An ionospheric total electron content prediction method, system, electronic device and medium

Abstract

The present invention discloses a method, a system, an electronic device and a medium for predicting the total electron content of the ionosphere, which relates to the field of predicting the total electron content of the ionosphere. The method includes: first, obtaining multi-source observation data of a to-be-predicted site at time t, and using a total electron content prediction model of the ionosphere to perform data assimilation on the multi-source observation data of the to-be-predicted site at time t to obtain the true value of the total electron content of the ionosphere. Among them, the total electron content prediction model of the ionosphere is obtained by training a layered Bayesian network using a training data set. The present invention improves the accuracy of predicting the total electron content of the ionosphere.

Description

Technical Field

[0001] The present invention relates to the field of ionospheric total electron content prediction, and particularly to a method, a system, an electronic device and a medium for predicting ionospheric total electron content. Background Art

[0002] The ionosphere is an important part of the near-Earth space environment. Its drastic spatial and temporal variations will seriously degrade the quality of global shortwave communications and the accuracy of satellite navigation and positioning. The total electron content (TEC) of the ionosphere is one of the important parameters characterizing the spatial and temporal variations of the ionosphere. How to accurately obtain the characteristics and variation laws of the ionospheric TEC distribution, establish a system that includes both intrinsic physics and reflects real observations, and at the same time meet the real-time monitoring of the space environment and provide high-precision quasi-real-time ionospheric correction information has become one of the key research contents in the ionosphere field.

[0003] Ionospheric TEC assimilation can comprehensively utilize various observation means, such as ground-based and space-based Global Navigation Satellite System (GNSS), ionosondes, Jason satellites and incoherent scatter radars, and at the same time combine physical models or empirical models to obtain a multi-scale ionospheric assimilation model with high precision and high time resolution. This is of great significance for the research and application of ionospheric science.

[0004] First, studying ionospheric TEC data assimilation can help people better understand the physical characteristics and spatial structure of the ionosphere. By comprehensively analyzing the data of different observation means, the global / regional distribution, high-low latitude differences, diurnal variations and seasonal variations of ionospheric TEC can be obtained. This helps to further study the formation and evolution mechanism of the ionosphere and explore the interaction between the Earth's atmosphere and solar activities.

[0005] Second, studying ionospheric TEC assimilation can also be used to improve the accuracy of satellite navigation and positioning. The ionosphere has a great influence on the propagation of radio waves. The inhomogeneity of the ionospheric TEC distribution will cause phenomena such as diffraction, scattering and absorption of radio waves, thus affecting the reliability and accuracy of communication and navigation. By assimilating the data of different observation means, a more accurate ionospheric TEC distribution can be obtained, thereby improving the performance of satellite navigation and positioning.

[0006] Finally, studying ionospheric TEC data assimilation can also be used to improve the prediction ability of solar storms and space weather. Solar storms and space weather have a great impact on the ionosphere, which may cause ionospheric disturbances and affect the normal operation of important facilities such as satellite navigation, communication, and ground power systems. Therefore, accurately predicting the impact of solar storms and space weather on the ionosphere is of great significance for maintaining national security and ensuring the safety of people's lives and property. By assimilating data from different observation means, a more accurate spatio-temporal distribution of ionospheric TEC can be obtained, further improving the early warning ability of the space environment.

[0007] Great progress has been made in data assimilation algorithms in the past few decades. However, traditional data assimilation methods represented by the Kalman filter still have the following three problems:

[0008] (1) Currently, due to the limitation of computing power, in large-scale data assimilation, in order to facilitate the calculation of large-scale matrix inversion and reduce the calculation time, it is usually assumed that the state quantity space is independent, that is, there is no relationship between the state quantities at adjacent positions. However, this is usually not the case in actual situations and will cause the loss of relevant information, thereby reducing the model accuracy.

[0009] (2) In traditional assimilation algorithms, there are usually some parameters defined as constants. The definition of these parameters requires strong prior knowledge, such as the error variances of observation data and model predictions. The setting of the magnitudes of these parameters often requires repeated verification, which affects production efficiency. At the same time, since they are set as constants, these parameters limit the consideration of the algorithm in terms of uncertainty to a large extent and reduce the accuracy of data assimilation.

[0010] (3) When data assimilation faces observation data composed of multiple data sources with different temporal and spatial resolutions, resampling is often required, that is, the data is resampled to the same temporal and spatial resolution. However, the negative effects brought by resampling are also quite obvious, and the accuracy after assimilation is often greatly affected. Summary of the Invention

[0011] The purpose of the present invention is to provide a method, system, electronic device, and medium for predicting the total electron content of the ionosphere to improve the accuracy of predicting the total electron content of the ionosphere.

[0012] To achieve the above object, the present invention provides the following solutions:

[0013] A method for predicting the total electron content of the ionosphere includes:

[0014] Obtain multi-source observation data at time t of the site to be predicted; the observation data is the total electron content of the ionosphere; multi-source includes the Global Navigation Satellite System, ionosonde, Jason satellite, and incoherent scatter radar;

[0015] Based on the multi-source observation data of the to-be-predicted site at time t, use the total ionospheric electron content prediction model to predict the true value of the total ionospheric electron content of the to-be-predicted site at time t; wherein, the total ionospheric electron content prediction model is obtained by training a layered Bayesian network using a training data set; the training data set includes the multi-source observation data of the training observation sites and the output data of the ionospheric physical model; the observation data is the observed value of the total ionospheric electron content; the layered Bayesian network includes a data model, a process model, and a parameter model.

[0016] Optionally, training the layered Bayesian network using the training data set specifically includes:

[0017] Use a distance cross matrix to process the missing data in the multi-source observation data of any one of the training observation sites to obtain multi-source continuous observation data;

[0018] Take the multi-source continuous observation data and the output data of the ionospheric physical model as the input of the current layered Bayesian network, and determine the true value of the total ionospheric electron content of the training observation site;

[0019] Use mean square error verification to determine the mean square error between the true value of the total ionospheric electron content of the training observation site and the multi-source observation data of the training observation site;

[0020] Judge whether the maximum number of iterations is reached;

[0021] If not, adjust the parameters of the current layered Bayesian network and return to the step of "using a distance cross matrix to process the missing data in the multi-source observation data of any one of the training observation sites to obtain multi-source continuous observation data";

[0022] If so, take the current layered Bayesian network corresponding to the minimum mean square error as the total ionospheric electron content prediction model.

[0023] Optionally, the process of determining the output data of the ionospheric physical model specifically includes:

[0024] Obtain the geomagnetic index and solar activity index of the training observation site;

[0025] Take the geomagnetic index and the solar activity index as the input of the ionospheric physical model, and determine the output data of the ionospheric physical model; the output data is the continuous value of the total ionospheric electron content.

[0026] Optionally, the data model is:

[0027] Z t =O t +ε t; where Z t is the multi-source observation data of all training observation sites at time t; O t is the true value of the total electron content of the ionosphere at all training observation sites at time t, and ε t is the observation error term of all training observation sites at time t.

[0028] Optionally, the process model is:

[0029] O t = ξ + ρO t-1 +(β0 + β S )X t + η t ; where O t is the true value of the total electron content of the ionosphere at all training observation sites at time t; ξ is the trend of the total electron content distribution of the ionosphere in the observation area; ρO t-1 represents the influence of the total electron content of the ionosphere at time t-1 on the total electron content of the ionosphere at time t; O t-1 is the total electron content of the ionosphere at all training observation sites at time t-1; X t is the output data of the ionospheric physical model; β0 is a constant that does not change with time and space; β S is a variable that changes with space; η t is the residual term.

[0030] An ionospheric total electron content prediction system, comprising:

[0031] A data acquisition module for acquiring multi-source observation data of a site to be predicted at time t; the observation data is the total electron content of the ionosphere; the multi-source includes the global navigation satellite system, ionosonde, Jason satellite, and incoherent scatter radar;

[0032] A prediction module for predicting the true value of the total electron content of the ionosphere at time t of the site to be predicted according to the multi-source observation data of the site to be predicted at time t by using an ionospheric total electron content prediction model; wherein, the ionospheric total electron content prediction model is obtained by training a layered Bayesian network using a training data set; the training data set includes multi-source observation data of training observation sites and output data of an ionospheric physical model; the observation data is the observed value of the total electron content of the ionosphere; the layered Bayesian network includes a data model, a process model, and a parameter model.

[0033] An electronic device, comprising: a memory and a processor, the memory is used for storing a computer program, and the processor runs the computer program to enable the electronic device to execute the above-mentioned ionospheric total electron content prediction method.

[0034] A computer-readable storage medium stores a computer program, and when the computer program is executed by a processor, the above-mentioned total electron content prediction method of the ionosphere is implemented.

[0035] According to the specific embodiments provided by the present invention, the following technical effects are disclosed:

[0036] For the total electron content prediction method, system, electronic device and medium of the present invention, first, multi-source observation data at time t of a station to be predicted is acquired, and the multi-source observation data at time t of the station to be predicted is data-assimilated by using a total electron content prediction model of the ionosphere to obtain the true value of the total electron content of the ionosphere. Among them, the total electron content prediction model of the ionosphere is obtained by training a layered Bayesian network using a training data set. The present invention uses the trained layered Bayesian network to perform data assimilation on multi-source observation data, and the predicted true value of the total electron content of the ionosphere is more accurate, improving the accuracy of the total electron content prediction of the ionosphere. Description of the Drawings

[0037] In order to more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings required in the embodiments. Obviously, the drawings in the following description are only some embodiments of the present invention, and those of ordinary skill in the art can also obtain other drawings based on these drawings without creative efforts.

[0038] Figure 1 It is a flowchart of the total electron content prediction method of the ionosphere provided by the present invention;

[0039] Figure 2 It is a flowchart of performing data assimilation using a layered Bayesian network provided by the present invention. Detailed Embodiments

[0040] The following will clearly and completely describe the technical solutions in the embodiments of the present invention with reference to the drawings in the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, rather than all embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts fall within the protection scope of the present invention.

[0041] The purpose of the present invention is to provide a total electron content prediction method, system, electronic device and medium of the ionosphere to improve the accuracy of the total electron content prediction of the ionosphere.

[0042] In order to make the above-mentioned objects, features and advantages of the present invention more obvious and understandable, the present invention will be further described in detail below with reference to the drawings and specific embodiments.

[0043] Embodiment 1

[0044] The total electron content prediction method of the present invention is an ionospheric data assimilation method based on the layered Bayesian network algorithm. The theoretical basis of the layered Bayesian network algorithm is conditional probability distribution, and its goal is to obtain the probability distribution of other unknown parameters under the condition of given known observation data. At the same time, the idea of conditional independence is also used to gradually split complex problems into several relatively simple models, and each model is split according to the idea of conditional independence, so that complex posterior probability reasoning is transformed into a series of relatively simple conditional probability reasonings. Due to the great advantages and application potential of the layered Bayesian network in data spatio-temporal analysis, it has been successfully used in the fields of medicine, environment, economy, ocean and atmosphere, and certain results have been achieved.

[0045] However, so far, the layered Bayesian network algorithm has not been widely applied to data assimilation and is still in the stage of scientific experiments, mainly due to the complexity of the algorithm mechanism and content. The specific analysis has the following three reasons:

[0046] 1. High computational complexity. The layered Bayesian method requires a large number of probability calculations and model updates, and the computational complexity is relatively high. Moreover, the formula derivation is rather cumbersome and requires a lot of related mathematical and physical background knowledge. And when the data volume is very large, the computational complexity will increase exponentially, resulting in computational difficulties.

[0047] 2. Difficult parameter selection. The layered Bayesian method needs to determine multiple prior probability distributions and conditional probability distributions, and the parameters of these probability distributions need to be estimated according to actual data. The selection and definition of the prior probability directly affect the convergence of the final sampling and require strong prior knowledge. However, different parameter selections may lead to different results, so how to select appropriate parameters has become a difficult point.

[0048] 3. Error propagation. The layered Bayesian method estimates the system state through prior probability distributions and conditional probability distributions, and the errors of these probability distributions will be transmitted to the final estimation result. If there are errors in the prior probability distribution or conditional probability distribution, it will affect the final estimation result, thereby reducing the estimation accuracy.

[0049] 4. Overfitting problem. The layered Bayesian method needs to select prior probability distributions and conditional probability distributions, and these distributions are usually determined by minimizing errors. If the selected distribution is too complex, it may lead to the problem of overfitting, that is, it performs well on the training data but poorly on new data.

[0050] 5. The most important part of the layered Bayesian network algorithm is the process model. Its definition must reflect the characteristics of the parameters changing over time and space. However, its definition generally depends on the understanding of the physical process mechanism and data analysis, and there is no simplified general method.

[0051] For the global or regional scale, by establishing a layered Bayesian network, assimilate the total electron content (TEC) data obtained from multi-source observations (ground-based and space-based GNSS, ionosondes, Jason satellites, incoherent scatter radars) into the ionospheric physical model or empirical model to construct a high-precision multi-scale (global or regional) ionospheric TEC model. Compared with the data assimilation methods of three-dimensional variational and Kalman filtering, the present invention can achieve high-precision ionospheric data assimilation.

[0052] As Figure 1 shown, the method for predicting the total electron content of the ionosphere provided by the present invention includes:

[0053] Step 101: Obtain multi-source observation data at time t of the site to be predicted; the observation data is the total electron content of the ionosphere; the multi-source includes the global navigation satellite system, ionosondes, Jason satellites, and incoherent scatter radars.

[0054] Step 102: According to the multi-source observation data at time t of the site to be predicted, use the total electron content prediction model of the ionosphere to predict the true value of the total electron content of the ionosphere at time t of the site to be predicted; wherein, the total electron content prediction model of the ionosphere is obtained by training a layered Bayesian network using a training data set; the training data set includes the multi-source observation data of the training observation site and the output data of the ionospheric physical model; the observation data is the observed value of the total electron content of the ionosphere; the layered Bayesian network includes a data model, a process model, and a parameter model.

[0055] The ionospheric physical / empirical model is a type of mathematical model established using observation data and can be used to predict some key parameters in the ionosphere. Common ionospheric physical / empirical models include the International Reference Ionosphere model, the NeQuick model, and the URSI model. In the present invention, the NeQuick model is used.

[0056] The NeQuick model is a semi-empirical digital model used to predict the electron content in the global ionosphere. This model was initially developed in 1996 by the European Conference of Postal and Telecommunications Administrations (CEPT) under the support of the European Union, and its original version was called the QUICK program. The development of the NeQuick model mainly relies on ground-based and satellite observation data, as well as data such as the Earth's magnetic field and solar activity indices. The principle of the NeQuick model is based on the three-dimensional Maxwell-Boltzmann equations, which are used to calculate the position, solar activity, and vertical and horizontal ionospheric (IP) electron content. Its core idea is to simulate the effects such as path delay and aliasing of radio wave propagation by modeling the ionospheric electron content, and then to optimize communication and navigation applications such as satellite navigation, television broadcasting, wireless communication, and radar communication.

[0057] The NeQuick model includes two types: NeQuick-1 and NeQuick-2. Among them, NeQuick-1 is mainly used for the calculation of ionospheric partitioning and the number of ionospheric layers, while NeQuick-2 is used for the calculation and prediction of electron content on a global scale. The main output parameters of the NeQuick model include parameters such as electron content, vertical ionospheric delay, total ionospheric delay, satellite antenna phase center and electron delay error, satellite user position error, signal-to-noise ratio, etc.

[0058] Among them, the data model is:

[0059] Z t =O t +ε t (1).

[0060] Among them, Z t is the multi-source observation data of all training observation sites at time t; O t is the true value of the total ionospheric electron content of all training observation sites at time t, and ε t is the observation error term of all training observation sites at time t.

[0061] The process model is:

[0062] O t =ξ + ρO t-1 +(β0 + β S )X t +η t (2).

[0063] Among them, O t is the true value of the total ionospheric electron content of all training observation sites at time t; ξ is the trend of the total ionospheric electron content distribution in the observation area; ρO t-1Indicates the impact of the total ionospheric electron content at time t-1 on the total ionospheric electron content at time t; O t-1 Is the total ionospheric electron content of all training observation sites at time t-1; X t Is the output data of the ionospheric physical model; β0 is a constant that does not change with time and space; β S Is a variable that changes with space; η t Is the residual term.

[0064] The process of data assimilation using a layered Bayesian network is as Figure 2 Shown, and it consists of three parts: data preparation, network learning verification, and prediction. The task of data preparation is to prepare the input data required by the layered Bayesian network. For multi-source observation data, the main data processing includes: processing missing data at stations, selecting training points and verification points according to the observation conditions and data situations of each station, and format conversion. For ionospheric physical model or empirical model data, the main data processing includes: preparing model-driven data, analyzing the spatio-temporal distribution characteristics of parameters based on existing data, and processing and storing them according to the data format required by the layered Bayesian network. Network learning verification is to train the layered Bayesian network using the observation data of training stations, evaluate the network learning results using VMSE (Validation Mean Squared Error), and adjust some key parameters. When the verification accuracy meets the requirements, the layered Bayesian network can be used to predict the TEC of any point.

[0065] In practical applications, the layered Bayesian network is trained using a training dataset, specifically including:

[0066] Using a distance cross-matrix to process the missing data of the multi-source observation data of any one of the training observation sites to obtain multi-source continuous observation data.

[0067] The distance cross-matrix refers to the process of calculating the distance between any two objects in a group of objects and combining these distances into a symmetric matrix. The distance can be measured in various ways, such as Euclidean distance, Manhattan distance, cosine similarity, Jaccard similarity, Mahalanobis distance, etc. The distance cross-matrix is usually used in multiple fields such as clustering, dimensionality reduction, and similarity search. The size of the distance cross-matrix is n×n, where n represents the number of objects. The i-th row of the distance cross-matrix represents the distance between the i-th object and other objects, and the j-th column represents the distance between the j-th object and other objects. Several basic properties of the distance cross-matrix are as follows:

[0068] 1. Non-negativity: d i,j ≥0.

[0069] 2. Symmetry: d i,j = d j,i .

[0070] 3. Zero-distance property: d i,i = 0.

[0071] 4. Triangle inequality: For any i, j, k, d i,j ≤ d i,k + d k,j .

[0072] In practical applications, using the distance cross matrix to process missing data is divided into two steps: calculating the distance cross matrix and predicting the missing values. First, calculate the distance cross matrix using the existing data, and its specific formula is:

[0073] d i,j = dist(x i , x j ) (3).

[0074] In the formula, x i and x j are data at different positions respectively. Suppose there are n samples in total, and each data source has p features. Denote the matrix composed of the above data as X n×p , where the i-th row represents the i-th sample and the j-th column represents the j-th feature. Obtain the distance cross matrix D of the above data through the calculation formula of the distance cross matrix. Secondly, use the distance cross matrix D to complete the missing values of the matrix. Suppose the j-th data of the i-th sample is missing, then the formula for completing this data is as follows:

[0075]

[0076] Among them, represents the predicted value of the missing data of the multi-source observation data of the training observation site, ω i,k represents the distance between the i-th sample and the k-th sample, and X k,j is the j-th value of the k-th sample. Several sample points closest to the i-th sample can be selected, for example, the first k sample points closest in distance, to calculate the weighted average value, where the weight of each sample is assigned by the reciprocal of the distance. The estimated value calculated in this way is the predicted value of the missing value. Use the predicted value of the missing value to complete the missing data of the multi-source observation data of any one of the training observation sites.

[0077] Use the multi-source continuous observation data and the output data of the ionospheric physical model as the input of the current layered Bayesian network to determine the true value of the total electron content of the ionosphere at the training observation site.

[0078] Verify using the mean square error to determine the true value of the total electron content of the ionosphere at the training observation site and the mean square error of the multi-source observation data at the training observation site.

[0079] Judge whether the maximum number of iterations is reached.

[0080] If not, adjust the parameters of the current layered Bayesian network and return to the step of "performing missing data processing on the multi-source observation data of any one of the training observation sites using the distance cross matrix to obtain multi-source continuous observation data".

[0081] If so, use the current layered Bayesian network corresponding to the minimum mean square error as the total electron content prediction model of the ionosphere.

[0082] Among them, the determination process of the output data of the ionospheric physical model specifically includes:

[0083] Obtain the geomagnetic index and solar activity index of the training observation site.

[0084] Use the geomagnetic index and the solar activity index as the input of the ionospheric physical model to determine the output data of the ionospheric physical model; the output data is the continuous value of the total electron content of the ionosphere.

[0085] In practical applications, before training the layered Bayesian network, the layered Bayesian network needs to be constructed first, specifically as follows:

[0086] Step 1: Establish a data model. For any time t, there is a true value O t , and the ultimate goal of data assimilation is to infer the posterior probability distribution of O t and obtain the maximum posterior probability of O t . Define the data model of multi-source observation data, as shown in formula (1). In the formula, t = 1, 2, 3, ···, T; O t = [(S1,t), (S2,t), ···, (S N ,t)] represents the true value of the ionospheric TEC of all training observation sites at time t, ε t = ((S1,t), (S2,t), ···, (S N ,t)) T is the observation error term of all training observation sites at time t, which follows the distribution 0 is a vector with all elements being 0, I N is the N-dimensional identity matrix, is a constant, which is invariant within the spatio-temporal range. i = 1, 2, 3, ···, N, and N is the number of training observation sites. The output data X t of the ionospheric physical model or empirical model is used as O(S i,t) covariates, output data X of the ionospheric physical model or empirical model t and the true value O(S i ,t) relationship is shown in Equation (2).

[0087] Step 2: Establish a process model, the purpose of which is to describe the spatio-temporal distribution and variation of the total electron content TEC in the ionosphere. Define the process model, such as Equation (2), where ξ represents the trend of TEC distribution in the observation area and is a constant that does not change with time and space. ρO t-1 represents the influence of the TEC at time t-1 on the TEC at time t. 0 < ρ < 1, and sequential data assimilation is achieved through ρ. β0 is a constant that does not change with time and space. β S is a variable that varies with space, making Equation (2) a non-stationary model, β S = [β(S1), β(S2), ···, β(S N )] T . η t is the residual term, which varies with different spatial positions. β S ~N(0, ∑ β ), η t ~N(0, ∑ η ), ∑ η , ∑ β are covariance matrices. For ease of calculation, the covariance function can be defined as an exponential function. Each element of the ∑ η matrix is exp(-φ β d(S i , S j )) is the distance between the observation sites S i , S j . Similarly, each element of the ∑ η matrix is For subsequent convenience of representation,

[0088] Step 3: Establish a parameter model. The parameters used in the data model and process model are Theoretically, to obtain the most accurate posterior probability distribution, all parameters should be obtained through Bayesian inference, but this will greatly increase the computational complexity and it is difficult to achieve real-time data assimilation and update. Therefore, to reduce the computational complexity, the parameter model only defines the prior probability distributions of five parameters, and other parameters are obtained through data analysis and model verification. ρ follows a normal distribution with a mean of 0 and a large variance, and its value is between [0, 1]. ξ is analyzed by an auto regressive moving average model (ARMA) based on site data, and variance-like parameters Obey IG distribution.

[0089] Step 4: After completing the definition of the data model, process model, and parameter model, the construction of the HBN (hierarchical Bayesian network) is completed. In order to make up for the lack of prior knowledge and obtain the posterior probability distribution of other parameters, the hierarchical Bayesian network must be trained first. The goal is to use the training data to continuously adjust the parameters of the hierarchical Bayesian network so that the hierarchical Bayesian network is suitable for the current training data. During the learning process of the hierarchical Bayesian network, VMSE is used as the main indicator for evaluating the performance of the hierarchical Bayesian network. The definition of VMSE is shown in formula (5). The main method is to use multi-source observation data and ionospheric physics or empirical model output data within the assimilation period to train the hierarchical Bayesian network, predict the TEC posterior probability of the checkpoint, compare the difference between the predicted value and the observed data using VMSE as the standard, and adjust φ β ,φ η value until VMSE is minimum.

[0090]

[0091] Where n v is the number of all the verification data of the verification points in the assimilation period; Z * (S i , t) is the predicted value (true value) of the total electron content in the ionosphere; Z(S i , t) is the observed value of the total electron content of the ionosphere (multi-source observation data at the predicted site at time t), and φ is the minimum VMSE. β ,φ η is the optimal parameter value. In order to verify the network parameters, we must first obtain the i The predicted value Z at * (S i , t). According to formula (1), the site to be predicted S′ i The predicted value Z at time t * (S′ i , t) obeys the distribution as shown in formula (6):

[0092]

[0093] O(S i ′t)=ξ+ρO(S i ′, t-1)+(β0+β(S i ′))X(S i ′, t)+η(S i ′, t) (7).

[0094] In the formula, O(S i′, t - 1) is the true value of the site S′ to be predicted at the previous moment i , so the acquisition of O(S i ′, t) can only be achieved through sequential step - by - step iteration. Define O(S i ′, [t]) to represent all the true values of point S i ′ at t moments.

[0095] o(S i ′, [t]) = [O(S i ′, 1), O(S i ′, 2), …, O(S i ′, t)]′ (8).

[0096] That is, the posterior probability distribution of Z(S′ i , t) is:

[0097] p[Z(S i ′, t)|z] = ∫p(Z(S i ′, t)|O(S i ′, [t]), σ 2 )p(O(S i ′, [t]|β(S i ′), w, θ)p(β(S i ′)|θ)

[0098] dO(S i ′,[t]dβ(S i ′)dθdw, i = 1, 2, ···, Num (9).

[0099] w = (O t , O t ′, Z t ′) represents all the variables to be inferred and all the parameters in the HBN, z = (X t , Z t ) represents all the known observed data. In formula (9), β(S i ′) is a quantity that varies with the spatial position, and the conditional probability of β(S i ′) is:

[0100]

[0101] In the formula, β = (β1, β1, ···, β n ,)′ is the value of β = (S i ) at the learning site, S β,12 is a 1×N - dimensional row vector, representing the correlation between the site S i ′ to be predicted and the training observation sites (S1, S2, ···, S N ), which is represented by a distance function; Sβ,21 is an N×1 column vector, and is S β,12 transpose of, S β,12 The i-th element in is:

[0102] S β,12 (i,j) = exp(φ β d(S i , S′ j ), i = 1, 2, ···, N (11).

[0103] In the formula, d(S i , S′ j ) represents the distance between the site S′ to be predicted and the training observation site S i . According to formulas (10) and (11), the posterior probability distribution of β(S i ′) is as in formula (12):

[0104]

[0105] Similar to formula (10), the posterior probability distribution of O(S′ i , t) is:

[0106]

[0107] In the formula, O t = [O(S1, t), O(S2, t) ··· O(S N , t)]′, represents the true value of the learning site at time t, S η,12 is a 1×N row vector, representing the correlation between the site S i ′ to be predicted and the training observation sites (S1, S2 ··· S N ) changing with distance, S β,21 is an N×1 column vector, and is the transpose of S β,12 , and the i-th element in S η,12 is:

[0108] S η,12 (i) = exp(φ η d(S i , S′ j ), i = 1, 2, ···, N (14).

[0109] In formula (14), d(S i , S′ j ) represents the distance between the site S i ′ to be predicted and the training observation site S i .

[0110] Finally, according to formulas (13) and (14), determine O(S′i , the posterior probability distribution of \(p[O(S',t)|\beta(S'),O,\theta,w]\) is as shown in Equation (15), that is, the data assimilation is completed.

[0111] p[O(S′ i ,t)|β(S′ i ),O t ,θ,w] ∼ N(χ,Λ) (15).

[0112]

[0113]

[0114] The data model assumes that the data is conditionally dependent on the process, making the HBN data assimilation applicable to the observed data with multiple data sources. In addition, the requirements for data in HBN data assimilation are more in line with the real situation in nature, and the requirement for data independence is reduced from independent of each other to conditionally independent.

[0115] The data assimilation algorithm has made great progress in the past few decades. The present invention proposes a layered Bayesian network algorithm for the traditional data assimilation methods represented by the Kalman filter.

[0116] Aiming at the problems existing in the Kalman filter data assimilation method, the layered Bayesian network algorithm has excellent algorithm mechanism and advantages. In data assimilation, the layered Bayesian network algorithm is a more efficient and accurate method. Compared with the traditional Kalman filter series algorithms and variational algorithms, the layered Bayesian network algorithm has the advantages of not being restricted by the assumptions of state linear change and error Gaussian distribution, and also has the advantages of Bayesian network and layered modeling theory, which are mainly manifested in the following four aspects.

[0117] (1) The layered modeling theory disassembles the data assimilation problem step by step, uses conditional probability to represent the spatial dependence relationship of state variables, gets rid of the limitation of the spatial independence requirement, and disassembles the complex problem into multiple simple problems. At the same time, in the Bayesian network, the parameters representing the spatial dependence relationship can also change with time. Therefore, the layered Bayesian network has great application potential in spatio-temporal analysis.

[0118] (2) Traditional data assimilation algorithms (such as the Kalman filter algorithm) can only estimate the mean and variance of state variables, while the layered Bayesian network can obtain the posterior probability distribution of the target state variables and parameters through Monte Carlo method sampling, and can more accurately describe the law of the nonlinear system changing with time.

[0119] (3) The layered Bayesian network can process data from different sources and with different resolutions, and does not need to force the change of data resolution through resampling.

[0120] (4) In the hierarchical Bayesian network, the complex problem of solving the posterior probability is transformed into a series of simple posterior probability solutions, which can be easily achieved through the Monte Carlo sampling method.

[0121] Under the framework of the hierarchical Bayesian theory, data assimilation is split into three layers: data, process, and parameters. Data includes in-situ observation data, remote sensing observation data, and land surface process model simulation data. The process represents the spatio-temporal distribution and variation of the parameters to be assimilated, and the parameters include all parameters in data acquisition, process models, and the assimilation process. The hierarchical Bayesian theory defines data, process, and parameters as three kinds of random variables and establishes conditional probability distribution models respectively, such as formulas (19)-(21), and transforms the data assimilation problem into inferring the posterior probability distributions of the process and parameters under the condition of existing data, such as formula (18).

[0122] p(process, parameter|data) ∝ (18).

[0123] (The first layer) p(data|process, parameter) (19).

[0124] (The second layer) p(process|parameter) (20).

[0125] (The third layer) p(parameter) (21).

[0126] In the formula, p() represents the probability distribution; p(a|b) represents the conditional probability distribution of a under the condition of known b. The first layer is the data model p(data|process, parameter), the second layer is the process model p(process|parameter), and the third layer is the parameter model p(parameter). Only by defining the above three models can the posterior probability be inferred. The data model, process model, and hierarchical model can be further split level by level. Therefore, in the hierarchical Bayesian method, complex models can be defined using simple conditional probabilities. Since the hierarchical Bayesian theory defines data, process, and parameters as random variables, it can infer the posterior probability distribution of any variable, including unobserved processes and parameters.

[0127] The advantages exhibited by the data model are as follows:

[0128] (1) The complex characteristics exhibited by the data X are determined by the corresponding process Y. The definition method of the conditional probability p(X|Y,θ D ) avoids considering the characteristics of the data X itself, and this definition method greatly simplifies the definition of the data model.

[0129] (2) The greatest advantage of the data model is that it models multi-source data separately, making the hierarchical Bayesian network algorithm have good applicability to multi-source data and scale differences in data assimilation.

[0130] (3) p(X|Y,θ D) The defined data condition depends on the corresponding process Y. When there is multi-source data, it is assumed that the data are conditionally independent of each other. That is, the requirement for the mutual independence of the observed data is relaxed to conditional independence, and this assumption is more reasonable.

[0131] (4) When the input data are multi-source data with different resolutions, the layered Bayesian network establishes data models for each sub-data respectively. The conditional dependence of each sub-data corresponds to the true process Y at the corresponding scale. i and parameters Each scale can be reflected in the process model. Therefore, the layered Bayesian network has certain advantages in solving scale differences.

[0132] The advantages shown by the process model are as follows:

[0133] When there is multi-source data with different platforms and different resolutions, data models that their conditions depend on the corresponding true processes are established for each data. At this time, the task of the process model is to complete the process model of process I corresponding to each scale. The establishment of the process model has great flexibility. In practical applications, it can be selected according to specific problems whether to reflect the non-stationarity, anisotropy of the state quantity in space and time, and the separability of the spatial and temporal distributions and changes, etc.

[0134] Embodiment 2

[0135] In order to execute the method corresponding to the above Embodiment 1 to achieve the corresponding functions and technical effects, a total electron content prediction system for the ionosphere is provided below, including:

[0136] A data acquisition module for acquiring multi-source observation data at time t of the site to be predicted; the observation data is the total electron content of the ionosphere; the multi-source includes the Global Navigation Satellite System, ionosonde, Jason satellite, and incoherent scatter radar.

[0137] A prediction module for predicting the true value of the total electron content of the ionosphere at time t of the site to be predicted according to the multi-source observation data at time t of the site to be predicted by using the total electron content prediction model of the ionosphere; wherein, the total electron content prediction model of the ionosphere is obtained by training a layered Bayesian network with a training data set; the training data set includes the multi-source observation data of the training observation site and the output data of the ionospheric physical model; the observation data is the observed value of the total electron content of the ionosphere; the layered Bayesian network includes a data model, a process model, and a parameter model.

[0138] Embodiment 3

[0139] The present invention provides an electronic device, comprising: a memory and a processor, where the memory is used to store a computer program, and the processor runs the computer program to enable the electronic device to execute the total electron content prediction method of Embodiment 1.

[0140] Embodiment 4

[0141] The present invention provides a computer-readable storage medium storing a computer program, and when the computer program is executed by a processor, the total electron content prediction method of Embodiment 1 is implemented.

[0142] In this specification, the various embodiments are described in a progressive manner. The key point of each embodiment is to illustrate the differences from other embodiments. For the same or similar parts among the various embodiments, reference can be made to each other. For the system disclosed in the embodiments, since it corresponds to the method disclosed in the embodiments, the description is relatively simple, and reference can be made to the description in the method part for the relevant parts.

[0143] In this article, specific examples are used to elaborate on the principle and implementation manner of the present invention. The description of the above embodiments is only used to help understand the method and its core idea of the present invention; at the same time, for those of ordinary skill in the art, according to the idea of the present invention, there will be changes in the specific implementation manner and application scope. In summary, the content of this specification should not be construed as a limitation on the present invention.

Claims

1. A method for predicting the total electron content of the ionosphere, characterized in that, Including: Obtain multi-source observation data of the site to be predicted at time t; the observation data is the total electron content of the ionosphere; the multi-source includes the Global Navigation Satellite System, ionosonde, Jason satellite, and incoherent scatter radar; According to the multi-source observation data of the site to be predicted at time t, use the total electron content prediction model of the ionosphere to predict the true value of the total electron content of the ionosphere at time t of the site to be predicted; wherein, the total electron content prediction model of the ionosphere is obtained by training a layered Bayesian network using a training data set; the training data set includes multi-source observation data of the training observation site and output data of the ionospheric physical model; the observation data is the observed value of the total electron content of the ionosphere; the layered Bayesian network includes a data model, a process model, and a parameter model; The data model is: Z t = O t + ε t ; where Z t is the multi-source observation data of all training observation stations at time t; O t is the true value of the total electron content of the ionosphere at all training observation stations at time t, and ε t is the observation error term of all training observation stations at time t; The process model is: O t = ξ + ρO t-1 + (β0 + β S )X t + η t ; where ξ is the trend of the total electron content distribution in the observation area; ρO t-1 represents the influence of the total ionospheric electron content at time t - 1 on the total ionospheric electron content at time t; O t-1 is the total ionospheric electron content of all training observation sites at time t - 1; X t is the output data of the ionospheric physical model; β0 is a constant that does not change with time and space; β S is a variable that changes with space; η t is the residual term; The parameter model only defines the prior probability distributions of five parameters; among them, the trend ξ of the total electron content distribution in the ionosphere within the observation area is analyzed by an autoregressive moving average model based on the site data, and the variance-like parameter obeys the IG distribution, where 0 < ρ < 1.

2. The total electron content prediction method of the ionosphere according to claim 1, characterized in that Training the layered Bayesian network using the training data set specifically includes: Performing missing data processing on the multi-source observation data of any one of the training observation sites using a distance cross matrix to obtain multi-source continuous observation data; Using the multi-source continuous observation data and the output data of the ionospheric physical model as the input of the current layered Bayesian network, determine the true value of the total electron content of the ionosphere of the training observation site; Using mean square error verification, determine the mean square error between the true value of the total electron content of the ionosphere of the training observation site and the multi-source observation data of the training observation site; Judge whether the maximum number of iterations is reached; If not, adjust the parameters of the current layered Bayesian network and return to the step of performing missing data processing on the multi-source observation data of any one of the training observation sites using the distance cross matrix to obtain multi-source continuous observation data; If so, use the current layered Bayesian network corresponding to the minimum mean square error as the total electron content prediction model of the ionosphere.

3. The total electron content prediction method of the ionosphere according to claim 1, characterized in that The determination process of the output data of the ionospheric physical model specifically includes: Obtain the geomagnetic index and solar activity index of the training observation site; Using the geomagnetic index and the solar activity index as the input of the ionospheric physical model, determine the output data of the ionospheric physical model; the output data is the continuous value of the total electron content of the ionosphere.

4. An ionospheric total electron content prediction system, characterized in that, The total electron content prediction system is used to implement the total electron content prediction method according to any one of claims 1-3; the total electron content prediction system includes: A data acquisition module, configured to obtain multi-source observation data of the site to be predicted at time t; the observation data is the total electron content of the ionosphere; the multi-source includes the Global Navigation Satellite System, ionosonde, Jason satellite, and incoherent scatter radar; A prediction module, configured to predict the true value of the total electron content of the ionosphere at time t of the to-be-predicted site according to the multi-source observation data of the to-be-predicted site at time t by using an ionospheric total electron content prediction model; wherein, the ionospheric total electron content prediction model is obtained by training a layered Bayesian network by using a training data set; the training data set includes multi-source observation data of training observation sites and output data of an ionospheric physical model; the observation data is the observed value of the total electron content of the ionosphere; the layered Bayesian network includes a data model, a process model, and a parameter model.

5. An electronic device, characterized in that, Comprising: A memory and a processor, the memory is used for storing a computer program, and the processor runs the computer program to enable the electronic device to execute the ionospheric total electron content prediction method according to any one of claims 1-3.

6. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a computer program, and when the computer program is executed by a processor, it implements the ionospheric total electron content prediction method according to any one of claims 1-3.

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