A sky-wave over-the-horizon radar coordinate registration method based on reference source assistance

Abstract

The application relates to a sky-wave over-the-horizon radar coordinate registration method based on a reference source auxiliary, which comprises the following steps: firstly, acquiring prior information of ionospheric activity parameters in an estimated ionospheric region and reference source data; secondly, constructing a posterior distribution of the ionospheric activity parameters in the estimated ionospheric region under a Bayesian framework based on the prior information of the ionospheric activity parameters in the estimated ionospheric region and the reference source data; thirdly, solving a moment estimation value of the posterior distribution of the ionospheric activity parameters in the estimated ionospheric region based on a Markov chain, Gibbs sampling and importance sampling; fourthly, substituting the moment estimation value of the posterior distribution of the ionospheric activity parameters in the estimated ionospheric region into an international reference ionospheric model to obtain a posterior ionosphere; and finally, calculating an electromagnetic wave propagation path in the posterior ionosphere by using a three-dimensional ray tracing method to obtain a coordinate registration result of a to-be-positioned target. The application can significantly improve the coordinate registration precision and the sky-wave over-the-horizon radar target positioning precision.

Description

Technical Field

[0001] This invention relates to the field of over-the-horizon radar data processing technology, and in particular to a skywave over-the-horizon radar coordinate registration method based on reference source assistance. Background Technology

[0002] As part of the environmental perception system, modern military medium- and long-range early warning systems play an increasingly important role. Skywave over-the-horizon radar (OTHR) (or simply skywave radar) breaks through the radar line-of-sight limitation by using the ionospheric reflection effect, enabling long-range detection of high-value targets at a distance. It is the most economical and cost-effective long-range early warning method and plays an important role in long-range early warning systems.

[0003] In skywave radar target tracking and localization, what is needed is the target's position in the geodetic coordinate system (such as latitude and longitude), while the measurements received by skywave radar are information in the radar coordinate system (such as radial / slant range and azimuth). Therefore, coordinate registration (CR) needs to be performed in skywave radar target tracking and localization, which is to transform the target position information between the two coordinate systems.

[0004] OTHR position error analysis shows that errors in the ionospheric model and its parameters lead to a decrease in the accuracy of skywave radar target localization. Summary of the Invention

[0005] Therefore, it is necessary to provide a reference source-assisted coordinate registration method for skywave over-the-horizon radar to address the aforementioned technical problems, which can improve the accuracy of target positioning by skywave radar.

[0006] This invention provides a reference source-assisted skywave over-the-horizon radar coordinate registration method, comprising:

[0007] Obtain prior information and reference source data for ionospheric activity parameters in the region to be estimated;

[0008] Based on prior information and reference source data of ionospheric activity parameters in the region to be estimated, the posterior distribution of ionospheric activity parameters in the region to be estimated is constructed within a Bayesian framework.

[0009] The posterior distribution of ionospheric activity parameters in the region to be estimated is as follows:

[0010]

[0011] In the formula, y=(y 1 ,…,y l ), z = (z 1 ,…,z l) represent the radar measurement vector and ground range vector of the reference source, respectively; ζ represents the ionospheric activity parameters in the ionospheric region to be estimated; l represents the number of reference sources; β = (β 1 ,…,β l ) represents the elevation angle information of each ray, ψ(ζ,β) l ) and φ(ζ,β l ) represents the forward model, and π(ζ,β) represents the joint prior distribution of (ζ,β);

[0012] The moment estimates of the posterior distribution of ionospheric activity parameters within the ionospheric region to be estimated are obtained based on Markov chains, Gibbs sampling, and importance sampling.

[0013] The moment estimates of the posterior distribution of ionospheric activity parameters in the region to be estimated are substituted into the international reference ionospheric model to obtain the posterior ionospheric layer.

[0014] The coordinate registration results of the target to be located are obtained by calculating the electromagnetic wave propagation path in the posterior ionosphere using the three-dimensional ray tracing method.

[0015] In one embodiment, obtaining prior information on ionospheric activity parameters within the region to be estimated includes:

[0016] The ionosphere region to be estimated is gridded;

[0017] By setting the ionospheric parameters on each small grid as random variables, the ionospheric parameters of the region to be estimated are obtained.

[0018]

[0019] In the formula, ζ ij , i = (1,…,n), j = (1,…,m) represent the values ​​of ionospheric activity parameters in the ionospheric region to be estimated at the ij-th longitude and latitude step.

[0020] In one embodiment, constructing the posterior distribution of the ionospheric activity parameters within the region to be estimated, based on prior information and reference source data of the ionospheric activity parameters within the region to be estimated, within a Bayesian framework, includes:

[0021] A probabilistic graphical model of prior information of ionospheric activity parameters in the region to be estimated is established based on Gaussian Markov random fields.

[0022] A radar measurement model of the reference source is established using the three-dimensional ray tracing method based on the reference source data;

[0023] Within a Bayesian framework, the posterior distribution of ionospheric activity parameters within the region to be estimated is constructed based on a probabilistic graphical model of prior information of ionospheric activity parameters within the region to be estimated and a radar measurement model of the reference source.

[0024] In one embodiment, the probabilistic graphical model for establishing prior information on ionospheric activity parameters within the ionospheric region to be estimated, based on a Gaussian Markov random field, includes:

[0025] Make the ionospheric activity parameters in the region to be estimated follow a high-dimensional normal distribution.

[0026]

[0027] In the formula, Q is the precision matrix, η is the potential vector, η = Qμ, and μ is the mean vector;

[0028] The undirected graph G = (V, E) is used to graphically represent the prior information of ionospheric activity parameters in the region to be estimated as a probabilistic graphical model. Here, V = 1, 2, ..., mn represents the set of nodes in the probabilistic graphical model, and E represents the set of edges (i, j) in the probabilistic graphical model, i, j ∈ V and i ≠ j.

[0029] The moment estimates of ionospheric activity parameters within the ionospheric region to be estimated are obtained based on Markov chains, Gibbs sampling, and importance sampling.

[0030] In one embodiment, the moment estimates of the posterior distribution of ionospheric activity parameters within the ionospheric region to be estimated, based on Markov chains, Gibbs sampling, and importance sampling, include:

[0031] Walk through the Markov chain of ionospheric activity parameters in the region to be estimated to obtain the node values ​​of the Markov chain of ionospheric activity parameters in the region to be estimated.

[0032] The moment estimates of the posterior distribution of ionospheric activity parameters are calculated using the node values ​​of a Markov chain of ionospheric activity parameters within the region to be estimated.

[0033] In one embodiment, when walking the Markov chain of ionospheric activity parameters in the region to be estimated, each step of the walk is as follows:

[0034] Gibbs sampling is used to decompose the posterior distribution of ionospheric activity parameters within the region to be estimated, obtaining multiple one-dimensional conditional posterior distributions of the ionospheric activity parameters within the region to be estimated. The conditional posterior distributions of the ionospheric activity parameters within the one-dimensional region to be estimated are as follows:

[0035]

[0036] In the formula, For ζ i The conditional marginal prior distribution of one-dimensional ionospheric parameters is calculated using the message-passing method. For radar measurement models, ζ -i This represents the dimensions other than the i-th dimension. Represents ζ -i For known values Known value The node values ​​obtained from the previous step are obtained;

[0037] Importance sampling is used to estimate the conditional posterior distributions of ionospheric activity parameters within a single-dimensional region of the ionosphere to be estimated. The estimated value of the conditional posterior distribution of each ionospheric activity parameter within this region is obtained as the sampling result. The estimated values ​​of the expectation and variance of the conditional posterior distributions of the ionospheric activity parameters within the region are then obtained.

[0038]

[0039] in, Here, m represents the importance weight, and ζ represents the number of importance samples. i,l l=(1,…,m) is a proposed value for the ionospheric activity parameter in the one-dimensional region of the ionosphere to be estimated;

[0040] By combining the sampling results of the conditional posterior distribution of all ionospheric activity parameters in the one-dimensional ionospheric region to be estimated according to the scanning order of Gibbs sampling, a node value of the Markov chain of ionospheric activity parameters is obtained.

[0041] In one embodiment, importance weights are calculated using an approximate forward model, which is obtained by data fitting from an exact forward model. Specifically, this includes:

[0042] A local approximate model is constructed near the prior information of ionospheric activity parameters in the region to be estimated. The approximate model is a mapping relationship between ionospheric activity parameters in the region to be estimated and radar measurements and ground distance.

[0043] A local approximate model is constructed near the prior information of ionospheric activity parameters in the region to be estimated. The approximate model is a mapping relationship between ionospheric activity parameters in the region to be estimated and radar measurements and ground distance.

[0044] Using the data from the accurate forward model obtained during the importance sampling process, the model parameters in the approximate model can be calculated based on the multimodal data fitting method.

[0045] By comparing the approximation effects of different models, the approximation model with the best approximation effect is used to obtain a large number of ionospheric activity parameters and radar measurement and ground distance data pairs in the ionospheric region to be estimated, and the importance weight of the data pairs is calculated.

[0046] In one embodiment, calculating the moment estimate of the posterior distribution of the ionospheric activity parameters using the node values ​​of a Markov chain of ionospheric activity parameters within the region to be estimated includes:

[0047] Filter the node values ​​of the Markov chain for ionospheric activity parameters in the region to be estimated;

[0048] The node values ​​of the Markov chain for the ionospheric activity parameters in the selected ionospheric region to be estimated are calculated as moment estimates of the ionospheric activity parameters in the selected ionospheric region.

[0049] This invention discloses a skywave over-the-horizon radar coordinate registration method based on a reference source. First, prior information and reference source data of ionospheric activity parameters within the region to be estimated are obtained. Then, based on the prior information and reference source data, a posterior distribution of the ionospheric activity parameters within the region to be estimated is constructed within a Bayesian framework. Next, moment estimates of the posterior distribution of the ionospheric activity parameters within the region to be estimated are obtained based on Markov chains, Gibbs sampling, and importance sampling. Then, these moment estimates are substituted into the international reference ionospheric model to obtain the posterior ionosphere. Finally, a three-dimensional ray tracing method is used to calculate the electromagnetic wave propagation path within the posterior ionosphere to obtain the coordinate registration result of the target to be located. This invention uses prior information on ionospheric activity parameters and reference source data within a Bayesian framework to obtain estimated ionospheric parameters with accuracy closer to actual values ​​through Gibbs sampling and importance sampling. Then, the estimated ionospheric parameters are substituted into the international reference ionospheric model to obtain a posterior ionospheric model with high parameter accuracy. Coordinate registration is then performed in the posterior ionospheric model, which can significantly improve the accuracy of coordinate registration and thus enhance the accuracy of target positioning for skywave over-the-horizon radar. Attached Figure Description

[0050] Figure 1 This is one of the flowcharts of the skywave over-the-horizon radar coordinate registration method based on reference source assistance provided in the embodiments of the present invention;

[0051] Figure 2 This is one of the flowcharts of the skywave over-the-horizon radar coordinate registration method based on reference source assistance provided in the embodiments of the present invention;

[0052] Figure 3 This is a schematic diagram of the ionospheric gridding of the region to be estimated;

[0053] Figure 4 This is one of the flowcharts of the skywave over-the-horizon radar coordinate registration method based on reference source assistance provided in the embodiments of the present invention;

[0054] Figure 5This is a schematic diagram of an undirected graph introduced in an embodiment of the present invention;

[0055] Figure 6 This is one of the flowcharts of the skywave over-the-horizon radar coordinate registration method based on reference source assistance provided in the embodiments of the present invention;

[0056] Figure 7 This is one of the flowcharts of the skywave over-the-horizon radar coordinate registration method based on reference source assistance provided in the embodiments of the present invention;

[0057] Figure 8 This is a schematic diagram of the geographical location of the target to be located in an embodiment of the present invention;

[0058] Figure 9 This is a schematic diagram of the RMSE (Reference Mean Squared Error) for estimating ionospheric parameters in an embodiment of the present invention;

[0059] Figure 10 This is a schematic diagram illustrating coordinate registration in different scenarios according to an embodiment of the present invention. Detailed Implementation

[0060] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0061] In one embodiment, such as Figure 1 As shown, Figure 1 This is one of the flowcharts of the skywave over-the-horizon radar coordinate registration method based on a reference source provided in this embodiment of the invention, including the following steps:

[0062] S101. Obtain prior information and reference source data of ionospheric activity parameters in the region to be estimated.

[0063] It should be noted that ionospheric activity parameters are the controlling parameters of the ionospheric electron concentration profile, and the reference source is a reference target with known geographical location information within the ionospheric region to be estimated. External reference sources may include high-frequency beacons, transponders, terrain features, microwave radar, and position information of flights obtained through ADS-B and ships obtained through AIS within the skywave radar detection area. In this invention, the reference source data includes the radar measurement (group range) vector and ground range vector of the reference source.

[0064] S102. Based on the prior information of the ionospheric activity parameters in the region to be estimated and the reference source data, construct the posterior distribution of the ionospheric activity parameters in the region to be estimated within the Bayesian framework.

[0065] Specifically, the posterior distribution of ionospheric activity parameters in the region to be estimated is as follows:

[0066]

[0067] In the formula, y=(y 1 ,…,y l ), z = (z 1 ,…,z l ) represent the radar measurement vector and ground range vector of the reference source, respectively; ζ represents the ionospheric activity parameters in the ionospheric region to be estimated; l represents the number of reference sources; β = (β 1 ,…,β l ) represents the elevation angle information of each ray, ψ(ζ,β) l ) and φ(ζ,β l ) represents the forward model, and π(ζ,β) represents the joint prior distribution of (ζ,β).

[0068] S103. Based on Markov chains, Gibbs sampling, and importance sampling, solve for the moment estimates of the posterior distribution of ionospheric activity parameters in the region to be estimated.

[0069] S104. Substitute the moment estimates of the posterior distribution of ionospheric activity parameters in the region to be estimated into the international reference ionospheric model to obtain the posterior ionosphere.

[0070] The International Reference Ionospheric Model (IRI) uses a series of ionospheric activity parameters to describe the characteristics of the ionosphere, including: maximum electron density in the F region, F region height, maximum electron density in the E region, E region height, D region height, and electron densities in the F1, F2, E, and D layers. These parameters are derived through modeling and analysis of observational data and may vary across different geographical locations and time periods. Physically, these parameters characterize the key influence of solar activity on ionospheric behavior. Introducing spatiotemporally variable ionospheric activity parameters will make it possible for the IRI model to assimilate real-time ionospheric measurements. Compared to analytical models in traditional methods, the IRI, based on global observational data, better reflects the spatiotemporal variations of the ionosphere. This will benefit the accuracy of ionospheric inference and coordinate registration.

[0071] S105. The coordinate registration result of the target to be located is obtained by calculating the electromagnetic wave propagation path in the posterior ionosphere using the three-dimensional ray tracing method.

[0072] It should be noted that the use of three-dimensional ray tracing for coordinate registration in the ionosphere is well known to those skilled in the art and will not be elaborated upon here.

[0073] This embodiment presents a reference-source-assisted skywave over-the-horizon radar coordinate registration method. It constructs a posterior distribution of ionospheric activity parameters within the region to be estimated using prior information and reference source data. Then, the moment estimates of this posterior distribution are substituted into the international reference ionospheric model to obtain the posterior ionosphere. Compared to the prior ionosphere, the posterior ionosphere more closely resembles the real ionosphere, resulting in higher accuracy during coordinate registration.

[0074] In one embodiment, such as Figure 2 As shown, Figure 2 This is one of the flowcharts illustrating a reference-source-assisted skywave over-the-horizon radar coordinate registration method provided in this embodiment of the invention. This embodiment relates to an optional implementation of how to obtain prior information on ionospheric activity parameters within the region to be estimated. Based on the above embodiment, obtaining prior information on ionospheric activity parameters within the region to be estimated includes:

[0075] S201. Mesh the ionosphere of the region to be estimated. In the vast surveillance area of ​​skywave radar, the ionospheric region of reflected radar signals is also large, and the behavior of the ionosphere is relatively complex. Therefore, we mesh the ionosphere to facilitate calculation and modeling.

[0076] Specifically, such as Figure 3 As shown, Figure 3 This is a schematic diagram of the ionospheric grid of the region to be estimated, which divides the selected ionospheric area into several small checkerboard-shaped regions.

[0077] S202. Set the ionospheric parameters on each small grid as random variables to obtain the ionospheric parameters of the region to be estimated.

[0078]

[0079] In the formula, ζ ij Where i = (1,…,n) and j = (1,…,m) represent the values ​​of ionospheric activity parameters in the ionospheric region to be estimated at the i-th and j-th longitude and latitude steps.

[0080] In one embodiment, such as Figure 4 As shown, Figure 4 This is one of the flowcharts illustrating a reference-source-assisted skywave over-the-horizon radar coordinate registration method provided in this embodiment of the invention. This embodiment relates to an optional implementation of how to construct the posterior distribution of ionospheric activity parameters within the ionospheric region to be estimated, based on prior information of ionospheric activity parameters within the region to be estimated and reference source data, within a Bayesian framework. Based on the above embodiment, S102 includes the following steps:

[0081] S401. A probabilistic graphical model is established based on Gaussian Markov random fields to obtain prior information on ionospheric activity parameters within the region to be estimated. Within the framework of the probabilistic graphical model, for high-dimensional joint Gaussian distributions, we use a message-passing algorithm to solve for the marginal distributions of random variables.

[0082] Probabilistic graphical models are powerful mathematical tools for describing large-scale, high-dimensional systems. They can effectively describe the relationships between variables and clearly express the structure of the system. As a combination of graph theory and probability theory, probabilistic graphical models provide a rich framework for large-scale multivariate statistical models.

[0083] S402. Based on the reference source data, establish a radar measurement model of the reference source using the three-dimensional ray tracing method.

[0084] Ray tracing (RT) is a digital technique used to determine the path of high-frequency (HF) radio waves in anisotropic and inhomogeneous media that differ from a vacuum. Given information such as the ionospheric electron concentration profile, transmitter location, operating frequency, and elevation angle, the propagation path of radar waves in the ionosphere can be approximated using numerical methods. In this invention, we model radar measurements based on ray tracing technology.

[0085] External reference sources may include high-frequency beacons, transponders, terrain features, microwave radar, and position information of flights obtained via ADS-B and ships obtained via AIS within the skywave radar detection area. Assuming that the distance to a reference source existing within the skywave radar detection area can be written as z...

[0086] z=φ(ζ,β)+u (6)

[0087] Where ζ represents the ionospheric activity parameter, β represents the ray elevation angle information, and u represents the error in the external source location information. It is assumed that this error term is also zero-mean Gaussian white noise, and its covariance data can be given by historical data. For some high-quality reference source information such as ADS-B, the error is very small and can be ignored; in this case, u does not need to be considered.

[0088] Similarly, for a reference source existing within the detection area of ​​a skywave radar, its radar measurement (group range) in the radar coordinate system can be written as:

[0089] y=ψ(ζ,β)+v (7)

[0090] Where ζ represents the ionospheric activity parameter, β represents the ray elevation angle information, and v represents the measurement error generated by the radar when observing the target. We assume that this error term is zero-mean Gaussian white noise, and its covariance matrix can be given by historical data.

[0091] The functions φ(·) and ψ(·) mentioned above represent the forward model, respectively, and represent the functional mapping relationship between the target (or reference source) group (ground) range and the radar emission elevation angle and ionospheric activity parameters. The forward model contains two models: one is the mapping from ionospheric activity parameters to the ionospheric electron concentration profile, which corresponds to the international reference ionospheric model and Gaussian Markov random field modeling; the other is the mapping from the ionospheric electron concentration profile and transmitter operating parameters to the propagation path of radio waves in the ionosphere, which corresponds to the numerical ray tracing model.

[0092] Based on the above model, further, we assume that the reference sources l1, l2, ..., l within the radar detection range are... n Assuming that radar measurements and ground distances are independent of each other, the radar measurement model of this invention, i.e., the likelihood function of the measurement, is:

[0093]

[0094] Where y and z represent the radar measurement (group range) and ground range vectors of the reference sources, respectively. ζ is the ionospheric activity parameter, β... l This provides elevation angle information for each ray. φ(ζ,β) l )φ(ζ,β l ) represents the forward model.

[0095] S403. Under the Bayesian framework, construct the posterior distribution of the ionospheric activity parameters in the region to be estimated based on the probabilistic graphical model of the prior information of the ionospheric activity parameters in the region to be estimated and the radar measurement model of the reference source.

[0096] Specifically, this invention formulates the inference problem of ionospheric parameters as an inference problem under a Bayesian inverse framework. Combining the prior distribution of ionospheric activity parameters modeled by Gaussian Markov random fields as described above, the posterior distribution of ionospheric activity parameters is written as follows.

[0097]

[0098] Furthermore, assuming that ionospheric activity parameters are independent of radar elevation information, then we have:

[0099] π(ζ,β)=π(ζ)π(β) (9)

[0100] In this invention, we focus on the inference of ionospheric activity parameters. Therefore, we assume that the radar elevation information is known. Thus, in the following description, β is removed from the posterior distribution of ionospheric activity parameters.

[0101] Secondly, assuming the radar ray elevation angle is a known quantity, the posterior distribution of the ionospheric parameters can be written as:

[0102]

[0103] In one embodiment, the ionospheric activity parameters within the region to be estimated are made to follow a high-dimensional normal distribution.

[0104]

[0105] In the formula, Q is the precision matrix, η is the potential vector, η = Qμ, and μ is the mean vector.

[0106] The undirected graph G = (V, E) is used to graphically represent the prior information of ionospheric activity parameters in the region to be estimated as a probabilistic graphical model. Here, V = 1, 2, ..., mn represents the set of nodes in the probabilistic graphical model, and E represents the set of edges (i, j) in the probabilistic graphical model, i, j ∈ V and i ≠ j.

[0107] Specifically, the information matrix can reflect the conditional independence between nodes in a probabilistic graphical model. Furthermore, considering the Markov property between nodes—that is, a node is only correlated with its neighboring nodes, while conditionally independent with more distant nodes—[e.g., ...] Figure 5 As shown, Figure 5 This is a schematic diagram of the undirected graph introduced in this embodiment of the invention. The probabilistic graphical model of the prior distribution of ionospheric activity parameters is also chessboard-shaped, resulting in a highly sparse information matrix. The parameters in the Gaussian Markov random field model, namely the mean vector, covariance matrix, information matrix, and potential vector, can be learned from historical data.

[0108] In our probabilistic graph, the Gaussian message passed between nodes is defined as follows:

[0109]

[0110] in,

[0111]

[0112] in, It refers to the neighborhood of node i, with the index... This refers to moving node i from Excluded from the middle. The edge distribution of a node is obtained by combining all information of its neighboring nodes and the local information converged iteratively, as shown in the following equation.

[0113]

[0114] Using a message passing mechanism, we can easily obtain the one-dimensional conditional distribution of ionospheric parameters from the probabilistic graphical model.

[0115] The moment estimates of ionospheric activity parameters within the ionospheric region to be estimated are obtained based on Markov chains, Gibbs sampling, and importance sampling.

[0116] In one embodiment, such as Figure 6 As shown, Figure 6 This is one of the flowcharts illustrating a reference-source-assisted skywave over-the-horizon radar coordinate registration method provided in this embodiment of the invention. This embodiment involves an optional implementation of how to solve for the moment estimates of the posterior distribution of ionospheric activity parameters within the ionospheric region to be estimated based on Markov chains, Gibbs sampling, and importance sampling. Based on the above embodiment, S401 includes the following steps:

[0117] S601. Walk the Markov chain of the ionospheric activity parameters in the region to be estimated to obtain the node values ​​of the Markov chain of the ionospheric activity parameters in the region to be estimated.

[0118] S602. Calculate the moment estimates of the posterior distribution of the ionospheric activity parameters using the node values ​​of the Markov chain of the ionospheric activity parameters in the region to be estimated.

[0119] In an optional embodiment, when walking the Markov chain of ionospheric activity parameters in the region to be estimated, each step of the walk is as follows:

[0120] Gibbs sampling is used to decompose the posterior distribution of ionospheric activity parameters within the region to be estimated, obtaining multiple one-dimensional conditional posterior distributions of the ionospheric activity parameters within the region to be estimated. The conditional posterior distributions of the ionospheric activity parameters within the one-dimensional region to be estimated are as follows:

[0121]

[0122] In the formula, For ζ i The prior distribution, For radar measurement models, ζ -i This represents the dimensions other than the i-th dimension. Represents ζ -i For known values Known value The node value obtained from the previous step is obtained.

[0123] Due to the complexity of the skywave radar detection process, it is difficult to directly solve for the posterior probability density. This invention is based on the Gibbs sampling algorithm and uses numerical sampling to obtain the posterior estimate of ionospheric activity parameters.

[0124] By sampling the conditional distribution of high-dimensional random variables using Gibbs sampling, we can avoid the performance degradation, waste of samples, and slow convergence speed of the classic MH algorithm when dealing with high-dimensional problems.

[0125] Considering the complexity of the conditional posterior distribution of ionospheric activity parameters within the ionospheric region to be estimated, making it difficult to formulate a compact expression, but given that all terms are Gaussian distributed, the importance sampling method can be used to obtain an estimate of the one-dimensional posterior distribution. Importance sampling is an important sampling strategy in Monte Carlo integration. When the distribution of a random variable is very complex and it is difficult to obtain the expected value of the random variable, a simpler and easier-to-sample distribution can be introduced to replace the original distribution for indirect sampling, and different weights can be assigned to the indirectly sampled samples. The expected value of the original distribution can then be obtained using Monte Carlo integration. The introduced distribution function is called the importance distribution, and the weights of the samples are called importance weights.

[0126]

[0127] In the above formula, the prior distribution of the selected parameters in this invention is... As an importance distribution, it is easy to sample because it originates from our assumption (in fact, it is a one-dimensional normal distribution). Sampling from it yields proposal samples; the number of proposal samples is called the importance sampling count. The normalized likelihood function is calculated as the importance weight of the samples, resulting in the current dimension ζ. i The point estimate is used as the sampling result.

[0128] Distribution of importance After m samplings, the estimated values ​​of the conditional posterior distribution expectation and variance of the ionospheric activity parameters in the region to be estimated are as follows:

[0129]

[0130] in, The importance weights are normalized, where m is the number of importance samples, and ζ is the number of samples. i,l l = (1,…,m) is a proposed value for the ionospheric activity parameter in the one-dimensional region of the ionosphere to be estimated.

[0131] Specifically, when the ionospheric parameters ζ are arranged into a Markov chain χ, during state transitions, for the ionospheric parameters ζ of the (k+1)th step state... k+1 Each dimension ζ in i All use the previous state ζ k In As ζ -i One implementation is to calculate the distribution for each dimension according to equation (15) and obtain samples, thus obtaining the complete Markov chain state transition ζ. k+1As can be seen from the properties of Gibbs sampling, the ζ obtained in this way... k+1 Its acceptance rate is 1. At the same time, the samples obtained in this way follow a stationary distribution of a Markov chain, that is, the posterior distribution of ionospheric activity parameters.

[0132] By combining the sampling results of the conditional posterior distribution of all ionospheric activity parameters in the one-dimensional ionospheric region to be estimated according to the scanning order of Gibbs sampling, a node value of the Markov chain of ionospheric activity parameters is obtained.

[0133] In one embodiment, importance weights are obtained through an approximate forward model, which is obtained by multimodal fitting of data from the precise forward model. Specifically, this includes: constructing a local approximate model near the prior information of ionospheric activity parameters within the region to be estimated; the approximate model representing the mapping relationship between ionospheric activity parameters and radar measurements and ground distances within the region to be estimated; using data from the precise forward model obtained during importance sampling, the model parameters in the approximate model can be calculated based on a multimodal data fitting method; comparing the approximation effects of different models, and using the approximate model with the best approximation effect to obtain a large number of ionospheric activity parameter and radar measurement / ground distance data pairs within the region to be estimated, and calculating the importance weights of the data pairs.

[0134] Specifically, the multimodal fitting in this embodiment can be, but is not limited to, least squares fitting.

[0135] In this embodiment, the computation of the complex forward model constitutes the main part of the computational overhead. Specifically, during Monte Carlo sampling, each importance sampling requires calling the international reference ionospheric model to calculate the ionospheric electron concentration profile and calling the ray tracing model to calculate the ray propagation path for each reference source related to the current sampling node location. Since the forward model is a highly complex function mapping, its computational overhead increases significantly with the number of importance samplings, leading to excessive computational load and limiting the algorithm's practical application. Therefore, to reduce the computational load, we need to consider bypassing this mapping and directly establishing the functional relationship between the ionospheric activity parameter ζ and the measurement (y,z) of the reference source. This invention draws on the basic idea of ​​system identification, treating the complex forward model as a black box and calculating an approximate model of the forward model through its inputs and outputs. This approximate model has a simple functional expression and, within a local range, has outputs similar to the exact forward model. This allows for the easy acquisition of a large number of approximate samples. These approximate samples are then used to calculate the estimated values ​​of the ionospheric parameters.

[0136] Specifically, for ζi ∈ζ and a related reference source r, calculating their posterior distribution requires calling the forward model ψ(·), φ(·). During importance sampling, m pairs of input-output (ζ) pairs of the forward model are obtained. l ,y l ,z l ), l=(1…m), where the independent variable ζ l For the sample taken from the importance distribution, that is, the prior distribution of ionospheric activity parameters, the dependent variable y l ,z l Let r be the group and ground distances at this point. The forward model ψ(·) for calculating the group distance y is obtained, and the ground distance is calculated similarly.

[0137] The first step is to define the fitting model. To do this, we can first observe the basic characteristics of the output data from the accurate forward model and design the required model accordingly. Within a larger scale range of ionospheric activity parameters (80-115), the radar measurement data (group distance) from the reference source shows a negative correlation with the ionospheric parameters. Simultaneously, some noise factors cause the curve to be uneven. At smaller scales, this noise is particularly pronounced, especially near the true values ​​of the set ionospheric parameters. This is presumably due to numerical errors in the calculations of the high-performance ray tracing model. This error is partly due to the relatively large latitude and longitude step size during mesh modeling, which weakens the smoothness of the ionospheric electron concentration profile. However, further refining the mesh model would introduce additional computational costs. On the other hand, this error may be due to unavoidable approximation errors when numerically calculating complex partial differential equations. Due to the limitation on the number of importance samplings, it is impossible to obtain a large amount of data for calculating the approximate forward model, making it neither possible nor necessary to design a complex approximate model to accurately fit this noisy negative correlation. In the actual sampling approximation process, the influence of noise was coincidentally ignored because only a small number of data points were used. This makes the local input-output relationship of the approximate forward model often smoother than that of the exact forward model, which brings additional benefits to sampling accuracy.

[0138] Regarding the selection of fitting models, in order to compensate for the large error of a single model, this invention sets up multiple models for fitting.

[0139] After obtaining the approximate forward model, a large number of model input-output pairs can be easily obtained. Specifically, p samples are then taken from the importance distribution. The sampling results are substituted into the approximate forward model to obtain the corresponding group distance, thus obtaining approximate forward model input-output pairs. These data pairs are then compared with the input of the precise forward model to calculate approximate values ​​of ionospheric activity parameters in the current dimension of the ionospheric region to be estimated.

[0140] In one embodiment, such as Figure 7 As shown, Figure 7 This is one of the flowcharts illustrating a reference-source-assisted skywave over-the-horizon radar coordinate registration method provided in this embodiment of the invention. This embodiment involves an optional implementation of how to calculate the moment estimate of the posterior distribution of ionospheric activity parameters using the node values ​​of a Markov chain of ionospheric activity parameters within the region to be estimated. Based on the above embodiment, S602 includes the following steps:

[0141] S701. Filter the node values ​​of the Markov chain for the ionospheric activity parameters in the region to be estimated.

[0142] S702. Calculate the node values ​​of the Markov chain of the ionospheric activity parameters in the filtered region to be estimated as moment estimates of the ionospheric activity parameters in the region to be estimated.

[0143] Specifically, the screening process involves obtaining a Markov chain, discarding the initial portion of the Markov chain, and sparsifying the samples. After the Markov chain passes through the burning phase and enters a stationary distribution, the walking process continues until a sufficient number of samples that conform to the stationary distribution of the Markov chain, i.e., the posterior distribution of the ionospheric parameters, are collected. Samples from before the burning phase are discarded, and the remaining samples are sparsified to obtain independent and identically distributed (IoD) samples. Averaging these IoD samples yields the moment estimate of the posterior distribution of the ionospheric activity parameters.

[0144] In one specific embodiment, a rectangular region extending from 33°N to 35°N and 15°E to 19°E was selected within the radar's surveillance area to estimate ionospheric activity parameters. The gridding modeling step size was 2 degrees. Within this range, several reference sources with precisely known geographical locations were placed, as detailed below. Figure 8 As shown, Figure 8 This is a schematic diagram of the geographical locations in this embodiment of the invention. Five targets of interest (targets to be located) are deployed simultaneously to verify the performance of the method of this invention; their geographical locations are shown in Table 1. The radar transmitter is located at (15°E, 30°N) and operates at a frequency of 12MHz. For the ionospheric activity index, its true value is set to 100, and the mean, autocovariance, and crosscovariance of the prior distribution are 90, 30, and 10, respectively. In this process, the radius of the Earth is assumed to be 6371 kilometers.

[0145] Table 1. Geographical locations of the targets to be located

[0146]

[0147] To demonstrate the effectiveness of the method of this invention, and to explore the impact of reference source information density and importance sampling number on its performance, this invention considers three cases:

[0148] Scenario 1: Dense reference sources are arranged in the sampling area, with a reference source orientation angle step of 1° and an importance sampling number of 10 times.

[0149] Scenario 2: The reference source arrangement is the same as in Scenario 1, but the importance sampling count is set to 5, generating 5 approximate samples from the fitted model. The fitted model used here is as follows:

[0150] Linear model: y = ax + b

[0151] Quadratic form model: y = ax 2 +bx+c

[0152] Gaussian model: y = aexp(-((xb) / c) 2 )

[0153] Where a, b, and c are the parameters used in the model.

[0154] Scenario 3: The reference source is arranged in the same way as in Scenario 1, the importance sampling number is set to 5, and no approximate model is generated.

[0155] Scenario 4: Sparse reference sources are arranged in the sampling area. The reference source direction angle step is 5°, the importance sampling number is 5, and 5 approximate samples are generated at the same time. The generation method is the same as in Scenario 2.

[0156] For each simulation scenario, this paper performs twenty Monte Carlo simulations. During data processing, the results of the twenty Monte Carlo simulations are first averaged. Each Monte Carlo simulation involves 75 walks of the Markov chain. The RMSE (root mean square error) of the ionospheric parameter estimates is as follows: Figure 9 As shown, Figure 9 This is a schematic diagram of the RMSE of the estimated ionospheric parameters in an embodiment of the present invention, where the horizontal axis represents the number of samples and the vertical axis represents the estimated RMSE.

[0157] The results show that in all four simulation scenarios, the cumulative mean square error decreases significantly with the movement of the Markov chain. This indicates that compared to estimation using a prior distribution, the ionospheric activity parameters are closer to the simulated true values, and the accuracy of ionospheric parameter inference is significantly improved. Table 2 provides the specific numerical values ​​of this improvement, where the improvement rate is the rate of increase in the mean error relative to the prior values ​​of the ionospheric parameters.

[0158] Table 2. RMSE and improvement rate of posterior samples relative to prior samples in various scenarios.

[0159]

[0160] As shown in Table 2, comparing scenarios one and three, we can see the impact of the number of importance samples on the algorithm's performance, particularly for IG. 12 The estimation accuracy decreased by approximately 20%, and the algorithm converged slowly. Compared to Scenario 3, Scenario 2 involved the generation of additional approximate samples, resulting in a relatively better cumulative improvement in ionospheric parameter inference, increasing from 65% to 79%. This demonstrates that the approximate forward model of this invention, which uses data from the accurate forward model for multimodal fitting calculations, can improve the estimation accuracy of ionospheric activity parameters. Statistical analysis on the simulation platform showed that achieving one Markov chain walk in Scenario 1 took ten minutes, while Scenario 2 and Scenario 3 showed no significant difference in computation time, requiring approximately six minutes for one walk. This indicates that the approximate forward model of this invention, which uses data from the accurate forward model for multimodal fitting calculations, adds almost no additional computation time.

[0161] Compared to Scenario 4, Scenario 2 has a lower reference source density (one-fifth that of Scenario 4). It can be seen that within the effective sampling area, a lower reference source density also degrades performance, with the cumulative improvement rate of ionospheric parameter inference decreasing by approximately 12%. The same conclusion can be seen in the coordinate registration results.

[0162] like Figure 10 As shown, Figure 10 This is a schematic diagram illustrating coordinate registration in different scenarios according to an embodiment of the present invention. The hollow dots in the diagram represent the true and prior values ​​of the target of interest, respectively. STEP represents the number of walks, and RMSE represents the root mean square error. Asterisks of different gray levels represent the coordinate registration results of the target in different scenarios. It can be seen that, compared to the prior value, the posterior value of the target in all four simulation scenarios approaches the true value, indicating that the coordinate registration accuracy of the skywave over-the-horizon radar coordinate registration method based on reference source assistance in this invention is improved. The improvement results are shown in Table 3. From Table 3, scenario one shows the best coordinate registration effect, with an average improvement rate of approximately 96% in estimated error. Scenario three has fewer importance sampling times, resulting in an average improvement rate of 42%. Scenario two uses an additional approximation model to generate samples, and its average improvement rate is slightly higher than scenario three, at approximately 50%, demonstrating the effectiveness of the approximation calculation method. This improvement is particularly significant for targets 1 and 2. Compared to scenario two, scenario four has a sparser distribution of reference sources, with an average improvement rate of only about 28%. In summary, we can draw the same conclusions as in the analysis of the effectiveness of ionospheric activity parameter estimation.

[0163] Table 3 Data on coordinate registration improvement

[0164]

[0165] It should be understood that although the steps in the flowcharts of the embodiments described above are shown sequentially according to the arrows, these steps are not necessarily executed in the order indicated by the arrows. Unless explicitly stated herein, there is no strict order restriction on the execution of these steps, and they can be executed in other orders. Moreover, at least some steps in the flowcharts of the embodiments described above may include multiple steps or multiple stages. These steps or stages are not necessarily completed at the same time, but can be executed at different times. The execution order of these steps or stages is not necessarily sequential, but can be performed alternately or in turn with other steps or at least some of the steps or stages of other steps.

[0166] The embodiments described above are merely examples of several implementations of the present invention, and while the descriptions are relatively specific and detailed, they should not be construed as limiting the scope of the present invention. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of the present invention, and these modifications and improvements all fall within the scope of protection of the present invention.

Claims

1. A skywave over-the-horizon radar coordinate registration method based on a reference source, characterized in that, include: Obtain prior information and reference source data for ionospheric activity parameters in the region to be estimated; Based on prior information and reference source data of ionospheric activity parameters in the region to be estimated, the posterior distribution of ionospheric activity parameters in the region to be estimated is constructed within a Bayesian framework. The posterior distribution of ionospheric activity parameters within the region to be estimated is as follows: , In the formula, These represent the radar measurement vector and ground range vector of the reference source, respectively. To estimate ionospheric activity parameters within the ionospheric region, For the number of reference sources, For the elevation angle information of each ray, and Represents the forward model, It represents The joint prior distribution of; The moment estimates of the posterior distribution of ionospheric activity parameters within the ionospheric region to be estimated are obtained based on Markov chains, Gibbs sampling, and importance sampling. The moment estimates of the posterior distribution of ionospheric activity parameters in the region to be estimated are substituted into the international reference ionospheric model to obtain the posterior ionospheric layer. The coordinate registration results of the target to be located are obtained by calculating the electromagnetic wave propagation path in the posterior ionosphere using the three-dimensional ray tracing method.

2. The skywave over-the-horizon radar coordinate registration method based on reference source assistance according to claim 1, characterized in that, Prior information for obtaining ionospheric activity parameters within the region to be estimated includes: The ionosphere region to be estimated is gridded; By setting the ionospheric activity parameters on each small grid as random variables, the ionospheric activity parameters of the region to be estimated are obtained. , In the formula, , Indicates the first The values ​​of ionospheric activity parameters within the ionospheric region to be estimated at each longitude and latitude step.

3. The skywave over-the-horizon radar coordinate registration method based on reference source assistance according to claim 2, characterized in that, Based on prior information and reference source data of ionospheric activity parameters within the region to be estimated, the posterior distribution of these parameters is constructed within a Bayesian framework, including: A probabilistic graphical model of prior information of ionospheric activity parameters in the region to be estimated is established based on Gaussian Markov random fields. A radar measurement model of the reference source is established using the three-dimensional ray tracing method based on the reference source data; Within a Bayesian framework, the posterior distribution of ionospheric activity parameters within the region to be estimated is constructed based on a probabilistic graphical model of prior information of ionospheric activity parameters within the region to be estimated and a radar measurement model of the reference source.

4. The skywave over-the-horizon radar coordinate registration method based on reference source assistance according to claim 3, characterized in that, The probabilistic graphical model for establishing prior information of ionospheric activity parameters in the region to be estimated based on Gaussian Markov random fields includes: Make the ionospheric activity parameters in the region to be estimated follow a high-dimensional normal distribution. , In the formula, Q is the accuracy matrix. Let be the potential vector. , It is the mean vector; Using undirected graphs Equation (3) is graphically represented as a probabilistic graphical model of the prior information of ionospheric activity parameters in the region to be estimated, where, It represents the set of nodes in a probabilistic graphical model. Represents the edges in a probabilistic graphical model set and ; The moment estimates of ionospheric activity parameters in the region to be estimated are obtained based on Markov chains, Gibbs sampling, and importance sampling.

5. The skywave over-the-horizon radar coordinate registration method based on reference source assistance according to claim 3, characterized in that, The moment estimates of the posterior distribution of ionospheric activity parameters within the ionospheric region to be estimated, based on Markov chains, Gibbs sampling, and importance sampling, include: Walk through the Markov chain of ionospheric activity parameters in the region to be estimated to obtain the node values ​​of the Markov chain of ionospheric activity parameters in the region to be estimated. The moment estimates of the posterior distribution of ionospheric activity parameters are calculated using the node values ​​of a Markov chain of ionospheric activity parameters within the region to be estimated.

6. The skywave over-the-horizon radar coordinate registration method based on reference source assistance according to claim 3, characterized in that, When walking a Markov chain to estimate ionospheric activity parameters within an ionospheric region, each step of the walk is as follows: Gibbs sampling is used to decompose the posterior distribution of ionospheric activity parameters within the region to be estimated, resulting in multiple one-dimensional conditional posterior distributions of the ionospheric activity parameters within the region to be estimated. These one-dimensional conditional posterior distributions of the ionospheric activity parameters within the region to be estimated are: , In the formula, for The conditional marginal prior distribution of one-dimensional ionospheric activity parameters was calculated using the message-passing method. For radar measurement models, Indicates except the first The other dimensions besides the first dimension, express For known values The known value The node values ​​obtained from the previous step are obtained; Importance sampling is used to estimate the conditional posterior distribution of ionospheric activity parameters within a single-dimensional region of the ionosphere to be estimated. The estimated value of the conditional posterior distribution of each ionospheric activity parameter within this region is obtained as the sampling result. The estimated values ​​of the expectation and variance of the conditional posterior distribution of the ionospheric activity parameters within the region are... , in, Here, m represents the importance weight, and m is the number of importance samples. These are proposed values ​​for ionospheric activity parameters within a one-dimensional region of the ionosphere to be estimated. ; By combining the sampling results of the conditional posterior distribution of all ionospheric activity parameters in the one-dimensional ionospheric region to be estimated according to the scanning order of Gibbs sampling, a node value of the Markov chain of ionospheric activity parameters is obtained.

7. The skywave over-the-horizon radar coordinate registration method based on reference source assistance according to claim 6, characterized in that, Importance weights are obtained through an approximate forward model, which is calculated by multimodal fitting of data from the exact forward model. Specifically, this includes: A local approximate model is constructed near the prior information of ionospheric activity parameters in the region to be estimated. The approximate model is a mapping relationship between ionospheric activity parameters in the region to be estimated and radar measurements and ground distance. Using the data from the accurate forward model obtained during the importance sampling process, the model parameters in the approximate model can be calculated based on the multimodal data fitting method. By comparing the approximation effects of different models, the approximation model with the best approximation effect is used to obtain a large number of ionospheric activity parameters and radar measurement and ground distance data pairs in the ionospheric region to be estimated, and the importance weight of the data pairs is calculated.

8. The skywave over-the-horizon radar coordinate registration method based on a reference source as described in claim 6 or 7, characterized in that, The moment estimates of the posterior distribution of ionospheric activity parameters are calculated using the node values ​​of a Markov chain representing the ionospheric activity parameters within the region to be estimated. This includes: Filter the node values ​​of the Markov chain for ionospheric activity parameters in the region to be estimated; The node values ​​of the Markov chain for the ionospheric activity parameters in the selected ionospheric region to be estimated are calculated as moment estimates of the ionospheric activity parameters in the selected ionospheric region.

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