A slant-path atmospheric coherence length prediction method for satellite-to-ground laser links

Abstract

The application discloses a slant-path atmospheric coherence length prediction method for a satellite-ground laser link. The method determines a target link area and a dynamic slant-path propagation path according to the position of a target ground station, target satellite orbit information and a link zenith angle or elevation angle time sequence; constructs a high-resolution meteorological space-time feature field based on regional meteorological data, and generates a slant-path atmospheric coherence length, i.e., a Fried parameter space-time distribution sequence, along the slant-path, which represents the link turbulence intensity; multi-scale non-stationary features are constructed for the sequence to obtain local fluctuations, short-time mutations and link geometric modulation features; a fusion wavelet KAN module is constructed based on a fusion wavelet boundary function, a nonlinear dynamic model is established for the non-stationary evolution process, and a future time period prediction distribution and a target link prediction result are output in combination with a window attention feature updating unit. The application can improve the turbulence state prediction accuracy of the satellite-ground laser link, and provide support for link evaluation, link establishment window judgment and scheduling optimization.

Description

Technical Field

[0001] This invention belongs to the field of free-space optical communication (FSO) and atmospheric environment monitoring technology, specifically relating to a method for predicting the slant path atmospheric coherence length for satellite-to-ground laser links. Background Technology

[0002] In free-space optical communication (FSO) systems consisting of low-Earth orbit (LEO) satellites and ground stations, the transmission quality of optical signals is highly susceptible to the constraints of complex atmospheric environments. Geographical differences and dynamic changes in meteorological conditions such as clouds, fog, rain, and haze often lead to severe power attenuation of optical signals, thus limiting the reach and robustness of the communication link. Among numerous environmental interference factors, random channel fading caused by atmospheric turbulence is the core bottleneck limiting system performance. Due to the non-uniformity of atmospheric refractive index (i.e., optical turbulence, OT), laser beams experience wavefront distortion, beam flicker, drift, and dispersion as they penetrate the atmosphere. These effects not only cause significant fluctuations in the signal-to-noise ratio at the receiver, inducing a sharp increase in the bit error rate (BER), but under strong turbulence conditions, they can even lead to frequent communication link interruptions, making it impossible to complete the effective acquisition, tracking, and aiming (ATP) process. Therefore, achieving real-time and accurate prediction of atmospheric turbulence intensity is of crucial decision-making value for link budget assessment, adaptive optics compensation strategy formulation, and communication protocol switching in satellite-to-ground laser communication systems. However, atmospheric turbulence has highly nonlinear and time-varying characteristics, and traditional linear prediction models are unable to capture its complex dynamic evolution, which has become a common problem restricting the development of efficient space-to-ground laser communication systems.

[0003] In recent years, the rapid development of machine learning (ML) technology has significantly enhanced modeling capabilities in atmospheric science, with some data-driven models demonstrating potential to surpass traditional numerical weather prediction (NWP) systems in spatiotemporal evolution prediction. However, for the specific scenario of satellite-to-ground laser communication (SGLC), the stochastic transient characteristics of atmospheric optical turbulence (OT) remain a core challenge restricting system reliability. The lack of prior assessment of turbulence intensity will directly lead to satellite-to-ground link switching failures, downlink interruptions of payload data, and ineffective consumption of satellite energy resources. The core indicator for quantitatively characterizing the intensity of optical turbulence is the refractive index structure constant. To build a highly robust free-space optical communication (FSOC) network, it is essential to conduct in-depth analysis of different geographical locations and complex weather conditions. The nonlinear evolution of atmospheric turbulence is a key challenge. Currently, the academic community's ability to characterize the dynamic characteristics of atmospheric channels remains limited. Traditional empirical models often rely on fitting local observation data, lacking physical universality; while purely numerical physics models, constrained by computational complexity and parameterization schemes for microscale physical processes, struggle to balance real-time performance and high accuracy. Therefore, developing physics-driven deep learning algorithms and constructing integrated modeling frameworks coupled with multiple physics fields has become a cutting-edge research trend. For the high nonstationarity and energy cascading characteristics of atmospheric turbulence in satellite-to-ground laser links, existing deep learning models often struggle to achieve both precise extraction of spatiotemporal features and physical consistency.

[0004] The applicant, Nanjing University, previously filed a patent application entitled "A Method for Determining the Availability of Satellite-to-Ground Laser Link Communication Based on Sky Infrared Remote Sensing Images," authorized by publication number CN 116192251 B. This patent utilizes meteorological information and infrared remote sensing images to invert cloud base height and optical depth, and combines this with machine learning to predict cloud evolution. However, this prior art focuses on solving the macroscopic connectivity issues caused by cloud cover, and does not yet cover the microscopic impact of atmospheric optical turbulence on communication quality. Since turbulence-induced fading is a core factor limiting channel stability, it is urgent to conduct pre-assessment to avoid data transmission failures and wasted satellite resources.

[0005] The applicant, the Hefei Institutes of Physical Science, Chinese Academy of Sciences, previously filed an invention patent application entitled "A Method for Synchronously Predicting the Coherence Length of the Entire Atmosphere Based on Near-Surface Measured Atmospheric Optical Turbulence," application number 202410300496.8. In this patent application, near-surface measured data is accumulated using a temperature pulsator, a mathematical model of the turbulence profile is constructed, and the coherence length of the entire atmospheric layer is obtained by integration. However, this prior art only achieves the synchronous inversion of physical parameters and lacks a prediction time lead. Therefore, there is an urgent need to use deep learning technology to model the spatiotemporal evolution of atmospheric optical turbulence to achieve accurate short-term predictions, thereby improving the system's adaptability to complex and variable atmospheric environments.

[0006] However, existing atmospheric turbulence prediction methods are mostly designed for medium- to long-term weather forecasting scenarios, and their spatiotemporal resolution is ill-suited to the minute-level real-time prediction requirements of low-Earth orbit (LEO) satellite communication windows with extremely short communication windows and rapidly changing channel parameters. Furthermore, traditional deep learning prediction models tend to rely on black-box static weight mapping, making it difficult to explicitly characterize the complex energy cascade dynamics and non-stationary transient characteristics within turbulence. This results in limited prediction accuracy and generalization ability under complex and variable atmospheric conditions. Therefore, how to combine physical prior constraints with advanced neural operator architectures to achieve high-precision, high-resolution spatiotemporal evolution prediction of atmospheric turbulence has become a critical issue that urgently needs to be addressed to optimize the communication quality of LEO satellite-to-ground laser links. Summary of the Invention

[0007] Objective: This invention aims to improve the prediction accuracy of atmospheric turbulence in satellite-to-ground laser communication scenarios, thereby enhancing the ability to characterize link state changes under complex meteorological conditions. Addressing the multi-scale, highly stochastic, and non-stationary evolution characteristics of atmospheric turbulence, this invention proposes a slant-path atmospheric coherence length prediction method for satellite-to-ground laser links. This method, through high-resolution meteorological field construction, turbulence physics parameter calculation, multi-scale feature analysis, and nonlinear spatiotemporal modeling, predicts the future evolution trends of key parameters such as atmospheric coherence length, providing reliable prior information on atmospheric turbulence for satellite-to-ground laser links, thus supporting link scheduling and communication performance optimization.

[0008] The above objectives are achieved through the following technical solutions:

[0009] A method for predicting the slant path atmospheric coherence length for satellite-to-ground laser links includes the following steps:

[0010] Meteorological field construction and slant-path turbulence parameter generation for S1 link geometric constraints: Based on the target ground station location, target satellite orbit information, communication wavelength, and the zenith or elevation angle time series information of the target satellite-to-ground laser link, the target link region and the time-varying slant-path propagation path are determined; a high-resolution meteorological spatiotemporal characteristic field is constructed based on the meteorological data of the target link region, and turbulence parameter integration is performed along the slant-path propagation path to generate the slant-path atmospheric coherence length characterizing the turbulence intensity of the target satellite-to-ground laser link. Spatiotemporal distribution sequence;

[0011] S2 Multi-scale feature construction for link turbulent nonstationary characteristics: The slant path atmospheric coherence length obtained in step S1... Multi-scale feature extraction is performed on the spatiotemporal distribution sequence to generate multi-scale non-stationary feature representations that characterize the effects of local fluctuations in atmospheric turbulence, abrupt changes in stratification, cross-scale evolution, and changes in link geometry. ;

[0012] S3 Non-stationary evolution modeling based on fused wavelet KAN: Based on the multi-scale non-stationary feature representation obtained in step S2 A nonlinear dynamic modeling module of the Kolmogorov-Arnold network containing fused wavelet side functions was constructed to model the non-stationary temporal evolution of atmospheric turbulence in the target satellite-to-ground laser link, and to obtain temporal features characterizing the dynamic changes of turbulence.

[0013] S4 Spatiotemporal Correlation Prediction for Satellite-to-Ground Laser Links: Based on the Multi-Scale Non-stationary Feature Representation Obtained in Step S2 Based on the temporal features obtained in step S3, a spatiotemporal correlation prediction model is constructed to predict the atmospheric turbulence state of the target link region in the future, and outputs the slant path atmospheric coherence length at the future time. The distribution is predicted, and based on the target ground station location, target satellite orbit information, and link zenith angle or elevation angle information, the slant path atmospheric coherence length is calculated. The atmospheric coherence length prediction result corresponding to the target satellite-to-ground laser link is extracted from the predicted distribution.

[0014] Furthermore, step S1 specifically includes the following sub-steps:

[0015] S1.1 Multidimensional Feature Extraction of Meteorological Parameters: Based on the target ground station location, target satellite orbit information, and the zenith angle or elevation angle time series information of the target satellite-to-ground laser link, the target link region and its corresponding meteorological calculation range are determined; meteorological data of the target region are acquired as the initial field and boundary conditions, including ERA5 reanalysis data or GFS forecast data; multidimensional meteorological parameters are extracted from the meteorological data, including temperature, specific humidity, three-dimensional wind speed components, and pressure field, and a meteorological feature set is constructed; the meteorological feature set is used as input, and nested simulation and dynamic downscaling are performed using numerical models to obtain a high-resolution meteorological spatiotemporal feature field corresponding to the meteorological feature set.

[0016] S1.2 Calculation of the spatiotemporal distribution sequence of slant-path atmospheric coherence length: Based on the high-resolution meteorological spatiotemporal characteristic field obtained in step S1.1, the slant-path propagation path varying with time is determined according to the target satellite orbit information, target ground station location, communication wavelength, and the zenith angle or elevation angle of the target satellite-to-ground laser link at different times. Using the air pressure, absolute temperature, and potential temperature gradient in the high-resolution meteorological spatiotemporal characteristic field, turbulence parameters are integrated along the slant-path propagation path to obtain the slant-path atmospheric coherence length characterizing the turbulence intensity of the target satellite-to-ground laser link at the corresponding time and corresponding spatial grid location. Its expression is: in, For wavelength, Zenith angle, This is the maximum height for the points. Pi For height The air pressure at that location For height The absolute temperature at that location It is an empirical constant. It is an exoscale parameter and is related to atmospheric stability. For potential temperature gradient, This refers to the potential temperature.

[0017] Furthermore, step S2 specifically includes the following sub-steps:

[0018] S2.1 Wavelet Function Selection and Link Turbulence Multi-Scale Feature Extraction: Multi-scale feature extraction is performed on the spatiotemporal distribution sequence of the slant path atmospheric coherence length obtained in step S1. The slant path atmospheric coherence length... The spatiotemporal distribution sequence contains non-stationary fluctuations caused by changes in atmospheric turbulent stratification, local abrupt changes, short-term degradation, and variations in link zenith or elevation angles; the slant path atmospheric coherence length is extracted using the Morlet wavelet function. The local oscillation and frequency variation characteristics of the spatiotemporal distribution sequence were analyzed, and the slant atmospheric coherence length was extracted using the Mexican-Hat wavelet function. Peak-valley structure and local abrupt change characteristics in spatiotemporal distribution sequences;

[0019] S2.2 Generation of Multi-Scale Fusion Wavelet Basis Functions: Fusion weights between the Morlet and Mexican-Hat wavelet functions are generated based on learnable gating parameters, and multi-scale fusion wavelet basis functions are generated by combining scale and translation parameters; these multi-scale fusion wavelet basis functions are then applied to the atmospheric coherence length. The spatiotemporal distribution sequence yields a multi-scale non-stationary characteristic representation of the effects of local atmospheric turbulence fluctuations, short-term abrupt changes, cross-scale evolution, and link geometric modulation in the target satellite-to-ground laser link. .

[0020] Furthermore, step S3 specifically includes the following sub-steps:

[0021] S3.1 Construction of Fusion Wavelet Side Functions for Non-stationary Evolution of Slant-Path Turbulence: Based on a learnable fusion form of the Morlet wavelet and Mexican-Hat wavelet functions, a method is constructed to characterize the slant-path atmospheric coherence length. The non-stationary fusion wavelet side function, which is represented as the superposition of a linear term and a multi-scale fusion wavelet expansion term, is expressed as follows: in, The scalar eigenvalues ​​are input to the fused wavelet side functions. For the first Layer The input node to the th Layer The fusion of wavelet side functions between output nodes For the weights of the linear terms, For the first The first scale and the first The wavelet expansion coefficients corresponding to each translation position For the first Each scale parameter For the first One translation parameter, For scale quantity This represents the number of translation positions. For Morlet wavelet functions, For Mexican-Hat wavelet functions, To integrate weights, Sigmoid , Sigmoid is a learnable gating parameter. For activation functions;

[0022] S3.2 Construction of the Fusion Wavelet Kolmogorov-Arnold Network Module: The fusion wavelet side functions constructed in step S3.1 are used as learnable side functions in the Kolmogorov-Arnold network layer to construct a fusion wavelet KAN module, denoted as the FW-KAN module; the multi-scale non-stationary feature representation obtained in step S2 is input into the FW-KAN module to obtain the temporal features characterizing the dynamic changes of turbulence. Its expression is ,in, The input feature vector is composed of multi-scale non-stationary feature representations. This represents the Kolmogorov-Arnold network mapping function that embeds and fuses wavelet side functions.

[0023] Furthermore, step S4 specifically includes the following sub-steps:

[0024] S4.1 Construction and feature modeling of the spatiotemporal correlation prediction sub-model for satellite-to-ground laser links: The multi-scale non-stationary feature representation obtained in step S2 and the temporal features obtained in step S3 are aligned and fused according to the spatial grid position of the target link region and the temporal information of the link zenith angle or elevation angle to obtain the spatiotemporal fused feature map for the target satellite-to-ground laser link.

[0025] A spatiotemporal correlation prediction sub-model is constructed, comprising a feature embedding layer, at least one window attention feature update unit group, and a prediction mapping head; wherein, the window attention feature update unit group integrates a window multi-head self-attention unit, a shifted window multi-head self-attention unit, and the FW-KAN nonlinear feature mapping unit constructed in step S3; the FW-KAN nonlinear feature mapping unit is used to replace the conventional feedforward network to determine the slant path atmospheric coherence length. Mapping the relationships between local oscillations, short-term drops, and cross-scale nonlinear evolution;

[0026] The spatiotemporal fusion feature map is input into the feature embedding layer and window attention feature update unit group in the spatiotemporal correlation prediction sub-model to obtain the predicted feature sequence. The calculation process for each window attention feature update block is as follows: Wherein, W-MSA is window multi-head self-attention, SW-MSA is shift window multi-head self-attention, and FW-KAN is the fused wavelet KAN nonlinear feature mapping unit constructed in step S3. For layer normalization operation; Indicates the sequence number of the window attention feature update unit group. This represents the total number of window attention feature update unit groups; Indicates the first The input features of the window attention feature update unit group are updated. Representing input features The first intermediate feature obtained after updating by the W-MSA unit; Indicates the first intermediate feature The first updated feature obtained after FW-KAN nonlinear mapping; Indicates the first updated feature The second intermediate feature obtained after updating by the SW-MSA unit; Indicates the second intermediate feature The first one obtained after FW-KAN nonlinear mapping The output features of N window attention feature update unit groups are updated step by step to obtain the final predicted feature sequence zᴺ.

[0027] S4.2 Slant-path atmospheric coherence length prediction output: The predicted feature sequence is reconstructed into a slant-path atmospheric coherence length consistent with the spatial grid size of the target region using a prediction mapping function that includes linear mapping and spatial reconstruction. Predict the distribution to obtain future times. The atmospheric coherence length is predicted and distributed; further, based on the target satellite orbit information, ground station location, communication wavelength, and link zenith angle, the atmospheric coherence length is predicted from the slant path. The atmospheric coherence length prediction result corresponding to the target satellite-to-ground laser link is extracted from the predicted distribution.

[0028] This invention provides an effective solution for predicting atmospheric optical turbulence parameters in satellite-to-ground laser communication. Compared with existing technologies, the advantages of this invention are as follows:

[0029] First, by extracting multi-scale non-stationary features from the spatiotemporal distribution sequence of atmospheric coherence length, this invention can characterize the local fluctuations, abrupt changes, and cross-scale evolution of atmospheric turbulence, improving the physical consistency and interpretability of the prediction results. Second, leveraging the nonlinear dynamic modeling capabilities of FW-KAN, this invention can depict the nonlinear evolution of turbulence parameters over time, enhancing the response capability to rapidly changing states of satellite-to-ground laser links. Third, by modeling spatiotemporal fusion features through windowed multi-head self-attention and shifted windowed multi-head self-attention, this invention can capture spatial correlations within and across local windows, achieving the prediction and reconstruction of the spatiotemporal distribution of atmospheric coherence length. Finally, the atmospheric coherence length prediction results can be used for satellite-to-ground laser communication link evaluation, link switching, and transmission scheduling, thereby improving the stability and data transmission efficiency of satellite-to-ground laser communication links under complex meteorological environments. Attached Figure Description

[0030] Figure 1 This is a schematic diagram of the overall process of a method for predicting the slant path atmospheric coherence length for a satellite-to-ground laser link according to the present invention.

[0031] Figure 2 This is a schematic diagram illustrating the low-Earth orbit satellite-to-ground laser communication scenario and the physical damage to the atmospheric channel involved in the present invention. Figure 2 In the middle, (a) is a schematic diagram of global dynamic communication and atmospheric environment distribution of low-orbit satellites; (b) is a schematic diagram of laser beam phase distortion caused by atmospheric turbulence and multi-source heterogeneous sensor data integration (C-DIMM, SSM).

[0032] Figure 3 The three-dimensional atmospheric refractive index structure constant in the embodiments of the present invention ( A schematic diagram of the spatiotemporal evolution of the field at different points in time. Figure 3 In the above, (a) is 12:00 on February 15, 2025; (b) is 12:00 on April 15, 2025; (c) is 12:00 on June 15, 2025; and (d) is 12:00 on September 15, 2025.

[0033] Figure 4 This is a diagram illustrating the architecture of the atmospheric turbulence prediction method for the satellite-to-ground laser link of this invention. Figure 4 (a) shows the physical evolution module consisting of a fused wavelet kernel and a fused wavelet Kolmogorov-Arnold network; (b) shows the integrated topology of the hierarchical FW-KAN operator in the backbone network; (c) shows the process of applying this architecture to atmospheric turbulence field prediction; and (d) shows the window attention feature update structure in the W-KAST model.

[0034] Figure 5 This is a schematic diagram of the W-KAST module structure of the present invention. Figure 5 In the diagram, (a) represents the W-KAST module; (b) represents the window attention module; and (c) represents the adaptive fusion wavelet-KAN module.

[0035] Figure 6 This is a schematic diagram showing the atmospheric coherence length prediction results and spatial error distribution of the present invention: Figure 6 In the diagram, (a) shows the reference atmospheric coherence length distribution at a zenith angle of 30°. Figure 6 (b) in the figure shows the predicted atmospheric coherence length distribution when the zenith angle is 30°. Figure 6 (c) in the figure represents the spatial error distribution when the zenith angle is 30°; Figure 6 In the figure, (d) represents the reference atmospheric coherence length distribution at a zenith angle of 80°. Figure 6 In the diagram, (e) represents the predicted atmospheric coherence length distribution when the zenith angle is 80°. Figure 6 In the figure, (f) represents the spatial error distribution when the zenith angle is 80°. Detailed Implementation

[0036] The technical solutions of this invention have been clearly and completely described with reference to the accompanying drawings of the embodiments. It should be noted that the embodiments described represent only a part of this invention, and not all of it. Other embodiments obtained by those skilled in the art based on these embodiments are all within the scope of protection of this invention.

[0037] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0038] like Figure 1 As shown, this invention provides a method for predicting the slant-range atmospheric coherence length of a satellite-to-ground laser link. The method comprises four stages: link-constrained meteorological field and slant-range parameter generation, multi-scale feature construction, non-stationary evolution modeling, and spatiotemporal correlation prediction. First, the target link region is determined based on the target ground station location, target satellite orbit information, and the link zenith or elevation angle time series. A high-resolution meteorological spatiotemporal feature field is constructed, and a spatiotemporal distribution sequence of the slant-range atmospheric coherence length is generated through dynamic slant-range propagation path integration. Subsequently, multi-scale features are constructed from this sequence to obtain a multi-scale non-stationary feature representation of the link turbulence. Next, an FW-KAN module is constructed based on fused wavelet side functions to model the non-stationary evolution process of the slant-range atmospheric coherence length and extract the temporal features of the turbulent dynamic changes. Finally, the multi-scale non-stationary features are aligned and fused with the link geometric features, and a predicted feature sequence is obtained through a window attention feature update unit group. The predicted distribution of the slant-range atmospheric coherence length and the target link prediction results are then output.

[0039] A method for predicting the slant-path atmospheric coherence length for satellite-to-ground laser links, characterized by comprising the following steps:

[0040] Step 1: Construction of the meteorological field and generation of slant-path turbulence parameters for link geometry constraints: Based on the target ground station location, target satellite orbit information, communication wavelength, and the temporal information of the zenith angle or elevation angle of the target satellite-to-ground laser link, the target link region and the time-varying slant-path propagation path are determined; a high-resolution meteorological spatiotemporal characteristic field is constructed based on the meteorological data of the target link region, and turbulence parameter integration is performed along the slant-path propagation path to generate the slant-path atmospheric coherence length characterizing the turbulence intensity of the target satellite-to-ground laser link. Spatiotemporal distribution sequences, specifically including:

[0041] S1.1 Multidimensional Feature Extraction of Meteorological Parameters: Based on the target ground station location, target satellite orbit information, and the zenith angle or elevation angle time series information of the target satellite-to-ground laser link, the target link region and its corresponding meteorological calculation range are determined; meteorological data of the target region are acquired as the initial field and boundary conditions, including ERA5 reanalysis data or GFS forecast data; multidimensional meteorological parameters are extracted from the meteorological data, including temperature, specific humidity, three-dimensional wind speed components, and pressure field, and a meteorological feature set is constructed; the meteorological feature set is used as input, and nested simulation and dynamic downscaling are performed using numerical models to obtain a high-resolution meteorological spatiotemporal feature field corresponding to the meteorological feature set.

[0042] In the model configuration, a physical parameterization scheme capable of resolving small-scale perturbations within the optical channel was selected. Specifically, the planetary boundary layer (PBL) was parameterized using the Mellor-Yamada-Nakanishi-Niino (MYNN) 2.5-order turbulent kinetic energy (TKE) scheme, while the surface layer was described using the MM5 similarity theory scheme. The MYNN scheme incorporates turbulent kinetic energy prediction equations to describe the hydrodynamic energy distribution.

[0043] S1.2 Calculation of the spatiotemporal distribution sequence of slant-path atmospheric coherence length: Based on the high-resolution meteorological spatiotemporal characteristic field obtained in step S1.1, the slant-path propagation path varying with time is determined according to the target satellite orbit information, target ground station location, communication wavelength, and the zenith angle or elevation angle of the target satellite-to-ground laser link at different times. Using the air pressure, absolute temperature, and potential temperature gradient in the high-resolution meteorological spatiotemporal characteristic field, turbulence parameters are integrated along the slant-path propagation path to obtain the slant-path atmospheric coherence length characterizing the turbulence intensity of the target satellite-to-ground laser link at the corresponding time and corresponding spatial grid location. Its expression is: in, For wavelength, Zenith angle, This is the maximum height for the points. Pi For height The air pressure at that location For height The absolute temperature at that location It is an empirical constant. For potential temperature gradient, For potential temperature, This is an external-scale parameter related to atmospheric stability, expressed as: Obtain the horizontal wind component and Calculate wind shear , Regarding wind shear Piecewise function of potential temperature gradient: .

[0044] like Figure 2 As shown, the prediction method of this invention is designed for the complex physical environment of low-Earth orbit satellite-to-ground laser communication. Among other things, Figure 2 (a) in the image shows a dynamic communication scenario between a low-orbit satellite constellation and a ground station. When the laser link penetrates the atmosphere, it is affected by the meteorological environment and faces significant non-stationary turbulent fluctuations. Figure 2 (b) further reveals the random phase distortion induced by optical turbulence, which manifests as spot flicker and wavefront distortion at the receiver, severely affecting link performance. To achieve accurate characterization, measured data acquired by the C-DIMM and SSM equipped at the ground station, combined with the high-resolution feature field generated by WRF numerical simulation, jointly drive the W-KAST model to predict the evolution of non-stationary atmospheric channels.

[0045] like Figure 3 The figure shows a three-dimensional high-resolution reconstruction of the intensity of atmospheric optical turbulence (OT) in the target airspace. Figures (a) to (d) show the atmospheric refractive index structure constant at typical times in different seasons. The spatiotemporal dynamic evolution of optical turbulence with altitude and horizontal geographic coordinates is depicted. In this 3D volumetric rendering, the vertical axis covers a key atmospheric region from the near-surface layer to the lower stratosphere (approximately 0-30 km), while the horizontal axis corresponds to latitude and longitude grid indices. This reconstructed field clearly demonstrates the vertical stratification characteristics of optical turbulence, particularly capturing the significant turbulence enhancement layer near the tropopause, which is crucial for accurate estimation. It provides a robust physical basis.

[0046] Step 2, Multi-scale feature construction for link turbulent non-stationary characteristics: The slant path atmospheric coherence length obtained in step S1... Multi-scale feature extraction is performed on the spatiotemporal distribution sequence to generate multi-scale non-stationary feature representations that characterize the effects of local fluctuations in atmospheric turbulence, abrupt changes in stratification, cross-scale evolution, and changes in link geometry. Specifically, it includes:

[0047] S2.1 Wavelet Function Selection and Link Turbulence Multi-Scale Feature Extraction: Multi-scale feature extraction is performed on the spatiotemporal distribution sequence of the slant path atmospheric coherence length obtained in step S1. The slant path atmospheric coherence length... The spatiotemporal distribution sequence contains non-stationary fluctuations caused by changes in atmospheric turbulent stratification, local abrupt changes, short-term degradation, and variations in link zenith or elevation angles; the slant path atmospheric coherence length is extracted using the Morlet wavelet function. The local oscillation and frequency variation characteristics of the spatiotemporal distribution sequence were analyzed, and the slant atmospheric coherence length was extracted using the Mexican-Hat wavelet function. Peak-valley structure and local abrupt change characteristics in spatiotemporal distribution sequences; based on learnable gating parameters Generate fusion weights Sigmoid The fusion wavelet kernel is obtained: in, For input feature variables, For Morlet wavelet functions, For Mexican-Hat wavelet functions, For weighting;

[0048] S2.2 Generation of Multi-Scale Fusion Wavelet Basis Functions: Fusion weights between the Morlet and Mexican-Hat wavelet functions are generated based on learnable gating parameters, and multi-scale fusion wavelet basis functions are generated by combining scale and translation parameters; these multi-scale fusion wavelet basis functions are then applied to the atmospheric coherence length. The spatiotemporal distribution sequence yields a multi-scale non-stationary characteristic representation of the effects of local atmospheric turbulence fluctuations, short-term abrupt changes, cross-scale evolution, and link geometric modulation in the target satellite-to-ground laser link. Based on scale parameters Translation parameters Generate multi-scale wavelet basis functions: in, To fuse wavelet kernels, For the first The first scale and the first The multi-scale fused wavelet basis functions corresponding to each translation position The parameters are learnable gating parameters, and Sigmoid(·) is the activation function. For the first Each scale parameter For the first A translation parameter is used. Fusion weights are generated based on learnable gating parameters, and the Morlet wavelet function and the Mexican-Hat wavelet function are weighted and fused to generate a multi-scale fused wavelet basis function at the corresponding scale and translation position. This multi-scale fused wavelet basis function is applied to the spatiotemporal distribution sequence of atmospheric coherence length to obtain a multi-scale non-stationary feature representation. .

[0049] Step 3, Non-stationary evolution modeling based on fused wavelet KAN: Based on the multi-scale non-stationary feature representation obtained in step S2 A nonlinear dynamic modeling module of the Kolmogorov-Arnold network, incorporating fused wavelet side functions, is constructed to model the nonstationary temporal evolution of atmospheric turbulence in the target satellite-to-ground laser link, obtaining temporal characteristics characterizing the dynamic changes of turbulence, specifically including:

[0050] S3.1 Construction of Fusion Wavelet Side Functions for Non-stationary Evolution of Slant-Path Turbulence: Based on a learnable fusion form of the Morlet wavelet and Mexican-Hat wavelet functions, a method is constructed to characterize the slant-path atmospheric coherence length. The non-stationary fusion wavelet side function, which is represented as the superposition of a linear term and a multi-scale fusion wavelet expansion term, is expressed as follows: in, The scalar eigenvalues ​​are input to the fused wavelet side functions. For the first Layer The input node to the th Layer The fusion of wavelet side functions between output nodes For the weights of the linear terms, For the first The first scale and the first The wavelet expansion coefficients corresponding to each translation position For the first Each scale parameter For the first One translation parameter, For scale quantity This represents the number of translation positions. For Morlet wavelet functions, For Mexican-Hat wavelet functions, To integrate weights, Sigmoid , Sigmoid is a learnable gating parameter. For activation functions;

[0051] S3.2 Construction of the Fusion Wavelet Kolmogorov-Arnold Network Module: The fusion wavelet side functions constructed in step S3.1 are used as learnable side functions in the Kolmogorov-Arnold network layer to construct a fusion wavelet KAN module, denoted as the FW-KAN module; the multi-scale non-stationary feature representation obtained in step S2 is input into the FW-KAN module to obtain the temporal features characterizing the dynamic changes of turbulence. Its expression is ,in, The input feature vector is composed of multi-scale non-stationary feature representations. This represents the Kolmogorov-Arnold network mapping function that embeds and fuses wavelet side functions.

[0052] FW-KAN edge function construction: Constructing a hierarchical evolutionary model based on function composition, targeting models with... input nodes and The KAN (Kolmogorov-Arnold network) layers with output nodes have a mapping relationship determined by a learnable one-dimensional activation function matrix. control; Indicates the first Layer The input value of the nth neuron, the nth The first in the layer Activation value of each neuron It is determined by the sum of the activated values ​​of all input nodes in the previous layer, and the calculation formula is as follows: For deep architectures, through Each successive layer extends the above transformation to construct a composite function form representing the overall representation: Using function composition operators Hierarchical mapping is achieved to approximate the complex multi-scale nonlinear characteristics in turbulent evolution.

[0053] Step 4, Spatiotemporal correlation prediction for satellite-to-ground laser links: based on the multi-scale non-stationary feature representation obtained in step S2. Based on the temporal features obtained in step S3, a spatiotemporal correlation prediction model is constructed to predict the atmospheric turbulence state of the target link region in the future, and outputs the slant path atmospheric coherence length at the future time. The distribution is predicted, and based on the target ground station location, target satellite orbit information, and link zenith angle or elevation angle information, the slant path atmospheric coherence length is calculated. The predicted atmospheric coherence length of the target satellite-to-ground laser link is extracted from the predicted distribution, specifically including:

[0054] S4.1 Construction and feature modeling of the spatiotemporal correlation prediction sub-model for satellite-to-ground laser links: The multi-scale non-stationary feature representation obtained in step S2 and the temporal features obtained in step S3 are aligned and fused according to the spatial grid position of the target link region and the temporal information of the link zenith angle or elevation angle to obtain the spatiotemporal fused feature map for the target satellite-to-ground laser link.

[0055] A spatiotemporal correlation prediction sub-model is constructed, comprising a feature embedding layer, at least one window attention feature update unit group, and a prediction mapping head; wherein, the window attention feature update unit group integrates a window multi-head self-attention unit, a shifted window multi-head self-attention unit, and the FW-KAN nonlinear feature mapping unit constructed in step S3; the FW-KAN nonlinear feature mapping unit is used to replace the conventional feedforward network to determine the slant path atmospheric coherence length. Mapping the relationships between local oscillations, short-term drops, and cross-scale nonlinear evolution;

[0056] The spatiotemporal fusion feature map is input into the feature embedding layer and window attention feature update unit group in the spatiotemporal correlation prediction sub-model to obtain the predicted feature sequence. The calculation process for each window attention feature update block is as follows: Wherein, W-MSA is window multi-head self-attention, SW-MSA is shift window multi-head self-attention, and FW-KAN is the fused wavelet KAN nonlinear feature mapping unit constructed in step S3. For layer normalization operation; Indicates the sequence number of the window attention feature update unit group. This represents the total number of window attention feature update unit groups; Indicates the first The input features of the window attention feature update unit group are updated. Representing input features The first intermediate feature obtained after updating by the W-MSA unit; Indicates the first intermediate feature The first updated feature obtained after FW-KAN nonlinear mapping; Indicates the first updated feature The second intermediate feature obtained after updating by the SW-MSA unit; Indicates the second intermediate feature The first one obtained after FW-KAN nonlinear mapping The output features of N window attention feature update unit groups are updated step by step to obtain the final predicted feature sequence zᴺ.

[0057] S4.2 Slant-path atmospheric coherence length prediction output: The predicted feature sequence is reconstructed into a slant-path atmospheric coherence length consistent with the spatial grid size of the target region using a prediction mapping function that includes linear mapping and spatial reconstruction. Predict the distribution to obtain future times. The atmospheric coherence length is predicted and distributed; further, based on the target satellite orbit information, ground station location, communication wavelength, and link zenith angle, the atmospheric coherence length is predicted from the slant path. The atmospheric coherence length prediction result corresponding to the target satellite-to-ground laser link is extracted from the predicted distribution.

[0058] The spatial reconstruction layer employs at least one of the following: a tile expansion layer, a transposed convolutional layer, or a bilinear upsampling layer, to convert the feature sequence output by the last window attention block into a single layer. Restored to the same spatial grid size as the target area Spatial distribution of atmospheric coherence length, and obtaining future times. Predicted distribution of atmospheric coherence length Its expression is: in, Predict the distribution of atmospheric coherence length in the target region. To predict the time step, The feature sequence output by the last window attention block. This is the prediction mapping function.

[0059] During the model training phase, the spatiotemporal distribution sequence of atmospheric coherence length within a continuous historical time window is used as the training input, and the spatial distribution of atmospheric coherence length corresponding to future times is used as the supervision label. The mean absolute error, mean square error, or a weighted combination of the two between the predicted distribution and the reference distribution is used as the loss function to optimize the parameters of the prediction model. Furthermore, based on the target satellite orbit information, ground station location, and link zenith angle, the predicted atmospheric coherence length of the target satellite-to-ground laser link is extracted from the predicted atmospheric coherence length distribution of the target region.

[0060] Figure 4This invention presents a spatiotemporal correlation prediction model based on the fusion of wavelet KAN and window attention mechanisms, denoted as the W-KAST model. This model takes historical atmospheric coherence length spatial field data as input and outputs predictions of the spatial distribution of atmospheric coherence length at future times. Figure 4 (a) in the diagram illustrates the overall input-output flow of the model; Figure 4 (b) shows the construction process of the multi-scale fusion wavelet basis function, in which Morlet wavelet and Mexican-Hat wavelet are used as basis functions, and the fusion weight is adaptively adjusted through learnable gating parameters. The multi-scale fusion wavelet response is generated by combining the scale parameters and translation parameters. Figure 4 (c) shows the FW-KAN nonlinear feature mapping unit, in which multi-scale fused wavelet basis functions are used as FW-KAN input basis to construct the nonlinear mapping in the Kolmogorov-Arnold network; Figure 4 Figure (d) shows the window attention feature update structure in the W-KAST model, which captures the spatial correlation within and across windows through window multi-head self-attention units and shift window multi-head self-attention units, and enhances the feature mapping capability by using FW-KAN nonlinear feature mapping units.

[0061] Figure 5 The structure of key modules in the spatiotemporal correlation prediction model is further illustrated. For example... Figure 5 As shown in (a), the window attention feature update unit group adopts a pre-normalized residual structure, which consists of a window attention sub-layer and an FW-KAN nonlinear feature mapping sub-layer. Layer scaling mechanism and random depth mechanism are introduced to improve the model training stability. Figure 5 (b) shows a windowed multi-head self-attention unit that divides the input feature map into local windows of a preset size and performs query, key-value linear mapping and multi-head scaling dot product attention calculation within each local window to extract local spatially relevant features. Figure 5 (c) shows the fusion wavelet KAN module, which includes a wavelet basis branch and a linear mapping branch. The wavelet basis branch performs learnable gating fusion of Mexican-Hat wavelets and Morlet wavelets through learnable scale parameters and translation parameters to form a fusion wavelet kernel, and combines it with the Kolmogorov-Arnold network mapping framework to realize multi-scale nonlinear representation of non-stationary features.

[0062] Figure 6The reference distribution, predicted distribution, and spatial error distribution of atmospheric coherence length under different zenith angles are presented. Specifically, (a) shows the reference atmospheric coherence length distribution at a zenith angle of 30°, (b) shows the predicted atmospheric coherence length distribution at a zenith angle of 30°, (c) shows the spatial error distribution at a zenith angle of 30°, (d) shows the reference atmospheric coherence length distribution at a zenith angle of 80°, (e) shows the predicted atmospheric coherence length distribution at a zenith angle of 80°, and (f) shows the spatial error distribution at a zenith angle of 80°. The spatial error is the difference between the predicted atmospheric coherence length and the reference atmospheric coherence length. Figure 6 It can be seen that the prediction model can maintain the main spatial distribution characteristics of the atmospheric coherence length field under different zenith angle conditions, so that the predicted distribution and the reference distribution are consistent in overall shape and local variation trend, thus providing a data basis for the prediction of atmospheric turbulence intensity and link status assessment of the satellite-to-ground laser communication link.

Claims

1. A method for predicting the slant path atmospheric coherence length for satellite-to-ground laser links, characterized in that, Includes the following steps: S1. Construction of meteorological field and generation of slant-path turbulence parameters for link geometry constraints: Based on the target ground station location, target satellite orbit information, communication wavelength, and the zenith angle or elevation angle time series information of the target satellite-to-ground laser link, the target link region and the time-varying slant-path propagation path are determined; a high-resolution meteorological spatiotemporal characteristic field is constructed based on the meteorological data of the target link region, and turbulence parameter integration is performed along the slant-path propagation path to generate the slant-path atmospheric coherence length characterizing the turbulence intensity of the target satellite-to-ground laser link. Spatiotemporal distribution sequence; S2. Construction of multi-scale features for link turbulent nonstationary characteristics: The slant path atmospheric coherence length obtained in step S1... Multi-scale feature extraction is performed on the spatiotemporal distribution sequence to generate multi-scale non-stationary feature representations that characterize the effects of local fluctuations in atmospheric turbulence, abrupt changes in stratification, cross-scale evolution, and changes in link geometry. ; S3. Non-stationary evolution modeling based on fused wavelet KAN: Based on the multi-scale non-stationary feature representation obtained in step S2 A nonlinear dynamic modeling module of the Kolmogorov-Arnold network containing fused wavelet side functions was constructed to model the non-stationary temporal evolution of atmospheric turbulence in the target satellite-to-ground laser link, and to obtain temporal features characterizing the dynamic changes of turbulence. S4. Spatiotemporal correlation prediction for satellite-to-ground laser links: based on the multi-scale non-stationary feature representation obtained in step S2. Based on the temporal features obtained in step S3, a spatiotemporal correlation prediction model is constructed to predict the atmospheric turbulence state of the target link region in the future, and outputs the slant path atmospheric coherence length at the future time. The distribution is predicted, and based on the target ground station location, target satellite orbit information, and link zenith angle or elevation angle information, the slant path atmospheric coherence length is calculated. The predicted atmospheric coherence length of the target satellite-to-ground laser link is extracted from the predicted distribution. The specific steps of step S2 are as follows: S2.1 Wavelet Function Selection and Multi-Scale Feature Extraction of Link Turbulence: Multi-scale feature extraction is performed on the spatiotemporal distribution sequence of the slant path atmospheric coherence length obtained in step S1. The slant path atmospheric coherence length... The spatiotemporal distribution sequence contains non-stationary fluctuations caused by changes in atmospheric turbulent stratification, local abrupt changes, short-term degradation, and variations in link zenith or elevation angles; the slant path atmospheric coherence length is extracted using the Morlet wavelet function. The local oscillation and frequency variation characteristics of the spatiotemporal distribution sequence were analyzed, and the slant atmospheric coherence length was extracted using the Mexican-Hat wavelet function. Peak-valley structure and local abrupt change characteristics in spatiotemporal distribution sequences; S2.2 Generation of Multi-Scale Fusion Wavelet Basis Function: Based on learnable gating parameters, fusion weights between the Morlet wavelet function and the Mexican-Hat wavelet function are generated, and combined with scale and translation parameters to generate a multi-scale fusion wavelet basis function; the multi-scale fusion wavelet basis function is then applied to the atmospheric coherence length. The spatiotemporal distribution sequence yields a multi-scale non-stationary characteristic representation of the effects of local atmospheric turbulence fluctuations, short-term abrupt changes, cross-scale evolution, and link geometric modulation in the target satellite-to-ground laser link. .

2. The method for predicting the slant path atmospheric coherence length for a satellite-to-ground laser link according to claim 1, characterized in that, The specific steps of step S1 are as follows: S1.1 Multidimensional Feature Extraction of Meteorological Parameters: Based on the target ground station location, target satellite orbit information, and the zenith angle or elevation angle time series information of the target satellite-to-ground laser link, the target link region and its corresponding meteorological calculation range are determined; meteorological data of the target region are acquired as the initial field and boundary conditions, including ERA5 reanalysis data or GFS forecast data; multidimensional meteorological parameters are extracted from the meteorological data, including temperature, specific humidity, three-dimensional wind speed components, and pressure field, and a meteorological feature set is constructed; the meteorological feature set is used as input, and nested simulation and dynamic downscaling are performed using numerical models to obtain a high-resolution meteorological spatiotemporal feature field corresponding to the meteorological feature set; S1.2 Calculation of the spatiotemporal distribution sequence of slant-path atmospheric coherence length: Based on the high-resolution meteorological spatiotemporal characteristic field obtained in step S1.1, the slant-path propagation path varying with time is determined according to the target satellite orbit information, target ground station location, communication wavelength, and the zenith angle or elevation angle of the target satellite-to-ground laser link at different times. Using the air pressure, absolute temperature, and potential temperature gradient in the high-resolution meteorological spatiotemporal characteristic field, turbulence parameters are integrated along the slant-path propagation path to obtain the slant-path atmospheric coherence length characterizing the turbulence intensity of the target satellite-to-ground laser link at the corresponding time and corresponding spatial grid location. Its expression is: in, For wavelength, Zenith angle, This is the maximum height for the points. Pi For height The air pressure at that location For height The absolute temperature at that location It is an empirical constant. It is an exoscale parameter and is related to atmospheric stability. For potential temperature gradient, This refers to the potential temperature.

3. The method for predicting the slant path atmospheric coherence length for a satellite-to-ground laser link according to claim 1, characterized in that, The specific steps of step S3 are as follows: S3.1 Construction of Fusion Wavelet Side Functions for Non-stationary Evolution of Slant-Path Turbulence: Based on the learnable fusion form of the Morlet wavelet function and the Mexican-Hat wavelet function, a method for characterizing the slant-path atmospheric coherence length is constructed. The non-stationary fusion wavelet side function, which is represented as the superposition of a linear term and a multi-scale fusion wavelet expansion term, is expressed as follows: in, The scalar eigenvalues ​​are input to the fused wavelet side functions. For the first Layer The input node to the th Layer The fusion of wavelet side functions between output nodes For the weights of the linear terms, For the first The first scale and the first The wavelet expansion coefficients corresponding to each translation position For the first Each scale parameter For the first One translation parameter, For scale quantity This represents the number of translation positions. For Morlet wavelet functions, For Mexican-Hat wavelet functions, To integrate weights, Sigmoid , Sigmoid is a learnable gating parameter. For activation functions; S3.2 Construction of the Fusion Wavelet Kolmogorov-Arnold Network Module: The fusion wavelet side functions constructed in step S3.1 are used as learnable side functions in the Kolmogorov-Arnold network layer to construct a fusion wavelet KAN module, denoted as the FW-KAN module; the multi-scale non-stationary feature representation obtained in step S2 is input into the FW-KAN module to obtain the temporal features characterizing the dynamic changes of turbulence. Its expression is ,in, The input feature vector is composed of multi-scale non-stationary feature representations. This represents the Kolmogorov-Arnold network mapping function that embeds and fuses wavelet side functions.

4. The method for predicting the slant-path atmospheric coherence length for a satellite-to-ground laser link according to claim 1, characterized in that... The specific steps of step S4 are as follows: S4.1 Construction and feature modeling of the spatiotemporal correlation prediction sub-model for satellite-to-ground laser links: The multi-scale non-stationary feature representation obtained in step S2 and the temporal features obtained in step S3 are aligned and fused according to the spatial grid position of the target link region and the temporal information of the link zenith angle or elevation angle to obtain the spatiotemporal fusion feature map for the target satellite-to-ground laser link. A spatiotemporal correlation prediction sub-model is constructed, comprising a feature embedding layer, at least one window attention feature update unit group, and a prediction mapping head; wherein, the window attention feature update unit group integrates a window multi-head self-attention unit, a shifted window multi-head self-attention unit, and the FW-KAN nonlinear feature mapping unit constructed in step S3; the FW-KAN nonlinear feature mapping unit is used to replace the conventional feedforward network to determine the slant path atmospheric coherence length. Mapping the relationships between local oscillations, short-term drops, and cross-scale nonlinear evolution; The spatiotemporal fusion feature map is input into the feature embedding layer and window attention feature update unit group in the spatiotemporal correlation prediction sub-model to obtain the predicted feature sequence. The calculation process for each window attention feature update block is as follows: Wherein, W-MSA is window multi-head self-attention, SW-MSA is shift window multi-head self-attention, and FW-KAN is the fused wavelet KAN nonlinear feature mapping unit constructed in step S3. For layer normalization operation; Indicates the sequence number of the window attention feature update unit group. This represents the total number of window attention feature update unit groups; Indicates the first The input features of the window attention feature update unit group are updated. Representing input features The first intermediate feature obtained after updating by the W-MSA unit; Indicates the first intermediate feature The first updated feature obtained after FW-KAN nonlinear mapping; Indicates the first updated feature The second intermediate feature obtained after updating by the SW-MSA unit; Indicates the second intermediate feature The first one obtained after FW-KAN nonlinear mapping The output features of N window attention feature update unit groups are updated step by step to obtain the final predicted feature sequence zᴺ. S4.2, Slant-path atmospheric coherence length prediction output: Through a prediction mapping function including linear mapping and spatial reconstruction, the predicted feature sequence is reconstructed into a slant-path atmospheric coherence length consistent with the spatial grid size of the target region. Predict the distribution to obtain future times. The atmospheric coherence length is predicted and distributed; further, based on the target satellite orbit information, ground station location, communication wavelength, and link zenith angle, the atmospheric coherence length is predicted from the slant path. The atmospheric coherence length prediction result corresponding to the target satellite-to-ground laser link is extracted from the predicted distribution.

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