Geomagnetic soft partition and height disturbance correction projection function modeling method and system

Abstract

The application discloses a geomagnetic soft partition and height disturbance correction projection function modeling method and system, and the method comprises the following steps: obtaining a piercing point observation sample; converting into geomagnetic latitude and constructing a periodic characteristic; calculating low, medium and high latitude sub-model weights by using a fixed center and a continuous weight soft partition mechanism; establishing an effective height function of each sub-model and obtaining a basic effective height by weighted fusion; calculating a basic explicit projection function; inputting the characteristic into a data-driven model to output an effective height correction amount, a residual error and an uncertainty; mapping the correction amount into an interpretable correction term based on sensitivity and combining the correction term with the residual error; and adaptively outputting a complete result or falling back to a basic model according to the uncertainty. The application has physical interpretability and data driving capability, improves the projection function precision, region adaptability and robustness, and can be used for satellite navigation ionospheric delay correction.

Description

Technical Field

[0001] This invention relates to a method and system for modeling projection functions for geomagnetic soft partitioning and height disturbance correction. Background Technology

[0002] The ionosphere, a neutral ionized region extending from approximately 60 to 2000 km above the Earth's surface, is a crucial component of the Sun-Earth space environment. The distribution and evolution of free electrons in the ionosphere not only influence changes in the space environment but also significantly impact applications such as satellite navigation, positioning, timing, and remote sensing. Total electron content (TEC) is a vital physical parameter characterizing the distribution of electrons in the ionosphere. High-precision TEC models are essential for improving navigation and positioning accuracy, conducting ionospheric delay corrections, and studying the patterns of ionospheric variation.

[0003] In existing ionospheric modeling and applications, the thin-layer assumption of the ionosphere is typically adopted. This assumption equates free electrons distributed along the signal propagation path to a thin shell at a fixed height, and a vertical electron content model is established on this shell. Based on this, an ionospheric projection function is introduced to achieve the conversion between the tilted total electron content (STEC) and the vertical total electron content (VTEC). Since the mapping relationship between STEC and VTEC is involved in ionospheric modeling, single-frequency navigation and positioning correction, and ionospheric product applications, the modeling accuracy of the projection function directly affects the ionospheric delay correction effect and the accuracy of related applications.

[0004] Most existing projection function models are based on a fixed thin-layer height and are generally assumed to be only related to the satellite elevation angle. While these methods are simple in form and computationally convenient, the actual ionospheric electron density exhibits significant spatial and temporal non-uniformity, influenced by multiple factors such as solar activity, geomagnetic disturbances, seasonal variations, and regional electrodynamic processes. Therefore, a fixed-height, single-form projection function is insufficient to accurately describe the true ionospheric structure. Particularly in low- and high-latitude regions, where the ionospheric electron density distribution is more complex, traditional projection function models are prone to significant mapping errors under low elevation angles and complex regional conditions, thus limiting further improvements in ionospheric modeling accuracy.

[0005] On the other hand, existing projection function models typically use a uniform parameter form for global or regional modeling, lacking an effective characterization of the differences in the ionosphere across different regions, resulting in insufficient regional adaptability of the models. Although some studies have attempted to improve the projection function by introducing variable thin-layer height or empirical correction terms, most of them still belong to a single explicit model framework, which has limited ability to express complex nonlinear changes and is difficult to simultaneously take into account model accuracy, stability, and applicability.

[0006] With the development of machine learning methods, data-driven modeling techniques have been gradually applied to the field of ionospheric modeling, which can improve the expressive power of models by learning complex nonlinear relationships in observational data. However, pure data-driven methods usually lack explicit physical constraints and are prone to problems such as insufficient physical meaning, weak regional generalization ability, and insufficient stability under complex ionospheric conditions. Therefore, they are difficult to directly meet the requirements of high reliability and high precision applications.

[0007] Therefore, existing technologies still lack a modeling method for ionospheric projection functions that can reflect the spatiotemporal nonuniformity of the ionosphere while also possessing physical interpretability, regional adaptability, and data-driven nonlinear expression capabilities. Summary of the Invention

[0008] To address the technical problems of existing projection function models, such as large errors in fixed height assumptions, insufficient regional adaptability, limited expressive power of explicit models, and lack of physical constraints, stability, and generalization ability in purely data-driven models, this invention provides a projection function modeling method based on geomagnetic soft partitioning and height perturbation correction. By introducing geomagnetic partitioning mechanisms and physical constraint gradient learning strategies as technical means, this invention achieves the technical effects of improving model accuracy, regional adaptability, expressive power, stability, and generalization ability.

[0009] According to one aspect of the present invention, a projection function modeling method for geomagnetic soft partitioning and height disturbance correction is provided, comprising: Obtain observation samples of ionospheric puncture points, wherein the observation samples include at least the satellite elevation angle, the geographic coordinates of the puncture point, and the observation epoch time; The geographic coordinates of the puncture points of the observed samples are converted into geomagnetic latitude, and the periodic characteristics of local time and annual accumulated days are constructed based on the observation epoch time. Based on the geomagnetic latitude, a soft partitioning mechanism with a fixed center and continuous weights is used to calculate the weights of the observed samples belonging to the low-latitude, mid-latitude, and high-latitude sub-models, respectively. For each sub-model, a single-layer effective height function is established using the pre-calculated true projection function with geomagnetic latitude, local time, and annual day as input, and the basic single-layer effective height of the observation sample is obtained by weighted fusion according to the weights. Based on the effective height of the basic single layer and the satellite elevation angle of the observed samples, the basic explicit projection function is calculated; The geomagnetic latitude, satellite elevation angle, periodic characteristics, and weights of the observed samples are input into the data to drive the model, and the effective height correction, residual, and model uncertainty are output. Calculate the sensitivity of the underlying explicit projection function to the effective height, and multiply the effective height correction by the sensitivity to obtain the interpretable correction term; The basic explicit projection function, the interpretable correction term, and the remaining residual are added together to obtain the complete projection function prediction result; Based on the relationship between the model uncertainty and the preset threshold, the system adaptively selects to output the prediction result of the complete projection function or to fall back to the basic explicit projection function.

[0010] As a further technical solution, in the soft partitioning mechanism, for geomagnetic latitude... The observed samples, and their weights in relation to the i-th sub-model. for: , It is the center of the i-th region; Let be the bandwidth parameter for the i-th region.

[0011] As a further technical solution, the complete projection function prediction result MF is expressed as: , in As the basic explicit projection function, The effective height correction amount is r, where r is the residual. For sensitivity.

[0012] As a further technical solution, the adaptive selection includes: if the model uncertainty... If the prediction is successful, output the complete projection function prediction result; otherwise, output the basic explicit projection function. ;in This is a preset threshold.

[0013] As a further technical solution, the data-driven model is trained using a joint loss function, which includes a mean squared error term between the predicted value and the true projection function, as well as a physical constraint penalty term. The physical constraint penalty term includes a constraint that the projection function decreases monotonically with the satellite elevation angle, a geometric upper bound constraint based on the minimum effective altitude, and an effective altitude range constraint.

[0014] According to one aspect of the present invention, a projection function modeling system for geomagnetic soft partitioning and height disturbance correction is provided, comprising: The data acquisition module is used to acquire observation samples of the ionospheric puncture point, and the observation samples include at least the satellite elevation angle, the geographic coordinates of the puncture point, and the observation epoch time. The feature calculation module is used to convert the geographic coordinates of the puncture points of the observed samples into geomagnetic latitude and to construct the periodic features of local time and annual day. The soft partitioning weight calculation module is used to calculate the weights of the observed samples belonging to the low-latitude, mid-latitude, and high-latitude sub-models based on the soft partitioning mechanism of geomagnetic latitude with a fixed center and continuous weights. The basic effective height calculation module is used to establish a single-layer effective height function for each sub-model using the pre-calculated true projection function, with geomagnetic latitude, local time, and annual day as input, and to obtain the basic single-layer effective height of the observation sample by weighted fusion according to the weights. The basic projection function calculation module is used to calculate the basic explicit projection function based on the effective height of the basic single layer and the satellite elevation angle of the observation sample; The data-driven prediction module is used to input the geomagnetic latitude, satellite elevation angle, periodic characteristics, and weights of the observed samples into the data-driven model, and output the effective height correction, residual, and model uncertainty. The correction term generation module is used to calculate the sensitivity of the basic explicit projection function to the effective height, and multiply the effective height correction by the sensitivity to obtain the interpretable correction term; The fusion module is used to add the basic explicit projection function, the interpretable correction term, and the remaining residual to obtain the complete projection function prediction result; The adaptive output module is used to adaptively select to output the full projection function prediction result or fall back to the basic explicit projection function based on the relationship between the model uncertainty and the preset threshold.

[0015] As a further technical solution, in the soft partition weight calculation module, for geomagnetic latitude... The observed samples, and their weights in relation to the i-th sub-model. for: , It is the center of the i-th region; Let be the bandwidth parameter for the i-th region.

[0016] As a further technical solution, the adaptive output module is also used to: if the model uncertainty If the prediction is true, output the complete projection function prediction result; otherwise, output the basic explicit projection function. ;in This is a preset threshold.

[0017] According to one aspect of the present invention, an electronic device is provided, including a memory and a processor, the memory storing program instructions executable by the processor, the processor invoking the program instructions to perform the method described.

[0018] According to one aspect of the present invention, a non-transitory computer-readable storage medium is provided, the non-transitory computer-readable storage medium storing computer instructions that cause the computer to perform the method described herein.

[0019] Compared with the prior art, the beneficial effects of the present invention are as follows: 1. Improve modeling accuracy: By replacing fixed height with dynamic single-layer effective height and combining data-driven correction, the projection function mapping error under low elevation angles and complex areas is significantly reduced, thereby improving the conversion accuracy between STEC and VTEC.

[0020] 2. Enhance regional adaptability: A soft zoning mechanism based on geomagnetic latitude is adopted to establish independent and effective height functions for low, middle and high latitudes and smooth the transition through continuous weights, effectively characterizing the differences in ionospheric structure at different latitudes.

[0021] 3. Combining physical interpretability and data-driven capability: It adopts a hierarchical structure of "explicit basic model + interpretable correction term + residual residual + credibility control", transforms the black box output into physical correction term through sensitivity mapping, and introduces physical constraint penalty term to balance nonlinear fitting and physical rationality; at the same time, it enhances the reliability of the model through uncertainty perception and adaptive backoff mechanism.

[0022] 4. Enhance robustness and practicality: Introduce uncertainty awareness and adaptive backoff mechanism to automatically backoff to the basic model under complex conditions, avoid abnormal predictions, and enhance model stability and engineering practicality.

[0023] 5. Ensure model continuity: By smoothing continuous weights and periodic features, model jumps at spatial and temporal boundaries are avoided. Attached Figure Description

[0024] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the accompanying drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the accompanying drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0025] Figure 1 A schematic diagram of the overall technical route for the projection function modeling method for geomagnetic soft partitioning and height disturbance correction provided in the embodiments of the present invention; Figure 2 This is a schematic diagram of CPP calculation of MF provided in an embodiment of the present invention; Figure 3 A schematic diagram of geomagnetic soft partitioning based on a fixed center and continuous weights provided in an embodiment of the present invention; Figure 4 A schematic diagram of the core mechanism for height disturbance-driven correction provided in an embodiment of the present invention; Figure 5 This is a schematic diagram of the adaptive backoff model provided in an embodiment of the present invention. Detailed Implementation

[0026] The terms “comprising” and “having”, and any variations thereof, in the specification, claims, and accompanying drawings of this invention are intended to cover a non-exclusive inclusion, such as a process, method, system, product, or apparatus that includes a series of steps or units, not necessarily limited to those explicitly listed, but may include other steps or units not explicitly listed or inherent to such processes, methods, products, or apparatus.

[0027] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention. In addition, the technical features of the various embodiments or individual embodiments provided by the present invention can be arbitrarily combined to form new technical solutions. Such combinations are not bound by the order of steps and / or structural composition patterns, but must be based on the ability of those skilled in the art to implement them. When the combination of technical solutions is contradictory or cannot be implemented, it should be considered that such a combination of technical solutions does not exist and is not within the scope of protection claimed by the present invention.

[0028] This invention proposes an adaptive ionospheric projection function modeling method based on dynamic geomagnetic zoning and height disturbance-driven correction. This method is consistently based on the thin ionospheric assumption, treating the ionospheric as an equivalent single-layer spherical shell located at a certain effective height, and enhancing the traditional projection function accordingly.

[0029] This invention no longer uses the traditional projection function form with fixed shell height and uniform parameters, nor does it directly use a pure data-driven approach to perform black-box fitting of the projection function. Instead, it adopts a hierarchical modeling approach of "explicit basic model + interpretable correction term + residual term + credibility control".

[0030] like Figure 1The overall technical process is as follows: First, a fixed-center, continuously weighted regional model is constructed based on the geomagnetic latitude of the puncture point to obtain the weights of the low-latitude, mid-latitude, and high-latitude sub-models for the current sample. Second, a single-layer effective height field is established on the basis of each regional sub-model, and the weighted effective height of the current sample is obtained. Then, an explicit projection function is calculated based on this effective height. Furthermore, the data-driven model output is used to determine the effective height correction, residual, and model uncertainty. Then, based on the sensitivity of the basic projection function to the effective height, the effective height correction is mapped to an interpretable correction term and combined with the residual to obtain the final correction result. Finally, based on the model output uncertainty, an adaptive decision is made to adopt the complete correction result or revert to the basic model.

[0031] As a preferred embodiment, the method provided by the present invention includes the following steps:

[0032] The first step is to read the input observation sample data and extract its temporal, geometric, and spatial features.

[0033] The input data required in this embodiment includes satellite observation geometric information, time information, and spatial location information of the puncture point. For any observation sample, the following variables are extracted: observation epoch time; satellite elevation angle E; satellite azimuth angle A; and geographical latitude of the puncture point. Geographical longitude of the puncture point ; Puncture point corresponds to local time LT; Modified Julian Day MJD; Yearly Accumulation Day DOY.

[0034] The second step is to calculate the geomagnetic latitude of the puncture point and construct the periodic characteristics of the local time and annual accumulated days.

[0035] To improve the model's adaptability to structural differences in different ionospheric regions, this embodiment uses geomagnetic coordinates instead of simple geographic coordinates for partitioning and modeling. For each puncture point, its geographic coordinates are... Convert to the geomagnetic coordinate system to obtain geomagnetic latitude. The geomagnetic latitude serves as the core spatial variable for soft zoning and effective height modeling in this embodiment. Compared to geographic latitude, geomagnetic latitude better reflects the regional differences in ionospheric structure under the influence of the geomagnetic field, and is particularly useful for expressing the different characteristics of low-latitude anomaly regions, mid-latitude stable regions, and high-latitude perturbation regions.

[0036] To better characterize the diurnal and annual variations of the ionosphere, this embodiment further constructs periodic features: , By expanding the time cycle as described above, we can avoid the problem of discontinuity of time variables at the boundaries. For example, 23:00 and 0:00 are numerically different but physically adjacent.

[0037] The third step involves calculating the weights of the sub-models for the low-latitude, mid-latitude, and high-latitude regions based on geomagnetic latitude and using a soft partitioning mechanism with a fixed center and continuous weights.

[0038] This embodiment employs a geomagnetic soft partitioning mechanism based on fixed centers and continuous weights. This mechanism sets representative regional centers in low-latitude, mid-latitude, and high-latitude regions, without assigning unique classifications to samples. Instead, it calculates the continuous weights of the samples in each regional sub-model based on the distance relationship between the sample's geomagnetic latitude and each regional center, and then weights and fuses the outputs of each sub-model to obtain the final projection function result.

[0039] This method achieves a smooth transition between different latitudinal regions, effectively improving the model's continuity and adaptability to spatial differences in the ionosphere. For example... Figure 3 As shown, the soft partition comprises three regional sub-models, with corresponding regional centers c1 (low latitude), c2 (mid latitude), and c3 (high latitude). The regional centers are located near representative geomagnetic latitudes in the low, mid, and high latitudes, respectively, preferably 0°, 15°, and 45° in practice.

[0040] For any sample, let its geomagnetic latitude be... Then its weight for the i-th region sub-model is defined as: , The continuous weights of the i-th region; It is the center of the i-th region; Let be the bandwidth parameter for the i-th region.

[0041] As can be seen from the above definition, the closer a sample is to the center of a region, the greater the weight of that region; the farther away it is, the smaller the weight. The sum of the weights of the three regions is 1.

[0042] Bandwidth parameters This is used to control the influence range of each region's center on surrounding samples. Preferably, the low-latitude bandwidth controls the influence range near the equatorial anomaly; the mid-latitude bandwidth can be set appropriately larger to enhance transition smoothness; and the high-latitude bandwidth controls the influence range of the high-latitude disturbance region. Initial values ​​are determined during model building and improved through parameter optimization.

[0043] The fourth step involves solving for the discrete single-layer effective height within each sub-model region using the least squares method based on the pre-calculated samples of the true projection function. Then, the discrete effective height is parametrically fitted to establish a single-layer effective height function for each region with geomagnetic latitude, local time, and annual day as input. Finally, the base single-layer effective height of the current observation sample is obtained by weighted fusion based on the region weights.

[0044] This embodiment first describes the construction of the true projection function samples. The target value required during the training phase of this invention is the true projection function MF, defined as: , Here, STEC represents the total tilted electron content of the sample, and VTEC represents the total vertical electron content of the sample. In this embodiment, high-precision STEC is estimated based on dual-frequency GNSS observation data, preferably using PPP or precise ionospheric inversion methods to obtain the reference STEC. Compared with traditional ionospheric observation inversion methods, STEC obtained based on PPP has higher calculation accuracy and stability, thus providing high-quality input data for subsequent ionospheric modeling and parameter inversion.

[0045] For obtaining the MF (Mean Function), the coinciding pierce point (CPP) technique is used to construct the ionospheric projection function. For example... Figure 2 As shown, when the geographical latitude and longitude of the two ionospheric puncture points are IPP1 IPP2 The following requirements must be met: , Furthermore, when the satellite elevation angle corresponding to IPP1 is greater than 70° and greater than the satellite elevation angle corresponding to IPP2, the two "high-low" paired penetration points can be considered as coincident penetration points (CPP).

[0046] Assuming multiple lines of sight exist at the same ionospheric puncture point, with corresponding tilted electron total contents of STEC1 and STEC2, respectively, and given that the differences between different projection functions are negligible when the elevation angle is greater than 70°, this embodiment preferably approximates the projection function within this elevation angle range as the single-layer model (SLM) projection function. Based on this assumption, using high-elevation-angle observation data, the VTEC reference value at the puncture point is obtained by multiplying the STEC and SLM projection functions. Furthermore, combining this with STEC data from low-elevation-angle observations, the corresponding mapping function MF is inverted, achieving adaptive construction of the projection function for each puncture point.

[0047] , In the formula, MF true It is the projection function at the actual cpp point, STEC low These are STEC observations with elevation angle regions. high These are STEC observations at high elevation angles, where SLM is the thin-layer projection function, and E... highThe elevation angle is high. Next, this embodiment explains the solution and parametric modeling of the effective height of a single layer. This invention maintains the thin ionospheric layer assumption throughout; therefore, the core geometry of the projection function is still based on the single-layer shell model. However, in traditional methods, the height of the single-layer shell is usually a fixed constant, which makes it difficult to truly reflect the changing characteristics of the ionosphere in different regions and at different times.

[0048] Therefore, the single-layer effective height h in this invention eff Instead of directly presetting it to a fixed constant or assuming it to be a known function, the discrete effective height is first obtained through sample inversion, and then these discrete results are further fitted through parameterized functions.

[0049] For the i-th region sub-model, within a certain time window or statistical unit, suppose there are N samples in total, and the true projection function of the k-th sample is: The corresponding satellite elevation angle is The discrete effective height corresponding to this statistical unit can be obtained by the following least squares problem: , In the formula, is the weight of the k-th sample; R is the average radius of the Earth; h is the effective height of the single layer to be estimated. By repeating the above solution process in different regions, different local time intervals and different time periods, a series of discrete estimates of the effective height of the single layer can be obtained.

[0050] After obtaining the discrete effective height estimate, the parameterized effective height function for the i-th region is further constructed: , in: LT is the geomagnetic latitude; DOY is the local time; and S is the background status item.

[0051] After obtaining the parameterized effective height function for each region, for any sample, a weighted fusion is performed based on the region weights to obtain the global basic single-layer effective height: .

[0052] To ensure the physical rationality of the model, further constraints are selected and set according to the actual conditions of each region. To ensure the physical feasibility of the effective height of a single floor, it is often considered during implementation. The peak height of the ionosphere f2 layer in the model region is set to hmf2. This is the highest height of layer f2 in the current region.

[0053] The fifth step is to calculate the explicit projection function of the foundation based on the effective height of the foundation single layer and the satellite elevation angle.

[0054] After obtaining the effective height h of the basic single layer eff Subsequently, this invention uses a single-layer geometric mapping formula to calculate the fundamental explicit projection function: , R is the Earth's average radius; E is the satellite's elevation angle; h eff This is to obtain the effective height of the basic single layer.

[0055] This expression is consistent with the structure of the classic single-layer projection function model, thus maintaining good physical interpretability and engineering compatibility.

[0056] It should be noted that, as Figure 4 As shown, the data-driven model design of this invention is as follows.

[0057] The optimal definition of input features for a data-driven model is: , In the formula, MJD is the Modified Julian Day; LT is the local time; E is the satellite elevation angle; and A is the satellite azimuth angle. Geomagnetic latitude; LT sin LT cos DOY sin DOY cos The periodic expansion feature is represented by w1, w2, and w3, which are the soft partition weights.

[0058] The data-driven model adopts a multi-task output format, and its output is: , Δh is the effective height correction; r is the residual. This is the uncertainty estimate that the model gives for the current prediction results.

[0059] To ensure the final model conforms to physical requirements during training, a certain amount of physical constraints needs to be incorporated. The projection function should decrease as the satellite elevation angle increases; therefore, the following requirements must be met: This is used to suppress the model from producing inverse changes that do not conform to the laws of physics, and its penalty term is defined as: .

[0060] In the assumption of a single-layer thin layer system, a geometric upper bound can be constructed based on the minimum allowable effective height. Let the minimum effective height be h. min To prevent the model output from exceeding the physically feasible range, then: , The corresponding penalty items are: , The corrected effective height should meet the following requirements: This is used to ensure that the effective height is physically plausible and to avoid non-physical interpretations. The corresponding penalty is: .

[0061] Based on this, the present invention employs a joint loss function during the training phase: , in, , , These are the weighting coefficients.

[0062] The sixth step involves inputting the sample's geomagnetic latitude, satellite elevation angle, periodic characteristics, and weights into the data-driven model, outputting the effective altitude correction Δh, residual r, and model uncertainty. .

[0063] Basic explicit projection function Traditional models have been enhanced using dynamic effective height fields, but deviations may still exist between them and the true projection function. This invention argues that a significant portion of these deviations stems from single-layer effective height estimation errors; therefore, it is preferable to first learn the effective height correction value and then map it to the projection function correction value. Let the effective height correction value output by the data-driven model be... The corrected effective height of a single floor is: .

[0064] Step 7: Calculate the sensitivity of the underlying explicit projection function to the effective height, multiply the effective height correction Δh by this sensitivity, and convert it into an interpretable correction term.

[0065] The sensitivity of the fundamental explicit projection function to the effective height is defined as: , This describes the degree of response of the projection function value when the effective height of a single story changes under the current geometric conditions. The effective height correction amount... The mapping to interpretable correction terms is as follows: .

[0066] The eighth step is to combine the basic explicit projection function, the interpretable correction term, and the remaining residual r to obtain the complete projection function prediction result.

[0067] Since not all errors can be explained by the effective height correction, this invention further introduces a residual term *r* to compensate for other unmodeled errors. The final projection function is expressed as: .

[0068] This structure allows error correction to be decomposed into interpretable high-level perturbation correction and small residual compensation, resulting in higher physical interpretability and more stable modeling performance.

[0069] Step 9: Based on the model uncertainty In relation to a preset threshold, it adaptively decides whether to use the full output or fall back to the basic explicit projection function.

[0070] To improve the stability and robustness of the model under complex ionospheric conditions, this invention introduces an uncertainty-based adaptive backoff mechanism to achieve dynamic fusion of the data-driven model and the fundamental physical model.

[0071] like Figure 5 As shown, when the model output uncertainty satisfies Then the complete correction result will be used. ,in The preset uncertainty threshold can be obtained through validation set statistics or empirical settings.

[0072] When the model output uncertainty satisfies If the current model's predictions are deemed to have significant uncertainty or potential anomalies, a conservative strategy is adopted, and the model is reverted directly to the base model. This is to avoid abnormal predictions affecting the final ionospheric inversion results.

[0073] Based on the same inventive concept as the above-described method embodiments, this invention also provides a projection function modeling system for geomagnetic soft partitioning and height disturbance correction. This system includes the following modules: The data acquisition module is used to acquire observation samples of ionospheric puncture points. These observation samples include at least the satellite elevation angle, the geographic coordinates of the puncture point, and the observation epoch time. In practice, this module can read raw data from observation files on a GNSS receiver or receive real-time data streams from a network interface.

[0074] The feature calculation module converts the geographic coordinates of the puncture points of the observed samples into geomagnetic latitude and constructs periodic features of local time and annual cumulative days based on the observation epoch. Specifically, the periodic features include sine / cosine function values ​​of local time and sine / cosine function values ​​of annual cumulative days to avoid jumps at time boundaries.

[0075] The soft-region weight calculation module is used to calculate the weights of observed samples belonging to low-latitude, mid-latitude, and high-latitude sub-models based on geomagnetic latitude and employing a soft-region mechanism with a fixed center and continuous weights. For an observed sample with a given geomagnetic latitude, the weight for each sub-model is calculated using a Gaussian radial basis function. This involves exponentially calculating the difference between the sample's geomagnetic latitude and the region center by dividing the negative value of the bandwidth parameter, and then dividing by the sum of the exponents of the same type for the three regions, thus achieving continuous weighting. The low-latitude center, mid-latitude center, and high-latitude center are preset values. The bandwidth parameter for each region can be set according to the intensity of ionospheric changes: a smaller bandwidth in low-latitude regions to characterize the fine structure of equatorial anomalies, a slightly larger bandwidth in mid-latitude regions to ensure a smooth transition, and a smaller bandwidth in high-latitude regions to capture disturbances.

[0076] The basic effective height calculation module is used to establish a single-layer effective height function for each sub-model using a pre-calculated true projection function, with geomagnetic latitude, local time, and annual day as input. This function is then weighted and fused according to the aforementioned weights to obtain the basic single-layer effective height of the observation sample. Specifically, this module first inverts the discrete single-layer effective height from the true projection function sample within each sub-model region using the least squares method. Then, it uses polynomial or spline functions to parametrically fit the discrete values, obtaining the continuous effective height function for each sub-model. Finally, it sums the effective heights of each sub-model according to the aforementioned weights to obtain the basic single-layer effective height.

[0077] The basic projection function calculation module is used to calculate the basic explicit projection function based on the effective height of the basic single layer and the satellite elevation angle of the observation sample.

[0078] The data-driven prediction module is used to input the geomagnetic latitude, satellite elevation angle, periodic characteristics, and weights of the observed samples into a pre-trained data-driven model, and output the effective altitude correction, residual, and model uncertainty.

[0079] The correction term generation module calculates the sensitivity of the underlying explicit projection function to the effective height and multiplies the effective height correction by this sensitivity to obtain an interpretable correction term. The sensitivity reflects the rate of change of the projection function when a single-layer effective height changes by a unit amount under given geometric conditions; its expression is derived based on the Earth's radius, satellite elevation angle, and underlying effective height. The interpretable correction term is simply the product of the sensitivity and the effective height correction.

[0080] The fusion module is used to add the basic explicit projection function, the interpretable correction term, and the remaining residual to obtain the complete projection function prediction result.

[0081] The adaptive output module is used to adaptively select between outputting the complete projection function prediction result or reverting to the basic explicit projection function based on the relationship between the model uncertainty and a preset threshold. Specifically, if the model uncertainty is less than or equal to the preset threshold, the complete result of the fusion module is output; otherwise, the basic explicit projection function is output to avoid prediction errors of the data-driven model under abnormal conditions.

[0082] The modules described above can be implemented, in whole or in part, through software, hardware, or a combination thereof. Each module can be embedded in the processor of a computer device in hardware form or independent of it, or it can be stored in the memory of the computer device in software form, so that the processor can call and execute the operations corresponding to each module.

[0083] Preferably, the system can be deployed on a single computer device (such as a server or personal computer) or distributed across multiple devices. In a specific physical implementation, the data acquisition module is connected to a GNSS receiver or data server, while the remaining modules run on a central processing unit or graphics processing unit, utilizing the parallel computing capabilities of the graphics processing unit to accelerate the forward computation of the data-driven model.

[0084] The parts not described in detail in this system embodiment (such as the pre-calculation method of the true projection function, the least squares inversion of the discrete effective height, the specific method of parameterized fitting, etc.) can be implemented using the same technical means as in the method embodiment, and will not be repeated here.

[0085] The above system can achieve the same technical effects as the method implementation: improve the modeling accuracy of the ionospheric projection function, enhance the model's adaptability to differences in ionospheric structure in different latitudinal regions, introduce data-driven nonlinear corrections while maintaining physical interpretability, and improve the system's stability and robustness through an adaptive backoff mechanism.

[0086] Based on the same inventive concept as the above-described method embodiments, the present invention also provides an electronic device, which may be a server, a personal computer, an embedded device, or a mobile terminal, etc. The electronic device includes a memory and a processor, wherein the memory stores a computer program that can run on the processor.

[0087] Specifically, the processor may be a central processing unit (CPU), a graphics processing unit (GPU), a digital signal processor (DSP), an application-specific integrated circuit (ASIC), a field-programmable gate array (FPGA), or other programmable logic devices. The memory may be a read-only memory (ROM), random access memory (RAM), flash memory, hard disk, solid-state drive, etc., used to store computer programs and various types of data required.

[0088] When the processor executes the computer program stored in the memory, it implements the steps of the projection function modeling method for geomagnetic soft partitioning and height perturbation correction as described in any of the above method embodiments. Specifically, this includes: acquiring observation samples of ionospheric puncture points; converting the geographic coordinates of the puncture points to geomagnetic latitude and constructing periodic features; calculating weights based on the soft partitioning mechanism; establishing a single-layer effective height function and weighted fusing it to obtain the basic effective height; calculating the basic explicit projection function; inputting sample features into the data-driven model to obtain the effective height correction, residual, and uncertainty; calculating the sensitivity to obtain the interpretable correction term; fusing to obtain the complete projection function prediction result; and adaptively selecting to output the complete result or revert to the basic projection function based on the uncertainty.

[0089] This electronic device can be used to process GNSS observation data in real time or offline, and output a high-precision ionospheric projection function to serve applications such as navigation and positioning, ionospheric delay correction and space weather monitoring.

[0090] Based on the same inventive concept as the above method embodiments, the present invention also provides a computer-readable storage medium storing computer instructions (or computer programs) that, when executed by a processor, cause the processor to perform the steps of the projection function modeling method for geomagnetic soft partitioning and height disturbance correction as described in any of the above method embodiments.

[0091] The computer-readable storage medium can be any volatile or non-volatile storage device, including but not limited to: disks, optical disks, flash memory, solid-state drives, read-only memory (ROM), random access memory (RAM), erasable programmable read-only memory (EPROM), registers, etc. This storage medium can exist independently of the electronic device or be integrated within the electronic device.

[0092] As one application scenario, users can insert a CD or USB flash drive containing the computer instructions into their computer, install it, and then run the method of this invention. Alternatively, the computer instructions can be transmitted via a network (such as the Internet or a local area network) and stored in a cloud server for users to download and use.

[0093] By executing the computer instructions, the same technical effects as those in the above-described method embodiments can be achieved: improving the modeling accuracy of the ionospheric projection function, enhancing regional adaptability, balancing physical interpretability and data-driven capabilities, and improving system robustness through adaptive backoff.

[0094] In summary, the purpose of this invention is to provide an adaptive ionospheric projection function modeling method based on geomagnetic zoning and physical constraint gradient learning, to address the technical problems of existing projection function models, such as large errors in the fixed height assumption, insufficient regional adaptability, limited expressive power of explicit models, and the lack of physical constraints, stability, and generalization ability of purely data-driven models. This invention constructs a hierarchical modeling structure that combines an explicit physical model with a data-driven error correction model. Specifically, an explicit physical model provides the basic projection function, while a data-driven model learns and corrects errors in the basic model. Simultaneously, a geomagnetic latitude-based zoning modeling mechanism is introduced to enhance the model's adaptability to structural differences in different ionospheric regions. Furthermore, physical constraints and gradient constraints are introduced to improve the physical rationality, continuity, and stability of the model's output results. Finally, an accuracy adaptive mechanism is set up to allow the model to flexibly switch between different accuracy modes according to different application requirements. By adopting the above technical solutions, this invention can improve the ability of the ionospheric projection function to express complex spatiotemporal variation characteristics while maintaining the physical interpretability of the model, enhance the adaptability, stability and generalization ability of the model in different regions and under different ionospheric conditions, thereby improving the conversion accuracy between STEC and VTEC, and providing more reliable technical support for ionospheric modeling, navigation and positioning correction and related applications.

[0095] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features therein; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the technical solutions of the embodiments of the present invention.

Claims

1. A projection function modeling method for geomagnetic soft partitioning and height disturbance correction, characterized in that, include: Obtain observation samples of ionospheric puncture points, wherein the observation samples include at least the satellite elevation angle, the geographic coordinates of the puncture point, and the observation epoch time; The geographic coordinates of the puncture points of the observed samples are converted into geomagnetic latitude, and the periodic characteristics of local time and annual accumulated days are constructed based on the observation epoch time. Based on the geomagnetic latitude, a soft partitioning mechanism with a fixed center and continuous weights is used to calculate the weights of the observed samples belonging to the low-latitude, mid-latitude, and high-latitude sub-models, respectively. For each sub-model, a single-layer effective height function is established using the pre-calculated true projection function with geomagnetic latitude, local time, and annual day as input, and the basic single-layer effective height of the observation sample is obtained by weighted fusion according to the weights. Based on the effective height of the basic single layer and the satellite elevation angle of the observed samples, the basic explicit projection function is calculated; The geomagnetic latitude, satellite elevation angle, periodic characteristics, and weights of the observed samples are input into the data to drive the model, and the effective height correction, residual, and model uncertainty are output. Calculate the sensitivity of the underlying explicit projection function to the effective height, and multiply the effective height correction by the sensitivity to obtain the interpretable correction term; The basic explicit projection function, the interpretable correction term, and the remaining residual are added together to obtain the complete projection function prediction result; Based on the relationship between the model uncertainty and the preset threshold, the system adaptively selects to output the prediction result of the complete projection function or to fall back to the basic explicit projection function.

2. The projection function modeling method for geomagnetic soft partitioning and height disturbance correction according to claim 1, characterized in that, In the aforementioned soft partitioning mechanism, for geomagnetic latitude The observed samples, and their weights in relation to the i-th sub-model. for: ， It is the center of the i-th region; Let be the bandwidth parameter for the i-th region.

3. The projection function modeling method for geomagnetic soft partitioning and height disturbance correction according to claim 1, characterized in that, The prediction result MF of the complete projection function is expressed as follows: ， in As the basic explicit projection function, The effective height correction amount is r, where r is the residual. For sensitivity.

4. The projection function modeling method for geomagnetic soft partitioning and height disturbance correction according to claim 1, characterized in that, The adaptive selection includes: if the model uncertainty... If the prediction is successful, output the complete projection function prediction result; otherwise, output the basic explicit projection function. ;in This is a preset threshold.

5. The projection function modeling method for geomagnetic soft partitioning and height disturbance correction according to claim 1, characterized in that, The data-driven model is trained using a joint loss function, which includes a mean squared error term between the predicted value and the true projection function, as well as a physical constraint penalty term. The physical constraint penalty term includes a constraint that the projection function decreases monotonically with the satellite elevation angle, a geometric upper bound constraint based on the minimum effective altitude, and an effective altitude range constraint.

6. A projection function modeling system for geomagnetic soft partitioning and height disturbance correction, characterized in that, include: The data acquisition module is used to acquire observation samples of the ionospheric puncture point, and the observation samples include at least the satellite elevation angle, the geographic coordinates of the puncture point, and the observation epoch time. The feature calculation module is used to convert the geographic coordinates of the puncture points of the observed samples into geomagnetic latitude and to construct the periodic features of local time and annual day. The soft partitioning weight calculation module is used to calculate the weights of the observed samples belonging to the low-latitude, mid-latitude, and high-latitude sub-models based on the soft partitioning mechanism of geomagnetic latitude with a fixed center and continuous weights. The basic effective height calculation module is used to establish a single-layer effective height function for each sub-model using the pre-calculated true projection function, with geomagnetic latitude, local time, and annual day as input, and to obtain the basic single-layer effective height of the observation sample by weighted fusion according to the weights. The basic projection function calculation module is used to calculate the basic explicit projection function based on the effective height of the basic single layer and the satellite elevation angle of the observation sample; The data-driven prediction module is used to input the geomagnetic latitude, satellite elevation angle, periodic characteristics, and weights of the observed samples into the data-driven model, and output the effective height correction, residual, and model uncertainty. The correction term generation module is used to calculate the sensitivity of the basic explicit projection function to the effective height, and multiply the effective height correction by the sensitivity to obtain the interpretable correction term; The fusion module is used to add the basic explicit projection function, the interpretable correction term, and the remaining residual to obtain the complete projection function prediction result; The adaptive output module is used to adaptively select to output the full projection function prediction result or fall back to the basic explicit projection function based on the relationship between the model uncertainty and the preset threshold.

7. The projection function modeling system for geomagnetic soft partitioning and height disturbance correction according to claim 6, characterized in that, In the soft partition weight calculation module, for geomagnetic latitude The observed samples, and their weights in relation to the i-th sub-model. for: ， It is the center of the i-th region; Let be the bandwidth parameter for the i-th region.

8. The projection function modeling system for geomagnetic soft partitioning and height disturbance correction according to claim 6, characterized in that, The adaptive output module is also used to: if the model uncertainty If the prediction is true, output the complete projection function prediction result; otherwise, output the basic explicit projection function. ;in This is a preset threshold.

9. An electronic device, characterized in that, The method includes a memory and a processor, the memory storing program instructions that are executed by the processor, the processor invoking the program instructions to perform the method according to any one of claims 1 to 5.

10. A non-transitory computer-readable storage medium, characterized in that, The non-transitory computer-readable storage medium stores computer instructions that cause the computer to perform the method described in any one of claims 1 to 5.

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