A method for calibrating space-time distortion of microwave link in extreme weather

Abstract

The application discloses a kind of microwave link electromagnetic feature distortion's space-time calibration method under extreme weather condition, belong to microwave communication monitoring and meteorological sensing field.Synchronous acquisition multi-frequency point and / or dual-polarization electromagnetic feature and multi-source meteorological data, obtains debasement electromagnetic distortion by double time scale robust baseline decomposition;Reconstruction and segmented propagation path, heterogeneous meteorological data is standardized as observation unit with space-time support domain and quality confidence, using non-equilibrium optimal transport completes the space-time alignment of observation unit and path unit;Using physical constraint hybrid expert model for segmented calibration, and by propagation path graph residual model correction distortion migration, accumulation and attenuation;By path integral conservation constraint and physical feasible region projection obtains calibration result, according to reliability implements safety backoff, and using fast and slow parameter online update forms closed loop calibration.The application can improve the alignment accuracy, calibration reliability and environmental adaptability of asynchronous heterogeneous data under extreme weather.

Description

Technical Field

[0001] This invention relates to the field of microwave communication monitoring and meteorological observation technology, and in particular to a method for spatiotemporal calibration of microwave link distortion in extreme weather. Background Technology

[0002] With the rapid development of urban communication networks and mobile backhaul systems, numerous microwave links continuously output electromagnetic characteristics such as received signal levels, carrier phase, cross-polarization discrimination, and Doppler shift. Rainfall, hail, freezing rain, and their combined effects can alter these characteristics through absorption, scattering, depolarization, multipath propagation, and radome cladding (water or ice). Therefore, utilizing existing microwave links to sense meteorological information allows for path integral observations to be obtained without the need for large-scale deployment of dedicated sensors. This can be used for monitoring short-term heavy rainfall, issuing severe weather warnings, and assessing the operational status of communication links.

[0003] Existing microwave link meteorological inversion methods typically use the clear-sky received signal level as a reference, calculate rainfall based on the power function relationship between rainfall ratio attenuation and rainfall rate, or use empirical regression models to compensate for signal attenuation. These methods are applicable to light to moderate rain and when water condensate is relatively uniformly distributed along the link. However, in extreme weather conditions such as rainstorm cores, hail bands, freezing rain with icing, and mixed rain and hail, the medium along the link exhibits strong non-uniformity, and nonlinear coupling exists between different electromagnetic characteristics. This makes it difficult to maintain calibration accuracy using a single attenuation feature and a unified compensation model.

[0004] First, existing methods mostly use fixed clear-sky averages or simple moving averages as baselines, which makes it difficult to separate slowly varying components such as equipment temperature drift, changes in transmit power control, and antenna aging from rapidly varying distortions caused by extreme weather. Baseline shifts can cause additional attenuation, phase shifts, and polarization shifts to be systematically overestimated or underestimated.

[0005] Second, the sampling periods, transmission delays, and spatial support domains of microwave links, weather radars, satellite remote sensing, and ground weather stations are not consistent. Existing matching methods based on the nearest time, nearest station, or link midpoint do not consider the advection delay caused by the direction and speed of weather cell movement, which can easily lead to simultaneous temporal and spatial mismatches when rainstorm cores rapidly move into or out of the link.

[0006] Third, the mechanisms by which heavy rain, hail, and freezing rain affect microwave signals differ significantly. Heavy rain primarily causes absorption and scattering attenuation, hail also produces non-Rayleigh scattering, depolarization, and short-term scintillation, while freezing rain creates additional attenuation due to icing with accumulation and melting hysteresis characteristics. Using a single regression model to handle all operating conditions makes it difficult to accurately allocate the contributions of each physical mechanism in weather type transitions and complex events.

[0007] Fourth, existing physical models mostly output the average attenuation of the entire link, which makes it difficult to describe the segmented distribution and propagation relationship of local rainstorm cores or hail belts along the link; although pure data-driven models can fit nonlinear residuals, they may produce results that violate the propagation law, such as negative attenuation and inconsistent path segment integrals with the total link attenuation, in extreme conditions not covered by training samples.

[0008] Fifth, existing calibration methods typically output only a single-point estimate, lacking uncertainty assessments related to observation completeness, multi-source matching quality, and model extrapolation accuracy. When radar is blocked, ground stations are missing data, or weather changes abruptly, the calibration value will still output a deterministic result, making it difficult to provide reliable risk boundaries for meteorological warnings and data link maintenance.

[0009] Sixth, existing online calibrations typically use a uniform learning rate to update the baseline, propagation coefficient, and nonlinear correction parameters. This approach can lead to lag in tracking rapidly changing weather parameters, and can also cause the normally stable clear-sky baseline and physical propagation coefficient to be rewritten by a single anomalous event, resulting in long-term parameter drift.

[0010] Therefore, how to unify electromagnetic characteristic baseline separation, asynchronous multi-source observation spatiotemporal matching, propagation mechanisms of different extreme weather, path segment nonlinear calibration, uncertainty evaluation, and online parameter updates into the same closed loop has become a key technical issue for improving the accuracy, interpretability, and engineering usability of microwave link electromagnetic characteristic calibration under extreme weather conditions. Summary of the Invention

[0011] To address the aforementioned problems, this invention aims to provide a spatiotemporal calibration method for microwave link distortion in extreme weather. This method involves collecting electromagnetic characteristic data such as microwave link transmit / receive levels, attenuation, phase, and bit error rate, and fusing multi-source meteorological observation data including radar, rainfall, temperature and humidity, wind speed, and icing. A dynamic clear-sky baseline, adaptively updated according to equipment status changes, is constructed using fast and slow timescale decomposition to separate equipment drift from weather distortion. A spatiotemporal matching model for propagation delay perception is established based on the meteorological unit's moving speed, propagation direction, link location, and effective coverage length, achieving accurate correspondence between asynchronous meteorological observations and the link propagation path. Finally, a hybrid expert model is constrained by the physical attenuation laws of extreme weather to calibrate the distortion caused by heavy rain, hail, and freezing temperatures. This invention identifies rain, strong winds, and their combined effects, determining the contribution of different weather factors to link distortion. The propagation path is further divided into multiple spatially related link segments. A path graph residual calibration model describes the propagation, superposition, and attenuation of local distortion between adjacent segments, obtaining link-level distortion reconstruction values. Based on this, the uncertainty of the calibration results is quantified, outputting calibration values ​​and their confidence intervals. A safety backoff is implemented when observations are missing or model confidence is insufficient. Finally, a variable-point triggered fast and slow parameter collaborative update mechanism is used to update weather response parameters and equipment baseline parameters, forming a closed-loop calibration process of "data acquisition - spatiotemporal matching - weather type determination - path reconstruction - reliable calibration - online update". This invention improves the accuracy, stability, and interpretability of microwave link electromagnetic characteristic calibration under extreme and combined weather conditions, providing a reliable basis for link status monitoring, anomaly diagnosis, and communication quality assurance.

[0012] To achieve the above objectives, the present invention provides a method for spatiotemporal calibration of microwave link distortion in extreme weather as follows: A method for spatiotemporal calibration of microwave link distortion in extreme weather includes a multi-source data synchronous acquisition module, a dual-timescale robust baseline decomposition model, a propagation path segmentation model, a meteorological observation unit standardization model, a spatiotemporal nonequilibrium optimal transmission alignment model, a physically constrained hybrid expert model, a propagation path graph residual calibration model, a physical consistency constraint model, a calibration reliability assessment model, a safety backoff model, and a fast / slow parameter online update model. The multi-source data synchronous acquisition module acquires multi-frequency and / or dual-polarized electromagnetic characteristic sequences output from the microwave link transmitter and receiver, and acquires data from meteorological radar, satellite remote sensing, ground meteorological stations, and link location. It writes acquisition timestamps for various data types based on a unified timing signal. The characteristics include at least two of the following: received signal level, carrier phase, polarization angle, cross-polarization discrimination, and Doppler shift; the dual-time-scale robust baseline decomposition model is used to decompose the quality-controlled electromagnetic feature sequence to obtain clear-sky baseline components, extreme weather distortion components, equipment slow drift components, and random noise components, and to construct a counterfactual clear-sky reference using the clear-sky baseline components that do not change with a single extreme weather event; the propagation path segmentation model is used to reconstruct the link propagation path based on the three-dimensional coordinates of the microwave link transceiver, antenna height, digital elevation model, effective sphere radius, and atmospheric refraction parameters, and to divide the propagation path into multiple path units according to changes in the propagation environment and spatial resolution; the meteorological observation unit standardization model This method is used to convert meteorological observations from different sources, with different sampling periods, and different spatial resolutions into observation units that simultaneously possess temporal support domains, spatial support domains, and quality confidence levels. The spatiotemporal nonequilibrium optimal transmission alignment model is used to establish a joint cost matrix based on the sampling time difference between path units and observation units, weather cell advection lag, three-dimensional spatial distance, observation support domain overlap, and physical feature differences. It solves for the coupling matrix between path units and observation units using entropy-regularized nonequilibrium optimal transmission with edge relaxation terms, and aligns asynchronous multi-source meteorological observations to the corresponding path units based on the coupling matrix. The physically constrained hybrid expert model is used to receive the aligned meteorological observations, remove baseline electromagnetic distortion, perform multi-frequency differential features, and dual-polarization differential. The characteristics and observation quality characteristics are used to determine the initial weights of different extreme weather types through gating units. The initial weights are then corrected based on the violation of the physical propagation laws by the output results of each weather expert. Then, the candidate calibration quantities are output by rainstorm experts, hail experts, freezing rain experts, and composite event experts respectively, and weighted fusion is performed to obtain the segmented physical calibration results of each path unit. The propagation path graph residual calibration model is used to construct a propagation path graph with directed edges and edge weights based on the path unit as nodes and the adjacency relationship, spatial distance, weather cell movement direction, and propagation time delay between path units. The segmented physical calibration results are then subjected to nonlinear residual correction to characterize the migration, accumulation, and attenuation relationship of local electromagnetic distortion on the propagation path.The physical consistency constraint model applies path integral conservation constraints to the calibration results of each path unit and projects the corrected results onto a physically feasible region determined by the electromagnetic propagation mechanism and the range of meteorological parameters, obtaining the calibrated electromagnetic characteristics and corresponding meteorological parameters. The calibration reliability assessment model calculates finite sample quantiles based on the inconsistency scores of the calibration samples, generating a reliability interval for the calibrated electromagnetic characteristics or meteorological parameters. The safety backoff model suppresses the nonlinear residual output of the propagation path graph residual calibration model when the reliability of the calibration results is below a set threshold, switches to a conservative calibration mode based on physical propagation relationships, and outputs a low reliability marker. The fast and slow parameter online update model performs online change point detection on the calibration residuals. When the change point statistics exceed a set threshold, it quickly updates the gating parameters, graph residual parameters, and time delay parameters. When the change point statistics remain below the set threshold within a stable window, it updates the clear-sky baseline parameters and physical propagation parameters at a learning rate lower than the fast parameter update learning rate, thus forming a closed-loop spatiotemporal calibration mechanism that separates rapid response parameters for extreme weather from long-term equipment evolution parameters.

[0013] The dual-time-scale robust baseline decomposition model of this invention is as follows: For the The link at time The collected electromagnetic features are defined as follows: (1) In equation (1), Indicates the first The microwave link at time The collected electromagnetic feature vectors; This represents the clear-sky baseline component, which is related to the daily cycle, seasonal variations, and normal atmospheric refraction conditions. This indicates sparse or segmented sparse distortion components caused by heavy rain, hail, freezing rain, or a combination of extreme weather events. This indicates the slow drift component caused by equipment temperature drift, changes in transmit power control, or antenna aging. Represents random noise components; Indicates microwave link index. , This indicates the total number of microwave links participating in the calibration. Indicates the discrete sampling time; superscript The symbol represents the observable; the bold symbol represents a vector composed of different frequencies, polarization modes, or electromagnetic characteristic types.

[0014] Organize the multi-link observations within the sliding window into a matrix. The quality mask matrix is ​​denoted as The clear-sky baseline, weather distortion, and equipment drift are solved using the following formula: (2) In equation (2), This represents the observation matrix within the sliding window, which consists of multiple links, multiple frequency points, and multiple polarization electromagnetic features. , and Let represent the clear-sky baseline matrix, extreme weather distortion matrix, and equipment slow drift matrix to be solved, respectively; Indicates and For mass mask matrices of the same dimension, the effective observation locations are assigned corresponding mass weights, while the missing observation locations are assigned zeros. This indicates element-wise multiplication; Denotes the Frobenius norm; The kernel norm is used to maintain a low-rank common baseline for adjacent links and dual-polarization channels. and These represent the first-order and second-order difference operators along the time direction, respectively. Representing the baseline time difference Norms are used to maintain a slow change in the clear-sky baseline; This represents the group sparse norm, used to group the same extreme weather events together on relevant electromagnetic channels; The squared Frobenius norm represents the second-order difference of the device's slow drift, used to constrain the slow drift curvature; , , and represent the non-negative weight coefficients of the low-rank constraint, baseline time smoothing constraint, weather group sparsity constraint, and equipment drift smoothing constraint, respectively; Indicates in , and The above minimizes the objective function. After decomposition, using... As a counterfactual clear sky reference in the absence of the current extreme weather, among which, This is an estimate of the clear-sky baseline component, used to represent the normal electromagnetic characteristics of a microwave link when it is not affected by extreme weather. This is an estimate of the slow drift component of the device, used to represent the slow offset caused by device aging, temperature changes, or changes in system state. As the weather distortion input for subsequent calibration, among which Indicates the first The microwave link at time The baseline-de-baseline electromagnetic distortion vector; Indicates the first The microwave link at time The observed electromagnetic characteristic vector; This represents the clear-sky baseline vector estimated by equation (2); This represents the device slow drift vector estimated by equation (2); Indicates microwave link index; The variable represents a discrete sampling time; the pointed cap symbol above the variable indicates the estimated value of the corresponding parameter. This serves as the weather distortion input for subsequent spatiotemporal matching, weather pattern identification, and path segmentation calibration. Therefore, current weather events will not be written into the clear-sky reference, and slow device drift will not be misidentified as weather distortion.

[0015] The propagation delay-aware unbalanced optimal transmission matching model of this invention is as follows: The three-dimensional coordinates of the link transmitter and receiver are respectively and After considering the effective sphere radius and refraction correction, the link is divided into... The path unit, the first The center coordinates of each path unit are (3) In equation (3), Indicates the first The three-dimensional coordinate vector of the center of each path unit; and These represent the three-dimensional coordinate vectors of the microwave link's transmitting and receiving ends, respectively. Indicates the path unit index. ; This represents the total number of path units obtained from the propagation path partitioning; Indicates the first The normalized position of the center of each path unit on the straight path between the transceiver and receiver; Indicates the first Earth curvature correction vector for each path unit; Indicates the first Atmospheric refraction correction vector for the path unit. A multi-source meteorological observation unit, with its center time set as . The center coordinates are Weather unit speed is The advection time delay from the observation unit to the path unit is estimated as follows: (4) In equation (4), Indicates the first The weather cell represented by the meteorological observation unit advection to the first The estimated time delay required for each path unit; Indicates the candidate time delay to be searched; This represents the maximum absolute value of the time delay allowed for the search; This represents the candidate time delay that minimizes the objective function; Indicates the first The center coordinates of each path unit; Indicates the first The center coordinates of each meteorological observation unit; Indicates the first Each observation unit corresponds to a three-dimensional advection velocity vector of a weather cell; Indicates the duration of weather cell transit. The predicted position after; Represents the Euclidean norm; and These represent the path unit index and the meteorological observation unit index, respectively.

[0016] The joint matching cost is defined as (5) In equation (5), Indicates the first The path unit and the first The cost of joint matching among meteorological observation units; , , , and These represent the non-negative weights of the time difference term, the three-dimensional spatial distance term, the non-overlapping support domain term, the physical characteristic difference term, and the observation quality term, respectively. Indicates the first The sampling time of the link electromagnetic characteristics corresponding to each path unit; Indicates the first The center time of each observation unit; This represents the advection time delay obtained from equation (5); and These represent the scale-normalized parameters for time difference and spatial distance, respectively. A function representing the three-dimensional spatial distance between two coordinate points; , and These represent the center coordinates of the path unit, the center coordinates of the observation unit, and the advection velocity of the weather cell, respectively. This represents the intersection-union ratio of the influence domain of the path unit and the spatial support domain of the observation unit; Indicates the first Electromagnetic distortion description vector of each path unit; Indicates the first Meteorological physical description vectors for each observation unit; A scale or covariance matrix representing the differences in physical characteristics; Indicated by Weighted squared Mahalanobis distance; Indicates the first Quality confidence level of each observation unit; This indicates a positive number that prevents the logarithmic independent variable from being zero. This represents the natural logarithm. Therefore, observations that are close in time but do not intersect in space, or observations that are close in space but have been shifted by weather cells, will not receive unreasonably high weights.

[0017] Let the path unit mass vector be... The mass vector of the observation unit is The coupling matrix is ​​obtained by the following formula: (6) In equation (7), Represents the optimal coupling matrix; Let the non-negative coupling matrix to be solved be represented by its elements. Indicates the first The meteorological observation unit sent to the first The quality of each path unit allocation; Let represent the joint cost matrix formed by equation (5); This represents the sum of the products of corresponding elements of two matrices; Represents the entropy regularity coefficient; Indicates the Kullback-Leibler divergence; Represents the normalized quality vector of a path unit; Represents the normalized mass vector of a meteorological observation unit; express and outer product; superscript Indicates matrix transpose; This represents a column vector whose elements are all 1 and whose dimension matches the multiplication of the corresponding matrix. and These represent the row edge quality and column edge quality of the coupling matrix, respectively. and These represent the weights of the path unit edge relaxation term and the observation unit edge relaxation term, respectively. The latter two edge relaxation terms allow for radar obstruction, missing ground station data, and link quality degradation, without forcing an incorrect one-to-one correspondence. Alignment to path unit. The meteorological vector is: (7) In equation (7), Indicates alignment to the first Fusion meteorological observation vectors of each path unit; Represents the th element in the optimal coupling matrix. Line 1 Column elements; Indicates the first The meteorological element vector of each meteorological observation unit, wherein the meteorological element includes at least one of the following: rainfall rate, radar reflectivity, temperature, humidity, wind speed, hail probability, or icing amount; the summation operation in the formula represents the summation over all candidate meteorological observation units; This indicates a positive number that prevents the denominator from being zero. and These represent the path unit index and the meteorological observation unit index, respectively; the wavy symbol above the variable represents the parameter after weighted alignment by spatiotemporal coupling.

[0018] The physical constraint hybrid expert calibration model of this invention is as follows: The physical baseline for extreme weather is obtained by integrating the specific attenuation over path cells. Rainfall attenuation is... (8) In equation (8), This represents the path integral attenuation caused by heavy rain across the entire microwave link; Indicates the total number of path units; Indicates the operating frequency of the microwave link; Indicates horizontal polarization, vertical polarization, or other specified polarization mode; and They represent respectively by and The rainfall ratio attenuation coefficient and power exponent were determined jointly; Indicates the first Equivalent rainfall rate of each path unit; Indicates the first The effective rainfall coverage length of each path unit is given in km; the summation operation in the formula represents the summation of the first to the second path units. The rainfall attenuation contribution of each path unit is summed.

[0019] Hail's equivalent scattering attenuation is (9) In equation (9), This represents the equivalent attenuation of the entire link caused by hail particle scattering and absorption; Indicates the equivalent diameter of hail particles; and These represent the minimum and maximum diameters of the hail particles involved in the calculation, respectively. Indicates the first The particle size within each path unit is Hailstone number concentration spectrum distribution; Indicates diameter is Hailstone particles at working frequency Extinction efficiency factor; Represents the equivalent geometric cross-sectional area of ​​a hail particle; This represents a differential element that integrates over hailstone diameter; Indicates the first The effective hail coverage length of each path unit; the integral operation in the formula represents the effective hail coverage length of each path unit; to The extinction contribution integral within the particle size range, where the summation operation represents the summation of the first to the second particles. Summing of path units.

[0020] Freezing rain and icing add-on attenuation (10) In equation (10), Indicates time Additional attenuation caused by freezing rain and icing, in dB; Indicates the operating frequency polarization mode and ambient temperature The determined path icing attenuation coefficient per unit length; Indicates time The effective icing length of the link; Indicates operating frequency Additional attenuation coefficient per unit ice thickness of the lower radome; Indicates time The equivalent icing thickness of the radome; This indicates the ambient temperature near the path or radome.

[0021] The multi-source meteorological observations aligned to the i-th path unit via the spatiotemporal nonequilibrium optimal transport alignment model are combined with the baseline-removed electromagnetic distortion, multi-frequency differential characteristics, dual-polarization differential characteristics, and observation quality characteristics corresponding to that path unit to form the gated input z. i The physical violation of the kth weather expert is: (11) In equation (12), Indicates the first The weather expert commented on the first The physical violation of the output of each path unit; Indicates a weather expert index; Indicates the index of physical constraint terms; Indicates the total number of physical constraint terms; Indicates the first The first type of weather A physical constraint function, wherein the physical constraint includes at least two of the following: the range of meteorological parameter values, non-negativity of attenuation, polarization response, and path integral consistency; Indicates the first The weather expert commented on the first The candidate calibration vectors output by each path unit; This indicates that only the constraint violations greater than zero are retained; Represents the non-negative weighting coefficient of the path decay consistency term; This indicates that the data was assigned or converted from the link observation. Observational attenuation per path unit; Indicates the first The weather expert calculated the first [number] based on the corresponding physical propagation model. Physical attenuation of each path unit; Represents absolute value. The gating weight is... (12) In equation (12), Indicates the first The path unit belongs to or uses the first path unit. Normalized gating weights for individual weather experts; This indicates that the gating unit is based on the input vector The calculation of the first The raw scores of the weather experts; This represents the first characteristic consisting of aligned meteorological observations, baseline-removed electromagnetic distortion, multi-frequency difference characteristics, dual-polarization difference characteristics, and observation quality characteristics. Each path unit gated input vector; Indicates the physical violation penalty coefficient; This represents the physical violation quantity calculated by equation (11); A gated temperature parameter that indicates the smoothness of the weight distribution. This indicates the total number of weather experts; This indicates the weather expert index used for summing the denominators; This represents the natural exponential function; the denominator is used to ensure that the sum of the weights of all weather experts for the same path unit equals 1. Candidate calibration values ​​are determined by each expert... Output, the fusion result is (13) In equation (13), The physical constraint hybrid expert model represents the first... The fusion candidate calibration vectors output by each path unit; superscript This indicates the fusion results of mixed experts; Indicates the first A weather expert in the first Gating weights on each path unit; Indicates the first A candidate calibration mapping function for a weather expert; Indicates the first Gating and expert input vectors for each path unit; Indicates the first A set of parameters to be trained for a weather expert; Indicates a weather expert index; This represents the total number of weather experts; the summation operation in the formula represents the summation of the first to the last... The candidate outputs of several weather experts are weighted and summed; the pointed cap symbol above the variable indicates the estimated value.

[0022] When heavy rain and hail coexist, heavy rain experts and hail experts can both obtain non-zero weights; physical violation quantities will suppress experts who are incompatible with observations, thereby avoiding confusion of compound events caused by forced single labels.

[0023] The path segmentation graph residual calibration model of this invention is as follows: Graph constructed using path units as nodes The initial state of node i is From node The weight of the directed edge to node i is (14) In equation (14), The propagation path graph represents nodes. The normalized directed edge weight pointing to node i; Represents node i and node Spatial distance between the centers of corresponding path units; Indicates the spatial distance attenuation scale; The weather unit is represented by nodes. Propagate to the corresponding location to the node The time delay at the corresponding location; Indicates the propagation delay attenuation scale; The weight of the weather movement direction consistency term; Indicates that by node Pointing to node The direction angle of the connecting line; Indicates the direction angle of movement of a weather cell; This indicates the degree of consistency between the direction of the node connection and the direction of weather movement; Represents a node The set of incoming neighbor nodes; Indicates the index used when summing neighboring nodes; and Representing nodes respectively with neighboring nodes Spatial distance and propagation time delay between them; This represents the natural exponential function; the denominator is used to make the nodes... The sum of all incoming edge weights equals 1. Layer message updated to (15) In equation (15), Indicates the first After layer message passing, the node The state vector; and They represent the first Layer nodes and its neighboring nodes The state vector; Indicates the graph message passing layer index; Represents a nonlinear activation function; Indicates the first The weight matrix of the layer acting on the node's own state; Indicates the first The weight matrix applied to neighbor messages by the layer; The node obtained from equation (15) represents the node. Pointing to node The directed edge weight; Represents a node The set of incoming neighbor nodes; Indicates the first Layer bias vector; the summation operation in the formula represents the summation of the values ​​of the nodes. The sum of all neighbor messages.

[0024] Path graph models only learn residuals that the physical baseline fails to explain. The final calibration value is (16) In equation (16), Indicates the first The final calibrated electromagnetic characteristic or meteorological parameter vector of each path unit; Let represent the hybrid expert physical candidate calibration vector obtained from equation (13); The path graph residual model represents the first... The nonlinear residual correction vector output by each path unit; This represents the physically feasible region determined by the non-negativity of attenuation, the range of meteorological parameters, the polarization response, and the path integral relationship. This indicates projecting the vector within the parentheses onto the physically feasible region. The projection operator; Indicates the path unit index.

[0025] The model training objective is (17) In equation (17), This represents the total training loss of the path graph residual calibration model; This represents the data fitting loss caused by the difference between the calibration output and the self-test reference values ​​of co-located ground stations, radar quantitative products, or communication equipment. , and These represent the non-negative weights of the path integral consistency term, the graph total variational smoothing term, and the physical constraint term, respectively. This represents the actual observed total attenuation of the entire microwave link; Indicates the first The estimated specific attenuation after calibration of each path unit; Indicates the first The effective length of each path unit; Represents the Euclidean norm; The set of directed edges representing the propagation path graph; Indicates the connection node With nodes One of the edges; Indicate the corresponding directed edge weight; and Representing nodes respectively and nodes The calibration output vector; express Norm; Indicates the action applied to the node. The calibration output of the first Physical constraints; Indicates the index of physical constraint terms; This indicates that only the constraint violation portion greater than zero is penalized. The second term in the formula ensures that the integrated path segment calibration result is consistent with the actual total attenuation of the link, the third term suppresses non-physical oscillations within the continuous region of a weather cell, and the fourth term restricts the output from falling into the physically feasible region.

[0026] The trusted interval generation and secure fallback model of this invention is as follows: Define the first on independent calibration samples Inconsistency score of each sample (18) In equation (18), Indicates the first The inconsistency score of each independent calibration sample; Indicates the index of independent calibration samples; Indicates the first The true reference value or the reference quantity that has been quality audited for each sample; Indicates the first Model calibration estimates for each sample; This represents the absolute error between the calibration estimate and the reference value; The model represents the first The standard deviation or scale uncertainty estimate given for each sample; A positive number indicates a denominator of zero and represents the lower bound of irreducible noise; the pointed cap above the variable indicates an estimated value.

[0027] Take the quantiles after correction for a finite sample (19) In equation (19), Indicates the confidence level as Inconsistent score quantiles obtained after correction using finite samples; Indicates the target coverage rate, and ; Indicates the coverage rate of the target confidence interval; This represents the total number of independently calibrated samples; This represents the inconsistency score of all independent calibration samples calculated by equation (18); Denotes the first sample set quantiles; This indicates the rounding up operation; This represents the corrected quantile level after considering a finite number of samples.

[0028] The confidence interval of the real-time sample is then... (20) In equation (20), Indicates the real-time sample at time [time]. The confidence interval; Indicates time The calibration estimate; The finite sample corrected quantile is obtained from equation (19); The model represents time intervals. The standard deviation or scale uncertainty estimate of the output; The interval represents the lower bound of irreducible noise; the left and right endpoints of the interval represent the lower and upper bounds of the calibration result, respectively. Indicates the real-time sampling time. Defines the confidence level. ,in, Indicates time Overall credibility; Indicates the width of the confidence interval; Indicates the effective range of the calibrated electromagnetic characteristics or meteorological parameters; This indicates a positive number that prevents the denominator from being zero. The time is determined by the observation completeness, optimal transmission coupling quality, and sensor quality. Data quality coefficient; Represents the natural exponential function; This indicates the threshold for triggering a safe rollback. When... At that time, the graph residual coefficients are gradually decayed to zero, and the physical baseline output obtained from equations (8) to (10) is used to prevent low-quality data from driving unconstrained extrapolation.

[0029] The fast and slow parameter separation online update model of the present invention is as follows: Let the real-time residual be In length of Calculate change point statistics on the reference window (twenty one) In equation (21), Indicates time Online variable point statistics; Indicates the end time The recent The sample mean of the calibration residual vector within each sampling period; Indicates time The real-time residual vector satisfies ; Indicates time Reference electromagnetic characteristics or reference meteorological parameter vector; Indicates time The calibration estimation vector; Indicates the length of the reference window for change point detection; This represents the baseline mean of the residual vector under steady-state conditions. The reference covariance matrix represents the residual vector under steady-state conditions; The superscript represents the inverse of the reference covariance matrix. Indicates vector transpose; Indicates the real-time sampling time. The larger the value, the more significantly the current window residual distribution deviates from the steady state.

[0030] when When a sudden change occurs in weather type, movement speed, or data latency, slow parameters are frozen. Update fast parameters according to the larger learning rate : (twenty two) In equation (22), and They represent the first Before the first update and the first The updated fast parameter vector; the fast parameters include at least the hybrid expert gating parameters, the path graph residual parameters, and the propagation delay parameters; Indicates the fast parameter learning rate; Indicates time The loss function is calculated based on real-time calibration samples; Represents the loss function Regarding fast parameter vectors The gradient; This indicates the number of online parameter updates. When equation (21) yields... Greater than the change point threshold When executing formula (22), where, This represents the statistical threshold used to determine sudden changes in weather type, movement speed, or data latency.

[0031] when continued Update the slow parameter after one sampling period: (twenty three) In equation (23), and They represent the first Before the first update and the first The updated slow parameter vector; the slow parameters include at least clear-sky baseline parameters and physical propagation parameters; Indicates the learning rate of the slow parameter; The fast parameter learning rate in expression (22) and ; This indicates that the gradient is calculated over the slow parameter vector; Indicates time Real-time calibration loss; This indicates the non-negative weight of the historical parameter preservation term; Indicates the index of the slow parameter component; Indicating stable historical events on the first The importance of each slow parameter; Represents the th element in the current slow parameter vector. One component; Indicates the first The historical values ​​of each slow parameter saved before the start of the current stable update phase; the summation operation in the formula represents the summation of all slow parameter components; This indicates the change point statistics before allowing slow parameter updates. Not exceeding the threshold The required number of stable sampling periods. This enables rapid tracking of gating, graph residuals, and propagation lags during sudden extreme weather events, while preventing the propagation coefficient and clear-sky baseline from being disrupted by a single event.

[0032] Because this invention employs techniques such as dual-timescale robust baseline decomposition, time-delay-aware spatiotemporal matching, physical-constrained hybrid experts, propagation path graph residual calibration, reliable interval and safety backoff, and fast and slow parameter separation and updating, it constructs a closed-loop spatiotemporal calibration mechanism for microwave link electromagnetic characteristic distortion, thus achieving the following beneficial effects: 1. This invention separates extreme weather distortion from equipment slow drift through dual-timescale robust baseline decomposition; it achieves accurate matching of asynchronous multi-source meteorological observations with link path units by combining advection time delay, three-dimensional spatial distance, support domain overlap, and observation quality; and it further utilizes physical constraint hybrid experts and propagation path graph residual models to characterize the propagation characteristics and path segment distortion patterns of different extreme weather and composite events, thereby improving the accuracy, physical consistency, and stability of electromagnetic feature calibration under extreme weather conditions.

[0033] 2. This invention quantifies the uncertainty of calibration results through a limited sample confidence interval and automatically switches to a conservative physical baseline calibration mode when observations are missing, model extrapolation is performed, or confidence is insufficient. At the same time, it adopts a fast and slow parameter separation update mechanism triggered by a change point, so that weather response parameters are updated quickly and clear sky baseline parameters and physical propagation parameters are updated slowly, thereby taking into account both the ability to track sudden weather events and long-term operational stability. The calibration results can also be used for link signal recovery, path meteorological parameter inversion, and low confidence alarm. Attached Figure Description

[0034] Figure 1 This is a flowchart illustrating the overall process of a method for spatiotemporal calibration of microwave link distortion in extreme weather according to the present invention. Figure 2 This is a schematic diagram of the hardware and data connection relationship of a microwave link distortion spatiotemporal calibration method for extreme weather according to the present invention; Figure 3 This is a schematic diagram of dual-timescale robust baseline decomposition for a spatiotemporal calibration method for microwave link distortion in extreme weather according to the present invention. Figure 4 This is a schematic diagram of the unbalanced optimal transmission matching for propagation delay sensing in a microwave link distortion spatiotemporal calibration method for extreme weather according to the present invention. Figure 5 This is a schematic diagram of the physical constraint hybrid expert calibration of the extreme weather microwave link distortion spatiotemporal calibration method of the present invention; Figure 6 This is a schematic diagram of path segmentation residual calibration for a microwave link distortion spatiotemporal calibration method for extreme weather according to the present invention. Figure 7 This is a flowchart of the reliable interval generation and safe rollback process of a spatiotemporal calibration method for microwave link distortion in extreme weather according to the present invention. Figure 8 This is a schematic diagram of the online update closed loop for separating fast and slow parameters in a spatiotemporal calibration method for microwave link distortion in extreme weather according to the present invention. Figure 9 The figure shows the time series results of numerical simulation of the extreme weather microwave link distortion spatiotemporal calibration method of the present invention under heavy rain conditions, which involves dual-timescale baseline decomposition and spatiotemporal calibration. Figure 10 This is a comparison chart of the root mean square error of attenuation calibration under four types of extreme weather conditions, using the fixed baseline method, spatiotemporal interpolation method, and physical constraint-free residual method of the present invention for spatiotemporal calibration of microwave link distortion in extreme weather. Figure 11 This is a spatiotemporal reconstruction result of the path segment meteorological field under the condition of a moving rainstorm core, based on the spatiotemporal calibration method for microwave link distortion in extreme weather according to the present invention. Figure 12 The figure shows the results of online updating of confidence interval, safety backoff, and fast / slow parameters under conditions of observational gaps and sudden weather changes, for the spatiotemporal calibration method for microwave link distortion in extreme weather according to the present invention.

[0035] Figure labeling: 10-Spatiotemporal calibration system; 100-Microwave link transmitter; 110-Microwave link receiver; 120-Ground meteorological observation equipment; 121-Radar and satellite observation sources; 130-Data processing device; 140-Distortion sample and event memory bank; 150-Calibration result output terminal; 160-Unified time synchronization module; 201-Observation electromagnetic characteristics; 202-Quality control module; 203-Robust decomposition module; 204-Clear sky baseline component; 205-Weather distortion component; 206-Equipment drift component; 301-Unbalanced optimal transmission module; 401-Gated transmission... Input; 402 - Physical Constraint Gating Unit; 403 - Rainstorm Expert; 404 - Hail Expert; 405 - Freezing Rain Expert; 406 - Composite Event Expert; 407 - Fusion and Physical Projection Unit; 501 - Path Graph Construction Module; 502 - Message Passing Module; 503 - Residual Output; 601 - Calibration Input; 602 - Quantile Calculation Module; 603 - Confidential Interval; 604 - Confidential Output; 605 - Safety Rollback Module; 701 - Real-time Residual; 702 - Change Point Detection Module; 703 - Fast Parameter Update Module; 704 - Slow Parameter Update Module; 705 - Event Memory. Detailed Implementation

[0036] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0037] Please see Figures 1 to 12 The figure shows a spatiotemporal calibration method for microwave link distortion in extreme weather according to the present invention. The spatiotemporal calibration method is implemented based on the spatiotemporal calibration system 10.

[0038] like Figure 2As shown, the spatiotemporal calibration system 10 includes a microwave link transmitter 100, a microwave link receiver 110, a ground meteorological observation device 120, a radar and satellite observation source 121, a data processing device 130, a distortion sample and event memory bank 140, a calibration result output terminal 150, and a unified time synchronization module 160. The microwave link transmitter 100 and the microwave link receiver 110 form the microwave link to be calibrated; the ground meteorological observation device 120 and the radar and satellite observation source 121 provide multi-source meteorological observation data; the unified time synchronization module 160 provides a unified time reference for the electromagnetic characteristics of the microwave link and the multi-source meteorological observation data; the data processing device 130 performs the spatiotemporal calibration process; the distortion sample and event memory bank 140 stores historical extreme weather event samples, model parameters, calibration residuals, and confidence information; and the calibration result output terminal 150 outputs the calibrated electromagnetic characteristics, corresponding meteorological parameters, confidence intervals, and confidence markers.

[0039] like Figure 1 As shown, the data processing device 130 includes a multi-source data synchronous acquisition module, a dual-timescale robust baseline decomposition model, a propagation path segmentation model, a meteorological observation unit standardization model, a spatiotemporal unbalanced optimal transmission alignment model, a physically constrained hybrid expert model, a propagation path graph residual calibration model, a physical consistency constraint model, a calibration reliability assessment model, a safety backoff model, and a fast and slow parameter online update model. The multi-source data synchronous acquisition module is connected to the microwave link transmitter 100, the microwave link receiver 110, the ground meteorological observation equipment 120, the radar and satellite observation sources 121, and the unified timing module 160 via data acquisition interfaces.

[0040] The multi-source data synchronous acquisition module is connected to the dual-timescale robust baseline decomposition model, the propagation path segmentation model, and the meteorological observation unit standardization model, respectively. The dual-timescale robust baseline decomposition model outputs baseline-reduced electromagnetic distortion, the propagation path segmentation model outputs path units, and the meteorological observation unit standardization model outputs standardized meteorological observation units. The baseline-reduced electromagnetic distortion, path units, and standardized meteorological observation units are collectively input into the spatiotemporal nonequilibrium optimal transmission alignment model. The spatiotemporal alignment results are processed sequentially by the physical constraint hybrid expert model, the propagation path graph residual calibration model, and the physical consistency constraint model, and then input into the calibration credibility assessment model. The safety backoff model determines the final calibration mode based on the comprehensive credibility, and the fast and slow parameter online update model performs closed-loop updates of the corresponding model parameters based on the real-time calibration residuals.

[0041] The multi-source data synchronous acquisition module is used to acquire multi-frequency and / or dual-polarization electromagnetic feature sequences output by microwave link transmitter 100 and microwave link receiver 110, and to acquire multi-source meteorological observation data and microwave link location data output by ground meteorological observation equipment 120, radar and satellite observation source 121. It writes acquisition timestamps for various types of data according to the unified timing signal provided by unified timing module 160. The electromagnetic features include at least two of the following: received signal level, carrier phase, polarization angle, cross-polarization discrimination, and Doppler frequency shift.

[0042] The dual-timescale robust baseline decomposition model is used to decompose the quality-controlled electromagnetic feature sequence to obtain clear-sky baseline components, extreme weather distortion components, equipment slow drift components, and random noise components. Based on the clear-sky baseline components and equipment slow drift components, a counterfactual clear-sky reference adapted to the current equipment state is constructed to obtain baseline-free electromagnetic distortion.

[0043] The propagation path segmentation model is used to reconstruct the link propagation path based on the three-dimensional coordinates of the microwave link transmitter 100 and the microwave link receiver 110, the antenna height, the digital elevation model, the effective sphere radius, and the atmospheric refraction parameters, and to divide the propagation path into multiple path units according to the changes in the propagation environment and the spatial resolution.

[0044] The standardized model of the meteorological observation unit is used to convert meteorological observation data from different sources, with different sampling periods and different spatial resolutions into standardized meteorological observation units that simultaneously have a time support domain, a spatial support domain and a quality confidence level.

[0045] The spatiotemporal nonequilibrium optimal transmission alignment model is used to establish a joint cost matrix based on the sampling time difference between the path unit and the meteorological observation unit, the advection time lag of weather cells, the three-dimensional spatial distance, the overlap of the observation support domain, the difference in physical characteristics, and the observation quality. The coupling matrix between the path unit and the meteorological observation unit is solved by entropy regularization nonequilibrium optimal transmission with edge relaxation terms, and the asynchronous multi-source meteorological observations are aligned to the corresponding path units according to the coupling matrix.

[0046] The physical constraint hybrid expert model is used to receive aligned meteorological observations, baseline-removed electromagnetic distortion, multi-frequency differential features, dual-polarization differential features, and observation quality features. It determines the initial weights corresponding to different extreme weather types through gating units, corrects the initial weights according to the violation of the physical propagation law by the output results of each weather expert, and performs weighted fusion of the candidate calibration quantities output by rainstorm experts, hail experts, freezing rain experts, and composite event experts to obtain the segmented physical calibration results of each path unit.

[0047] The propagation path graph residual calibration model is used to construct a propagation path graph with directed edges and edge weights based on the path unit as nodes, the adjacency relationship between path units, spatial distance, weather cell movement direction and propagation time delay, and to perform nonlinear residual correction on the segmented physical calibration results to characterize the migration, accumulation and attenuation relationship of local electromagnetic distortion along the propagation path.

[0048] The physical consistency constraint model is used to apply path integral conservation constraints to the calibration results of each path unit, and project the calibration results after residual correction onto the physical feasible region determined by the electromagnetic propagation mechanism and the range of meteorological parameters, so as to obtain the calibrated electromagnetic characteristics and corresponding meteorological parameters.

[0049] The calibration reliability assessment model is used to calculate the finite sample corrected quantiles based on the inconsistency scores of independent calibration samples, generate a reliability interval for the calibrated electromagnetic characteristics or meteorological parameters, and determine the overall reliability by combining the reliability interval width, observation completeness, optimal transmission coupling quality, and sensor quality.

[0050] The safety rollback model is used to suppress the nonlinear residual output of the propagation path graph residual calibration model when the overall confidence level is lower than the set safety rollback trigger threshold, switch to a conservative calibration mode based on physical propagation relationship, and output a low confidence level mark.

[0051] The fast and slow parameter online update model is used to perform online change point detection on the calibration residual. When the change point statistic exceeds a set threshold, the gating parameters, path graph residual parameters, and propagation delay parameters are updated quickly. When the change point statistic remains below the set threshold within a stable window, the clear sky baseline parameters and physical propagation parameters are updated at a learning rate lower than that of the fast parameter update model. This forms a closed-loop spatiotemporal calibration mechanism that separates the rapid response parameters for extreme weather from the long-term evolution parameters of the equipment.

[0052] Example 1: Spatiotemporal calibration system and multi-source data acquisition The microwave link transmitter 100 and microwave link receiver 110 constitute the microwave link to be calibrated. The transmitter 100 transmits microwave signals according to a set operating frequency and polarization mode. The receiver 110 samples the received signal and outputs at least two electromagnetic characteristics from the following: received signal level, carrier phase, polarization angle, cross-polarization discrimination, and Doppler shift. When using a multi-frequency link, the electromagnetic characteristics of different frequencies form independent data channels; when using a dual-polarization link, the horizontal polarization channel and the vertical polarization channel form corresponding polarization data channels.

[0053] In this embodiment, the microwave link operates at at least one of 18 GHz, 23 GHz, or 38 GHz, with a link length of 5–30 km and an electromagnetic characteristic sampling period of 0.1–10 s. These values ​​are merely examples and can be adjusted in practical applications based on the link frequency band, transmission distance, and data processing capabilities.

[0054] Ground-based meteorological observation equipment 120 includes at least one of a rain gauge, a temperature and humidity sensor, an anemometer, and an icing monitoring device, used to collect rainfall rate, temperature, relative humidity, wind speed, wind direction, and icing thickness. Radar and satellite observation sources 121 are used to provide at least one of radar reflectivity, radial velocity, hail probability, cloud top temperature, and precipitation inversion products. Data processing unit 130 also receives longitude, latitude, elevation, antenna height, operating frequency, polarization, and antenna azimuth angle from the microwave link transceiver, as well as digital elevation model data and atmospheric refraction parameters.

[0055] The unified time synchronization module 160 uses BeiDou time synchronization signals, Global Positioning System time synchronization signals, or Network Time Protocol (NTP) time synchronization signals to write acquisition timestamps under a unified time reference for electromagnetic characteristics and meteorological observations. For external meteorological products that cannot be directly accessed by the unified time synchronization signal, the data processing device 130 corrects the timestamps based on the product generation time, scanning center time, transmission delay, and equipment clock deviation.

[0056] The data processing device 130 performs quality control on the collected data, including outlier identification, missing measurement marking, timestamp correction, range checking, abrupt jump checking, and continuity checking. For valid data, quality weights are generated based on data integrity rate, equipment self-test status, signal-to-noise ratio, time delay, and spatial representativeness; for missing measurement data, the corresponding quality weights are set to zero. The quality-controlled electromagnetic characteristics and meteorological observations are then fed into subsequent models.

[0057] Example 2: Robust Baseline Decomposition with Two Time Scales like Figure 3 As shown, the observed electromagnetic features 201 are processed by the quality control module 202 and then input into the robust decomposition module 203. The robust decomposition module 203 decomposes the observed electromagnetic features into clear sky baseline component 204, weather distortion component 205, equipment drift component 206 and random noise component according to equations (1) and (2).

[0058] In this embodiment, continuously acquired multi-link, multi-frequency, or dual-polarized electromagnetic features are arranged into an observation matrix according to a sliding time window. The sliding time window can be set to 30 min to 24 h, with partial overlap between adjacent windows to maintain the smoothness of the decomposition results at consecutive time points. The elements in the quality mask matrix are determined by the quality weights of the corresponding data channels.

[0059] The clear-sky baseline component primarily characterizes diurnal, seasonal, and multi-link co-variations under normal atmospheric conditions. Low-rank correlations between different links and polarization channels are maintained through nuclear norm constraints, and drastic changes in the clear-sky baseline between adjacent sampling times are limited by first-order temporal difference constraints.

[0060] Extreme weather distortion components are constrained by group sparsity, ensuring that the same extreme weather event appears in groups across relevant frequencies, polarization channels, and electromagnetic characteristics. Equipment slow drift components are constrained by second-order time difference to characterize the slow changes caused by device temperature drift, power control offset, feeder aging, and antenna condition variations.

[0061] Equation (2) can be solved using the alternating direction multiplier method, the near-end gradient method, or the iterative threshold method. The solution is stopped when the relative change of the objective function between two adjacent iterations is less than the set convergence threshold, or when the number of iterations reaches the set upper limit.

[0062] After decomposition, the sum of the clear-sky baseline estimate and the equipment slow drift estimate is used as the counterfactual clear-sky reference under the current equipment state. This counterfactual clear-sky reference is then subtracted from the observed electromagnetic characteristics to obtain the baseline-free electromagnetic distortion. Data corresponding to extreme weather events are not included in the rapid update of the clear-sky reference to avoid incorporating a single rainstorm, hail, or freezing rain event into the long-term clear-sky baseline.

[0063] Example 3: Segmentation of Propagation Path and Standardization of Meteorological Observation Units The data processing device 130 reconstructs the actual propagation path based on the three-dimensional coordinates of the microwave link transmitter 100 and receiver 110, the antenna height, the digital elevation model, the effective sphere radius, and the atmospheric refraction parameters.

[0064] In one specific embodiment, the effective sphere radius is taken as 4 / 3 times the average radius of the Earth; when a real-time atmospheric refractive index profile is available, the effective sphere radius and path curvature are dynamically corrected according to the refractive index profile. The center coordinates of each path unit are calculated according to equation (3), and the number of segments is determined by combining the terrain undulation, Fresnel zone clearance, meteorological observation spatial resolution, and total link length.

[0065] The path unit length can be set from 100m to 1000m. When the terrain height, atmospheric refraction conditions, or meteorological field of a certain road segment varies greatly, the path unit length should be reduced; when the propagation environment is relatively uniform, the path unit length should be increased. Each path unit should record at least the center coordinates, start and end coordinates, effective length, operating frequency, polarization mode, terrain height, propagation state, and spatial quality weight.

[0066] The meteorological observation unit standardization model establishes standardized data structures for meteorological observations from different sources. Each meteorological observation unit includes at least: • Meteorological element vectors; • Observation center time and time support domain; • Observation center coordinates and spatial support domain; • Spatial resolution and sampling period; • Data source identification; • Quality confidence level; • Weather unit movement speed and direction.

[0067] For weather radar products, the temporal support domain can be determined by adjacent scanning times, and the spatial support domain can be determined by radar grid cells or radar beam coverage volume; for satellite remote sensing products, the spatial support domain is determined by the pixel range; for ground weather station data, the spatial support domain is determined based on the surrounding terrain, station density, and relevant scales of meteorological elements.

[0068] Example 4: Propagation Delay-Aware Unbalanced Optimal Transmission Alignment like Figure 4 As shown, the unbalanced optimal transmission module 301 receives path units and standardized meteorological observation units. First, the moving speed of weather cells is estimated based on adjacent radar images, satellite images, or ground wind fields. Then, the advection time delay of the weather cell moving from the observation unit to the path unit is calculated according to equation (4).

[0069] When it is impossible to reliably estimate the velocity of weather cells from a single data source, a quality-weighted fusion of radar echo tracking velocity, ambient wind speed, and satellite cloud movement velocity can be performed. The maximum search range for the advection delay can be set to 5–30 minutes and adjusted according to link length, weather movement speed, and meteorological observation update cycle.

[0070] Then, a joint matching cost matrix is ​​established according to equation (5). The joint matching cost simultaneously considers sampling time difference, advection time delay, three-dimensional spatial distance, crossover ratio of spatial support domains, differences in physical characteristics, and observation quality. Each cost is normalized before being input into the model to ensure that cost terms of different dimensions remain comparable.

[0071] For observation units with low quality confidence, large time difference, or whose spatial support domain and path unit influence domain are basically non-intersecting, the joint matching cost increases; for observation units that can reach the corresponding path unit after advection correction and have compatible physical characteristics, the joint matching cost decreases.

[0072] The unbalanced optimal transmission coupling matrix is ​​solved according to equation (6). An iterative scaling algorithm with edge relaxation terms or an unbalanced Sinkhorn algorithm is used in the solution process. The edge relaxation terms allow for mismatched quality in path units or meteorological observation units, thus preventing the forced establishment of incorrect matching relationships in cases of radar obstruction, missing ground station data, satellite cloud interference, or degraded link electromagnetic data quality.

[0073] According to Equation (7), the meteorological observations corresponding to the coupling matrix are weighted and fused to obtain meteorological vectors aligned to each path unit. At the same time, the coupling quality, the number of effectively matched observations, and the quality of edge mismatches are used as the observation quality features of the subsequent model.

[0074] Example 5: Physical Constraint Hybrid Expert Calibration like Figure 5 As shown, the multi-source meteorological observations aligned to the i-th path unit, the baseline-removed electromagnetic distortion, multi-frequency differential features, dual-polarization differential features, and observation quality features corresponding to that path unit are combined into a gated input 401.

[0075] Multi-frequency differential features include the difference and ratio of received signal level changes, phase changes, or attenuation ratios at different operating frequencies; dual-polarization differential features include the attenuation difference, phase difference, and cross-polarization discrimination variation between horizontal and vertical polarization. These differential features are used to enhance the ability to distinguish between heavy rain, hail, and freezing rain.

[0076] The gating input 401 enters the physical constraint gating unit 402. The physical constraint gating unit 402 first calculates the initial score of each weather expert, then obtains the physical propagation baseline under the corresponding extreme weather according to equations (8) to (10), and calculates the physical violation amount of each weather expert's candidate output according to equation (11).

[0077] The Rainstorm Expert 403 characterizes the relationship between rainfall rate, operating frequency, polarization mode, effective rainfall length, and microwave attenuation; the Hail Expert 404 characterizes the relationship between hail particle size distribution, particle number concentration, extinction efficiency, path coverage length, and scattering attenuation; the Freezing Rain Expert 405 characterizes the relationship between path icing length, radome icing thickness, temperature, polarization mode, and additional attenuation; and the Composite Event Expert 406 characterizes the coupling propagation effect when two or more extreme weather events coexist.

[0078] The physical constraint gating unit 402 corrects the initial gating weights using physical violation quantities according to equation (12). When the attenuation direction, meteorological parameter range, polarization response, or path integral result output by a certain expert is significantly inconsistent with the actual observation, the gating weight of that expert is reduced; when rainstorms and hail exist simultaneously, rainstorm expert 403 and hail expert 404 can simultaneously obtain non-zero weights without having to forcibly classify the event into a single weather type.

[0079] The fusion and physical projection unit 407 performs weighted fusion of the candidate calibration quantities output by different experts according to equation (13) to obtain the segmented physical calibration results of each path unit. The candidate calibration quantities include at least one of the following: calibrated electromagnetic characteristics, path unit specific attenuation, rainfall rate, hail parameters, or icing parameters.

[0080] Example 6: Propagation Path Diagram Residual Calibration and Physical Consistency Constraints like Figure 6 As shown, the path graph construction module 501 uses each path unit as a node, and takes the baseline-removed electromagnetic distortion, aligned meteorological vector, mixed expert calibration results and observation quality characteristics of the path unit as the initial state of the node.

[0081] Directed edges are established based on the adjacency relationship, spatial distance, weather movement direction, and propagation delay between path units. When a weather unit moves from node j to node i, and the direction of the line connecting the nodes is consistent with the weather movement direction, the edge weight pointing from node j to node i is increased; when the distance between nodes is large, the propagation delay is long, or the movement direction is opposite, the corresponding edge weight is decreased. The incoming edge weight of the same node is normalized according to equation (14).

[0082] The message passing module 502 performs at least one graph message passing according to equation (15), enabling each path unit to integrate the distortion state, weather state, and propagation direction information of adjacent path units. The number of graph message passing layers can be set to 1 to 5 layers; when the number of layers is too large, excessive smoothing of node features can be suppressed by residual connection or inter-layer normalization.

[0083] The path graph model only outputs the nonlinear residual 503 that the physical constraint hybrid expert model could not explain. This residual is then added to the piecewise physical calibration result and projected onto the physical feasible region according to equation (16). The physical feasible region includes at least the attenuation nonnegativity constraint, meteorological parameter upper and lower limit constraints, polarization response constraints, and path integral constraints.

[0084] The path graph residual calibration model is trained according to Equation (17). Data fitting loss makes the calibration results close to the quality-audited ground station data, radar quantitative products or communication equipment self-test reference values; path integral consistency loss makes the ratio attenuation of each path unit consistent with the actual total attenuation of the link after integration along the link; graph total variation loss suppresses non-physical jumps in continuous weather areas; physical constraint loss limits the output from exceeding the physically feasible range.

[0085] Example 7: Credible Interval Generation and Secure Rollback like Figure 7 As shown, the calibration quantity after physical consistency constraint is input into 601 and sent to quantile calculation module 602. Based on the calibration samples that are independent of the model training samples, quantile calculation module 602 calculates the non-consistency score according to equation (18) and calculates the finite sample corrected quantile according to equation (19).

[0086] Independent calibration samples can be divided according to weather events to avoid adjacent sampling points from the same extreme weather event from being included in both the training and calibration sets simultaneously. For heavy rain, hail, freezing rain, and combined events, separate sets of inconsistent scores and corresponding quantiles can also be established.

[0087] The confidence interval 603 is generated for the real-time calibration results according to Equation (20), and the overall confidence level is calculated based on the confidence interval width, observation completeness, optimal transmission coupling quality and sensor quality.

[0088] When the overall confidence level is not lower than the safety backoff trigger threshold, a reliable output 604 is output, which includes the final calibration value, the confidence interval, and the normal confidence level mark. When the overall confidence level is lower than the safety backoff trigger threshold, the safety backoff module 605 gradually reduces the weight of the path graph residual output and switches to the conservative physical calibration result based on equations (8) to (10), while outputting a low confidence level mark.

[0089] To avoid frequent switching of calibration modes caused by fluctuations in confidence around the threshold, an entry threshold and an exit threshold can be set, with the exit threshold being higher than the entry threshold; alternatively, a continuous triggering period can be set, and a safe rollback will only be performed when the confidence level is lower than the entry threshold for multiple consecutive sampling periods.

[0090] Example 8: Online Update of Separate Fast and Slow Parameters like Figure 8 As shown, the real-time residual 701 is obtained from the difference between the reference electromagnetic characteristics or reference meteorological parameters and the current calibration estimate, and is input into the change point detection module 702.

[0091] The change point detection module 702 calculates the change point statistics according to formula (21) within the set window. When the change point statistics are greater than the change point threshold, it is determined that the weather type, weather movement speed, data delay or electromagnetic distortion mode has changed abruptly.

[0092] When a sudden change occurs, the slow parameters remain frozen, and the fast parameter update module 703 updates the gating parameters, path graph residual parameters and propagation delay parameters according to equation (22), so that the model can quickly adapt to weather type switching, changes in the direction of weather cell movement and changes in multi-source data delay.

[0093] When the number of consecutive sampling periods of the change point statistics does not exceed the change point threshold, the system is determined to have entered a relatively stable state. At this time, the slow parameter update module 704 updates the clear sky baseline parameters and physical propagation parameters according to equation (23). The learning rate of the slow parameters is lower than that of the fast parameters, and the historical parameter retention term limits the slow parameters from excessive deviation relative to the historical stable values.

[0094] Event memory 705 stores typical rainstorm, hail, freezing rain, and combined event samples that have undergone quality review, along with corresponding speed parameters, calibration residuals, reliability, and meteorological observation quality. When a new extreme weather event is detected, the corresponding parameters can be retrieved from event memory 705 as initial values ​​for the model based on the similarity between the current gating input and historical events, thus shortening the online adaptation time. New stable events are written to event memory 705 after quality review.

[0095] Example 9: Numerical Simulation under Heavy Rain Conditions like Figure 9 As shown, a numerical simulation example under mobile rainstorm weather conditions is constructed. The simulation microwave link length is set to 12 km, the operating frequencies are set to 18 GHz and 23 GHz, and horizontal and vertical dual-polarization observations are adopted. The propagation path is divided into 24 path units, and the electromagnetic feature sampling period is set to 1 s. During the simulation period, a clear-sky baseline that changes slowly with the diurnal cycle, equipment thermal drift, and rainstorm cells moving along the microwave link direction are set. Random noise and some missing data are superimposed on the observed electromagnetic features to simulate the uncertainties of actual communication equipment and meteorological observations.

[0096] like Figure 9 As shown in (a), the path-equivalent rainfall rate exhibits a bimodal variation as the storm cells enter, intensify, and leave. Specifically, the main storm peak occurs at approximately 49 minutes, with a path-equivalent rainfall rate reaching 51.09 mm / h; the secondary rainfall peak occurs at approximately 90 minutes, with a path-equivalent rainfall rate reaching 34.21 mm / h. This input condition is used to simulate the process of the main storm core and the tail rainband passing sequentially through the microwave link.

[0097] like Figure 9 As shown in (b), the reference weather attenuation varies with the equivalent rainfall rate along the path, forming attenuation peaks of approximately 16.75 dB and 10.83 dB near the two rainfall peaks, respectively. Equipment slow drift changes gradually throughout the simulation period, showing a significant difference in time scale compared to short-term weather attenuation. The observed signal, after superimposing equipment slow drift and random noise, simultaneously includes weather attenuation, equipment status changes, and measurement disturbances. The dual-timescale robust baseline decomposition model utilizes these timescale differences to separate the slowly changing clear-sky baseline and equipment slow drift from short-term rainstorm distortion, avoiding misidentification of equipment drift as rainfall attenuation.

[0098] like Figure 9As shown in (c), the fixed baseline method does not dynamically correct for slow equipment drift, resulting in significant deviations before and after the occurrence of heavy rain and during the rainfall attenuation phase, with an attenuation calibration root mean square error of 1.51 dB. The method of this invention, after dual-timescale robust baseline decomposition, propagation delay-aware unbalanced optimal transmission alignment, physical constraint hybrid expert calibration, and directed path graph residual correction, yields a calibration attenuation curve that essentially coincides with the reference attenuation curve. This allows the method to follow the formation, intensification, and dissipation of the main rainstorm peak and secondary rainfall peaks, reducing the attenuation calibration root mean square error to 0.26 dB.

[0099] like Figure 9 As shown in (d), using 1 dB as the instantaneous absolute error reference line, the fixed baseline method exhibits an instantaneous absolute error exceeding 1 dB for most of the simulation period, with a maximum instantaneous absolute error reaching 3.64 dB. Furthermore, it still suffers from significant residual error after the rainstorm has passed due to slow equipment drift. In contrast, the instantaneous absolute error of the method described in this invention remains below 1 dB throughout the entire simulation period, with a maximum value of approximately 0.91 dB. This demonstrates that the present invention can effectively separate two types of changes—rapid changes in rainstorm attenuation and slow equipment baseline drift—and improve the accuracy of electromagnetic characteristic calibration when both occur simultaneously.

[0100] Example 10: Comparison of different calibration methods like Figure 10 As shown, the root mean square error of attenuation calibration of the fixed baseline method, spatiotemporal interpolation method, residual method without physical constraints and the method of this invention are compared under heavy rain, hail, freezing rain and combined extreme weather conditions.

[0101] Among them, the fixed baseline method uses the pre-statistical clear sky mean as a fixed reference and does not perform online correction for slow equipment drift; the spatiotemporal interpolation method interpolates based on the distance between the meteorological observation location and the path unit, but does not consider the advection lag of weather cells, the difference in the observation support domain, and non-uniform evolution; the physical constraint-free residual method uses a data-driven model to directly predict the calibration residual, but does not set path integral conservation, attenuation non-negativity, and physical feasible domain constraints; the method of this invention sequentially adopts dual-timescale robust baseline decomposition, propagation delay-aware unbalanced optimal transmission alignment, physical constraint hybrid expert calibration, and directed path graph residual correction.

[0102] Depend on Figure 10As can be seen, under heavy rain conditions, the root mean square errors of attenuation calibration for the fixed baseline method, spatiotemporal interpolation method, unconstrained residual method, and the method of this invention are 1.51 dB, 0.81 dB, 0.63 dB, and 0.26 dB, respectively; under hail conditions, the root mean square errors for the four methods are 1.60 dB, 0.87 dB, 0.60 dB, and 0.25 dB, respectively; under freezing rain conditions, the root mean square errors for the four methods are 1.65 dB, 0.83 dB, 0.54 dB, and 0.26 dB, respectively; and under combined extreme weather conditions, the root mean square errors for the four methods are 1.66 dB, 0.87 dB, 0.53 dB, and 0.27 dB, respectively.

[0103] The fixed baseline method showed errors exceeding 1.50 dB under all four weather conditions, indicating its inability to adapt to slow equipment drift and dynamic changes in weather distortion. The spatiotemporal interpolation method had errors of 0.81–0.87 dB, suggesting that interpolation based solely on spatial distance still resulted in spatiotemporal misalignment due to weather cell movement and inconsistent observation times. The unconstrained residual method had errors of 0.53–0.63 dB, which, while superior to the previous two methods, could still produce residual outputs that did not conform to propagation laws outside of combined weather conditions and training sample distributions. The method of this invention maintained root mean square errors of 0.25–0.27 dB under all four extreme weather conditions, with small error fluctuations between different weather types, indicating that it not only improves attenuation calibration accuracy but also maintains good adaptability and stability among heavy rain, hail, freezing rain, and combined events.

[0104] Example 11: Spatiotemporal Reconstruction of a Moving Rainstorm Core like Figure 11 As shown in (a), the 8.2 km microwave link is divided into 82 100 m path cells, and further divided into four path segments S1-S4 according to the propagation environment and spatial adjacency. A main rainstorm core migrating nonlinearly from S1 to S4 is set in the reference meteorological field, superimposed with the tail rainband, secondary convective cores near the S2 segment, and locally short-term enhanced cells within the S4 segment, to form a non-uniform extreme rainfall field simultaneously exhibiting migration, expansion, splitting, and local enhancement characteristics. Figure 11 As shown in (b), the comparison method first selects the most recent meteorological observation field in time, then calculates the average rainfall rate of the entire link, and assigns this average value to 82 path units at the same time. Figure 11 (d) and Figure 11 (e) refers to this combined method as the "mean method". Because the mean method eliminates spatial differences along the link direction, its reconstructed field only presents a transverse stepped color band that varies with time. Since each segment from S1 to S4 receives the same rainfall rate at the same time, it cannot recover the movement trajectory of the main rainstorm core, the tail rainband, the secondary convection core, locally enhanced cells, and the segment boundary gradients. For example... Figure 11 As shown in (c), this invention determines the spatiotemporal correspondence between meteorological cells and link observations through non-equilibrium optimal transmission alignment based on propagation delay perception. Then, it uses a directed path graph to perform residual correction on different path segments, thereby continuously recovering the nonlinear movement trajectory of the main rainstorm core, secondary convection cores, locally enhanced cells, and their spatial boundaries. Figure 11 As shown in (d), the path field reconstruction error of the mean method remains at a high level at all times, with an overall root mean square error of 22.63 mm / h; the error curve of the method of this invention remains in a lower range, with the overall root mean square error reduced to 1.28 mm / h. Figure 11 As shown in (e), at the characteristic time t = 60 min, the path profile of the reference field has an obvious bimodal structure and segmented boundary gradient. The mean method only obtains an approximately horizontal average rainfall rate curve, and the two peaks and local variations are smoothed out. The reconstructed curve of the method of the present invention basically coincides with the reference curve, indicating that it can effectively maintain the non-uniform spatial structure and local peak characteristics of the extreme rainfall field along the microwave link.

[0105] Example 12: Missing Tests, Mutations, and Safety Rollback like Figure 12 As shown, the simulation process included continuous data loss from meteorological radar, intermittent data loss from ground meteorological stations, and sudden changes in the propagation state of the weather field. Specifically, two observation loss windows were set at 63–86 min and 122–134 min respectively to simulate situations where multi-source meteorological observations were interrupted or the amount of effective data decreased significantly under extreme weather conditions.

[0106] like Figure 12 As shown in (a), when meteorological observations are normal, the observation completeness rate is 1.00, and the overall reliability (C_t) is approximately 0.97, which is higher than the safety backoff threshold of 0.55. After entering two missing observation windows, the observation completeness rate drops to 0.30, and the overall reliability simultaneously drops to approximately 0.32, falling below the safety backoff threshold. This result indicates that the overall reliability can respond promptly as the effective observations decrease, providing a triggering basis for the safety backoff module.

[0107] like Figure 12 As shown in (b), when the observation is complete, the calibration output basically coincides with the reference attenuation, and the 95% confidence interval remains relatively narrow. After entering the missing measurement window, due to the decrease in the effective coupling quality of optimal transmission and the increase in input uncertainty, the 95% confidence interval widens accordingly. The calibration output after safe rollback can still follow the overall trend of the reference attenuation. The actual coverage rate of the reference attenuation falling into the 95% confidence interval during the entire simulation period is 96.7%, indicating that the output confidence interval can effectively reflect the increase in the uncertainty of the calibration result under the missing measurement condition.

[0108] like Figure 12As shown in (c), when the overall confidence level is higher than the safety backoff threshold, the data-driven residual weight remains at 1, and the physical baseline backoff weight remains at 0. The calibration results are mainly output by the path graph residual model. When the overall confidence level is lower than the safety backoff threshold, the data-driven residual weight drops to 0, and the physical baseline backoff weight rises to 1. The system switches to a conservative physical calibration mode to avoid abnormal output results from the path graph residual model due to missing data. After the missing data is completed and the overall confidence level is higher than the exit threshold again, the data-driven residual weight is restored, and the system exits the safety backoff state.

[0109] like Figure 12 As shown in (d), the change point statistic (D_t) is used to characterize the abrupt changes in the weather field propagation state and calibration residual distribution, with the change point threshold set to 1.50. Around 68–72 min and 95–97 min, the change point statistic exceeds the change point threshold, triggering the fast parameter update module, which immediately updates the propagation delay parameters, hybrid expert gating parameters, and path graph residual parameters; the clear-sky baseline parameters and physical propagation parameters remain frozen during the fast parameter update. When the change point statistic remains below the threshold within a preset stability window, the system enters a slow parameter update-allowed state and updates the clear-sky baseline parameters and long-term physical propagation parameters at a lower learning rate. Figure 12 The slow parameter in (d) allows the updated region to only represent the point of change where the stability condition is satisfied; when the region is... Figure 12 When the low-confidence missing test windows overlap as shown in (a), slow parameter updates are still constrained by the overall confidence level and remain paused to avoid writing missing test errors into long-term parameters.

[0110] Finally, the calibration result output terminal 150 outputs at least one of the following: calibrated received signal level, carrier phase, polarization angle, cross-polarization discrimination, and Doppler frequency shift, and simultaneously outputs the corresponding path rainfall rate, hail parameters, icing parameters, confidence interval, and confidence level. The output can be used for microwave link signal recovery, link adaptive modulation, extreme weather monitoring, path meteorological parameter inversion, and low-confidence alarm.

[0111] The working principle and process of this invention are as follows: During operation, the microwave link transmitter 100 transmits microwave signals according to the set operating frequency and polarization mode, while the microwave link receiver 110 synchronously acquires at least two electromagnetic features among the received signal level, carrier phase, polarization angle, cross-polarization discrimination, and Doppler frequency shift. Simultaneously, the ground meteorological observation equipment 120 and radar and satellite observation sources 121 acquire at least one meteorological observation data among rainfall, hail, freezing rain, temperature, humidity, wind speed, wind direction, radar reflectivity, and cloud characteristics. The unified time synchronization module 160 writes the acquisition timestamps under a unified time reference for each electromagnetic feature data and meteorological observation data. The data processing device 130 first performs outlier removal, missing data marking, time correction, and quality assessment on the acquired data. Then, using a dual-timescale robust baseline decomposition model, it decomposes the electromagnetic feature sequence into clear-sky baseline components, extreme weather distortion components, equipment slow drift components, and random noise components. Based on the clear-sky baseline components and equipment slow drift components, it constructs a counterfactual clear-sky reference adapted to the current equipment state, thereby obtaining the baseline-de-polarization electromagnetic distortion caused by extreme weather. Subsequently, the propagation path segmentation model reconstructs the actual propagation path based on the three-dimensional coordinates of microwave link transmitter 100 and microwave link receiver 110, antenna height, digital elevation model, effective sphere radius, and atmospheric refraction parameters. It then divides the propagation path into multiple path units based on terrain, building obstruction, changes in the atmospheric propagation environment, and the spatial resolution of meteorological observations. The meteorological observation unit standardization model converts meteorological observation data from different sources, with different sampling periods, and different spatial resolutions into standardized meteorological observation units containing meteorological elements, temporal support domains, spatial support domains, and quality confidence levels. The spatiotemporal nonequilibrium optimal transmission alignment model calculates the advection delay based on the movement speed and direction of weather cells. It establishes a joint cost matrix by integrating the sampling time difference between path units and meteorological observation units, three-dimensional spatial distance, support domain overlap, physical characteristic differences, and observation quality. The coupling matrix is ​​solved using entropy-regularized nonequilibrium optimal transmission with edge relaxation terms, aligning asynchronous, heterogeneous multi-source meteorological observations to the corresponding path units actually reached by the weather cells. The physical constraint hybrid expert model takes aligned meteorological observations, baseline-removed electromagnetic distortion, multi-frequency differential features, dual-polarization differential features, and observation quality features as inputs. The gating unit determines the initial weights of the rainstorm expert, hail expert, freezing rain expert, and composite event expert. Then, the initial weights are corrected according to the degree of violation of the electromagnetic propagation law by each expert candidate calibration result. The segmented physical calibration results of each path unit are obtained by weighted fusion.Based on this, the propagation path graph residual calibration model uses path units as nodes and establishes directed edges and edge weights according to adjacency relationships, spatial distances, weather cell movement directions, and propagation time delays. It performs nonlinear residual correction on the segmented physical calibration results to describe the migration, accumulation, and attenuation process of electromagnetic distortion caused by extreme weather along the propagation path. The physical consistency constraint model further applies path integral conservation constraints to the residual correction results and projects them onto a physically feasible region jointly defined by the attenuation non-negativity condition, electromagnetic propagation mechanism, polarization response relationship, and meteorological parameter value range to obtain calibration electromagnetic characteristics and path meteorological parameters that satisfy physical laws. The calibration reliability assessment model determines the finite sample corrected quantiles based on the inconsistency scores of independent calibration samples, generates corresponding reliability intervals, and calculates the comprehensive reliability by combining the reliability interval width, observation completeness rate, optimal transmission coupling quality, and sensor quality. When the comprehensive reliability is not lower than the safety backoff trigger threshold, the calibration result after propagation path graph residual correction and physical consistency constraints is adopted. When the comprehensive reliability is lower than the safety backoff trigger threshold, the safety backoff model reduces or suppresses the nonlinear residual output, switches to a conservative calibration mode based on physical propagation relationships, and outputs a low reliability marker. The calibration result output terminal 150 finally outputs at least one of the calibrated received signal level, carrier phase, polarization angle, cross-polarization discrimination, and Doppler frequency shift, and simultaneously outputs the corresponding path rainfall rate, hail parameters, icing parameters, reliability interval, and reliability marker. Simultaneously, the fast and slow parameters are updated online, the model continuously calculates real-time calibration residuals and performs online change point detection. When the change point statistics exceed the set threshold, the hybrid expert gating parameters, path graph residual parameters, and propagation delay parameters are quickly updated, while the clear sky baseline parameters and physical propagation parameters are frozen. When the change point statistics remain below the set threshold within the stable window, the clear sky baseline parameters and physical propagation parameters are updated again with a lower learning rate. Typical extreme weather samples, calibration residuals, and updated model parameters are written into the distortion samples and event memory 140, thus forming a closed-loop spatiotemporal calibration process from multi-source data synchronous acquisition, spatiotemporal alignment, segmented calibration, physical constraints, credibility determination, safety rollback to online updating of fast and slow parameters.

Claims

1. A method for spatiotemporal calibration of microwave link distortion in extreme weather, characterized in that, Executed by a data processing device, the system includes: a multi-source data synchronous acquisition module, a dual-timescale robust baseline decomposition model, a propagation path segmentation model, a meteorological observation unit standardization model, a spatiotemporal nonequilibrium optimal transmission alignment model, a physically constrained hybrid expert model, a propagation path graph residual calibration model, a physical consistency constraint model, a calibration reliability assessment model, a safety backoff model, and a fast / slow parameter online update model. The multi-source data synchronous acquisition module is used to acquire multi-frequency and / or dual-polarization electromagnetic feature sequences output from the microwave link transmitter and receiver, and to acquire data from meteorological radar, satellite remote sensing, ground meteorological stations, and link location. It writes acquisition timestamps for various data types based on a unified timing signal. The electromagnetic features include at least the following: The signal level, carrier phase, polarization angle, cross-polarization discrimination, and two of Doppler shift are selected. The dual-time-scale robust baseline decomposition model is used to decompose the quality-controlled electromagnetic feature sequence to obtain clear-sky baseline components, extreme weather distortion components, equipment slow drift components, and random noise components, and to construct a counterfactual clear-sky reference using the clear-sky baseline components that do not change with a single extreme weather event. The propagation path segmentation model is used to reconstruct the link propagation path based on the three-dimensional coordinates of the microwave link transceiver, antenna height, digital elevation model, effective sphere radius, and atmospheric refraction parameters, and to divide the propagation path into multiple path units according to changes in the propagation environment and spatial resolution. The meteorological observation unit standardization model is used to classify the non-standardized meteorological observation units into multiple path units. Meteorological observations from the same source but with different sampling periods and spatial resolutions are converted into observation units that simultaneously possess temporal support domains, spatial support domains, and quality confidence levels. The spatiotemporal nonequilibrium optimal transmission alignment model is used to establish a joint cost matrix based on the sampling time difference between path units and observation units, weather cell advection lag, three-dimensional spatial distance, overlap of observation support domains, and differences in physical characteristics. The coupling matrix between path units and observation units is solved using entropy-regularized nonequilibrium optimal transmission with edge relaxation terms, and asynchronous multi-source meteorological observations are aligned to the corresponding path units based on the coupling matrix. The physically constrained hybrid expert model is used to receive the aligned meteorological observations, remove baseline electromagnetic distortion, perform multi-frequency differential features, and dual-polarization differential features. Based on observation quality characteristics, initial weights for different extreme weather types are determined through gating units. These initial weights are then corrected according to the deviations of each weather expert's output from the physical propagation laws. Subsequently, rainstorm experts, hail experts, freezing rain experts, and composite event experts output candidate calibration values, which are then weighted and fused to obtain segmented physical calibration results for each path unit. The propagation path graph residual calibration model is used to construct a propagation path graph with directed edges and edge weights, using path units as nodes and based on the adjacency relationships, spatial distances, weather cell movement directions, and propagation delays between path units. This model performs nonlinear residual correction on the segmented physical calibration results to characterize the migration, accumulation, and attenuation relationships of local electromagnetic distortion along the propagation path.The physical consistency constraint model applies path integral conservation constraints to the calibration results of each path unit and projects the corrected results onto a physically feasible region determined by the electromagnetic propagation mechanism and the range of meteorological parameters, obtaining the calibrated electromagnetic characteristics and corresponding meteorological parameters. The calibration reliability assessment model calculates finite sample quantiles based on the inconsistency scores of the calibration samples. The safety backoff model suppresses the nonlinear residual output of the propagation path graph residual calibration model when the reliability of the calibration results falls below a set threshold, switches to a conservative calibration mode based on physical propagation relationships, and outputs a low reliability marker. The online update model for fast and slow parameters performs online change point detection on the calibration residuals.

2. The method for spatiotemporal calibration of microwave link distortion in extreme weather according to claim 1, characterized in that, The dual-timescale robust baseline decomposition model is as follows: For the The link at time The collected electromagnetic features are defined as follows: （1） In equation (1), Indicates the first The microwave link at time The collected electromagnetic feature vectors; This represents the clear-sky baseline component, which is related to the daily cycle, seasonal variations, and normal atmospheric refraction conditions. This indicates sparse or segmented sparse distortion components caused by heavy rain, hail, freezing rain, or a combination of extreme weather events. This indicates the slow drift component caused by equipment temperature drift, changes in transmit power control, or antenna aging. Represents random noise components; Indicates microwave link index. , This indicates the total number of microwave links participating in the calibration. Indicates the discrete sampling time; superscript The bold symbol represents an observable quantity; a bold symbol represents a vector composed of different frequencies, polarization modes, or electromagnetic characteristic types. Organize the multi-link observations within the sliding window into a matrix. The quality mask matrix is ​​denoted as The clear-sky baseline, weather distortion, and equipment drift are solved using the following formula: （2） In equation (2), This represents the observation matrix within the sliding window, which consists of multiple links, multiple frequency points, and multiple polarization electromagnetic features. , and Let represent the clear-sky baseline matrix, extreme weather distortion matrix, and equipment slow drift matrix to be solved, respectively; Indicates and Quality mask matrices of the same dimension; This indicates element-wise multiplication; Denotes the Frobenius norm; Represents the nuclear norm; and These represent the first-order and second-order difference operators along the time direction, respectively. Representing the baseline time difference Norm; Represents the sparse norm of a group; The squared Frobenius norm represents the second-order difference of the device's slow drift. , , and represent the non-negative weight coefficients of the low-rank constraint, baseline time smoothing constraint, weather group sparsity constraint, and equipment drift smoothing constraint, respectively; Indicates in , and To minimize the objective function, after decomposition, use... As the weather distortion input for subsequent calibration, among which Indicates the first The microwave link at time The baseline-de-baseline electromagnetic distortion vector; Indicates the first The microwave link at time The observed electromagnetic characteristic vector; This represents the clear-sky baseline vector estimated by equation (2); This represents the device slow drift vector estimated by equation (2); Indicates microwave link index; Indicates the discrete sampling time; Weather distortion is used as the input for subsequent spatiotemporal matching, weather type determination, and path segmentation calibration.

3. The method for spatiotemporal calibration of microwave link distortion in extreme weather according to claim 1, characterized in that, The propagation delay-aware unbalanced optimal transmission matching model is as follows: The three-dimensional coordinates of the link transmitter and receiver are respectively and Divide the link into The path unit, the first The center coordinates of each path unit are （3） In equation (3), Indicates the first The three-dimensional coordinate vector of the center of each path unit; and These represent the three-dimensional coordinate vectors of the microwave link's transmitting and receiving ends, respectively. Indicates the path unit index. ; This represents the total number of path units obtained from the propagation path partitioning; Indicates the first The normalized position of the center of each path unit on the straight path between the transceiver and receiver; Indicates the first Earth curvature correction vector for each path unit; Indicates the first The atmospheric refraction correction vector of the i-th path unit, for the i-th A multi-source meteorological observation unit, with its center time set as . The center coordinates are Weather unit speed is The advection time delay from the observation unit to the path unit is estimated as follows: （4） In equation (4), Indicates the first The weather cell represented by the meteorological observation unit advection to the first The estimated time delay required for each path unit; Indicates the candidate time delay to be searched; This represents the maximum absolute value of the time delay allowed for the search; This represents the candidate time delay that minimizes the objective function; Indicates the first The center coordinates of each path unit; Indicates the first The center coordinates of each meteorological observation unit; Indicates the first Each observation unit corresponds to a three-dimensional advection velocity vector of a weather cell; Indicates the duration of weather cell transit. The predicted position after; Represents the Euclidean norm; and These represent the path unit index and the meteorological observation unit index, respectively. The joint matching cost is defined as （5） In equation (5), Indicates the first The path unit and the first The cost of joint matching among meteorological observation units; , , , and These represent the non-negative weights of the time difference term, the three-dimensional spatial distance term, the non-overlapping support domain term, the physical characteristic difference term, and the observation quality term, respectively. Indicates the first The sampling time of the link electromagnetic characteristics corresponding to each path unit; Indicates the first The center time of each observation unit; This represents the advection time delay obtained from equation (5); and These represent the scale-normalized parameters for time difference and spatial distance, respectively. A function representing the three-dimensional spatial distance between two coordinate points; , and These represent the center coordinates of the path unit, the center coordinates of the observation unit, and the advection velocity of the weather cell, respectively. This represents the intersection-union ratio of the influence domain of the path unit and the spatial support domain of the observation unit; Indicates the first Electromagnetic distortion description vector of each path unit; Indicates the first Meteorological physical description vectors for each observation unit; A scale or covariance matrix representing the differences in physical characteristics; Indicated by Weighted squared Mahalanobis distance; Indicates the first Quality confidence level of each observation unit; This indicates a positive number that prevents the logarithmic independent variable from being zero. Represents the natural logarithm; Let the path unit mass vector be... The mass vector of the observation unit is The coupling matrix is ​​obtained by the following formula: （6） In equation (7), Represents the optimal coupling matrix; Let the non-negative coupling matrix to be solved be represented by its elements. Indicates the first The meteorological observation unit sent to the first The quality of each path unit allocation; Let represent the joint cost matrix formed by equation (5); This represents the sum of the products of corresponding elements of two matrices; Represents the entropy regularity coefficient; Indicates the Kullback-Leibler divergence; Represents the normalized quality vector of a path unit; Represents the normalized mass vector of a meteorological observation unit; express and outer product; superscript Indicates matrix transpose; This represents a column vector whose elements are all 1 and whose dimension matches the multiplication of the corresponding matrix. and These represent the row edge quality and column edge quality of the coupling matrix, respectively. and These represent the weights of the path unit edge relaxation term and the observation unit edge relaxation term, respectively, aligned to the path unit. The meteorological vector is: （7） In equation (7), Indicates alignment to the first Fusion meteorological observation vectors of each path unit; Represents the th element in the optimal coupling matrix. Line 1 Column elements; Indicates the first Meteorological element vectors for each meteorological observation unit; This indicates a positive number that prevents the denominator from being zero. and These represent the path unit index and the meteorological observation unit index, respectively.

4. The method for spatiotemporal calibration of microwave link distortion in extreme weather according to claim 1, characterized in that, The physical constraint hybrid expert calibration model is as follows: The physical baseline for extreme weather is obtained by the ratio attenuation integral over the path unit, with the attenuation of heavy rainfall being... （8） In equation (8), This represents the path integral attenuation caused by heavy rain across the entire microwave link; Indicates the total number of path units; Indicates the operating frequency of the microwave link; Indicates horizontal polarization, vertical polarization, or other specified polarization mode; and They represent respectively by and The rainfall ratio attenuation coefficient and power exponent were determined jointly; Indicates the first Equivalent rainfall rate of each path unit; Indicates the first Effective rainfall coverage length of each path unit; Hail's equivalent scattering attenuation is （9） In equation (9), This represents the equivalent attenuation of the entire link caused by hail particle scattering and absorption; Indicates the equivalent diameter of hail particles; and These represent the minimum and maximum diameters of the hail particles involved in the calculation, respectively. Indicates the first The particle size within each path unit is Hailstone number concentration spectrum distribution; Indicates diameter is Hailstone particles at working frequency Extinction efficiency factor; Represents the equivalent geometric cross-sectional area of ​​a hail particle; This represents a differential element that integrates over hailstone diameter; Indicates the first The effective hail coverage length of each path unit; the integral operation in the formula represents the effective hail coverage length of each path unit; to Extinction contribution integral within the particle size range; Freezing rain and icing add-on attenuation （10） In equation (10), Indicates time Additional attenuation caused by freezing rain and icing, in dB; Indicates the operating frequency polarization mode and ambient temperature The determined path icing attenuation coefficient per unit length; Indicates time The effective icing length of the link; Indicates operating frequency Additional attenuation coefficient per unit ice thickness of the lower radome; Indicates time The equivalent icing thickness of the radome; Indicates the ambient temperature near the path or radome; The multi-source meteorological observations aligned to the i-th path unit via the spatiotemporal nonequilibrium optimal transport alignment model are combined with the baseline-removed electromagnetic distortion, multi-frequency differential characteristics, dual-polarization differential characteristics, and observation quality characteristics corresponding to that path unit to form the gated input z. i The physical violation of the k-th weather expert is: （11） In equation (12), Indicates the first The weather expert commented on the first The physical violation of the output of each path unit; Indicates a weather expert index; Indicates the index of physical constraint terms; Indicates the total number of physical constraint terms; Indicates the first The first type of weather A physical constraint function, wherein the physical constraint includes at least two of the following: the range of meteorological parameter values, non-negativity of attenuation, polarization response, and path integral consistency; Indicates the first The weather expert commented on the first The candidate calibration vectors output by each path unit; This indicates that only the constraint violations greater than zero are retained; Represents the non-negative weighting coefficient of the path decay consistency term; This indicates that the data was assigned or converted from the link observation. Observational attenuation per path unit; Indicates the first The weather expert calculated the first [number] based on the corresponding physical propagation model. Physical attenuation of each path unit; Represents the absolute value, and the gating weight is... （12） In equation (12), Indicates the first The path unit belongs to or uses the first path unit. Normalized gating weights for individual weather experts; This indicates that the gating unit is based on the input vector The calculation of the first The raw scores of the weather experts; This represents the first characteristic consisting of aligned meteorological observations, baseline-removed electromagnetic distortion, multi-frequency difference characteristics, dual-polarization difference characteristics, and observation quality characteristics. Each path unit gated input vector; Indicates the physical violation penalty coefficient; This represents the physical violation quantity calculated by equation (11); A gated temperature parameter that indicates the smoothness of the weight distribution. This indicates the total number of weather experts; This indicates the weather expert index used for summing the denominators; Represents the natural exponential function; The number of candidate calibrations was determined by each expert. Output, the fusion result is （13） In equation (13), The physical constraint hybrid expert model represents the first... The fusion candidate calibration vectors output by each path unit; superscript This indicates the fusion results of mixed experts; Indicates the first A weather expert in the first Gating weights on each path unit; Indicates the first A candidate calibration mapping function for a weather expert; Indicates the first Gating and expert input vectors for each path unit; Indicates the first A set of parameters to be trained for a weather expert; Indicates a weather expert index; This represents the total number of weather experts; the summation operation in the formula represents the summation of the first to the last... The candidate outputs of each weather expert are weighted and summed.

5. The method for spatiotemporal calibration of microwave link distortion in extreme weather according to claim 1, characterized in that, The path segmentation graph residual calibration model is as follows: Graph constructed using path units as nodes The initial state of node i is From node The weight of the directed edge to node i is （14） In equation (14), The propagation path graph represents nodes. The normalized directed edge weight pointing to node i; Represents node i and node Spatial distance between the centers of corresponding path units; Indicates the spatial distance attenuation scale; The weather unit is represented by nodes. Propagate to the corresponding location to the node The time delay at the corresponding location; Indicates the propagation delay attenuation scale; The weight of the weather movement direction consistency term; Indicates that by node Pointing to node The direction angle of the connecting line; Indicates the direction angle of movement of a weather cell; This indicates the degree of consistency between the direction of the node connection and the direction of weather movement; Represents a node The set of incoming neighbor nodes; Indicates the index used when summing neighboring nodes; and Representing nodes respectively with neighboring nodes Spatial distance and propagation time delay between them; Represents the natural exponential function; the first Layer message updated to （15） In equation (15), Indicates the first After layer message passing, the node The state vector; and They represent the first Layer nodes and its neighboring nodes The state vector; Indicates the graph message passing layer index; Represents a nonlinear activation function; Indicates the first The weight matrix of the layer acting on the node's own state; Indicates the first The weight matrix applied to neighbor messages by the layer; The node obtained from equation (15) represents the node. Pointing to node The directed edge weight; Represents a node The set of incoming neighbor nodes; Indicates the first Layer bias vector; the summation operation in the formula represents the summation of the values ​​of the nodes. Summing all incoming neighbor messages; Path graph models only learn residuals that the physical baseline fails to explain. The final calibration value is （16） In equation (16), Indicates the first The final calibrated electromagnetic characteristic or meteorological parameter vector of each path unit; Let represent the hybrid expert physical candidate calibration vector obtained from equation (13); The path graph residual model represents the first... The nonlinear residual correction vector output by each path unit; This represents the physically feasible region determined by the non-negativity of attenuation, the range of meteorological parameters, the polarization response, and the path integral relationship. This indicates projecting the vector within the parentheses onto the physically feasible region. The projection operator; Indicates the path unit index; The model training objective is （17） In equation (17), This represents the total training loss of the path graph residual calibration model; This represents the data fitting loss caused by the difference between the calibration output and the self-test reference values ​​of co-located ground stations, radar quantitative products, or communication equipment. , and These represent the non-negative weights of the path integral consistency term, the graph total variational smoothing term, and the physical constraint term, respectively. This represents the actual observed total attenuation of the entire microwave link; Indicates the first The estimated specific attenuation after calibration of each path unit; Indicates the first The effective length of each path unit; Represents the Euclidean norm; The set of directed edges representing the propagation path graph; Indicates the connection node With nodes One of the edges; Indicate the corresponding directed edge weight; and Representing nodes respectively and nodes The calibration output vector; express Norm; Indicates the action applied to the node. The calibration output of the first Physical constraints; Indicates the index of physical constraint terms; This indicates that only the constraint violation that is greater than zero will be penalized.

6. The method for spatiotemporal calibration of microwave link distortion in extreme weather according to claim 1, characterized in that, The trusted interval generation and safe fallback model is as follows: Define the first on independent calibration samples Inconsistency score of each sample （18） In equation (18), Indicates the first The inconsistency score of each independent calibration sample; Indicates the index of independent calibration samples; Indicates the first The true reference value or the reference quantity that has been quality audited for each sample; Indicates the first Model calibration estimates for each sample; This represents the absolute error between the calibration estimate and the reference value; The model represents the first The standard deviation or scale uncertainty estimate given for each sample; A positive number indicates a measure to prevent the denominator from being zero and represents the lower bound of irreducible noise; the pointed cap above the variable indicates an estimated value; Take the quantiles after correction for a finite sample （19） In equation (19), Indicates the confidence level as Inconsistent score quantiles obtained after correction using finite samples; Indicates the target coverage rate, and ; Indicates the coverage rate of the target confidence interval; This represents the total number of independently calibrated samples; This represents the inconsistency score of all independent calibration samples calculated by equation (18); Denotes the first sample set quantiles; This indicates the rounding up operation; This represents the corrected quantile level after considering a finite number of samples; The confidence interval of the real-time sample is then... （20） In equation (20), Indicates the real-time sample at time [time]. The confidence interval; Indicates time The calibration estimate; The finite sample corrected quantile is obtained from equation (19); The model represents time intervals. The standard deviation or scale uncertainty estimate of the output; The interval represents the lower bound of irreducible noise; the left and right endpoints of the interval represent the lower and upper bounds of the calibration result, respectively. Indicates the real-time sampling time and defines the confidence level. ,in, Indicates time Overall credibility; Indicates the width of the confidence interval; Indicates the effective range of the calibrated electromagnetic characteristics or meteorological parameters; This indicates a positive number that prevents the denominator from being zero. The time is determined by the observation completeness, optimal transmission coupling quality, and sensor quality. Data quality coefficient; Represents the natural exponential function; This indicates the threshold for triggering a safe rollback.

7. The method for spatiotemporal calibration of microwave link distortion in extreme weather according to claim 1, characterized in that, The fast and slow parameter separation online update model is as follows: Let the real-time residual be In length of Calculate change point statistics on the reference window （21） In equation (21), Indicates time Online variable point statistics; Indicates the end time The recent The sample mean of the calibration residual vector within each sampling period; Indicates time The real-time residual vector satisfies ; Indicates time Reference electromagnetic characteristics or reference meteorological parameter vector; Indicates time The calibration estimation vector; Indicates the length of the reference window for change point detection; This represents the baseline mean of the residual vector under steady-state conditions. The reference covariance matrix represents the residual vector under steady-state conditions; The superscript represents the inverse of the reference covariance matrix. Indicates vector transpose; Indicates the real-time sampling time; when When a sudden change occurs in weather type, movement speed, or data latency, slow parameters are frozen. Update fast parameters according to the larger learning rate : （22） In equation (22), and They represent the first Before the first update and the first The updated fast parameter vector; the fast parameters include at least the hybrid expert gating parameters, the path graph residual parameters, and the propagation delay parameters; Indicates the fast parameter learning rate; Indicates time The loss function is calculated based on real-time calibration samples; Represents the loss function Regarding fast parameter vectors The gradient; This represents the number of online parameter updates, when equation (21) yields... Greater than the change point threshold When executing formula (22), where, This represents the statistical threshold for determining sudden changes in weather type, movement speed, or data latency. when continued Update the slow parameter after one sampling period: （23） In equation (23), and They represent the first Before the first update and the first The updated slow parameter vector; the slow parameters include at least clear-sky baseline parameters and physical propagation parameters; Indicates the learning rate of the slow parameter; The fast parameter learning rate in expression (22) and ; This indicates that the gradient is calculated over the slow parameter vector; Indicates time Real-time calibration loss; This indicates the non-negative weight of the historical parameter preservation term; Indicates the index of the slow parameter component; Indicating stable historical events on the first The importance of each slow parameter; Represents the th element in the current slow parameter vector. One component; Indicates the first The historical values ​​of each slow parameter saved before the start of the current stable update phase; the summation operation in the formula represents the summation of all slow parameter components; This indicates the change point statistics before allowing slow parameter updates. Not exceeding the threshold The number of stable sampling periods required.

Images