System, and Galileo Navigation Satellite System. In this embodiment, the observations from each navigation system include pseudorange observations and carrier wave observations; in other embodiments, Doppler observations are also included.

[0024] A receiver calculates its position using trilateration by receiving signals from multiple satellites of a navigation system. The calculation process includes determining the distance between the receiver and the satellites based on the time delay of their arrival, and then determining the receiver's position information based on the distances between the receiver and the multiple satellites. (Example) Indicates based on the first Time delay corresponding to each satellite Calculated distance, This represents the speed of light. Taking pseudorange observations as an example, a receiver determines its own position information using pseudorange observations from multiple satellites. If the receiver needs to determine its own three-dimensional position (longitude, latitude, and altitude), it requires pseudorange observations from at least four satellites.

[0025] Furthermore, the time delay between the receiver and the satellite can be obtained by processing the ranging code or signal carrier in the satellite signal. In this embodiment, the distance calculated based on the ranging code is used as the pseudorange observation value, and the distance calculated based on the signal carrier is used as the carrier observation value. Due to the clock errors between the satellite and the navigation system, the clock errors between the receiver and the navigation system, and interference such as ionization refraction and convection refraction during signal transmission, the time delay obtained by processing the ranging code or signal carrier in the satellite signal deviates from the actual event delay. Therefore, the calculated distance is not accurate. Navigation integrity can be used to quantitatively evaluate this inaccuracy and uncertainty. The higher the navigation integrity, the more reliable the calculated distance and the determined position information.

[0026] (2) Ephemeris data In this embodiment, the ephemeris data includes the orbital parameters and time information of each satellite, used to determine the satellite's three-dimensional coordinates. This data can be obtained through a navigation system, by receiving broadcast ephemeris data, or through other existing technologies; no limitation is imposed here. The determination of the satellite's three-dimensional coordinates can be based on existing technologies; no limitation is imposed here either.

[0027] (3) Approximate three-dimensional coordinates of the receiver In this embodiment, the receiver's approximate three-dimensional coordinates are the receiver's initial coordinates in the Earth coordinate system. During continuous navigation, these can be the receiver's three-dimensional coordinates determined by one or more navigation systems at the previous moment. During the initial navigation and positioning, the low-precision initial coordinates can be calculated based on the observations of any navigation system as the receiver's approximate three-dimensional coordinates. Alternatively, other external auxiliary information, such as base station positioning or map coordinates, can be used to determine these coordinates. No restrictions are imposed here.

[0028] Furthermore, to improve the effectiveness of the data, the acquired observations and ephemeris data are preprocessed using ephemeris calculation and cycle slip detection, and the observations are updated using Kalman filtering. These processes can be performed using existing technologies and will not be elaborated here.

[0029] Step S12: Construct a function model based on the observation dataset, ephemeris data, and receiver approximate three-dimensional coordinates.

[0030] Based on ephemeris data and the receiver's approximate three-dimensional coordinates, linearization is performed on each observation value at the receiver's approximate three-dimensional coordinates to construct a function model. This model is used to solve for the approximate correction values ​​corresponding to the parameters to be estimated using the observation values ​​in the observation dataset. In this embodiment, a corresponding function model is established for each navigation system, represented as follows: In the formula, Represents the coefficient matrix. This represents the matrix composed of the parameters to be estimated. Represents a constant matrix. This represents the residual matrix. Furthermore, corresponding function models are established for each type of observation for each navigation system. For example, for the BeiDou navigation system, function models are established for pseudorange observations and carrier wave observations, respectively.

[0031] In this embodiment, the coefficient matrix The size of the matrix is ,in, This indicates the number of observations. If the navigation system is a single-point positioning system, the number of observations is the number of satellites. If the navigation system is a relative positioning system, the number of observations is the number of satellites minus one. Indicates the number of parameters to be estimated; the matrix formed by the parameters to be estimated. The size of the matrix is constant matrix residual matrix The size of the matrix is .

[0032] In this embodiment, taking pseudorange observations as an example, if the navigation system is a single-point positioning navigation system consisting of five satellites, the distance between the satellite position and the receiver's actual position, and the time deviation corresponding to the time delay of the signal emitted by the satellite reaching the receiver, are used as the parameters to be estimated, expressed as follows: ,in express The transpose of the matrix, , , This represents the distance between the satellite's position and the receiver's actual position in different directions, for example... , Representing the three-dimensional coordinates of a satellite 3D coordinates Representing the receiver's true three-dimensional coordinates 3D coordinates; This represents the time deviation corresponding to the time delay. For carrier observations, the corresponding parameters to be estimated may also include ambiguity.

[0033] Based on the aforementioned example, the construction of the coefficient matrix, constant matrix, and residual matrix is ​​illustrated. The relevant calculation principles are applicable to carrier observations and relative positioning.

[0034] First, based on ephemeris data and the receiver's approximate three-dimensional coordinates, the approximate distance between each satellite and the receiver is calculated. In this embodiment, the approximate distance is expressed as... The cosines in the three directions are respectively expressed as , , In the formula, Indicates the first Approximate distance between the satellite and the receiver, Indicates the first The three-dimensional coordinates of the satellite This represents the receiver's approximate three-dimensional coordinates; in this embodiment, ECEF coordinates are used. A coefficient matrix is ​​constructed based on the three-dimensional coordinates of the four satellites. constant matrix ,in express The transpose of .

[0035] Then, based on the approximate distance and pseudorange observations, the observation residuals are calculated. Observation residuals corresponding to each satellite In the formula, Indicates the first The observation distance between the satellite and the receiver is determined by the pseudorange observations corresponding to the five satellites. Based on the approximate distances of the five satellites and the pseudorange observations, a residual matrix is ​​constructed. The corresponding function model can then be expressed as: .

[0036] Step S2: Using the observed dataset, calculate the final correction approximation of the parameters to be estimated in the function model, and determine the final a posteriori standard deviation.

[0037] Using the observation dataset, the final correction approximation of the parameters to be estimated in the function model is calculated, and the final posterior standard deviation is determined based on the final correction approximation. In this embodiment, the final correction approximation and final posterior standard deviation of the parameters to be estimated can be calculated according to the observation dataset corresponding to a fixed period (e.g., every hour), and the navigation integrity assessment result corresponding to each fixed period is determined according to steps S3-S5; alternatively, the navigation integrity assessment result for each time step can be determined using a preset time step and a rolling time window, and the navigation integrity assessment result for the next time step is determined after the observation dataset is updated to the observation value corresponding to the next time step. For example, if the preset time step is 1 minute and the time window is 1 hour, the observation dataset corresponding to the current time step is constructed using all observation values ​​of the current time step and the previous hour, and the navigation integrity assessment result corresponding to the current time step is determined through steps S2-S5. After obtaining the observation value of the next time step, the observation dataset corresponding to the next time step is determined according to the rolling time window, and the navigation integrity assessment result corresponding to the current time step is determined through steps S2-S5. This embodiment uses the observation dataset corresponding to the current time step as an example to illustrate the calculation process of the navigation integrity assessment result.

[0038] Step S2 includes steps S21-S22.

[0039] Step S21: Extract multiple minimum observation subsets from the observation dataset, calculate the approximate correction value of the parameter to be estimated corresponding to each minimum observation subset based on the function model, and determine the optimal correction approximate value from all the correction approximate values.

[0040] Multiple minimum observation subsets are extracted from the observation dataset. Based on a function model, the approximate correction value of the parameter to be estimated corresponding to each minimum observation subset is calculated. The optimal correction approximation value is determined from all the correction approximations. For example, a predetermined number (e.g., 10) of minimum observation data subsets are randomly extracted from the observation dataset. Based on a function model, the approximate correction value of the parameter to be estimated corresponding to each minimum observation subset is calculated, and the corresponding post-hoc residual matrix is ​​calculated. The inlier rate corresponding to the post-hoc residual matrix is ​​statistically analyzed, and the maximum value is selected from all inlier rates. The correction approximation value corresponding to this maximum value is taken as the optimal correction approximation value.

[0041] Furthermore, to improve the reliability of the optimal correction approximation, this embodiment determines the optimal correction approximation through steps a-d.

[0042] Step a: Extract the minimum observation subset from the observation dataset, and calculate the approximate value of the correction number and the post-hoc residual matrix corresponding to the minimum observation subset based on the function model.

[0043] In this embodiment, based on the observations of each navigation system, the optimal correction approximation value corresponding to the parameters to be estimated in the function model of that navigation system is calculated. For example, according to the source of the observations, the observation dataset is divided into multiple single-system datasets, such as a GPS single-system dataset and a BeiDou single-coefficient dataset. For any single-system dataset, the smallest observation subset is randomly selected, and based on the function model of the navigation system, the correction approximation value corresponding to the smallest observation subset is calculated. Step a specifically includes steps a1-a3.

[0044] Step a1: Extract the minimum observation subset from the observation dataset, and calculate the corresponding coefficient matrix, constant matrix, variance matrix, and sum based on all observations and function model of the minimum observation subset.

[0045] The smallest subset of observations is randomly selected from the observation dataset, and the corresponding coefficient matrix and constant matrix are determined based on the function model.

[0046] In this embodiment, for each navigation system's single-system dataset, based on the receiver's signal reception time, observations from multiple satellites with the same signal reception time are grouped into observation groups. Each observation group is further divided into multiple observation subgroups based on the type of observations, such as pseudorange observation subgroups and carrier observation subgroups. Observation groups are randomly sampled from each single-system dataset, and observations are randomly sampled from each subgroup within the sampled observation groups, forming multiple minimum observation subsets. The number of observations in each minimum observation subset is the same as the number of parameters to be estimated. The same method is used for each minimum observation subset to determine the corresponding approximate correction value, post-hoc residual matrix, and inlier rate.

[0047] In other embodiments, when the parameters to be estimated need to be solved based on multiple observations of the same satellite, for each navigation system's corresponding single-system dataset, taking the satellite that transmits the signal as the reference, all observations of that satellite can be taken as an observation group. According to the type of observation, each observation group can be divided into multiple observation subgroups, such as pseudorange observation subgroups and carrier observation subgroups. The observations in each single-system dataset and each satellite's observation group can be randomly sampled to form multiple minimum observation subsets.

[0048] Based on all observations and the function model of the minimum observation subset, refer to step S12 to determine the coefficient matrix and constant matrix corresponding to the minimum observation subset. The matrix sizes are respectively... , .

[0049] Calculate the prior variance for each satellite and determine the variance matrix corresponding to the smallest subset of observations.

[0050] In this embodiment, an elevation angle stochastic model is used to determine the prior variance for each satellite. For example, In the formula, , Indicates a fixed constant. Indicates the first The elevation angle of the satellite can be obtained through the first The three-dimensional coordinates of the satellite and the approximate three-dimensional coordinates of the receiver are calculated.

[0051] Based on the prior variances of all observations corresponding to the satellites in the minimum subset of observations, a variance matrix is ​​constructed, with the following matrix sizes: Taking four parameters to be estimated as an example, if the minimum subset of observations consists of pseudorange observations, then the variance matrix corresponding to the minimum subset of observations is a non-differential variance matrix, represented as follows: If the minimum subset of observations consists of carrier observations, then RTK (Real-time kinematic) differential calculation is used. The variance matrix corresponding to the minimum subset of observations is the variance matrix after double difference, expressed as follows: ,in, , These are the coefficients for the inter-station differential and inter-satellite differential designed in the double-difference processing, respectively. , , This represents the identity matrix, where all diagonal elements are 1 and the rest are zero. This represents a vector whose elements are all 1s.

[0052] Step a2: Calculate the approximate correction value based on the coefficient matrix, constant matrix and variance matrix corresponding to the smallest observation subset.

[0053] Based on the coefficient matrix, constant matrix, and variance matrix corresponding to the minimum observation subset, the approximate correction value corresponding to the parameter to be estimated is calculated. In this embodiment, the formula is used... Calculate the approximate value of the correction, where, Indicates the first The approximate correction value corresponding to the smallest subset of observations, for the first subset of observations, then ; Indicates the first The coefficient matrix corresponding to the smallest subset of observations The transpose of the matrix; Indicates the first The variance matrix corresponding to the smallest subset of observations The inverse matrix; Indicates the first The constant matrix corresponding to the smallest subset of observations.

[0054] Step a3: Based on the approximate correction value corresponding to the minimum observation subset, use the function model to calculate the a priori residual matrix corresponding to the minimum observation subset.

[0055] Substituting the approximate correction values ​​corresponding to the minimum observation subset into the parameters to be estimated in the function model yields the a posteriori residual matrix corresponding to the minimum observation subset. This allows determination of the a posteriori residual of each observation in the minimum observation subset relative to the approximate correction value. In this embodiment, the formula is used... Calculate the post-hoc residual matrix corresponding to the smallest subset of observations, where, Indicates the first The a priori residual matrix corresponding to the smallest subset of observations; Indicates the first The basic approximation value corresponding to the smallest subset of observations is 0 in this embodiment, and the receiver's approximate three-dimensional coordinates in other embodiments. This represents an approximate value of the correction.

[0056] Step b: Based on the post-hoc residual matrix and gross error threshold, calculate the inlier rate corresponding to the smallest observation subset.

[0057] In this embodiment, for the post-hoc residual matrix of the minimum observation subset, the number of elements whose absolute values ​​are less than a gross error threshold is counted. The ratio of this number of elements to the number of observations in the minimum observation subset is used as the interior rate corresponding to that minimum observation subset. Taking four parameters to be estimated as an example, with a gross error threshold of 0.2 and a post-hoc residual matrix of... The corresponding interior point rate .

[0058] Furthermore, to improve the accuracy of in-point rate statistics, gross error thresholds are determined based on satellite altitude.

[0059] First, for each satellite, calculate the corresponding single-satellite gross error threshold.

[0060] In the formula, Describes the smallest observation subset. The gross error threshold for each satellite; This represents the gross error coefficient. In this embodiment, if the observations of the smallest subset are pseudorange observations, then... The value range is 0.3-3m. If the observations of the smallest subset are carrier observations, then... The value range is 1-5m; Indicates the first The elevation angle corresponding to each satellite.

[0061] Secondly, the gross error threshold corresponding to the smallest observation subset is determined based on the gross error threshold of each individual star.

[0062] In this embodiment, the average value of the single-satellite gross error thresholds corresponding to all observations in the minimum observation subset is used as the gross error threshold corresponding to the minimum observation subset.

[0063] In other embodiments, the single-satellite gross error thresholds of all satellites corresponding to the observations in the minimum observation subset are used as the gross error thresholds corresponding to that minimum observation subset. The satellite order corresponding to multiple single-satellite gross error thresholds is the same as the satellite order corresponding to the post-hoc residual matrix. The absolute value of each element in the post-hoc residual matrix corresponding to each satellite is determined to be less than the corresponding single-satellite gross error threshold to determine the corresponding interior rate. Taking four parameters to be estimated as an example, the single-satellite gross error thresholds of the satellites corresponding to the four observations are 0.2, 0.4, 0.3, and 0.3 respectively. The post-hoc residual matrix corresponding to the minimum observation subset is... If the result of each judgment is less than, less than, greater than, less than, the corresponding interior point rate is... .

[0064] Step c: Update the current maximum in-point rate and the corresponding current repetition count based on the in-point rate and the current maximum in-point rate.

[0065] The current maximum interior rate is updated based on the interior rate and the current maximum interior rate. This includes: if the interior rate calculated in step b is greater than the current maximum interior rate, then the interior rate calculated in step b is used as the new current maximum interior rate, and the current repetition count of this new current maximum interior rate is recorded as 1; if the interior rate calculated in step b is not greater than the current maximum interior rate, then the current maximum interior rate remains unchanged, and the current repetition count of this current maximum interior rate is increased by 1. In this embodiment, the initial current maximum interior rate is a very small number, for example... In other embodiments, the initial current maximum in-point rate is null, and any in-point rate is greater than null.

[0066] For example, for the smallest subset of observations extracted in the first step, the corresponding interior rate is obtained through step b. If the in-point rate is greater than the initial current maximum in-point rate (a very small number), update the current maximum in-point rate to this in-point rate, denoted as: Record the current repetition count of the updated current maximum interior point rate. For the smallest subset of observations drawn in the second sampling, a new interior rate is obtained through step b. After that, compare it with the current maximum interior rate. If the new interior rate is greater than the current maximum interior rate, then update the current maximum interior rate to the new interior rate, denoted as: The current repetition count of the updated maximum interior point rate is 1, i.e. If the new interior rate is not greater than the current maximum interior rate, then the current maximum interior rate remains unchanged. ), and increment the current repetition count of the current maximum interior rate by 1, that is .

[0067] Step d: Based on the updated current maximum inlier rate and the corresponding current repetition count, determine whether the subset extraction stopping condition has been met. If the subset extraction stopping condition has been met, determine the optimal correction approximation value based on the correction approximation value corresponding to the updated current maximum inlier rate. If the subset extraction stopping condition has not been met, return to step a.

[0068] In this embodiment, the subset extraction stopping condition includes the minimum number of repetitions: if the current repetition count of the updated current maximum interior point rate reaches the minimum number of repetitions. If the minimum number of repetitions is not reached, it is determined that the subset extraction stopping condition has been met, and the approximate value of the correction corresponding to the current maximum inlier rate is taken as the optimal approximate value of the correction; if the minimum number of repetitions is not reached, it is determined that the subset extraction stopping condition has not been met, and the process returns to step a.

[0069] Furthermore, to improve the accuracy of the judgment, in this embodiment, the minimum number of repetitions is determined based on the confidence level, the current maximum inlier rate, and the number of parameters to be estimated. In the formula, Indicates the minimum number of repetitions. This indicates the preset confidence level, such as 0.85. This represents the current maximum interior point ratio. This indicates the number of parameters to be estimated.

[0070] Step S22: Calculate the final correction approximation and the final a posteriori standard deviation based on the optimal correction approximation, the observation dataset, and the function model.

[0071] Based on the best correction approximation, the observation dataset, and the function model, the final correction approximation and the final a posteriori standard deviation corresponding to the observation dataset are calculated. In this embodiment, for each type of observation for each navigation system, the corresponding best correction approximation is determined. For each type of observation for each navigation system, the final correction approximation and the final a posteriori standard deviation are calculated based on the best correction approximation for the same navigation system and the same observation type. Step S22 includes steps S221-S224.

[0072] Step S221: Substitute the approximate value of the best correction into the function model and calculate the post-hoc residual matrix corresponding to the observed dataset.

[0073] The optimal correction approximation is substituted into the function model to calculate the post-hoc residual matrix corresponding to the observation dataset. In this embodiment, based on the optimal correction approximation, the corresponding post-hoc residual matrix is ​​calculated for each subgroup of observations in the observation dataset.

[0074] Referring to step a1, construct the corresponding coefficient matrix, constant matrix, and variance matrix using all observations of each observation subgroup in the observation dataset, and calculate the corresponding post-hoc residual matrix. In the formula, Indicates the first The post-hoc residual matrix corresponding to each subgroup of observations; Indicates the first The initial approximation value corresponding to each subgroup of observations is constructed using the same principle as the initial approximation value corresponding to the smallest subset of observations. This represents the approximate value of the best correction. Indicates the first The constant matrix corresponding to each subgroup of observations.

[0075] Step S222: Extract observations without gross errors from the observation dataset based on the post-hoc residual matrix and gross error threshold corresponding to the observation dataset.

[0076] Based on the post-hoc residual matrix and gross error threshold corresponding to the observation dataset, observations free of gross errors are extracted from the observation dataset. In this embodiment, for each observation subgroup in the observation dataset, observations with post-hoc residuals less than the gross error threshold are selected as observations free of gross errors, based on the corresponding post-hoc residual matrix and gross error threshold. For example, the observation subgroup includes observations from 4 satellites, with single-satellite gross error thresholds of 0.2, 0.4, 0.3, and 0.3 for each satellite. The satellite order corresponding to the multiple single-satellite gross error thresholds is the same as the satellite order corresponding to the post-hoc residual matrix. The post-hoc residual matrix corresponding to this observation subgroup is as follows: Then, the observations without gross errors are the observations corresponding to the first, second, and fourth satellites.

[0077] Step S223: Calculate the final correction approximation based on all observations without gross errors.

[0078] The final correction approximation is calculated based on all observations excluding outliers. In this embodiment, for each observation subgroup, if the number of observations excluding outliers in the subgroup is not less than the number of parameters to be estimated, then based on all observations excluding outliers in the subgroup, the corresponding coefficient matrix, constant matrix, and variance matrix are constructed. Calculate the approximate final correction value for the corresponding single group, where, Indicates the first Approximate final correction values ​​for each observation subgroup, excluding gross errors; express The coefficient matrix is ​​constructed from all observations of each observation subgroup that do not contain outliers. The transpose of the matrix; Indicates the first The variance matrix constructed from all observations excluding outliers for each observation subgroup The inverse matrix; Indicates the first A constant matrix constructed from all observations of each observation subgroup that do not contain gross errors.

[0079] In this embodiment, for each type of observation for each navigation system, the final correction approximation is determined based on adjustment processing. In other embodiments, the mean of all single-group final correction approximations can be used as the final correction approximation; alternatively, each single-group final correction approximation can be substituted into the corresponding function model, and a new posterior residual matrix corresponding to the observation dataset can be calculated according to step S231. The smallest residual matrix is ​​selected from all posterior residual matrices, and the corresponding single-group final correction approximation is used as the final correction approximation.

[0080] Further, for each observation subgroup containing at least as many observations as the number of parameters to be estimated, referring to step S231, the gross error-free post-hoc residual matrix corresponding to that observation subgroup is calculated based on all gross error-free observations and the final correction approximation value. For each type of observation for each navigation system, referring to the method for determining the final correction approximation value, the gross error-free post-hoc residual matrix corresponding to the observation dataset is determined based on the gross error-free post-hoc residual matrices of all observation subgroups. For example, ,in, Indicates the first The post-hoc residual matrix of all observations without outliers for each observation subgroup. Indicates the first The initial approximation values ​​corresponding to all observations without gross errors in each observation subgroup This represents the approximate value of the final correction. Indicates the first The constant matrix corresponding to all observations without gross errors in each observation subgroup.

[0081] Furthermore, for each observation subgroup containing at least as many observations as the number of parameters to be estimated without gross errors, refer to step a1 to calculate the gross error-free variance matrix corresponding to the observation subgroup based on all observations without gross errors and the final correction approximation; for each type of observation for each navigation system, refer to the method for determining the final correction approximation to determine the gross error-free variance matrix corresponding to the observation dataset based on the gross error-free variance matrices of all observation subgroups.

[0082] Step S224: Calculate the final posterior standard deviation of the observed dataset based on the final correction approximation.

[0083] Based on the approximate final correction value, the final posterior standard deviation corresponding to the observation dataset is calculated. In this embodiment, for each type of observation value for each navigation system, the standard deviation is calculated using the formula... Calculate the final post-hoc standard deviation for each item, and use the mean of all individual final post-hoc standard deviations as the final post-hoc standard deviation for the observed dataset. Indicates the first The first navigation system, the first The final posterior standard deviation of each item corresponding to a class of observations. Represents the square root function. Indicates the first The first navigation system, the first Gross-free post-hoc residual matrix corresponding to the observations The transpose of the matrix; Indicates the first The first navigation system, the first The variance matrix without gross errors corresponding to the observations The inverse matrix; Indicates the first The first navigation system, the first The number of observations without gross errors corresponding to each class of observations. This indicates the number of parameters to be estimated.

[0084] Step S3: Based on the final correction approximation and the final a posteriori standard deviation, extract the observations containing gross errors from the observation dataset; based on all the observations containing gross errors, calculate the maximum number of gross error clusters and determine the risk of multiple gross error processing.

[0085] Based on the final correction approximation and the final a posteriori standard deviation, the observations containing gross errors are extracted from the observation dataset; based on all observations containing gross errors, the maximum number of gross error clusters is calculated, and the risk of multiple gross error processing is determined, including steps S31-S33.

[0086] Step S31: Based on the observation dataset, the final correction approximation, and the function model, calculate the final a posteriori residual corresponding to each observation value.

[0087] In this embodiment, for each observation subgroup of the observation dataset, based on all the observation values ​​of the observation subgroup, the coefficient matrix, constant matrix, and variance matrix corresponding to the observation subgroup are constructed according to step a1. According to step S231, based on the final correction approximation value, the coefficient matrix, constant matrix, and variance matrix corresponding to the observation subgroup, the function model is substituted to calculate the final a posteriori residual matrix corresponding to the observation subgroup. Each element in the matrix is ​​the final a posteriori residual corresponding to each observation value of the observation subgroup. All observation subgroups of the observation dataset are traversed to determine the final a posteriori residual corresponding to each observation value.

[0088] For example, the observation subgroup includes observations from 4 satellites. The corresponding coefficient matrix, constant matrix, and variance matrix are constructed in the order of satellite 1-observation, satellite 2-observation, satellite 3-observation, and satellite 4-observation. The value of the first element in the final a posteriori residual matrix is ​​the final a posteriori residual corresponding to satellite 1-observation. The final a posteriori residual corresponding to each observation is determined in turn.

[0089] Step S32: Extract the observations containing gross errors from the observation dataset based on the final a posteriori residual of each observation and the gross error threshold.

[0090] Based on the final a posteriori residual and the outlier threshold for each observation, extract observations containing outliers from the observation dataset. For each observation in the observation dataset, if the corresponding final a posteriori residual is not less than the outlier threshold, the observation is determined to contain outliers; if the corresponding final a posteriori residual is less than the outlier threshold, the observation is determined to be free of outliers. Iterate through each observation in the observation dataset to extract all observations containing outliers.

[0091] In this embodiment, all observations use a uniform gross error threshold, which is the average of the single-satellite gross error thresholds for all satellites in the observation dataset. In other embodiments, depending on the gross error threshold used, for all observations corresponding to each satellite, the single-satellite gross error threshold corresponding to that satellite is used as the gross error threshold for all observations of that satellite.

[0092] Step S33: Based on all the observations containing gross errors, the final correction approximation, and the final a posteriori standard deviation, calculate the maximum number of gross error clusters and determine the risk of multiple gross error handling.

[0093] Based on all observations containing gross errors, the final correction approximation, and the final a posteriori standard deviation, the maximum number of gross error clusters is calculated. The risk of multiple gross error processing is determined based on the maximum number of gross error clusters to quantitatively assess the reliability of the gross error processing structure. This includes steps S331-S333.

[0094] Step S331: Determine the clustering distance threshold based on the final posterior standard deviation.

[0095] Based on the final posterior standard deviation, a clustering distance threshold is determined as a multiple of the final posterior standard deviation. For example, using... As a clustering distance threshold.

[0096] Step S332: Calculate the maximum number of gross error clusters based on the final post-hoc residuals corresponding to all observations containing gross errors and the clustering distance threshold.

[0097] Based on the final a posteriori residuals corresponding to all observations containing outliers, a residual set is constructed. The number of outlier clusters in the residual set whose distance is less than a clustering distance threshold is counted, and the maximum number of outlier clusters is determined, denoted as: In the formula, This represents the maximum number of gross clusters. Represents the residual set The target sample in Describes the first element in the residual set. The final post-test residual, This indicates the calculation of residual distance. This represents conditional statistics, where the target sample is any final posterior residual in the residual set. For example, it calculates the distance between any two final posterior residuals in the residual set, using any final posterior residual as the target sample, and statistically analyzes the residual set. China satisfies The final number of post-test residuals is taken as the number of gross error clusters corresponding to the target sample. The maximum value among all gross error cluster numbers is selected as the maximum number of gross error clusters corresponding to the observation dataset.

[0098] Step S333: Calculate the multi-gross processing risk based on the number of all observations containing gross errors and the number of the largest gross error cluster.

[0099] Based on the number of observations in the subset containing outliers and the maximum number of outlier clusters, the risk of handling multiple outliers is calculated. In this embodiment, the risk of handling multiple outliers is calculated using the following formula: In the formula, This indicates the risk of handling multiple gross errors; This represents the probability of gross error handling failure. ,in, This represents the maximum number of gross clusters. This indicates the number of all observations containing outliers; , This represents the risk assessment coefficient, and in this embodiment, the corresponding value ranges are as follows: , Among them, the probability of gross error processing failure. Used to describe the failure probability of a gross error handling algorithm based on sample consistency.

[0100] By comparing the failure probability of gross error processing with the risk assessment coefficient and calculating the risk of multiple gross error processing, we can determine the quantitative evaluation result of the settlement result (i.e. the approximate value of the final correction) of the parameters to be estimated by multiple gross error processing. The smaller the risk value of multiple gross error processing, the more reliable the multiple gross error processing is.

[0101] Furthermore, the multi-gross error processing risk in different directions can be calculated based on the unit vector in the three-dimensional direction corresponding to the final correction approximation and the multi-gross error processing risk. For example, the final correction approximation... ,based on , , Constructing a three-dimensional vector By normalizing the vectors, we obtain the corresponding three-dimensional unit vector. Using the vector elements corresponding to each direction as direction coefficients, the risk of handling multiple gross errors in different directions is calculated based on the sum of the direction coefficients and the risk of handling multiple gross errors. For example, for... The direction, and the risk of handling multiple gross errors in this direction are... ,in, Representing a three-dimensional vector The corresponding module length.

[0102] Step S4: Based on the observation dataset and the final correction approximation, calculate the single-system positioning result for each navigation system and determine the risk of ambiguity fixation error.

[0103] Based on the observation dataset and the final correction approximation, calculate the single-system positioning result corresponding to each navigation system and determine the ambiguity fixation error risk, including steps S41-S44.

[0104] Step S41: Based on the final correction approximation and the function model, perform gross error removal on the observation dataset to obtain the corrected observation dataset.

[0105] Based on the final correction approximation and function model, gross errors are removed from the observation dataset, and the observations without gross errors are retained to obtain the corrected observation dataset.

[0106] First, based on the observation dataset, the final correction approximation, and the function model, the final a posteriori residual corresponding to each observation is calculated. The specific principle is the same as in step S31, and will not be repeated here.

[0107] Secondly, based on the final post-hoc residual and gross error threshold of each observation, observations without gross errors are extracted from the observation dataset. The specific process is the same as step S32, but the difference is that step S32 extracts observations with gross errors, while step S41 removes observations with gross errors, and the corrected observation dataset is composed of all observations without gross errors.

[0108] Step S42: Solve for ambiguity in the corrected observation dataset to determine the fixed ambiguity.

[0109] The ambiguity of the corrected observation dataset is solved to determine the fixed ambiguity, specifically including steps S411-S412.

[0110] Step S421: Solve the ambiguity of the corrected observation dataset, determine the optimal ambiguity and the second-best ambiguity, and determine whether the optimal ambiguity is reliable.

[0111] In this embodiment, the LAMBDA algorithm (least squares ambiguity reduction adjustment method) is used to solve for ambiguity in the corrected observation dataset, determine the corresponding optimal and second-best ambiguities, and judge whether the optimal ambiguity is reliable. The LAMBDA algorithm improves the positioning accuracy to the centimeter or even millimeter level by reducing the correlation between ambiguity parameters and performing ambiguity search in the transformed space to obtain integer solutions for ambiguity.

[0112] First, for all carrier observations in the corrected observation dataset, the corresponding ambiguity floating-point solution is determined based on the corresponding final correction approximation. The LAMBDA algorithm is used to search for ambiguity and determine multiple ambiguity candidate solutions. Based on the distance between each ambiguity candidate solution and the ambiguity floating-point solution, the optimal ambiguity and the second-best ambiguity are selected.

[0113] For example, when constructing the function model in step S12 for carrier observations in the observation dataset, the corresponding parameters to be estimated also include ambiguity. Based on step S2, the final correction approximation value corresponding to the parameters to be estimated includes the final value corresponding to the ambiguity. This final value is used as the floating-point solution for the ambiguity. For example, if the navigation system includes 4 satellites, the parameters to be estimated are expressed as follows: The coefficient matrix is ​​represented as The constant matrix is ​​represented as The residual matrix is ​​represented as ,in, Indicates matrix transpose. This represents the number of carrier observations in the observation dataset. If there are 8 parameters to be estimated, then... The corresponding function model can be represented as Based on step S2, determine the approximate final correction value corresponding to the parameter to be estimated. This includes the final value corresponding to the ambiguity. , , , The ambiguity floating-point solution corresponding to the four satellites is The LAMBDA algorithm is used to perform ambiguity search, determine multiple ambiguity candidate solutions (a list of integer solutions), and the distance between each ambiguity candidate solution and the ambiguity floating-point solution. The ambiguity candidate solution with the smallest distance is taken as the optimal ambiguity, and the ambiguity candidate solution with the second smallest distance is taken as the suboptimal ambiguity.

[0114] in, , , , , , Indicates the first The three-dimensional coordinates of the satellite corresponding to each carrier observation. This represents the receiver's approximate three-dimensional coordinates. Indicates the first The observation distance between the satellite and the receiver is determined by each carrier observation.

[0115] Secondly, the reliability of the optimal ambiguity is determined using the Ratio test method. For example, this is based on the distance between the optimal ambiguity and the floating-point solution of the ambiguity. Distance between suboptimal ambiguity and the floating-point solution of ambiguity Calculate the Ratio value. If the Ratio value is less than the evaluation threshold, the optimal ambiguity is determined to be unreliable and is used as the qualitative evaluation result of the navigation integrity evaluation result; if the Ratio value is not less than the evaluation threshold, the optimal ambiguity is determined to be reliable and proceed to step S422.

[0116] Step S422: If the optimal ambiguity is reliable, then the optimal ambiguity is determined as the fixed ambiguity.

[0117] If the optimal ambiguity is reliable, then the optimal ambiguity is determined as the fixed ambiguity, and the process proceeds to step S43 to perform cross-validation of the ambiguity.

[0118] Step S43: For the observation values ​​of each navigation system in the corrected observation dataset, calculate the corresponding single-system positioning result based on the final correction approximation and the fixed ambiguity.

[0119] For the observations of each navigation system in the corrected observation dataset, the corresponding single-system positioning result is calculated based on the final correction approximation and the fixed ambiguity. The fixed ambiguity is then replaced with the final value corresponding to the ambiguity in the final correction approximation to obtain the corrected final correction approximation. This approximation is then substituted into the observation equations corresponding to each navigation system to solve for the receiver's true three-dimensional coordinates, thus obtaining the corresponding single-system positioning result.

[0120] For example, the observation equation corresponding to the carrier observation. In the formula, For the first Carrier observation values ​​corresponding to each satellite; Indicates the first The actual distance between the satellite and the receiver is ,in, Indicates the first The three-dimensional coordinates of the satellite Represents the receiver's three-dimensional positioning coordinates; Indicates the carrier wavelength. Indicates the carrier frequency. This represents the final value corresponding to the time deviation. Indicates ionospheric delay, Indicates tropospheric delay, Indicates the first Fixed ambiguity of a satellite This represents other errors, such as multipath effects and measurement noise. Based on carrier observations from multiple satellites of the same navigation system simultaneously received by the receiver, the observation equations are fitted and solved using the final correction approximation to determine the receiver's three-dimensional positioning coordinates, which serve as the single-system positioning result for the receiver from the navigation system.

[0121] Furthermore, if the modified observation dataset includes multiple observations at multiple times for each navigation system, then all observations at each time time can be substituted into the observation equation for fitting and solving to determine the single-system positioning result of the navigation system for the receiver at that time.

[0122] Step S44: Calculate the ambiguity fixation error risk based on the positioning results of each single system.

[0123] In this embodiment, based on the positioning results of each individual system, the result deviation between different navigation systems is calculated as the risk of ambiguity fixation error, used to quantify the impact of fixation error on navigation integrity. Taking two navigation systems as an example... In the formula, This indicates the risk of fixed ambiguity errors. Navigation system The corresponding single-system positioning results, Navigation system The corresponding single-system positioning results.

[0124] Furthermore, the corresponding ambiguity and error risk can be fixed by separately solving the ambiguity in the three-dimensional directions. Taking two navigation systems as an example, , , In the formula, , , They represent direction, direction, The risk of fixed ambiguity corresponding to the direction , They represent navigation systems. Navigation system The corresponding single-system positioning results.

[0125] Furthermore, if each navigation system corresponds to single-system positioning results at multiple time points, then the ambiguity fixation error risk can be calculated for the multiple single-system positioning results at each time point, and the ambiguity fixation error risk at all time points can be used as the ambiguity fixation error risk corresponding to the observation dataset. The ambiguity fixation error risk in three-dimensional directions can be calculated based on the same principle.

[0126] The Ratio value test is used to qualitatively assess the risk of ambiguity fixation, and subsystem cross-validation is used to quantitatively assess the risk of ambiguity fixation error. A two-step risk assessment strategy is adopted to more accurately analyze the impact of ambiguity fixation error risk on navigation integrity.

[0127] Step S5: Determine the navigation integrity assessment result based on the observation dataset and the corresponding final posterior standard deviation, the multiple gross error processing risk, and the ambiguity fixing error risk.

[0128] In this embodiment, the navigation integrity assessment result is determined based on the final post-test standard deviation, the risk of handling multiple gross errors, and the risk of ambiguity fixation error. The protection level corresponding to the navigation integrity assessment result is then determined. In the formula, This represents the quantitative value corresponding to the navigation integrity assessment result. This indicates the risk of handling multiple gross errors. This indicates the risk of fixed ambiguity errors. This represents the final posterior standard deviation corresponding to the observed dataset.

[0129] A comprehensive assessment of navigation integrity is achieved by qualitatively evaluating the fixed risk of ambiguity using the Ratio value test and quantitatively evaluating the navigation integrity assessment results using the protection level.

[0130] Furthermore, the navigation integrity assessment results also include the protection level in different spatial directions, and step S5 also includes steps S51-S53.

[0131] Step S51: Extract the corresponding three-dimensional coefficient matrix and variance matrix from the observation dataset.

[0132] Based on all observations in the observation dataset, extract the corresponding three-dimensional coefficient matrix and variance matrix. The size of the three-dimensional coefficient matrix is... For example, a three-dimensional coefficient matrix In the formula, , , Represents the first in the observation dataset The cosine of each observation in three directions, , , In the formula, Indicates the first The positioning distance between the satellite and the receiver corresponding to each measurement value. , Indicates the first The three-dimensional coordinates of the satellite corresponding to each measurement value. Indicates the first The single-system positioning result corresponding to each measurement value This represents the number of observations in the observed dataset. The size of the variance matrix corresponding to the observed dataset is... You can refer to the method in step a1, according to the first... The three-dimensional coordinates of the satellite corresponding to each measurement value and the positioning results of the single system are used to determine the prior variance for each satellite using an elevation angle stochastic model, and then the variance matrix corresponding to the observation dataset is constructed.

[0133] Step S52: Determine the final a posteriori variance for different spatial directions based on the three-dimensional coefficient matrix corresponding to the observation dataset, the variance matrix, and the final a posteriori standard deviation.

[0134] The three-dimensional posterior variance matrix is ​​calculated based on the three-dimensional coefficient matrix, variance matrix, and final posterior standard deviation corresponding to the observed dataset. The elements on the diagonal of the three-dimensional posterior variance matrix are used as the final posterior variances for the three directions. In this embodiment, the formula is used... Calculate the three-dimensional posterior variance matrix, where, Represents the three-dimensional posterior variance matrix. This represents the final posterior standard deviation corresponding to the observed dataset. Represents the three-dimensional coefficient matrix The transpose of the matrix, Represents the variance matrix corresponding to the observed dataset. The inverse matrix, express The inverse matrix.

[0135] Step S53: Determine the protection level for different spatial directions based on each of the final posterior variances, the multiple gross error handling risks, and the ambiguity fixation error risks.

[0136] Based on the variance of each final verification, the risk of handling multiple gross errors, and the risk of ambiguity fixation errors, the protection level for different spatial directions is determined. For Taking direction as an example, through the formula calculate The protection level of the direction, in the formula, express The level of protection in the direction; express Risk of multiple gross errors in direction handling; express The risk of fixed errors due to ambiguity in direction; express The final posterior variance of the direction.

[0137] This embodiment generates a comprehensive integrity index for navigation and positioning results by integrating multiple gross error processing risks, ambiguity fixation risks, and post-verification standard deviation, including the protection level in three dimensions, thus completing the assessment of navigation integrity.

[0138] Furthermore, to illustrate the technical effects of the embodiments of the present invention, an open environment and a forest environment are used as examples to assess navigation integrity using the method disclosed in this embodiment. Figure 2 This example demonstrates the horizontal and vertical positioning deviations and protection levels for each time step (e.g., x-axis epoch) in an open environment. Figure 3 The horizontal and vertical positioning deviations and protection levels at each time step in the example understory environment were used, respectively, in an open environment ( Figure 2 ) and understory environment ( Figure 3 Using the navigation and positioning results of high-precision inertial navigation as the true value, the relationship between the positioning deviations in the horizontal and vertical directions and the protection level is analyzed. The red lines represent... To represent positioning deviation, the blue triangle indicates the calculated protection level, and the black triangle indicates the navigation alarm threshold. From... Figure 2 As can be seen, in open environments, the consistency between protection level and positioning deviation is good, the integrity monitoring system is working normally, and the assessment results in both directions are clustered in the normal area (below the alarm threshold in each direction); from Figure 3 As can be seen, in forest environments, navigation and positioning results are unreliable, with more than 50% of the results being unreliable. The protection direction calculated in this embodiment can detect risks in a timely and accurate manner and provide timely warnings.

[0139] This invention provides a navigation integrity assessment system that integrates the influence of multiple factors, such as... Figure 4 As shown, it includes: An observation acquisition module is used to acquire an observation dataset and approximate three-dimensional coordinates of a receiver; wherein, the observation dataset includes observations from multiple navigation systems; The gross error processing module is used to calculate the final correction approximation and the final a posteriori standard deviation of the parameter to be estimated based on the observation dataset. The gross error processing module is further configured to extract the observations containing gross errors from the observation dataset based on the final correction approximation and the final posterior standard deviation; and to calculate the maximum gross error cluster number based on all the observations containing gross errors to determine the risk of multiple gross error processing. The ambiguity fixing module is used to observe the dataset, the approximate value of the final correction, calculate the single-system positioning result, and determine the risk of ambiguity fixing errors. The integrity assessment module is used to determine the navigation integrity assessment result based on the final correction approximation, the final posterior standard deviation, the multiple gross error handling risk, and the ambiguity fixation error risk.

[0140] The above-described method and system embodiments are based on the same principles, and their related aspects can be referenced from each other to achieve the same technical effects. For specific implementation processes, please refer to the foregoing embodiments, which will not be repeated here.

[0141] In summary, the navigation integrity assessment method and system based on multiple factors according to embodiments of the present invention have at least one of the following beneficial effects: By using the observation dataset and receiver approximate three-dimensional coordinates, the approximate final correction value and final posterior standard deviation of the parameters to be estimated are calculated, thereby achieving a quantitative assessment of the impact of the posterior standard deviation on navigation integrity. This is then used to extract the observations containing gross errors, calculate the maximum number of gross error clusters, determine the risk of handling multiple gross errors, and quantify the impact of environmentally generated gross errors on navigation integrity. The observation dataset and the approximate final correction value are used to determine the risk of ambiguity fixing errors, quantifying the impact of observation ambiguity on navigation integrity. Finally, the navigation integrity assessment results under the influence of multiple factors are determined, improving the quantitative accuracy of the uncertainty in the positioning results.

[0142] Those skilled in the art will understand that all or part of the processes of the methods described in the above embodiments can be implemented by a computer program instructing related hardware, and the program can be stored in a computer-readable storage medium. The computer-readable storage medium may be a disk, optical disk, read-only memory, or random access memory, etc.

[0143] The above description is only a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any changes or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in the present invention should be included within the scope of protection of the present invention.

Claims

1. A navigation integrity assessment method that integrates multiple factors, characterized in that, include: Acquire observation datasets, ephemeris data, and approximate three-dimensional coordinates of the receiver to construct a function model; wherein, the observation datasets include observation values ​​from multiple navigation systems; Using the observed dataset, calculate the final correction approximation of the parameters to be estimated in the function model, and determine the final posterior standard deviation; Based on the final correction approximation and the final posterior standard deviation, the observations containing gross errors are extracted from the observation dataset; based on all the observations containing gross errors, the maximum number of gross error clusters is calculated to determine the risk of multiple gross error processing. Based on the observation dataset and the approximate final correction value, calculate the single-system positioning result for each navigation system and determine the risk of ambiguity fixation error. Based on the observed dataset and the corresponding final posterior standard deviation, the risk of multiple gross errors, and the risk of ambiguity fixation error, the navigation integrity assessment result is determined; wherein, the protection level corresponding to the navigation integrity assessment result is expressed as... In the formula, This represents the quantified value of the protection level corresponding to the navigation integrity assessment result. This indicates the risk of handling multiple gross errors. This indicates the risk of a fixed ambiguity. This represents the final posterior standard deviation corresponding to the observed dataset; Using the observed dataset, calculate the final correction approximation of the parameters to be estimated in the function model, and determine the final a posteriori standard deviation, including: Multiple minimum observation subsets are extracted from the observation dataset. Based on the function model, the correction approximation value of the parameter to be estimated corresponding to each minimum observation subset is calculated. The best correction approximation value is determined from all the correction approximation values. Based on the optimal correction approximation, the observation dataset, and the function model, calculate the final correction approximation and the final a posteriori standard deviation; Based on the optimal correction approximation, the observed dataset, and the function model, the final correction approximation and the final a posteriori standard deviation are calculated, including: Substitute the approximate value of the best correction into the function model to calculate the post-hoc residual matrix corresponding to the observation dataset; Based on the post-hoc residual matrix and outlier threshold corresponding to the observation dataset, the observation values ​​free of outliers are extracted from the observation dataset; wherein, the outlier threshold is determined based on the satellite altitude; The final correction approximation is calculated based on all the observations excluding gross errors; Based on the approximate final correction value, calculate the final posterior standard deviation corresponding to the observed dataset.

2. The method according to claim 1, characterized in that, Multiple minimal observation subsets are extracted from the observation dataset. Based on the function model, a correction approximation value for the parameter to be estimated corresponding to each minimal observation subset is calculated. The optimal correction approximation value is determined from all the correction approximation values, including: Step a: Extract the minimum observation subset from the observation dataset, and calculate the approximate value of the correction and the post-hoc residual matrix corresponding to the minimum observation subset based on the function model; Step b: Based on the post-hoc residual matrix and gross error threshold, calculate the inlier rate corresponding to the minimum observation subset; Step c: Update the current maximum interior rate based on the interior rate and the current maximum interior rate; Step d: Based on the updated current maximum inlier rate, determine whether the subset extraction stopping condition has been met. If the subset extraction stopping condition has been met, determine the optimal correction approximation value based on the correction approximation value corresponding to the updated current maximum inlier rate. If the subset extraction stopping condition has not been met, return to step a.

3. The method according to claim 1, characterized in that, Based on the final correction approximation, the final a posteriori standard deviation, and the function model, the observation values ​​containing gross errors are extracted from the observation dataset; Based on all the observations containing outliers, the maximum outlier cluster number is calculated to determine the risk of handling multiple outliers, including: Based on the observation dataset, the final correction approximation, and the function model, calculate the final a posteriori residual corresponding to each observation value; Based on the final a posteriori residual of each observation and the gross error threshold, extract the observations containing gross errors from the observation dataset; Based on all the observations containing gross errors, the final correction approximation, and the final a posteriori standard deviation, the maximum number of gross error clusters is calculated to determine the risk of multiple gross error handling.

4. The method according to claim 3, characterized in that, Based on all the observations containing outliers, the final correction approximation, and the final a posteriori standard deviation, the maximum outlier cluster number is calculated to determine the risk of handling multiple outliers, including: Based on the final posterior standard deviation, the clustering distance threshold is determined; The maximum number of outlier clusters is calculated based on the final a posteriori residuals corresponding to all the observations containing outliers and the clustering distance threshold. The multi-gross handling risk is calculated based on the number of all observations containing gross errors and the number of the largest gross error cluster.

5. The method according to claim 4, characterized in that, The risk of handling multiple gross errors is calculated using the following formula: In the formula, This indicates the risk of handling multiple gross errors; This represents the probability of gross error handling failure. ,in, This represents the maximum number of gross clusters. This indicates the number of all observations containing outliers; , This represents the risk assessment coefficient.

6. The method according to claim 1, characterized in that, Based on the observation dataset and the final correction approximation, calculate the single-system positioning result for each navigation system to determine the ambiguity fixation error risk, including: Based on the approximate final correction value and the function model, gross errors are removed from the observation dataset to obtain the corrected observation dataset; The ambiguity of the corrected observation dataset is solved to determine the fixed ambiguity; For each observation value of the navigation system in the corrected observation dataset, the corresponding single-system positioning result is calculated based on the final correction approximation and the fixed ambiguity. Based on the positioning results of each single system, the risk of ambiguity fixation error is calculated.

7. The method according to claim 6, characterized in that, The ambiguity of the corrected observation dataset is solved to determine the fixed ambiguity, including: The ambiguity of the corrected observation dataset is solved to determine the optimal ambiguity and the second-best ambiguity, and to determine whether the optimal ambiguity is reliable. If the optimal ambiguity is reliable, then the optimal ambiguity is determined as the fixed ambiguity.

8. The method according to claim 1, characterized in that, The navigation integrity assessment results include protection levels in different spatial directions; Based on the observed dataset and the corresponding final posterior standard deviation, the risk of multiple gross errors, and the risk of ambiguity fixation error, the navigation integrity assessment result is determined, including: Extract the corresponding three-dimensional coefficient matrix and variance matrix from the observation dataset; Based on the three-dimensional coefficient matrix, the variance matrix, and the final posterior standard deviation corresponding to the observation dataset, determine the final posterior variance for different spatial directions; The protection level for different spatial orientations is determined based on each of the final posterior variances, the multiple gross error handling risk, and the ambiguity fixation error risk.

9. A navigation integrity assessment system that integrates multiple factors, characterized in that, include: The observation acquisition module is used to acquire observation datasets, ephemeris data, and approximate three-dimensional coordinates of the receiver, and to construct a function model; wherein, the observation dataset includes observations from multiple navigation systems; The gross error processing module is used to calculate the final correction approximation and the final a posteriori standard deviation of the parameters to be estimated in the function model based on the observation dataset. The gross error processing module is further configured to extract the observations containing gross errors from the observation dataset based on the final correction approximation and the final posterior standard deviation; and to calculate the maximum number of gross error clusters based on all the observations containing gross errors, thereby determining the risk of multiple gross error processing. The ambiguity fixing module is used to calculate the single-system positioning result for each navigation system based on the observation dataset and the final correction approximation, and to determine the risk of ambiguity fixing errors. The integrity assessment module is used to determine the navigation integrity assessment result based on the observed dataset and the corresponding final posterior standard deviation, the multiple gross error handling risk, and the ambiguity fixing error risk; wherein, the protection level corresponding to the navigation integrity assessment result is expressed as... In the formula, This represents the quantified value of the protection level corresponding to the navigation integrity assessment result. This indicates the risk of handling multiple gross errors. This indicates the risk of a fixed ambiguity. This represents the final posterior standard deviation corresponding to the observed dataset; Using the observed dataset, calculate the final correction approximation of the parameters to be estimated in the function model, and determine the final a posteriori standard deviation, including: Multiple minimum observation subsets are extracted from the observation dataset. Based on the function model, the correction approximation value of the parameter to be estimated corresponding to each minimum observation subset is calculated. The best correction approximation value is determined from all the correction approximation values. Based on the optimal correction approximation, the observation dataset, and the function model, calculate the final correction approximation and the final a posteriori standard deviation; Based on the optimal correction approximation, the observed dataset, and the function model, the final correction approximation and the final a posteriori standard deviation are calculated, including: Substitute the approximate value of the best correction into the function model to calculate the post-hoc residual matrix corresponding to the observation dataset; Based on the post-hoc residual matrix and gross error threshold corresponding to the observation dataset, extract the observation values ​​that do not contain gross errors from the observation dataset; The final correction approximation is calculated based on all the observations excluding gross errors; Based on the approximate final correction value, calculate the final posterior standard deviation corresponding to the observed dataset.

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