A method for ionospheric delay correction of a space-based data-driven broadcast ionospheric model

Abstract

The present application belongs to the technical field of satellite navigation, and specifically discloses an ionospheric delay correction method of a space-based data driven broadcast ionospheric model. The present application aims to use the occultation observation data of a low earth orbit (LEO) constellation to directly obtain global total electron content (TEC) which is independent of ground stations by integrating from the occultation electron density profile; and to introduce a neural network model to quickly calibrate and optimize the quality of the space-based TEC data; finally, to directly drive the NTCM-G broadcast ionospheric model using the calibrated TEC product which is high-precision and globally uniformly covered, to generate its global broadcast correction coefficients and broadcast them to users. The present application method establishes a new method of realizing a broadcast ionospheric model with space-based data as the core driving source, avoids the limitations of the ground-based observation network from the data source, and improves the autonomy, complete coverage and overall precision of the ionospheric correction service of the global navigation system.

Description

Technical Field

[0001] This invention belongs to the field of satellite navigation technology, and specifically relates to a method for ionospheric delay correction of a space-based data-driven broadcast ionospheric model. Background Technology

[0002] Ionospheric delay is one of the biggest sources of error in the positioning accuracy of satellite navigation systems, especially for widely used single-frequency receivers. To correct this error, Global Navigation Satellite Systems (GNSS) generally employ broadcast ionospheric models, which transmit a finite set of model coefficients to users via navigation messages. Users then use this model to calculate the ionospheric delay correction in the zenith or slant path in real time. For a long time, traditional empirical models, such as the Klobuchar, NeQuick-G, and BDGIM models, have been the standard in the field of broadcast ionospheric models. The data driven by these models mainly comes from the globally distributed GNSS ground-based receiver observation network. However, this ground-based data-driven approach has significant inherent limitations and potential risks.

[0003] First, uneven global coverage and observation blind spots are prominent issues. The deployment of ground-based GNSS receivers heavily relies on terrestrial infrastructure and areas of human activity, resulting in large observational gaps in vast oceans, the North and South Poles, deserts, primeval forests, and remote mountainous regions. Ionospheric delay data in these areas can only be obtained through spatial interpolation or model extrapolation, with uncertain accuracy and reliability. This directly limits the accuracy of broadcast ionospheric models driven by these methods globally, especially in critical gap areas. Second, there are risks associated with changes in international relations and infrastructure dependence. Building and maintaining a globally uniform and stable ground-based monitoring network is not only costly but also involves complex data sharing protocols and transnational cooperation. Changes in international relations may affect the continuous operation and data acquisition of monitoring stations in key areas, increasing the vulnerability of the global ionospheric monitoring data chain and threatening the stability, independence, and continuity of broadcast ionospheric services that rely on it.

[0004] Therefore, exploring a new technological approach that can autonomously acquire global uniform ionospheric data without relying on a global ground-based monitoring network has become crucial for improving the robustness, accuracy, and autonomous controllability of satellite navigation systems. In recent years, the rapidly developing low Earth orbit (LEO) satellite constellations and their occultation detection technologies have provided the ability to directly and uniformly perceive the global ionospheric electron density structure from space. Therefore, how to efficiently utilize this space-based occultation data to generate high-precision global TEC products that can directly drive and optimize next-generation broadcast ionospheric models, and to achieve automated calibration and broadcasting of model parameters, is a core problem that urgently needs to be solved to overcome the inherent defects of ground-based data-driven models and achieve high-performance global ionospheric delay correction services.

[0005] In recent years, occultation data acquired using low Earth orbit (LEO) satellite constellations (such as COSMIC, LEMUR, Tianmu, and Yunyao satellites) has provided a revolutionary new means to obtain globally uniform coverage and high vertical resolution ionospheric electron density information. However, there is a significant discrepancy between the ionospheric TEC obtained from occultation profiles and the total electron content (TEC) from the GNSS signal link to the ground. A key technical bottleneck is how to effectively integrate this emerging, massive amount of space-based occultation data, transform it into a high-precision global TEC product that can directly drive and optimize satellite navigation broadcast ionospheric models, and ultimately generate real-time / near-real-time broadcast correction coefficients.

[0006] Therefore, there is an urgent need for an accurate, efficient, and automated method for implementing a space-based data-driven satellite navigation broadcast ionospheric model, in order to fully utilize the global coverage advantage of space-based observations, make up for the shortcomings of ground-based observation networks, and thus improve the global applicability and real-time correction accuracy of the broadcast ionospheric model. Currently, there is no method for implementing a space-based data-driven broadcast ionospheric model.

[0007] The statements in this section are merely background information related to the present invention and do not necessarily constitute prior art. Summary of the Invention

[0008] The purpose of this invention is to propose an ionospheric delay correction method for a space-based data-driven broadcast ionospheric model. This method proposes a broadcast ionospheric model implementation method with space-based data as the core driving source. By utilizing occultation observation data from the LEO constellation, a high-precision global total electron content (TEC) product can be generated, which can then be used to drive and calibrate the NTCM-G broadcast ionospheric model, ultimately facilitating the realization of broadcast ionospheric delay correction without relying on ground-based stations.

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

[0010] A method for ionospheric delay correction in a space-based data-driven broadcast ionospheric model includes the following steps:

[0011] Step 1. Using GNSS occultation observation data acquired by the LEO satellite constellation, perform data quality control on the occultation data, obtain the occultation electron density profile, and calculate the total ionospheric electron content along the occultation path through vertical integration. ;

[0012] Step 2. For data directly calculated from occultation data... A neural network model is introduced for data fusion and calibration;

[0013] First, a neural network model is constructed and trained to correct and optimize the systematic bias of the occultation TEC data; then, the trained neural network model is used to output the calibrated ionospheric TEC value, i.e. ;

[0014] Step 3. Calculate the calibrated ionospheric TEC value. As input parameters, the global broadcast correction coefficients of the NTCM-G model, i.e., the NTCM-G model coefficients, are calculated using an optimization estimation algorithm.

[0015] Step 4. Encode the set of NTCM-G model coefficients obtained from the solution and inject them into the navigation message of the satellite navigation system, and broadcast them to global users through geostationary orbit or medium Earth orbit navigation satellites;

[0016] Step 5. The user's single-frequency receiver receives and decodes the NTCM-G model coefficients in the navigation message. Combining the user's own position, time, and satellite line-of-sight direction, it uses the NTCM-G model to calculate the ionospheric delay correction amount on the current propagation path in real time and applies it to the positioning calculation to realize global ionospheric delay correction service.

[0017] Furthermore, based on the aforementioned method for ionospheric delay correction of the space-based data-driven broadcast ionospheric model, this invention also proposes a corresponding ionospheric delay correction system for the space-based data-driven broadcast ionospheric model, the scheme of which is as follows:

[0018] An ionospheric delay correction system for a space-based data-driven broadcast ionospheric model includes the following modules:

[0019] The Space-based TEC data acquisition and data quality control module is used to perform data quality control on occultation data and obtain occultation electron density profiles using GNSS occultation observation data acquired from the LEO satellite constellation.

[0020] The total electron content of the ionosphere along the occultation path is calculated by vertical integration of the occultation electron density profile. ;

[0021] An occultation TEC data calibration module based on a neural network model is used to calibrate data directly calculated from occultation data. A neural network model is introduced for data fusion and calibration;

[0022] First, a neural network model is constructed and trained to correct and optimize the systematic bias of the occultation TEC data; then, the trained neural network model is used to output the calibrated ionospheric TEC value, i.e. ;

[0023] The NTCM-G model-driven and coefficient generation module is used to... As input parameters, the global broadcast correction coefficients of the NTCM-G model, i.e., the NTCM-G model coefficients, are calculated using an optimization estimation algorithm.

[0024] The broadcast message generation and broadcasting module is used to encode a set of NTCM-G model coefficients obtained from the solution and inject them into the navigation message of the satellite navigation system, and broadcast them to global users through geostationary orbit or medium Earth orbit navigation satellites;

[0025] The user-end delay correction module is used to receive and decode the NTCM-G model coefficients in the navigation message from the user's single-frequency receiver. Combined with the user's own position, time and satellite line of sight, it uses the NTCM-G model to calculate the ionospheric delay correction amount on the current propagation path in real time and applies it to the positioning calculation to realize global ionospheric delay correction service.

[0026] Furthermore, based on the aforementioned method for correcting ionospheric delay in a space-based data-driven broadcast ionospheric model, this invention also proposes a computer device comprising a memory and one or more processors.

[0027] Executable code is stored in memory. When the processor executes the executable code, it implements the steps of the ionospheric delay correction method for the aforementioned space-based data-driven broadcast ionospheric model.

[0028] Furthermore, based on the aforementioned method for correcting ionospheric delay in a space-based data-driven broadcast ionospheric model, this invention also proposes a computer-readable storage medium storing a program that, when executed by a processor, implements the steps of the aforementioned method for correcting ionospheric delay in a space-based data-driven broadcast ionospheric model.

[0029] The present invention has the following advantages:

[0030] As described above, this invention discloses an ionospheric delay correction method for a space-based data-driven broadcast ionospheric model. By constructing a broadcast ionospheric model with space-based occultation data as the core driving source, this novel method generates a high-precision global ionospheric delay correction service independent of ground-based networks. This invention eliminates the inherent dependence of traditional broadcast ionospheric models on global ground-based GNSS receiver networks. By directly utilizing occultation observation data from low Earth orbit satellites to drive the model, it fundamentally avoids the risks of data loss, uneven accuracy, and service interruption caused by changes in international relations, infrastructure construction, and observation blind spots (such as oceans, polar regions, and deserts). This enhances the autonomy, robustness, and spatial continuity of the global navigation system's ionospheric correction service. Furthermore, this invention employs a neural network model for high-precision calibration of space-based occultation TEC data and combines it with the multi-scale ionospheric feature representation capabilities of the NTCM-G (Neustrelitz Total Electron Content Model for Galileo Satellite Navigation Systems) broadcast ionospheric model, enabling a more accurate description of the real-time and spatial variation characteristics of the ionosphere. Compared to ground-based driven models that rely on regional interpolation, the method of this invention provides more consistent and accurate ionospheric delay correction globally, especially in traditional observation blind areas, effectively improving the global positioning accuracy for single-frequency users. In summary, the method of this invention achieves a complete automated process from automatic processing of occultation data, neural network calibration of space-based occultation TEC data, model coefficient calculation to broadcast message generation. This process can be embedded in onboard or ground-based processing systems, achieving near real-time response to global ionospheric conditions. It can quickly capture and correct severe ionospheric disturbances caused by solar flares, geomagnetic storms, etc., thereby improving the availability and reliability of navigation services during space weather events. The method of this invention provides global users with a more uniform, robust, and accurate ionospheric delay correction service. Attached Figure Description

[0031] Figure 1 This is a flowchart of the ionospheric delay correction method for a space-based data-driven broadcast ionospheric model in an embodiment of the present invention. Detailed Implementation

[0032] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments:

[0033] Example 1

[0034] To address the inherent dependence of existing broadcast ionospheric models on ground-based GNSS data, and the resulting risks of uneven global coverage, limited correction accuracy, and service stability affected by changes in international relations, this invention proposes a space-based data-driven ionospheric model ionospheric delay correction method. This method constructs a broadcast ionospheric model implementation method with space-based data as the core driving source. Its core lies in utilizing occultation observation data from the LEO constellation to generate a high-precision global total electron content (TEC) product, which is then used to drive and calibrate the NTCM-G broadcast ionospheric model, ultimately achieving broadcast ionospheric delay correction independent of ground-based stations. Figure 1 As shown, the main technical steps of this invention include: using GNSS occultation observation data obtained from the LEO satellite constellation, performing data quality control on the occultation data to obtain a high-quality ionospheric electron density profile, and calculating the total ionospheric electron content (TEC) along the occultation path using a vertical integration algorithm on the occultation electron density profile; and introducing a neural network model to perform data fusion and calibration for the TEC directly calculated from the occultation data. This neural network model is trained using historical high-precision reference data to correct and optimize the systematic bias of occultation TEC data, improving its absolute accuracy and ultimately outputting a globally high-precision, highly consistent calibrated TEC grid product. Using this globally calibrated TEC grid product as core driving data, an optimization estimation algorithm is employed to calculate the global broadcast correction coefficients of the NTCM-G model in real-time or near real-time. The set of NTCM-G model coefficients obtained in the previous step is encoded and injected into the navigation message of the satellite navigation system, broadcast to global users via geostationary orbit (GEO) or medium Earth orbit (MEO) navigation satellites. The user's single-frequency receiver receives and decodes the NTCM-G model coefficients in the navigation message, and, combined with the user's position, time, and satellite line-of-sight direction, uses this model to calculate the ionospheric delay correction on the current propagation path in real time, applying it to positioning calculations, ultimately achieving a high-precision global ionospheric delay correction service.

[0035] like Figure 1 As shown, the ionospheric delay correction method for space-based data-driven broadcast ionospheric models includes the following steps:

[0036] Step 1. Space-based TEC data acquisition and data quality control.

[0037] Using GNSS occultation observation data acquired by the LEO satellite constellation, data quality control was performed on the occultation data to obtain the occultation electron density profile, and the total ionospheric electron content along the occultation path was calculated through vertical integration. .

[0038] Step 1.1. Obtain GNSS occultation electron density profile products from the LEO satellite constellation and perform data quality control.

[0039] I. A sliding window is used to analyze the original electron density sequence of the occultation. Mean filtering of points eliminates random noise interference. For example, odd numbers The formula for calculating mean filtering is:

[0040] (1)

[0041] In the formula, This represents the b-th altitude point, where Ne is the observed electron density of the occultation. For the first height points The observed electron density of the occultation is the raw data; This represents the filtered data.

[0042] II. Calculate the average relative deviation between the original data and the filtered data. The formula is as follows:

[0043] (2)

[0044] in The total number of samples representing the electron density profile. This represents the b-th elevation point. The observed electron density of the occultation. A threshold for judging the average relative deviation is set. ,exclude Abnormal profile.

[0045] In this embodiment, It can be set to 0.1.

[0046] III. Calculate the normalized variance index σ of the electron density using the following formula:

[0047] (3)

[0048] in This represents the peak electron density of the F2 layer. A threshold for normalized variance is set. Eliminate σ≥ Abnormal data. In this embodiment, It is set to 0.05.

[0049] IV. Calculate the electron density gradient within the preset height range. The formula is as follows:

[0050] (4)

[0051] in, The height of the upper level The height of the lower level; express Observations of occultation electron density at altitude express Observed electron density of the occultation at altitude.

[0052] Eliminate non-negative gradients, i.e. The unusual profile ensures that the F-layer structure conforms to the physical properties of the ionosphere. Typically, in this embodiment, the upper layer height... Set to 490km, lower level altitude Set to 420km.

[0053] V. Exclude anomalous data where NmF2 is less than 0, and remove abnormal observations where the peak height hmF2 of layer F2 is less than 200km.

[0054] Step 1.2. Calculate the total electron content of the ionosphere along the occultation path using the vertical integration algorithm from the occultation electron density profile. The calculation formula is as follows:

[0055] (5)

[0056] in, This represents the bottom height of the electron density profile. This represents the top height of the electron density profile.

[0057] Step 2. TEC data fusion and calibration based on neural network driven.

[0058] For calculations directly from occultation data This paper introduces a neural network model for data fusion and calibration. Traditional data processing methods struggle to handle the inherent, complex systematic biases and errors caused by non-standard geometric paths in space-based occultation data. However, neural networks, with their powerful nonlinear fitting and data representation capabilities, can learn and correct these errors end-to-end. They can directly extract clean, accurate, and physically consistent ionospheric TEC values ​​from noisy and biased raw occultation observations, enabling more realistic and robust driving of broadcast ionospheric models and ultimately improving the positioning accuracy of global single-frequency navigation users.

[0059] First, a neural network model is constructed and trained to correct and optimize the systematic bias of the occultation TEC data; then, the trained neural network model is used to output the calibrated ionospheric TEC value, i.e. .

[0060] In this embodiment, the neural network model is preferably a feedforward neural network model.

[0061] Step 2.1. First, construct the training dataset for the feedforward neural network model. The specific process is as follows:

[0062] I. Collect occultation electron density data after data quality control in step 1, and TEC data calculated from global GNSS ground stations, abbreviated as... , construct the training dataset for the feedforward neural network model.

[0063] II. Extract input features from each occultation event, including those obtained from the occultation path integral. Peak parameters NmF2, hmF2, spatiotemporal parameters, and geometric parameters of the electron density profile.

[0064] The spatiotemporal parameters include year, year-day (DOY), local time (LT), and the longitude and latitude of the hmF2 point; the geometric parameters of the electron density profile include the top and bottom heights of the electron density and the longitude and latitude coordinates.

[0065] III. Establish the input-output pairs, i.e., paired data, required for supervised learning of the feedforward neural network model.

[0066] Each occultation event is associated with a spacetime "co-located" location. The observation pairing and co-location criteria are as follows: the hmF2 point of the occultation event is located within a preset great circle distance of a certain GNSS receiving station, and the observation time is within a preset time window.

[0067] Pairing The value is used as the target value, i.e., the true value, for model training.

[0068] In this embodiment, the great circle distance can be set to 5°, and the time window can be set to ±10 minutes.

[0069] IV. Filter the paired data and remove invalid or unreliable data points.

[0070] Quality control standards include removal or Data that is not positive or has missing values; exclude electron density profiles whose hmF2 height is not within the preset range (in this embodiment, the range can be set to 200-600 km).

[0071] Step 2.2. Next, feature engineering and selection are performed on the training data. The specific process is as follows:

[0072] I. Perform sine and cosine transforms on the periodic time features, namely the annual day of birth (DOY) and local time (LT), to encode their annual and diurnal periodicity and avoid introducing discontinuities at the period boundaries. The calculation method is as follows:

[0073] (6)

[0074] (7)

[0075] (8)

[0076] (9)

[0077] in, The cosine component of the accumulated days of a year, This represents the sine component of the accumulated days over a year. Represents the cosine component of local time. The sine component representing local time.

[0078] II. Use the random forest method to evaluate the relative importance of each input feature and identify key driving factors.

[0079] Each input feature includes ,years, , , , Parameters such as the longitude and latitude of point hmF2, the top and bottom heights of electron density, the longitude and latitude of electron density.

[0080] The identified key drivers include ,years, , , , The longitude and latitude of the hmF2 point, the top height of the electron density, and the key driving factors are used as inputs for model training.

[0081] The construction and training process of the feedforward neural network model is as follows:

[0082] I. Construct a feedforward neural network, with the input layer of the feedforward neural network being the key driving factors identified above.

[0083] In this embodiment, the feedforward neural network includes a hidden layer that uses the hyperbolic tangent sigmoid activation function. The output layer of the feedforward neural network is a single neuron that outputs the predicted GNSS equivalent TEC value.

[0084] II. Use 80% of the training dataset for training and reserve 20% for independent testing.

[0085] III. To improve robustness, a sub-model aggregation strategy is adopted, which involves further dividing the training data into three subsets on an equal basis and training a sub-model, i.e., a feedforward neural network, on each subset.

[0086] IV. Use the Bayesian regularized backpropagation algorithm for model training.

[0087] The process of deploying the trained model and using it to predict outputs is as follows:

[0088] When new occultation electron density data is received, the system automatically performs data quality checks and feature extraction. Then, it calls three pre-trained sub-model feedforward neural networks to calculate the calibrated ionospheric TEC value. , .

[0089] For each one that needs calibration The input is first predicted by three pre-trained sub-models; the final calibrated ionospheric TEC value is... It is obtained by averaging the prediction results of three trained sub-models, as shown in the following formula:

[0090] .

[0091] Step 3. As input parameters, the NTCM-G broadcast ionospheric model is driven to solve for the optimal model broadcast coefficients, minimizing the overall difference between the NTCM-G model predictions and all occultation observations, thereby solving for the optimal broadcast parameter vector. This leads to a set of NTCM-G model coefficients. .

[0092] Organize and calibrate the occultation observation dataset, including Each independent observation point.

[0093] For the One observation point, The information includes the following:

[0094] Geographic coordinates, i.e., latitude, at the occultation profile hmF2 (radians) and longitude (radian).

[0095] Time parameters, including year-round days and local time (Hour).

[0096] and total electron content observation values The unit is TECU.

[0097] The NTCM-G model function is denoted as function. Its input is the broadcast parameter vector. Spatiotemporal parameters of an observation point The output is the predicted TEC value for that observation point, and the formula is as follows:

[0098] (10)

[0099] in Indicates the first TEC prediction values ​​for each observation point This represents a set of NTCM-G model coefficients.

[0100] Specifically, the calculation method of the NTCM-G model is carried out according to the following steps:

[0101] Step 3.1. Calculate the broadcast coefficient to calculate the effective ionization level driving the NTCM-G model. :

[0102] (11)

[0103] In formula (10), NTCM-G calculates the vertical TEC by multiplying five factors:

[0104] (12)

[0105] in, , , , , The formulas for calculating the five factors are as follows:

[0106] I. Calculate the local time dependency factor .

[0107] (13)

[0108] in The zenith angle of the sun. , , , , All are fixed coefficients, daily variation Half-day changes and three-day changes The angular phases are defined as follows:

[0109] (14)

[0110] (15)

[0111] (16)

[0112] in The hour is a phase shift. Local time, in hours, for occultation observation grid points.

[0113] in and The calculation formula is as follows:

[0114] (17)

[0115] (18)

[0116] in The geographical latitude of the occultation observation point. The solar declination is used, and all angles are expressed in radians.

[0117] II. Calculate seasonality dependence factors .

[0118] (19)

[0119] (20)

[0120] (twenty one)

[0121] in, , For fixed coefficients, the phase shifts relative to the beginning of the year represent the annual changes. Tianhe changes in half a year sky, This refers to the accumulated days of the year corresponding to the occultation observation data.

[0122] III. Calculation of geomagnetic field dependence factor .

[0123] (twenty two)

[0124] in, For fixed coefficients, The geomagnetic latitude of the occultation observation grid points, in radians.

[0125] IV. Calculating the equatorial anomaly-dependent factor .

[0126] (twenty three)

[0127] (twenty four)

[0128] (25)

[0129] in , For fixed coefficients, The latitude of the north-facing hump is the geomagnetic coordinate. The geomagnetic latitude of the south-facing camel hump. and For the best fit value, The latitude is expressed in degrees.

[0130] V. Calculate the solar activity dependence factor .

[0131] (26)

[0132] Depends on the broadcast coefficient (via formula (11) ) Calculated, , It is a fixed coefficient.

[0133] All coefficients arrive The possible values ​​are shown in Table 1.

[0134] Table 1 Model Coefficients

[0135]

[0136] Step 3.2. Solve for the optimal broadcast parameter vector This makes the NTCM-G broadcast ionosphere model predictions consistent with... The overall difference between the values ​​is minimal.

[0137] I. For given parameters, calculate the residual between the model predictions and the observed values ​​at each observation point. :

[0138] (27)

[0139] Combine all residuals into one 3D column vector:

[0140] (28)

[0141] II. Define the objective function using the least squares criterion. For the sum of squared residuals:

[0142] (29)

[0143] The goal of data-driven approaches is to find ways to make... Minimized .

[0144] III. The parameter inversion problem can be formulated as an unconstrained nonlinear least squares optimization problem, as shown in the following formula:

[0145] (30)

[0146] Where argmin represents the objective function The value of the variable when it reaches its minimum value.

[0147] IV. Select and apply an optimization algorithm to solve the problem.

[0148] Due to the model Regarding parameters It is nonlinear, and this optimization problem is solved using an iterative optimization algorithm.

[0149] IV.1. Initialization:

[0150] Set the initial guess value for the parameter vector. It can usually be set to .

[0151] Az_guess can be estimated based on the current solar activity level F10.7 index.

[0152] IV.2. Iterative Updates:

[0153] For iteration steps Using the Levenberg-Marquardt (LM) algorithm, a search direction is calculated. And step size, to update parameters:

[0154] (31)

[0155] in It's the step length.

[0156] The LM algorithm is an improvement on the Gauss-Newton method, and its search direction... The following system of linear equations was obtained by solving:

[0157] (32)

[0158] in, It is the residual vector exist Jacobian matrix at ( (Matrix). The line is the first individual residuals For parameters gradient: . It is the damping factor, which is dynamically adjusted during iteration to control the switching of the algorithm between the Gauss-Newton method and the steepest descent method. yes The identity matrix. Due to the model The analytical derivative of the Jacobian matrix is ​​quite complex, and in practical programming, the numerical difference method is often used to approximate the calculation of each element of the Jacobian matrix.

[0159] The iteration stops when any of the following convergence conditions is met, and the current parameters are... That is, the approximate optimal solution :

[0160] a. The parameter change is small enough: ;

[0161] b. The objective function decreases sufficiently: ;

[0162] c. The gradient norm is sufficiently small: ;

[0163] d. Reach the preset maximum number of iterations .

[0164] in , , This is a preset tolerance for small positive numbers, typically set to 1e-6. Set it to 1000.

[0165] V. Output optimal parameters: .

[0166] Step 4. Generation and broadcasting of broadcast messages.

[0167] The calculated set of NTCM-G model coefficients are encoded and injected into the navigation message of the satellite navigation system, and broadcast to global users via geostationary orbit (GEO) or medium Earth orbit (MEO) navigation satellites.

[0168] Step 5. Client-side latency correction.

[0169] The user-side single-frequency receiver receives and decodes the NTCM-G model coefficients in the navigation message. Combining the user's own position, time, and satellite line-of-sight direction, the NTCM-G model is used to calculate the ionospheric delay correction amount on the current propagation path in real time, and applied to the positioning solution, ultimately achieving a high-precision global ionospheric delay correction service.

[0170] Example 2

[0171] This embodiment 2 describes an ionospheric delay correction system for a space-based data-driven broadcast ionospheric model, which is based on the same inventive concept as the ionospheric delay correction method for a space-based data-driven broadcast ionospheric model in embodiment 1.

[0172] An ionospheric delay correction system for a space-based data-driven broadcast ionospheric model includes the following modules:

[0173] The Space-based TEC data acquisition and data quality control module is used to perform data quality control on occultation data and obtain occultation electron density profiles using GNSS occultation observation data acquired from the LEO satellite constellation.

[0174] The total electron content of the ionosphere along the occultation path is calculated by vertical integration of the occultation electron density profile. ;

[0175] An occultation TEC data calibration module based on a neural network model is used to calibrate data directly calculated from occultation data. A neural network model is introduced for data fusion and calibration;

[0176] First, a neural network model is constructed and trained to correct and optimize the systematic bias of the occultation TEC data; then, the trained neural network model is used to output the calibrated ionospheric TEC value, i.e. ;

[0177] The NTCM-G model-driven and coefficient generation module is used to... As input parameters, the global broadcast correction coefficients of the NTCM-G model, i.e., the NTCM-G model coefficients, are calculated using an optimization estimation algorithm.

[0178] The broadcast message generation and broadcasting module is used to encode a set of NTCM-G model coefficients obtained from the solution and inject them into the navigation message of the satellite navigation system, and broadcast them to global users through geostationary orbit or medium Earth orbit navigation satellites;

[0179] The user-end delay correction module is used to receive and decode the NTCM-G model coefficients in the navigation message from the user's single-frequency receiver. Combined with the user's own position, time and satellite line of sight, it uses the NTCM-G model to calculate the ionospheric delay correction amount on the current propagation path in real time and applies it to the positioning calculation to realize global ionospheric delay correction service.

[0180] It should be noted that any content not mentioned in the above-described functional modules of the system described in Embodiment 2 can be referred to the step description of the corresponding method in Embodiment 1 above, and will not be repeated in detail here.

[0181] Example 3

[0182] This embodiment 3 describes a computer device including a memory and one or more processors. Executable code is stored in the memory. When the processor executes the executable code, it implements the steps of the ionospheric delay correction method for the space-based data-driven broadcast ionospheric model described in embodiment 1 above.

[0183] In this embodiment, the computer device can be any device or apparatus with data processing capabilities, and will not be described in detail here.

[0184] Example 4

[0185] This embodiment 4 describes a computer-readable storage medium storing a program that, when executed by a processor, implements the steps of the ionospheric delay correction method for the space-based data-driven broadcast ionospheric model in embodiment 1 above.

[0186] The computer-readable storage medium can be an internal storage unit of any device or apparatus with data processing capabilities, such as a hard disk or memory, or an external storage device of any device with data processing capabilities, such as a plug-in hard disk, smart media card (SMC), SD card, flash card, etc.

[0187] Of course, the above description is only a preferred embodiment of the present invention. The present invention is not limited to the above-described embodiments. It should be noted that any equivalent substitutions or obvious modifications made by those skilled in the art under the guidance of this specification fall within the scope of this specification and should be protected by the present invention.

Claims

1. A method for ionospheric delay correction in a space-based data-driven broadcast ionospheric model, characterized in that, Includes the following steps: Step 1. Using GNSS occultation observation data acquired by the LEO satellite constellation, perform data quality control on the occultation data, obtain the occultation electron density profile, and calculate the total ionospheric electron content along the occultation path through vertical integration. ; Step 2. For data directly calculated from occultation data... A neural network model is introduced for data fusion and calibration; First, a neural network model is constructed and trained to correct and optimize the systematic bias of the occultation TEC data; then, the trained neural network model is used to output the calibrated ionospheric TEC values, i.e. ; Step 3. Calculate the calibrated ionospheric TEC value. As input parameters, the global broadcast correction coefficients of the NTCM-G model, i.e., the NTCM-G model coefficients, are calculated using an optimization estimation algorithm. Step 4. Encode the set of NTCM-G model coefficients obtained from the solution and inject them into the navigation message of the satellite navigation system, and broadcast them to global users through geostationary orbit or medium Earth orbit navigation satellites; Step 5. The user's single-frequency receiver receives and decodes the NTCM-G model coefficients in the navigation message. Combining the user's own position, time, and satellite line-of-sight direction, it uses the NTCM-G model to calculate the ionospheric delay correction amount on the current propagation path in real time and applies it to the positioning calculation to realize global ionospheric delay correction service.

2. The ionospheric delay correction method for a space-based data-driven broadcast ionospheric model according to claim 1, characterized in that, Step 1 specifically involves: Step 1.

1. Obtain GNSS occultation electron density profile products from the LEO satellite constellation and perform data quality control; I. A sliding window is used to analyze the original electron density sequence of the occultation. The mean filtering process for points is calculated using the following formula: （1） In the formula, This represents the b-th altitude point, where Ne is the observed electron density of the occultation. It is an odd number; For the first height points The observed electron density of the occultation, i.e., the raw data; This represents the filtered data; II. Calculate the average relative deviation between the original data and the filtered data. The formula is as follows: （2） in The total number of samples representing the electron density profile. This represents the b-th elevation point. Observed electron density values ​​for occultation; set a threshold for judging the average relative deviation. ,exclude Abnormal profile; III. Calculate the normalized variance index σ of the electron density using the following formula: （3） in This indicates the peak electron density of the F2 layer; Set the threshold for normalized variance. Eliminate σ≥ Abnormal data; IV. Calculate the electron density gradient within the preset height range. The formula is as follows: （4） in, The height of the upper level The height of the lower level; express Observations of occultation electron density at altitude express Observed electron density of occultation at altitude; Eliminate non-negative gradients, i.e. The abnormal profile ensures that the F-layer structure conforms to the physical properties of the ionosphere; V. Exclude anomalous data where NmF2 is less than 0, and remove abnormal observations where the peak height of F2 layer hmF2 is less than 200km; Step 1.

2. Calculate the total electron content of the ionosphere along the occultation path using the vertical integration algorithm from the occultation electron density profile. The calculation formula is as follows: （5） in, This represents the bottom height of the electron density profile. This represents the top height of the electron density profile.

3. The ionospheric delay correction method for a space-based data-driven broadcast ionospheric model according to claim 1, characterized in that, In step 2, the neural network model adopted is a feedforward neural network model; First, a training dataset for the feedforward neural network model is constructed; second, feature engineering and selection are performed on the training data; then, the feedforward neural network model is built and trained; finally, the trained model is used to predict the output.

4. The ionospheric delay correction method for a space-based data-driven broadcast ionospheric model according to claim 3, characterized in that, In step 2, the process of constructing the training dataset for the feedforward neural network model is as follows: I. Collect occultation electron density data after data quality control in step 1, and TEC data calculated from global GNSS ground stations, abbreviated as... , construct the training dataset for the feedforward neural network model; II. Extract input features from each occultation event, including those obtained from the occultation path integral. Peak parameters NmF2, hmF2, spatiotemporal parameters, and geometric parameters of the electron density profile; The spatiotemporal parameters include year, day of year (DOY), local time (LT), and the longitude and latitude of the hmF2 point; the geometric parameters of the electron density profile include the top and bottom heights of the electron density and the longitude and latitude coordinates. III. Establish the input-output pairs, i.e., paired data, required for supervised learning of the feedforward neural network model; Each occultation event is associated with a spacetime "co-located" event. The co-location criteria for observation pairing are: the hmF2 point of the occultation event is located within a preset great circle distance of a certain GNSS receiving station, and the observation time is within a preset time window; Pairing The value is used as the target value for model training, i.e., the true value; IV. Filter the paired data and remove invalid or unreliable data points; Quality control standards include removal or Data with non-positive or missing values; exclude electron density profiles where the hmF2 height is outside the preset range.

5. The ionospheric delay correction method for a space-based data-driven broadcast ionospheric model according to claim 4, characterized in that, In step 2, the process of feature engineering and selection of the training data is as follows: I. Perform sine and cosine transforms on the periodic time features, namely the annual day of birth (DOY) and local time (LT), to encode their annual and diurnal periodicity and avoid introducing discontinuities at the period boundaries. The calculation method is as follows: （6） （7） （8） （9） in, Represents the cosine component of the accumulated days of a year. This represents the sine component of the accumulated days over a year. Represents the cosine component of local time. The sine component representing local time; II. Use the random forest method to evaluate the relative importance of each input feature, identify key driving factors, and use these key driving factors as inputs for model training; the identified key driving factors include... ,years, , , , The longitude of hmF2 point, the latitude of hmF2 point, and the top height of the electron density.

6. The ionospheric delay correction method for a space-based data-driven broadcast ionospheric model according to claim 4, characterized in that, In step 2, the construction and training process of the feedforward neural network model is as follows: I. Construct a feedforward neural network, where the input layer of the feedforward neural network is the key driving factor determined by the random forest method; The feedforward neural network contains a hidden layer that uses the hyperbolic tangent sigmoid activation function. The output layer of the feedforward neural network is a single neuron that outputs the predicted GNSS equivalent TEC value. II. Use 80% of the training dataset for training and reserve 20% for independent testing; III. To improve robustness, a sub-model aggregation strategy is adopted, which involves further dividing the training data into three subsets on an equal basis and training a sub-model, i.e., a feedforward neural network, on each subset. IV. Use the Bayesian regularized backpropagation algorithm for model training.

7. The ionospheric delay correction method for a space-based data-driven broadcast ionospheric model according to claim 6, characterized in that, In step 2, the process of predicting the output using the trained model is as follows: Deploy the trained model in practice; When new occultation electron density data is received, the system automatically performs data quality checks and feature extraction. Then, it calls three pre-trained sub-model feedforward neural networks to calculate the calibrated ionospheric TEC value. , ; For each one that needs calibration The input is first predicted by three pre-trained sub-models; Final calibrated ionospheric TEC value It is obtained by averaging the prediction results of three trained sub-models, as shown in the following formula: 。 8. The ionospheric delay correction method for a space-based data-driven broadcast ionospheric model according to claim 1, characterized in that, Step 3 specifically involves: The calibrated ionospheric TEC value As input parameters, the NTCM-G broadcast ionospheric model is driven to solve for the optimal model broadcast coefficients, which minimize the overall difference between the NTCM-G model predictions and all occultation observations. Organize and calibrate the occultation observation dataset, including Each independent observation point; For the One observation point, The information includes the following: Geographic coordinates, i.e., latitude, at the occultation profile hmF2 and longitude ; Time parameters, including year-round days and local time ; and total electron content observation values The unit is TECU; The NTCM-G model function is denoted as function. Its input is the broadcast parameter vector. Spatiotemporal parameters of an observation point The output is the predicted TEC value for that observation point, and the formula is as follows: （10） in Rank TEC prediction values ​​for each observation point This represents a set of NTCM-G model coefficients.

9. The ionospheric delay correction method for a space-based data-driven broadcast ionospheric model according to claim 8, characterized in that, In step 3, the process of solving for the optimal broadcast parameter vector is as follows: I. Calculate the model prediction value at each observation point. Compared with observed values The residuals between : ； Combine all residuals into one 3D column vector: ； in Represents the residual vector; II. Define the objective function using the least squares criterion. For the sum of squared residuals: ； The goal of data-driven approaches is to find ways to make... Minimized ; III. The parameter inversion problem can be formulated as an unconstrained nonlinear least squares optimization problem, as shown in the following formula: ； Where argmin represents the objective function The value of the variable when it reaches its minimum value; IV. Model Regarding parameters Since it is nonlinear, this optimization problem is solved using an iterative optimization algorithm, as follows: IV.

1. Setting the initial guess values ​​for the parameter vector ; IV.

2. For the iteration step The search direction is calculated using the LM algorithm. And step size, to update parameters: ； in It is the step size; The LM algorithm is an improvement on the Gauss-Newton method, and its search direction... The following system of linear equations was obtained by solving: ； in, Is the residual vector in Jacobian matrix at the location, It is the damping factor. yes The identity matrix; iteration stops when the convergence condition is met, and the current parameters... That is, the approximate optimal solution ; V. Output optimal parameters: , This represents a set of NTCM-G model coefficients obtained through the solution process.

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