A graph neural network enhanced cooperative positioning integrity monitoring method

Abstract

The application provides a kind of graph neural network enhanced cooperative positioning integrity monitoring method, first, the spatio-temporal correlation characteristics between nodes are mined using graph neural network, and the covariance estimation under non-Gaussian noise is corrected by learning scaling factor, so that the protection level calculated is more compact than the traditional method, and the system availability is improved.Secondly, the conformal prediction theory is introduced, which mathematically strictly guarantees that the coverage rate of the protection level to the positioning error meets the preset integrity risk requirement.Finally, the OOD detection and fallback mechanism based on latent space is designed to ensure that when encountering extreme environments that have not been learned, i.e., the test set data environment is significantly different from the training set, the protection level result output by each node can be automatically switched to the physical model (traditional protection level), avoiding the overconfidence of neural networks and ensuring the safety of actual deployment, suitable for cooperative positioning integrity monitoring in complex urban environments.

Description

Technical Field

[0001] This invention belongs to the fields of navigation and positioning, and aerospace telemetry and control technology, and particularly relates to a collaborative positioning integrity monitoring method enhanced by graph neural networks. Background Technology

[0002] High-precision navigation and positioning are key technologies supporting the effective use of wireless sensor networks such as aircraft swarms and intelligent connected vehicles. Cooperative positioning (CL) significantly improves the positioning accuracy of the network by fusing relative ranging information from the Global Navigation Satellite System (GNSS) and network nodes to construct geometric constraints between nodes. Integrity monitoring is crucial to ensuring the reliability of positioning results. Its core task is to identify and eliminate abnormal observations and estimate the upper bound of the positioning error, i.e., the protection level (PL), under preset integrity risk conditions, thereby determining the usability of the positioning results.

[0003] Existing cooperative positioning integrity monitoring methods based on physical observation models typically assume that the observation noise follows an ideal zero-mean Gaussian distribution, thereby estimating the positioning state covariance matrix and calculating the positional variance (PL). However, in complex signal propagation environments such as urban canyons, signal obstruction, multipath effects, and non-line-of-sight propagation often cause measurement noise to exhibit non-ideal characteristics such as non-zero mean and heavy-tailed distributions, significantly deviating from the zero-mean Gaussian distribution. This leads to a mismatch between the ideal physical observation model and the actual situation. Therefore, in complex signal propagation environments, the PL calculated by conventional model-based methods is either too optimistic, leading to integrity risks, or too conservative, reducing system availability.

[0004] Deep neural network (DNN)-based methods can fit complex noise characteristics and improve the performance of integrity monitoring in complex signal propagation environments. However, they are essentially "black box" models, lacking rigorous statistical boundaries and unable to mathematically guarantee that the probability of PL coverage positioning error meets the preset integrity risk requirements. Furthermore, when the test environment is out-of-distribution (OOD) compared to the training data, the neural network is prone to overconfident and erroneous predictions, leading to serious hidden dangers. Summary of the Invention

[0005] To address the aforementioned issues, this invention provides a graph neural network-enhanced collaborative localization integrity monitoring method. Based on the latent space OOD detection and backoff mechanism, it ensures that when encountering extreme environments that have not been learned before, the protection level output of each node can be automatically switched to the physical model, avoiding the blind confidence of the neural network and ensuring the security of actual deployment.

[0006] A graph neural network-enhanced cooperative localization integrity monitoring method, in which each node in the cooperative localization network uses its real-time node features at the current epoch. The distribution covariance matrix of a pre-trained graph neural network The empirical mean of the latent feature vectors of all nodes in the cooperative localization network Obtain the Mahalanobis distance for each node:

[0007]

[0008] in, Indicates the first Mahalanobis distances corresponding to each node Indicates transpose; Each node is judged to determine whether its Mahalanobis distance is greater than a set threshold. For nodes that are judged to be yes, the traditional protection level of each node in the current epoch is used as an indicator to monitor the cooperative positioning integrity of each node. For nodes that are judged to be no, the conformal protection level of each node in the current epoch obtained by using a pre-trained graph neural network is used as an indicator to monitor the cooperative positioning integrity of each node.

[0009] Furthermore, the first Conformal protection level corresponding to each node The method for obtaining it is as follows:

[0010] in, To calculate the first output based on the pre-trained graph neural network. Each node in the current epoch The corresponding correction factor yields the level of correction protection. For the first Each node in the current epoch The corresponding target integrity risk probability quantiles, The target risk probability.

[0011] Furthermore, the level of protection was revised. The method for obtaining it is as follows:

[0012] in, For deterministic error limits, For statistical error limits, The output of the pre-trained graph neural network is the first... Each node in the current epoch The corresponding correction factor.

[0013] Furthermore, the output of the pre-trained graph neural network is the first... Each node in the current epoch The corresponding correction factor The method for obtaining it is as follows: Extracting node features as follows:

[0014] in, For the first Each node in the current epoch The covariance matrix of the corresponding posterior state estimate The covariance factor obtained by performing Cholesky decomposition. For the calculation using traditional methods, the first Each node in the current epoch The corresponding traditional level of protection, For the first Each node in the current epoch The corresponding number of valid satellites; Extract the first GNSS side features corresponding to the GNSS receivers equipped on each node as follows:

[0015] in, , For the first The node and the first New information between effective satellites For the first The node and the first Geometric vectors between valid satellites For the first The node and the first Noise variance between effective satellites For the first The node and the first Integrity slope between valid satellites; Extract the first Features of collaborative edges corresponding to each node as follows:

[0016] in, For the first The node and the first Information between neighboring nodes For the first The node and the first Geometric vectors between neighboring nodes For the equivalent noise variance, For the first The node and the first The integrity slope between neighboring nodes; Node features GNSS edge features Collaborative edge characteristics The input is processed through a pre-trained graph neural network iteratively until the maximum number of iterations L is reached, thus obtaining the result at the Lth iteration. Each node in the current epoch Hidden state in ; according to Obtain the correction factor as follows:

[0017] in, Let be the activation function of the graph neural network. This is the output layer mapping function of the graph neural network.

[0018] Furthermore, the first Each node in the current epoch The covariance matrix of the corresponding posterior state estimate The method for obtaining it is as follows: The first Each node in the current epoch The effective observation input in the algorithm is based on a distributed cooperative localization algorithm with Gaussian confidence propagation, which solves the problem to obtain the first... Each node in the current epoch The covariance matrix of the corresponding posterior state estimate Among them, the posterior state estimation includes the first... Each node in the current epoch The ENU coordinates and receiver clock bias in the data.

[0019] Furthermore, the first Each node in the current epoch The method for obtaining effective observations in the data is as follows: Get the The node and the first New information between effective satellites and its theoretical variance And according to the new information and theoretical variance Get the The node and the first Information statistics between valid satellites ; will not exceed the preset threshold Corresponding new information Pseudo-distance observation As a valid observation; Get the The node and the first News between neighboring nodes and its theoretical variance And according to the new information and theoretical variance Get the The node and the first Information statistics between neighboring nodes ; will not exceed the preset threshold Corresponding new information Pseudo-distance observation As a valid observation.

[0020] Furthermore, covariance factor The method for obtaining it is as follows: Based on covariance matrix With covariance factor Relationship For the covariance matrix Perform Cholesky decomposition to obtain the covariance factor .

[0021] Furthermore, the first The probability of target integrity risk corresponding to each node in the current epoch. quantiles The fixed parameters, which are pre-calculated during the offline calibration phase, are calculated as follows:

[0022]

[0023] in, To calibrate the first in the dataset The node at the th The corresponding non-consistent scores in each epoch It is a quantile function. To calibrate the first in the dataset The node at the th The horizontal difference between the actual position and the estimated position in each epoch. To determine the first output of the pre-trained graph neural network on the calibration dataset The node at the th The correction protection level is obtained from the correction factor corresponding to each epoch.

[0024] Beneficial effects: This invention provides a graph neural network-enhanced collaborative localization integrity monitoring method. First, it utilizes graph neural networks to mine the spatiotemporal correlation features between nodes and corrects the covariance estimation under non-Gaussian noise by learning scaling factors, resulting in a more compact calculated protection level compared to traditional methods and improving system availability. Second, it introduces conformal prediction theory to mathematically guarantee that the protection level's coverage of positioning errors meets the preset integrity risk requirements. Finally, it designs an OOD detection and backoff mechanism based on latent space to ensure that when encountering extreme environments not previously learned (i.e., when the test set data environment differs significantly from the training set), it can automatically switch the protection level output of each node to the physical model (traditional protection level). This avoids the blind confidence of neural networks, ensures the security of actual deployment, and is suitable for collaborative positioning integrity monitoring in complex urban environments. Attached Figure Description

[0025] Figure 1 This invention provides a schematic diagram of a graph neural network-enhanced collaborative localization integrity monitoring method. Detailed Implementation

[0026] To enable those skilled in the art to better understand the present application, the technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the accompanying drawings.

[0027] This invention first constructs a normalized innovation statistic based on statistical hypothesis testing methods to detect and eliminate anomalies in GNSS pseudorange and relative ranging observations between nodes, thereby removing observations with significant anomalies. Next, it uses a Gaussian confidence propagation algorithm to perform distributed cooperative positioning, obtaining the posterior state estimate of nodes and their precise posterior covariance matrix through iterative message passing. Then, it constructs an integrity heterogeneous graph containing node covariance features and edge observation features, using a graph neural network to mine spatial geometric correlations and observation features in the cooperative network and output correction factors to adaptively correct the statistical error limits of the protection level. Finally, it introduces conformal prediction theory to calibrate the corrected protection level to meet preset integrity risks, and combines an OOD detection mechanism based on latent feature space to automatically revert to the traditional protection level when an unknown scenario is identified, thus achieving high-precision cooperative positioning integrity monitoring while ensuring system safety.

[0028] The structural block diagram of this invention is as follows: Figure 1As shown, the process includes five main steps: observation acquisition, anomaly observation detection, cooperative localization calculation, protection level calculation, and protection level correction. Each node (an intelligent agent with an entity) independently executes these five steps, eliminating the need to transmit all data to a central node for processing. The rollback decision in protection level correction is also performed independently by each node. If node A finds itself in an unknown scenario, it rolls back to the traditional protection level; if node B determines it is in a known scenario, it continues to use the neural network output, without interfering with each other.

[0029] Without loss of generality, consider a subset of M A cooperative positioning network of nodes (intelligent agents with physical entities), each node equipped with a GNSS receiver and a communication terminal. In the epoch... t ,node i The state vector is represented as ,in For three-dimensional position coordinates, This refers to the clock bias of the receiver relative to different satellite systems.

[0030] Specifically, a graph neural network-enhanced cooperative localization integrity monitoring method is proposed, in which each node in the cooperative localization network uses its real-time node features at the current epoch. The distribution covariance matrix of a pre-trained graph neural network The empirical mean of the latent feature vectors of all nodes in the cooperative localization network Obtain the Mahalanobis distance for each node:

[0031] in, Indicates the first Mahalanobis distances corresponding to each node Indicates transpose; Each node is judged to determine whether its Mahalanobis distance is greater than a set threshold. For nodes that are judged to be yes, the traditional protection level of each node in the current epoch is used as an indicator to monitor the cooperative positioning integrity of each node. For nodes that are judged to be no, the conformal protection level of each node in the current epoch obtained by using a pre-trained graph neural network is used as an indicator to monitor the cooperative positioning integrity of each node.

[0032] Among them, the Conformal protection level corresponding to each node The method for obtaining it is as follows:

[0033] in, To calculate the first output based on the pre-trained graph neural network. Each node in the current epoch The corresponding correction factor yields the level of correction protection. For the first Each node in the current epoch The corresponding target integrity risk probability quantiles, The target risk probability.

[0034] Furthermore, the level of protection was revised. The method for obtaining it is as follows:

[0035] in, For deterministic error limits, For statistical error limits, The output of the pre-trained graph neural network is the first... Each node in the current epoch The corresponding correction factor.

[0036] It should be noted that, in order to address covariance in complex environments... To address the issue of inaccurate estimation leading to distorted protection levels (PL), this step utilizes a graph neural network to correct and enhance the PL. The output of the pre-trained graph neural network is the first... Each node in the current epoch The corresponding correction factor The method for obtaining it is as follows: First, construct a integrity heterogeneous graph and extract features, including node features. as follows:

[0037] in, For the first Each node in the current epoch The covariance matrix of the corresponding posterior state estimate The covariance factor obtained by performing Cholesky decomposition. For the calculation using traditional methods, the first Each node in the current epoch The corresponding traditional level of protection, For the first Each node in the current epoch The corresponding number of valid satellites; Extract the first GNSS side features corresponding to the GNSS receivers equipped on each node as follows:

[0038] in, , For the first The node and the first New information between effective satellites For the first The node and the first Geometric vectors between valid satellites For the first The node and the first Noise variance between effective satellites For the first The node and the first Integrity slope between valid satellites; Extract the first Features of collaborative edges corresponding to each node as follows:

[0039] in, For the first The node and the first Information between neighboring nodes For the first The node and the first Geometric vectors between neighboring nodes For the equivalent noise variance, For the first The node and the first The integrity slope between neighboring nodes; Node features GNSS edge features Collaborative edge characteristics The pre-trained graph neural network is input for iteration, that is, message passing is performed using the graph neural network, until the maximum number of iterations L is reached, and the result of the Lth iteration is obtained. Each node in the current epoch Hidden state in ; in the t In this iteration, the nodes aggregate messages from the satellite. And news from the neighbors and update its hidden state. :

[0040]

[0041]

[0042] After multiple rounds of message relay, according to Obtain the correction factor as follows:

[0043] in, Let be the activation function of the graph neural network. This is the output layer mapping function of the graph neural network.

[0044] Furthermore, the first Each node in the current epoch The covariance matrix of the corresponding posterior state estimate The method for obtaining it is as follows: The first Each node in the current epoch The effective observation input in the algorithm is based on a distributed cooperative localization algorithm with Gaussian confidence propagation, which solves the problem to obtain the first... Each node in the current epoch The covariance matrix of the corresponding posterior state estimate Among them, the posterior state estimation includes the first... Each node in the current epoch The ENU coordinates and receiver clock bias in the data.

[0045] It should be noted that this invention utilizes a valid set of observations to execute a distributed cooperative localization algorithm based on Gaussian confidence propagation to calculate the posterior state of nodes. This process is an iterative message passing process, where nodes... i The marginal posterior distribution is approximated by exchanging Gaussian messages with neighboring nodes.

[0046] Specifically, in the k In this iteration, the state estimate from the previous round is first used as the basis. and The nonlinear observation function is linearized using a first-order Taylor expansion. For GNSS observations, the linearized observation equation is: For relative observations, the linearized observation equation is: Subsequently, the node i Receive messages from anchor points or satellites And from Neighborhood Festival j News These messages are all Gaussian distributed and each carries information about a node. i State observation information. Finally, node i Multiply the prior information by all received messages, representing the sum of the information matrix and information vector in the logarithmic field, and update the state confidence. The specific update calculation formula is as follows: First, calculate the information matrix for the current iteration, which is the inverse of the posterior covariance matrix:

[0047] Next, calculate the information vector for the current iteration, which is the product of the inverse of the posterior covariance matrix and the state mean:

[0048] In the above formula, and These are the prior covariance matrix and the state mean at the initial time, respectively; and These are the set of visible satellites and the set of neighboring nodes, respectively. , and The observation function with respect to the nodes are respectively i and nodes j The Jacobian matrix of the state; and These are the noise variances of GNSS observations and relative ranging observations, respectively. and The equivalent observation after linearization, i.e. .

[0049] By solving the above system of linear equations, we obtain the latest posterior state estimate. Covariance Matrix .

[0050] The covariance matrix It accurately characterizes the positioning uncertainty under the current geometric configuration, and outputs the final covariance matrix after the maximum number of iterations. Enter the input for calculating the protection level in subsequent steps.

[0051] Furthermore, the first Each node in the current epoch The method for obtaining effective observations in the data is as follows: Get the The node and the first New information between effective satellites and its theoretical variance And according to the new information and theoretical variance Get the The node and the first Information statistics between valid satellites ; will not exceed the preset threshold Corresponding new information Pseudo-distance observation As a valid observation; Get the The node and the first News between neighboring nodes and its theoretical variance And according to the new information and theoretical variance Get the The node and the first Information statistics between neighboring nodes ; will not exceed the preset threshold Corresponding new information Pseudo-distance observation As a valid observation.

[0052] Furthermore, covariance factor The method for obtaining it is as follows: Based on covariance matrix With covariance factor Relationship For the covariance matrix Perform Cholesky decomposition to obtain the covariance factor .

[0053] For example, without loss of generality, consider a set containing M A cooperative positioning network of nodes (intelligent agents with physical entities), each node equipped with a GNSS receiver and a communication terminal. In the epoch... t ,node i The state vector is represented as ,in For three-dimensional position coordinates, This refers to the clock bias of the receiver relative to different satellite systems.

[0054] In each epoch, the nodes in the network i First, acquire GNSS pseudorange observations and relative distance measurements between nodes. For GNSS observations, nodes... i Receive from visible satellite set China Satellite n The signal is used to obtain the pseudorange observations received by node i from satellite n. Its physical observation model is as follows:

[0055] in, Let n be the known position of satellite n, and c be the speed of light. Let n be the satellite clock bias. and These represent the ionospheric and tropospheric delays received by node i from satellite n, respectively. This represents the measurement noise received by node i from satellite n. For relative observations, node... i set of neighboring nodes within the communication radius Neighbors jInteract to obtain relative distance observations Its physical observation model is as follows:

[0056] in, For neighboring nodes j Location, This refers to relative measurement noise. These two types of observations (i.e., pseudorange observations) Relative distance observation These constitute the basic input data for collaborative positioning.

[0057] Then, statistical hypothesis testing methods are used to detect and remove anomalies in the previously obtained raw observations, in order to eliminate significantly abnormal observations. Specifically, based on nodes... i Prior state estimation (Usually predicted from the previous epoch), first calculate the new information from GNSS observations. and its theoretical variance The calculation formula is as follows:

[0058]

[0059] Simultaneously calculate the new information relative to the observation. and its theoretical variance The calculation formula is as follows:

[0060]

[0061] In the above formula, For the observation function, and These are the corresponding linearized Jacobian matrices. For the prior state covariance, For the joint covariance that includes the uncertainty of neighbor states, and The pre-defined variance of the observation noise is used. Subsequently, a normalized innovation statistic is constructed. Its definition is:

[0062] like Greater than the threshold determined based on the preset false alarm rate If the observation is deemed abnormal, it is removed; otherwise, the observation is retained and proceeds to the next stage.

[0063] It should be noted that the first The probability of target integrity risk corresponding to each node in the current epoch. quantiles The fixed parameters, which are pre-calculated during the offline calibration phase, are calculated as follows:

[0064]

[0065] in, To calibrate the first in the dataset The node at the th The corresponding non-consistent scores in each epoch It is a quantile function. To calibrate the first in the dataset The node at the th The horizontal difference between the actual position and the estimated position in each epoch. To determine the first output of the pre-trained graph neural network on the calibration dataset The node at the th The correction protection level is obtained from the correction factor corresponding to each epoch.

[0066] Therefore, this invention aims to introduce conformal prediction for calibration, and use the calibration dataset to calculate the inconsistency score in order to obtain the risk of conforming to the target integrity. quantiles After obtaining the conformal protection level, OOD detection is performed. First, real-time features are extracted to obtain the current node. The latent feature vector output from the last layer of the graph neural network Then, offline statistical parameters are introduced. These parameters are obtained during the offline training phase. That is, after training is completed, the training set is input into the network again, and the empirical mean of the latent feature vectors of all nodes is calculated. And the obtained training distribution covariance matrix Finally, calculate the real-time features of the current node. With the mean of the training distribution Mahalanobis distance ; like Greater than the threshold If the scenario is unknown, it will be automatically reverted to the traditional protection level (HPL calculated using the traditional formula). Otherwise output This allows for high-precision monitoring of the integrity of the positioning results of each node in the cooperative positioning network while ensuring security.

[0067] Of course, the present invention may have other various embodiments. Without departing from the spirit and essence of the present invention, those skilled in the art can make various corresponding changes and modifications according to the present invention, but these corresponding changes and modifications should all fall within the protection scope of the appended claims.

Claims

1. A graph neural network-enhanced cooperative localization integrity monitoring method, characterized in that, In a cooperative localization network, each node determines its real-time node characteristics based on its current epoch. The distribution covariance matrix of a pre-trained graph neural network The empirical mean of the latent feature vectors of all nodes in the cooperative localization network Obtain the Mahalanobis distance for each node: in, Indicates the first Mahalanobis distances corresponding to each node Indicates transpose; Each node is judged to determine whether its Mahalanobis distance is greater than a set threshold. For nodes that are judged to be yes, the traditional protection level of each node in the current epoch is used as an indicator to monitor the cooperative positioning integrity of each node. For nodes that are judged to be no, the conformal protection level of each node in the current epoch obtained by using a pre-trained graph neural network is used as an indicator to monitor the cooperative positioning integrity of each node.

2. The graph neural network-enhanced cooperative localization integrity monitoring method as described in claim 1, characterized in that, No. Conformal protection level corresponding to each node The method for obtaining it is as follows: in, To calculate the first output based on the pre-trained graph neural network. Each node in the current epoch The corresponding correction factor yields the level of correction protection. For the first Each node in the current epoch The corresponding target integrity risk probability quantiles, The target risk probability.

3. The graph neural network-enhanced cooperative localization integrity monitoring method as described in claim 2, characterized in that, Correct protection level The method for obtaining it is as follows: in, For deterministic error limits, For statistical error limits, The output of the pre-trained graph neural network is the first... Each node in the current epoch The corresponding correction factor.

4. The graph neural network-enhanced cooperative localization integrity monitoring method as described in claim 3, characterized in that, The output of the pre-trained graph neural network is the first Each node in the current epoch The corresponding correction factor The method for obtaining it is as follows: Extracting node features as follows: in, For the first Each node in the current epoch The covariance matrix of the corresponding posterior state estimate The covariance factor obtained by performing Cholesky decomposition. For the calculation using traditional methods, the first Each node in the current epoch The corresponding traditional level of protection, For the first Each node in the current epoch The corresponding number of valid satellites; Extract the first GNSS side features corresponding to the GNSS receivers equipped on each node as follows: in, , For the first The node and the first New information between effective satellites For the first The node and the first Geometric vectors between valid satellites For the first The node and the first Noise variance between effective satellites For the first The node and the first Integrity slope between valid satellites; Extract the first Features of collaborative edges corresponding to each node as follows: in, For the first The node and the first Information between neighboring nodes For the first The node and the first Geometric vectors between neighboring nodes For the equivalent noise variance, For the first The node and the first The integrity slope between neighboring nodes; Node features GNSS edge features Collaborative edge characteristics The input is processed through a pre-trained graph neural network iteratively until the maximum number of iterations L is reached, thus obtaining the result at the Lth iteration. Each node in the current epoch Hidden state in ; according to Obtain the correction factor as follows: in, Let be the activation function of the graph neural network. This is the output layer mapping function of the graph neural network.

5. The graph neural network-enhanced cooperative localization integrity monitoring method as described in claim 4, characterized in that, No. Each node in the current epoch The covariance matrix of the corresponding posterior state estimate The method for obtaining it is as follows: The first Each node in the current epoch The effective observation input in the algorithm is based on a distributed cooperative localization algorithm with Gaussian confidence propagation, which solves the problem to obtain the first... Each node in the current epoch The covariance matrix of the corresponding posterior state estimate Among them, the posterior state estimation includes the first... Each node in the current epoch The ENU coordinates and receiver clock bias in the data.

6. The graph neural network-enhanced cooperative localization integrity monitoring method as described in claim 5, characterized in that, No. Each node in the current epoch The method for obtaining effective observations in the data is as follows: Get the The node and the first New information between effective satellites and its theoretical variance And according to the new information and theoretical variance Get the The node and the first Information statistics between valid satellites ; Will not exceed the preset threshold Corresponding new information Pseudo-distance observation As a valid observation; Get the The node and the first News between neighboring nodes and its theoretical variance And according to the new information and theoretical variance Get the The node and the first Information statistics between neighboring nodes ; Will not exceed the preset threshold Corresponding new information Pseudo-distance observation As a valid observation.

7. The graph neural network-enhanced cooperative localization integrity monitoring method as described in claim 4, characterized in that, covariance factor The method for obtaining it is as follows: Based on covariance matrix With covariance factor Relationship For the covariance matrix Perform Cholesky decomposition to obtain the covariance factor .

8. The graph neural network-enhanced cooperative localization integrity monitoring method as described in claim 2, characterized in that, No. The probability of target integrity risk corresponding to each node in the current epoch. quantiles The fixed parameters, which are pre-calculated during the offline calibration phase, are calculated as follows: in, To calibrate the first in the dataset The node at the th The corresponding non-consistent scores in each epoch It is a quantile function. To calibrate the first in the dataset The node at the th The horizontal difference between the actual position and the estimated position in each epoch. To determine the first output of the pre-trained graph neural network on the calibration dataset The node at the th The correction protection level is obtained from the correction factor corresponding to each epoch.

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