Method, apparatus and medium for ionospheric delay product prediction

Abstract

The application provides a method, device and medium for predicting ionospheric delay products, wherein the method comprises: obtaining M sets of ionospheric delay parameters at epochs, each set of ionospheric delay parameters comprising at least one ionospheric delay parameter; performing robustness detection processing based on the M sets of ionospheric delay parameters at epochs to obtain N sets of ionospheric delay parameters at epochs; and performing segmented modeling and robustness fusion prediction based on the N sets of ionospheric delay parameters at epochs to obtain corresponding predicted ionospheric delay products, wherein the predicted ionospheric delay products at least comprise polynomial coefficients of a background field or ionospheric delay corrections. Thus, the technical problem of low prediction accuracy in the prior art can be solved.

Description

Technical Field

[0001] This application relates to the field of satellite communication technology, specifically to a method, apparatus, and medium for predicting ionospheric delay products. Background Technology

[0002] PPP-RTK positioning technology combines the advantages of Precise Point Positioning (PPP) and Real-Time Kinematic (RTK) technologies, finding wide application in fields such as transportation, agriculture, forestry, fisheries, and disaster relief. With the rise of intelligent industries such as artificial intelligence, autonomous driving, and unmanned delivery, there are higher demands for the service accuracy, timeliness, and reliability of PPP-RTK technology. The rapid convergence of PPP-RTK positioning relies on atmospheric delay products; among these, ionospheric delay is complex in its spatiotemporal variations and is a key factor affecting PPP-RTK positioning performance. In practical applications, factors such as reference station receiver hardware failure, environmental interference, and extreme weather can cause ionospheric delay product propagation interruptions in service data centers. Furthermore, network failures and insufficient bandwidth on the user side can also prevent timely delivery of ionospheric delay products, impacting PPP-RTK positioning performance. Therefore, to achieve robust PPP-RTK positioning, high-precision short-term forecasts of ionospheric delay products are necessary.

[0003] Existing ionospheric delay prediction schemes typically use common models such as Long Short-Term Memory (LSTM), Klobuchar models, and the International Reference Ionosphere (IRI) for ionospheric delay prediction. However, in practice, it has been found that these schemes all suffer from low prediction accuracy. For example, Klobuchar and IRI models cannot accurately capture / represent the dynamic changes in ionospheric delay, resulting in low prediction accuracy; similarly, LSTM models also suffer from low prediction accuracy when trained with limited data. Summary of the Invention

[0004] In view of this, the embodiments of this application aim to provide a method, apparatus and medium for forecasting ionospheric delayed products, which can solve the technical problem of low forecast accuracy in the prior art.

[0005] In a first aspect, this application provides a method for predicting ionospheric delayed products, including: Obtain an ionospheric delay parameter set for M epochs, wherein the ionospheric delay parameter set includes at least one ionospheric delay parameter, and M is a positive integer; Based on the ionospheric delay parameter set of M epochs, robust detection processing is performed to obtain the ionospheric delay parameter set of N epochs, where N is a positive integer less than or equal to M; Based on the ionospheric delay parameter set of N epochs, segmented modeling and robust fusion forecasting are performed to obtain the corresponding forecast ionospheric delay product. The forecast ionospheric delay product includes at least the polynomial coefficients of the background field or the ionospheric delay correction.

[0006] In some embodiments, the segmented modeling and robust fusion forecasting based on the ionospheric delay parameter set over N epochs to obtain the corresponding predicted ionospheric delay product includes: The ionospheric delay parameter set of N epochs is segmented based on the time interval of N epochs to obtain L ionospheric delay parameter sequences for each segment. The ionospheric delay parameter sequence includes at least one ionospheric delay parameter for different epochs within the corresponding segment, where L is a positive integer. Differential modeling is performed based on the ionospheric delay parameter sequences of each of the L segments to obtain the corresponding ionospheric delay prediction model and the differential sequences of each of the L segments, wherein the differential sequences correspond to the ionospheric delay parameter sequences. Based on the ionospheric delay forecast model and the differential sequences of the L segments, robust fusion forecasts are performed to obtain the forecasted ionospheric delay product.

[0007] In some embodiments, the robust fusion forecast based on the ionospheric delay prediction model and the differential sequences of the L segments to obtain the predicted ionospheric delay product includes: Based on the ionospheric delay prediction model, ionospheric delay prediction is performed on the differential sequences of the L segments respectively to obtain the predicted differential ionospheric products corresponding to the L segments. Differential reconstruction is performed based on the predicted differential ionospheric products corresponding to each of the L segments to obtain the predicted ionospheric products corresponding to each of the L segments. The predicted ionospheric delay product is obtained by weighted fusion of the predicted ionospheric products corresponding to each of the L segments.

[0008] In some embodiments, the weighted fusion of the predicted ionospheric products corresponding to each of the L segments to obtain the predicted ionospheric delay product includes: Based on the time distance between the L differential sequences and the latest epoch, and the segment length corresponding to the differential sequence, the weighting weight of the predicted ionospheric product of the L segments is determined, and the latest epoch is the latest epoch among the M epochs; Based on the weighted weights of the predicted ionospheric products in the L segments, the predicted ionospheric products corresponding to each of the L segments are weighted and calculated to obtain the predicted ionospheric delay product.

[0009] In some embodiments, the step of performing differential modeling based on the ionospheric delay parameter sequences of each of the L segments to obtain the corresponding ionospheric delay prediction model and the differential sequences of each of the L segments includes: Based on the ionospheric delay parameter sequences of each of the L segments, a differential calculation of a preset order is performed to obtain the differential sequences of each of the L segments; Based on the difference sequences of the L segments, a model is constructed and solved to obtain a solution prediction model. The solution prediction model has the same model structure as the ionospheric delayed prediction model. The residual test is performed on the solved prediction model, and the solved prediction model that passes the test is determined as the ionospheric delayed prediction model.

[0010] In some embodiments, the robust detection processing based on the ionospheric delay parameter set of M epochs to obtain the ionospheric delay parameter set of N epochs includes: Time-effective detection is performed based on the ionospheric delay parameter set of M epochs to obtain the ionospheric delay parameter set of P epochs, where P is a positive integer less than or equal to M. Anomaly detection is performed based on the ionospheric delay parameter set of P epochs, and the ionospheric delay parameter set of abnormal epochs is removed to obtain the ionospheric delay parameter set of N epochs, where N is a positive integer less than or equal to P. The anomaly detection includes at least one of the following: epoch number detection, local jump detection, window dispersion detection, segmented anomaly detection, and anomaly rate detection.

[0011] In some embodiments, the anomaly detection based on the ionospheric delay parameter set of P epochs includes at least one of the following: When the anomaly detection includes the epoch count detection, the number of the P epochs is counted and determined to be greater than a preset first number; When the anomaly detection includes the local jump detection, if the absolute value of the difference between any ionospheric delay parameter of the first epoch and any ionospheric delay parameter of the previous epoch is greater than a preset first threshold, then both the first epoch and the previous epoch are marked as anomaly epochs. The first epoch is any epoch among the P epochs, and the previous epoch is an epoch among the P epochs that precedes the first epoch. When the anomaly detection includes the window dispersion detection, the median and median absolute deviation of any ionospheric delay parameter located Q epochs before and after the second epoch are determined. If any ionospheric delay parameter of the second epoch exceeds a preset first range, the second epoch is marked as an anomalous epoch. The preset first range is determined based on the median and the median absolute deviation. The second epoch is any epoch among the P epochs, and Q is a positive integer. When the anomaly detection includes the segmented anomaly detection, a preset segment number and segment number spacing of any ionospheric delay parameter within any segment of the P epochs are determined. If any ionospheric delay parameter of the third epoch within any segment of the P epochs exceeds a preset second range, the third epoch is marked as an anomalous epoch. The preset second range is determined based on the preset segment number and segment number spacing. The third epoch is any epoch within any segment of the P epochs. When the anomaly detection includes the anomaly rate detection, it is determined that the number of all anomalous epochs in the P epochs must be less than or equal to a preset second number.

[0012] In some embodiments, when the method is applied to the PPP-RTK positioning service side, the predicted ionospheric delay product includes polynomial coefficients of the background field at least one forecast epoch, grid residuals of the latest epoch, and a product identifier; or, when the method is applied to the PPP-RTK positioning user side, the predicted ionospheric delay product includes at least one ionospheric delay correction for the forecast epoch.

[0013] Secondly, this application provides a forecasting device for ionospheric delayed products, comprising: The acquisition module is used to acquire an ionospheric delay parameter set for M epochs, wherein the ionospheric delay parameter set includes at least one ionospheric delay parameter, and M is a positive integer; The processing module is used to perform robust detection processing based on the ionospheric delay parameter set of M epochs to obtain the ionospheric delay parameter set of N epochs, where N is a positive integer less than or equal to M. The processing module is also used to perform segmented modeling and robust fusion forecasting based on the ionospheric delay parameter set of N epochs to obtain the corresponding forecast ionospheric delay product, wherein the forecast ionospheric delay product includes at least polynomial coefficients of the background field or ionospheric delay corrections.

[0014] For any content not introduced or described in the embodiments of this application, please refer to the relevant descriptions in the foregoing method embodiments; they will not be repeated here.

[0015] Thirdly, this application provides a computer device, including: a processor; a memory for storing processor-executable instructions; wherein the processor is configured to execute the executable instructions to implement the steps of the above-described method for predicting ionospheric delay products.

[0016] Fourthly, this application provides a computer-readable storage medium storing computer program instructions thereon, which, when executed by a processor, implement the steps of the above-described method for predicting ionospheric delay products.

[0017] The technical solution provided in this application embodiment may include the following beneficial effects: This application obtains an ionospheric delay parameter set of M epochs, wherein the ionospheric delay parameter set includes at least one ionospheric delay parameter, and M is a positive integer; robust detection processing is performed based on the ionospheric delay parameter set of M epochs to obtain an ionospheric delay parameter set of N epochs, where N is a positive integer less than or equal to M; segmented modeling and robust fusion forecasting are performed based on the ionospheric delay parameter set of N epochs to obtain a corresponding forecast ionospheric delay product, wherein the forecast ionospheric delay product includes at least polynomial coefficients of the background field or ionospheric delay corrections. Thus, this application first performs robust detection processing to remove anomalous ionospheric delay parameters, which is beneficial to improving the accuracy or precision of subsequent segmented modeling and forecasting. By adopting a combination of segmented modeling and robust fusion for ionospheric delay product forecasting, problems such as the inability to capture the real-time variation of ionospheric delay and low forecast accuracy due to insufficient or missing data (ionospheric delay parameters) can be avoided, thereby improving the accuracy and reliability of ionospheric delay forecasting.

[0018] The above description is only an overview of the technical solution of this application. In order to better understand the technical means of this application and to implement it in accordance with the contents of the specification, and to make the above and other objects, features and advantages of this application more obvious and understandable, the following are specific embodiments of this application. Attached Figure Description

[0019] Various other advantages and benefits will become apparent to those skilled in the art upon reading the following detailed description of preferred embodiments. The accompanying drawings are for illustrative purposes only and are not intended to limit the scope of this application. Furthermore, the same reference numerals denote the same parts throughout the drawings.

[0020] Figure 1 This is a flowchart illustrating a method for predicting ionospheric delayed products provided in an embodiment of this application.

[0021] Figure 2 This is a schematic diagram of the structure of a forecasting device for ionospheric delay products provided in an embodiment of this application.

[0022] Figure 3 A schematic diagram of the structure of another ionospheric delay product prediction device provided in an embodiment of this application.

[0023] Figure 4 This is a schematic diagram of the structure of a computer device provided in an embodiment of this application. Detailed Implementation

[0024] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0025] Unless otherwise defined, the technical or scientific terms used in the embodiments of this specification shall have the ordinary meaning understood by one of ordinary skill in the art to which this specification pertains. The terms "first," "second," and similar terms used in the embodiments of this specification do not indicate any order, quantity, or importance, but are merely used to avoid confusion of constituent elements.

[0026] Unless the context otherwise requires, throughout this specification, "a plurality of" means "at least two," and "including" is interpreted as open-ended or encompassing, that is, "including, but not limited to." In the description of this specification, terms such as "one embodiment," "some embodiments," "exemplary embodiment," "example," "specific example," or "some examples" are intended to indicate that a particular feature, structure, material, or characteristic associated with that embodiment or example is included in at least one embodiment or example of this specification. The illustrative representations of the above terms do not necessarily refer to the same embodiment or example.

[0027] Exemplary embodiments of the present application will now be described in more detail with reference to the accompanying drawings. While exemplary embodiments of the present application are shown in the drawings, it should be understood that the present application may be implemented in various forms and should not be limited to the embodiments set forth herein. Rather, these embodiments are provided so that this application will be thorough and complete, and will fully convey the scope of the present application to those skilled in the art.

[0028] In the process of filing this application, the applicant also discovered that in PPP-RTK positioning technology, users can quickly fix ambiguities and achieve high-precision positioning by utilizing the precise ionospheric delay product, tropospheric delay product, and phase fractional deviation product provided by the ground-based reference network. However, in practical applications, on the PPP-RTK service side, due to uncertainties such as reference station receiver hardware failure, environmental interference, communication link interruptions caused by sudden extreme weather or construction, sudden power outages in the service data center, server crashes, and software algorithm anomalies, the propagation of real-time ionospheric delay products may be interrupted. On the PPP-RTK user side, network failures and insufficient bandwidth can also cause real-time ionospheric delay products to fail to arrive in a timely manner, affecting PPP-RTK positioning performance. To avoid these problems and achieve continuous and robust PPP-RTK positioning, it is necessary to perform high-precision short-term forecasting of ionospheric delay products.

[0029] Currently, there are three main types of existing ionospheric delay forecasting schemes. The first type is empirical models, such as the Klobuchar model and the International Reference Ionosphere (IRI) model. These empirical models are mainly used for long-term ionospheric delay forecasts and cannot accurately capture and represent the real-time dynamic changes in ionospheric delay, resulting in low forecast accuracy. The second type is time series analysis methods, such as exponential smoothing models and the Autoregressive Integrated Moving Average (ARIMA) model. Their forecast accuracy depends on the completeness and accuracy of historical ionospheric delay data, whether it contains outliers, and the appropriateness of model parameter selection; for example, incomplete or inaccurate data will lead to low forecast accuracy. The third type is neural network models, such as the Long Short-Term Memory (LSTM) model. Due to the complexity of these models, they require a large amount of training data and have a long training time. If the amount of training data is small, the forecast accuracy will also be low, and they cannot meet real-time requirements.

[0030] To address the aforementioned problems, this application proposes a method, apparatus, and medium for predicting ionospheric delayed products. Please refer to [link / reference]. Figure 1 This is a flowchart illustrating a method for predicting ionospheric delayed products provided in an embodiment of this application. Figure 1 The method shown may include the following implementation steps: S101. Obtain an ionospheric delay parameter set of M epochs, wherein the ionospheric delay parameter set includes at least one ionospheric delay parameter, and M is a positive integer.

[0031] The ionospheric delay parameter set mentioned above in this application may include one or more ionospheric delay parameters, which may include, but are not limited to, polynomial coefficients of the background field of ionospheric delay at any point in any region, ionospheric delay corrections at any point, or other custom delay parameters used for short-term forecasting. In practical applications, this application can first obtain the ionospheric delay product of the latest epoch, and then update the above-mentioned ionospheric delay parameter set based on the ionospheric delay product of the latest epoch, thereby collecting ionospheric delay parameter sets of different epochs (such as M epochs) in historical time. Wherein, M is a positive integer that the system or user pre-defined according to the actual situation. It can be an empirical value set according to user experience, or a statistical value calculated based on a series of experimental data. The above-mentioned ionospheric delay product may include a background field characterized by polynomial coefficients and grid residuals other than the background field. The ionospheric delay correction at any point in any region of the ionosphere can be expressed by the following formula (1): Formula (1) in, These represent the longitude and latitude of any point in any region, respectively. These represent the longitude and latitude of the center point of any region, respectively. This represents the ionospheric delay correction at any given point. These represent the background field and the grid residual, respectively. a0, a1, a2, and a3 represent the polynomial coefficients. w represents the grid residual of the grid points surrounding any given point. k This represents the weight value of the corresponding grid point k. This weight value can be pre-defined by the system, such as by calculating it based on the inverse distance method. This application does not impose any restrictions or elaborate on this.

[0032] Understandably, for the PPP-RTK positioning service side, since the polynomial coefficients (also known as fitting coefficients) determine the main part of the ionospheric delay, the polynomial coefficients (a0, a1, a2, a3) can be predicted, and the grid residuals also use the grid residuals from the latest epoch. For the PPP-RTK positioning user side, considering the computational pressure in data processing, the ionospheric delay correction numbers can be adjusted. For forecasting, this application may use the polynomial coefficients (a0, a1, a2, a3) and / or ionospheric delay corrections for both historical epochs and the current latest epoch. Collectively referred to as the ionospheric delay parameter set, it can be represented as {I par This application will not impose further limitations or elaborate on this matter.

[0033] S102. Based on the ionospheric delay parameter set of M epochs, robust detection processing is performed to obtain the ionospheric delay parameter set of N epochs, where N is a positive integer less than or equal to M.

[0034] This application does not limit the specific implementation of the above-described robust detection processing. For example, this application can first perform time-effective detection on the ionospheric delay parameter set of the above M epochs to obtain the ionospheric delay parameter set of P epochs, where P is a positive integer less than or equal to M. Specifically, for example, this application denotes the ionospheric delay parameter set of the latest epoch as I. par，t Let I denote the set of ionospheric delay parameters that is furthest from the latest epoch among the M epochs. par，t0 Then the time difference between their two epochs can be expressed as This application can delete / remove the set of ionospheric delay parameters from the aforementioned M epochs whose time difference with the latest epoch is greater than a first time threshold (e.g., 30 minutes), and determine all epochs whose time difference is greater than a second time threshold as the aforementioned P epochs, facilitating subsequent outlier robustness detection (hereinafter referred to as anomaly detection). The aforementioned first time threshold and second time threshold are both time thresholds pre-defined by the system according to actual conditions. Typically, the second time threshold is smaller than the first time threshold; for example, the first time threshold is 30 minutes, and the second time threshold is 15 minutes, etc.

[0035] Next, this application performs anomaly detection (i.e., outlier robustness detection) on the aforementioned P epochs of ionospheric delay parameter sets, and removes the ionospheric delay parameter sets of outlier epochs, obtaining N epochs of ionospheric delay parameter sets, where N is a positive integer less than or equal to P. The aforementioned anomaly detection can be a pre-defined outlier robustness detection system based on actual conditions, which may include, but is not limited to, any one or more combinations of the following: epoch number detection, local jump detection, window dispersion detection, segmented anomaly detection, and anomaly rate detection. Several specific implementation methods may be described below.

[0036] In one implementation, the anomaly detection includes epoch count detection (also known as minimum epoch count check). Specifically, this application can count and determine the total number of the aforementioned P epochs, and directly discard ionospheric delay parameter sets whose total number is less than a preset first number without further processing. That is, the detection needs to determine that the total number of the aforementioned P epochs must be greater than the preset first number. The preset first number is a number pre-defined by the system according to actual conditions, such as 10.

[0037] In another embodiment, the anomaly detection includes local jump detection. Specifically, assuming continuous epoch time, this application can perform local jump detection on the ionospheric delay parameter set of the P epochs. In specific implementation, this application can first calculate and determine the absolute value of the difference between any ionospheric delay parameter of the first epoch and any ionospheric delay parameter of the previous epoch. Then, it is determined whether the absolute value of the difference is greater than a preset first threshold. If it is greater, this application can mark both the first epoch and the previous epoch as anomalous epochs, and then remove the ionospheric delay parameters of these anomalous epochs. The first epoch can be any epoch among the P epochs, and the previous epoch is the epoch preceding the first epoch. Any ionospheric parameter can refer to any ionospheric delay parameter in the ionospheric delay parameter set, such as ionospheric delay correction, polynomial coefficients a0, a1, a2, and a3, etc. The aforementioned preset first threshold is a local jump threshold that the system pre-sets according to the actual situation. It can be an empirical value set based on user experience, or a statistical value calculated based on a series of experimental data, etc. This application will not make any further limitations or details on this.

[0038] In another embodiment, the above-mentioned anomaly detection includes window dispersion detection. Specifically, assuming continuous epoch time, this application can perform local sliding window dispersion detection on the ionospheric delay parameter set of the above-mentioned P epochs. The length of the local sliding window is pre-defined by the system according to the actual situation, such as 2Q+1, where Q is a positive integer defined according to the actual situation, typically 5. In specific implementation, this application can first determine Q epochs before and after the second epoch from the above-mentioned P epochs, where Q is a positive integer less than or equal to P / 2, and the second epoch is any epoch among the above-mentioned P epochs. Then, this application can calculate and determine the median and median absolute deviation of any ionospheric delay parameter of the Q epochs before and after the second epoch (2Q epochs, excluding the second epoch). The absolute deviation of the median can refer to the median of the absolute values ​​of the differences between any ionospheric delay parameter and the median over 2Q epochs. That is, first, the absolute values ​​of the differences between any ionospheric delay parameter and the median over 2Q epochs are calculated, resulting in 2Q absolute values ​​of difference. Then, the median of these 2Q absolute values ​​of difference is determined as the aforementioned absolute deviation of the median. This application does not impose further limitations or details on this. Next, this application determines whether any ionospheric delay parameter of the aforementioned second epoch exceeds a preset first range, which is determined based on the aforementioned median and the absolute deviation of the median. If it exceeds the aforementioned preset first range, this application can mark the aforementioned second epoch as an anomalous epoch, and then remove the ionospheric delay parameters of the anomalous epoch. Specifically, for example, after determining the aforementioned median and the absolute deviation of the median, this application can determine whether the absolute value of the difference between any ionospheric delay parameter and the median of the aforementioned second epoch exceeds three times the absolute deviation of the median. If it does, the aforementioned second epoch is marked as an anomalous epoch, etc. This application does not impose further limitations or details on this.

[0039] In another embodiment, the above-mentioned anomaly detection includes segmented anomaly detection. This application can segment the ionospheric delay parameter set of the P epochs based on the time interval between the P epochs to obtain at least one segment. Each segment can include the ionospheric delay parameter set of one or more epochs, which is not limited in this application. Then, the preset segment bit position and segment bit spacing of any ionospheric delay parameter in any segment are determined; specifically, for example, in the quartile segment, the lower quartile S1, upper quartile S2, and quartile spacing IQR can be calculated. The lower quartile S1, upper quartile S2, and quartile spacing IQR can be calculated by referring to conventional calculation formulas, which are not limited or detailed in this application. Next, this application can determine whether any ionospheric delay parameter of the third epoch within any segment exceeds a preset second range. The preset second range can be determined based on the preset number of segments and the interval between the segments; for example, referring to the quartile example, the preset second range can be [S1-3IQR, S2+3IQR], and the third epoch can be any epoch within any segment of the P epochs. If any ionospheric delay parameter of the third epoch exceeds the preset second range, this application can mark the third epoch as an anomalous epoch, and then remove the ionospheric delay parameters of the anomalous epoch. This results in a set of ionospheric delay parameters without outliers, which this application does not further limit or elaborate on.

[0040] In another embodiment, the anomaly detection includes anomaly rate detection. This application can statistically determine the total number of anomalous epochs for any ionospheric delay parameter in the aforementioned P epochs. Then, it determines whether the total number of anomalous epochs is greater than a preset second number. If it is greater, no further processing, such as segmented modeling and short-term forecasting, is performed. That is, the detection needs to determine that the total number of anomalous epochs for any ionospheric delay parameter in the aforementioned P epochs must be less than or equal to the preset second number. This preset second number is a number of epochs pre-defined by the system based on actual conditions; for example, it could be 40% of the total number of epochs P, etc., and this application does not impose further limitations on this.

[0041] S103. Based on the ionospheric delay parameter set of N epochs, perform segmented modeling and robust fusion forecasting to obtain the corresponding forecast ionospheric delay product. The forecast ionospheric delay product includes at least the polynomial coefficients of the background field or the ionospheric delay correction.

[0042] This application does not limit the specific implementation of the above-mentioned segmented modeling and robust fusion forecast. For example, this application can segment the ionospheric delay parameter set of the above-mentioned N epochs based on the time interval of the above-mentioned N epochs to obtain L ionospheric delay parameter sequences for each segment. The ionospheric delay parameter sequence may include at least one ionospheric delay parameter for different epochs within the corresponding segment, such as the ionospheric delay correction coefficient, polynomial coefficients a0, a1, a2, and a3 for all epochs within any segment. L is a positive integer that the system pre-defined according to the actual situation. For example, this application can traverse the ionospheric delay parameter set of all epochs (such as the above-mentioned N epochs) and divide the ionospheric delay parameter set of the above-mentioned N epochs into 4 consecutive valid ionospheric delay parameter sequences according to the time interval between consecutive epochs, etc. This application does not limit or elaborate on this.

[0043] Next, this application can perform differential modeling based on the ionospheric delay parameter sequences of the aforementioned L segments to obtain the corresponding ionospheric delay prediction model and the differential sequences of the aforementioned L segments, wherein the differential sequences correspond to the aforementioned ionospheric delay parameter sequences. In specific implementation, this application can perform differential calculations of a preset order based on the ionospheric delay parameter sequences of the aforementioned L segments to obtain the differential sequences of the aforementioned L segments, i.e., L differential sequences. Then, based on the aforementioned L differential sequences, model construction and solution are performed to obtain the solved prediction model; then, the solved prediction model is subjected to residual verification, and the solved prediction model that passes the residual verification is determined as the corresponding ionospheric delay prediction model; otherwise, the model parameters of the solved prediction model are adjusted and the solution is re-solved. Among them, the above-mentioned delayed ionospheric prediction model and the above-mentioned solution prediction model have the same model structure. This application does not limit the specific implementation of the above-mentioned delayed ionospheric prediction model / solution prediction model. For example, it can usually be an Autoregressive Integrated Moving Average (ARIMA) model. The mathematical expression of this model is shown in the following formula (2): Formula (2) Among them, Y t This represents the difference sequence after d differences. This represents the set of ionospheric delay parameters. This represents the model parameters to be solved in the ARIMA(p,d,q) model. This represents noise signal data.

[0044] In practical applications, this application can determine the preset difference order d using stepwise differencing and the Augmented Dickey-Fuller (ADF) test. Typically, the difference order d is no greater than 2, meaning d can be a positive integer less than or equal to 2. For the specific implementation process of stepwise differencing and the ADF test, please refer to the relevant introductions to traditional differencing and ADF tests; further details are not provided here. Then, the orders p and q are determined based on the truncation and tailing characteristics of the autocorrelation function (ACF) and partial autocorrelation function (PACF), as well as the Akaike Information Criterion (AIC). Typically, the orders p and q are also no greater than 2. The specific methods for determining the orders p and q are not detailed here; please refer to the relevant introductions to determining the order using the traditional Akaike Information Criterion and the truncation and tailing characteristics of functions. Further details are not provided here. Next, based on a determined order (p, d, q), this application solves the ARIMA model using algorithms such as the Hannan-Rissanen algorithm to obtain a solved prediction model (i.e., the ARIMA model). Finally, the solved prediction model is used to estimate the ionospheric delay parameters at the corresponding epoch and the actual ionospheric delay parameters at that epoch, and residuals are calculated. The calculated residual sequence is then subjected to a white noise Ljung-Box test. If the test result shows a p-value less than the significance level (e.g., 0.05), the null hypothesis that 'the residuals are white noise' is rejected, indicating that there is still autocorrelation information in the residuals that has not been extracted by the solved prediction model. In this case, the model order (p, d, q) needs to be adjusted, and the above process is repeated until the residual test passes. Accordingly, this application can use the ARIMA model that passes the residual test (i.e., the white noise test) as the final ionospheric delay prediction model.

[0045] After obtaining the aforementioned ionospheric delay forecasting model, this application can perform robust fusion forecasting based on the aforementioned ionospheric delay forecasting model and the differential sequences of the aforementioned L segments to obtain the corresponding forecasted ionospheric delay products. This application does not limit the specific implementation method of the aforementioned robust fusion forecasting. For example, this application can input the differential sequences of the aforementioned L segments (i.e., the differential sequences corresponding to the L ionospheric delay parameter sequences) into the aforementioned ionospheric delay forecasting model (such as the ARIMA model) to perform short-term ionospheric delay forecasting to obtain the forecasted differential ionospheric products corresponding to the aforementioned L segments. Then, the forecasted differential ionospheric products of the aforementioned L segments (i.e., the L forecasted differential ionospheric products) are subjected to inverse differential reduction, such as d-order inverse differential reduction, to obtain the forecasted ionospheric products (also referred to as forecast results) of the aforementioned L segments. The aforementioned inverse differential reduction is the inverse process of the aforementioned differential calculation, and the processing implementation process of traditional inverse differential reduction can be referred to. This application will not limit or elaborate on it further here. Finally, this application can perform weighted fusion of the predicted ionospheric products for each of the L segments. Specifically, this application can determine the weighting weights of the predicted ionospheric products for each of the L segments based on the time distance between the L difference sequences and the latest epoch, and the segment length corresponding to the difference sequences, i.e., determine the weighting weights of each of the L predicted ionospheric products. Then, based on the weighting weights of the predicted ionospheric products for each of the L segments, a weighted calculation is performed on the predicted ionospheric products corresponding to each of the L segments to obtain the final predicted ionospheric delay product (also known as the final forecast result). Then, short-term forecasts are made on the predicted ionospheric delay product, such as by sending the predicted ionospheric delay product. In practical applications, for the PPP-RTK positioning service side, this application can broadcast and send predicted ionospheric delay products, such as the polynomial coefficients of the background field of one or more forecast epochs in the future, the grid residuals of the latest epoch, and product identifiers, to the user. In other words, when the solution of this application is applied to the PPP-RTK positioning service side, the aforementioned ionospheric delay products can include, but are not limited to, ionospheric delay products such as polynomial coefficients of the background field at one or more forecast epochs, grid residuals of the latest epoch, and product identifiers. For the PPP-RTK positioning user side, this application can forecast ionospheric delay products such as ionospheric delay corrections for one or more forecast epochs within a future period. That is, when the solution of this application is applied to the PPP-RTK positioning user side, the aforementioned ionospheric delay products can include, but are not limited to, ionospheric delay corrections for one or more forecast epochs; this application will not impose further limitations or details in this regard.

[0046] It should be noted that the scheme in this application is applicable to the prediction of ionospheric delay parameters of a single satellite. When there are multiple satellites, the same principle of the above scheme in this application can be used to predict the ionospheric delay parameters of each satellite. This application will not impose any further limitations or details on this.

[0047] As can be seen, the proposed solution addresses the problems of traditional models that directly model ionospheric delay parameters. These models suffer from outliers introduced by factors such as extreme weather, solar activity, equipment failure, and electromagnetic interference, leading to biased model parameters and low forecast accuracy. This solution specifically introduces robust detection processing to remove outliers from the ionospheric delay parameter set in advance, thus mitigating their adverse effects on modeling and forecasting and demonstrating strong resistance to anomaly interference. Furthermore, considering that the ionospheric delay parameter set inevitably contains missing data due to network interruptions, service station initialization, and outlier removal, traditional models, when forcibly fitting multiple missing data segments, suffer from biased parameter estimation and low forecast accuracy due to the disruption of temporal correlation caused by the missing segments. This application employs an improved scheme combining segmented modeling and robust fusion, which can better fit the ionospheric delay forecast model (ARIMA model) even when the ionospheric delay parameter set is missing, thereby improving forecast accuracy. Furthermore, this application introduces a model parameter adjustment mechanism to better enhance and adapt the model to the real-time changes in ionospheric delay. For example, the activity level of ionospheric delay varies with geographical location and time (such as year, season, and day / night), and is also easily affected by extreme weather, solar activity, and geomagnetic activity. This application does not impose further limitations or details on these aspects. In specific implementation, this application obtains an ionospheric delay parameter set of M epochs, wherein the ionospheric delay parameter set includes at least one ionospheric delay parameter, and M is a positive integer. Based on the ionospheric delay parameter set of M epochs, robust detection processing is performed to obtain an ionospheric delay parameter set of N epochs, where N is a positive integer less than or equal to M. Based on the ionospheric delay parameter set of N epochs, segmented modeling and robust fusion forecasting are performed to obtain the corresponding forecast ionospheric delay product, wherein the forecast ionospheric delay product includes at least the polynomial coefficients of the background field or the ionospheric delay correction. Thus, this application first performs robust detection processing to remove anomalous ionospheric delay parameters, which is beneficial to improving the accuracy or precision of subsequent segmented modeling and forecasting. By adopting a combination of segmented modeling and robust fusion for ionospheric delay product forecasting, problems such as low forecast accuracy caused by insufficient or missing data (ionospheric delay parameters) can be avoided, thereby improving the accuracy and reliability of ionospheric delay forecasts.

[0048] Based on the above embodiments, please refer to Figure 2 This is a schematic diagram of the structure of a forecasting device for ionospheric delayed products provided in an embodiment of this application. Figure 2The apparatus 200 shown may include an acquisition module 201 and a processing module 202, wherein: The acquisition module 201 is used to acquire an ionospheric delay parameter set of M epochs, wherein the ionospheric delay parameter set includes at least one ionospheric delay parameter, and M is a positive integer; The processing module 202 is used to perform robust detection processing based on the ionospheric delay parameter set of M epochs to obtain the ionospheric delay parameter set of N epochs, where N is a positive integer less than or equal to M. The processing module 202 is also used to perform segmented modeling and robust fusion forecasting based on the ionospheric delay parameter set of N epochs to obtain the corresponding forecast ionospheric delay product, wherein the forecast ionospheric delay product includes at least polynomial coefficients of the background field or ionospheric delay corrections.

[0049] In some embodiments, the processing module 202 is specifically used for: The ionospheric delay parameter set of N epochs is segmented based on the time interval of N epochs to obtain L ionospheric delay parameter sequences for each segment. The ionospheric delay parameter sequence includes at least one ionospheric delay parameter for different epochs within the corresponding segment, where L is a positive integer. Differential modeling is performed based on the ionospheric delay parameter sequences of each of the L segments to obtain the corresponding ionospheric delay prediction model and the differential sequences of each of the L segments, wherein the differential sequences correspond to the ionospheric delay parameter sequences. Based on the ionospheric delay forecast model and the differential sequences of the L segments, robust fusion forecasts are performed to obtain the forecasted ionospheric delay product.

[0050] In some embodiments, the processing module 202 is specifically used for: Based on the ionospheric delay prediction model, ionospheric delay prediction is performed on the differential sequences of the L segments respectively to obtain the predicted differential ionospheric products corresponding to the L segments. Differential reconstruction is performed based on the predicted differential ionospheric products corresponding to each of the L segments to obtain the predicted ionospheric products corresponding to each of the L segments. The predicted ionospheric delay product is obtained by weighted fusion of the predicted ionospheric products corresponding to each of the L segments.

[0051] In some embodiments, the processing module 202 is specifically used for: Based on the time distance between the L differential sequences and the latest epoch, and the segment length corresponding to the differential sequence, the weighting weight of the predicted ionospheric product of the L segments is determined, and the latest epoch is the latest epoch among the M epochs; Based on the weighted weights of the predicted ionospheric products in the L segments, the predicted ionospheric products corresponding to each of the L segments are weighted and calculated to obtain the predicted ionospheric delay product.

[0052] In some embodiments, the processing module 202 is specifically used for: Based on the ionospheric delay parameter sequences of each of the L segments, a differential calculation of a preset order is performed to obtain the differential sequences of each of the L segments; Based on the difference sequences of the L segments, a model is constructed and solved to obtain a solution prediction model. The solution prediction model has the same model structure as the ionospheric delayed prediction model. The residual test is performed on the solved prediction model, and the solved prediction model that passes the test is determined as the ionospheric delayed prediction model.

[0053] In some embodiments, the processing module 202 is specifically used for: Time-effective detection is performed based on the ionospheric delay parameter set of M epochs to obtain the ionospheric delay parameter set of P epochs, where P is a positive integer less than or equal to M. Anomaly detection is performed based on the ionospheric delay parameter set of P epochs, and the ionospheric delay parameter set of abnormal epochs is removed to obtain the ionospheric delay parameter set of N epochs, where N is a positive integer less than or equal to P. The anomaly detection includes at least one of the following: epoch number detection, local jump detection, window dispersion detection, segmented anomaly detection, and anomaly rate detection.

[0054] In some embodiments, the processing module 202 is specifically used for at least one of the following: When the anomaly detection includes the epoch count detection, the number of the P epochs is counted and determined to be greater than a preset first number; When the anomaly detection includes the local jump detection, if the absolute value of the difference between any ionospheric delay parameter of the first epoch and any ionospheric delay parameter of the previous epoch is greater than a preset first threshold, then both the first epoch and the previous epoch are marked as anomaly epochs. The first epoch is any epoch among the P epochs, and the previous epoch is an epoch among the P epochs that precedes the first epoch. When the anomaly detection includes the window dispersion detection, the median and median absolute deviation of any ionospheric delay parameter located Q epochs before and after the second epoch are determined. If any ionospheric delay parameter of the second epoch exceeds a preset first range, the second epoch is marked as an anomalous epoch. The preset first range is determined based on the median and the median absolute deviation. The second epoch is any epoch among the P epochs, and Q is a positive integer. When the anomaly detection includes the segmented anomaly detection, a preset segment number and segment number spacing of any ionospheric delay parameter within any segment of the P epochs are determined. If any ionospheric delay parameter of the third epoch within any segment of the P epochs exceeds a preset second range, the third epoch is marked as an anomalous epoch. The preset second range is determined based on the preset segment number and segment number spacing. The third epoch is any epoch within any segment of the P epochs. When the anomaly detection includes the anomaly rate detection, it is determined that the number of all anomalous epochs in the P epochs must be less than or equal to a preset second number.

[0055] In some embodiments, when the device is applied to the PPP-RTK positioning service side, the predicted ionospheric delay product includes polynomial coefficients of the background field for at least one forecast epoch, grid residuals for the latest epoch, and a product identifier; or, when the device is applied to the PPP-RTK positioning user side, the predicted ionospheric delay product includes at least one ionospheric delay correction for the forecast epoch.

[0056] Please see Figure 3 This is a schematic diagram of the structure of a forecasting device for another ionospheric delayed product provided in an embodiment of this application. For example... Figure 3 The device shown can be a mobile phone, computer, digital broadcasting terminal, messaging device, game console, tablet device, medical device, fitness equipment, personal digital assistant, or other computer device.

[0057] Reference Figure 3 The device 300 may include one or more of the following components: processing component 302, memory 304, power supply component 306, multimedia component 308, audio component 310, input / output interface 312, sensor component 314, and communication component 316.

[0058] Processing component 302 typically controls the overall operation of device 300, such as operations associated with display, telephone calls, data communication, camera operation, and recording. Processing component 302 may include one or more processors 320 to execute instructions to complete all or part of the steps of the aforementioned method for predicting ionospheric delay products. Furthermore, processing component 302 may include one or more modules to facilitate interaction between processing component 302 and other components. For example, processing component 302 may include a multimedia module to facilitate interaction between multimedia component 308 and processing component 302.

[0059] Memory 304 is configured to store various types of data to support the operation of device 300. Examples of such data include instructions for any application or method operating on device 300, contact data, phonebook data, messages, pictures, videos, etc. Memory 304 can be implemented by any type of volatile or non-volatile storage device or a combination thereof, such as static random access memory (SRAM), electrically erasable programmable read-only memory (EEPROM), erasable programmable read-only memory (EPROM), programmable read-only memory (PROM), read-only memory (ROM), magnetic storage, flash memory, magnetic disk, or optical disk.

[0060] Power supply component 306 provides power to various components of device 300. Power supply component 306 may include a power management system, one or more power supplies, and other components associated with generating, managing, and distributing power to device 300.

[0061] Multimedia component 308 includes a screen that provides an output interface between the device 300 and the user. In some embodiments, the screen may include a liquid crystal display (LCD) and a touch panel (TP). If the screen includes a touch panel, the screen may be implemented as a touchscreen to receive input signals from the user. The touch panel includes one or more touch sensors to sense touches, swipes, and gestures on the touch panel. The touch sensors may sense not only the boundaries of the touch or swipe action but also the duration and pressure associated with the touch or swipe operation. In some embodiments, multimedia component 308 includes a front-facing camera and / or a rear-facing camera. When the device 300 is in an operating mode, such as a shooting mode or a video mode, the front-facing camera and / or the rear-facing camera may receive external multimedia data. Each front-facing camera and rear-facing camera may be a fixed optical lens system or have focal length and optical zoom capabilities.

[0062] Audio component 310 is configured to output and / or input audio signals. For example, audio component 310 includes a microphone (MIC) configured to receive external audio signals when device 300 is in an operating mode, such as call mode, recording mode, and voice recognition mode. The received audio signals may be further stored in memory 304 or transmitted via communication component 316. In some embodiments, audio component 310 also includes a speaker for outputting audio signals.

[0063] Input / output interface 312 provides an interface between processing component 302 and peripheral interface modules, which may be keyboards, click wheels, buttons, etc. These buttons may include, but are not limited to, home buttons, volume buttons, start buttons, and lock buttons.

[0064] Sensor assembly 314 includes one or more sensors for providing status assessments of various aspects of device 300. For example, sensor assembly 314 may detect the on / off state of device 300, the relative positioning of components such as the display and keypad of device 300, changes in the position of device 300 or a component of device 300, the presence or absence of user contact with device 300, the orientation or acceleration / deceleration of device 300, and temperature changes of device 300. Sensor assembly 314 may include a proximity sensor configured to detect the presence of nearby objects without any physical contact. Sensor assembly 314 may also include a light sensor, such as a CMOS or CCD image sensor, for use in imaging applications. In some embodiments, sensor assembly 314 may also include an accelerometer, a gyroscope, a magnetometer, a pressure sensor, or a temperature sensor.

[0065] Communication component 316 is configured to facilitate wired or wireless communication between device 300 and other devices. Device 300 can access wireless networks based on communication standards, such as WiFi, 2G, or 3G, or combinations thereof. In one exemplary embodiment, communication component 316 receives broadcast signals or broadcast-related information from an external broadcast management system via a broadcast channel. In one exemplary embodiment, communication component 316 also includes a near-field communication (NFC) module to facilitate short-range communication. For example, the NFC module may be implemented based on radio frequency identification (RFID) technology, Infrared Data Association (IrDA) technology, ultra-wideband (UWB) technology, Bluetooth (BT) technology, and other technologies.

[0066] In an exemplary embodiment, the apparatus 300 may be implemented by one or more application-specific integrated circuits (ASICs), digital signal processors (DSPs), digital signal processing devices (DSPDs), programmable logic devices (PLDs), field-programmable gate arrays (FPGAs), controllers, microcontrollers, microprocessors, or other electronic components to perform the above-described method for predicting ionospheric delay products.

[0067] Understandably, the processor 320 in this embodiment can be an integrated circuit chip with signal processing capabilities. In implementation, each step of the above method embodiment can be completed by integrated logic circuits in the processor's hardware or by software instructions. The processor described above can be a general-purpose processor, a digital signal processor (DSP), an application-specific integrated circuit (ASIC), a field-programmable gate array (FPGA), or other programmable logic devices, discrete gate or transistor logic devices, or discrete hardware components.

[0068] Understandably, the memory 304 in the embodiments of this application can be volatile memory or non-volatile memory, or may include both volatile and non-volatile memory. The non-volatile memory can be read-only memory (ROM), programmable read-only memory (PROM), erasable programmable read-only memory (EPROM), electrically erasable programmable read-only memory (EEPROM), or flash memory. The volatile memory can be random access memory (RAM), which is used as an external cache. By way of example, but not limitation, many forms of RAM are available, such as static random access memory (SRAM), dynamic random access memory (DRAM), synchronous dynamic random access memory (SDRAM), double data rate synchronous dynamic random access memory (DDRSDRAM), enhanced synchronous dynamic random access memory (ESDRAM), synchronous linked dynamic random access memory (SLDRAM), and direct rambus RAM (DR RAM). It should be noted that the memory used in the systems and methods described herein is intended to include, but is not limited to, these and any other suitable types of memory.

[0069] In an exemplary embodiment, a non-transitory computer-readable storage medium including instructions is also provided, such as a memory 304 including instructions, which can be executed by a processor 320 of the device 300 to complete the above-described method for predicting upper ionospheric delay products. For example, the non-transitory computer-readable storage medium may be a ROM, random access memory (RAM), CD-ROM, magnetic tape, floppy disk, and optical data storage device, etc.

[0070] The aforementioned device can be a standalone electronic device or a part of a standalone electronic device. For example, in one embodiment, the device can be an integrated circuit (IC) or a chip, wherein the integrated circuit can be a single IC or a collection of multiple ICs. The chip can include, but is not limited to, the following types: GPU (Graphics Processing Unit), CPU (Central Processing Unit), FPGA (Field Programmable Gate Array), DSP (Digital Signal Processor), ASIC (Application Specific Integrated Circuit), and SoC (System on Chip). The aforementioned integrated circuit or chip can be used to execute executable instructions (or code) to implement the aforementioned method for predicting ionospheric delay products. The executable instructions can be stored in the integrated circuit or chip or obtained from other devices or equipment. For example, the integrated circuit or chip includes a processor, memory, and an interface for communicating with other devices. The executable instructions can be stored in the memory, and when the executable instructions are executed by the processor, the above-mentioned method for predicting ionospheric delay products can be implemented; or, the integrated circuit or chip can receive the executable instructions through the interface and transmit them to the processor for execution to implement the above-mentioned method for predicting ionospheric delay products.

[0071] Please see Figure 4 This is a schematic diagram of the structure of a computer device provided in an embodiment of this application. For example, as shown... Figure 4 As shown, the computer device 400 includes a memory 401 and a processor 402, wherein the memory 401 stores executable program code 4011, and the processor 402 is used to call and execute the executable program code 4011 to perform a method for predicting ionospheric delay products.

[0072] This application embodiment can divide a computer device into functional modules according to the above method embodiment. For example, each module can correspond to a specific function, or two or more functions can be integrated into a processing module. The integrated module can be implemented in hardware. It should be noted that the module division in this embodiment is illustrative and only represents one logical functional division. In actual implementation, there may be other division methods. When dividing each functional module according to a specific function, the computer device may include: a processing module and a communication module, etc.

[0073] It should be noted that all relevant content of each step involved in the above method embodiments can be referenced from the functional description of the corresponding functional module, and will not be repeated here. The computer device provided in this embodiment is used to execute the above-described method for predicting ionospheric delayed products, and therefore can achieve the same effect as the above implementation method.

[0074] In another exemplary embodiment, a computer program product is also provided, comprising a computer program executable by a programmable device, the computer program having a code portion for performing the forecasting method of the ionospheric delay product when executed by the programmable device.

[0075] It should be noted that the descriptions of the above embodiments of storage media, devices, and equipment are similar to the descriptions of the above method embodiments, and have similar beneficial effects. For technical details not disclosed in the embodiments of storage media, devices, and equipment of this application, please refer to the descriptions of the method embodiments of this application for understanding.

[0076] Other embodiments of this application will readily occur to those skilled in the art upon consideration of the specification and practice of this application. This application is intended to cover any variations, uses, or adaptations of this application that follow the general principles of this application and include common knowledge or customary techniques in the art not disclosed in this application. The specification and embodiments are to be considered exemplary only, and the true scope and spirit of this application are indicated by the following claims.

[0077] The above description is merely a preferred embodiment of this application and is not intended to limit this application. Any modifications or equivalent substitutions made within the spirit and principles of this application should be included within the protection scope of this application.

Claims

1. A method for predicting ionospheric delayed products, characterized in that, include: Obtain an ionospheric delay parameter set for M epochs, wherein the ionospheric delay parameter set includes at least one ionospheric delay parameter, and M is a positive integer; Based on the ionospheric delay parameter set of M epochs, robust detection processing is performed to obtain the ionospheric delay parameter set of N epochs, where N is a positive integer less than or equal to M; Based on the ionospheric delay parameter set of N epochs, segmented modeling and robust fusion forecasting are performed to obtain the corresponding forecast ionospheric delay product. The forecast ionospheric delay product includes at least the polynomial coefficients of the background field or the ionospheric delay correction.

2. The method according to claim 1, characterized in that, The segmented modeling and robust fusion forecasting based on the ionospheric delay parameter set of N epochs yields the corresponding predicted ionospheric delay products, including: The ionospheric delay parameter set of N epochs is segmented based on the time interval of N epochs to obtain L ionospheric delay parameter sequences for each segment. The ionospheric delay parameter sequence includes at least one ionospheric delay parameter for different epochs within the corresponding segment, where L is a positive integer. Differential modeling is performed based on the ionospheric delay parameter sequences of each of the L segments to obtain the corresponding ionospheric delay prediction model and the differential sequences of each of the L segments, wherein the differential sequences correspond to the ionospheric delay parameter sequences. Based on the ionospheric delay forecast model and the differential sequences of the L segments, robust fusion forecasts are performed to obtain the forecasted ionospheric delay product.

3. The method according to claim 2, characterized in that, The robust fusion forecast based on the ionospheric delay prediction model and the differential sequences of the L segments, yielding the predicted ionospheric delay product, includes: Based on the ionospheric delay prediction model, ionospheric delay prediction is performed on the differential sequences of the L segments respectively to obtain the predicted differential ionospheric products corresponding to the L segments. Differential reconstruction is performed based on the predicted differential ionospheric products corresponding to each of the L segments to obtain the predicted ionospheric products corresponding to each of the L segments. The predicted ionospheric delay product is obtained by weighted fusion of the predicted ionospheric products corresponding to each of the L segments.

4. The method according to claim 3, characterized in that, The weighted fusion of the predicted ionospheric products corresponding to each of the L segments to obtain the predicted ionospheric delay product includes: Based on the time distance between the L differential sequences and the latest epoch, and the segment length corresponding to the differential sequence, the weighting weight of the predicted ionospheric product of the L segments is determined, and the latest epoch is the latest epoch among the M epochs; Based on the weighted weights of the predicted ionospheric products in the L segments, the predicted ionospheric products corresponding to each of the L segments are weighted and calculated to obtain the predicted ionospheric delay product.

5. The method according to claim 2, characterized in that, The differential modeling based on the ionospheric delay parameter sequences of L segments, to obtain the corresponding ionospheric delay prediction model and the differential sequences of the L segments, includes: Based on the ionospheric delay parameter sequences of each of the L segments, a differential calculation of a preset order is performed to obtain the differential sequences of each of the L segments; Based on the difference sequences of the L segments, a model is constructed and solved to obtain a solution prediction model. The solution prediction model has the same model structure as the ionospheric delayed prediction model. The residual test is performed on the solved prediction model, and the solved prediction model that passes the test is determined as the ionospheric delayed prediction model.

6. The method according to claim 1, characterized in that, The robust detection processing of the ionospheric delay parameter set based on M epochs yields the ionospheric delay parameter set of N epochs, including: Time-effective detection is performed based on the ionospheric delay parameter set of M epochs to obtain the ionospheric delay parameter set of P epochs, where P is a positive integer less than or equal to M. Anomaly detection is performed based on the ionospheric delay parameter set of P epochs, and the ionospheric delay parameter set of abnormal epochs is removed to obtain the ionospheric delay parameter set of N epochs, where N is a positive integer less than or equal to P. The anomaly detection includes at least one of the following: epoch number detection, local jump detection, window dispersion detection, segmented anomaly detection, and anomaly rate detection.

7. The method according to claim 6, characterized in that, The anomaly detection based on the ionospheric delay parameter set of P epochs includes at least one of the following: When the anomaly detection includes the epoch count detection, the number of the P epochs is counted and determined to be greater than a preset first number; When the anomaly detection includes the local jump detection, if the absolute value of the difference between any ionospheric delay parameter of the first epoch and any ionospheric delay parameter of the previous epoch is greater than a preset first threshold, then both the first epoch and the previous epoch are marked as anomaly epochs. The first epoch is any epoch among the P epochs, and the previous epoch is an epoch among the P epochs that precedes the first epoch. When the anomaly detection includes the window dispersion detection, the median and median absolute deviation of any ionospheric delay parameter located Q epochs before and after the second epoch are determined. If any ionospheric delay parameter of the second epoch exceeds a preset first range, the second epoch is marked as an anomalous epoch. The preset first range is determined based on the median and the median absolute deviation. The second epoch is any epoch among the P epochs, and Q is a positive integer. When the anomaly detection includes the segmented anomaly detection, a preset segment number and segment number spacing of any ionospheric delay parameter within any segment of the P epochs are determined. If any ionospheric delay parameter of the third epoch within any segment of the P epochs exceeds a preset second range, the third epoch is marked as an anomalous epoch. The preset second range is determined based on the preset segment number and segment number spacing. The third epoch is any epoch within any segment of the P epochs. When the anomaly detection includes the anomaly rate detection, it is determined that the number of all anomalous epochs in the P epochs must be less than or equal to a preset second number.

8. The method according to any one of claims 1-7, characterized in that, When the method is applied to the PPP-RTK positioning service side, the predicted ionospheric delay product includes polynomial coefficients of the background field for at least one forecast epoch, grid residuals for the latest epoch, and a product identifier; or, when the method is applied to the PPP-RTK positioning user side, the predicted ionospheric delay product includes an ionospheric delay correction for at least one forecast epoch.

9. A forecasting device for ionospheric delayed products, characterized in that, include: processor; A memory for storing processor-executable instructions; wherein the processor is configured to execute the executable instructions to implement the steps of the method according to any one of claims 1 to 8.

10. A computer-readable storage medium having computer program instructions stored thereon, characterized in that, When the computer program instructions are executed by the processor, they implement the steps of the method according to any one of claims 1 to 8.

Images