A near real-time ionospheric modeling method based on multi-source observation data fusion

Abstract

The application provides a near real-time ionospheric modeling method based on multi-source observation data fusion, comprising: under a unified time alignment and time delay coordination framework, extracting equivalent ionospheric observation data corresponding to different data source observation data; constructing a time window for a target modeling time, comprehensively weighting ionospheric observation data in the window, and based on the ionospheric observation data and the comprehensive weight, jointly estimating ionospheric spherical harmonic coefficients and bias parameters to construct an ionospheric background model, while retaining the corresponding bias parameter estimation results and observation comprehensive weight; based on the model error evaluation results, performing adaptive updating and reconstruction on the ionospheric background model; using the ionospheric background model to initialize a near real-time state estimation model, and recursively updating based on the Kalman filtering method at each update epoch to obtain a near real-time ionospheric modeling result.

Description

Technical Field

[0001] This invention belongs to the field of ionospheric modeling, specifically relating to a near-real-time ionospheric modeling method based on multi-source observation data fusion. Background Technology

[0002] Retrieving the total electron content of the ionosphere based on GNSS observations is one of the main methods for ionospheric detection, offering high measurement accuracy. However, global ionospheric observation data still exhibits significant spatial unevenness, with densely distributed observation stations in land areas, while data is significantly insufficient in ocean areas and the Southern Hemisphere. Furthermore, existing global ionospheric models typically employ low spatial resolution, making it difficult to effectively characterize small-scale structural changes in the ionosphere, resulting in the loss of feature information in some regions.

[0003] To compensate for the limitations of ground-based GNSS observations, multi-source observation data has been increasingly incorporated into ionospheric modeling. With the development of low-Earth orbit (LEO) satellite observation technologies, technologies such as the Doppler Radio Orbit Determination System (DORIS), Altimeter (ALT), and GNSS Radio Occultation (RO) can provide independent and complementary ionospheric observation information. Among these, the DORIS system provides stable observations over both land and ocean regions, ALT technology offers good coverage in ocean areas, and RO technology boasts advantages such as globally uniform sampling and high vertical resolution. These multi-source observation methods provide crucial support for improving the performance of ionospheric models in sparsely observed regions.

[0004] Despite this, most existing multi-source data fusion methods are based on post-hoc data modeling, meaning that after all observation data is acquired, the final products of various observation data are used for unified processing and inversion. Because the final products from different data sources require processing such as orbit determination, error correction, and inversion calculations, their release generally involves a certain time delay, and inconsistencies exist between different data in terms of timeliness and update frequency. Therefore, multi-source fusion ionospheric models built based on these final products are generally post-hoc models. Although these models have high accuracy, due to their reliance on delayed data, they cannot reflect the dynamic changes of the ionosphere in a timely manner, making it difficult to meet the requirements of near-real-time applications. However, the ionosphere exhibits significant time-varying characteristics; its electron content is affected by factors such as solar activity and geomagnetic disturbances, and may change rapidly over short timescales. Applications such as navigation and positioning, precise point positioning, shortwave communication, and space weather monitoring place high demands on the timeliness of ionospheric information. Post-hoc models, due to their significant time delay, cannot meet the real-time or near-real-time requirements of these applications, thus limiting their engineering application value and exhibiting the following shortcomings:

[0005] (1) The differences in timeliness of different observation data have not been fully considered. Various types of observation data (such as GNSS, RO, ALT and DORIS) have different data acquisition delays and update frequencies. Existing methods usually adopt a unified processing strategy and lack a coordination and fusion mechanism for multi-source near real-time data;

[0006] (2) The parameters are solved by batch processing, relying on the complete observation dataset for unified inversion. It lacks the ability to dynamically respond to newly arrived observation data and it is difficult to achieve near real-time updates of the model.

[0007] (3) Existing real-time or near-real-time modeling methods usually rely on continuous filtering updates. They lack an effective error response mechanism during model operation. When the filtering error increases or the model performance degrades, they cannot make timely adaptive adjustments or reconstructions, which can easily lead to a decrease in model accuracy or even drift.

[0008] (4) There are differences in the ionospheric observation heights corresponding to different observation data, and there is a systematic deviation between them and GNSS observations. Existing methods lack a unified error coordination and correction mechanism, making it difficult to achieve consistent fusion of multi-source observation data. Summary of the Invention

[0009] To overcome the problems in existing post-event ionospheric modeling methods, such as the lack of a coordination and fusion mechanism for multi-source near-real-time data, the lack of dynamic response capability to newly arrived observation data, the difficulty in achieving near-real-time model updates, and the lack of an effective error response mechanism during model operation, this invention provides a near-real-time ionospheric modeling method based on the fusion of multi-source observation data.

[0010] This invention constructs a unified time alignment and delay coordination framework, and extracts equivalent ionospheric observations corresponding to observation data from different data sources within this framework, providing a foundation for unified error coordination and joint modeling of multi-source observation data. Under the prior constraints of the ionospheric background model, the Kalman filter method is used to sequentially update the observation data acquired within the current update epoch time delay window, achieving near real-time dynamic updating of the ionospheric model. Simultaneously, through a model error evaluation and adaptive reconstruction mechanism, ionospheric background model reconstruction is triggered when model error increases or model performance degrades, thereby providing stable, continuous, and highly accurate near real-time ionospheric information products under finite time delay conditions.

[0011] According to one aspect of the present invention, a near-real-time ionospheric modeling method based on multi-source observation data fusion is provided, comprising:

[0012] Acquire multi-source observation data, construct a unified time alignment and delay coordination framework, and extract equivalent ionospheric observations from observation data from different data sources under the time alignment and delay coordination framework, including the total electron content of the ionosphere and the total electron content of the ionosphere along the oblique path;

[0013] A target time point is selected and a time window is constructed. Ionospheric observations within the time window are comprehensively weighted. The ionospheric spherical harmonic coefficient and bias parameters are jointly estimated using the ionospheric observations and their comprehensive weights. An ionospheric background model is constructed based on the ionospheric spherical harmonic coefficient obtained by the joint estimation, and the corresponding bias parameter estimation results and the comprehensive weights of each ionospheric observation are retained. The ionospheric background model is updated using a model error evaluation and adaptive reconstruction mechanism.

[0014] The near-real-time update model is initialized using the modeling results of the ionospheric background model. Whenever the update cycle is reached, the near-real-time update model is iteratively updated based on the Kalman filter method, combined with the ionospheric observations obtained within the current update epoch time delay window, the retained bias parameter estimation results, and the comprehensive weight of each ionospheric observation.

[0015] As a further technical solution, the steps for extracting equivalent ionospheric observations from different data sources within the framework of time alignment and time delay coordination include:

[0016] The steps for extracting equivalent ionospheric observations from different data sources within the framework of time alignment and time delay coordination include:

[0017] The time labels of multi-source observation data are uniformly converted to the same time base;

[0018] A unified time delay window mechanism is established on the time base. For any target modeling time, the available multi-source observation data are collected within the preset time delay window, and the ionospheric observations equivalent to the observation data of each data source corresponding to the target modeling time are obtained.

[0019] As a further technical solution, the comprehensive weighting adopts a joint weighting method combining basic weighting with GNSS grid density correction, the steps of which include:

[0020] The basic weights of each data source are determined using the variance component estimation method.

[0021] The number of GNSS ionospheric penetration points within the latitude and longitude grid cells where ionospheric observations are located is counted, and the GNSS grid density correction factor is calculated.

[0022] An observation timeliness correction factor is constructed based on the time difference between the observation time of ionospheric observations and the target modeling time.

[0023] Based on the aforementioned basic weights, GNSS grid density correction factors, and observation timeliness correction factors, the comprehensive weights of each ionospheric observation quantity are determined.

[0024] As a further technical solution, in the ionospheric background model, the ionosphere is approximated as a single-layer shell model at a predetermined shell height, and the vertical total electron content at any ionospheric puncture point is expanded using a spherical harmonic function, the mathematical expression of which is:

[0025]

[0026] In the formula, This indicates the vertical total electron content at the ionospheric puncture point; Latitude of the ionospheric puncture point; Longitude of the ionospheric puncture point; For the association of Legendre functions; , These are the spherical harmonic coefficients; Indicates the order of the spherical harmonic expansion. Indicates the degree of spherical harmonic expansion; This is the maximum order of the spherical harmonic expansion.

[0027] As a further technical solution, the steps for jointly estimating the ionospheric harmonic coefficient and bias parameter using ionospheric observations and their integrated weights include:

[0028] For the target time of constructing the ionospheric background model, the ionospheric observations within a preset time window before the target time are selected to form a time window, and the total electron content of the ionospheric oblique path in the ionospheric observations corresponding to different data sources within the time window is converted into the total electron content of the vertical ionospheric path.

[0029] A unified observation model for multi-source ionospheric observations is constructed, which converts the total electron content observations of the ionosphere corresponding to different data sources into a consistent expression of observation parameters, and introduces the systematic deviation parameter of non-GNSS data sources relative to GNSS data sources to establish a unified observation equation.

[0030] The ionospheric harmonic coefficient, satellite differential code deviation and station differential code deviation of the GNSS data source, and the inter-system deviation of each non-GNSS data source relative to the GNSS data source are used as the parameter vector to be estimated. A joint method equation is constructed by combining the observation model of total ionospheric electron content corresponding to all data sources and the comprehensive weight, and the parameter vector to be estimated is solved.

[0031] As a further technical solution, the near real-time update model is initialized using the modeling results of the ionospheric background model, including: initializing the spherical harmonic coefficient state of the near real-time update model with the ionospheric harmonic coefficients of the ionospheric background model, and initializing the state covariance matrix of the near real-time update model with the covariance matrix corresponding to the ionospheric harmonic coefficient estimation results in the ionospheric background model.

[0032] As a further technical solution, the steps for iteratively updating the near real-time update model include:

[0033] When the update epoch of the near real-time update model is reached, based on the posterior spherical harmonic coefficient state of the previous epoch, the prior spherical harmonic coefficient state and the prior state covariance matrix of the current epoch are calculated using the state transition matrix of the random walk model.

[0034] Within the time delay window of the current epoch, the bias parameters estimated during the ionospheric background modeling stage are used to correct the ionospheric observations from each data source, and the observation equations for the current epoch are constructed.

[0035] Based on the comprehensive weights retained during the ionospheric background model construction phase, and combined with the current epoch ionospheric observation correction values, the current epoch observation weights are corrected to construct the observation noise covariance matrix; at the same time, based on the prediction error and historical statistics of the near real-time updated model, the process noise covariance matrix is ​​dynamically adjusted.

[0036] Using the state model, observation model, observation noise covariance matrix, and process noise covariance matrix of the current epoch, the posterior spherical harmonic coefficient state vector and corresponding posterior covariance matrix of the current epoch are obtained by recursively updating the model using Kalman filtering, thus completing the iterative update of the near real-time update model of the current epoch.

[0037] As a further technical solution, the ionospheric background model is updated using a model error assessment and adaptive reconstruction mechanism, including:

[0038] For any near real-time update model epoch, an innovation vector is constructed based on the prior spherical harmonic coefficient state and the observation vector of that epoch, and the error index is calculated by combining the innovation vector and the observation noise covariance matrix.

[0039] When the ionospheric background model reconstruction trigger condition is met, the ionospheric background model reconstruction is triggered, and the near real-time update model is reinitialized with the reconstruction result; wherein, the reconstruction trigger condition includes at least one of the following conditions: the error index of the near real-time update model exceeds a preset threshold for several consecutive epochs; the preset periodic reconstruction cycle of the ionospheric background model is reached; the amount of ionospheric observation data within the time delay window reaches a preset threshold.

[0040] According to another aspect of the present invention, a near-real-time ionospheric modeling system based on multi-source observation data fusion is provided for implementing the above-mentioned near-real-time ionospheric modeling method based on multi-source observation data fusion, comprising:

[0041] The multi-source data preprocessing module is used to acquire multi-source observation data, construct a unified time alignment and delay coordination framework, and extract equivalent ionospheric observations corresponding to observation data from different data sources under the time alignment and delay coordination framework.

[0042] The ionospheric background modeling module is used to comprehensively weight ionospheric observations and use the ionospheric observations and their comprehensive weights to jointly estimate the ionospheric spherical harmonic coefficient and bias parameters to construct an ionospheric background model.

[0043] The near real-time update model module is used to initialize the near real-time update model based on the modeling results of the ionospheric background model, and iteratively update the near real-time update model based on the Kalman filter method.

[0044] The model error assessment and adaptive reconstruction module is used to assess the error of the near real-time updated model and to trigger the reconstruction of the ionospheric background model when the triggering conditions for ionospheric background model reconstruction are met.

[0045] According to another aspect of the present invention, an electronic device is provided, including a memory and a processor, wherein the memory stores program instructions that are executed by the processor, and the processor invokes the program instructions to execute the above-described near-real-time ionospheric modeling method based on multi-source observation data fusion.

[0046] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0047] (1) By constructing a unified time alignment and delay coordination framework, it is possible to coordinate multi-source observation data with different delays and update frequencies, and realize the collaborative utilization of multi-source near real-time data;

[0048] (2) Through the data source availability grading mechanism, multi-source observation data can be used in a graded manner according to the data acquisition latency, current availability and observation completeness of different data sources, thereby improving the data utilization efficiency and model continuity in the near real-time modeling process;

[0049] (3) By constructing a unified observation model and jointly estimating the bias parameters, the consistency and fusion of multi-source observation data such as GNSS, RO, ALT and DORIS can be improved;

[0050] (4) The comprehensive weighting method, which combines basic weighting, GNSS grid density correction factor and observation timeliness correction factor, can take into account the observation accuracy, spatial distribution differences and time validity of different data sources, enhance the constraint ability of non-GNSS observation data on the model in sparse GNSS observation areas, and reduce the influence of observation data that are far from the target modeling time.

[0051] (5) By combining the ionospheric background model with adaptive Kalman filter recursive update, the process noise and observation noise parameters can be dynamically adjusted, improving the model's adaptability to rapid changes in the ionosphere and realizing continuous near real-time updates of the ionospheric model.

[0052] (6) Through model error evaluation and adaptive reconstruction mechanism, the risk of model drift or accuracy degradation during continuous filtering can be reduced, and the stability and reliability of near real-time ionospheric model can be improved. Attached Figure Description

[0053] To more clearly illustrate the technical solutions in the embodiments of the present invention, the accompanying drawings used in the description of the embodiments are briefly described below. Obviously, the drawings described below are only some embodiments of the present invention, and those skilled in the art can obtain other drawings based on these drawings without creative effort.

[0054] Figure 1 A flowchart illustrating a near-real-time ionospheric modeling method based on multi-source observation data fusion provided in an embodiment of the present invention;

[0055] Figure 2 This is a schematic diagram of the structure of a near-real-time ionospheric modeling system based on multi-source observation data fusion, provided in an embodiment of the present invention.

[0056] Figure 3 This is a schematic diagram of the structure of an electronic device provided in an embodiment of the present invention. Detailed Implementation

[0057] It should be noted that:

[0058] The terms "comprising" and "having," and any variations thereof, used in the specification, claims, and drawings of this invention are intended to cover non-exclusive inclusion. For example, a process, method, system, product, or apparatus that comprises a series of steps or units is not limited to the steps or units already expressly listed, but may also include other steps or units not expressly listed or inherent to these processes, methods, systems, products, or apparatuses.

[0059] The block diagrams shown in the accompanying drawings represent functional entities only and do not necessarily correspond to physically independent entities. These functional entities can be implemented in software or in one or more hardware modules, integrated circuits, processor devices, or microcontroller devices. The flowcharts shown in the accompanying drawings are for illustrative purposes only and do not imply that all steps must be included, nor that they must be executed in the order shown. Depending on the actual application requirements, some steps can be decomposed, combined, or their execution order adjusted.

[0060] 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 a part of the embodiments of the present invention, and not all of them. Other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative effort are all within the protection scope of the present invention. Furthermore, the technical features of the various embodiments of the present invention can be combined to form new technical solutions; however, such combinations should be based on the ability of those skilled in the art to implement them. When there are contradictions between technical solutions or when they cannot be implemented, such combinations should not be considered as the technical solutions claimed by the present invention.

[0061] like Figure 1 As shown in the figure, an embodiment of the present invention provides a near-real-time ionospheric modeling method based on multi-source observation data fusion, comprising the following steps:

[0062] Step 1: Acquire multi-source observation data, construct a unified time alignment and delay coordination framework, and extract equivalent ionospheric observations from observation data from different data sources under the time alignment and delay coordination framework, including the total electron content of the ionosphere and the total electron content of the ionosphere along the oblique path.

[0063] Step 2: Select the target time and construct a time window. Perform comprehensive weighting on the ionospheric observations within the time window. Use the ionospheric observations and their comprehensive weights to jointly estimate the ionospheric harmonic coefficient and bias parameters. Construct an ionospheric background model based on the ionospheric harmonic coefficient obtained from the joint estimation, and retain the corresponding bias parameter estimation results and the comprehensive weights of each ionospheric observation.

[0064] Step 3: Initialize the near real-time update model using the ionospheric background model modeling results. Whenever the update cycle is reached, the near real-time update model is iteratively updated based on the Kalman filter method, combined with the ionospheric observations obtained within the current update epoch time delay window, the retained bias parameter estimation results, and the comprehensive weight of each ionospheric observation.

[0065] In step 1, multi-source observation data for ionospheric modeling is acquired. This multi-source observation data includes one or more of the following: Global Navigation Satellite System (GNSS) observation data, Radio Occultation (RO) observation data, Satellite Altimetry (ALT) observation data, and Doppler Orbitography and Radiopositioning Integrated by Satellite (DORIS) observation data.

[0066] Optionally, the multi-source observation data can be acquired through ground-based observation networks, low-Earth orbit satellite observation platforms, satellite altimetry missions, or related data service platforms. The GNSS observation data may include multi-system GNSS observation data such as GPS, BDS, GLONASS, and Galileo.

[0067] Different data sources differ in observation methods, temporal resolution, spatial distribution, acquisition latency, and data quality. Step 1 involves uniform preprocessing of various observation data to extract equivalent ionospheric observations suitable for ionospheric modeling, and establishing a unified time alignment and latency coordination mechanism to ensure the fusion and consistency of multi-source data within the same modeling framework.

[0068] As a preferred implementation, within a unified time alignment and delay coordination framework, multi-source observation data is divided into real-time updated data, delayed supplementary data, and background reconstruction data based on the data acquisition delay, current availability, and observation completeness of each data source. Real-time updated data is used for near-real-time filtering updates at the current update epoch; delayed supplementary data is used for supplementary constraints within a unified time delay window; and background reconstruction data is used for ionospheric background model construction or reconstruction. This data source availability tiering mechanism improves the utilization efficiency of multi-source observation data and the continuity of near-real-time updated models even when different data sources arrive at inconsistent times.

[0069] Firstly, for Global Navigation Satellite System (GNSS) observation data, preprocessing mainly includes: reading and parsing the raw GNSS observation data to extract pseudorange and carrier phase observations; performing quality control on the GNSS observation data, including outlier removal, observation continuity checks, and removal of low-quality observations; performing cycle slip detection and repair to eliminate discontinuities in carrier phase observations; setting elevation angle cutoff thresholds to filter low elevation angle observations to reduce the impact of multipath effects and low-quality observations; and extracting total electron content observations along the ionospheric oblique path based on dual-frequency observation combinations.

[0070] Secondly, for radio occultation (RO) observation data, preprocessing mainly includes: reading RO observation data and extracting electron density profiles and related parameters; screening the validity of electron density profile data, removing abnormal, incomplete, or low-quality profiles; sorting the electron density profile data by altitude and standardizing the altitude and electron density units; performing altitude integration or equivalent transformation based on the electron density profile to obtain the total electron content observation of the ionosphere; and standardizing the time label and spatial coordinate representation of RO observation data.

[0071] Third, for satellite radar altimetry (ALT) observation data, preprocessing mainly includes: reading ALT observation data and corresponding orbital information; extracting dual-frequency observation data; obtaining corrections related to ionospheric delay based on dual-frequency observation information, and converting the ionospheric delay-related corrections into total ionospheric electron content observations; performing coordinate transformation and longitude range unification processing on the observation data; screening marine area observation data and removing land area observations and anomalous observations; and performing outlier detection and necessary data smoothing processing.

[0072] Fourth, for Doppler Radio Orbit Determination and Positioning System (DORIS) observation data, preprocessing mainly includes: reading the original DORIS observation data and corresponding station, satellite orbit, and other auxiliary information; extracting dual-frequency pseudorange observations and dual-frequency carrier phase observations, and performing data quality checks to remove abnormal and low-quality observations; dividing the observation data into arc segments according to continuity and identifying each continuous observation arc segment; constructing a phase-type ionospheric oblique path total electron content observation based on dual-frequency phase observations; correcting the deviations of integer ambiguity and arc segment constants in carrier phase observations for each continuous observation arc segment; and unifying the observation time, spatial coordinates, and observation expression format.

[0073] Through the above preprocessing, GNSS and DORIS observation data can be further converted into total electron content observations of the ionosphere along the oblique path or other equivalent ionosphere observations in subsequent steps, and RO and ALT observation data can be further converted into total electron content observations of the ionosphere in subsequent steps, thus providing a unified data foundation for the subsequent construction and near real-time updating of multi-source ionospheric background models.

[0074] Furthermore, to eliminate the differences in temporal resolution, release time, and acquisition latency among different observation data, and to achieve collaborative fusion of multi-source observation data, step 1, which involves constructing a unified time alignment and latency coordination framework, includes the following steps:

[0075] Step 1-1-1: Convert the time labels of multi-source observation data to the same time base;

[0076] Step 1-1-2: Establish a unified time delay window mechanism on the time base. For any target modeling time, collect the available multi-source observation data within the preset time delay window, and obtain ionospheric observations equivalent to the observation data of each data source corresponding to the target modeling time.

[0077] Optionally, in step 1-1-1, the time reference is GPS time or UTC time to ensure consistency in time description of data from different sources.

[0078] Optionally, under the unified time delay window mechanism, multi-source observation data is divided into real-time updated data, delayed supplementary data, and background reconstruction data based on the data acquisition latency, current availability, and observation completeness of each data source. The real-time updated data is used for near-real-time filtering updates at the current update epoch; the delayed supplementary data is used for supplementary constraints within the unified time delay window; and the background reconstruction data is used for ionospheric background model construction or reconstruction. Through this data source availability grading mechanism, the utilization efficiency of multi-source observation data and the continuity of near-real-time updated models can be improved even when different data sources arrive at inconsistent times.

[0079] In step 1-1-2, the extraction of equivalent ionospheric observations from each data source includes:

[0080] Firstly, for GNSS observation data, a dual-frequency observation combination model is constructed, and the phase smoothing pseudorange method is used to extract the equivalent total electron content (STEC) observation value of the ionospheric oblique path as ionospheric delay information. The equivalent total electron content of the ionospheric oblique path of the GNSS observation data can be expressed as:

[0081]

[0082] In the formula, This represents the total electron content of the ionospheric oblique path equivalent to GNSS observation data. , This is a combination of dual-frequency observation frequencies for the GNSS system; These are the pseudorange observations after smoothing. and The DCB values ​​at the receiver and satellite ends represent the differential code offsets, used to characterize the hardware code delay deviation at either the receiver or satellite end. This formula allows for the acquisition of high-precision STEC observations for subsequent ionospheric modeling.

[0083] Secondly, for RO observation data, the electron density profile is extracted from the RO observation data, and the electron density profile is integrated or equivalently transformed to obtain the equivalent total electron content (VTEC) observation value of the ionosphere, which is used as the RO equivalent ionospheric observation.

[0084] Optionally, the observed VTEC values ​​of the ionosphere are obtained by integrating the electron density profile along the height direction, mathematically expressed as:

[0085]

[0086] In the formula, This represents the equivalent VTEC (Vacuum-Temperature Coronavirus) observations in the ionosphere based on RO (Return to Earth) observation data. For height electron density at that location, and These represent the lower and upper limits of the electron density profile, respectively. Through this formula, RO observation data is converted into equivalent ionospheric observations, improving the modeling capabilities for data-sparse regions such as the ocean.

[0087] Third, for ALT observation data, the delay correction for the ionosphere A frequency dependency relationship exists between it and VTEC:

[0088]

[0089] In the formula, Indicates the operating frequency of the altimeter. This is the ionospheric delay correction.

[0090] Therefore, for frequency combinations as , The dual-frequency altimeter can calculate the equivalent total electron content of the ionosphere from ALT observation data based on the frequency correlation difference between the dual-frequency ranging observations or based on the dual-frequency ionospheric delay correction provided in the product. Mathematically, this is expressed as:

[0091]

[0092] Through the above processing, ALT observation data can be used to form ionospheric observation information in the ocean region, thereby enhancing the model's ability to constrain the ocean region.

[0093] Fourth, for DORIS observation data, a phase-type STEC of DORIS is constructed using dual-frequency phase observations, mathematically represented as:

[0094]

[0095] In the formula, Indicates DORIS phase type STEC; , This indicates the combination of dual-frequency observations for DORIS; This represents the combined quantity of dual-frequency phase observations; This indicates the deviation of the arc segment constant caused by integer ambiguity, etc.

[0096] Due to integer ambiguity in phase observations, the directly obtained STEC lacks an absolute reference and cannot be directly used for ionospheric modeling. Reference ionospheric STEC observations are calculated using the ionospheric background model at the DORIS ionospheric puncture point location, and the average deviation for each arc segment is obtained.

[0097]

[0098] In the formula, It represents the average deviation of the arc segment corresponding to the DORIS continuous observation arc segment, and is used to characterize the systematic shift within the arc segment caused by integer ambiguity, initial phase deviation and other arc segment constant terms; This indicates the number of valid observations that participated in the bias estimation within the continuous observation arc. Indicates the first arc segment within the arc segment. One valid observation epoch or observation point; Indicates the first The total electron content of the reference slant path at each DORIS ionospheric puncture point location, calculated based on the ionospheric background model, initial background model, or external reference ionospheric model. This represents the total electron content of the original phase-type oblique path obtained directly from DORIS dual-frequency phase observations without arc bias correction.

[0099] The DORIS observation data is corrected for the average bias to obtain the equivalent total ionospheric electron content. Mathematically, this is expressed as:

[0100]

[0101] In other implementations, equivalent ionospheric observations can be constructed based on DORIS dual-frequency pseudorange observations or phase-smoothed pseudorange observations, or the DORIS arc bias can be used as a parameter to be estimated during multi-source joint estimation. The processed DORIS observation data can be converted into equivalent total electron content observations of the ionosphere, which have a relatively uniform spatial distribution, helping to improve the spatial coverage of subsequent ionospheric models. Furthermore, the corrected DORIS equivalent STEC can be converted into equivalent VTEC observations using a projection function for subsequent multi-source ionospheric modeling.

[0102] In step 1-1-2, a unified time delay window mechanism is constructed to address the acquisition latency characteristics of different data sources. Specifically, for any target modeling time... In its corresponding preset time delay window The system collects available multi-source observation data and extracts the equivalent ionospheric observations corresponding to each data source within a window, based on the observation type and data delay characteristics of different data sources; after the time delay window ends... Using the multi-source observation data already acquired within the window, the ionospheric state corresponding to the modeling time of the target is estimated.

[0103] Optionally, the time delay window can be set according to the acquisition characteristics of different data sources, product timeliness requirements, and modeling accuracy requirements, so as to balance the ionospheric modeling accuracy and near real-time product timeliness.

[0104] Furthermore, under the unified time delay window mechanism, the availability of multi-source observation data is dynamically assessed based on the data acquisition delay, current availability, and observation completeness of each data source. For any target modeling time, GNSS observation data is used as the continuously available primary observation data in the near-real-time filtering update of the current update epoch. For non-GNSS observation data such as ALT, DORIS, and RO, when they are available within the corresponding preset time delay window, they are used as supplementary observation data and participate in the near-real-time update modeling of that target modeling time together with GNSS observation data. During the ionospheric background model construction or reconstruction phase, the multi-source observation data acquired within the corresponding time period, including GNSS, ALT, DORIS, and RO, are uniformly incorporated into the joint modeling. Through this dynamic data source availability assessment mechanism, the utilization efficiency of multi-source observation data and the continuity of the near-real-time update model can be improved even when the arrival times of different data sources are inconsistent.

[0105] Specifically, in step 1-1-2, under a unified time alignment and delay coordination framework:

[0106] (1) GNSS observation data, as high-frequency continuous observation data, participates in the near real-time update of the current update epoch after acquisition, and is used as basic observation data in the subsequent construction or reconstruction of the ionospheric background model;

[0107] (2) ALT and DORIS observation data are collected as delayed supplementary observation data within a unified time delay window and allocated to the corresponding epoch according to the target time resolution. When they are available within the corresponding time delay window, they participate in the near real-time update modeling of the corresponding target epoch together with GNSS observation data, and are included in the joint modeling as part of the multi-source observation data in the ionospheric background model construction or reconstruction stage.

[0108] (3) RO observation data, as high-precision delayed observation data, is gradually introduced in the near real-time stage according to its arrival status and time delay window; when it is available within the corresponding time delay window, it is used to enhance the observation constraints of the corresponding target epoch, and in the ionospheric background model construction or reconstruction stage, it is used to improve the ionospheric modeling accuracy of the global and sparsely observed regions.

[0109] Through the aforementioned time alignment and delay coordination framework, multi-source observation data can be collaboratively utilized under a unified time reference and a unified time delay window. This enables observation data with different acquisition delays, different time resolutions, and different spatial coverage characteristics to participate in near real-time updates and ionospheric background model construction based on their availability, thereby providing a consistent data foundation for subsequent model updates and reconstruction.

[0110] After completing the preprocessing, time alignment, and delay coordination of multi-source observation data in step 1, step 2 utilizes the equivalent ionospheric observations extracted from the multi-source observation data (GNSS, RO, DORIS, and ALT) acquired within the corresponding time period to construct an ionospheric background model. This ionospheric background model serves as a priori field for subsequent near-real-time dynamic updates, providing a continuous, stable, and consistent description of the ionospheric state globally.

[0111] Because different observation systems differ in terms of observation accuracy, observation principles, data scale, spatial distribution, and acquisition timeliness, if a unified weighting method is used in the global ionospheric modeling process, GNSS data with a larger number of observations will receive a larger overall weight. This would make it difficult to fully reflect the constraining effect of multi-source data such as RO, ALT, and DORIS in ocean areas, the Southern Hemisphere, and other sparsely observed regions. To take into account the accuracy characteristics, spatial coverage features, and observation timeliness of different observation systems, step 2 adopts a comprehensive weighting method that combines basic weighting, GNSS grid density correction, and observation timeliness correction to calculate the comprehensive weight of ionospheric observations from each data source.

[0112] Specifically, the steps of the comprehensive weighting include:

[0113] Step 2-1-1: Determine the basic weights of each data source using the variance component estimation method;

[0114] Step 2-1-2: Count the number of GNSS ionospheric penetration points within the latitude and longitude grid cells where the ionospheric observations are located, and calculate the GNSS grid density correction factor;

[0115] Step 2-1-3: Construct an observation timeliness correction factor based on the time difference between the observation time of the ionospheric observation and the target modeling time;

[0116] Step 2-1-4: Based on the aforementioned basic weights, GNSS grid density correction factor, and observation timeliness correction factor, determine the comprehensive weights of each ionospheric observation.

[0117] Specifically, in step 2-1-1, for the first... For data sources of this type, the underlying variance is determined using the variance component estimation method. The basic weights are determined based on the basic variance, mathematically expressed as:

[0118]

[0119] In the formula, For the first The underlying variance is estimated from the variance components of the data source.

[0120] Specifically, in step 2-1-2, to reflect the spatial distribution differences of GNSS observation data in different regions, the modeling area is divided into latitude and longitude grid cells of a preset size. As an optional implementation, the latitude and longitude grid cells can be divided into 1°×1° grids. For any given grid cell... The number of GNSS ionospheric penetration points falling into the grid cell during the current ionospheric background modeling period is counted and denoted as . The number of GNSS ionospheric puncture points was normalized to obtain:

[0121]

[0122] in, Indicates that the cell falls into the grid after normalization. Number of GNSS ionospheric puncture points; , These represent the minimum and maximum number of GNSS penetration points for all grid cells during the current ionospheric background modeling period, respectively. To prevent tiny positive numbers with a denominator of zero.

[0123] For GNSS observation data, the formulas for calculating the grid correction factor and the comprehensive weight are as follows:

[0124]

[0125]

[0126] In the formula, Representing grid cells Grid correction factor for internal GNSS observation data; To adjust the parameters. This represents the basic weights corresponding to GNSS observation data; Indicates the first The overall weight of each GNSS ionospheric observation.

[0127] This correction factor can appropriately reduce the relative weight of GNSS observation data in areas with dense GNSS penetration points, thus avoiding excessive dominance of GNSS data in the joint modeling results due to an excessive number of GNSS observations.

[0128] For RO, ALT, and DORIS observation data, the formulas for calculating the grid correction factor and the overall weight are as follows:

[0129]

[0130]

[0131] In the formula, Representing grid cells Inner Grid correction factor for non-GNSS observation data Indicates non-GNSS data source types, including RO, ALT, or DORIS; To adjust the parameters; Indicates the first Basic weights corresponding to non-GNSS observation data; Indicates the first In non-GNSS data sources The comprehensive weight of each ionospheric observation. This correction factor can enhance the constraint effect of non-GNSS observation data such as RO, ALT, and DORIS in sparse regions of GNSS ionospheric penetration points.

[0132] Specifically, in step 2-1-3, an observation timeliness correction factor is constructed to consider the time differences between different observation data and the target modeling time. For the first... One ionospheric observation, with an observation time of [time period missing]. The target modeling time is Then the observation timeliness correction factor can be expressed as:

[0133]

[0134] In the formula, Indicates the first Observation timeliness correction factor for each ionospheric observation; Indicates the first The observation time for each ionospheric observation; τ represents the target modeling time; τ represents the time decay scale parameter. Through the aforementioned observation time-related correction factor, the weight of observation data that is far from the target modeling time can be attenuated, allowing observation data that is closer to the target modeling time to obtain a relatively higher weight in near-real-time modeling.

[0135] Therefore, in step 2-1-4, for the first... A cell located in the grid The final weighted composite value of the GNSS ionospheric observations within the region can be expressed as:

[0136]

[0137] For the A cell located in the grid The first The final composite weight of non-GNSS ionospheric observations can be expressed as:

[0138]

[0139] By combining the aforementioned basic weights, GNSS grid density correction factors, and observation timeliness correction factors, the spatial distribution characteristics and temporal validity of observation data can be considered while maintaining the rationality of the statistical weights of different observation systems. In areas with dense GNSS ionospheric puncture points, the modeling results are avoided from being overly dominated by GNSS data due to an excessive number of observations. In areas with sparse GNSS ionospheric puncture points, the constraint effect of non-GNSS observation data such as RO, ALT, and DORIS is enhanced, and the response capability of near-real-time ionospheric modeling to short-term changes is improved.

[0140] This invention approximates the ionosphere as a single-layer shell model. In step 2, an ionospheric background model is established at a predetermined shell height. The ionospheric background model is expanded using a spherical harmonic function to represent the vertical total electron content at any ionospheric penetration point, mathematically expressed as:

[0141]

[0142] In the formula, This indicates the vertical total electron content at the ionospheric puncture point; Latitude of the ionospheric puncture point; Longitude of the ionospheric puncture point; For the association of Legendre functions; , These are the spherical harmonic coefficients; Indicates the order of the spherical harmonic expansion. Indicates the degree of spherical harmonic expansion; This is the maximum order of the spherical harmonic expansion.

[0143] Step 2 employs a bias parameter estimation strategy based on a sliding time window, where the bias parameters are considered constant during the current ionospheric background modeling period. Further considering the potential for stable systematic differences between different satellites within the same type of observation source, this invention models the biases of different satellites from the same type of observation source separately, and continuously uses the corresponding estimation results during the current ionospheric background modeling period and subsequent near-real-time update phases until the next bias parameter update time arrives, at which point the bias parameters are re-estimated based on a new sliding time window.

[0144] Step 2, which involves jointly estimating the ionospheric harmonic coefficient and bias parameters using ionospheric observations and their combined weights, includes:

[0145] Step 2-2-1: For the target time of ionospheric background model construction, select the ionospheric observations within the preset time window before the target time to form a time window, and convert the total electron content of the ionospheric oblique path in the ionospheric observations corresponding to different data sources within the time window into the total electron content of the vertical ionospheric path.

[0146] Step 2-2-2: Construct a unified observation model for multi-source ionospheric observations, convert the total electron content observations of the ionosphere corresponding to different data sources into a consistent expression of observation parameters, and introduce the systematic deviation parameter of non-GNSS data sources relative to GNSS data sources to establish a unified observation equation;

[0147] Step 2-2-3: Using the ionospheric harmonic coefficient, satellite differential code bias and station differential code bias of the GNSS data source, and the inter-system bias of each non-GNSS data source relative to the GNSS data source as the parameter vector to be estimated, a joint normal equation is constructed by combining the total ionospheric electron content observation models and comprehensive weights corresponding to all data sources, and the parameter vector to be estimated is solved. Specifically, in step 2-2-1, in order to integrate GNSS, RO, ALT and DORIS multi-source observation data, it is necessary to unify various observations into the same observation parameter expression form. For RO and ALT observation data, the extracted result is the total ionospheric electron content observation; for GNSS observation data and DORIS observation data, the extracted result can be the total ionospheric electron content observation along the slant path, which needs to be converted into the total ionospheric electron content observation through a projection function.

[0148] Specifically, for the s-th type of data source, the first... The unified observation model for each VTEC observation can be expressed as:

[0149] In the formula, For the s-th type of data source, the first One VTEC observation; Design matrices for the corresponding spherical harmonic basis functions; The vector of spherical harmonic coefficients to be estimated; This represents the GNSS station differential code offset parameter vector; This represents the vector of differential code offset parameters for GNSS satellites; This is the system bias parameter vector of the non-GNSS observation source relative to the GNSS reference frame; , and This is the corresponding observation mapping matrix. This represents the observed noise term.

[0150] Specifically, for GNSS data sources, the first The observation model for each VTEC observation is:

[0151]

[0152] In the formula; Indicates the GNSS data source number One VTEC observation, This represents the spherical harmonic basis function design matrix corresponding to GNSS observations; This represents the DCB deviation term for the station corresponding to the GNSS observation value; This represents the satellite DCB bias term corresponding to the GNSS observations. This represents the observed noise term.

[0153] For non-GNSS data sources such as RO, ALT, and DORIS, the observation model for each VTEC observation is written as follows:

[0154]

[0155] In the formula, Indicates the m-th type of non-GNSS data source. One VTEC observation, This represents the spherical harmonic basis function design matrix corresponding to the m-th type of non-GNSS data source; This represents the system bias parameter of the m-th type of non-GNSS data source. This represents the observed noise term.

[0156] Furthermore, in step 2-2-3, based on the comprehensive weights of the single ionospheric observations obtained in step 2-1, a VTEC observation weight matrix jointly calculated from multiple sources is constructed. The weight matrix is ​​in the form of a diagonal matrix or a block diagonal matrix, where the diagonal elements are the comprehensive weights corresponding to each observation, i.e.:

[0157]

[0158] In the formula, P represents the VTEC observation weight matrix; Indicates the first The combined weight of each ionospheric observation; M represents the total number of ionospheric observations participating in the joint estimation.

[0159] By using the above weighting method, while maintaining the rationality of the statistical weights of different observation systems, the goal of multi-source collaborative modeling can be achieved, with GNSS as the main source in areas rich in GNSS puncture points and other observation sources as the constraints in areas sparse in GNSS puncture points.

[0160] In step 2-2-3, the parameter vector to be estimated The mathematical representation of is:

[0161]

[0162] In the formula, The vector representing the spherical harmonic coefficients of the ionospheric background model; This is the DCB parameter vector of the GNSS data source station; This is the satellite DCB parameter vector from the GNSS data source; This is the system deviation parameter vector of the non-GNSS data source relative to the GNSS reference frame.

[0163] When the observation equations of each VTEC observation from each data source are summed, the overall normal equation is obtained:

[0164]

[0165]

[0166] In the formula, Representation of the normal equation matrix; Representation of the constant matrix of the normal equation, Indicates the first One data source; Indicates the number of data sources participating in the joint estimation; Indicates the first The design matrix of each data source, with each row corresponding to the observation equation of a VTEC observation; Indicates the first Weight matrix of VTEC observations from each data source; This represents the VTEC observation matrix.

[0167] Where N COMB In its actual implementation, it presents a block structure, mathematically represented as:

[0168]

[0169] In the formula, Indicates parameters With parameters The normal equation submatrices between them are SH, recDCB, and satDCB, which represent the ionospheric harmonic coefficient, GNSS station differential code bias, and GNSS satellite differential code bias, respectively; RO, ALT, and DORIS represent the inter-system bias parameters of the corresponding non-GNSS data source relative to the GNSS data source, respectively.

[0170] As a supplement, to reduce the risk of rank deficiency in the solution process of the normal equations, a zero-centroid reference constraint is added to the satellite differential code deviation parameter of each GNSS system to ensure that the normal equation matrix has stable solvability.

[0171] After solving the joint method equations, the spherical harmonic coefficient vector of the ionospheric background model, the DCB parameter vector of the GNSS station, the DCB parameter vector of the GNSS satellite, and the inter-system bias parameter vectors of non-GNSS observation sources such as RO, ALT, and DORIS relative to the GNSS data source can be obtained.

[0172] Given that deviation parameters, such as the DCB of GNSS stations, the DCB of GNSS satellites, and the deviations between non-GNSS observation source systems, typically exhibit slow changes, step 2 employs a deviation parameter estimation strategy based on a sliding time window. Specifically, before the current ionospheric background model is constructed, observation data within the previous preset time window ΔT is selected to form a sliding time window, and various deviation parameters are jointly estimated within this sliding time window. The estimated deviation parameters are used for constructing the ionospheric background model at the current target time and continue to be used as observation correction parameters in subsequent near-real-time updates.

[0173] In a specific implementation, the deviation parameters are considered constant during the current ionospheric background model modeling period. Furthermore, considering the potential for stable systematic differences between different satellites, observation platforms, or observation missions within the same type of data source, corresponding deviation parameters are established, and the estimation results of these parameters are continuously used during the current ionospheric background model modeling period and subsequent near-real-time update phases. Upon reaching the next deviation parameter update time, the deviation parameters are re-estimated based on a new sliding time window.

[0174] After obtaining the ionospheric background model, to achieve near-real-time continuous estimation of the ionospheric state, step 3 constructs a near-real-time ionospheric model update method based on Kalman filtering. This method uses the ionospheric background model as a priori field and collects available multi-source observation data within a unified time delay window. The observation data is merged and mapped according to a preset product time resolution. Then, the ionospheric state corresponding to each product epoch is recursively estimated, thereby generating continuous near-real-time ionospheric products.

[0175] In one specific implementation, the time resolution of the near-real-time ionospheric model is set to 15 minutes. The inter-system deviations of the satellite DCB, station DCB, RO, ALT, and DORIS of each GNSS system relative to the GNSS data source are all estimated using the results of the previous sliding time window, and are used as known correction parameters within the current near-real-time update cycle. Therefore, during the near-real-time update phase, the near-real-time ionospheric model only performs dynamic recursive estimation of the ionospheric harmonic coefficients.

[0176] In step 3, the near-real-time update model is initialized using the modeling results of the ionospheric background model. This includes: initializing the spherical harmonic coefficient state of the near-real-time update model with the ionospheric harmonic coefficients of the ionospheric background model, and initializing the state covariance matrix of the near-real-time update model with the covariance matrix corresponding to the ionospheric harmonic coefficient estimation results in the ionospheric background model. Specifically, let the spherical harmonic coefficient solution of the ionospheric background model obtained by solving the normal equations in step 2 be... Then the spherical harmonic coefficient state vector of the model is updated in near real-time. satisfy: .

[0177] The initial state covariance matrix is ​​denoted as This is the variance of the spherical harmonic coefficients of the ionospheric background model, which is used to initialize the near real-time update model.

[0178] Furthermore, in step 3, the iterative update of the near real-time update model includes:

[0179] Step 3-1: When the update epoch of the near real-time update model is reached, based on the posterior spherical harmonic coefficient state of the previous epoch, the prior spherical harmonic coefficient state and the prior state covariance matrix of the random walk model are calculated using the state transition matrix of the random walk model.

[0180] Step 3-2: Within the time delay window of the current epoch, use the bias parameters estimated during the ionospheric background modeling stage to correct the ionospheric observations from each data source and construct the observation equation for the current epoch.

[0181] Step 3-3: Based on the comprehensive weights retained during the ionospheric background model construction phase, and combined with the current epoch ionospheric observation correction values, the current epoch observation weights are corrected to construct the observation noise covariance matrix; at the same time, the process noise covariance matrix is ​​dynamically adjusted based on the prediction error and historical statistics of the near real-time updated model.

[0182] Steps 3-4: Using the state model, observation model, observation noise covariance matrix, and process noise covariance matrix of the current epoch, Kalman filtering is used to recursively update the posterior spherical harmonic coefficient state vector and the corresponding posterior covariance matrix of the current epoch, thus completing the iterative update of the near real-time update model for the current epoch.

[0183] Specifically, in step 3-1, let the first... The spherical harmonic coefficient state vector corresponding to each epoch is: , which indicates the first The spherical harmonic coefficients of the ionosphere at each epoch. Treating the spherical harmonic coefficients as a slowly changing process between adjacent epochs, a random walk model is used between adjacent epochs, and its state transition model is expressed as:

[0184]

[0185]

[0186] In the formula, Indicates the first The prior spherical harmonic coefficient state vector of each epoch; Indicates the first The posterior spherical harmonic coefficient state vector of each epoch; express From the first epoch to the 1st century The state transition matrix of each epoch; Indicates the first From the first epoch to the 1st century The process noise vector of each epoch has a covariance matrix denoted as Q. k When using a random walk model between adjacent epochs, It is an identity matrix.

[0187] Specifically, in step 3-2, within the time delay window of the current epoch, the bias parameters estimated during the ionospheric background modeling stage are used to correct the ionospheric observations from each data source, and the observation equation for the current epoch is constructed. For the target epoch, the ionospheric observations from each data source are collected within a subsequent preset time delay window. Let the length of the time delay window be... Then with the first The observation collection period related to the epoch of each product is: In the formula, Indicates the first The target modeling time corresponding to each product epoch; Indicates the length of the time delay window.

[0188] For GNSS observations, the receiver-satellite differential code offset parameters obtained by inversion when using background SH modeling and Make corrections and convert to VTEC mathematical representation as follows:

[0189]

[0190] In the formula, This represents the equivalent VTEC observations from the GNSS data source; For projection function, The satellite's elevation angle;

[0191] For ionospheric observations corresponding to non-GNSS data sources, after unifying them into VTEC observations, the inter-system biases of each non-GNSS data source relative to the GNSS data source, estimated during the ionospheric background modeling stage, are corrected to obtain the corrected VTEC observations. .

[0192] For the For each product epoch, construct the observation equation for the spherical harmonic state vector, mathematically represented as:

[0193]

[0194] In the formula, For the first The observation vector for each epoch consists of the corrected VTEC observations; Indicates the first The design matrix for each epoch consists of the spherical harmonic basis functions corresponding to each VTEC observation; For the first The spherical harmonic state vector of each epoch is denoted as the prior state during the filtering prediction and update processes, respectively. and posterior state ; The observation noise vector has its covariance matrix denoted as . .

[0195] Firstly, considering the limited number of observations within a near-real-time epoch, directly re-establishing a complete weighting system based on the current epoch could easily lead to unstable weighting. Therefore, step 3-3 adopts a near-real-time weighting method combining weight inheritance with limited corrections at the current epoch. Specifically, let the weighting obtained in the ionospheric background modeling stage be... The overall weight of each observation is The correction weights for the current epoch, determined based on the distribution of observation sources, observation quality, and observation timeliness, are... In the near real-time observation model, the first... Final weights of the corrected VTEC observations Mathematically, this is expressed as:

[0196]

[0197] In the formula, μ∈[0,1] is the contraction coefficient.

[0198] Therefore, the first... Weight matrix of each epoch , And further obtained the first epoch-level observation noise covariance matrix .

[0199] The above design inherits the relatively stable multi-source weighting system of the ionospheric background model stage, and enables near real-time updates to adequately reflect the differences in current observation source distribution, observation quality and data timeliness.

[0200] Secondly, to improve the filter's adaptability to dynamic changes in the ionosphere, it is necessary to balance the stability of near real-time updates with the ability to respond to rapid changes in the ionosphere. Step 3-3 uses a combination of baseline statistics and adaptive scaling factors to construct an adaptive process noise covariance matrix.

[0201] Assume the process noise satisfies: Then the mathematical expression of the noise covariance matrix of the adaptive process is: .

[0202] In the formula, The reference process noise covariance matrix; This is an adaptive adjustment factor.

[0203] Specifically, the reference process noise covariance matrix Determined based on statistical analysis of changes in the spherical harmonic coefficients of the historical background model:

[0204] Let the first The difference between the spherical harmonic coefficients of each spherical harmonic model and the adjacent background models is: In the formula, and They represent the first The spherical harmonic coefficient at the th... The first ionospheric background model and the first Estimated values ​​when modeling an ionospheric background model; Indicates the first The spherical harmonic coefficient at the th... The first ionospheric background model and the first Differences between individual ionospheric background models.

[0205] Statistics The standard deviation of the spherical harmonic coefficient difference sequence is used as the square of the first standard deviation on the diagonal of the baseline process noise covariance matrix. One element:

[0206]

[0207]

[0208] The first element on the diagonal of the reference process noise covariance matrix represents the... One element; Indicates the first The standard deviation of the spherical harmonic coefficient difference sequence is given by m, which represents the dimension of the spherical harmonic coefficient state vector in the near real-time update model.

[0209] Furthermore, to enable the process noise covariance matrix to automatically adjust with the current degree of ionospheric change, an adaptive adjustment factor is constructed based on the innovation statistic of the previous epoch, mathematically expressed as:

[0210]

[0211] In the formula, To adjust the parameters, For the first The innovation statistic of an epoch is expressed as:

[0212]

[0213] in, Indicates the first The innovation vector of an epoch is the difference between the observed value and the model's prior prediction. Indicates the first Innovation covariance matrix of epochs; Indicates the first The dimension of the epoch innovation vector is the number of effective observations participating in the filtering update of that epoch.

[0214] The innovation vector can be represented as follows: The innovation covariance matrix can be represented as, ;

[0215] In the formula, Indicates the first The observation vector of an epoch; Indicates the first The design matrix of the epoch; Indicates the first The prior spherical harmonic coefficient state vector of an epoch; Indicates the first The prior state covariance matrix of an epoch; Indicates the first The observation noise covariance matrix of an epoch.

[0216] when When ≤1, it indicates that the current near-real-time model's state predictions are basically consistent with the observations, and the process noise covariance matrix remains at the baseline level; when When the value is greater than 1, it indicates that the current ionospheric state is changing more strongly or the model prediction error is increasing. In this case, the adaptive adjustment factor should be increased accordingly. This increases the process noise covariance matrix. This is to improve the filter's ability to respond to state changes.

[0217] Specifically, in steps 3-4, after obtaining the state model, observation model, observation noise covariance matrix, and process noise covariance matrix of the current epoch, the Kalman filter method is used to recursively update the near real-time update model of each epoch.

[0218] The prediction steps are as follows: Based on the filtering results of the previous epoch, predict the state of the spherical harmonic coefficients in the current epoch. ;

[0219] The predicted state covariance matrix is: ;

[0220] In the formula, Indicates the first The prior spherical harmonic coefficient state vector of an epoch; Indicates the first The posterior spherical harmonic coefficient state vector of an epoch; Indicates the first Liyuan Zhidi The state transition matrix of an epoch; Indicates the first The prior state covariance matrix of an epoch; Indicates the first The posterior state covariance matrix of an epoch; Indicates the first Liyuan Zhidi The process noise covariance matrix of each epoch. The update steps are as follows:

[0221]

[0222] In the formula, Indicates the first Kalman filter gain at each epoch; Indicates the first The design matrix for each epoch is composed of the spherical harmonic basis functions corresponding to each VTEC observation; Indicates the first The observation noise covariance matrix of an epoch; Indicates the first The observation vector of an epoch consists of the corrected VTEC observations; Indicates the first The posterior spherical harmonic coefficient state vector of an epoch; Indicates the first The posterior state covariance matrix of an epoch; Represents the identity matrix.

[0223] Alternatively, to improve numerical stability, the posterior state covariance matrix can also be calculated in the following form:

[0224]

[0225] In obtaining the first After obtaining the posterior spherical harmonic coefficient state at an epoch, the global or regional VTEC distribution of the ionosphere at that epoch can be recovered based on the posterior spherical harmonic coefficient state, and a near-real-time ionospheric model product can be generated. After completing the update and product generation for the current epoch, the posterior spherical harmonic coefficient state vector and posterior state covariance matrix of the current epoch are passed to the next epoch, and the prediction and update process is repeated, thereby achieving continuous near-real-time updates of the ionospheric model.

[0226] In one specific implementation, the time resolution of the near-real-time ionospheric model is set to 15 minutes. The inter-system deviations of the satellite DCB, station DCB, RO, ALT, and DORIS of each GNSS system relative to the GNSS data source are all estimated using the results of the previous sliding time window, and are used as known correction parameters within the current near-real-time update cycle. Therefore, during the near-real-time update phase, only the ionospheric harmonic coefficients are dynamically recursively estimated.

[0227] To ensure the stability and accuracy of the near-real-time ionospheric model during continuous operation, this invention further constructs a model error assessment and adaptive reconstruction mechanism. This mechanism monitors the operational status of the near-real-time updated model; when the model error is small, Kalman filtering recursive updates continue; when the model error continues to increase or the model performance significantly degrades, step 2 is called again to trigger the reconstruction of the ionospheric background model, and the near-real-time updated model is reinitialized with the reconstruction results, thereby ensuring the continuity, stability, and accuracy of the near-real-time ionospheric product.

[0228] Specifically, the error evaluation steps for near real-time updated models include:

[0229] In the For each near real-time updated model epoch, an innovation vector is constructed based on the prior spherical harmonic coefficient state and the observation vector of that epoch:

[0230]

[0231] In the formula, Indicates the first The innovation vector of an epoch is used to characterize the difference between the observations at that epoch and the prior predictions of the near-real-time model;

[0232] Furthermore, by combining the innovation vector and the observation noise covariance matrix to calculate the error index, the model error index is defined as:

[0233]

[0234] In the formula, Indicates the first Near real-time update model error index for each epoch; For the first Number of ionospheric observations at each epoch. For the first The observation noise covariance matrix of an epoch.

[0235] when When the value is small, it indicates that the current model matches the observations well; when When the error continues to increase, it indicates that the model error is increasing and model degradation may occur.

[0236] When the ionospheric background model reconstruction trigger conditions are met, ionospheric background model reconstruction is triggered, and the near real-time update model is reinitialized with the reconstruction results. The ionospheric background model reconstruction trigger conditions include at least one of the following:

[0237] (1) The error index of the near real-time updated model exceeds the preset threshold for several consecutive epochs;

[0238] (2) The preset epochal period of the ionospheric background model is reconstructed periodically;

[0239] (3) The amount of newly added ionospheric observation data within the time delay window reaches the preset threshold.

[0240] When any of the above conditions are met, step 2 is called again to reconstruct the ionospheric background model using the multi-source observation data such as GNSS, RO, ALT and DORIS acquired within the corresponding time period, and the near real-time update model is reinitialized with the reconstructed ionospheric background model.

[0241] The implementation of the various embodiments of the present invention is based on programmed processing through a system with processor functionality. Therefore, in practical engineering, the technical solutions and functions of the various embodiments of the present invention can be encapsulated into multiple functional modules. Based on this, the embodiments of the present invention provide a near-real-time ionospheric modeling system based on multi-source observation data fusion, which is used to execute the near-real-time ionospheric modeling method based on multi-source observation data fusion in the above method embodiments.

[0242] See Figure 2 The system includes:

[0243] A multi-source data preprocessing module is used to acquire multi-source observation data, construct a unified time alignment and delay coordination framework, and extract equivalent ionospheric observations corresponding to observation data from different data sources under the time alignment and delay coordination framework. The equivalent ionospheric observations include the total electron content of the ionosphere and the total electron content of the ionospheric oblique path.

[0244] The ionospheric background modeling module is used to select the target modeling time and construct a time window, comprehensively weight the ionospheric observations within the time window, use the ionospheric observations and their comprehensive weights to jointly estimate the ionospheric harmonic coefficient and bias parameters, construct the ionospheric background model based on the ionospheric harmonic coefficient obtained by the joint estimation, and retain the corresponding bias parameter estimation results and the comprehensive weights of each ionospheric observation.

[0245] The near real-time update model update module is used to initialize the near real-time update model using the modeling results of the ionospheric background model. Whenever the update cycle is reached, the near real-time update model is iteratively updated based on the Kalman filter method, combined with the ionospheric observations obtained within the current update epoch time delay window, the retained bias parameter estimation results, and the comprehensive weight of each ionospheric observation.

[0246] The model error assessment and adaptive reconstruction module is used to assess the error of the near real-time updated model and, when the ionospheric background model reconstruction trigger condition is met, to trigger the reconstruction of the ionospheric background model and reinitialize the near real-time updated model with the reconstruction result.

[0247] It should be noted that the system embodiments provided by this invention, in addition to implementing the methods in the above method embodiments, can also be used to implement the methods in other method embodiments provided by this invention. The difference lies only in setting corresponding functional modules according to different method embodiments, and the principle is basically the same as that of the above system embodiments. Technical means obtained by those skilled in the art, based on the above system embodiments and referring to the specific technical solutions in other method embodiments, by combining corresponding technical features, and technical solutions constituted by these technical means, should all fall within the protection scope of this invention, provided they are feasible.

[0248] The method in this embodiment of the invention is implemented using an electronic device; therefore, it is necessary to introduce the relevant electronic device. For this purpose, embodiments of the present invention provide an electronic device, such as... Figure 3 As shown, the electronic device includes: at least one processor, a communication interface, at least one memory, and a communication bus, wherein the at least one processor, the communication interface, and the at least one memory communicate with each other via the communication bus. The at least one processor invokes logical instructions stored in the at least one memory to execute all or part of the steps of the methods provided in the foregoing method embodiments.

[0249] Furthermore, when the logical instructions in at least one of the aforementioned memories are implemented as software functional units and sold or used as independent products, they are stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention, or the part that contributes to the prior art, or a part of the technical solution, is embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (a personal computer, server, or network device) to execute all or part of the steps of the methods described in the various method embodiments of the present invention. The aforementioned storage medium includes: USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks—various media for storing program code.

[0250] The system embodiments described above are merely illustrative. The units described as separate components may or may not be physically separate, and the components shown as units may or may not be physical units, located in one place, or distributed across multiple network units. The purpose of this embodiment is achieved by selecting some or all of the modules according to actual needs. Those skilled in the art will understand and implement this without any inventive effort.

[0251] Those skilled in the art will understand that embodiments of the present invention can be provided as methods, systems, or computer program products. Therefore, the present invention can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention can take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0252] This invention is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart illustrations and / or block diagrams. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0253] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0254] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0255] 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 near real-time ionospheric modeling method based on multi-source observation data fusion, characterized in that, include: Acquire multi-source observation data, construct a unified time alignment and delay coordination framework, and extract equivalent ionospheric observations from observation data from different data sources under the time alignment and delay coordination framework, including the total electron content of the ionosphere and the total electron content of the ionosphere along the oblique path; A target time point is selected and a time window is constructed. Ionospheric observations within the time window are comprehensively weighted. The ionospheric spherical harmonic coefficient and bias parameters are jointly estimated using the ionospheric observations and their comprehensive weights. An ionospheric background model is constructed based on the ionospheric spherical harmonic coefficients obtained from the joint estimation, and the corresponding bias parameter estimation results and the comprehensive weights of each ionospheric observation are retained. The ionospheric background model is updated using a model error evaluation and adaptive reconstruction mechanism. The comprehensive weighting adopts a joint weighting method that combines basic weighting, GNSS grid density correction, and observation timeliness correction. The basic weighting uses a variance component estimation method. The near-real-time update model is initialized using the modeling results of the ionospheric background model. Whenever the update cycle is reached, the near-real-time update model is iteratively updated based on the Kalman filter method, combined with the ionospheric observations obtained within the current update epoch time delay window, the retained bias parameter estimation results, and the comprehensive weight of each ionospheric observation.

2. The near real-time ionospheric modeling method based on multi-source observation data fusion of claim 1, wherein, The steps for extracting equivalent ionospheric observations from different data sources within the framework of time alignment and time delay coordination include: The time labels of multi-source observation data are uniformly converted to the same time base; A unified time delay window mechanism is established on the time base. For any target modeling time, the available multi-source observation data are collected within the preset time delay window, and the ionospheric observations equivalent to the observation data of each data source corresponding to the target modeling time are obtained.

3. The near real-time ionospheric modeling method based on multi-source observation data fusion of claim 1, wherein, The comprehensive weighting adopts a joint weighting method that combines basic weighting, GNSS grid density correction, and observation timeliness correction. The steps include: The basic weights of each data source are determined using the variance component estimation method. The number of GNSS ionospheric penetration points within the latitude and longitude grid cells where ionospheric observations are located is counted, and the GNSS grid density correction factor is calculated. An observation timeliness correction factor is constructed based on the time difference between the observation time of ionospheric observations and the target modeling time. Based on the aforementioned basic weights, GNSS grid density correction factors, and observation timeliness correction factors, the comprehensive weights of each ionospheric observation quantity are determined.

4. The near real-time ionospheric modeling method based on multi-source observation data fusion of claim 1, wherein, The ionospheric background model is expanded using spherical harmonic functions to represent the total electron content in the vertical direction at any ionospheric puncture point, mathematically expressed as: ； In the formula, This indicates the vertical total electron content at the ionospheric puncture point; Latitude of the ionospheric puncture point; Longitude of the ionospheric puncture point; For the association of Legendre functions; , These are the spherical harmonic coefficients; Indicates the order of the spherical harmonic expansion. Indicates the degree of spherical harmonic expansion; This is the maximum order of the spherical harmonic expansion.

5. A near-real-time ionospheric modeling method based on multi-source observation data fusion as described in claim 3 or claim 4, characterized in that, The steps for jointly estimating the spherical harmonic coefficient and bias parameters of the ionosphere using ionospheric observations and their combined weights include: For the target time of constructing the ionospheric background model, the ionospheric observations within a preset time window before the target time are selected to form a time window, and the total electron content of the ionospheric oblique path in the ionospheric observations corresponding to different data sources within the time window is converted into the total electron content of the vertical ionospheric path. A unified observation model for multi-source ionospheric observations is constructed, which converts the total electron content observations of the ionosphere corresponding to different data sources into a consistent expression of observation parameters, and introduces the systematic deviation parameter of non-GNSS data sources relative to GNSS data sources to establish a unified observation equation. The ionospheric harmonic coefficient, satellite differential code deviation and station differential code deviation of the GNSS data source, and the inter-system deviation of each non-GNSS data source relative to the GNSS data source are used as the parameter vector to be estimated. A joint method equation is constructed by combining the observation model of total ionospheric electron content corresponding to all data sources and the comprehensive weight, and the parameter vector to be estimated is solved.

6. The near-real-time ionospheric modeling method based on multi-source observation data fusion as described in claim 5, characterized in that, The initialization of the near real-time update model using the modeling results of the ionospheric background model includes: initializing the spherical harmonic coefficient state of the near real-time update model with the ionospheric harmonic coefficients of the ionospheric background model, and initializing the state covariance matrix of the near real-time update model with the covariance matrix corresponding to the ionospheric harmonic coefficient estimation results in the ionospheric background model.

7. The near-real-time ionospheric modeling method based on multi-source observation data fusion as described in claim 6, characterized in that, The steps for iteratively updating the near real-time update model include: When the update epoch of the near real-time update model is reached, based on the posterior spherical harmonic coefficient state of the previous epoch, the prior spherical harmonic coefficient state and the prior state covariance matrix of the current epoch are calculated using the state transition matrix of the random walk model. Within the time delay window of the current epoch, the bias parameters estimated during the ionospheric background modeling stage are used to correct the ionospheric observations from each data source, and the observation equations for the current epoch are constructed. Based on the comprehensive weights retained during the ionospheric background model construction phase, and combined with the current epoch ionospheric observation correction values, the current epoch observation weights are corrected to construct the observation noise covariance matrix; at the same time, based on the prediction error and historical statistics of the near real-time updated model, the process noise covariance matrix is ​​dynamically adjusted. Using the state model, observation model, observation noise covariance matrix, and process noise covariance matrix of the current epoch, the posterior spherical harmonic coefficient state vector and corresponding posterior covariance matrix of the current epoch are obtained by recursively updating the model using Kalman filtering, thus completing the iterative update of the near real-time update model of the current epoch.

8. The near-real-time ionospheric modeling method based on multi-source observation data fusion as described in claim 7, characterized in that, The ionospheric background model is updated using a model error evaluation and adaptive reconstruction mechanism, including: For any near real-time update model epoch, an innovation vector is constructed based on the prior spherical harmonic coefficient state and the observation vector of that epoch, and the error index is calculated by combining the innovation vector and the observation noise covariance matrix. When the ionospheric background model reconstruction trigger condition is met, the ionospheric background model reconstruction is triggered, and the near real-time update model is reinitialized with the reconstruction result; wherein, the reconstruction trigger condition includes at least one of the following conditions: the error index of the near real-time update model exceeds a preset threshold for several consecutive epochs; the preset periodic reconstruction cycle of the ionospheric background model is reached; the amount of ionospheric observation data within the time delay window reaches a preset threshold.

9. A near-real-time ionospheric modeling system based on multi-source observation data fusion, used to implement the near-real-time ionospheric modeling method based on multi-source observation data fusion as described in any one of claims 1-8, characterized in that, include: The multi-source data preprocessing module is used to acquire multi-source observation data, construct a unified time alignment and delay coordination framework, and extract equivalent ionospheric observations from observation data from different data sources under the time alignment and delay coordination framework, including the total electron content of the ionosphere and the total electron content of the ionosphere along the oblique path. The ionospheric background modeling module is used to select the target time and construct a time window, comprehensively weight the ionospheric observations within the time window, and jointly estimate the ionospheric spherical harmonic coefficient and bias parameters using the ionospheric observations and their comprehensive weights. Based on the ionospheric spherical harmonic coefficients obtained by the joint estimation, an ionospheric background model is constructed, and the corresponding bias parameter estimation results and the comprehensive weights of each ionospheric observation are retained. The comprehensive weighting adopts a joint weighting method that combines basic weighting, GNSS grid density correction, and observation timeliness correction, wherein the basic weighting adopts a variance component estimation method. The near real-time update model update module is used to initialize the near real-time update model using the modeling results of the ionospheric background model. Whenever the update cycle is reached, the near real-time update model is iteratively updated based on the Kalman filter method, combined with the ionospheric observations obtained within the current update epoch time delay window, the retained bias parameter estimation results, and the comprehensive weight of each ionospheric observation. The model error assessment and adaptive reconstruction module is used to assess the error of the near real-time updated model and, when the ionospheric background model reconstruction trigger condition is met, to trigger the reconstruction of the ionospheric background model and reinitialize the near real-time updated model with the reconstruction result.

10. An electronic device, characterized in that, The system includes a memory and a processor, wherein the memory stores program instructions that are executed by the processor, and the processor invokes the program instructions to execute a near-real-time ionospheric modeling method based on multi-source observation data fusion as described in any one of claims 1 to 8.

Images