A rail transit intelligent ray tracing channel modeling method based on local phase error calibration

Abstract

An embodiment of the present invention provides a rail transit intelligent ray tracing channel modeling method based on local phase error calibration, aiming to address the problem of inaccurate channel modeling caused by environmental modeling errors and dynamic phase distortion in traditional ray tracing technology in high-speed and dense rail transit scenarios. First, a three-dimensional geometric model of the intelligent railway communication system including the transmitter and receiver is constructed, and multipath parameters are generated using ray tracing simulation. A deterministic frequency response model is established based on the multipath parameters. Second, independent and identically distributed von Mises phase errors #imgabs0# are superimposed on the deterministic model to form a random channel model. Finally, the measured data set is used to optimize the material electromagnetic parameter vector to minimize the difference between the ray tracing prediction and the measured data, thereby improving the model's generalization ability in unknown locations.

Description

Technical Field

[0001] The present invention belongs to the fields of communication technology, channel modeling, and in particular relates to a rail transit intelligent ray tracing channel modeling method based on local phase error calibration. Background Art

[0002] As intelligent rail transit systems evolve toward higher speeds and higher density, highly reliable vehicle-to-ground communications are essential for ensuring operational safety and efficiency. In this context, the accuracy of wireless channel models directly determines key parameters in communication system design, such as modulation schemes, error correction coding thresholds, and resource allocation strategies. However, the unique electromagnetic propagation characteristics of the rail transit environment, including strong multipath effects within confined spaces, non-stationarity caused by high-speed movement, and the waveguide characteristics of tunnels and elevated structures, make traditional methods based on statistical modeling or empirical path loss difficult to meet the requirements of 5G-R and next-generation communication systems.

[0003] Ray tracing (RT) technology, based on its physical interpretability based on first-principles electromagnetics, has become a preferred solution to this problem. By simulating the interaction between rays and the environment (such as reflection, diffraction, and scattering), ray tracing can extract high-resolution spatial channel characteristics. However, the practical application of ray tracing in rail transit scenarios still faces bottlenecks. First, errors in environmental modeling significantly affect ray tracing accuracy. In closed environments (such as tunnel walls), the lack of precise prior knowledge of material properties (such as dielectric constant) leads to errors in the initial ray path calculation. Second, dynamic phase distortion becomes increasingly severe at high train speeds. The coupling of the Doppler effect caused by non-stationary motion and phase noise renders traditional power-domain calibration methods that rely on received signal strength (RSS) ineffective. Notably, in the millimeter-wave frequency band, the shortened wavelength amplifies the impact of phase error on the channel impulse response, and existing energy superposition models based on the Friis transmission equation have demonstrated theoretical inadequacy. These issues make traditional ray tracing technology even more difficult to effectively meet the needs of vehicle-to-ground wireless channel modeling in rail transit systems.

[0004] Traditional RT channel model calibration methods typically assume perfect phase prediction for all paths and construct the channel frequency response directly based on deterministic parameters (such as complex amplitude, delay, and angle) output by the RT. Such models achieve efficient simulation by simplifying the computational process (e.g., ignoring phase error terms) and are suitable for static or low-dynamic scenarios. However, in complex environments such as high-speed railways, significant deviations can occur between the RT-predicted path phases and the actual channel response due to geometric deviations (errors in size and position) and uncertainties in material electromagnetic parameters (such as dielectric constant measurement errors). This deviation is dynamically amplified in high-speed mobile scenarios, resulting in a phase mismatch between the model output and the measured data, which in turn affects key performance indicators such as channel capacity estimation and beamforming design. Furthermore, such models fail to represent the random phase fluctuations of multipath interference in real channels, resulting in overly idealized simulation results and making it difficult to support the design and optimization of high-reliability communication systems.

[0005] To address the shortcomings of deterministic models, some improved methods have introduced a uniform phase error assumption, assuming that the phase errors of all paths follow a uniform distribution within the interval [−π,π) (corresponding to the limiting case of κ→0 in the von Mises distribution) to account for worst-case phase randomness. This approach partially mitigates the phase sensitivity of deterministic models through statistical techniques such as Monte Carlo simulation. However, the uniform distribution assumption is overly conservative, ignoring the potential directional concentration of actual errors (e.g., the distribution of errors around the mean), causing calibration results to deviate from the statistical characteristics of real-world scenarios. Furthermore, this approach cannot dynamically adjust error distribution parameters (such as the concentration parameter κ) through data-driven methods, limiting the model's generalization to multiple scenarios. In highly dynamic scenarios such as high-speed railways, the uniform distribution model requires a large number of samples to account for randomness, significantly reducing computational efficiency. Furthermore, it struggles to capture the phase-time correlation caused by Doppler shift, resulting in insufficient dynamic channel prediction accuracy.

[0006] In summary, the core role of the calibration process in ray tracing (RT) channel modeling lies in optimizing model parameters through data-driven methods to account for the discrepancy between simulated predictions and actual channel responses. Existing calibration techniques, such as those that ignore phase error and directly use the RT output as a deterministic channel model, simplify the computational process but fail to characterize the statistical characteristics of random phase fluctuations in the actual channel. While the uniform phase error calibration method introduces phase randomness through statistical means, it assumes a uniform error distribution (i.e., a worst-case assumption), ignoring the potential directional concentration of actual errors (e.g., errors distributed around the mean). Neither of these methods dynamically adjusts the error distribution parameters based on measured data, and they lack joint optimization of material properties. This makes the calibrated model difficult to adapt to dynamic environmental changes and incapable of achieving high-precision channel predictions at unknown locations. Therefore, a calibration framework that integrates phase error modeling and data-driven parameter optimization is urgently needed to improve the generalization and reliability of RT models in complex scenarios. Summary of the Invention

[0007] In response to the problems existing in the prior art, the present invention provides a rail transit intelligent ray tracing channel modeling method based on local phase error calibration, aiming to solve the problem of inaccurate channel modeling caused by environmental modeling errors and dynamic phase distortion in traditional ray tracing technology in high-speed and dense rail transit scenarios. First, a three-dimensional geometric model of the intelligent railway communication system including the transmitter and receiver is constructed, and multipath parameters are generated by ray tracing simulation. A deterministic frequency response model is established based on the multipath parameters. Second, a local phase error term is superimposed in the deterministic model, and the phase error of each path is modeled as an independent and identically distributed von Mises distribution. , forming a random channel model; finally, the material electromagnetic parameter vector is optimized using the measured data set to minimize the difference between ray tracing predictions and measured data, thereby improving the model's generalization ability in unknown locations.

[0008] Technical solution of the present invention:

[0009] A rail transit intelligent ray tracing channel modeling method based on local phase error calibration includes the following steps:

[0010] Step 1: Construct a 3D geometric model of the intelligent railway communication system, including the transmitter and receiver. Use ray tracing simulation to generate multipath parameters, and then establish a deterministic frequency response model based on the multipath parameters.

[0011] Step 2: Superimpose the local phase error term in the deterministic model and model the phase error of each path as an independent and identically distributed von Mises distribution , its concentration parameter Adjustable to match actual error distribution;

[0012] Step 3: Use the measured data set to optimize the material electromagnetic parameter vector to minimize the difference between the ray tracing prediction and the measured data, and improve the generalization ability of the model in unknown locations.

[0013] The specific instructions are as follows:

[0014] In step 1, the deterministic frequency response model construction process is specifically as follows:

[0015] Step 1.1 In the smart railway scenario, the transmitter (Tx, ground station) and receiver (Rx, high-speed train) are located at the positions in the three-dimensional Cartesian coordinate system. and The transmitter and receiver are equipped with and The signal transmission between the vehicle and the ground occurs in a bandwidth of frequency band, where is the highest frequency of the signal, is the lowest frequency of the signal, and the center frequency of the carrier is .

[0016] Step 1.2 The path calculated by ray tracing, the simulation model is based on the scene geometry, the transmitter and receiver positions , and the material property vector Model the channel.

[0017] The scene geometric features include the spatial paths and height difference structures of one or more railway tracks, as well as platforms, tunnels, slopes, and building facades, which are used to simulate reflection, occlusion, and scattering effects. Each structure has a clear spatial position, boundary outline, and height information.

[0018] The material property vector Includes: dielectric constant, conductivity, magnetic permeability, scattering coefficient and cross-polarization cancellation.

[0019] Ray tracing (RT) takes input information (i.e., scene geometry, emitter and receiver positions, and material property vectors) and ) is mapped to The feasible propagation path parameters include complex amplitude, propagation delay, departure angle and arrival angle. The path characteristics generated by RT are expressed as follows:

[0020]

[0021] The input coordinates and material parameters Map to In the parameters of each path, each propagation path By complex amplitude ,Delay s, a pair of departure angles and a pair of arrival angles To describe.

[0022] in, Includes elevation angle from the transmitter's perspective , and azimuth , Contains the elevation angle at the receiver and azimuth .

[0023] Step 1.3 Multipath parameters generated by ray tracing , reconstruct the frequency response of each path at each subcarrier frequency. Specifically, the channel frequency response of a single path is expressed as

[0024]

[0025] in, is the complex amplitude of the path, is the path delay, and are the antenna steering vectors at the receiving and transmitting ends, respectively, is the Kronecker product, is the conjugate of the transmit antenna steering vector.

[0026] The contributions of all paths on all subcarriers are accumulated to obtain the frequency response model of the entire system:

[0027]

[0028] in, is the phase contribution determined by the time delay, departure angle and arrival angle:

[0029]

[0030] Propagation delay The projection of the relevant subcarrier frequency phase delay in the frequency domain, is a The vector represents the phase shift of the path p on different subcarriers:

[0031]

[0032] The frequency response model of the entire system obtained above does not take into account that there are slight differences between the geometry and material characteristics of the scene assumed by the ray tracing simulation and the actual physical system, which leads to errors in the phase prediction of the radio wave propagation path.

[0033] In step 2, the local phase error term is superimposed on the deterministic model, specifically:

[0034] In order to compensate for the error, the phase error term is introduced , the error follows the von Mises distribution , where the mean is 0 and the concentration parameter of the global prior von Mises distribution is .

[0035] Superimpose the local phase error for each path , after the phase error is introduced, the channel model becomes:

[0036]

[0037] is the independent and identically distributed phase error term

[0038]

[0039] in, represents the zero-order modified Bessel function, used for normalization.

[0040] It should be noted that when defining the probability density of this distribution, the universal variable represents an arbitrary concentration, which may be used in practice for the posterior distribution (such as ) or a priori (e.g. ).when , , the model degenerates into a deterministic model that ignores the phase error; when , the model degenerates into a channel model with uniform phase distribution.

[0041] In order to further enhance the adaptability of the channel model to complex environment propagation characteristics, the phase error vector of each path is modeled as follows:

[0042]

[0043] in, is the phase error vector of each path, which obeys the von Mises distribution.

[0044] The phase error After incorporating the deterministic model, the overall random channel model is obtained as follows:

[0045]

[0046] in, represents the deterministic part consisting of the amplitudes of all paths and the antenna steering vectors.

[0047] In step 3, based on the measured data set , minimizing the difference between ray tracing simulation data and measured data. The specific process is as follows:

[0048] Step 3.1 Obtain a training set containing N channel frequency response observation data:

[0049]

[0050] in, The coordinates of the receiving and transmitting ends The channel frequency response is obtained by measuring at . The calibration goal is to adjust the electromagnetic material parameters , so that at a known location Channel simulation results at Compared with the measured data Minimal difference and has the ability to be in unknown locations Good generalization on .

[0051] Step 3.2 In the phase error aware calibration scheme, the channel observation is modeled as a noisy observation based on a phase error perception model, expressed as

[0052]

[0053] in, is a complex Gaussian distribution The noise vector composed of yes Random phase vector, used to represent phase error. Phase Error are independent and identically distributed and follow the von Mises distribution , is the prior concentration parameter.

[0054] In order to solve the observation Likelihood function, the phase error of each path Marginalizing the joint distribution of the phase error yields:

[0055]

[0056] Furthermore, minimizing the marginal likelihood log value in the material parameter The negative logarithm of , thus achieving parameter calibration of the RT model:

[0057]

[0058] Step 3.3 Due to the marginal posterior It is not integrable. We use variational inference to approximate marginal likelihood and define variational distribution as ,in and are the mean parameter and the concentration parameter respectively. Describes all paths The corresponding phase error estimate is expressed as

[0059]

[0060] The variational expectation maximization algorithm approximates the problem by minimizing the variational free energy, and its free energy function Expressed as, by minimizing the variational free energy, the phase error distribution of each sample is updated, that is, the mean phase of the path and concentration , update the posterior approximate distribution:

[0061]

[0062] The free energy is specifically expressed as:

[0063]

[0064] in, It's Besselby, is the Bezier ratio vector, This means constructing a diagonal matrix for the vector.

[0065] Step 3.4 Use the variational expectation maximization algorithm to solve the calibrated parameters ;

[0066] Among them, in the desired step, the fixed material parameters , by minimizing the variational free energy, the phase error estimate of each data point is updated, and the phase mean of each path is updated.

[0067]

[0068] in, It means taking the phase of a complex vector element by element; is a dimension of A column vector where all elements are 1, which is the same as Together they constitute the prior part, introducing a unified prior term for each path component; the symbol i represents the current iteration index, which is used to identify the parameter estimation value of the i-th round in the variational expectation maximization algorithm.

[0069] Update the centralized parameters of each path

[0070]

[0071] In the maximization step, given the updated phase error parameter , update the material parameters by minimizing the variational free energy

[0072]

[0073] Update the centralized parameters of the prior

[0074]

[0075] When the maximum number of iterations is reached or the variational lower bound convergence criterion is met, the algorithm stops and outputs the final estimation result. .

[0076] Step 3.5

[0077] After final calibration, the phase error-aware channel frequency response model (applicable to any position ) can be expressed as:

[0078]

[0079] in, Indicates the electromagnetic parameters of the material after final calibration Constructed path structure matrix (including delay, angle, path gain, etc.); represents the mean phase error of each path estimated by variational inference.

[0080] The beneficial effects of the present invention are as follows:

[0081] The present invention significantly improves the accuracy and robustness of ray tracing channel calibration by using von Mises distribution to model the probability of multipath phase error. By explicitly modeling phase uncertainty, the systematic deviation of traditional phase calibration is avoided. The phase uncertainty of each path is statistically modeled, and the phase perturbation of each path is independently sampled as , realize the modeling of local phase error, and introduce variational concentration parameters to realize adaptive error compensation of ray tracing simulation, maintaining stable performance in high noise environment, and providing a more reliable channel modeling tool. BRIEF DESCRIPTION OF THE DRAWINGS

[0082] Figure 1 Schematic diagram of the processing steps of the method of the present invention;

[0083] Figure 2 A schematic diagram of the process of calibrating the intelligent ray tracing simulator of the present invention;

[0084] Figure 3This is a schematic diagram illustrating the definition of the example scenario and angle path parameters of the planar antenna array proposed in the present invention;

[0085] Figure 4 Schematic diagram of the change of calibration error with signal-to-noise ratio (normalized dielectric constant error) of the present invention;

[0086] Figure 5 Schematic diagram of the change of calibration error with signal-to-noise ratio (normalized conductivity error) of the present invention;

[0087] Figure 6 Schematic diagram of the change of calibration error with signal-to-noise ratio (normalized received power error) in the present invention. DETAILED DESCRIPTION

[0088] The technical solution provided by this application will be further described below in conjunction with specific embodiments and accompanying drawings. The advantages and features of this application will become more apparent with reference to the following description.

[0089] A rail transit intelligent ray tracing channel modeling method based on local phase error calibration includes the following steps: (e.g. Figure 1 )

[0090] Step 1: Construct a 3D geometric model of the intelligent railway communication system, including the transmitter and receiver. Use ray tracing simulation to generate multipath parameters, and then establish a deterministic frequency response model based on the multipath parameters.

[0091] Step 2: Superimpose independent and identically distributed von Mises phase errors in the deterministic model , forming a random channel model, whose concentration parameter Adjustable to match actual error distribution;

[0092] Step 3: Use the measured data set to optimize the material electromagnetic parameter vector to minimize the difference between the ray tracing prediction and the measured data, and improve the generalization ability of the model in unknown locations.

[0093] The flow chart of the calibration of the intelligent ray tracing simulator of the present invention is as follows: Figure 2 .

[0094] The specific steps are as follows:

[0095] Step 1: Combine the 3D geometric model of the intelligent railway communication system and establish a deterministic frequency response model based on ray tracing simulation

[0096] Step (11) In the smart railway scenario, the transmitter (Tx) and receiver (Rx) are located at the positions in the three-dimensional Cartesian coordinate system. and , representing the ground station and the high-speed train. The transmitter and receiver are equipped with and The signal transmission between the vehicle and the ground occurs in a bandwidth of The center frequency of the carrier is .

[0097] Step (12) The path calculated by ray tracing is simulated based on the scene geometry, transmitter and receiver positions. , and the material property vector Model the channel.

[0098] Among them, the material property vector Contains parameters such as dielectric constant, conductivity, magnetic permeability, scattering coefficient and cross-polarization cancellation.

[0099] RT maps these input information into The parameters of the feasible propagation paths include complex amplitude, propagation delay, departure angle and arrival angle, and their functions are expressed as follows:

[0100]

[0101] The input coordinates and material parameters Map to In the path parameters, each propagation path By complex amplitude ,Delay s, a pair of departure angles and a pair of arrival angles To describe.

[0102] in, Includes elevation angle from the transmitter's perspective , and azimuth , Contains the elevation angle at the receiver and azimuth ,like Figure 3 shown.

[0103] Step (13) generates multipath parameters by ray tracing , reconstruct the frequency response of each path at each subcarrier frequency. Specifically, the channel frequency response of each path is expressed as

[0104]

[0105] in, is the complex amplitude of the path, is the path delay, and are the antenna steering vectors at the receiving and transmitting ends, respectively, is the Kronecker product, is the conjugate of the transmit antenna steering vector.

[0106] The contributions of all paths on all subcarriers are accumulated to obtain the frequency response model of the entire system:

[0107]

[0108] in, is the phase contribution determined by the time delay, departure angle and arrival angle:

[0109]

[0110] and Propagation delay The contribution of the phase of the associated subcarrier frequency is:

[0111]

[0112] Step 2: There are slight differences between the geometry and material characteristics of the scene assumed by the ray tracing simulation and the actual physical system, which leads to errors in the phase prediction of the radio wave propagation path. In order to compensate for the error, the phase error term is introduced , the error follows the von Mises distribution , where the mean is 0 and the concentration parameter .

[0113] After the phase error is introduced, the channel model becomes:

[0114]

[0115] in, is an independent and identically distributed phase error term that satisfies the von Mises distribution. The phase error vector is obtained and the phase factor error vector .

[0116] The phase error After integrating the deterministic model, the random model is obtained:

[0117]

[0118] in, for The matrix represents the deterministic part consisting of the amplitudes of all paths and the antenna steering vectors.

[0119] Step 3: Minimize the difference between ray tracing predictions and measured data,

[0120] Step (31) obtains a training set containing N channel frequency response observation data:

[0121]

[0122] Among them, each observation data The coordinates of the receiving and transmitting ends The calibration goal is to adjust the electromagnetic material parameters , so that at a known location Channel simulation results and measured data at More consistent and able to expand to new locations .

[0123] Step (32) In the phase error sensing calibration scheme, the channel observation is modeled as a noisy observation based on a phase error perception model, expressed as

[0124]

[0125] in, is a complex Gaussian distribution The noise vector composed of yes Random phase vector, used to represent phase error. Phase Error are independent and identically distributed and follow the von Mises distribution , is the prior concentration parameter.

[0126] According to the data set , estimate the ray tracing simulation parameters The maximum likelihood solution of :

[0127]

[0128] Since the integral in step (33) is difficult to calculate analytically, variational inference is used to approximate the marginal likelihood and the variational distribution is defined as ,in and are the mean parameter and the concentration parameter respectively. represents the nominal estimate of the phase error, the concentration parameter The uncertainty of this estimate is quantified. Describes all paths The corresponding phase error estimate is expressed as

[0129]

[0130] The variational expectation maximization algorithm approximates the problem by minimizing the variational free energy, and its free energy function is expressed as

[0131]

[0132] The free energy is specifically expressed as:

[0133]

[0134] in, It's Besselby, is the Bezier ratio vector, This means constructing a diagonal matrix for the vector.

[0135] Step (34) uses the variational expectation maximization algorithm to solve the calibrated parameters ;

[0136] Among them, in the desired step, the fixed material parameters , by minimizing the variational free energy, the phase error estimate of each data point is updated, and the phase mean of each path is updated.

[0137]

[0138] in, It means taking the phase of a complex vector element by element; is a dimension of A column vector where all elements are 1, which is the same as Together they form the prior part, introducing a unified prior term for each path component;

[0139] Update the centralized parameters of each path

[0140]

[0141] In the maximization step, given the updated phase error parameter , update the material parameters by minimizing the variational free energy

[0142]

[0143] Update the centralized parameters of the prior

[0144]

[0145] When the maximum number of iterations is reached or convergence is reached, the final estimated parameters are output .

[0146] Step (35)

[0147] After final calibration, the phase error-aware channel frequency response model (applicable to any position ) can be expressed as:

[0148]

[0149] in, Indicates the electromagnetic parameters of the material after final calibration Constructed path structure matrix (including delay, angle, path gain, etc.); represents the mean phase error of each path estimated by variational inference.

[0150] Channel modeling is complete.

[0151] A simulation environment was built using a Linux server to compare the performance of the method of the present invention with that of a typical method. The comparison methods included calibration based on local phase error, calibration based on ignoring phase error, and calibration based on average phase error.

[0152] During calibration, the real material parameters are assumed is unknown, through known observation data To perform calibration By modeling and simulating the paths of the receiver and transmitter, the goal is to estimate the electromagnetic material parameters using different calibration methods. The final calibration effect is evaluated by the following indicators: normalized dielectric constant error, ; Normalized conductivity error, ; and the normalized received power error, ,in is to use the ray tracing model and calibration parameters All propagation paths estimated at location The total power received at .

[0153] Normalized dielectric constant error, normalized conductivity error and normalized received power error are used as evaluation indicators to quantitatively evaluate the performance of various calibration methods under different signal-to-noise ratio conditions, such as Figure 4 、 Figure 5 and Figure 6 .in:

[0154] Normalized dielectric constant error, ;

[0155] Normalized conductivity error, ;

[0156] Normalized received power error, , which reflects the accuracy of the calibration parameters in predicting the received power at various locations.

[0157] Experimental results show that the calibration based on local phase error significantly outperforms other methods in all indicators. Specifically, Figure 4 and Figure 5 It shows that the calibration based on local phase error maintains the lowest dielectric constant and conductivity estimation errors in the entire SNR range from 0 dB to 30 dB, indicating that it has obvious advantages in parameter identification accuracy and anti-interference ability. Figure 6 Further results show that, in the received power prediction task, calibration based on local phase error achieves approximately 10 dB performance improvement over calibration based on uniform phase error at an SNR of 0 dB, reaching 20 dB at an SNR of 30 dB, and performance continues to improve with increasing SNR. In contrast, calibration based on ignoring phase error fails to converge to the true parameters at all SNR levels, causing its power predictions to deviate significantly from the true values. While calibration based on uniform phase error shows some improvement at high SNRs, its overall prediction capability remains inferior to calibration based on local phase error. It is noteworthy that the shaded area in the figure represents the range between the first and third quartiles (Q1–Q3), reflecting the degree of dispersion in the results of each algorithm across multiple independent experiments. Narrower shading indicates a more concentrated and stable algorithm output across experiments. It can be observed that the calibration method based on local phase error has the smallest interquartile range under all SNR conditions, indicating that its estimation results maintain high accuracy while also being robust. In contrast, the calibration method based on ignoring phase error has a very scattered distribution, further confirming its characteristic of prediction failure in the presence of phase perturbations. In summary, the calibration method based on local phase error proposed in this paper, by introducing a path-level phase uncertainty modeling mechanism, outperforms existing ray tracing calibration methods in terms of accuracy, stability, and generalization capability.

[0158] The foregoing description is merely a preferred embodiment of the present invention, and the scope of the rights claimed by the present invention is not limited thereto. The present invention has various other embodiments, and those skilled in the art may make various corresponding changes and modifications based on the present invention without departing from the spirit and essence of the present invention. Such changes and modifications are intended to fall within the scope of protection of the appended claims.

Claims

1. A rail transit intelligent ray tracing channel modeling method based on local phase error calibration, characterized in that: The following steps are involved: Step 1: Construct a 3D geometric model of the intelligent railway communication system, including the transmitter and receiver. Use ray tracing simulation to generate multipath parameters, and then establish a deterministic frequency response model based on the multipath parameters. Step 2: Superimpose the local phase error term in the deterministic model and model the phase error of each path as an independent and identically distributed von Mises distribution , its concentration parameter Adjustable to match actual error distribution; Step 3: Optimize the material electromagnetic parameter vector using the measured data set to minimize the difference between the ray tracing prediction and the measured data, thereby improving the model's generalization ability in unknown locations. Step 1 includes the following steps: Step 1.1 In the smart railway scenario, the transmitter Tx and receiver Rx are located at the positions in the three-dimensional Cartesian coordinate system. and ; The transmitter and receiver are equipped with and Antenna array; the signal transmission between the vehicle and the ground occurs in a bandwidth of frequency band, where is the highest frequency of the signal, is the lowest frequency of the signal, and the center frequency of the carrier is ; Step 1.2 The path calculated by ray tracing, the simulation model is based on the scene geometry, the transmitter and receiver positions , and the material property vector Modeling the channel; The ray tracing method maps the input information into The feasible propagation path parameters include complex amplitude, propagation delay, departure angle and arrival angle. The path characteristics generated by RT are expressed as follows: The input coordinates and material parameters Map to In the parameters of each path, each propagation path By complex amplitude ,Delay s, a pair of departure angles and a pair of arrival angles to describe; in, Includes elevation angle from the transmitter's perspective , and azimuth , Contains the elevation angle at the receiver and azimuth ; Step 1.3 Multipath parameters generated by ray tracing , reconstruct the frequency response of each path at each subcarrier frequency; specifically, the channel frequency response of a single path is expressed as in, is the complex amplitude of the path, is the path delay, and are the antenna steering vectors at the receiving and transmitting ends, respectively, is the Kronecker product, is the conjugate of the transmitting antenna steering vector; The contributions of all paths on all subcarriers are accumulated to obtain the frequency response model of the entire system: in, is the phase contribution determined by the time delay, departure angle and arrival angle: Propagation delay The projection of the relevant subcarrier frequency phase delay in the frequency domain, is a The vector represents the phase shift of the path p on different subcarriers: ； In step 2, in order to compensate for the error, the phase error term is introduced , the error follows the von Mises distribution , where the mean is 0 and the concentration parameter ; After the phase error is introduced, the channel model becomes: in, is an independent and identically distributed phase error term that satisfies the von Mises distribution; the phase error vector is obtained and the phase factor error vector ; The phase error After integrating the deterministic model, the random model is obtained: in, for The matrix represents the deterministic part consisting of the amplitudes of all paths and the antenna steering vectors.

2. The method according to claim 1, characterized in that In step 1.2, The scene geometry includes the spatial path of one or more railway tracks, height difference structures, as well as platforms, tunnels, slopes, and building facades, which are used to simulate reflection, occlusion, and scattering effects. Each structure has a clear spatial position, boundary outline, and height information. The material property vector Includes: dielectric constant, conductivity, magnetic permeability, scattering coefficient and cross-polarization cancellation.

3. The method according to claim 1, characterized in that Step 3 includes the following steps: Step 3.1 Obtain a training set containing N channel frequency response observation data: in, The coordinates of the receiving and transmitting ends The channel frequency response is obtained by measuring at ; the calibration goal is to adjust the electromagnetic material parameters , so that at a known location Channel simulation results at Compared with the measured data Minimal difference and has the ability to be in unknown locations Good generalization on Step 3.2 In the phase error aware calibration scheme, the channel observation is modeled as a noisy observation based on a phase error perception model, expressed as in, is a complex Gaussian distribution The noise vector composed of yes Random phase vector, used to represent phase error; phase error are independent and identically distributed and follow the von Mises distribution , is the a priori concentration parameter; In order to solve the observation Likelihood function, the phase error of each path Marginalizing the joint distribution of the phase error yields: Minimize the marginal likelihood log value in the material parameter The negative logarithm of , thus achieving parameter calibration of the RT model: Step 3.3 Due to the marginal posterior It is not integrable. We use variational inference to approximate marginal likelihood and define variational distribution as ,in and are the mean parameter and the concentration parameter respectively; variational distribution Describes all paths The corresponding phase error estimate is expressed as The variational expectation maximization algorithm approximates the problem by minimizing the variational free energy, and its free energy function Expressed as, by minimizing the variational free energy, the phase error distribution of each sample is updated, that is, the mean phase of the path and concentration , update the posterior approximate distribution: The free energy is specifically expressed as: in, It's Besselby, is the Bezier ratio vector, It means constructing a diagonal matrix for the vector; Step 3.4 Use the variational expectation maximization algorithm to solve the calibrated parameters ; Among them, in the desired step, the fixed material parameters , by minimizing the variational free energy, the phase error estimate of each data point is updated, and the phase mean of each path is updated. in, It means taking the phase of a complex vector element by element; is a dimension of A column vector where all elements are 1, which is the same as Together they constitute the prior part, introducing a unified prior term for each path component; the symbol i represents the current iteration index, which is used to identify the parameter estimation value of the i-th round in the variational expectation maximization algorithm; Update the centralized parameters of each path In the maximization step, given the updated phase error parameter , update the material parameters by minimizing the variational free energy Update the centralized parameters of the prior When the maximum number of iterations is reached or convergence is reached, the final estimated parameters are output ; Step 3.5 After the final calibration, the phase error-aware channel frequency response model is expressed as: in, Indicates the electromagnetic parameters of the material after final calibration The constructed path structure matrix; represents the mean phase error of each path estimated by variational inference.

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