Automatic modeling method of GNSS multipath error for integrity monitoring needs

Abstract

This invention discloses an automated modeling method for GNSS multipath errors tailored to integrity monitoring needs, including: statistically analyzing raw multipath error data to generate a CDF; designing a model form; binary encoding; and estimating model parameters using a multi-objective genetic algorithm. The invention quantifies the CDF envelope requirement within the genetic algorithm's objective function, effectively enveloping the error. A sinusoidal adaptive function for the elevation angle is designed within the genetic algorithm's objective function, allowing the algorithm to automatically adjust the relative weights of the two modeling requirements, thereby reducing the conservatism of the modeling results for high-elevation angle scenarios and improving the fit to the true error. In the multipath error model form, one or more expansion factors are used to improve the model's fit to the true error, further reducing the conservatism of the modeling results and improving the fit to the true error.

Description

Technical Field

[0001] The present invention belongs to the field of civil aviation technology, and in particular relates to a GNSS multipath error automatic modeling method oriented to integrity monitoring needs. Background Art

[0002] The integrity of Global Navigation Satellite System (GNSS) services remains a top concern for GNSS users in safety-of-life (SoL) sectors, such as civil aviation. Currently, GNSS service integrity monitoring is primarily achieved by modeling various error sources to calculate protection levels. Multipath error, a ranging error caused by reflected or refracted GNSS signals, primarily arises from the impact of these indirect signals on the correlation peaks of GNSS receivers. It is one of the most significant error sources affecting GNSS service accuracy and must be considered during GNSS service integrity monitoring.

[0003] In recent years, multipath error modeling has been a research hotspot in GNSS integrity monitoring. To further advance GNSS applications in civil aviation, the United States and the European Union have conducted systematic research on multipath error modeling. The EU has partnered with internationally renowned aerospace companies and research institutions, including the German Aerospace Center (DLR), Airbus, and Collins, to launch the DUFMAN (Dual-Frequency Multipath Model for Aviation) research program.

[0004] The main idea behind existing multipath error modeling methods is to first classify and count the raw multipath error data by elevation angle to generate probability distribution functions (CDFs) for different elevation angle intervals. The CDF envelope method is then used to envelop the multipath error CDF to obtain a multipath error random model (in the form of standard deviation) that meets the envelope error requirements for integrity monitoring. The principle of the CDF envelope method is as follows:

[0005]

[0006]

[0007]

[0008] Where F represents the CDF, and f represents the probability density function (PDF). The subscript "o" stands for "overbounding," indicating the model used to model the envelope error. The subscript "a" stands for "actual," indicating the actual error. The CDF envelope method is also the general approach recommended by the International Civil Aviation Organization (ICAO) Annex 10 for multipath error modeling.

[0009] In 2018, Dr. Fan Guochao of Beijing Institute of Technology proposed a multipath error modeling algorithm based on the CDF envelope method in his doctoral dissertation, "Research on RAIM Technology and Simulation System Design for Typical Urban Canyons." He also applied genetic algorithms to multipath error modeling for the first time, laying the foundation for automated multipath error modeling. Considering that multipath effects often occur in low-altitude scenarios, to reduce the false alarm rate of the integrity monitoring system, a direct fit of the CDF of multipath errors above 15° was performed, using a 15° elevation angle as a threshold. For elevation angles below 15°, an additional envelope term was added to the model, and additional expansion factor parameters were estimated to achieve an envelope for the multipath error. Finally, the difference between the CDF sampling points of the model and the true error was used as an indicator, and the model parameters were optimized to minimize the sum of squares of the differences.

[0010] A multipath error model that meets the needs of GNSS integrity monitoring should meet the following two basic requirements: 1. The multipath error model should be able to envelop all real errors in the modeling data set to ensure that the multipath errors under real extreme conditions are still within the consideration range; 2. The error model should be as close to the real error as possible and not be too conservative.

[0011] Currently, published international literature has yet to address how to comprehensively consider these two requirements during the modeling process. In current domestic engineering practice, manual adjustments to model parameter values ​​are often used to manually balance these two requirements to determine the final model parameters. However, this manual approach is not only inefficient but also only applicable to scenarios with simple modeling requirements and requirements, resulting in numerous limitations.

[0012] Dr. Fan Guochao's multipath error modeling method uses the sum of squared CDF differences as the optimization metric. This square summation eliminates the sign differences in the CDF envelope error requirements. Therefore, Dr. Fan's multipath modeling process is essentially still a least-squares fitting problem, and the CDF envelope requirements are still not fully considered. Furthermore, the universality of the 15° threshold remains to be studied. Summary of the Invention

[0013] To address the shortcomings of the above-mentioned existing technologies, the present invention proposes an automated GNSS multipath error modeling method for integrity monitoring. This method aims to automate the modeling process, effectively and comprehensively consider modeling requirements, and improve the model's fit to the actual error. The specific technical solutions of the present invention are as follows:

[0014] The automated modeling method for GNSS multipath error for integrity monitoring needs includes the following steps:

[0015] S1: With the support of IGS broadcast ephemeris historical data, the multipath error data in the pseudorange observation values ​​of the GNSS signal is extracted using the pseudorange and carrier phase historical observation data of the airborne GNSS receiver or the ground GNSS monitoring station to generate the CDF;

[0016] S2: Design the multipath error model using the elevation angle as the characteristic quantity;

[0017] S3: Binary encode the model parameters and convert the decimal values ​​into binary sequences as the operation objects of the multi-objective genetic algorithm;

[0018] S4: The optimization goal is set to meet the CDF envelope error requirements, and the difference between the CDF of the model and the true error is minimized. The multi-objective genetic algorithm is used to select the optimal binary sequence to estimate the model parameters.

[0019] Furthermore, the step S1 includes:

[0020] S1-1: Extract multipath error data using the multipath error combination of the observed values, specifically:

[0021]

[0022] Among them, f a and f b are the frequency values ​​of two different frequency signals a and b respectively; ε a is the multipath error data extracted from the pseudorange observation value of the a signal, P a is the pseudorange observation value obtained using the a signal, L a and L b are the carrier phase observation values ​​obtained using signals a and b respectively;

[0023] S1-2: Divide the priori numerical value variation range and altitude angle variation range of the data point into equal parts to form a grid with the horizontal axis variable being the numerical value of the data point and the vertical axis variable being the altitude angle of the data point;

[0024] S1-3: Count the number of data points corresponding to each grid and the number of data points corresponding to each elevation angle sub-interval;

[0025] S1-4: Normalize the number of data points corresponding to each grid by dividing it by the total number of data points in the corresponding altitude subinterval:

[0026]

[0027] Among them, PDF ij is the PDF value corresponding to the grid with horizontal coordinate i and vertical coordinate j, n ij is the number of data points in the grid with horizontal coordinate i and vertical coordinate j, n kj is the number of data points in the grid with abscissa k and ordinate j, i, j, k are the grid abscissa, grid ordinate and grid abscissa variable used for accumulation respectively;

[0028] S1-5: Convert PDF points to CDF points by accumulation to generate CDF for modeling:

[0029]

[0030] Among them, CDF ij is the CDF value corresponding to the grid with horizontal coordinate i and vertical coordinate j.

[0031] Furthermore, the step S2 includes:

[0032] S2-1: Assume that the multipath error consists of three parts:

[0033] ε=ε1+ε2+ε3 (4)

[0034] Among them, ε1 is the height angle correlation quantity that obeys Gaussian distribution, ε2 is a Gaussian distribution that is independent of the altitude angle. ε3 is a component with unknown distribution characteristics, which is set to a linear combination of ε1 and ε2 to envelop the fat-tail error;

[0035] ε3=α·ε1+β·ε2 (5)

[0036] S2-2: Introduce additional expansion factors to refine the model form of ε3:

[0037] ε3=η·(ε1+ε2) (6)

[0038] ε=(1+α)·ε1+(1+β)·ε2 (7)

[0039] At this time, the standard deviation of ε is:

[0040]

[0041] Finally, the standard deviation of ε2 is set to:

[0042] σ2=a2+b2·exp(-c2·El) (9)

[0043] Among them, El is the altitude angle of the angle value, and the six unknown parameters of the model σ1, α, β, a2, b2, and c2 are estimated by genetic algorithm.

[0044] Furthermore, in step S3, binary coding is used to abstract the parameters to be solved into binary chromosomes:

[0045]

[0046] Value Para =CA·Value BS +Value Start (11)

[0047] Among them, CA is Coding Accuracy, which indicates the coding accuracy; Value is a decimal value, N is the specified binary sequence length, Value End and Value Start Corresponding to the two ends of the prior search interval of the estimated parameter, Value Para Indicates the decimal value of the parameter to be estimated, Value BS Indicates the decimal code value of the binary sequence relative to the start of the data;

[0048] The binary chromosomes are constantly changing as the genetic algorithm is executed and the chromosome set evolves.

[0049] Furthermore, the step S4 includes:

[0050] S4-1: Construct the objective function; by designing the objective function, the genetic algorithm is specified as an optimization problem to be minimized, that is, individuals with smaller objective function values ​​are better; then, the best individuals will be assigned a larger fitness;

[0051] The objective function is designed as:

[0052]

[0053]

[0054]

[0055] Where p and q are the altitude angle and the number of numerical subintervals respectively, ω i ,k and 1-sin(El i ) are weight factors, ω iIt is a random number that varies between 0 and 1 and is used to prevent the genetic algorithm from performing random searches in only one direction.

[0056] k is a constant used to specify the weight of the envelope error modeling target relative to the optimal fitting effect modeling target and needs to be set in advance;

[0057] Sine function of altitude angle 1-sin(El i ) is an adaptive function that changes with the altitude angle and is used to automatically set different weights for different altitude angle intervals;

[0058] y min and y ob It is the specific implementation of the envelope error target and the fitting target, y min Describes the average CDF difference between the constructed model and the actual error; y ob It is designed as a penalty function. When the CDF envelope error requirement is met, y ob Corresponds to "success", otherwise corresponds to "fail";

[0059] Reduce the probability that genes of individuals that do not meet the envelope error requirements will enter the next generation;

[0060] S4-2: Individual hierarchical sorting; individuals with similar objective function values ​​are divided into one level, and individuals in the same level will have the same probability of being selected;

[0061] S4-3: Individual selection: New individuals are randomly selected to enter the next generation in a "roulette wheel" manner with a specified probability. Individuals in the population are abstracted as sectors on a roulette wheel. The ratio of the sector area to the total area of ​​the roulette wheel is equal to the ratio of the individual fitness to the total fitness of the population. A certain number of individuals with the highest fitness values ​​in each generation are allowed to enter the next generation directly without random selection.

[0062] S4-4: Chromosome crossover; the two-point crossover method is used, and the crossover point positions are randomly determined with equal probability;

[0063] S4-5: Chromosome mutation; for each bit on the binary chromosome, generate a Boolean random number with a specified mutation probability. If the random number is true, flip the binary number, that is, change 0 to 1 or 1 to 0. The number of elite individuals, chromosome crossover and mutation probability must be specified.

[0064] Furthermore, in step S3, the values ​​at both ends of the priori search interval of the parameter to be estimated are set to one third of the maximum variation range of the priori value.

[0065] Furthermore, in step S4, the number of iterations of the genetic algorithm is set to 200 to 1000 generations.

[0066] The beneficial effects of the present invention are:

[0067] 1. This invention quantifies the CDF envelope requirement in the objective function of the genetic algorithm. This allows for the automation of the modeling process while comprehensively considering these two modeling requirements: the multipath error model should be able to envelop all true errors in the modeling dataset to ensure that multipath errors under real extreme conditions remain within the consideration range; and the error model should be as close to the true error as possible without being overly conservative. This effectively envelops the error.

[0068] 2. In the objective function of the genetic algorithm, the present invention designs a sinusoidal adaptive function of the elevation angle, so that the algorithm can automatically adjust the relative weights of the two modeling requirements according to the elevation angle corresponding to the multipath error, thereby reducing the conservatism of the modeling results of high-elevation-angle scenes and improving the fitting effect of the actual error.

[0069] 3. In terms of the multipath error model of the present invention, one or more expansion factors are used to improve the model's fitting effect on the true error, thereby further reducing the conservatism of the modeling results and improving the fitting effect on the true error. BRIEF DESCRIPTION OF THE DRAWINGS

[0070] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments. By referring to the drawings, the features and advantages of the present invention will be more clearly understood. The drawings are schematic and should not be understood as limiting the present invention in any way. Those skilled in the art can derive other drawings based on these drawings without inventive effort. Among them:

[0071] Figure 1 It is a flow chart of the multipath error automatic modeling method of the present invention;

[0072] Figure 2 It is a statistical diagram of original multipath error data of the present invention;

[0073] Figure 3 It is the principle diagram of the two-point intersection method;

[0074] Figure 41 is an effective envelope error effect diagram of the present invention, wherein (a) is the envelope effect of the multipath error in the B1I signal broadcast by the Beidou satellite with a PRN (Pseudo-Random Noise) number of C19, (b) is the envelope effect of the multipath error in the B3I signal broadcast by the Beidou satellite with a PRN number of C19, (c) is the envelope effect of the multipath error in the B1I signal broadcast by the Beidou satellite with a PRN number of C30, (d) is the envelope effect of the multipath error in the B3I signal broadcast by the Beidou satellite with a PRN number of C30, (e) is the envelope effect of the multipath error in the B1I signal broadcast by the Beidou satellite with a PRN number of C43, and (f) is the envelope effect of the multipath error in the B3I signal broadcast by the Beidou satellite with a PRN number of C43;

[0075] Figure 5 1 is an adaptive envelope error effect diagram of the present invention, wherein (a) is the adaptive envelope effect of the standard deviation of the multipath error in the B1I signal broadcast by the BeiDou-3 satellite, and (b) is the adaptive envelope effect of the standard deviation of the multipath error in the B3I signal broadcast by the BeiDou-3 satellite;

[0076] Figure 6 2 is a diagram of the fitting error effect of the present invention, wherein (a) is the average CDF difference between the modeling result during the convergence process of the genetic algorithm and the B1I true multipath error, and (b) is the average CDF difference between the modeling result during the convergence process of the genetic algorithm and the B3I true multipath error. DETAILED DESCRIPTION

[0077] In order to more clearly understand the above-mentioned objects, features and advantages of the present invention, the present invention is further described in detail below with reference to the accompanying drawings and specific embodiments. It should be noted that the embodiments of the present invention and the features therein can be combined with each other without conflict.

[0078] In the following description, many specific details are set forth to facilitate a full understanding of the present invention. However, the present invention may also be implemented in other ways different from those described herein. Therefore, the scope of protection of the present invention is not limited to the specific embodiments disclosed below.

[0079] like Figure 1 As shown in FIG, the automated modeling method for GNSS multipath error for integrity monitoring needs includes the following steps:

[0080] S1: With the support of historical IGS broadcast ephemeris data, using historical pseudorange and carrier phase observation data from an airborne GNSS receiver or a ground-based GNSS monitoring station, extract multipath error data from the pseudorange observation values ​​of the GNSS signal and generate a CDF. Step S1 includes:

[0081] S1-1: Extract multipath error data using the multipath error combination of the observed values, specifically:

[0082]

[0083] Among them, f a and f b are the frequency values ​​of two different frequency signals a and b respectively; ε a is the multipath error data extracted from the pseudorange observation value of the a signal, P a is the pseudorange observation value obtained using the a signal, L a and L b are the carrier phase observation values ​​obtained using signals a and b respectively;

[0084] S1-2: Divide the priori numerical value variation range and altitude angle variation range of the data point into equal parts to form a grid with the horizontal axis variable being the numerical value of the data point and the vertical axis variable being the altitude angle of the data point;

[0085] S1-3: Count the number of data points corresponding to each grid and the number of data points corresponding to each elevation angle sub-interval;

[0086] S1-4: Normalize the number of data points corresponding to each grid by dividing it by the total number of data points in the corresponding altitude subinterval:

[0087]

[0088] Among them, PDF ij is the PDF value corresponding to the grid with horizontal coordinate i and vertical coordinate j, n ij is the number of data points in the grid with horizontal coordinate i and vertical coordinate j, n kj is the number of data points in the grid with abscissa k and ordinate j, i, j, k are the grid abscissa, grid ordinate and grid abscissa variable used for accumulation respectively;

[0089] S1-5: Convert PDF points to CDF points by accumulation to generate CDF for modeling:

[0090]

[0091] Among them, CDF ij is the CDF value corresponding to the grid with horizontal coordinate i and vertical coordinate j.

[0092] S2: Designing a multipath error model using the elevation angle as a characteristic quantity; Step S2 includes:

[0093] S2-1: Assume that the multipath error consists of three parts:

[0094] ε=ε1+ε2+ε3 (4)

[0095] Among them, ε1 is the height angle correlation quantity that obeys Gaussian distribution, ε2 is a Gaussian distribution that is independent of the altitude angle. ε3 is a component with unknown distribution characteristics, which is set to a linear combination of ε1 and ε2 to envelop the fat-tail error;

[0096] ε3=α·ε1+β·ε2 (5)

[0097] The existing art typically uses a single inflation factor approach. While this model is simple, it leaves much room for improvement in fitting the unknown components of the distribution characteristics. Therefore, the present invention introduces additional inflation factors to refine the ε3 model, achieving better error fitting and reducing the model's conservatism.

[0098] S2-2: Introduce additional expansion factors to refine the model form of ε3:

[0099] ε3=η·(ε1+ε2) (6)

[0100] ε=(1+α)·ε1+(1+β)·ε2 (7)

[0101] At this time, the standard deviation of ε is:

[0102]

[0103] Finally, the standard deviation of ε2 is set to:

[0104] σ2=a2+b2·exp(-c2·El) (9)

[0105] Among them, El is the altitude angle of the angle value, and the six unknown parameters of the model σ1, α, β, a2, b2, and c2 are estimated by genetic algorithm.

[0106] S3: Binary encode the model parameters and convert the decimal values ​​into binary sequences as the operation objects of the multi-objective genetic algorithm;

[0107] In step S3, binary coding is used to abstract the parameters to be solved into binary chromosomes:

[0108]

[0109] Value Para =CA·Value BS +Value Start (11)

[0110] Among them, CA is Coding Accuracy, which indicates the coding accuracy; Value is a decimal value, N is the specified binary sequence length, Value End and Value Start Corresponding to the two ends of the prior search interval of the estimated parameter, Value Para Indicates the decimal value of the parameter to be estimated, Value BS Indicates the decimal code value of the binary sequence relative to the start of the data;

[0111] The binary chromosomes are constantly changing as the genetic algorithm is executed and the chromosome set evolves.

[0112] Preferably, in step S3, the values ​​at both ends of the priori search interval of the parameter to be estimated are set to one third of the maximum variation range of the priori value.

[0113] S4: The optimization goal is set to meet the CDF envelope error requirements, and the difference between the CDF of the model and the true error is minimized. The multi-objective genetic algorithm is used to select the optimal binary sequence to estimate the model parameters;

[0114] Step S4 includes:

[0115] S4-1: Construct the objective function; by designing the objective function, the genetic algorithm is specified as an optimization problem to be minimized, that is, individuals with smaller objective function values ​​are better; then, the best individuals will be assigned a larger fitness;

[0116] The objective function is designed as:

[0117]

[0118]

[0119]

[0120] Where p and q are the altitude angle and the number of numerical subintervals respectively, ω i ,k and 1-sin(El i ) are weight factors, ω i It is a random number that varies between 0 and 1 and is used to prevent the genetic algorithm from performing random searches in only one direction.

[0121] k is a constant used to specify the weight of the envelope error modeling target relative to the optimal fitting effect modeling target and needs to be set in advance;

[0122] Sine function of altitude angle 1-sin(El i) is an adaptive function that changes with the altitude angle and is used to automatically set different weights for different altitude angle intervals; that is, in the low altitude angle interval where "fat-tail errors" most often occur, the envelope error target is given the largest weight; but as the altitude angle increases, the "fat-tail errors" decrease, and the sine function value is automatically adjusted at this time to reduce the envelope error target weight in order to achieve a better fit of the model.

[0123] y min and y ob It is the specific implementation of the envelope error target and the fitting target, y min Describes the average CDF difference between the constructed model and the actual error; y ob It is designed as a penalty function. When the CDF envelope error requirement is met, y ob Corresponds to "success", otherwise corresponds to "fail";

[0124] Reduce the probability that genes of individuals that do not meet the envelope error requirements will enter the next generation;

[0125] S4-2: Individual hierarchical sorting; individuals with similar objective function values ​​are divided into one level, and individuals in the same level will have the same probability of being selected;

[0126] Premature convergence is a common problem faced by genetic algorithm design. It causes the random search process of the genetic algorithm to end prematurely before obtaining an optimal solution. The hierarchical method of the present invention can effectively ensure the genetic diversity of different generations of populations, thereby weakening the impact of premature convergence on the solution.

[0127] S4-3: Individual selection: New individuals are randomly selected to enter the next generation in a "roulette wheel" manner with a specified probability. Individuals in the population are abstracted as sectors on a roulette wheel. The ratio of the sector area to the total area of ​​the roulette wheel is equal to the ratio of the individual fitness to the total fitness of the population. A certain number of individuals with the highest fitness values ​​in each generation are allowed to enter the next generation directly without random selection.

[0128] S4-4: Chromosome crossover; the two-point crossover method is used, and the crossover point positions are randomly determined with equal probability;

[0129] S4-5: Chromosome mutation; for each bit on the binary chromosome, generate a Boolean random number with a specified mutation probability. If the random number is true, flip the binary number, that is, change 0 to 1 or 1 to 0. The number of elite individuals, chromosome crossover and mutation probability must be specified.

[0130] Preferably, in step S4, the number of iterations of the genetic algorithm is set to 200 to 1000 generations.

[0131] In order to facilitate understanding of the above technical solutions of the present invention, the above technical solutions of the present invention are described in detail below through specific embodiments.

[0132] Example 1

[0133] This embodiment uses one year of Beidou satellite multipath data collected by 23 global stations for illustration.

[0134] Set the maximum range of the prior value to -6m to 6m; set the cutoff elevation angle to 5°, that is, the elevation angle range is 5° to 90°. Set the value sub-interval size to 0.03m and the elevation angle sub-interval size to 1°, such as Figure 2 shown.

[0135] Binary encoding is used, with the encoding precision set to 0.001, and the values ​​at both ends of the prior search interval of the parameter to be estimated are set to one-third of the maximum variation range of the prior value. In this embodiment, the prior search interval of the parameter to be estimated should be set to (-2m, 2m), and N should be set to 14.

[0136] In the genetic algorithm, a value of 1 in the objective function indicates that the user considers the envelope error and fitting objectives to be equally important. A value of 0 indicates that the user considers only the fitting objective to be important. In this case, the multipath error modeling problem is essentially a least squares problem. In this embodiment, the value of k is set to 1.

[0137] Individual hierarchical sorting: In this embodiment, the total number of individuals in the population is set to 150, and the number of levels is set to 30. Then, the maximum fitness is set to 150, the minimum fitness is set to 0, and the fitness is linearly distributed to individuals of different levels.

[0138] Chromosome crossover uses the commonly used two-point crossover method. The principle of the method is as follows Figure 3 As shown, the intersection positions are randomly determined with equal probability.

[0139] Chromosome mutation: In this embodiment, the number of elite individuals is set to 30, the chromosome crossover probability is set to 0.6, and the chromosome mutation probability is set to 0.001.

[0140] In summary, by quantifying the CDF envelope requirement in the objective function of the genetic algorithm, the present invention can, on the basis of realizing the automation of the modeling process, comprehensively consider the CDF envelope error modeling requirements in the background technology and effectively envelop the error, such as Figure 4As shown in the figure, the modeling results before and after the CDF envelope requirement is introduced into the objective function are compared. The solid line and the dotted line correspond to the following figures: (a) is the envelope effect of the multipath error in the B1I signal broadcast by the BeiDou satellite with a PRN (Pseudo-Random Noise) number of C19; (b) is the envelope effect of the multipath error in the B3I signal broadcast by the BeiDou satellite with a PRN number of C19; (c) is the envelope effect of the multipath error in the B1I signal broadcast by the BeiDou satellite with a PRN number of C30; (d) is the envelope effect of the multipath error in the B3I signal broadcast by the BeiDou satellite with a PRN number of C30; (e) is the envelope effect of the multipath error in the B1I signal broadcast by the BeiDou satellite with a PRN number of C43; (f) is the envelope effect of the multipath error in the B3I signal broadcast by the BeiDou satellite with a PRN number of C43.

[0141] By designing a sinusoidal adaptive function of the elevation angle in the objective function of the genetic algorithm, the algorithm can automatically adjust the relative weights of the two modeling requirements according to the elevation angle corresponding to the multipath error, thereby reducing the conservatism of the modeling results for high elevation angle scenarios. Figure 5 The figure shows the modeling results and the true error in standard deviation form. The dashed line corresponds to the modeling result, and the solid line corresponds to the true error. (a) shows the adaptive envelope effect on the standard deviation of the multipath error in the B1I signal broadcast by the BeiDou-3 satellite, and (b) shows the adaptive envelope effect on the standard deviation of the multipath error in the B3I signal broadcast by the BeiDou-3 satellite. As can be seen from the figure, as the elevation angle increases, the difference between the model and the error gradually decreases, and the algorithm achieves the expected effect.

[0142] Genetic algorithms have a random search property that supports parameter solving for complex models. Leveraging this property, the present invention employs one or more expansion factors in model design to refine the model form, improving the model's fit to the true error and further reducing the model's conservatism.

[0143] Figure 6 The average CDF differences when using one expansion factor and two expansion factors during the genetic algorithm convergence process are compared. (a) shows the average CDF difference between the modeled results and the true B1I multipath error during the genetic algorithm convergence process, and (b) shows the average CDF difference between the modeled results and the true B3I multipath error during the genetic algorithm convergence process. The CDF difference values ​​after genetic algorithm convergence are shown in the caption in the upper right corner. The smaller the difference value, the less conservative the model. The convergence values ​​show that after the model form is refined, the average CDF difference values ​​decrease from 0.193 and 0.081 to 0.063 and 0.040, respectively, representing significant improvements of 67.4% and 50.6%, respectively.

[0144] In the present invention, the terms "first", "second", "third", and "fourth" are used for descriptive purposes only and should not be understood as indicating or implying relative importance. The term "plurality" refers to two or more, unless otherwise clearly defined.

[0145] The foregoing description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Those skilled in the art will readily appreciate that various modifications and variations of the present invention are possible. Any modifications, equivalent substitutions, or improvements made within the spirit and principles of the present invention are intended to be within the scope of protection of the present invention.

Claims

1. An automated GNSS multipath error modeling method for integrity monitoring needs, characterized by: The following steps are involved: S1: With the support of IGS broadcast ephemeris historical data, the multipath error data in the pseudorange observation values ​​of the GNSS signal is extracted using the pseudorange and carrier phase historical observation data of the airborne GNSS receiver or the ground GNSS monitoring station to generate the CDF; S2: Design the multipath error model using the elevation angle as the characteristic quantity; S3: Binary encode the model parameters and convert the decimal values ​​into binary sequences as the operation objects of the multi-objective genetic algorithm; S4: The optimization goal is set to meet the CDF envelope error requirements, and the difference between the CDF of the model and the true error is minimized. The multi-objective genetic algorithm is used to select the optimal binary sequence to estimate the model parameters; The step S1 comprises: S1-1: Extract multipath error data using the multipath error combination of the observed values, specifically: Among them, f a and f b are the frequency values ​​of two different frequency signals a and b respectively; ε a is the multipath error data extracted from the pseudorange observation value of signal a, P a is the pseudorange observation value obtained using the a signal, L a and L b are the carrier phase observation values ​​obtained using signals a and b respectively; S1-2: Divide the a priori numerical value variation range and altitude angle variation range of the data point into equal parts to form a grid with the horizontal axis variable being the numerical value of the data point and the vertical axis variable being the altitude angle of the data point; S1-3: Count the number of data points corresponding to each grid and the number of data points corresponding to each elevation angle sub-interval; S1-4: Normalize the number of data points corresponding to each grid by dividing it by the total number of data points in the corresponding altitude subinterval: Among them, PDF ij is the PDF value corresponding to the grid with horizontal coordinate i and vertical coordinate j, n ij is the number of data points in the grid with horizontal coordinate i and vertical coordinate j, n kj is the number of data points in the grid with abscissa k and ordinate j, i, j, k are the grid abscissa, grid ordinate and grid abscissa variable used for accumulation respectively; S1-5: Convert PDF points to CDF points by accumulation to generate CDF for modeling: Among them, CDF ij is the CDF value corresponding to the grid with horizontal coordinate i and vertical coordinate j.

2. The modeling method according to claim 1, characterized in that The step S2 comprises: S2-1: Assume that the multipath error consists of three parts: ε=ε1+ε2+ε3 (4) Among them, ε1 is the height angle correlation quantity that obeys Gaussian distribution, ε2 is a Gaussian distribution that is independent of the altitude angle. ε3 is a component with unknown distribution characteristics, which is set to a linear combination of ε1 and ε2 to envelop the fat-tail error; ε3=α·ε1+β·ε2 (5) S2-2: Introduce additional expansion factors to refine the model form of ε3: ε3=η·(ε1+ε2) (6) ε=(1+α)·ε1+(1+β)·ε2 (7) At this time, the standard deviation of ε is: Finally, the standard deviation of ε2 is set to: σ2=a2+b2·exp(-c2·El) (9) Among them, El is the altitude angle of the angle value, and the six unknown parameters of the model σ1, α, β, a2, b2, and c2 are estimated by genetic algorithm.

3. The modeling method according to claim 2, characterized in that In step S3, binary coding is used to abstract the parameters to be solved into binary chromosomes: Value Para =CA·Value BS +Value Start (11) Among them, CA is Coding Accuracy, which indicates the coding accuracy; Value is a decimal value, N is the specified binary sequence length, Value End and Value Start Corresponding to the two ends of the prior search interval of the estimated parameter, Value Para Indicates the decimal value of the parameter to be estimated, Value BS Indicates the decimal code value of the binary sequence relative to the start of the data; The binary chromosomes are constantly changing as the genetic algorithm is executed and the chromosome set evolves.

4. The modeling method according to claim 3, characterized in that The step S4 includes: S4-1: Construct the objective function; by designing the objective function, the genetic algorithm is specified as an optimization problem to be minimized, that is, individuals with smaller objective function values ​​are better; then, the best individuals will be assigned a larger fitness; The objective function is designed as: Where p and q are the altitude angle and the number of numerical subintervals respectively, ω m ,h and 1-sin(El m ) are weight factors, ω m It is a random number that varies between 0 and 1 and is used to prevent the genetic algorithm from performing random searches in only one direction. h is a constant used to specify the weight of the envelope error modeling target relative to the optimal fitting effect modeling target and needs to be set in advance; Sine function of altitude angle 1-sin(El m ) is an adaptive function that changes with the altitude angle and is used to automatically set different weights for different altitude angle intervals; y min and y ob It is the specific implementation of the envelope error target and the fitting target, y min Describes the average CDF difference between the constructed model and the actual error; y ob It is designed as a penalty function. When the CDF envelope error requirement is met, y ob Corresponds to "success", otherwise corresponds to "fail"; Reduce the probability that genes of individuals that do not meet the envelope error requirements will enter the next generation; S4-2: Individual hierarchical sorting; individuals with similar objective function values ​​are divided into one level, and individuals in the same level will have the same probability of being selected; S4-3: Individual selection: A "roulette wheel" approach is used to randomly select new individuals for the next generation with a specified probability. Individuals in the population are represented as sectors on a roulette wheel. The ratio of the sector area to the total area of ​​the wheel is equal to the proportion of the individual fitness to the total fitness of the population. A certain number of individuals with the highest fitness values ​​in each generation are allowed to enter the next generation without random selection. S4-4: Chromosome crossover; the two-point crossover method is used, and the crossover point position is randomly determined with equal probability; S4-5: Chromosome mutation; for each bit on the binary chromosome, generate a Boolean random number with a specified mutation probability. If the random number is true, flip the binary number, that is, change 0 to 1 or 1 to 0. The number of elite individuals, chromosome crossover and mutation probability must be specified.

5. The modeling method according to claim 3, characterized in that: In step S3, the values ​​at both ends of the priori search interval of the parameter to be estimated are set to one third of the maximum variation range of the priori value.

6. The modeling method according to any one of claims 1 to 5, characterized in that: In step S4, the number of iterations of the genetic algorithm is set to 200 to 1000 generations.

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