PPP-AR ambiguity error fixing soundness risk modeling method and device

Abstract

The application provides a PPP-AR ambiguity error fixed integrity risk modeling method and device, and belongs to the technical field of satellite navigation integrity, which comprises the following steps: determining whether the ambiguity of each satellite is correctly fixed at each epoch based on a resolution separation method, generating an ambiguity fixed label, and extracting relevant feature information; using the above label and feature information, a logistic regression model and a fault tree analysis model are respectively constructed, an ambiguity error fixed probability model is established, the model is optimized by K-fold cross-validation, and the outputs of the two are fused to obtain a robust total probability of error fixing; the worst case spatial signal ranging error of each satellite is combined to distribute the total probability by taking the square of the ranging error as the weight to obtain the error fixing probability of each satellite; based on the error fixing probability of each satellite, a satellite exclusion mechanism is constructed, and an integrity model is introduced to calculate the protection level containing risk items. The application meets the user integrity and continuity risk requirements.

Description

Technical Field

[0001] This invention relates to the field of satellite navigation integrity technology, specifically to a method and apparatus for modeling integrity risks of fixed PPP-AR ambiguity errors. Background Technology

[0002] With the continuous improvement of the measurement accuracy and stability of Global Navigation Satellite Systems (GNSS), Precise Point Positioning (PPP-AR) technology based on fixed integer ambiguity has been widely applied in high-precision scenarios such as autonomous driving, crustal deformation monitoring, and unmanned operations, achieving centimeter-level or even millimeter-level accuracy. Compared with traditional floating-point solutions, PPP-AR can shorten convergence time from the 30-minute level to the 5-minute level and compress 3D positioning error from the 10-cm level to the 1-cm level, maintaining its advantages even in dynamic environments. However, in practical applications, the coupling of multiple error sources, such as satellite orbit / clock error residuals, ionospheric / tropospheric model errors, multipath effects, and observation noise, makes it extremely easy for integer ambiguity fixing to result in errors that are difficult to detect afterward. A single incorrect fixing can cause the positioning error to jump instantaneously to 20 cm-1 m, directly compromising system integrity and threatening life-saving scenarios such as autonomous driving.

[0003] Therefore, existing PPP-AR integrity studies mainly have the following shortcomings:

[0004] 1. The fixed probability of error is difficult to quantify in real time: Traditional test measures only provide a binary decision of "pass / fail" and lack a continuous probability output of the fixed probability of error. In complex scenarios with active ionosphere and severe multipath, there is a deviation of hundreds or even thousands of times between the fixed success rate and the actual fixed probability of error, which cannot be directly used for risk budgeting.

[0005] 2. Multi-source observation information is not fully utilized: Most current methods only use double-difference / single-difference residuals or a simple ratio, ignoring the joint modeling of multi-dimensional features such as satellite geometry, signal quality, and atmospheric delay spatiotemporal gradient, resulting in a misjudgment rate as high as 5%–15% in complex environments.

[0006] 3. Protection level calculation of uncoupled error fixation probability: Existing integrity frameworks generally assume that "once the ambiguity is fixed, it is 100% correct", which approximates the error fixation probability as 0; or they use fixed conservative boundaries to superimpose at once, resulting in either overly conservative or overly optimistic results, which are difficult to meet the integrity risk index.

[0007] Therefore, how to construct a real-time modeling and allocation mechanism within the PPP-AR framework that is based on learning from real error fixed samples and coupled with multi-source observation features to accurately reflect integrity risks while maintaining availability has become a core technical problem that urgently needs to be solved in current PPP-AR integrity research. Summary of the Invention

[0008] To address the aforementioned technical problems, this invention provides a method and apparatus for modeling the integrity risk of fixed ambiguity errors in PPP-AR.

[0009] To achieve the above objectives, the present invention adopts the following technical solution:

[0010] Step 1: Determine whether the ambiguity of each satellite is correctly fixed epoch by epoch using the deseparation method, generate the corresponding fixation correctness label, and simultaneously extract multi-dimensional features related to fixation correctness;

[0011] Step 2: Construct a logistic regression model and a fault tree analysis model using the fixed correctness labels and multidimensional features respectively. Optimize and weight the outputs of the logistic regression model and the fault tree analysis model through K-fold cross-validation to obtain a robust fixed total probability of error.

[0012] Step 3: Using the square of the worst-case space signal ranging error of each satellite as the weight, perform satellite-level allocation on the total error fixed probability to obtain the error fixed probability of each satellite;

[0013] Step 4: Construct a satellite exclusion mechanism based on the error fixation probability of each satellite, and introduce the error fixation probability of each satellite into the integrity protection level calculation, so that the integrity protection level includes the ambiguity error fixation risk item;

[0014] PPP-AR stands for Precision Point Positioning.

[0015] The present invention also provides a PPP-AR ambiguity error fixation integrity risk modeling device for implementing the above method, comprising the following modules:

[0016] The multidimensional feature generation module determines whether the ambiguity of each satellite is correctly fixed epoch by epoch using a deseparation method, generates corresponding fixation correctness labels, and simultaneously extracts multidimensional features related to fixation correctness.

[0017] The error fixed total probability acquisition module uses the fixed correctness label and multi-dimensional features to construct a logistic regression model and a fault tree analysis model respectively. It optimizes and weights the outputs of the logistic regression model and the fault tree analysis model through K-fold cross-validation to obtain a robust error fixed total probability.

[0018] The error fixed probability acquisition module uses the square of the worst-case space signal ranging error of each satellite as a weight to perform satellite-level allocation on the total error fixed probability, thereby obtaining the error fixed probability of each satellite.

[0019] The exclusion module constructs a satellite exclusion mechanism based on the fixed error probability of each satellite and incorporates the fixed error probability of each satellite into the integrity protection level calculation, so that the integrity protection level includes the ambiguity error fixed risk item.

[0020] PPP-AR stands for Precision Point Positioning.

[0021] The present invention also provides an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement the steps of the above-described PPP-AR ambiguity error fixation integrity risk modeling method.

[0022] The present invention also provides a non-transitory computer-readable storage medium storing a computer program thereon, which, when executed by a processor, implements the steps of the above-described PPP-AR ambiguity error fixation integrity risk modeling method.

[0023] Beneficial effects:

[0024] (1) This invention can accurately identify ambiguity error fixed events and their potential causes through deseparation method and label extraction mechanism, laying the foundation for establishing a reliable risk model;

[0025] (2) This invention integrates two types of models, logistic regression and fault tree analysis, to achieve feature-driven and causal structure collaborative modeling, which significantly improves the accuracy and robustness of ambiguity error fixed probability estimation;

[0026] (3) This invention introduces the worst-case spatial signal ranging error index as a risk allocation weight, which can reflect the structural differences in ranging errors among satellites and realize reasonable risk allocation and difference modeling.

[0027] (4) This invention explicitly introduces the fixed risk of ambiguity error into the protection level calculation framework, improves the integrity assurance capability of PPP-AR, has good versatility and scalability, and is suitable for safety-critical positioning applications with multiple constellations, multiple frequencies and high reliability requirements. Attached Figure Description

[0028] Figure 1 This is a flowchart of a PPP-AR ambiguity error fixation integrity risk modeling method according to the present invention;

[0029] Figure 2 This is a schematic diagram of a PPP-AR ambiguity error fixation integrity risk modeling device according to the present invention;

[0030] Figure 3 This is a schematic diagram comparing the convergence process. Detailed Implementation

[0031] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention. Furthermore, the technical features involved in the various embodiments of the invention described below can be combined with each other as long as they do not conflict with each other.

[0032] like Figure 1 As shown, this invention proposes a method for modeling the integrity risk of fixed ambiguity errors in PPP-AR, comprising the following steps:

[0033] S1. Preparatory work before constructing a fixed probability model for ambiguity errors:

[0034] This invention first processes the PPP-AR positioning samples using the Solution Separation (SS) method to identify whether the ambiguity of each satellite at each epoch is correctly fixed and generates corresponding ambiguity fixation correctness labels. At the same time, it extracts feature information closely related to fixation correctness from the entire ambiguity resolution process to provide data support for subsequent modeling.

[0035] S2. Construction and probability determination of a fixed probability model for ambiguity errors:

[0036] After obtaining the ambiguity fixation correctness labels and feature information, a Logistic Regression (LR) model and a Fault-tree Analysis (FTA) model are constructed to characterize the probabilistic relationship between features and error fixation, as well as the causal logical structure of error events. The LR and FTA models are trained and evaluated using K-fold cross-validation, and their outputs are weighted and fused to obtain a more robust and generalized overall probability of ambiguity error fixation.

[0037] S3. Allocation of fixed probability of ambiguity error based on SISRE index:

[0038] For the total probability of fixing the obtained ambiguity error, the worst-case space signal ranging error (SISRE) of each satellite is combined with the square of SISRE as the weight to weight the total probability of fixing the ambiguity error, so as to reasonably reflect the contribution of each satellite to the error fixing risk, and finally obtain the ambiguity error fixing probability of each satellite, thus realizing satellite-level risk modeling.

[0039] S4. Calculation of user protection level considering fixed risk of ambiguity error:

[0040] By utilizing the fixed probability of ambiguity errors for each satellite, a satellite exclusion mechanism is constructed to identify and eliminate potentially erroneous satellites, thereby improving the reliability of PPP-AR solutions. Simultaneously, the fixed probability of ambiguity errors for each satellite is incorporated into the Protection Level (PL) calculation model, explicitly including the ambiguity error fixation risk term to meet the user-defined integrity and continuity risk requirements.

[0041] Specifically, S1 includes:

[0042] The positioning samples are processed using the Solution Separation (SS) method to determine whether the ambiguities of each satellite at each epoch are correctly fixed, thereby generating ambiguity fixation correctness labels. Subsequently, feature information related to fixation correctness is extracted from the entire ambiguity resolution process. These ambiguity fixation correctness labels and corresponding feature information will serve as input to S2, specifically including:

[0043] S1.1. Use the de-separation method to determine the ambiguity fixation correctness label for each satellite.

[0044] For each epoch, assume Corresponding to a visible satellite The ambiguity of each deionization combination is fixed, so we can let ,in Represents the ambiguity vector. Indicates the first The fixed ambiguity of each satellite, with the superscript T indicating the transpose of the matrix.

[0045] In order to determine Which specific satellite among the satellites had its ambiguity incorrectly fixed? Let's assume, in turn, the 1st... One satellite is faulty; it is excluded, and the subset position solution is recalculated.

[0046] (1)

[0047] in, Is it excluding the first The ambiguity vector after each satellite; Is it excluding the first The subset position solution obtained after recalculating the solution for each satellite; It is an ionosphere-reducing combination PPP-AR calculation.

[0048] The deviation between the recalculated subset location solution and the universal set location solution, i.e., excluding the first... Positional deviation after each satellite for:

[0049] (2)

[0050] in, It is the complete set of positional solutions obtained by using all available satellites; To exclude the first The positional deviation after each satellite; This represents the L2 norm.

[0051] If the position changes deviation Exceeding a predefined threshold Then the first The ambiguity of the first satellite is considered an error fixation. Therefore, the ambiguity of the second satellite... The accuracy label for fixing the ambiguity of each satellite for:

[0052] (3)

[0053] in, It is a predefined threshold for the location solution; It is the first The ambiguity of each satellite is fixed with a correctness label, which takes values ​​of 0 or 1, representing the correctness of the first satellite. The ambiguity of each satellite is fixed correctly and incorrectly.

[0054] Determine the ambiguity vector in sequence according to the above steps. Each satellite in the dataset has a corresponding fixed ambiguity correctness label, which ultimately forms the ambiguity fixed correctness label vector for that epoch. ,in Indicates the first The ambiguity of each satellite is fixed with a correctness label.

[0055] S1.2 In the entire ionosphere elimination combined PPP-AR process, the successfully fixed ambiguities are used as samples to extract features that affect integrity risk or continuity risk.

[0056] This embodiment selects six features. The first feature is the satellite elevation angle. Low satellite elevation angles often result in poor observation quality, increasing the likelihood of incorrect positioning. The second feature is the continuous tracking time. Short tracking times may lead to unstable ambiguity fixation. The third feature is the wide-lane ambiguity fixation status. Incorrect wide-lane ambiguity fixation increases the likelihood of incorrect narrow-lane ambiguity fixation. The fourth feature is the carrier phase residual. A large carrier phase residual may indicate incorrect ambiguity fixation. The fifth feature is the ambiguity variance. A large covariance implies high uncertainty in ambiguity estimation, increasing the likelihood of incorrect fixation. The sixth feature is the phase deviation product status. Anomalies or discontinuities in the phase deviation product directly affect the reliability of ambiguity fixation.

[0057] Specifically, S2 includes:

[0058] Using the ambiguity fixation correctness labels and related feature information obtained in S1, a Logistic Regression (LR) model and a Fault-tree Analysis (FTA) model are constructed to establish a probabilistic model for ambiguity error fixation. The LR model characterizes the probabilistic relationship between feature variables and ambiguity error fixation events, while the FTA model is used to uncover the causal paths and logical combinations of ambiguity errors. To improve the prediction accuracy and generalization ability of the models, K-fold cross-validation is used to train and evaluate the two models separately. Finally, the outputs of the LR and FTA models are weighted and fused to obtain a more robust total probability of ambiguity error fixation. This total probability serves as the input to S3, specifically including:

[0059] Using a logistic regression model, based on the ambiguity fixation correctness label and six feature information output by S1, the probability of ambiguity error fixation driven by the logistic regression model is estimated.

[0060] Assume the logistic regression model satisfies the following probability function:

[0061] (4)

[0062] in, The fixed probability of ambiguity error is obtained based on the logistic regression model; The feature vector is constructed based on the six feature information output by S1; It is a parameter vector obtained from the training data; It is a deviation term. This represents an exponential function.

[0063] By minimizing Cross-entropy loss for each training sample To estimate model parameters, i.e., the parameter vector obtained from the training data. Sum of deviations :

[0064] (5)

[0065] in, To fix the correctness label based on the ambiguity output of S1; The first output of the logistic regression model The predicted probability that a sample belongs to the correct category.

[0066] Fault tree analysis models estimate the probability of ambiguity error fixation by considering multiple independent fault events that may lead to ambiguity error fixation. The overall risk of ambiguity error fixation is modeled as follows:

[0067] (6)

[0068] in, The fixed probability of ambiguity error is obtained based on the fault tree analysis model; The multiplication symbol represents the result of multiplying terms within a given range of subscripts; Indicates the first A basic failure event; It corresponds to the experienced incidence rate of this event; This represents the total number of basic failure events considered.

[0069] Under the assumption of low probability, that is The above expression can be approximated as:

[0070] (7)

[0071] Each basic fault event The empirical probability of each basic fault event corresponds to a feature type output by S1. The calculation is as follows:

[0072] (8)

[0073] in, Basic fault events The epoch number of the occurrence; It represents the total number of epochs evaluated in the entire dataset.

[0074] To integrate logistic regression and fault tree analysis models and reduce over-reliance on either model, this invention employs a weighted combination approach:

[0075] (9)

[0076] in, Indicates based on weight parameters The total probability of a fixed ambiguity error after fusion; The fusion weights are optimized through K-fold cross-validation.

[0077] Optimal weight By minimizing the overall log loss on the K-fold cross-validation dataset To choose:

[0078] (10)

[0079] in, Indicates the weight parameters The overall log loss of the controlled fusion model on the validation dataset; The output of the fusion model represents the first... The predicted probability that a sample belongs to the correct category.

[0080] The optimization problem is described as follows:

[0081] (11)

[0082] in, Indicates the interval Internal search variables In order to obtain the parameters that minimize the objective function value.

[0083] Once the optimal weights are found Then, the fixed probability of ambiguity error after fusion can be calculated according to formula (9).

[0084] Specifically, S3 includes:

[0085] Based on the total probability of ambiguity error fixation after fusion in S2, and considering the worst-case Signal-in-Space Range Error (SISRE) for each satellite, this total probability is reasonably allocated. Given that satellites with larger SISREs contribute more to the overall ambiguity error fixation risk, the square of the SISRE is used as a weight, and the allocation is weighted according to the total probability of error fixation for each satellite. This yields the ambiguity error fixation probability for each satellite, which will serve as the input to S4, specifically including:

[0086] Calculate the worst-case space signal ranging error for each satellite:

[0087] (12)

[0088] in, Indicates satellite The worst-case spatial signal ranging error; Indicates satellite The corresponding worst-case satellite orbit error in the user's line-of-sight direction; Indicates satellite The corresponding satellite clock error.

[0089] Satellites after fault allocation The corresponding ambiguity error has a fixed probability. for:

[0090] (13)

[0091] in, The ambiguity error probability obtained after fusion is fixed as S2; The total number of satellites participating in the positioning is given by , and p is the index value of each satellite participating in the positioning.

[0092] Specifically, S4 includes:

[0093] Using the ambiguity error fixation probability of each satellite calculated in S3, a satellite exclusion mechanism is designed to exclude satellites with potential ambiguity fixation, thereby improving the reliability of the solution. Simultaneously, the error fixation probability of each satellite is incorporated into the integrity assessment model to construct a Protection Level (PL) calculation method that includes risk terms. This method comprehensively considers the probability of positioning errors exceeding the protection level under both "no ambiguity fixation" and "ambiguity fixation with ambiguity error fixation" scenarios, thus achieving comprehensive monitoring of ambiguity fixation reliability while meeting the user-defined integrity and continuity risk requirements. Specifically, this includes:

[0094] Faulty satellites are eliminated based on the ambiguity error fixation probability of each satellite obtained from S3. This faulty satellite elimination mechanism aims to address two key issues: first, determining whether satellites with potential ambiguity errors should be retained or excluded; and second, determining whether the cause of the error fixation is due to cycle slips or general faults. This logic ensures the integrity of the positioning solution while avoiding the unnecessary exclusion of useful satellites.

[0095] First, the fixed probability of ambiguity error for each satellite output in S3 is evaluated. A predefined threshold is then introduced. To determine whether further ambiguity checks are needed.

[0096] if Then it is considered a satellite The ambiguity is sufficiently reliable and preserved, and robustness can be achieved through inclusion even at marginal risk levels. This supports fault-tolerant applications such as conservative integrity boundary calculations.

[0097] if Then the satellite is suspected. The ambiguity is unreliable, and a cycle slip detection procedure is performed to obtain the corresponding satellite data. Cycle slip detection label If a cycle slip is confirmed, reset the satellite. The ambiguity. If no cycle slip is detected, the correctness label needs to be fixed based on the ambiguity output by S1. Further assessment is needed. If the label indication ambiguity has been correctly fixed, the satellite will be retained. And reset it. If the label indicates ambiguity is incorrectly fixed, then the satellite... Ambiguity is considered an error fix and needs to be excluded.

[0098] The overall faulty satellite removal mechanism can be expressed mathematically as follows:

[0099] (14)

[0100] in, , and These represent hold, reset, and exclude operations, respectively. The satellite obtained for S3 The ambiguity error has a fixed probability; For predefined risk thresholds; For satellite The indicator of whether a cycle slip was successfully detected includes the following values: and There are two categories, representing successful detection (True) and failed detection (False). For the satellite corresponding to S1 The ambiguity is fixed and the correctness label has the following values: and There are two categories, representing correctly fixed and incorrectly fixed, respectively. Indicates intersection.

[0101] After excluding satellites with fixed ambiguity errors, the protection level will be calculated. First, the integrity risk expressions for the horizontal and vertical directions will be constructed:

[0102] (15)

[0103] (16)

[0104] in, and These represent the probabilities of Hazardous Misleading Information (HMI) in the horizontal and vertical directions, respectively. This represents the probability that the ambiguity of all satellites is correctly fixed, calculated using the following formula: ,in Satellites output by S3 The ambiguity error has a fixed probability; This indicates the assumption that there is no fixed ambiguity error; Indicates the first The assumption that the ambiguity error of each satellite is fixed; Indicates the total number of satellites; and These represent the horizontal positioning error and the vertical positioning error, respectively. and These represent the horizontal protection level and the vertical protection level, respectively.

[0105] Without the assumption that ambiguity error is fixed. and only a single satellite The assumption of fixed ambiguity error In this case, the present invention assumes that the user's positioning error can be approximately modeled as a zero-mean normal distribution:

[0106] (17)

[0107] in, and These respectively represent the absence of ambiguity error fixing and the first The standard deviation of the horizontal positioning error is fixed for each satellite's ambiguity error; and These respectively represent the absence of ambiguity error fixing and the first The standard deviation of the fixed vertical positioning error for each satellite. N represents a zero-mean normal distribution.

[0108] because and It is a non-standard normal distribution, therefore it needs to be standardized, that is:

[0109] (18)

[0110] in, and These represent the horizontal and vertical positioning errors, respectively, which conform to a standard normal distribution after standardization.

[0111] Therefore, we can obtain the following expression:

[0112] (19)

[0113] (20)

[0114] in, Represents a random variable that follows a standard normal distribution. The corresponding right-tail probability function is defined as follows: , Let be a random variable that follows a standard normal distribution; Represents random variables The corresponding cumulative distribution function is defined as follows: t represents time.

[0115] Substituting formula (19) into formula (15) and formula (20) into formula (16), we can obtain a new expression for integrity risk:

[0116] (twenty one)

[0117] (twenty two)

[0118] in, and These represent the updated probabilities of dangerous misleading information in the horizontal and vertical directions, respectively.

[0119] In order to solve for the updated horizontal protection level corresponding to formulas (20) and (21) and vertical protection horizontal The goal is to find the minimum condition. and :

[0120] (twenty three)

[0121] (twenty four)

[0122] in, and These are the horizontal and vertical protection levels, respectively, that make formulas (21) and (22) hold true. and These represent the user's risk tolerance in the vertical and horizontal directions, respectively.

[0123] Based on the objectives of formulas (23) and (24), the updated protection levels corresponding to formulas (21) and (22) are calculated respectively. Here, the horizontal protection level calculation method is taken as an example, and the vertical protection level calculation method will be consistent with the horizontal protection level calculation method.

[0124] The Brent method is used to solve for the root of the nonlinear protection level risk function. This method improves the solution efficiency while ensuring numerical stability by combining the convergence of the bisection method with the secant method and parabolic interpolation.

[0125] Assume the objective function is:

[0126] (25)

[0127] in, The function representing the difference in risk of horizontal integrity; This represents the protected-level variable being substituted. Solving for it allows... Established horizontal protection level variables To determine the level of protection that meets the integrity risk constraints.

[0128] The first step is initialization. This involves setting up the search space. The function must undergo a sign change within this interval, i.e., satisfy the condition... ,in and These represent the lower and upper boundaries of the initial search interval, respectively; then the initial values ​​are calculated: , Finally, set the current solution to And record: , , , ,in , and Representing functions respectively At point , , The value at that point is used to determine the interpolation direction and update the search interval.

[0129] The second step is to determine convergence. At each iteration, it is checked whether the convergence condition is met. or If the iteration stops, return. If it is an approximate root, then continue iterating; otherwise, continue iterating. It is the function tolerance. It is the range tolerance.

[0130] If the second step fails, proceed to the third step: use parabolic interpolation. and Try three-point parabolic interpolation:

[0131] Let the parabola pass through the point , , Its interpolation points for:

[0132] (26)

[0133] in, Candidate interpolation points; The function values ​​for the candidate interpolation points. If If convergence is satisfied, then accept. This serves as the next iteration point.

[0134] If the third step fails, proceed to the fourth step: use the secant method.

[0135] If the above interpolation conditions are not met, the method degenerates into the secant method: Linear interpolation is performed using only the two nearest points.

[0136] If step four fails, proceed to step five: use the binary search method.

[0137] If the secant method also fails to converge, for example... Not here Internally, it reverts to a conservative dichotomy: Then determine based on the sign: if Then let Otherwise Simultaneously updated and And continue to the next iteration.

[0138] Thus, the present invention will achieve a protection level that at least meets the user-defined horizontal integrity risk tolerance. Similarly, by following the steps above, the protection level of the user-defined vertical integrity risk tolerance can also be obtained. .

[0139] Example:

[0140] This embodiment presents the solution process for the nonlinear protection level risk function based on the Brent method. In this embodiment, the user's horizontal integrity risk tolerance is set to... Let the initial search interval be... Function tolerance Interval tolerance The endpoint function value is obtained by calculating , ,satisfy This ensures that a root exists within the interval.

[0141] During the iteration process, the algorithm automatically switches between parabolic interpolation, secant method, and bisection method while maintaining the sign change condition. When the interpolation result does not meet the convergence requirement or exceeds the interval range, the method automatically reverts to secant or bisection update to ensure the stability and reliability of the calculation process.

[0142] like Figure 3 As shown, the Brent method can bring the horizontal integrity risk difference function to converge after about 10 iterations. The magnitude of the convergence is approximately 14 times for the secant method and approximately 16 times for the bisection method. The results show that the Brent method used in this invention significantly improves the convergence speed while ensuring numerical stability, and can efficiently obtain the protection level that satisfies the integrity risk constraint.

[0143] like Figure 2 As shown, the present invention also provides a PPP-AR ambiguity error fixation integrity risk modeling device for implementing the above method, comprising the following modules:

[0144] The multidimensional feature generation module determines whether the ambiguity of each satellite is correctly fixed epoch by epoch using a deseparation method, generates corresponding fixation correctness labels, and simultaneously extracts multidimensional features related to fixation correctness.

[0145] The error fixed total probability acquisition module uses the labels and features to construct a logistic regression model and a fault tree analysis model respectively. It optimizes and weights the outputs of the two models through K-fold cross-validation and fuses them to obtain a robust error fixed total probability.

[0146] The error fixed probability acquisition module uses the square of the worst-case space signal ranging error of each satellite as a weight to perform satellite-level allocation on the total probability, thereby obtaining the error fixed probability of each satellite.

[0147] The exclusion module constructs a satellite exclusion mechanism based on the fixed probability of satellite-level errors and introduces this probability into the calculation of the integrity protection level, so that the protection level includes a fixed risk item for ambiguity errors, thereby meeting the integrity and continuity risk requirements.

[0148] The present invention also provides an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement the steps of the above-described PPP-AR ambiguity error fixation integrity risk modeling method.

[0149] The present invention also provides a non-transitory computer-readable storage medium storing a computer program thereon, which, when executed by a processor, implements the steps of the above-described PPP-AR ambiguity error fixation integrity risk modeling method.

[0150] Those skilled in the art will understand that embodiments of the present invention can be provided as methods, systems, or computer program products. Therefore, the present invention can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention can take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code. The solutions in the embodiments of the present invention can be implemented using various computer languages, such as the object-oriented programming language Java and the interpreted scripting language JavaScript.

[0151] This invention is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart illustrations and / or block diagrams. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0152] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0153] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0154] Although preferred embodiments of the invention have been described, those skilled in the art, upon learning the basic inventive concept, can make other changes and modifications to these embodiments. Therefore, the appended claims are intended to be interpreted as including both the preferred embodiments and all changes and modifications falling within the scope of the invention.

[0155] Obviously, those skilled in the art can make various modifications and variations to this invention without departing from its spirit and scope. Therefore, if these modifications and variations fall within the scope of the claims of this invention and their equivalents, this invention also intends to include these modifications and variations.

Claims

1. A method for modeling the integrity risk of fixed ambiguity errors in PPP-AR, characterized in that, Includes the following steps: Step 1: Determine whether the ambiguity of each satellite is correctly fixed epoch by epoch using the deseparation method, generate the corresponding fixation correctness label, and simultaneously extract multi-dimensional features related to fixation correctness; The decomposition method includes: first calculating the position solution with the ambiguity of the whole set fixed, then removing individual satellites one by one and recalculating the position solution of the subset. By comparing the deviation between the position solution of the subset and the whole set with the size of the preset threshold, it is determined whether the ambiguity of the removed satellite is correctly fixed and a corresponding fixation correctness label is generated. Step 2: Construct a logistic regression model and a fault tree analysis model using the fixed correctness labels and multidimensional features respectively. Optimize and weight the outputs of the logistic regression model and the fault tree analysis model through K-fold cross-validation to obtain a robust fixed total probability of error. Step 3: Using the square of the worst-case spatial signal ranging error of each satellite as the weight, perform satellite-level allocation on the total error fixed probability to obtain the error fixed probability of each satellite; Calculate the worst-case space signal ranging error for each satellite: （12） in, Indicates satellite The worst-case spatial signal ranging error; Indicates satellite The corresponding worst-case satellite orbit error in the user's line-of-sight direction; Indicates satellite Corresponding satellite clock error; Step 4: Construct a satellite exclusion mechanism based on the error fixation probability of each satellite, and introduce the error fixation probability of each satellite into the integrity protection level calculation, so that the integrity protection level includes the ambiguity error fixation risk item; PPP-AR stands for Precise Point Positioning with Fixed Ambiguity.

2. The PPP-AR ambiguity error fixation integrity risk modeling method according to claim 1, characterized in that, In step 1, the multidimensional features include satellite elevation angle, continuous tracking time, wide-lane ambiguity fixed state, carrier phase residual, ambiguity variance, and phase deviation product state.

3. The PPP-AR ambiguity error fixation integrity risk modeling method according to claim 1, characterized in that, In step 2, the logistic regression model takes the multidimensional features as input, uses fixed correctness labels as supervision, and obtains a feature-driven fixed probability output of errors by minimizing cross-entropy loss during training.

4. The PPP-AR ambiguity error fixation integrity risk modeling method according to claim 1, characterized in that, In step 2, the fault tree analysis model takes the out-of-limit events corresponding to each multi-dimensional feature as basic events, calculates the occurrence rate of each basic event based on historical data, and calculates the fixed total probability of error according to the logic of independent fault superposition.

5. The PPP-AR ambiguity error fixation integrity risk modeling method according to claim 1, characterized in that, In step 2, the weighted fusion determines the optimal weights by minimizing the log loss through K-fold cross-validation, and linearly combines the output of the logistic regression model with the output of the fault tree analysis model to obtain the fused fixed total probability of error.

6. The PPP-AR ambiguity error fixation integrity risk modeling method according to claim 1, characterized in that, In step 4, the satellite exclusion mechanism includes: comparing the error fixed probability of each satellite with a preset threshold, performing cycle slip detection, ambiguity reset or satellite exclusion operation sequentially on satellites that exceed the preset threshold, and introducing the error fixed probability of the remaining satellites into the protection level equation to iteratively solve the minimum horizontal protection value and vertical protection value that satisfy the risk tolerance.

7. A PPP-AR ambiguity error fixation integrity risk modeling device, characterized in that, Includes the following modules: The multidimensional feature generation module determines whether the ambiguity of each satellite is correctly fixed epoch by epoch using a deseparation method, generates corresponding fixation correctness labels, and simultaneously extracts multidimensional features related to fixation correctness. The decomposition method includes: first calculating the position solution with the ambiguity of the whole set fixed, then removing individual satellites one by one and recalculating the position solution of the subset. By comparing the deviation between the position solution of the subset and the whole set with the size of the preset threshold, it is determined whether the ambiguity of the removed satellite is correctly fixed and a corresponding fixation correctness label is generated. The error fixed total probability acquisition module uses the fixed correctness label and multi-dimensional features to construct a logistic regression model and a fault tree analysis model respectively. It optimizes and weights the outputs of the logistic regression model and the fault tree analysis model through K-fold cross-validation to obtain a robust error fixed total probability. The error fixed probability acquisition module assigns the total error fixed probability to each satellite at the satellite level, using the square of the worst-case spatial signal ranging error of each satellite as the weight, to obtain the error fixed probability of each satellite. Calculate the worst-case space signal ranging error for each satellite: （12） in, Indicates satellite The worst-case spatial signal ranging error; Indicates satellite The corresponding worst-case satellite orbit error in the user's line-of-sight direction; Indicates satellite Corresponding satellite clock error; The exclusion module constructs a satellite exclusion mechanism based on the fixed error probability of each satellite and incorporates the fixed error probability of each satellite into the integrity protection level calculation, so that the integrity protection level includes the ambiguity error fixed risk item. PPP-AR stands for Precise Point Positioning with Fixed Ambiguity.

8. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the program, it implements the steps of the PPP-AR ambiguity error fixation integrity risk modeling method as described in any one of claims 1 to 6.

9. A non-transitory computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements the steps of a PPP-AR ambiguity error fixation integrity risk modeling method as described in any one of claims 1 to 6.

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