Luoga No.2 SAR flow velocity correction method based on Bragg orbit velocity

Abstract

The invention belongs to the technical field of ocean surface flow velocity remote sensing measurement, and particularly relates to a Luoga No.2 SAR (Synthetic Aperture Radar) flow velocity correction method based on Bragg orbit velocity, which comprises the following steps of: verifying the physical correctness of an orbit velocity mechanism relative to a phase velocity mechanism; under a DopRIM framework, a physically consistent sea wave error correction model is established; calibrating parameters of the sea wave error correction model; applying the calibrated sea wave error correction model to along-orbit interference SAR observation data of the Luoma No. 2 satellite, and calculating the radial surface flow velocity and sea wave error of each resolution unit; comparing an output result with a matched reference truth value to evaluate the effectiveness of the sea wave error correction model; comparing the sea wave error correction model with a KaDOP model, and respectively counting and analyzing simulated sea wave errors under different methods; the sea wave error simulation result is visually displayed, and the improvement effect is quantitatively evaluated through in-situ observation data and a KaDOP simulation result.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of remote sensing measurement of ocean surface flow velocity, in particular to a Lujia No. 2 SAR flow velocity correction method based on Bragg orbital velocity. BACKGROUND

[0002] Ocean surface currents (OSC) are important parameters for describing ocean dynamic processes and material transport mechanisms, and are widely used in fields such as climate change analysis, ocean circulation research, and ecosystem modeling. Synthetic aperture radar (SAR) has become an important remote sensing means for obtaining ocean surface flow velocity information due to its all-weather, high-resolution, and large-range imaging capabilities. However, the Doppler velocity measured by SAR not only contains the true ocean current drift component, but also superimposes the non-flow velocity component caused by the motion of the wave scattering unit and its modulation by long-wave orbits, collectively known as the wave-induced bias (WB). This bias can cause systematic errors in flow velocity inversion, severely limiting the application effect of SAR in accurate observation of ocean flow velocity.

[0003] Traditional WB correction models, represented by DopRIM and its derivatives, usually simplify the inherent motion of Bragg scattering units as their phase velocity contribution. This modeling assumption is mainly derived from the observation phenomenon of early high-frequency (HF) radar, that is, in open sea areas, a pair of symmetric peaks often appears in the Doppler power spectrum, which is explained as the phase velocity Doppler shift caused by the forward and backward Bragg waves propagating along the radar line of sight. However, this phase velocity-based modeling approach ignores the orbital motion characteristics of Bragg waves itself, and its physical rationality and applicability under more extensive radar bands and wind wave conditions are still controversial.

[0004] Recent wave tank experiments have provided new physical evidence for revealing the actual role of Bragg waves in Doppler frequency shift contribution. Experimental results show that even if there is only a single-direction propagating Bragg wave (without the reverse component), the measured radar power spectrum still shows a double-peak structure, which cannot be explained by the phase velocity mechanism. Further reconstruction of the Doppler spectrum based on the orbital velocity of Bragg waves shows that the predicted frequency peaks are highly consistent with the measured results, indicating that the orbital motion of Bragg waves is the fundamental mechanism for its contribution to radar Doppler frequency shift. This finding provides a theoretical basis for the improvement of WB error physical modeling.

[0005] With the increasing demand for ocean observation, the deficiencies of traditional WB error correction models in physical consistency and adaptation to complex sea conditions are increasingly prominent. In recent years, academia and engineering have increasingly focused on combining theory, experiment and multi-source observation data to deepen the understanding of the relationship between sea wave orbital motion and radar scattering mechanism. How to establish a high-precision WB error correction model that can accurately reflect the actual dynamics of sea waves and adapt to different radar bands and wind wave environments has become a key technical problem to improve the reliability and engineering applicability of SAR sea current retrieval. SUMMARY

[0006] In view of the physical inconsistency and insufficient sea wave error correction precision of the existing technology based on the Bragg wave phase velocity model, the present application aims to provide a LoGaSat SAR flow velocity correction method based on Bragg orbital velocity. Through wave tank experiment and theoretical analysis, the Bragg wave orbital velocity is established as the theoretical basis of the dominant physical mechanism of Doppler shift, and a physically consistent sea wave error correction model is constructed under the DopRIM framework with orbital velocity as the core. Through joint calibration and verification of airborne and satellite SAR observation data, the present application can significantly improve the inversion precision and reliability of the ocean surface flow velocity, and provide an effective technical solution for realizing large-scale and high-precision operational ocean flow velocity remote sensing monitoring.

[0007] The technical scheme adopted by the present application to achieve the above-mentioned purpose is: a LoGaSat SAR flow velocity correction method based on Bragg orbital velocity, comprising the following steps:

[0008] Step S1: based on wave tank experiment and theoretical analysis, a Doppler shift theoretical model based on Bragg wave orbital velocity is established, and its quantitative expression and theoretical Doppler power spectrum are obtained to verify the physical correctness of the orbital velocity mechanism relative to the phase velocity mechanism;

[0009] Step S2: based on the orbital velocity mechanism verified in step S1, the Bragg wave inherent motion term is replaced by orbital velocity under the DopRIM framework, and a physically consistent sea wave error correction model is established by combining the scattering modulation characteristics of Bragg wave itself;

[0010] Step S3: use airborne Ka-band along-track interferometric SAR observation data, GNSS drift buoy measurement results and Copernicus wind field data to calibrate the parameters of the sea wave error correction model to make it consistent with the actual observation;

[0011] Step S4: apply the calibrated sea wave error correction model to LoGaSat satellite along-track interferometric SAR observation data to calculate the radial surface flow velocity and sea wave error of each resolution unit;

[0012] Step S5: The assimilated GDP drift buoy data and Copernicus current data, which are matched in space and time with the observations of LK-02 satellite, are used as reference true values to compare with the output results of step S4 to evaluate the effectiveness of the sea wave error correction model;

[0013] Step S6: The sea wave error correction model is compared with the KaDOP model, and the simulated sea wave errors under different methods are statistically calculated and analyzed by root mean square error, bias and correlation coefficient to quantitatively measure the performance improvement of the model;

[0014] Step S7: The sea wave error simulation results are visualized and displayed, and the improvement effect is quantitatively evaluated by in-situ observation data and KaDOP simulation results.

[0015] The step S1 comprises the following steps:

[0016] S11: According to the wave tank experiment and theoretical derivation, the Bragg wave of one-way propagation is observed, and its orbital velocity is quantified to confirm that the orbital velocity is the actual physical mechanism of producing Doppler shift;

[0017] S12: Analyze the component of Bragg wave orbital velocity in the radar line-of-sight direction , that is,

[0018] ;

[0019] wherein, is the horizontal orbital velocity component of the Bragg wave, is the vertical orbital velocity component of the Bragg wave, is the amplitude of the Bragg wave, is the angular frequency of the Bragg wave, is the wave number of the Bragg wave, is the horizontal coordinate, is the time, is the radar incidence angle;

[0020] S13: Based on the Jacobi-Anger expansion, the phase-modulated radar signal under the control of the orbital velocity is converted into a discrete spectrum, and the formula is:

[0021]

[0022] ;

[0023] wherein, is the discrete spectrum of the phase-modulated radar echo in the frequency domain; is the amplitude weight of the nth spectral line given by the Bessel function; is the phase modulation index, which is determined by the amplitude of the Bragg wave orbital velocity in the line-of-sight direction and the radar parameters; is the initial phase factor corresponding to the nth harmonic; is the frequency domain variable, representing the value point of the echo signal in the Doppler frequency domain after phase modulation; is the fundamental frequency, is the Bragg wave angular frequency, is the Dirac delta function;

[0024] According to the discrete spectrum, the position of the main peak of the theoretical Doppler power spectrum is calculated;

[0025] S14: Comparing the theoretical Doppler power spectrum with the wave tank experimental observation results, verifying the consistency of the Doppler power spectrum driven by the orbital velocity with the measured results, and providing a theoretical basis for the sea wave error correction of the interferometric SAR flow measurement.

[0026] The step S2 is specifically:

[0027] Step S21: Under the DopRIM framework, a radial surface flow velocity expression is established, which includes the surface layer flow, the inherent motion of the Bragg scatterer, and the long wave modulation term;

[0028] Step S22: The inherent motion term of the Bragg scatterer is replaced by the orbital velocity expression, and the tilt modulation transfer function and the hydrodynamic modulation transfer function are introduced in the Bragg ring domain. The Bragg term velocity expression is obtained by integral weighting;

[0029] Step S23: Based on the integral of the Bragg term orbital velocity and the modulation transfer function, a physically consistent error correction model is completed for the quantitative correction of the radial surface flow velocity deviation.

[0030] The step S23 is specifically:

[0031] a. The contribution of the Bragg wave to the radial Doppler velocity is written as a modulation weighted integral of the Bragg ring domain, that is:

[0032]

[0033] wherein, is the radar incidence angle, is the radar line-of-sight azimuth, is the Bragg wave direction; is the Bragg wave tilt and hydrodynamic modulation function, is the real part of the Bragg wave tilt and hydrodynamic modulation function, is the imaginary part of the Bragg wave tilt and hydrodynamic modulation function; is the Bragg wave phase velocity; is the Bragg wave number; is the Bragg wave directivity saturation wave number spectrum; is the integral domain;

[0034] b. Determine the integration domain For the Bragg ring domain, i.e.:

[0035] ;

[0036] where, is the polar wave number of the sea surface short wave in the spectral space, i.e. the azimuth pair; is the wave number module of the integrated water dynamic short wave; is the radial wave number half bandwidth of the Bragg resonance ring; is the Bragg wave wave number;

[0037]

[0038] where, is the radar wave number, is the radar wavelength;

[0039] c. Determine the relationship between the directional displacement spectrum and the saturation spectrum, i.e. the Bragg saturation spectrum and the directional displacement spectrum satisfy:

[0040]

[0041] where is represented as:

[0042]

[0043] where, is the directional wave number spectrum of the Bragg wave, is the friction wind speed of the sea surface, is the threshold friction wind speed, is the directional spreading function of the capillary wave, is the short wave dissipation factor caused by the modulation effect of large-scale long waves on small-scale short waves, is the vortex dissipation factor caused by the sea surface turbulence, is the capillary wave curvature spectrum, is the wind speed at 10 meters on the sea surface; is the peak rise factor of the capillary wave curvature spectrum;

[0044] The wind stress is determined by the relationship between the friction velocity and the 10 m wind speed:

[0045] ;

[0046] where, is the drag coefficient;

[0047] d. The calculation results based on the orbital velocity The term based on Bragg wave phase velocity calculation is replaced in the DopRIM framework, and a sea wave error correction model WBCM is obtained.

[0048] The step S3 comprises the following steps.

[0049] Step S31: Collecting data of multiple spatial sub-regions in the observation area through airborne Ka-band along-track interferometric SAR experiment, and performing spatial and temporal registration with GNSS drift buoy observation and CMEMS wind field data; Step S32: Taking the GNSS drift buoy observation flow rate as a reference, comparing the observation values and reference values of each sub-region, obtaining the wave error observation of each sub-region, and recording the corresponding wind field information and radar observation parameters; Step S33: Calibrating the modulation transfer function parameters by using a weighted nonlinear least squares method, and evaluating the calibration results by using root mean square error, bias and correlation coefficient statistical indicators, and selecting the optimal parameter group for model correction.

[0050] In step S33, the modulation transfer function parameters are calibrated by using a weighted nonlinear least squares method, specifically:

[0051] a) In the airborne Ka-band along-track interferometric SAR imaging area, a plurality of spatial sub-regions are selected which are synchronously registered with the wind field and the GNSS drift buoy, and the radial surface flow rate is inverted by using the interferometric phase difference , that is,

[0052] ;

[0053] wherein, is the platform velocity, is the interferometric phase, is the radar wave number, is the along-track baseline length, is the radar incidence angle;

[0054] b) For each sub-region, the sea wave error observation is defined as:

[0055]

[0056] wherein, is the radial surface flow rate measured by the GNSS drift buoy;

[0057] c) The Bragg wave modulation term in the sea wave error correction model is introduced with a tilt and a hydrodynamic modulation transfer function, and the parameter vector is: ;

[0058] The model output for the first sub-region is:

[0059]

[0060] wherein, is the model predicted sea wave error of the i th observation point, is the angle between radar look direction and wind direction, is the wind speed at 10 meters above sea surface, is the radar incidence angle, is the to-be-solved parameter;

[0061] The weighted nonlinear least squares method is adopted for fitting, and the objective function is:

[0062]

[0063] wherein, is the weight; is the observed sea wave error;

[0064] The Levenberg-Marquardt iterative algorithm is adopted to optimize and solve the parameter vector p, and the parameter update formula is:

[0065]

[0066] wherein, is the Jacobian matrix, is the residual vector, is the damping factor, is the diagonal weight matrix, is the unit matrix, is the transpose of the Jacobian matrix;

[0067] The parameters are updated through iteration: until the convergence condition is met;

[0068] d) The calibrated modulation transfer function parameter set is evaluated by using the root mean square error, the bias and the correlation coefficient, and the parameter uncertainty is estimated by the residual.

[0069] The step S4 is specifically:

[0070] Step S41: applying the calibrated sea wave error correction model to the Loach-2 satellite along-track interferometric SAR data, and performing flow velocity inversion and wind field registration on each resolution unit divided in the observation area;

[0071] Step S411: performing standard interferometric processing on the satellite raw data, including registration, flat earth phase removal, interferogram generation, and dividing the entire observation area into regular geographic grids, i.e., each resolution unit;

[0072] Step S412: according to the interferometric phase difference Δ , using the basic principle of along-track interferometric SAR, the uncorrected radial surface current velocity of each resolution cell is preliminarily inverted ;

[0073] Step S42: on each resolution cell, the sea wave error is calculated by using the correction model, and compared with the observation result of the LK-2 satellite;

[0074] For each resolution cell:

[0075] Step S421: the wind speed, the included angle between the radar line-of-sight direction and the wind direction of the cell are extracted;

[0076] Step S422: the environmental parameters and radar geometric parameters of step S421 are substituted into the calibrated WBCM model to calculate the velocity deviation caused by the sea wave movement in the cell, i.e. the sea wave error ;

[0077] Step S423: the error is deducted from the initial inverted flow velocity to obtain the corrected real radial surface flow velocity:

[0078]

[0079] Step S43: the calculation result is formatted as a grid data product to obtain two core layers, respectively: the spatial distribution of the corrected radial surface flow velocity field, i.e. , and the spatial distribution of the sea wave error field, i.e. .

[0080] The step S5 specifically comprises:

[0081] Step S51: in the satellite observation area, the reference flow field is generated by assimilating the GDP drift buoy and Copernicus current data, and is matched in time and space with the along-track interferometric SAR observation data of the LK-2 satellite, and is interpolated to the same grid as the satellite according to the resolution cell;

[0082] Step S52: on each resolution cell, the sea wave error calculated by the model is compared with the satellite observation result to calculate the root mean square error, the bias and the correlation coefficient statistical indicators, and the effectiveness of the sea wave error correction model is evaluated and verified.

[0083] The step S6 specifically comprises:

[0084] Step S61: a statistical evaluation system is established by using the unit-level error sequence matched with the reference data, and the evaluation indicators include the root mean square error, the bias and the correlation coefficient;

[0085] Step S62: Under the condition of spatial and temporal consistency with the satellite observation area, respectively generate a unit-level sea wave error sequence with the sea wave error correction model and the KaDOP model, and compare and evaluate with the reference error;

[0086] Step S63: Quantify the performance improvement with the root mean square error as the main index, and the improvement rate

[0087]

[0088] Wherein, The root mean square error of the KaDOP model, The root mean square error of the sea wave error correction model.

[0089] In step S7, the sea wave error simulation result is visualized and displayed, and specifically includes:

[0090] Step S71: Based on the corrected radial surface flow velocity product obtained in step S4, a two-dimensional spatial distribution map is generated, the color mapping is used to represent the flow velocity, and the coastline, contour line and scale element are superimposed;

[0091] Step S72: Based on the sea wave error field data separated in step S4, a sea wave error spatial distribution map is generated, the diverging color scheme is used to distinguish the positive and negative error values, and the maximum and minimum error areas are marked;

[0092] Step S73: Based on the comparison and evaluation result of step S6, a statistical comparison chart is generated, including:

[0093] (1) The scatter distribution chart of the flow velocity before and after correction and the reference value;

[0094] (2) The error distribution histogram of the WBCM model and the KaDOP model;

[0095] (3) The performance index comparison table of each model in different wind speed intervals;

[0096] Step S74: A comprehensive evaluation report is generated, including the original observation data quality evaluation index, the root mean square error, the bias and the correlation coefficient statistical table before and after model correction, the correction effect analysis under different sea conditions, and the performance improvement quantitative index of the KaDOP model;

[0097] Step S75: The spatial distribution map, the statistical chart and the evaluation report are integrated into a visual product, and are output in a standardized format, supporting GIS platform loading and interactive query.

[0098] The present application has the following beneficial effects and advantages:

[0099] ​1. The sea wave error correction method provided by the present application is based on the principle of physical consistency, and the model is more rigorous in theory by replacing the phase velocity of the Bragg scattering unit with the orbital velocity, effectively solving the problem of inconsistent physical assumptions in traditional methods.

[0100] 2. The present application uses wave tank experiment Doppler spectrum reconstruction experimental evidence to clarify the dominant role of Bragg wave orbital motion in SAR observation, effectively improving the scientificity and reliability of the model.

[0101] 3. The present application uses weighted nonlinear least squares method to accurately calibrate MTFs parameters by assimilating airborne Ka-band ATI-SAR measured data, GNSS drift buoy, Copernicus wind field and other multi-source data, improving the adaptability of the model to actual marine environment.

[0102] 4. The bias correction model of the present application can be directly applied to the observation data of Luojia No. 2 satellite-borne ATI-SAR, realizing the automatic error correction of large-scale and high-resolution marine surface flow velocity products, and having good engineering application value.

[0103] 5. According to the experimental and measured data verification, the model of the present application can realize about 81% RMSE reduction compared with the existing KaDOP method under typical observation conditions, and significantly improve the performance indicators such as bias and correlation coefficient, significantly improving the overall precision and reliability of the sea current inversion.

[0104] 6. The present application can accurately depict the variation law of sea wave error with wind speed, observation azimuth and other environmental parameters, has stronger generalization ability and robustness, and is suitable for various complex sea conditions and different observation geometrical conditions.

[0105] 7. The present application supports visual analysis and pixel-level comparison and verification of output results, which is convenient for quantitative evaluation and business promotion of the correction effect of the model in practical application. BRIEF DESCRIPTION OF DRAWINGS

[0106] Figure 1 is a Luojia No. 2 along-track interferometric SAR flow velocity measurement sea wave error correction method flow chart provided by an embodiment of the present application based on Bragg wave orbital velocity;

[0107] Figure 2 is a comparison chart of experimental observation and theoretical reconstruction results of the double-peak structure of Doppler power spectrum under Bragg wave orbital velocity modulation provided by the present application;

[0108] Figure 3is a radial surface velocity spatial distribution diagram obtained by airborne inversion along the observation path of the GNSS drift buoy in the experimental area provided by the embodiment of the present application; wherein (a) is a radial surface velocity spatial distribution diagram when the wind speed at 10 meters above the sea surface is 5.98 m / s; (b) is a radial surface velocity spatial distribution diagram when the wind speed at 10 meters above the sea surface is 6.05 m / s; (c) is a radial surface velocity spatial distribution diagram when the wind speed at 10 meters above the sea surface is 6.12 m / s; (d) is a radial surface velocity spatial distribution diagram when the wind speed at 10 meters above the sea surface is 6.19 m / s; (e) is a radial surface velocity spatial distribution diagram when the wind speed at 10 meters above the sea surface is 6.27 m / s; and (f) is a radial surface velocity spatial distribution diagram when the wind speed at 10 meters above the sea surface is 6.34 m / s;

[0109] Figure 4 is a wave error simulation result comparison statistical diagram of the WBCM model calibration provided by the embodiment of the present application and the measured reference value;

[0110] Figure 5 is a radial surface flow speed spatial distribution diagram corresponding to different wind speeds and observation geometries in the observation area of the Luojia No. 2 satellite ATI-SAR provided by the embodiment of the present application;

[0111] Figure 6 is a Luojia No. 2 observation area and GDP drift buoy measured point spatial position distribution diagram provided by the embodiment of the present application;

[0112] Figure 7 is a ground true flow speed diagram corresponding to different wind speeds and observation geometries inverted by the CMEMS and GDP assimilation data provided by the embodiment of the present application;

[0113] Figure 8 is a wave error simulation result comparison statistical diagram of the WBCM and KaDOP model under the condition of the Luojia No. 2 satellite provided by the embodiment of the present application and the measured data. DETAILED DESCRIPTION

[0114] The present application will be further described in detail below in combination with the drawings and embodiments.

[0115] Synthetic Aperture Radar (SAR) based OSC remote sensing measurements play an important role in the study of global ocean dynamics and climate systems, but the accuracy of Doppler velocity retrieval is difficult to meet the high standard application requirements due to the wave-induced bias (WB) in the observations. Traditional WB correction models (such as DopRIM) generally assume that the inherent motion of the Bragg wave scattering unit is determined by its phase velocity, which is based on the double-peak structure of the Doppler power spectrum observed by high-frequency radar, but fails to consider the orbital motion contribution of the Bragg wave. Recent wave tank observation experiments show that the positive and negative peak values in the radar power spectrum cannot be explained by the phase velocity alone, and the orbital motion is the dominant mechanism of the Doppler frequency shift. Therefore, the present application proposes to replace the phase velocity with the orbital velocity of the Bragg wave, maintain the same modeling method as the long-wave modulation term, and calibrate the modulation transfer function (MTF) through airborne ATI-SAR measured data. The measured results show that the proposed method can reduce the root mean square error (RMSE) of OSC inversion by about 81% in the application of Luojia-2 satellite, significantly improving the accuracy and reliability of flow velocity inversion.

[0116] As Figure 1 shown, a Luojia-2 along-track interferometric SAR flow velocity measurement sea wave error correction method based on Bragg wave orbital velocity provided by the embodiment of the present application, the Luojia-2 along-track interferometric SAR flow velocity measurement sea wave error correction method based on Bragg wave orbital velocity, includes the following steps:

[0117] Step S1: Through wave tank experiments and theoretical analysis, it is clear that the orbital velocity of the Bragg wave is the physical mechanism of the Doppler frequency shift, which provides a physical basis for sea wave error correction;

[0118] Step S11: According to the wave tank experiment and theoretical derivation, the Bragg wave propagating in one direction is observed, and its orbital velocity is quantified, and it is clear that the orbital velocity is the actual physical mechanism of the Doppler frequency shift;

[0119] S12: Analysis of the component of the Bragg wave orbital velocity in the radar line-of-sight direction , that is,

[0120] ;

[0121] Wherein, is the horizontal orbital velocity component of the Bragg wave, is the vertical orbital velocity component of the Bragg wave, is the amplitude of the Bragg wave, is the angular frequency of the Bragg wave, is the wave number of the Bragg wave, is the horizontal coordinate, is the time, the radar incidence angle;

[0122] Step S13: Based on the Jacobi-Anger expansion, the phase-modulated radar signal dominated by the orbital velocity is converted into a discrete spectrum, and the formula is:

[0123]

[0124] wherein, the discrete spectrum of the phase-modulated radar echo in the frequency domain; the amplitude weight of the nth spectral line is given by the Bessel function; the phase modulation index is determined by the orbital velocity amplitude of the Bragg wave boresight direction and the radar parameters; the initial phase factor corresponding to the nth harmonic; is a frequency domain variable, representing the value point of the phase-modulated echo signal in the Doppler frequency domain; is the base frequency, is the Bragg wave angular frequency, is the Dirac delta function;

[0125] According to the discrete spectrum, the main peak position of the theoretical Doppler power spectrum is calculated;

[0126] Step S14: Comparing the above theoretical results with experimental observations, it is found that the Doppler power spectrum driven by the orbital velocity is highly consistent with the actual wave tank observation results, verifying the physical correctness of the method and providing a theoretical basis for subsequent interferometric SAR flow measurement sea wave error correction.

[0127] Step S2: In the DopRIM framework, the Bragg wave inherent motion term is replaced by the orbital velocity expression, combined with the Bragg wave scattering modulation characteristics, and a physically consistent sea wave error correction model is established;

[0128] Specifically, the physically consistent sea wave error correction model is established, including the following steps:

[0129] Step S21: Based on the DopRIM framework, the decomposition expression of the radial surface velocity is given, and it is clear that only the inherent motion term of the Bragg scattering unit is replaced;

[0130] Step S22: The inherent motion of the Bragg scattering unit is changed from the phase velocity expression to the Doppler velocity expression induced by the orbital velocity, and the inherent motion contribution of the Bragg scattering unit is obtained:

[0131]

[0132] wherein, the radar incidence angle, the radar line-of-sight direction, is the Bragg wave direction; is the Bragg wave tilt and the hydrodynamic modulation function, is the real part of the Bragg wave tilt and the hydrodynamic modulation function, is the imaginary part of the Bragg wave tilt and the hydrodynamic modulation function; is the Bragg wave phase speed; is the Bragg wave number; is the Bragg directional saturation wave number spectrum; is the integration domain;

[0133] Step S23: Substitute the orbit velocity integral expression of the Bragg intrinsic motion term into the DopRIM framework to replace the phase velocity expression, and obtain the basic equation of the WBCM.

[0134] Step S24: Explicitly obtain the Bragg ring domain and the directional spectrum parameters, give the relationship between the directional saturation spectrum and the directional displacement spectrum, and the calculation method of the friction velocity, 10 m wind speed and the drag coefficient;

[0135] Specifically, the calculation method includes the following steps:

[0136] Step S25: Determine the Bragg ring domain as:

[0137] ;

[0138] wherein, is the polar wave number of the sea surface short wave in the spectral space, i.e., the azimuth pair; is the wave number module length of the integrated hydrodynamic short wave; is the radial wave number half-bandwidth of the Bragg resonance ring; is the Bragg wave number;

[0139]

[0140] wherein, is the radar wave number, is the radar wavelength;

[0141] Step S26: Use the capillary-gravity wave directional displacement spectrum to construct the Bragg directional saturation spectrum , both of which satisfy:

[0142]

[0143] wherein is represented as:

[0144]

[0145] wherein, is the directional wave number spectrum of Bragg waves, is the friction wind speed of sea surface, is the threshold friction wind speed, is the directional spreading function of capillary waves, is the short wave dissipation factor caused by the modulation effect of large-scale long waves on small-scale short waves, is the vortex dissipation factor caused by sea surface turbulence, is the curvature spectrum of capillary waves, is the 10 m wind speed on sea surface; is the peak rise factor of the curvature spectrum of capillary waves;

[0146] Step S27: the relationship between the friction velocity and the 10 m wind speed is taken , wherein the drag coefficient formula is:

[0147]

[0148] wherein, is the drag coefficient; is the friction wind speed of sea surface;

[0149] The above relationship is used to uniformly map the observed or reanalyzed 10 m wind speed to the input required by the spectral model. .

[0150] Step S28: the Bragg tilt modulation and the hydrodynamic modulation transfer functions (MTFs) are introduced to establish the coupling expression of the geometric factors and the modulation terms on the Doppler velocity contribution, and to determine the MTFs parameter set to be calibrated;

[0151] Step S3: the model parameters are calibrated to be consistent with the actual observation by using the airborne Ka-band along-track interferometric SAR observation data, GNSS drift buoy measurement results and Copernicus wind field data.

[0152] Step S31: through the airborne Ka-band along-track interferometric SAR experiment, a plurality of groups of spatial sub-area data in the observation area are collected, and are matched in space and time with the GNSS drift buoy observation and the CMEMS wind field data; Step S32: taking the GNSS drift buoy observation flow rate as a reference, the observation value and the reference value of each sub-area are compared to obtain the wave error observation of each sub-area, and the corresponding wind field information and radar observation parameters are recorded; Step S33: the modulation transfer function parameters are calibrated by using the weighted nonlinear least square method, and the calibration results are evaluated by the root mean square error, the bias and the correlation coefficient statistical indicators, and the optimal parameter group is selected for model correction.

[0153] In step S33, the modulation transfer function parameters are calibrated by using the weighted nonlinear least square method, specifically:

[0154] Based on the airborne Ka-band ATI-SAR experiment, six sub-regions are selected within the imaging strip, which are spatially overlapped with the GNSS drifters' trajectories and strictly spatio-temporally registered with the CMEMS wind field; the radial surface velocity is retrieved from the along-track interferometric phase , the GNSS drifter measured flow velocity results are used as the benchmark to define the observed sea wave error , and the 10 m wind speed and radar line-of-sight-wind direction relative azimuth angle are recorded synchronously as input quantities;

[0155] a) Within the along-track interferometric SAR imaging region of the airborne Ka-band, several spatial sub-regions are selected which are synchronously registered with the wind field and GNSS drifters, and the radial surface flow velocity is retrieved from the interferometric phase difference , that is:

[0156] ;

[0157] wherein is the platform velocity, is the interferometric phase, is the radar wave number, is the along-track baseline length, is the radar incidence angle;

[0158] b) For each sub-region, the sea wave error observation is defined as:

[0159]

[0160] wherein is the radial surface flow velocity measured by the GNSS drifters;

[0161] c) The Bragg wave modulation term in the sea wave error correction model is introduced with a tilt and a hydrodynamic modulation transfer function, and the parameter vector is: ;

[0162] The model output for the th sub-region is:

[0163]

[0164] wherein is the angle between the radar viewing direction and the wind direction, is the 10 m wind speed on the sea surface, is the radar incidence angle, is the to-be-solved parameter;

[0165] The weighted nonlinear least squares method is used for fitting, and the objective function is:

[0166]

[0167] wherein, is the weight; is the observed sea wave error;

[0168] The parameter vector p is optimized by using Levenberg-Marquardt iterative algorithm, and the parameter update formula is:

[0169]

[0170] wherein, is the Jacobian matrix, is the residual vector, is the damping factor, is the diagonal weight matrix, is the identity matrix, is the transpose of the Jacobian matrix;

[0171] The parameters are updated by iteration: until the convergence condition is met;

[0172] d) The fitting effect of the calibrated MTFs is evaluated by RMSE, Bias, correlation coefficient (CC), and the calibrated is used as the fixed input for subsequent Luojia-2 ATI-SAR business error correction.

[0173] Step S4: Apply the calibrated sea wave error correction model to the Luojia-2 satellite along-track interferometric SAR observation data to calculate the radial surface flow velocity and sea wave error of each resolution unit;

[0174] Step S41: Apply the calibrated sea wave error correction model to the Luojia-2 satellite along-track interferometric SAR data, and perform flow velocity inversion and wind field registration on each resolution unit divided in the observation area;

[0175] Step S411: Perform standard interferometric processing on the satellite raw data, including registration, flat phase removal, interferogram generation, and division of the entire observation area into regular geographic grids, i.e., each resolution unit;

[0176] Step S412: According to the interferometric phase difference Δ , the uncorrected radial surface flow velocity of each resolution unit is preliminarily inverted by using the basic principle of along-track interferometric SAR;

[0177] Step S42: In each resolution unit, the sea wave error is calculated using the correction model, and compared with the Luojia-2 satellite observation results;

[0178] For each resolution unit:

[0179] Step S421: Extract the wind speed of the unit, the angle between the radar line-of-sight direction and the wind direction;

[0180] Step S422: Substitute the environmental parameters and radar geometric parameters of step S421 into the calibrated WBCM model to calculate the velocity deviation caused by sea wave motion at the unit, i.e., the sea wave error ;

[0181] Step S423: Subtract the error from the initial inverted flow velocity to obtain the corrected true radial surface flow velocity:

[0182]

[0183] Step S43: Format the calculation results into raster data products to obtain two core layers, respectively: the spatial distribution of the corrected radial surface flow velocity, i.e., , and the spatial distribution of the sea wave error field, i.e., .

[0184] Step S5: Use the assimilated GDP drift buoy and Copernicus current data that spatially and temporally match the satellite observation area as a reference to evaluate and verify the effectiveness of the correction model;

[0185] Step S51: In the satellite observation area, generate a reference flow field using the assimilated GDP drift buoy and Copernicus current data, and perform registration with the Loica satellite in-track interferometric SAR observation data in time and space, and interpolate to the same grid as the satellite according to the resolution unit;

[0186] Step S52: At each resolution unit, compare the sea wave error calculated by the model with the satellite observation results to calculate the root mean square error, bias, and correlation coefficient statistical indicators, and evaluate and verify the effectiveness of the sea wave error correction model.

[0187] 6) Compared with the KaDOP model, the simulated sea wave error (RMSE, Bias, correlation coefficient, etc.) under each method is counted and analyzed to quantitatively measure the performance improvement of the model. The experimental results show that the method can reduce the root mean square error by about 81%;

[0188] Step S61: Use the unit-level error sequence registered with the reference data to establish a statistical evaluation system, and the evaluation indicators include root mean square error, bias, and correlation coefficient;

[0189] Step S62: Under the condition of spatial and temporal consistency with the satellite observation area, generate unit-level sea wave error sequences using the sea wave error correction model and the KaDOP model, respectively, and compare them with the reference error for evaluation;

[0190] Step S63: Quantify the performance improvement with the root mean square error as the main indicator, and the improvement rate is defined as:

[0191]

[0192] wherein, is the root mean square error of the KaDOP model, is the root mean square error of the sea wave error correction model.

[0193] 7) Visualize the sea wave error simulation results, and quantitatively evaluate the improvement effect through in-situ observation data and KaDOP simulation results, to provide technical support for sea current remote sensing measurement products and actual application.

[0194] The sea wave error simulation results are visualized, including:

[0195] Step S71: Based on the corrected radial surface current velocity product obtained in step S4, generate a two-dimensional spatial distribution map, use color mapping to represent the flow velocity, and superimpose the coastline, contour line and scale elements;

[0196] Step S72: Based on the sea wave error field data separated in step S4, generate a sea wave error spatial distribution map, use the diverging color scheme to distinguish positive and negative error values, and label the maximum and minimum error areas;

[0197] Step S73: Based on the comparison and evaluation results of step S6, generate statistical comparison charts, including:

[0198] (1) Scatter plot of flow velocity before and after correction and reference value;

[0199] (2) Error distribution histogram of WBCM model and KaDOP model;

[0200] (3) Performance index comparison table of each model in different wind speed intervals;

[0201] Step S74: Generate a comprehensive evaluation report containing original observation data quality evaluation indicators, root mean square error, bias and correlation coefficient statistics before and after model correction, correction effect analysis under different sea conditions, and performance improvement quantitative indicators of KaDOP model;

[0202] Step S75: Integrate the spatial distribution map, statistical charts and evaluation report into a visual product, output in a standardized format, support GIS platform loading and interactive query.

[0203] This invention proposes a wave error correction model (WBCM) based on Bragg wave orbital velocity. Addressing the limitations of traditional DopRIM-like methods that equate the inherent motion of Bragg scattering with phase velocity, leading to systematic errors in Doppler power spectrum interpretation and OSC inversion, this invention rewrites the velocity term as an orbital velocity expression without altering the overall framework, ensuring consistency with long-wavelength orbital modulation. Simultaneously, MTFs are calibrated using airborne ATI-SAR observations. The model is validated using ATI-SAR data from the Luojia-2 satellite, achieving approximately 81% reduction in root mean square error compared to KaDOP, significantly improving the physical consistency and retrieval accuracy of ocean surface current velocity inversion.

[0204] Example 1:

[0205] like Figure 1 As shown in the figure, an embodiment of the present invention provides a method for correcting ocean wave errors in Luojia-2 in-orbit interferometric SAR current velocity measurement based on Bragg wave orbital velocity, comprising the following steps:

[0206] S1: Reconstruct the wave-induced error model within the DopRIM framework, rewriting the inherent motion term of the Bragg scattering surface from phase velocity to orbital velocity, forming the WBCM fundamental equations with orbital velocity as the core. This rewriting maintains the original form of the long-wave orbit modulation and geometric terms, allowing the inherent motion of the scattering surface and long-wave modulation to be handled within the same physical framework, improving the physical consistency of the model. Figure 2 Under the experimental conditions shown, the Bragg wave propagates only in a single direction; if the phase velocity is used to characterize the inherent motion of the scattering unit, the Doppler power spectrum can only show a one-sided frequency shift and cannot generate a signal. Figure 2 The positive and negative peaks exist simultaneously in the spectrum. When expressed as orbital velocity, the reciprocating motion of water particles within one wavelength generates linear velocity components toward and away from the radar, thus forming a symmetrical double-peak structure in the Doppler spectrum consistent with the observation. This is the physical basis for calculations based on orbital velocity.

[0207] The relevant expression for calculating Doppler velocity based on Bragg wave orbital motion in the model is as follows:

[0208]

[0209] in, For radar incident angle, This indicates the radar's line-of-sight orientation. In the direction of the Bragg wave; For the Bragg wave tilt and hydrodynamic modulation function, Let be the real part of the Bragg wave tilt and hydrodynamic modulation function. For the imaginary part of the Bragg wave tilt and hydrodynamic modulation function; The phase velocity of the Bragg wave; For the Bragg wave number; The Bragg wave directivity saturation wavenumber spectrum; For the integration domain;

[0210] S2: Clarify the acquisition methods of Bragg ring domain and directional spectrum parameters, give the relationship between directional saturation spectrum and directional displacement spectrum, as well as the calculation methods of friction velocity, 10 m wind speed and drag coefficient, and determine the model input and observation geometry; among which, the directional displacement spectrum refers to the standard expression of wind-generated gravity-capillary spectrum, and the friction velocity and 10 m wind speed are correlated through empirical drag coefficient;

[0211] By precisely defining the Bragg scattering wave vector annular domain parameters—that is, within a grid set satisfying the range of wave vector and azimuth angle values—the power spectrum and displacement spectrum parameters in each direction are integrated and analyzed. The specific integration interval is expressed as follows:

[0212] ;

[0213] in, The wave number of short waves over the sea surface in polar coordinates in spectral space, i.e., the azimuth pair; The integral is the hydrodynamic shortwave wavenumber modulus. The radial wavenumber half-bandwidth of the Bragg resonance ring; The Bragg wave number; This is the radar incident angle.

[0214] The relationship between the saturation spectrum and the directional displacement spectrum of capillary gravity waves is as follows: This ensures that the input spectral parameters of the model match the actual physical process.

[0215] Friction speed and The relationship between the drag coefficient and the drag coefficient is as follows: The acquisition and calculation of the above input parameters ensure that the observation geometry and environmental parameters required by the model of this invention can be directly obtained from remote sensing measurement and reanalysis products, thereby improving the engineering applicability of the model.

[0216] S3: Introduce Bragg tilt modulation and hydrodynamic modulation MTFs to determine the set of MTFs parameters to be calibrated; in this expression, the tilt MTF and hydrodynamic MTF (real / imaginary parts) act together on the Bragg wave direction saturation spectrum integral to form a weighted sum of Doppler velocities;

[0217] Within the DopRIM framework, Bragg tilt modulation and hydrodynamic modulation MTFs are introduced and coupled with the integral expression of the directional saturation spectrum to form a weighted contribution to the Doppler velocity. Specifically, the modulation term of the long-wavelength scattering surface velocity is expressed as a "tilt MTF ( ) + hydrodynamic MTF (M ) in the integral kernel, together with the incidence angle geometry factor and the radar line-of-sight-wave direction angle term, to weight the directional saturated spectrum within the Bragg domain, so as to obtain the contribution of the modulation to the Doppler velocity; wherein the integral domain is defined by the Bragg wavenumber band and the directional range, and the integral variable is the wavenumber vector In this expression, the framework structure of the existing DopRIM model is retained, and the "intrinsic motion" of the Bragg scattering unit is expressed in terms of the orbital velocity, and the remaining terms (including the coupled form of the MTFs and the geometry factor) are kept consistent to ensure physical self-consistency and compatibility. The parameter set to be expressed is .

[0218] S4: Conduct airborne Ka-band ATI-SAR experiments to obtain measured radial velocities, and register the inversion results with wind field angle information to form data sub-regions;

[0219] An airborne Ka-band ATI-SAR experiment was conducted over a certain sea area, and the system consisted of a Ka-band ATI-SAR, a data acquisition unit, and an inertial navigation system. The platform heading was nearly north, the radar line-of-sight pointed east, and the working system was VV polarization. The key parameters included a vehicle speed of about 58 m / s, a flight height of about 4018 m, a working frequency of 35.75 GHz, a along-track physical baseline of about 4.64 cm, an incidence angle of 20°-35°, and an azimuth / distance pixel interval of about 0.58 m / 0.27 m, respectively. A single scene imaging covered an area of about 1.91 km (azimuth) x 4.15 km (range). Based on the interference phase difference of two along-track complex maps, the radial surface velocity (negatively defined as moving away from the radar) was extracted and registered with the wind speed interpolated to the radar resolution and the relative azimuth angle of the "radar line-of-sight-wind direction" to ensure the consistency of the data for subsequent calibration and verification. The results of the above experiment correspond to Figure 3 , as shown in Figure 3 , which shows the radial surface velocity distribution at 10 meters above the sea surface at different wind speeds;

[0220] S5: Synchronize the deployment of GNSS drift buoys within the imaging strip and register the CMEMS wind vector to construct a sample set consistent with the SAR observation space and time in sub-regions; define the observation sea wave error as the difference between the radial surface velocity inverted by the ATI-SAR and the east-west component of the surface current velocity measured by the GNSS to provide a reference quantity for subsequent calibration;

[0221] ​The GNSS drift buoys were synchronously deployed in the onboard Ka-band ATI-SAR imaging swath to obtain the in-situ surface current velocity series along six drift paths; the GNSS trajectories were time-interpolated at the imaging time, and divided into several sub-zones (typical size of 540 m x 290 m) in the swath according to the spatial overlap. The radial surface velocities The 10 m wind speed and the radar line-of-sight-wind direction relative azimuth angle were obtained by spatio-temporal assimilation and resolution matching with the CMEMS wind field, which were used for subsequent model input and weight setting. To form a calibrated sample set consistent with the spatio-temporal observation of SAR, the east-west component of the surface current velocity recorded by the GNSS drift buoy was extracted under the geometric condition that the aircraft heading was nearly north and the radar line-of-sight pointed east as the reference quantity, and the observation wave error was defined

[0222]

[0223] The spatio-temporal calibration sample set for MTFs determination and model validation was constructed.

[0224] S6: The three coefficients of the MTFs were calibrated and the uncertainty was evaluated by using weighted nonlinear least squares combined with Levenberg-Marquardt iteration, and the optimal parameters consistent with the observation were obtained; the calibration target function was constructed by the observation uncertainty weighted residual sum of squares, and the parameter variance-covariance estimation was given after convergence;

[0225] Specifically, the input of each data sub-zone and the wave error observation were used to construct the model prediction , where the MTF parameter vector to be estimated . .

[0226] The target function weighted by the observation uncertainty was established , and the Levenberg-Marquardt iteration was used to solve:

[0227] At the kth iteration, the residual , , the Jacobian , and the weight matrix were recorded, then the parameter increment was obtained by , and the update was updated. The convergence criterion was that the relative change of the target function and were both lower than the threshold value.

[0228] After convergence, the variance-covariance matrix of the parameter estimation value was used The estimated value of the error variance Evaluate the parameter variance-covariance and uncertainty, and use evaluation metrics such as RMSE, Bias, and correlation coefficient (CC) to evaluate the calibrated results. Figure 4 As shown, this is a comparison between the WB predicted by the model after calibration and the actual WB.

[0229] S7 applies the calibrated WBCM to the Luojia-2 along-orbit ATI-SAR data, calculates the wave error cell by cell, and outputs a standardized rasterized product; it also provides the correspondence with wind speed and the relative azimuth angle of radar line of sight-wind direction.

[0230] The effectiveness of the model was verified by applying the calibrated model to the WB measured by the Luojia-2 satellite. The measured WB is the velocity retrieved from the Luojia-2 satellite minus the actual reference velocity. Figure 5 As shown, the radial surface velocity is retrieved from the Luojia-2 satellite. Figure 5 In the image, each cell represents the spatial distribution of radial surface velocity within the ATI-SAR observation area of ​​the Luojia-2 satellite, corresponding to different wind speeds and observation geometries; specifically... Figure 5 Analysis of wind direction angle ( ) and wind speed (U 10 The changing trends between () are shown in Table 1:

[0231] Table 1. Trends in the relationship between wind direction angle and wind speed at 10m above sea level

[0232] Column 1 Column 2 Column 3 Column 4 Column 5 Column 6 Column 7 Column 8 Column 9 Column 10 Row 1 φ = 163.3°; U 10 = 6.08 m / s φ = 162.7°; U 10 = 6.12 m / s φ = 162.0°; U 10 = 6.16 m / s φ = 161.4°; U 10 = 6.21 m / s φ = 160.8°; U 10 = 6.26 m / s φ = 160.3°; U 10 = 6.32 m / s φ = 159.7°; U 10 = 6.40 m / s φ = 159.0°; U 10 = 6.48 m / s φ = 158.2°; U 10 = 6.55 m / s φ = 157.3°; U 10 = 6.61 m / s Row 2 φ = 156.5°; U 10 = 6.66 m / s φ = 155.8°; U 10 = 6.71 m / s φ = 155.3°; U 10 = 6.78 m / s φ = 154.9°; U 10 = 6.84 m / s φ = 154.6°; U 10 = 6.91 m / s φ = 154.4°; U 10 = 6.97 m / s φ = 154.3°; U 10 = 7.02 m / s φ = 154.3°; U 10 = 7.06 m / s φ = 154.2°; U 10 = 7.11 m / s φ = 154.2°; U 10 = 7.15 m / s Row 3 φ = 153.9°; U 10 = 7.19 m / s φ = 153.6°; U 10 = 7.22 m / s φ = 153.2°; U 10 = 7.25 m / s φ = 152.9°; U 10 = 7.28 m / s φ = 152.7°; U 10 = 7.32 m / s φ = 152.5°; U 10 = 7.35 m / s φ = 152.3°; U 10 = 7.37 m / s φ = 152.0°; U 10 = 7.39 m / s φ = 151.7°; U 10 = 7.41 m / s φ = 151.2°; U 10 = 7.42 m / s Row 4 φ = 150.6°; U 10 = 7.41 m / s φ = 150.0°; U 10 = 7.40 m / s φ = 149.4°; U 10 = 7.40 m / s φ = 148.9°; U 10 = 7.40 m / s φ = 148.4°; U 10 = 7.38 m / s φ = 147.7°; U 10 = 7.34 m / s φ = 147.0°; U 10 = 7.29 m / s φ = 146.2°; U 10 = 7.25 m / s φ = 145.4°; U 10 = 7.20 m / s φ = 144.8°; U 10 = 7.15 m / s Row 5 φ = 144.4°; U 10 = 7.11 m / s φ = 144.1°; U 10 = 7.07 m / s φ = 143.9°; U 10 = 7.02 m / s φ = 143.7°; U 10 = 6.98 m / s φ = 143.6°; U 10 = 6.94 m / s φ = 143.6°; U 10 = 6.90 m / s φ = 143.7°; U 10 = 6.86 m / s φ = 143.8°; U 10 = 6.82 m / s φ = 143.9°; U 10 = 6.79 m / s φ = 144.2°; U 10 = 6.76 m / s

[0233] S8: Select assimilated GDP drifting buoy and CMEMS ocean current data that match the spatiotemporal matching of satellite observations as references, construct a "ground true value" product and interpolate it to the satellite resolution, and conduct pixel-level and sub-region-level consistency checks on the model simulation results;

[0234] The actual ground current velocity (GDP) was obtained from drifting buoy and CMEMS ocean current data using optimal interpolation, with spatial resolution corresponding to that of the Luojia-2 satellite. Figure 6 The location of the GDP drift buoys around the imaging area. Figure 7 This represents the actual ground velocity obtained after processing.

[0235] S9: In parallel comparison with the KaDOP baseline model, statistical calculations were performed on indicators such as RMSE, Bias, and correlation coefficient (CC) to quantify performance improvement and analyze stability under different wind speeds and orientations; the results show that WBCM is significantly better than KaDOP in agreement with actual measurements.

[0236] Specifically, Figure 8The WB predicted by the model of the application is consistent with the measured results of the LK-2 satellite, and the simulation accuracy is greatly improved relative to existing models.

[0237] S10: visualizing the comparison results and summarizing the technology to form method applicability and engineering suggestions, providing basis for business processing flow and downstream applications; in typical scenarios, RMSE is reduced by about 81% compared to KaDOP, verifying the engineering value of the method.

[0238] Embodiment 2

[0239] In combination with the steps of embodiment 1, taking the along-track interferometric SAR observation of LK-2 satellite as an example, the application and verification process of the wave error correction model (WBCM) of the application under the condition of satellite are illustrated. As shown in Figures 5-8 , the ATI-SAR imaging data of LK-2 satellite in the target sea area are selected as the object to be corrected, and the GDP drift buoy observation and CMEMS assimilated current field matched in time and space are collected to construct the reference data set for evaluation. Under the same geometric and environmental conditions, the spatial distribution characteristics of the uncorrected radial surface flow velocity and wave error are calculated first to obtain the original comparison baseline.

[0240] In the observation area of LK-2, according to the imaging coverage and data availability, a number of GDP drift buoy trajectories (see Figure 6 ) consistent in time and space with the satellite transit are selected, and they are spatially and temporally matched with the ATI-SAR pixels to form a plurality of sample paths for verification. For each SAR sub-area corresponding to each path, the satellite-inverted radial surface flow velocity field (see Figure 5 ) is extracted, and the ground true flow velocity (see Figure 7 ) corresponding to different wind speeds and observation geometries generated by the CMEMS / GDP assimilation product is combined to obtain pixel-level and sub-area-level paired samples. The unified data basis for subsequent model evaluation is provided, as shown in Table 1.

[0241] On the basis of the above data, the MTFs parameters obtained by calibration in embodiment 1 are substituted into WBCM to correct the wave error of the LK-2 ATI-SAR inversion result pixel by pixel, and the corrected radial surface flow velocity product is output. Then, taking the GDP / CMEMS reference field as the true value, the results before and after correction are compared, and the root mean square error (RMSE), average bias (Bias) and correlation coefficient (CC) and other statistical indicators are calculated, and the stability and consistency under different sea states and observation geometries are quantified according to the 10 m wind speed and the relative azimuth of radar line-of-sight and wind direction. The results are shown in Figure 8As shown: under the conditions of the whole sample and each group, WBCM shows lower RMSE and |Bias| and higher CC compared with the baseline model (KaDOP); the RMSE reduction is about 81%, indicating that the model has significant precision improvement and good engineering applicability in spaceborne applications.

[0242] Finally, the correction effect is visualized: Figure 5 The spatial distribution of the radial surface flow velocity in the observation area of LuoJia-2 is given. Figure 6 The relationship between satellite observation coverage and GDP drift buoy position is shown. Figure 7 The ground true flow velocity corresponding to different wind speeds and observation geometries is shown. Figure 8 The statistical comparison of WBCM and KaDOP under the same data and conditions is summarized. From the above verification, it can be seen that the present application can effectively suppress the influence of waves on OSC inversion, and significantly improve the precision and robustness of LuoJia-2 ATI-SAR radial flow velocity inversion.

[0243] In summary, the results of the embodiments show that the method of the present application effectively overcomes the defects of insufficient precision of traditional wave error correction, and optimizes and improves at the mechanism level. Compared with existing models, the present method can quantitatively depict the contribution of Bragg wave orbital motion to wave-induced error, significantly improve the accuracy and processing efficiency of error correction, and provide a practical technical path for suppressing the interference of sea waves on sea flow observation in actual marine environment. The method has important supporting significance for marine observation, navigation support and marine climate research, and has wide application prospect.

[0244] Those skilled in the art can understand that the above description is only preferred embodiments of the present application, and the features described in each embodiment of the present disclosure and / or the claims can be combined or combined, even if such combination or combination is not explicitly described in the present disclosure. It is not intended to limit the present application, although the present application has been described in detail with reference to the foregoing embodiments, and those skilled in the art can modify the technical solutions described in the foregoing embodiments or make equivalent replacement of part of the technical features, and any modification, equivalent replacement, improvement, etc. made within the spirit and principles of the present application shall be included in the protection scope of the present application.

[0245] While the preferred embodiments of the application have been described, additional variations and modifications can be made to these embodiments by those skilled in the art once they have the benefit of the foregoing description without departing from the spirit and scope of the application. Accordingly, it is intended that the appended claims be interpreted as including all such variations and modifications as fall within the spirit and scope of the application. It is apparent that those skilled in the art can modify and adapt the application without departing from the spirit and scope of the application. It is therefore intended that the application not be limited to the disclosed embodiments, but that it can also cover modifications and variations within the scope of the present application.

Claims

1. A SAR flow velocity correction method based on the Bragg orbital velocity, characterized in that, The method comprises the following steps: Step S1: based on wave tank experiment and theoretical analysis, a Doppler frequency shift theoretical model is established based on Bragg wave orbital velocity as physical basis, and quantitative expression and theoretical Doppler power spectrum are obtained to verify the physical correctness of the orbital velocity mechanism relative to the phase velocity mechanism; Step S2: based on the orbital velocity mechanism verified in step S1, the Bragg wave inherent motion term is replaced by the orbital velocity in the DopRIM framework, and a physically consistent sea wave error correction model is established by combining the Bragg wave scattering modulation characteristics; Step S3: the parameters of the sea wave error correction model are calibrated by using airborne Ka-band along-track interferometric SAR observation data, GNSS drift buoy measurement results and Copernicus wind field data, so that they are consistent with the actual observation; Step S4: the calibrated sea wave error correction model is applied to the along-track interferometric SAR observation data of LK-2 satellite, and the radial surface flow velocity and sea wave error of each resolution unit are calculated; Step S5: the assimilated GDP drift buoy data and Copernicus current data which are matched in space and time with the observation of LK-2 satellite are used as reference true value, and the output results of step S4 are compared to evaluate the effectiveness of the sea wave error correction model; Step S6: the sea wave error correction model is compared with the KaDOP model, the simulated sea wave errors under different methods are calculated, analyzed and statistically processed by calculating the root mean square error, bias and correlation coefficient to quantitatively measure the performance improvement of the model; Step S7: the sea wave error simulation results are visualized and displayed, and the improvement effect is quantitatively evaluated by the in-situ observation data and the KaDOP simulation results.

2. The Lugu No. 2 SAR flow velocity correction method based on Bragg orbital velocity according to claim 1, characterized in that, The step S1 comprises the following steps: S11: according to the wave tank experiment and theoretical derivation, the Bragg wave propagating in one direction is observed, and the orbital velocity is quantified to confirm that the orbital velocity is the actual physical mechanism to produce the Doppler frequency shift; S12: Analyzing the component of the Bragg wave orbital velocity in the radar line-of-sight direction i.e.: ； wherein, is the Bragg wave horizontal orbital velocity component, is the Bragg wave vertical orbital velocity component, is the Bragg wave amplitude, is the Bragg wave angular frequency, is the Bragg wave wave number, is the horizontal direction coordinate, is the time, is the radar incidence angle; S13: based on Jacobi-Anger expansion, the phase modulation radar signal under the action of orbital velocity is converted into discrete frequency spectrum, and the formula is: ； ； wherein, the discrete spectrum of the phase-modulated radar echo in the frequency domain; the amplitude weight of the nth spectral line given by the Bessel function; the phase modulation index determined by the Bragg wave line-of-sight orbital velocity amplitude and the radar parameters; the initial phase factor corresponding to the nth harmonic; the frequency domain variable representing the value point of the phase-modulated echo signal in the Doppler frequency domain; the fundamental frequency, the Bragg wave angular frequency, the Dirac δ function; According to the discrete frequency spectrum, the main peak position of the theoretical Doppler power spectrum is calculated; S14: the theoretical Doppler power spectrum is compared with the observation results of the wave tank experiment to verify the consistency of the Doppler power spectrum driven by the orbital velocity with the actual measurement results, thereby providing a theoretical basis for the sea wave error correction of interferometric SAR flow measurement.

3. The Lugu No. 2 SAR flow velocity correction method based on Bragg orbital velocity according to claim 1, characterized in that, The step S2 comprises the following steps: Step S21: in the DopRIM framework, a radial surface flow velocity expression is established, which includes surface flow, inherent motion of Bragg scatterers and long wave modulation term; Step S22: the inherent motion term of Bragg scatterers is replaced by the orbital velocity, and the tilt modulation transfer function and hydrodynamic modulation transfer function are introduced in the Bragg ring domain, and the Bragg term velocity expression is obtained by integral weighting; Step S23: based on the integral of the Bragg term orbital velocity and the modulation transfer function, a physically consistent error correction model is completed for quantitative correction of the radial surface flow velocity deviation.

4. The Lugu No. 2 SAR flow velocity correction method based on Bragg orbital velocity according to claim 3, characterized in that, The step S23 comprises the following steps: a. the contribution of Bragg wave to the radial Doppler velocity is written as a modulation weighted integral of the Bragg ring domain, that is: ； wherein, is the radar incidence angle, is the radar line-of-sight azimuth, is the Bragg wave direction; is the Bragg wave tilt and hydrodynamic modulation function, is the real part of the Bragg wave tilt and hydrodynamic modulation function, is the imaginary part of the Bragg wave tilt and hydrodynamic modulation function; is the Bragg wave phase speed; is the Bragg wave number; is the Bragg wave directional saturation wave number spectrum; is the integration domain; b. Determining the integration domain for the Bragg ring domain, i.e.: ； where, is the polar wave number of the sea surface short waves in spectral space, i.e. the azimuth pair; is the wave number modulus of the integrated hydrodynamic short waves; is the radial wave number half-bandwidth of the Bragg resonance ring; is the Bragg wave number; ； wherein is the radar wave number, is the radar wavelength; c. The relationship between the directional displacement spectrum and the saturation spectrum, i.e. the Bragg saturation spectrum and the directional displacement spectrum, satisfies: ； wherein is represented by: ； wherein, is the directional wave number spectrum of the Bragg waves, is the friction wind speed of the sea surface, is the threshold friction wind speed, is the directional spreading function of the capillary waves, is the short wave dissipation factor due to the modulation effect of the large scale long waves on the small scale short waves, is the vortex dissipation factor due to the sea surface turbulence, is the capillary wave curvature spectrum, is the wind speed at 10 meters above the sea surface; is the peak elevation factor of the capillary wave curvature spectrum; The wind stress is determined by the relationship between the friction velocity and the 10 m wind speed: ； wherein, is the drag coefficient; d. The results of the orbital velocity-based calculation are used to The Bragg wave phase velocity-based term is replaced within the DopRIM framework, i.e. the sea wave error correction model WBCM is obtained.

5. The Lugu No. 2 SAR flow velocity correction method based on Bragg orbital velocity according to claim 1, characterized in that, The step S3 comprises the following steps: Step S31: Collecting data of multiple spatial sub-regions in the observation area through the onboard Ka-band along-track interferometric SAR experiment, and performing spatial and temporal registration with the GNSS drift buoy observation and the CMEMS wind field data; Step S32: Taking the GNSS drift buoy observation flow rate as a reference, comparing the observation values and the reference values of each sub-region, obtaining the wave error observation of each sub-region, and recording the corresponding wind field information and radar observation parameters; Step S33: Calibrating the modulation transfer function parameters by using a weighted nonlinear least squares method, and evaluating the calibration results by using the root mean square error, the bias and the correlation coefficient statistical indicators, and selecting the optimal parameter group for model correction.

6. The Lugu No. 2 SAR flow velocity correction method based on Bragg orbital velocity according to claim 5, characterized in that, In step S33, the modulation transfer function parameters are calibrated by using the weighted nonlinear least squares method, and the calibration is specifically performed as follows: a) In the along-track interferometric SAR imaging area in Ka band, several spatial sub-regions are selected in synchronization with the wind field and GNSS drift buoy, and the radial surface flow velocity is inverted by using the interferometric phase difference Δφ That is: ； wherein, is the platform velocity, is the interference phase, is the radar wave number, is the along track baseline length, is the radar incidence angle; b) for each sub-area, defining a sea wave error observation is: ； wherein, is the radial surface current velocity measured for the GNSS drifters; c) Introducing the tilt and hydrodynamic modulation transfer function to the Bragg wave modulation term in the sea state error correction model, the parameter vector is: ; The model outputs for the first sub-region are: ； wherein, is the model predicted sea error for the i-th observation point, is the angle between the radar look direction and the wind direction, is the wind speed at 10 meters above sea level, is the radar incidence angle, is the parameter to be solved. Using weighted nonlinear least squares fitting, the objective function is: ； wherein, is a weight; is an observed sea error; The Levenberg-Marquardt iterative algorithm is used to optimize and solve the parameter vector p, and the parameter update formula is as follows: ； wherein, is a Jacobian matrix, is a residual vector, is a damping factor, is a diagonal weight matrix, is an identity matrix, is a Jacobian matrix transpose; The parameters are updated by iteration: until a convergence condition is met. d) The calibrated modulation transfer function parameter group is evaluated by using the root mean square error, the bias and the correlation coefficient, and the parameter uncertainty is estimated by using the residual error.

7. The Lugu No. 2 SAR flow velocity correction method based on Bragg orbital velocity according to claim 1, characterized in that, The step S4 is specifically performed as follows: Step S41: Applying the calibrated sea wave error correction model to the Luojia-2 satellite along-track interferometric SAR data to perform flow rate inversion and wind field registration on each resolution unit divided in the observation area; Step S411: Performing standardized interferometric processing on the satellite original data, including registration, flat earth phase removal, interferogram generation, and dividing the entire observation area into regular geographical grids, i.e. each resolution unit; Step S412: According to the interference phase difference Δ , using the basic principle of along-track interferometric SAR, the uncorrected radial surface flow velocity of each resolution unit is preliminarily inverted ; Step S42: In each resolution unit, the sea wave error is calculated by using the correction model, and the Luojia-2 satellite observation results are compared; For each resolution unit: Step S421: Extracting the angle between the wind speed, the radar line-of-sight direction and the wind direction of the unit; Step S422: Substitute the environmental parameters and radar geometry parameters of step S421 into the calibrated WBCM model to calculate the velocity bias caused by sea wave motion in the cell, i.e. sea wave error ; Step S423: Subtracting the error from the initial inverted flow rate to obtain the corrected true radial surface flow rate as follows: ； Step S43: Format the calculation results into raster data products, obtaining two core layers, respectively: the spatial distribution of the corrected radial surface current velocity field, i.e. ; and the spatial distribution of the sea wave error field, i.e. .

8. The Lugu No. 2 SAR flow velocity correction method based on Bragg orbital velocity according to claim 1, characterized in that, The step S5 is specifically performed as follows: Step S51: In the satellite observation area, a reference flow field is generated by assimilating the GDP drift buoy and the Copernicus current data, and is registered with the Luojia-2 along-track interferometric SAR observation data in time and space, and is interpolated to the same grid as the satellite according to the resolution unit; Step S52: In each resolution unit, the sea wave error calculated by using the model is compared with the satellite observation results, the root mean square error, the bias and the correlation coefficient statistical indicators are calculated, and the effectiveness of the sea wave error correction model is evaluated and verified.

9. The Lugu No. 2 SAR flow velocity correction method based on Bragg orbital velocity according to claim 1, characterized in that, The step S6 is specifically performed as follows: Step S61: Using the unit-level error sequence registered with the reference data to establish a statistical evaluation system, and the evaluation indicators include the root mean square error, the bias and the correlation coefficient; Step S62: Under the condition of spatial and temporal consistency with the satellite observation area, respectively generate the sea wave error sequence with the sea wave error correction model and the KaDOP model generation unit, and compare and evaluate with the reference error; Step S63: Quantify the performance improvement with the root mean square error as the main index, and the improvement rate is defined as: ； wherein, is the root mean square error of the KaDOP model, is the root mean square error of the sea wave error correction model.

10. The Lugu No. 2 SAR flow velocity correction method based on Bragg orbital velocity according to claim 1, characterized in that, In step S7, the sea wave error simulation result is visualized and displayed, specifically including: Step S71: Based on the corrected radial surface flow velocity product obtained in step S4, a two-dimensional spatial distribution map is generated, the color mapping is used to represent the flow velocity, and the coastline, contour line and scale element are superimposed; Step S72: Based on the sea wave error field data separated in step S4, a sea wave error spatial distribution map is generated, the diverging color scheme is used to distinguish the positive and negative error values, and the maximum and minimum error regions are marked; Step S73: Based on the comparison and evaluation result of step S6, a statistical comparison chart is generated, including: (1) Scatter plot of flow velocity before and after correction and reference value; (2) Error distribution histogram of WBCM model and KaDOP model; (3) Performance index comparison table of each model in different wind speed intervals; Step S74: Generate a comprehensive evaluation report including original observation data quality evaluation index, root mean square error, bias and correlation coefficient statistics table before and after model correction, correction effect analysis under different sea conditions, and performance improvement quantitative index of KaDOP model; Step S75: The spatial distribution map, statistical chart and evaluation report are integrated into a visual product, output in a standardized format, support GIS platform loading and interactive query.

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