Ionized layer modeling method based on dynamic adaptive function optimization

Abstract

The invention discloses an ionosphere modeling method based on dynamic adaptive function optimization, and belongs to the technical field of earth space environment and satellite navigation, and the method comprises the steps: adaptively obtaining NeQuick model ionosphere background data of a target region in a preset time period through physical driving and a dynamic boundary; according to the NeQuick model ionized layer background data, determining an optimal polynomial order combination from a preset candidate order set by using an akaike information criterion; and on the basis of observation data of a global navigation satellite system, constructing a regional ionosphere refinement model by adopting the optimal polynomial order combination. According to the method, the simplest model is selected on the premise of ensuring the precision, and the calculation efficiency is improved.

Description

Technical Field

[0001] The present invention belongs to the field of earth space environment and satellite navigation technology, and in particular relates to an ionosphere modeling method based on dynamic adaptive function optimization. Background Art

[0002] The ionosphere is a critical component of the Earth's space environment. Its changes not only reflect space weather conditions but also significantly affect electromagnetic radio signal propagation, such as signal bending, refraction, attenuation, and polarization rotation. With the recent advancement of Global Navigation Satellite System (GNSS) technology, it has become possible to accurately determine the ionospheric total electron content (TEC) using GNSS observational data. Currently, ionospheric mathematical models are mainly divided into three categories: thin-shell interpolation models, function fitting models, and integrated models. The Ionosphere Working Group (IWG) of the International GNSS Service (IGS) is committed to providing GNSS users with global, high-precision ionospheric products, including delayed rapid global ionospheric maps (GIMs), final GIMs, real-time GIMs, and predicted GIMs. Furthermore, the NeQuick model, as a three-dimensional physical model, can more realistically reflect the ionospheric structure by incorporating solar activity parameters. Its ionospheric correction accuracy averages 70% of the ionospheric delay.

[0003] However, existing ionospheric modeling techniques still have some limitations. First, the order of most ionospheric models relies on empirical settings and lacks the ability to dynamically adjust the model structure according to the spatiotemporal changes of the ionosphere. Second, fixed models are difficult to accurately characterize the anisotropic distribution of the ionosphere, especially in low-latitude regions with strong ionospheric activity and during ionospheric disturbances. In addition, global ionospheric models (such as CODE GIM) have inherent defects in regional refined modeling and cannot capture low-latitude disturbances or local refined features in mid-latitudes. These shortcomings affect the application of ionospheric models in high-precision navigation, communications, space weather monitoring and other fields. Summary of the Invention

[0004] To solve the above technical problems, the present invention proposes an ionospheric modeling method based on dynamic adaptive function optimization to solve the dynamic modeling problem of the spatiotemporal changes of the ionosphere.

[0005] To achieve the above objectives, in a first aspect, the present invention provides an ionospheric modeling method based on dynamic adaptive function optimization, comprising:

[0006] Through physical driving and dynamic boundaries, the NeQuick model ionospheric background data of the target area within a preset period is adaptively obtained;

[0007] According to the NeQuick model ionospheric background data, an optimal polynomial order combination is determined from a preset candidate order set using the Akaike Information Criterion;

[0008] Based on global navigation satellite system observation data, the optimal polynomial order combination is used to construct a regional ionosphere refinement model.

[0009] Preferably, the process of adaptively acquiring NeQuick model ionospheric background data of the target area within a preset time period through physical driving and dynamic boundaries includes:

[0010] Input real-time solar activity parameters to the physical driving module of the NeQuick model;

[0011] Determine the latitude and longitude boundaries of the target area based on the distribution of ionospheric penetration points from global navigation satellite system observation data;

[0012] Based on the physical driving module and the longitude and latitude boundaries, vertical total electron content VTEC distribution data of the target area within a preset time period is calculated as NeQuick model ionospheric background data.

[0013] Preferably, the process of determining the optimal polynomial order combination from a preset candidate order set using the Akaike Information Criterion according to the NeQuick model ionospheric background data comprises:

[0014] Construct a candidate order set including latitude order N and longitude order M, where the value range of N and M is 1 to 10;

[0015] For each candidate order combination, the fitting residuals of the polynomial function and the NeQuick model VTEC data are calculated;

[0016] Based on the fitting residuals and the number of model parameters, the AIC value of each candidate order combination is calculated using the Akaike Information Criterion;

[0017] The candidate order combination with the smallest AIC value is selected as the optimal polynomial order combination.

[0018] Preferably, when the amount of observed data is lower than a preset threshold, the modified Akaike Information Criterion is used to replace the Akaike Information Criterion for calculation.

[0019] Preferably, the process of constructing a regional ionospheric refinement model based on global navigation satellite system observation data using the optimal polynomial order combination includes:

[0020] generating a polynomial function expression according to the optimal order combination;

[0021] The total electron content of the slant path is obtained by inversion using global navigation satellite system observations;

[0022] The total electron content of the oblique path is converted into the VTEC observation value at the puncture point through a mapping function;

[0023] The coefficients of the polynomial function expression are obtained by solving using the least squares method.

[0024] Preferably, the step of obtaining the total electron content of the slant path by inverting observations using the global navigation satellite system comprises:

[0025] Combined multi-frequency pseudorange and phase geometry-free observations;

[0026] Ionospheric observations and differential code biases are separated by function fitting and zero reference conditions.

[0027] Preferably, the preset time period is 1 hour, and the optimal order combination determination operation is performed independently in each time period.

[0028] In a second aspect, the present invention further provides an ionospheric error correction system, comprising:

[0029] Data acquisition module: used to receive global navigation satellite system observation data and NeQuick background VTEC data;

[0030] Model optimization module: configured to execute the method described in the first aspect to generate a refined ionospheric model;

[0031] Positioning correction module: applies the output parameters of the refined ionospheric model to the real-time positioning solution of the GNSS receiver.

[0032] In a third aspect, the present invention further discloses a computer device comprising a memory, a processor, and a computer program stored in the memory, wherein the processor executes the computer program to implement the steps of the method described in the first aspect.

[0033] In a fourth aspect, the present invention further discloses a computer-readable storage medium having a computer program stored thereon, which implements the steps of the method described in the first aspect when executed by a processor.

[0034] Compared with the prior art, the present invention has the following advantages and technical effects:

[0035] The present invention provides an ionospheric modeling method based on dynamic adaptive function optimization, comprising: first, obtaining NeQuick model ionospheric background data of a target area within a preset time period; second, determining an optimal polynomial order combination from a preset candidate order set based on the NeQuick model ionospheric background data using the Akaike information criterion; and finally, constructing a regional ionospheric refinement model using the optimal polynomial order combination based on global navigation satellite system observation data.

[0036] The present invention adopts the physical background data of the NeQuick model (rather than pure mathematical interpolation) to provide the polynomial with initial constraints that conform to the physical characteristics of the ionosphere, thereby enhancing the reliability of the model in complex regions (such as the low-latitude equatorial anomaly region).

[0037] The present invention uses the AIC criterion to select the optimal order combination from the candidate set, so that the model structure automatically adapts to the real-time changes of the ionosphere (such as using low order in calm periods and high order in disturbed periods). This solves the problem of a sharp increase in error in fixed-order models when the ionosphere is active. The simplest model is selected while ensuring accuracy, thereby improving computational efficiency.

[0038] The present invention forms a closed loop from background data acquisition → AIC order selection → GNSS data modeling, without manual intervention in order selection, and is suitable for real-time ionospheric correction systems (such as GNSS single-frequency receiver enhancement services). BRIEF DESCRIPTION OF THE DRAWINGS

[0039] The accompanying drawings, which constitute part of this application, are intended to provide a further understanding of this application. The exemplary embodiments and descriptions of this application are intended to explain this application and do not constitute an improper limitation on this application. In the accompanying drawings:

[0040] Figure 1 This is a flow chart of an ionospheric modeling method based on dynamic adaptive function optimization according to an embodiment of the present invention;

[0041] Figure 2 This is a time series diagram of the geomagnetic activity index (DST) and the solar activity index (F10.7) according to an embodiment of the present invention;

[0042] Figure 3 1 is a distribution diagram of ionospheric puncture points (IPPs) within a day according to an embodiment of the present invention; (a) is the distribution diagram of ionospheric puncture points in region A, and (b) is the distribution diagram of ionospheric puncture points in region B;

[0043] Figure 4 This is a VTEC distribution map over region A at 14:00 local time according to an embodiment of the present invention;

[0044] Figure 5 This is a graph showing the ionospheric VTEC variation gradient at 14:00 local time in region A according to an embodiment of the present invention; the upper graph is a graph showing the variation gradient in the latitude direction, and the lower graph is a graph showing the variation gradient in the longitude direction;

[0045] Figure 6 This is a VTEC distribution map over region B at 14:00 local time according to an embodiment of the present invention;

[0046] Figure 7This is a graph showing the ionospheric VTEC variation gradient at 14:00 local time in region B according to an embodiment of the present invention; the upper graph shows the latitudinal variation gradient, and the lower graph shows the longitudinal variation gradient;

[0047] Figure 8 This is a flowchart of the algorithm implementation steps of an embodiment of the present invention;

[0048] Figure 9 This is a timing diagram of the regional ionospheric model structure according to an embodiment of the present invention. DETAILED DESCRIPTION

[0049] It should be noted that, in the absence of conflict, the embodiments and features of the embodiments in this application can be combined with each other. The present application will be described in detail below with reference to the accompanying drawings and in combination with the embodiments.

[0050] It should be noted that the steps shown in the flowcharts of the accompanying drawings can be executed in a computer system such as a set of computer-executable instructions, and that, although a logical order is shown in the flowcharts, in some cases, the steps shown or described can be executed in an order different from that shown here.

[0051] Example 1

[0052] like Figure 1 As shown, this embodiment provides an ionospheric modeling method based on dynamic adaptive function optimization, including:

[0053] S1. Adaptively obtain NeQuick model ionospheric background data of the target area within a preset time period through physical driving and dynamic boundaries;

[0054] Furthermore, the process of adaptively acquiring the NeQuick model ionospheric background data of the target area within a preset period of time through physical driving and dynamic boundaries includes:

[0055] S101, inputting real-time solar activity parameters and observational spatiotemporal information into the physical driving module of the NeQuick model;

[0056] S102. Determine the latitude and longitude boundaries of the target area based on the distribution of ionospheric penetration points from global navigation satellite system observation data;

[0057] S103 , based on the physical driving module and the longitude and latitude boundaries, calculating vertical total electron content VTEC distribution data of the target area within a preset time period as NeQuick model ionospheric background data.

[0058] Specifically, the reasons for choosing NeQuick model VTEC as the background value mainly include: 1. Physical modeling advantages: Compared with broadcast models such as Klobuchar, NeQuick is a three-dimensional physical model that incorporates solar activity parameters (such as F10.7), which can more realistically reflect the ionospheric structure. 2. Accuracy verification: The correction accuracy of its vertical total electron content (VTEC) reaches an average of 70% of the ionospheric delay, which can provide a reliable background field for the refined model. 3. Dynamic adaptability: Based on the background field model driven by physical parameters, it dynamically simulates the changing characteristics of the ionospheric activity in the measurement area, and dynamically and adaptively determines the specific expression of the model according to the model selection theory, and selects data from different ionospheric activity periods for modeling, such as Figure 2 As shown, the adaptive ability of the model is verified.

[0059] The NeQuick model, based on the Di Giovanni Radicella (DRG) model, describes the electron density distribution above the E layer of the ionosphere in the study area. Because the EF layer (the bottom layer) is more active (and constitutes the majority of the ionosphere), it is divided into five Epstein layers, while the layer above the F layer (the top layer) is considered one layer. The electron density distribution is described by superimposing multiple Epstein functions, reflecting the complex structure of the bottom layer.

[0060] The electron density expression at the bottom layer height h is:

[0061] N bottom (h) = N E (h)+N F1 (h)+N F2 (h) 60km<h<1000km (1)

[0062]

[0063] Among them, Nm E ,Nm F1 and Nm F2 Represents the peak electron density of E layer, F1 layer and F2 layer (unit: 10 11 / m 3 ), defined as: Nm E =0.124(fo E ) 2 、Nm F1 =0.124(fo F1 ) 2 、Nm F2 =0.124(fo F2 ) 2 Where foE, foF1, and foF2 are the critical frequencies of the corresponding layers (unit: MHz); hmE, hmF1, and hmF2 are the heights corresponding to the peak electron density; BE 、B F1 、B F2 is the thickness of each layer; ξ(h)=exp(10 / (1+|h-hm F2 |)) is a function related to height. The electron density at the top layer height h is expressed as:

[0064]

[0065] The total electron content (TEC) value along a given path can be calculated by numerical integration based on the electron density at any point on the path. Currently, there are three versions of the NeQuick model: NeQuick1, NeQuick2 (Nava et al., 2008) and NeQuick-G (Arbesser-Rastburg, 2006). In formulas (1)-(2), NeQuick1 and NeQuick2 differ in the expressions of hm, fo, B and H0. In addition, the DIPLATS.asc file used to correct the magnetic inclination in NeQuick1 is replaced by the MODIP.asc file in NeQuick2. Compared with NeQuick2, NeQuick-G has higher computational efficiency and replaces the monthly average parameter of solar activity with the effective ionization level factor Az, whose expression is:

[0066] Az(μ)=a0+a1μ+a2μ 2 (5)

[0067] Among them, a0, a1, and a2 are the broadcast parameters used for real-time calculations in NeQuick. These parameters are calculated by the NeQuick model using Global Navigation Satellite System (GNSS) observations and are updated daily.

[0068] The NeQuick model is an empirical model used to describe the electron density distribution in the ionosphere. It has important applications in fields such as the Global Navigation Satellite System (GNSS), and is used to correct the impact of the ionosphere on satellite signal propagation and improve positioning accuracy. The model reflects the state characteristics of the ionosphere through some broadcast parameters (such as a0, a1, and a2). These parameters are calculated based on GNSS observation data and updated daily to adapt to the dynamic changes of the ionosphere. The corrected magnetic inclination μ is also an important input parameter in the model, playing a key role in ionospheric modeling and related calculations. μ is the corrected magnetic inclination, which is defined as follows:

[0069]

[0070] Magnetic inclination: The angle between the direction of the Earth's magnetic field and the local horizontal plane. It reflects the vertical component of the Earth's magnetic field and increases with increasing latitude (close to 0° near the equator and close to 90° at the poles).

[0071] Geographic latitude: The spherical angular distance from a point on the Earth's surface to the Earth's equatorial plane, used to locate positions in the northern and southern hemispheres (range: -90° to 90°).

[0072] Magnetic inclination and geographic latitude are often used in ionospheric modeling to describe the influence of the geomagnetic field and geographic location on the electron density distribution. For example, the formation of the equatorial anomaly is closely related to the magnetic inclination.

[0073] In this embodiment, the NeQuick model is superior to other broadcast models in describing the vertical profile of the ionosphere and can accurately provide TEC values ​​for any path and altitude (without considering the projection function error).

[0074] like Figure 3 As shown, the distribution of ionospheric puncture points (IPPs) in region A (a) and region B (b) within a day; the IPPs distribution in region A shows low-latitude characteristics, while the IPPs distribution in region B is relatively concentrated in mid-latitudes. The distribution range of IPPs actually determines the size of the modeling area.

[0075] This example compares and analyzes the accuracy of the final GIM, NeQuick-G, and Klobuchar models in the study area. Taking region A (15°–35°N, 100°–130°E) and region B (15°–60°N, 50°–140°W) as examples, Figure 4 Findings: (1) NeQuick-G is more consistent with the GIM: Compared with the Klobuchar model, the VTEC distribution trend of NeQuick-G is closer to the final GIM, with the numerical range of 10–40TECu; (2) Limitations of the Klobuchar model: VTEC only fluctuates slightly around 30TECu and cannot reflect the dynamic characteristics of the low-latitude ionosphere (such as significant spatiotemporal gradients).

[0076] Comparison of ionospheric latitude and longitude gradients in region A, such as Figure 5 As shown, it can be seen that:

[0077] NeQuick-G is consistent with the GIM trend;

[0078] Latitude direction: the amplitude of change decreases with increasing latitude, showing obvious latitude belt characteristics;

[0079] Longitude direction: the change first increases and then decreases, but the amplitude is small;

[0080] Latitude dominance: The latitudinal variation is more significant and continuous, which is consistent with the characteristic that the low-latitude ionosphere is dominated by latitudinal variation.

[0081] Broadcast model vs. GIM interpolation: The ionospheric variations calculated by broadcast models (such as NeQuick-G) are smoother than the GIM interpolation results, mainly due to the difference in spatial resolution (GIM relies on discrete point interpolation, which introduces interpolation errors).

[0082] Therefore, NeQuick-G is superior to the Klobuchar model in terms of VTEC distribution and gradient changes in mid- and low-latitude regions, and is closer to the high-precision GIM results. In particular, it shows stronger adaptability in the low-latitude dynamic ionospheric environment. This explains why the NeQuick model VTEC is chosen as the background value of the refined model (FM) - its physical modeling characteristics and accuracy can effectively support the capture of fine features of the regional ionosphere. The resolution of the Global Ionosphere Map (GIM) (2.5°×5°) is lower than that of the FM. Figure 4 The resolution set in .

[0083] same, Figure 6 and Figure 7 and Figure 4 and Figure 5 Similar, but showing the ionospheric variations in region B. Compared with the Klobuchar model, the results of the NeQuick model and GIM are more consistent with the actual ionospheric variations, which are similar to the results in region A.

[0084] Characteristics of longitude and latitude changes: The ionospheric changes in the latitude direction are more obvious and continuous than those in the longitude direction, and the areas of significant changes are concentrated in the low latitudes.

[0085] Figure 6 The “narrow trace” anomaly visible in the third column of subplots may be due to the discontinuity of the empirical model at the boundary.

[0086] Regional comparison: The ionospheric activity in region A (low latitudes) is stronger, and its latitudinal variation is significantly greater than that in region B (mid-latitudes), while the difference in the longitude direction is not obvious.

[0087] Model selection basis: The NeQuick model has better accuracy than Klobuchar and higher computational efficiency than the final GIM, so it was adopted in this study.

[0088] In summary, compared to region A, the peak latitudinal gradient in region B is lower and the gradient changes more gradually, confirming the conclusion that the low-latitude ionosphere is more spatiotemporally dynamic. Regarding model performance, the NeQuick model and the GIM show consistent gradient trends, both reflecting the relative stability of the mid-latitude ionosphere, while the Klobuchar model still fails to capture subtle changes.

[0089] S2. Determining an optimal polynomial order combination from a preset candidate order set using the Akaike Information Criterion based on the NeQuick model ionospheric background data;

[0090] Furthermore, according to the NeQuick model ionospheric background data, the process of determining the optimal polynomial order combination from a preset candidate order set using the Akaike Information Criterion includes:

[0091] S201, constructing a candidate order set including a latitude order N and a longitude order M, wherein the value range of N and M is 1 to 10;

[0092] S202, for each candidate order combination, calculating the fitting residual of the polynomial function and the NeQuick model VTEC data;

[0093] S203, calculating the AIC value of each candidate order combination using the Akaike Information Criterion based on the fitting residual and the number of model parameters;

[0094] S204 : Select the candidate order combination with the smallest AIC value as the optimal polynomial order combination.

[0095] Specifically, due to the different model structures, the Akaike Information Criterion (AIC) needs to be introduced to make a trade-off. Proposed by Japanese mathematician Akaike, AIC is used to evaluate the Kullback-Leibler divergence between the candidate model and the true data distribution. Its core goal is to balance the model's goodness of fit and complexity to avoid underfitting or overfitting. Based on the principles of information theory, AIC consists of two parts: one related to the goodness of fit between the model and the data, and the other related to the model's complexity. Its expression is:

[0096]

[0097] AIC components:

[0098] 2m: Model complexity term, which increases with the number of parameters m and penalizes complex models;

[0099] Log(L) is the goodness of fit term, where L is the likelihood function value, reflecting the degree of fit of the model to the data. That is, the larger the Log(L), the better the fit.

[0100] Optimization goal: Select the model with the smallest AIC value to achieve the best balance between complexity and fitting ability.

[0101] Where log(·) represents the logarithmic function with base 10, is the likelihood function value. When the modeling error follows a normal distribution, minimize Equivalent to maximizing the likelihood function value of the selected model Therefore, formula (12) can be rewritten as:

[0102]

[0103] The core logic of this embodiment is: Combined with the number of model parameters m, AIC can effectively screen out polynomial model structures that are both well-fitting and not too complex under given data, ensuring the adaptability and generalization ability of the refined model (FM) to the spatiotemporal variations of the ionosphere.

[0104] When the redundancy of observations is low, AICc (modified Akaike information criterion) is used to perform a second-order correction instead of AIC.

[0105]

[0106] In small sample sizes, AICc can more accurately assess model performance, avoid over-penalizing model complexity, and thus select a more appropriate model. Obviously, as n approaches infinity, AICc approaches AIC infinitely. Ultimately, the model with the smallest AIC or AICc value is determined.

[0107] S3. Based on the global navigation satellite system (GNSS) observation data, construct a regional ionospheric refinement model using the optimal polynomial order combination;

[0108] Furthermore, based on the global navigation satellite system GNSS observation data, the process of constructing the regional ionospheric refinement model using the optimal polynomial order combination includes:

[0109] S301, generating a polynomial function expression according to the optimal order combination;

[0110] S302, using global navigation satellite system observation inversion to obtain slant path total electron content (STEC) data;

[0111] S303, converting the STEC data into VTEC observation values ​​at the puncture point through a mapping function;

[0112] S304: Using the least square method, obtain the coefficients of the polynomial function expression.

[0113] Specifically, the ionospheric observations are inverted:

[0114] The Carrier Phase-Pseudorange Smoothing Technique (CPPS) is used to invert ionospheric observations. Its principle is as follows:

[0115]

[0116] Where i, r, and s are epoch, receiver, and satellite indices, respectively; P GF and L GFdenotes the combined pseudorange and phase observations of the geometry-free range based on the jth and kth frequency observations, respectively; p and l are the corresponding weights; N is the length of the continuous arc segment; A constant It is usually regarded as a constant and includes parameters such as receiver differential code bias (RDCB), satellite differential code bias (SDCB) and ambiguity that absorbs the phase code bias.

[0117] As an innovative implementation method, the geometric distance errors between the satellite and the receiver (such as orbit error and receiver position error) are eliminated through geometry-free combination, and the ionosphere-related STEC signals are separated by combining weight optimization and continuous arc segment processing to provide pure observation input for model training.

[0118]

[0119] Where f is the frequency; I TEC Slant Total Electron Content (STEC) along the observation path, unit: TECu. DCB j,k,r (receiver end j, k frequency differential code deviation) and (Satellite-side differential code bias) is an inherent parameter that needs to be processed in ionospheric modeling.

[0120] Specifically, the ionospheric model is constructed:

[0121] After extracting the ionospheric observations, to simplify processing, STEC needs to be converted into vertical total electron content (VTEC) through a mapping function, and then a polynomial function model based on VTEC is constructed. The specific steps are as follows:

[0122]

[0123] Where MP(z) represents the mapping function that depends on the satellite altitude z; k is the scaling factor; R and H ion denote the radius of the earth and the height of the thin layer, respectively, which are set to R = 6371 km, k = 0.9728, H ion =506.7km. and λ represent the geographical latitude and longitude of the IPP, respectively. t represents the observation time. and λ0 represent the geographical longitude and latitude of the center of the study area, respectively. t0 represents the solar hour angle. E nm represents the N × M model parameters to be estimated. Parameters N and M are typically chosen between 3 and 6 to accommodate regional ionospheric variations. A least squares algorithm is then used to obtain the parameter solution.

[0124] To overcome the shortcomings of the ionospheric mathematical function model, which lacks a predefined basis and is fixed at each modeling moment, thus ignoring the temporal variations of the ionosphere, we used NeQuick model data and the AIC to determine the structure of the polynomial within each modeling period. The data range was determined based on the actual IPP measurement locations within each time period, with a one-hour interval. The candidate parameter sets ranged from 1×1 to 10×10, and a total of 55 models were tested. The detailed process of this method is as follows:

[0125]

[0126] Where i is the universal time (unit: hour); A is the design matrix calculated based on the grid position; P is the weight matrix (set as the unit matrix in this paper); VTEC Nequick VTEC observation vector calculated for NeQuick-G; is the coefficient vector of the polynomial to be solved; is the residual vector.

[0127] Unit weight error Calculation formula:

[0128]

[0129] Where n and m represent the number of observations and the number of parameters respectively. When the model structure is the same, the unit weight error The smaller it is, the better the model.

[0130] S4. Observation and analysis of total electron content in differential oblique paths.

[0131] Differential slant path total electron content (dSTEC) observations are a common method for evaluating the accuracy of ionospheric models. This is achieved by calculating the TEC deviation between the line of sight and a reference direction using the formula:

[0132] dSTEC=(L(z1)-STEC model (z1))-(L(z2)-STEC model (z2)) (15)

[0133] Among them, z1 is the sight altitude angle, z2 is the reference direction altitude angle (usually the maximum altitude angle of the continuous arc segment); STEC model is the STEC calculated by the model to be evaluated; L is the geometry-free phase observation value, including phase ambiguity (which can be eliminated by intra-arc segment difference).

[0134] The quantitative evaluation data are shown in Table 1.

[0135] Table 1

[0136]

[0137] Figure 8 A flowchart of the proposed method is presented. First, using data from the NeQuick-G model, the specific form of the functional model for each time period is determined through the AIC. Second, a refined model is constructed using real TEC observations obtained from Global Navigation Satellite System (GNSS) measurements using the least squares (LS) method. Finally, the output results, including the ionospheric model and differential code bias (DCB), are analyzed for accuracy.

[0138] Figure 9 The order of the determined polynomial model is shown. Figure 9 As can be seen from the figure, the order changes more smoothly in the latitude direction than in the longitude direction over time. This is because the change in the latitude direction is more continuous than that in the longitude direction. Figure 9 The most striking result is that the number of parameters is strongly correlated with ionospheric variability. The more active the ionosphere, the greater the number of parameters. For example, a higher number of parameters are determined around noon and midnight, when the ionosphere is most dynamic. The number of parameters in Region B is roughly equal to that in Region A, as Region B is large and spans multiple time zones, while Region A is a smaller, more ionospheric region. A comparative analysis of the upper and lower panels shows that the model order changes more significantly in the lower sub-panel, which is consistent with the significant ionospheric disturbances observed on the 225th day of the 2024 annual accumulation.

[0139] In this example, FM outperforms the fixed-order model across the board: For the low-latitude region, Figure A shows a 46% reduction in FM RMS during the disturbance period (DOY 225) and a 36%-37% reduction during the quiet period (DOY 102). For the mid-latitude region, Figure B shows a 9%-11% improvement during the disturbance period and approximately 5% during the quiet period, indicating a positive correlation between ionospheric activity and model performance. DOY stands for "Day of Year," a number often used in ionospheric research to represent time series and analyze ionospheric variations on different dates.

[0140] In this example, the CODE GIM accuracy is insufficient: its RMS of dSTEC is as high as 8TECu during the disturbance period in region A, which is much higher than that of FM and Poly, indicating that the global model has limitations in correcting regional ionospheric delays.

[0141] In this embodiment, dynamic adaptability is verified: FM dynamically adjusts the model order through AIC, significantly reducing the error in ionospheric active regions (such as region A) and disturbance periods (such as DOY 225), verifying the rule that "the stronger the ionospheric activity, the more significant the optimization effect."

[0142] Example 2

[0143] Based on the same inventive concept, this embodiment further provides an ionospheric error correction system, including:

[0144] Data acquisition module: used to receive GNSS observation data and NeQuick background VTEC data;

[0145] Model optimization module: configured to execute the method described in embodiment 1 to generate a refined ionospheric model;

[0146] Positioning correction module: applies the output parameters of the refined ionospheric model to the real-time positioning solution of the GNSS receiver.

[0147] The ionospheric error correction system provided in this embodiment has all the advantages of the ionospheric modeling method based on dynamic adaptive function optimization provided in the first embodiment.

[0148] Example 3

[0149] This embodiment further discloses a computer device, including a memory, a processor, and a computer program stored in the memory, wherein the processor executes the computer program to implement the steps of the method described in the first embodiment.

[0150] Example 4

[0151] This embodiment further discloses a computer-readable storage medium on which a computer program is stored. When the computer program is executed by a processor, the steps of the method described in the first embodiment are implemented.

[0152] The above are merely preferred embodiments of the present application, but the scope of protection of the present application is not limited thereto. Any changes or substitutions that can be easily conceived by a person skilled in the art within the technical scope disclosed in this application should be included in the scope of protection of the present application. Therefore, the scope of protection of the present application should be based on the scope of protection of the claims.

Claims

1. An ionospheric modeling method based on dynamic adaptive function optimization, characterized in that: The following steps are involved: Through physical driving and dynamic boundaries, the NeQuick model ionospheric background data of the target area within a preset period is adaptively obtained; According to the NeQuick model ionospheric background data, an optimal polynomial order combination is determined from a preset candidate order set using the Akaike Information Criterion; Based on global navigation satellite system observation data, the optimal polynomial order combination is used to construct a regional ionosphere refinement model.

2. The method according to claim 1, characterized in that The process of adaptively acquiring NeQuick model ionospheric background data of the target area within a preset period through physical driving and dynamic boundaries includes: Input real-time solar activity parameters and observational spatiotemporal information into the physical driving module of the NeQuick model; Determine the latitude and longitude boundaries of the target area based on the distribution of ionospheric penetration points from global navigation satellite system observation data; Based on the physical driving module and the longitude and latitude boundaries, vertical total electron content VTEC distribution data of the target area within a preset time period is calculated as NeQuick model ionospheric background data.

3. The method according to claim 1, characterized in that The process of determining the optimal polynomial order combination from a preset candidate order set using the Akaike Information Criterion according to the NeQuick model ionospheric background data includes: Construct a candidate order set including latitude order N and longitude order M, where the value range of N and M is 1 to 10; For each candidate order combination, the fitting residuals of the polynomial function and the NeQuick model VTEC data are calculated; Based on the fitting residuals and the number of model parameters, the AIC value of each candidate order combination is calculated using the Akaike Information Criterion; The candidate order combination with the smallest AIC value is selected as the optimal polynomial order combination.

4. The method according to claim 1, wherein When the amount of observation data is lower than a preset threshold, the modified Akaike information criterion is used instead of the Akaike information criterion for calculation.

5. The method according to claim 1, characterized in that The process of constructing a regional ionospheric refinement model based on global navigation satellite system observation data using the optimal polynomial order combination includes: generating a polynomial function expression according to the optimal order combination; The total electron content of the slant path is obtained by inversion using global navigation satellite system observations; The total electron content of the oblique path is converted into the VTEC observation value at the puncture point through a mapping function; The coefficients of the polynomial function expression are obtained by solving using the least squares method.

6. The method according to claim 5, characterized in that The steps for inverting the slant path total electron content from global navigation satellite system observations include: Combined multi-frequency pseudorange and phase geometry-free observations; Ionospheric observations and differential code biases are separated by function fitting and zero reference conditions.

7. The method according to claim 1, characterized in that The preset time period is 1 hour, and the optimal order combination determination operation is performed independently in each time period.

8. An ionospheric error correction system, characterized in that: include: Data acquisition module: used to receive global navigation satellite system observation data and NeQuick background VTEC data; Model optimization module: configured to execute the method according to any one of claims 1 to 7 to generate a refined ionospheric model; Positioning correction module: applies the output parameters of the refined ionospheric model to the real-time positioning solution of the GNSS receiver.

9. A computer device comprising a memory, a processor, and a computer program stored in the memory, wherein: The processor executes the computer program to implement the steps of the method according to any one of claims 1 to 7.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the steps of the method according to any one of claims 1 to 7 are implemented.

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