A brahmaputra ii SAR flow velocity correction method based on bragg orbital velocity

Abstract

The present application belongs to the technical field of remote sensing measurement of ocean surface current velocity, and in particular to a Lujia-2 SAR current velocity correction method based on Bragg orbital velocity, comprising the following steps: verifying the physical correctness of the orbital velocity mechanism relative to the phase velocity mechanism; and under the DopRIM framework, establishing a physically consistent sea wave error correction model; calibrating the parameters of the sea wave error correction model; applying the calibrated sea wave error correction model to Lujia-2 satellite along-track interferometric SAR observation data to calculate the radial surface current velocity and sea wave error of each resolution unit; comparing the output results with the matched reference true value to evaluate the effectiveness of the sea wave error correction model; comparing the sea wave error correction model with the KaDOP model, respectively, to statistically analyze the simulated sea wave error under different methods; visualizing the sea wave error simulation results, and quantitatively evaluating the improvement effect through in-situ observation data and KaDOP simulation results.

Description

Technical Field

[0001] This invention belongs to the field of ocean surface current velocity remote sensing measurement technology, specifically a current velocity correction method based on the Bragg orbit velocity of the Luojia-2 SAR satellite. Background Technology

[0002] Ocean surface currents (OSCs) are crucial parameters describing ocean dynamic processes and material transport mechanisms, widely used in climate change analysis, ocean circulation research, and ecosystem modeling. Synthetic Aperture Radar (SAR), with its all-weather, high-resolution, and wide-area imaging capabilities, has become an important remote sensing tool for acquiring OSC information. However, the Doppler velocities measured by SAR, in addition to containing the actual ocean current drift component, also include non-velocity components caused by the motion of wave scattering units and their modulation by long-wavelength orbits, collectively known as wave-induced bias (WB). This bias introduces systematic errors into current velocity inversion, severely limiting the effectiveness of SAR in accurate ocean current observation.

[0003] Traditional WB correction models, represented by DopRIM and its derivatives, typically simplify the inherent motion of Bragg scattering cells to their phase velocity contribution. This modeling assumption primarily stems from early high-frequency (HF) radar observations, specifically the presence of a pair of symmetrical peaks in the Doppler power spectrum in open sea areas, interpreted as phase velocity Doppler shifts caused by forward and reverse Bragg waves propagating along the radar line of sight, respectively. However, this phase velocity-based modeling approach neglects the inherent orbital motion characteristics of the Bragg waves themselves, and its physical rationality and applicability remain controversial across a wider range of radar bands and under wind and wave conditions.

[0004] Recent wave flume experiments have provided new physical evidence for the actual role of Bragg waves in contributing to Doppler frequency shift. Experimental results show that even with only unidirectional propagating Bragg waves (without a reverse component), the measured radar power spectrum still exhibits a bimodal structure, which cannot be explained by the phase velocity mechanism. Further reconstruction of the Doppler spectrum based on the orbital velocity of the Bragg waves revealed a high degree of consistency between the predicted frequency peaks and the measured results, indicating that the orbital motion of the Bragg waves is the fundamental mechanism contributing to the radar Doppler frequency shift. This discovery provides a theoretical basis for improving the physical modeling of WB errors.

[0005] With the increasing demands for ocean observation, the shortcomings of traditional wave wave (WB) error correction models in terms of physical consistency and adaptability to complex sea conditions have become increasingly prominent. In recent years, academia and engineering communities have increasingly emphasized combining theoretical, experimental, and multi-source observational data to deepen the understanding of the relationship between wave trajectory motion and radar scattering mechanisms. How to establish a high-precision WB error correction model that accurately reflects the actual dynamic characteristics of ocean waves and adapts to different radar bands and wind and wave environments has become a key technical challenge for improving the reliability and engineering applicability of SAR ocean current inversion. Summary of the Invention

[0006] To address the issues of physical inconsistencies and insufficient accuracy in wave error correction of existing Bragg wave phase velocity models, this invention aims to provide a current velocity correction method based on Bragg orbit velocity using the Luojia-2 SAR satellite. Through wave flue experiments and theoretical analysis, the theoretical basis of Bragg wave orbit velocity as the dominant physical mechanism of Doppler frequency shift is established. Based on this, a physically consistent wave error correction model with orbit velocity as the core is constructed within the DopRIM framework. Through joint calibration and verification using airborne and spaceborne SAR observation data, this invention can significantly improve the inversion accuracy and reliability of ocean surface current velocity, providing an effective technical solution for large-scale, high-precision operational ocean current velocity remote sensing monitoring.

[0007] The technical solution adopted by this invention to achieve the above objectives is: a method for correcting the current velocity of the Luojia-2 SAR based on Bragg orbit velocity, comprising the following steps:

[0008] Step S1: Based on wave flume experiments and theoretical analysis, establish a Doppler frequency shift theoretical model with Bragg wave orbital velocity as the physical basis, and obtain its quantitative expression and theoretical Doppler power spectrum 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, under the DopRIM framework, the inherent motion term of the Bragg wave is replaced by the orbital velocity instead of the phase velocity, and a physically consistent wave error correction model is established by combining the scattering and modulation characteristics of the Bragg wave itself.

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

[0011] Step S4: Apply the calibrated wave error correction model to the in-orbit interferometric SAR observation data of Luojia-2 satellite, and calculate the radial surface velocity and wave error of each resolution cell;

[0012] Step S5: Assimilate GDP drift buoy data and Copernicus Current data that are spatially and temporally matched with observations from the Luojia-2 satellite are used as reference true values ​​and compared with the output of Step S4 to evaluate the effectiveness of the wave error correction model.

[0013] Step S6: Compare the wave error correction model with the KaDOP model, and calculate the root mean square error, bias and correlation coefficient to statistically analyze the simulated wave error under different methods, and quantitatively measure the improvement of model performance.

[0014] Step S7: Visualize the wave error simulation results and quantitatively evaluate the improvement effect using in-situ observation data and KaDOP simulation results.

[0015] Step S1 includes the following steps:

[0016] S11: Based on wave flume experiments and theoretical derivation, observe unidirectional propagating Bragg waves and quantify their orbital velocity to confirm that orbital velocity is the actual physical mechanism that generates Doppler frequency shift.

[0017] S12: Analyze the components of the Bragg wave trajectory velocity in the radar line-of-sight direction. ,Right now:

[0018] ;

[0019] in, For the horizontal orbital velocity component of the Bragg wave, For the vertical orbital velocity component of the Bragg wave, For the amplitude of the Bragg wave, Bragg wave angular frequency, For the Bragg wave number, The coordinates are in the horizontal direction. For time, The radar incident angle;

[0020] S13: Based on the Jacobi–Anger expansion, the phase-modulated radar signal dominated by orbital velocity is converted into a discrete spectrum, as shown in the formula:

[0021]

[0022] ;

[0023] in, Discrete spectrum of phase-modulated radar echo in the frequency domain; Give the amplitude weight of the nth spectral line to the Bessel function; The phase modulation index is determined by the amplitude of the Bragg wave trajectory velocity in the line-of-sight direction and radar parameters. This is the initial phase factor corresponding to the nth harmonic; For frequency domain variables, representing the value points of the phase-modulated echo signal in the Doppler frequency domain; For the fundamental frequency, For the Bragg wave angular frequency, It is the Dirac delta function;

[0024] Calculate the position of the main peak of the theoretical Doppler power spectrum based on the discrete spectrum;

[0025] S14: Compare the theoretical Doppler power spectrum with the experimental observation results of the wave flume to verify the consistency between the Doppler power spectrum driven by the orbital velocity and the measured results, and provide a theoretical basis for the wave error correction of interferometric SAR current measurement.

[0026] Step S2 specifically includes:

[0027] Step S21: Within the DopRIM framework, establish an expression for the radial surface velocity that includes surface flow, the inherent motion of the Bragg scatterer, and long-wavelength modulation terms;

[0028] Step S22: Replace the inherent motion term of the Bragg scatterer with the orbital velocity expression, and introduce the tilt modulation transfer function and the hydrodynamic modulation transfer function in the Bragg ring domain, and obtain the Bragg term velocity expression by integral weighting;

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

[0030] Step S23 specifically includes:

[0031] a. The contribution of the Bragg wave to the radial Doppler velocity can be expressed as a modulation-weighted integral over the Bragg ring domain, i.e.:

[0032]

[0033] in, The 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;

[0034] b. Determine the integration domain The Prague Ring, that is:

[0035] ;

[0036] 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;

[0037]

[0038] in, Radar wave number, 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] in Represented as:

[0042]

[0043] in, The directional wavenumber spectrum of the Bragg wave, The frictional wind speed over the sea surface. For threshold friction wind speed, Let be the directional spread function of the capillary wave. The shortwave dissipation factor is the result of the modulation effect of large-scale long waves on small-scale short waves. The eddy dissipation factor caused by sea surface turbulence. For capillary wave curvature spectrum, The wind speed is 10 meters above the sea surface. The peak elevation factor of the capillary curvature spectrum;

[0044] Wind stress was determined using the relationship between friction velocity and 10 m wind speed.

[0045] ;

[0046] in, This is the drag coefficient;

[0047] d. Calculation results based on orbital velocity By replacing the Bragg wave phase velocity calculation term within the DopRIM framework, the wave error correction model WBCM is obtained.

[0048] Step S3 includes the following steps:

[0049] Step S31: Through an airborne Ka-band along-track interferometric SAR experiment, collect data from multiple spatial sub-regions within the observation area and register them spatially and temporally with GNSS drifting buoy observations and CMEMS wind field data; Step S32: Using the current velocity observed by the GNSS drifting buoy as a reference, compare the observed values ​​of each sub-region with the reference values ​​to obtain the wave error observations for each sub-region, and record the corresponding wind field information and radar observation parameters; Step S33: The modulation transfer function parameters are calibrated using the weighted nonlinear least squares method, and the calibration results are evaluated using statistical indicators such as root mean square error, deviation, and correlation coefficient. The optimal parameter set is then selected for model calibration.

[0050] In step S33, the calibration of the modulation transfer function parameters using the weighted nonlinear least squares method specifically involves:

[0051] a) Within the airborne Ka-band along-track interferometric SAR imaging area, select several spatial sub-regions that are synchronously registered with the wind field and GNSS drifting buoys, and invert the radial surface velocity using the interferometric phase difference Δφ. ,Right now:

[0052] ;

[0053] in, For platform speed, For interference phase, Radar wave number, The length of the baseline along the track. The radar incident angle;

[0054] b) Define wave error observations for each sub-region. for:

[0055]

[0056] in, Radial surface velocity measured by a GNSS drifting buoy;

[0057] c) Introduce tilt and hydrodynamic modulation transfer functions into the Bragg wave modulation term in the wave error correction model, with the parameter vector as follows: ;

[0058] Model output for the first The sub-regions are:

[0059]

[0060] in, The wave error predicted by the model for the i-th observation point. The angle between the radar line of sight and the wind direction. The wind speed is at a depth of 10 meters above the sea surface. The radar incident angle, The parameter to be determined;

[0061] Weighted nonlinear least squares fitting is used, and the objective function is... for:

[0062]

[0063] in, As weight; To observe the error of ocean waves;

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

[0065]

[0066] in, For Jacobian matrices, For the residual vector, The damping factor, It is a diagonal weight matrix. As a unit array, This is the transpose of the Jacobian matrix;

[0067] Update parameters iteratively: Continue until the convergence condition is met;

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

[0069] Step S4 specifically includes:

[0070] Step S41: Apply the calibrated wave error correction model to the in-orbit interferometric SAR data of Luojia-2 satellite, and perform current velocity inversion and wind field registration for each resolution unit of the observation area.

[0071] Step S411: Perform standardized interferometric processing on the raw satellite data, including registration, removal of flat phase, interferogram generation, and dividing the entire observation area into regular geographic grids, i.e., resolution units;

[0072] Step S412: Based on the interference phase difference Δ Using the basic principles of in-orbit interferometric SAR, the uncorrected radial surface velocity of each resolution cell was initially inverted. ;

[0073] Step S42: Calculate the wave error using the correction model for each resolution unit and compare it with the observation results from the Luojia-2 satellite;

[0074] For each resolvable unit:

[0075] Step S421: Extract the wind speed and the angle between the radar line of sight and the wind direction for this unit;

[0076] Step S422: Substitute the environmental parameters and radar geometric parameters from step S421 into the calibrated WBCM model to calculate the velocity deviation caused by wave motion in this element, i.e., the wave error. ;

[0077] Step S423: Subtract the error from the initially inverted flow velocity to obtain the corrected true radial surface flow velocity:

[0078]

[0079] Step S43: Format the calculation results as a raster data product to obtain two core layers: the corrected radial surface velocity field, i.e. Spatial distribution; wave error field, i.e. Spatial distribution.

[0080] Step S5 specifically includes:

[0081] Step S51: Within the satellite observation area, a reference flow field is generated using assimilated GDP drift buoy and Copernicus Current data, and registered in time and space with the Luojia-2 in-orbit interferometric SAR observation data, and interpolated to a grid consistent with the satellite according to the resolution unit.

[0082] Step S52: On each resolution unit, compare the wave error calculated by the model with the satellite observation results, calculate the root mean square error, deviation and correlation coefficient statistical indicators, and evaluate and verify the effectiveness of the wave error correction model.

[0083] Step S6 specifically includes:

[0084] Step S61: Using the unit-level error sequence registered with the reference data, establish a statistical evaluation system, wherein the evaluation indicators include root mean square error, bias and correlation coefficient;

[0085] Step S62: Under the condition of consistency with the space and time of the satellite observation area, generate unit-level wave error sequences using the wave error correction model and the KaDOP model respectively, and compare and evaluate them with the reference error;

[0086] Step S63: Quantify the performance improvement, specifically the improvement rate, using root mean square error as the primary indicator. Defined as:

[0087]

[0088] in, denoted as the root mean square error of the KaDOP model. This represents the root mean square error of the wave error correction model.

[0089] In step S7, visualizing the wave error simulation results specifically includes:

[0090] Step S71: Based on the corrected radial surface velocity product obtained in step S4, generate a two-dimensional spatial distribution map, use color mapping to represent the velocity magnitude, and overlay coastline, contour lines and scale elements.

[0091] Step S72: Based on the wave error field data separated in step S4, generate a wave error spatial distribution map, use a diverging color scheme to distinguish positive and negative error values, and mark the maximum and minimum error areas;

[0092] Step S73: Based on the comparative evaluation results of step S6, generate statistical comparison charts, including:

[0093] (1) Scatter plot of flow velocity before and after correction versus reference value;

[0094] (2) Error distribution histograms of the WBCM model and the KaDOP model;

[0095] (3) Comparison table of performance indicators of each model in different wind speed ranges;

[0096] Step S74: Generate a comprehensive evaluation report that includes raw observation data quality assessment indicators, root mean square error, bias and correlation coefficient statistics before and after model correction, correction effect analysis under different sea state conditions, and quantitative indicators of performance improvement of the KaDOP model.

[0097] Step S75: Integrate the spatial distribution map, statistical charts, and evaluation report into a visualization product, output it in a standardized format, and support loading and interactive querying on the GIS platform.

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

[0099] 1. The wave error correction method proposed in this invention is based on the principle of physical consistency. By replacing the velocity term of the Bragg scattering unit with the orbital velocity, the model becomes more rigorous in theory and effectively addresses the problem of inconsistent physical assumptions in traditional methods.

[0100] 2. This invention utilizes Doppler spectrum reconstruction from wave flume experiments to reconstruct experimental evidence, clarifying the dominant role of Bragg wave orbital motion in SAR observations, and effectively enhancing the scientific validity and credibility of the model.

[0101] 3. This invention assimilates airborne Ka-band ATI-SAR measured data with multi-source data such as GNSS drifting buoys and Copernicus wind field, and uses the weighted nonlinear least squares method to accurately calibrate MTFs parameters, thereby improving the model's adaptability to the actual marine environment.

[0102] 4. The deviation correction model of the present invention can be directly applied to ATI-SAR observation data from satellites such as Luojia-2, realizing automatic error correction of large-scale, high-resolution ocean surface current velocity products, and has good engineering application value.

[0103] 5. Based on experimental and measured data, the model of this invention can achieve an average RMSE reduction of approximately 81% compared to the existing KaDOP method under typical observation conditions, and significantly improve performance indicators such as bias and correlation coefficient, thereby significantly enhancing the overall accuracy and reliability of ocean current inversion.

[0104] 6. This invention can accurately characterize the variation law of wave error with environmental parameters such as wind speed and observation azimuth, and has stronger generalization ability and robustness, making it suitable for various complex sea conditions and different observation geometry conditions.

[0105] 7. This invention supports visual analysis and pixel-level comparison verification of the output results, which facilitates the quantitative evaluation of the model correction effect and business promotion in practical applications. Attached Figure Description

[0106] Figure 1 This is a flowchart of a wave error correction method for measuring current velocity using Luojia-2 along-orbit interferometric SAR based on Bragg wave orbital velocity, provided by an embodiment of the present invention.

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

[0108] Figure 3These are spatial distribution maps of radial surface velocity obtained by airborne inversion along the observation path of a GNSS drifting buoy within the experimental area provided in this embodiment of the invention; wherein, (a) is the spatial distribution map of radial surface velocity at a wind speed of 5.98 m / s at 10 meters above the sea surface; (b) is the spatial distribution map of radial surface velocity at a wind speed of 6.05 m / s at 10 meters above the sea surface; (c) is the spatial distribution map of radial surface velocity at a wind speed of 6.12 m / s at 10 meters above the sea surface; (d) is the spatial distribution map of radial surface velocity at a wind speed of 6.19 m / s at 10 meters above the sea surface; (e) is the spatial distribution map of radial surface velocity at a wind speed of 6.27 m / s at 10 meters above the sea surface; and (f) is the spatial distribution map of radial surface velocity at a wind speed of 6.34 m / s at 10 meters above the sea surface.

[0109] Figure 4 This is a statistical chart comparing the simulated wave error results after WBCM model calibration with the measured reference values ​​provided in this embodiment of the invention.

[0110] Figure 5 This is a spatial distribution map of radial surface flow velocity corresponding to different wind speeds and observation geometries within the ATI-SAR observation area of ​​the Luojia-2 satellite provided in this embodiment of the invention;

[0111] Figure 6 This is a spatial distribution map of the observation area of ​​Luojia-2 and the actual measurement points of the GDP drifting buoy provided in the embodiments of the present invention;

[0112] Figure 7 This is a ground velocity map corresponding to different wind speeds and observation geometries, obtained by inverting CMEMS and GDP assimilation data according to an embodiment of the present invention.

[0113] Figure 8 This is a statistical chart comparing the simulation results of wave error and the measured data of the WBCM and KaDOP models provided in this embodiment of the invention under the conditions of the Luojia-2 satellite. Detailed Implementation

[0114] The present invention will now be described in further detail with reference to the accompanying drawings and embodiments.

[0115] OSC remote sensing measurements based on synthetic aperture radar (SAR) play a crucial role in global ocean dynamics and climate system research. However, due to wave-induced bias (WB) errors in observations, the accuracy of Doppler velocity inversion struggles to meet high-standard application requirements. Traditional WB correction models (such as DopRIM) generally assume that the inherent motion of Bragg wave scattering units is determined by their phase velocity. This theory is based on the bimodal structure of the Doppler power spectrum observed by high-frequency radar, but fails to consider the contribution of Bragg wave orbital motion. Recent wave flume observation experiments have shown that phase velocity alone cannot explain the positive and negative peak phenomena in the radar power spectrum; orbital motion is the dominant mechanism of Doppler frequency shift. Therefore, this invention proposes replacing phase velocity with Bragg wave orbital velocity, maintaining consistency with the long-wave modulation term in the modeling approach, and calibrating the modulation transfer function (MTF) using airborne ATI-SAR measured data. Experimental 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 velocity inversion.

[0116] like Figure 1 The diagram shows a flowchart of a wave error correction method for current velocity measurement using Luojia-2 along-orbit interferometric SAR based on Bragg wave orbital velocity, provided by an embodiment of the present invention. The wave error correction method for current velocity measurement using Luojia-2 along-orbit interferometric SAR based on Bragg wave orbital velocity of the present invention includes the following steps:

[0117] Step S1: Through wave tank experiments and theoretical analysis, it was clarified that the Bragg wave trajectory velocity is the physical mechanism that generates Doppler frequency shift, providing a physical basis for wave error correction;

[0118] Step S11: Based on wave tank experiments and theoretical derivation, observe the unidirectional propagating Bragg wave and quantify its orbital velocity to clarify that orbital velocity is the actual physical mechanism that generates Doppler frequency shift.

[0119] S12: Analyze the components of the Bragg wave trajectory velocity in the radar line-of-sight direction. ,Right now:

[0120] ;

[0121] in, For the horizontal orbital velocity component of the Bragg wave, For the vertical orbital velocity component of the Bragg wave, For the amplitude of the Bragg wave, Bragg wave angular frequency, For the Bragg wave number, The coordinates are in the horizontal direction. For time, The radar incident angle;

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

[0123]

[0124] in, Discrete spectrum of phase-modulated radar echo in the frequency domain; Give the amplitude weight of the nth spectral line to the Bessel function; The phase modulation index is determined by the amplitude of the Bragg wave trajectory velocity in the line-of-sight direction and radar parameters. This is the initial phase factor corresponding to the nth harmonic; For frequency domain variables, representing the value points of the phase-modulated echo signal in the Doppler frequency domain; For the fundamental frequency, For the Bragg wave angular frequency, It is the Dirac delta function;

[0125] Calculate the position of the main peak of the theoretical Doppler power spectrum based on the discrete spectrum;

[0126] Step S14: Comparing the above theoretical results with experimental observations, it was found that the Doppler power spectrum driven by orbital velocity is highly consistent with the actual wave flume observation results, which verifies the physical correctness of the method and provides a theoretical basis for subsequent error correction of interferometric SAR current measurement waves.

[0127] Step S2: Under the DopRIM framework, the inherent motion term of the Bragg wave is replaced by the orbital velocity, and a physically consistent wave error correction model is established by combining the scattering and modulation characteristics of the Bragg wave itself.

[0128] Specifically, establishing a physically consistent wave error correction model includes the following steps:

[0129] Step S21: Based on the DopRIM framework, give the decomposition expression of the radial surface velocity, and clarify that only the intrinsic motion terms of the Bragg scattering unit are replaced;

[0130] Step S22: Change the intrinsic motion of the Bragg scattering unit from the phase velocity description to the orbital velocity-induced Doppler velocity description to obtain the intrinsic motion contribution of the Bragg scattering unit:

[0131]

[0132] in, The 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;

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

[0134] Step S24: Clarify the methods for obtaining the Bragg ring domain and directional spectrum parameters, and give the relationship between the directional saturation spectrum and the directional displacement spectrum, the calculation methods for friction velocity, 10 m wind speed and drag coefficient;

[0135] Specifically, the calculation method is defined, including the following steps:

[0136] Step S25: Determine the Bragg ring region as follows:

[0137] ;

[0138] 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;

[0139]

[0140] in, Radar wave number, The radar wavelength;

[0141] Step S26: Employ the capillary-gravity wave directional displacement spectrum Constructing the Bragg directional saturation spectrum Both conditions are met:

[0142]

[0143] in Represented as:

[0144]

[0145] in, The directional wavenumber spectrum of the Bragg wave, The frictional wind speed over the sea surface. For threshold friction wind speed, Let be the directional spread function of the capillary wave. The shortwave dissipation factor is the result of the modulation effect of large-scale long waves on small-scale short waves. The eddy dissipation factor caused by sea surface turbulence. For capillary wave curvature spectrum, The wind speed is 10 meters above the sea surface. The peak elevation factor of the capillary curvature spectrum;

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

[0147]

[0148] in, This is the drag coefficient; The wind speed due to friction with the sea surface;

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

[0150] Step S28: Introduce Bragg tilt modulation and hydrodynamic modulation transfer functions (MTFs), establish a coupled expression of the contribution of geometric factors and modulation terms to Doppler velocity, and determine the set of MTFs parameters to be calibrated;

[0151] Step S3: Using airborne Ka-band along-track interferometric SAR observation data, GNSS drifting buoy measurement results, and Copernicus wind field data, calibrate the given model parameters to make them consistent with actual observations;

[0152] Step S31: Through an airborne Ka-band along-track interferometric SAR experiment, collect data from multiple spatial sub-regions within the observation area and register them spatially and temporally with GNSS drifting buoy observations and CMEMS wind field data; Step S32: Using the current velocity observed by the GNSS drifting buoy as a reference, compare the observed values ​​of each sub-region with the reference values ​​to obtain the wave error observations for each sub-region, and record the corresponding wind field information and radar observation parameters; Step S33: The modulation transfer function parameters are calibrated using the weighted nonlinear least squares method, and the calibration results are evaluated using statistical indicators such as root mean square error, deviation, and correlation coefficient. The optimal parameter set is then selected for model calibration.

[0153] In step S33, the calibration of the modulation transfer function parameters using the weighted nonlinear least squares method specifically involves:

[0154] Based on airborne Ka-band ATI-SAR experiments, six sub-regions were selected within the imaging strip that spatially overlap with the GNSS drifting buoy trajectory and are strictly spatiotemporally registered with the CMEMS wind field; radial surface velocity was retrieved from the track-side interferometric phase inversion. Results of GNSS buoy measurement of current velocity Define the observed wave error as a benchmark Simultaneously record input quantities such as 10 m wind speed and radar line-of-sight relative azimuth angle;

[0155] a) Within the airborne Ka-band along-track interferometric SAR imaging area, select several spatial sub-regions that are synchronously registered with the wind field and GNSS drifting buoys, and invert the radial surface velocity using the interferometric phase difference Δφ. ,Right now:

[0156] ;

[0157] in, For platform speed, For interference phase, Radar wave number, The length of the baseline along the track. The radar incident angle;

[0158] b) Define wave error observations for each sub-region. for:

[0159]

[0160] in, Radial surface velocity measured by a GNSS drifting buoy;

[0161] c) Introduce tilt and hydrodynamic modulation transfer functions into the Bragg wave modulation term in the wave error correction model, with the parameter vector as follows: ;

[0162] Model output for the first The sub-regions are:

[0163]

[0164] in, The angle between the radar line of sight and the wind direction. The wind speed is at a depth of 10 meters above the sea surface. The radar incident angle, The parameter to be determined;

[0165] Weighted nonlinear least squares fitting is used, and the objective function is... for:

[0166]

[0167] in, As weight; To observe the error of ocean waves;

[0168] The Levenberg-Marquardt iterative algorithm is used to optimize the parameter vector p, and the parameter update formula is as follows:

[0169]

[0170] in, For Jacobian matrices, For the residual vector, The damping factor, It is a diagonal weight matrix. As a unit array, This is the transpose of the Jacobian matrix;

[0171] Update parameters iteratively: Continue until the convergence condition is met;

[0172] d) Evaluate the fit of the calibrated MTFs using RMSE, Bias, and correlation coefficient (CC). This serves as a fixed input for subsequent operational error correction of the Luojia-2 ATI-SAR satellite.

[0173] Step S4: Apply the calibrated wave error correction model to the in-orbit interferometric SAR observation data of Luojia-2 satellite, and calculate the radial surface velocity and wave error of each resolution cell;

[0174] Step S41: Apply the calibrated wave error correction model to the in-orbit interferometric SAR data of Luojia-2 satellite, and perform current velocity inversion and wind field registration for each resolution unit of the observation area.

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

[0176] Step S412: Based on the interference phase difference Δ Using the basic principles of in-orbit interferometric SAR, the uncorrected radial surface velocity of each resolution cell was initially inverted. ;

[0177] Step S42: Calculate the wave error using the correction model for each resolution unit and compare it with the observation results from the Luojia-2 satellite;

[0178] For each resolvable unit:

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

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

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

[0182]

[0183] Step S43: Format the calculation results as a raster data product to obtain two core layers: the corrected radial surface velocity field, i.e. Spatial distribution; wave error field, i.e. Spatial distribution.

[0184] Step S5: Using assimilated GDP drift buoy and Copernicus Current data that are spatially and temporally matched to the satellite observation area as a reference, evaluate and verify the effectiveness of the calibration model;

[0185] Step S51: Within the satellite observation area, a reference flow field is generated using assimilated GDP drift buoy and Copernicus Current data, and registered in time and space with the Luojia-2 in-orbit interferometric SAR observation data, and interpolated to a grid consistent with the satellite according to the resolution unit.

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

[0187] 6) By comparing the KaDOP model, the simulated wave errors (RMSE, Bias, correlation coefficient, etc.) under each method were statistically analyzed to quantitatively measure the improvement in model performance. Experimental results show that this method can reduce the root mean square error by about 81%.

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

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

[0190] Step S63: Quantify the performance improvement using root mean square error as the main indicator. The improvement rate is defined as:

[0191]

[0192] in, denoted as the root mean square error of the KaDOP model. This represents the root mean square error of the wave error correction model.

[0193] 7) Visualize the simulation results of ocean wave errors and quantitatively evaluate the improvement effect through in-situ observation data and KaDOP simulation results, providing technical support for ocean current remote sensing measurement products and practical applications.

[0194] The simulation results of ocean wave errors are visualized, including:

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

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

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

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

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

[0200] (3) Comparison table of performance indicators of each model in different wind speed ranges;

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

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

[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, The 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 ( The signal enters the integral kernel in the manner described above, and, together with the incident angle geometry factor and the radar line-of-sight-wave direction angle term, performs a weighted integral on the directional saturation spectrum within the Bragg ring domain, thereby obtaining the contribution of modulation to the Doppler velocity; where the integral domain... Defined by the Bragg wavenumber band and directional range, the integration variable is the wavenumber vector. In this expression, the existing DopRIM model framework is retained, the "inherent motion" of the Bragg scattering unit is described by orbital velocity, and the remaining terms (including the coupling form of MTFs and geometric factors) remain consistent to ensure physical consistency and implementation compatibility. The parameter set to be expressed is... .

[0218] S4: Conduct an airborne Ka-band ATI-SAR experiment to obtain the measured radial velocity, and register the inversion results with the wind field angle information to form a data sub-region;

[0219] An airborne Ka-band ATI-SAR experiment was conducted over a certain sea area. The system consisted of a Ka-band ATI-SAR system, a data acquisition unit, and an inertial navigation system. The platform was oriented near due north, with the radar line of sight pointing east, and operated in VV polarization mode. Key parameters included: aircraft speed approximately 58 m / s, flight altitude approximately 4018 m, operating frequency 35.75 GHz, physical baseline along the track approximately 4.64 cm, incident angle 20°–35°, azimuth / range pixel spacing approximately 0.58 m / 0.27 m, and single-scene imaging coverage approximately 1.91 km (azimuth) × 4.15 km (range). Radial surface velocity was extracted based on the interferometric phase difference of two along-track composite images. (Avoiding the distance from the radar is defined as negative), and the wind speed interpolated to radar resolution from the assimilated wind field is pixel-by-pixel registered with the relative azimuth angle of "radar line of sight - wind direction" to ensure data consistency for subsequent calibration and verification. The above experimental results correspond to... Figure 3 As shown, Figure 3 The diagram shows the radial surface velocity distribution at a depth of 10 meters above the sea surface under different wind speeds.

[0220] S5: Simultaneously deploy GNSS drifting buoys within the imaging strip and register them with CMEMS wind vectors. Construct a sample set consistent with the SAR observation time and space according to sub-regions. Define the observation wave error by the difference between the radial surface velocity retrieved by ATI-SAR and the east-west component of the surface current velocity measured by GNSS, providing a reference for subsequent calibration.

[0221] In this embodiment, GNSS drifting buoys are simultaneously deployed within an airborne Ka-band ATI-SAR imaging strip to acquire measured surface velocity sequences along six drift paths. The GNSS trajectories are time-interpolated based on the imaging time, and the strip is divided into several sub-regions (typically approximately 540 m × 290 m) based on spatial overlap. The radial surface velocities within each sub-region are then inverted from the interferometric phase of two along-track composite images. Spatiotemporal assimilation and resolution matching with the CMEMS wind field were performed to obtain the 10m wind speed and the relative azimuth angle between the radar line of sight and the wind direction, which were used for subsequent model input and weight setting. To form a calibration sample set consistent with SAR observations in both time and space, under the geometric conditions of the aircraft heading near due north and the radar line of sight pointing east, the east-west component of the surface current velocity recorded by the GNSS drifting buoy was extracted. As a reference value, and to define the observed wave error

[0222]

[0223] Construct a spatiotemporal registration sample set for MTFs definition and model validation.

[0224] S6: Weighted nonlinear least squares combined with Levenberg-Marquardt iteration is used to calibrate and evaluate the uncertainty of the three coefficients of the MTFs to obtain the optimal parameters consistent with the observations; the calibration objective function is constructed by weighted sum of squared residuals of observation uncertainty, and the parameter variance-covariance estimate is given after convergence;

[0225] Specifically, for each data sub-region Input Error Observation of Ocean Waves Constructing Model Prediction Among them, the MTF parameter vector to be estimated .

[0226] Establish an objective function weighted by observation uncertainty. The Levenberg-Marquardt iterative solution was used.

[0227] In the k-th iteration, record the residual. , Jacobi weight matrix Then the parameter increment Depend on Request, update The relative change of the objective function and At the same time, being below the threshold is used as a convergence criterion.

[0228] After convergence, the variance-covariance matrix of the parameter estimates is 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 Analyzing the 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 the sea surface

[0232] Column 1 Column 2 Column 3 Column 4 Column 5 Column 6 Column 7 Column 8 Column 9 Column 10 Line 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 <![CDATA[φ = 160.8°;U 10 = 6.26 m / s]]> <![CDATA[φ = 160.3°;U 10 = 6.32 m / s]]> <![CDATA[φ = 159.7°;U 10 = 6.40 m / s]]> <![CDATA[φ = 159.0°;U 10 = 6.48 m / s]]> <![CDATA[φ = 158.2°;U 10 = 6.55 m / s]]> <![CDATA[φ = 157.3°;U 10 = 6.61 m / s]]> Line 2 <![CDATA[φ = 156.5°;U 10 = 6.66 m / s]]> <![CDATA[φ = 155.8°;U 10 = 6.71 m / s]]> <![CDATA[φ = 155.3°;U 10 = 6.78 m / s]]> <![CDATA[φ = 154.9°;U 10 = 6.84 m / s]]> <![CDATA[φ = 154.6°;U 10 = 6.91 m / s]]> <![CDATA[φ = 154.4°;U 10 = 6.97 m / s]]> <![CDATA[φ = 154.3°;U 10 = 7.02 m / s]]> <![CDATA[φ = 154.3°;U 10 = 7.06 m / s]]> <![CDATA[φ = 154.2°;U 10 = 7.11 m / s]]> <![CDATA[φ = 154.2°;U 10 = 7.15 m / s]]> Line 3 <![CDATA[φ = 153.9°;U 10 = 7.19 m / s]]> <![CDATA[φ = 153.6°;U 10 = 7.22 m / s]]> <![CDATA[φ = 153.2°;U 10 = 7.25 m / s]]> <![CDATA[φ = 152.9°;U 10 = 7.28 m / s]]> <![CDATA[φ = 152.7°;U 10 = 7.32 m / s]]> <![CDATA[φ = 152.5°;U 10 = 7.35 m / s]]> <![CDATA[φ = 152.3°;U 10 = 7.37 m / s]]> <![CDATA[φ = 152.0°;U 10 = 7.39 m / s]]> <![CDATA[φ = 151.7°;U 10 = 7.41 m / s]]> <![CDATA[φ = 151.2°;U 10 = 7.42 m / s]]> Line 4 <![CDATA[φ = 150.6°;U 10 = 7.41 m / s]]> <![CDATA[φ = 150.0°;U 10 = 7.40 m / s]]> <![CDATA[φ = 149.4°;U 10 = 7.40 m / s]]> <![CDATA[φ = 148.9°;U 10 = 7.40 m / s]]> <![CDATA[φ = 148.4°;U 10 = 7.38 m / s]]> <![CDATA[φ = 147.7°;U 10 = 7.34 m / s]]> <![CDATA[φ = 147.0°;U 10 = 7.29 m / s]]> <![CDATA[φ = 146.2°;U 10 = 7.25 m / s]]> <![CDATA[φ = 145.4°;U 10 = 7.20 m / s]]> <![CDATA[φ = 144.8°;U 10 = 7.15 m / s]]> Line 5 <![CDATA[φ = 144.4°;U 10 = 7.11 m / s]]> <![CDATA[φ = 144.1°;U 10 = 7.07 m / s]]> <![CDATA[φ = 143.9°;U 10 = 7.02 m / s]]> <![CDATA[φ = 143.7°;U 10 = 6.98 m / s]]> <![CDATA[φ = 143.6°;U 10 = 6.94 m / s]]> <![CDATA[φ = 143.6°;U 10 = 6.90 m / s]]> <![CDATA[φ = 143.7°;U 10 = 6.86 m / s]]> <![CDATA[φ = 143.8°;U 10 = 6.82 m / s]]> <![CDATA[φ = 143.9°;U 10 = 6.79 m / s]]> <![CDATA[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 8 The results show that the WB predicted by the model described in this invention is consistent with the actual measurement results of the Luojia-2 satellite, and the simulation accuracy is significantly improved compared with the existing model.

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

[0238] Example 2:

[0239] Following the steps of Example 1, and taking the in-orbit interferometric SAR observations of the Luojia-2 satellite as an example, this paper illustrates the application and verification process of the Wave Error Correction Model (WBCM) of this invention under spaceborne conditions. Figures 5-8 As shown, ATI-SAR imaging data from Luojia-2 in the target sea area was selected as the object to be corrected. Simultaneously, GDP drifting buoy observations and CMEMS assimilated ocean current fields, matched to the orbit's spatiotemporal conditions, were collected to construct a reference dataset for evaluation. Under the same geometric and environmental conditions, the spatial distribution characteristics of uncorrected radial surface velocity and wave error were first calculated to obtain the original contrast baseline.

[0240] Within the observation area of ​​Luojia-2, based on imaging coverage and data availability, several GDP drift buoy trajectories consistent with the satellite's transit time and space were selected (see...). Figure 6 The sample paths were then spatially and temporally registered with ATI-SAR pixels to form multiple sample paths for validation. For each path's corresponding SAR sub-region, the radial surface velocity field retrieved from the satellite was extracted. Figure 5 ), and combined with the CMEMS / GDP assimilation products to generate the actual ground flow velocity corresponding to different wind speeds and observation geometries ( Figure 7 We obtain paired samples at the pixel and sub-region levels, as shown in Table 1, to provide a unified data foundation for subsequent model evaluation.

[0241] Based on the above data, the MTFs parameters obtained from the calibration in Example 1 were substituted into the WBCM to perform wave error correction on a pixel-by-pixel basis on the Luojia-2 ATI-SAR inversion results, outputting the corrected radial surface velocity product. Subsequently, using the GDP / CMEMS reference field as the true value, the results before and after correction were compared, and statistical indicators such as root mean square error (RMSE), mean bias, and correlation coefficient (CC) were calculated. The results were then grouped and evaluated according to the relative azimuth of 10 m wind speed and radar line-of-sight-wind direction to quantify the stability and consistency under different sea states and observation geometries. The results are as follows: Figure 8 As shown, under the overall sample and various group conditions, WBCM shows lower RMSE and |Bias|, and higher CC compared to the baseline model (KaDOP); the RMSE reduction is approximately 81%, indicating that the model of this invention has significant accuracy improvement and good engineering applicability in spaceborne applications.

[0242] Finally, the correction results are visualized: Figure 5 The spatial distribution of radial surface velocity within the observation area of ​​Luojia-2 is given; Figure 6 This demonstrates the relationship between satellite observation coverage and the location of GDP drifting buoys; Figure 7 To correspond to the actual ground flow velocity for different wind speeds and observation geometries; Figure 8 A statistical comparison of WBCM and KaDOP under the same data and conditions is summarized. The above verification demonstrates that this invention can effectively suppress the influence of waves on OSC inversion, significantly improving the accuracy and robustness of radial velocity inversion using the Luojia-2 ATI-SAR satellite.

[0243] In summary, the results of the embodiments demonstrate that the method of the present invention effectively overcomes the shortcomings of insufficient accuracy in traditional wave error correction and makes optimizations and improvements at the mechanistic level. Compared with existing models, this method can quantitatively characterize the contribution of Bragg wave orbital motion to wave-induced errors, significantly improving the accuracy and processing efficiency of error correction, and providing a practical and feasible technical path for suppressing the interference of ocean waves on ocean current observations in actual marine environments. This method has important supporting significance for ocean observation, navigation support, and marine climate research, and has broad application prospects.

[0244] Those skilled in the art will understand that the above description is merely a preferred embodiment of the present invention, and the features described in the various embodiments and / or claims of this disclosure can be combined or combined in various ways, even if such combinations or combinations are not explicitly described in this disclosure. This is not intended to limit the present invention. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art can still modify the technical solutions described in the foregoing embodiments or make equivalent substitutions for some of the technical features. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

[0245] Although preferred embodiments of the invention have been described, those skilled in the art, upon learning the basic inventive concept, can make other changes and modifications to these embodiments. Therefore, the appended claims are intended to be interpreted as including both the preferred embodiments and all changes and modifications falling within the scope of the invention. Clearly, those skilled in the art can make various alterations and modifications to the invention without departing from its spirit and scope. Thus, if these modifications and modifications of the invention fall within the scope of the claims and their equivalents, the invention is also intended to include these modifications and modifications.

Claims

1. A method for correcting the current velocity of the Luojia-2 SAR satellite based on Bragg orbit velocity, characterized in that, Includes the following steps: Step S1: Based on wave flume experiments and theoretical analysis, establish a Doppler frequency shift theoretical model with Bragg wave orbital velocity as the physical basis, and obtain its quantitative expression and theoretical Doppler power spectrum 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, under the DopRIM framework, the inherent motion term of the Bragg wave is replaced by the orbital velocity instead of the phase velocity, and a physically consistent wave error correction model is established by combining the scattering and modulation characteristics of the Bragg wave itself. Step S3: Using airborne Ka-band along-track interferometric SAR observation data, GNSS drifting buoy measurement results, and Copernicus wind field data, calibrate the parameters of the wave error correction model to make them consistent with actual observations; Step S4: Apply the calibrated wave error correction model to the in-orbit interferometric SAR observation data of Luojia-2 satellite, and calculate the radial surface velocity and wave error of each resolution cell; Step S5: Assimilate GDP drift buoy data and Copernicus Current data that are spatially and temporally matched with observations from the Luojia-2 satellite are used as reference true values ​​and compared with the output of Step S4 to evaluate the effectiveness of the wave error correction model. Step S6: Compare the wave error correction model with the KaDOP model, and calculate the root mean square error, bias and correlation coefficient to statistically analyze the simulated wave error under different methods, and quantitatively measure the improvement of model performance. Step S7: Visualize the wave error simulation results and quantitatively evaluate the improvement effect using in-situ observation data and KaDOP simulation results.

2. The method for correcting the current velocity of Luojia-2 SAR based on Bragg orbit velocity according to claim 1, characterized in that, Step S1 includes the following steps: S11: Based on wave flume experiments and theoretical derivation, observe unidirectional propagating Bragg waves and quantify their orbital velocity to confirm that orbital velocity is the actual physical mechanism that generates Doppler frequency shift. S12: Analyze the components of the Bragg wave trajectory velocity in the radar line-of-sight direction. ,Right now: ； in, For the horizontal orbital velocity component of the Bragg wave, For the vertical orbital velocity component of the Bragg wave, For the amplitude of the Bragg wave, Bragg wave angular frequency, For the Bragg wave number, The coordinates are in the horizontal direction. For time, The radar incident angle; S13: Based on the Jacobi–Anger expansion, the phase-modulated radar signal dominated by orbital velocity is converted into a discrete spectrum, as shown in the formula: ； ； in, Discrete spectrum of phase-modulated radar echo in the frequency domain; Give the amplitude weight of the nth spectral line to the Bessel function; The phase modulation index is determined by the amplitude of the Bragg wave trajectory velocity in the line-of-sight direction and radar parameters. This is the initial phase factor corresponding to the nth harmonic; For frequency domain variables, representing the value points of the phase-modulated echo signal in the Doppler frequency domain; For the fundamental frequency, For the Bragg wave angular frequency, It is the Dirac delta function; Calculate the position of the main peak of the theoretical Doppler power spectrum based on the discrete spectrum; S14: Compare the theoretical Doppler power spectrum with the experimental observation results of the wave flume to verify the consistency between the Doppler power spectrum driven by the orbital velocity and the measured results, and provide a theoretical basis for the wave error correction of interferometric SAR current measurement.

3. The method for correcting the flow velocity of Luojia-2 SAR based on Bragg orbit velocity according to claim 1, characterized in that, Step S2 specifically includes: Step S21: Within the DopRIM framework, establish an expression for the radial surface velocity that includes surface flow, the inherent motion of the Bragg scatterer, and long-wavelength modulation terms; Step S22: Replace the inherent motion term of the Bragg scatterer with the orbital velocity expression, and introduce the tilt modulation transfer function and the hydrodynamic modulation transfer function in the Bragg ring domain, and obtain the Bragg term velocity expression by integral weighting; Step S23: Based on the Bragg term orbital velocity integral and modulation transfer function, complete the physically consistent error correction model for quantitative correction of radial surface velocity deviation.

4. The method for correcting the flow velocity of Luojia-2 SAR based on Bragg orbit velocity according to claim 3, characterized in that, Step S23 specifically includes: a. The contribution of the Bragg wave to the radial Doppler velocity can be expressed as a modulation-weighted integral over the Bragg ring domain, i.e.: ； in, The 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; b. Determine the integration domain The Prague Ring, that is: ； 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; ； in, Radar wave number, The radar wavelength; 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: ； in Represented as: ； in, The directional wavenumber spectrum of the Bragg wave, The frictional wind speed over the sea surface. For threshold friction wind speed, Let be the directional spread function of the capillary wave. The shortwave dissipation factor is the result of the modulation effect of large-scale long waves on small-scale short waves. The eddy dissipation factor caused by sea surface turbulence. For capillary wave curvature spectrum, The wind speed is 10 meters above the sea surface. The peak elevation factor of the capillary curvature spectrum; Wind stress was determined using the relationship between friction velocity and 10 m wind speed. ； in, This is the drag coefficient; d. Calculation results based on orbital velocity By replacing the Bragg wave phase velocity calculation term within the DopRIM framework, the wave error correction model WBCM is obtained.

5. The method for correcting the flow velocity of Luojia-2 SAR based on Bragg orbit velocity according to claim 1, characterized in that, Step S3 includes the following steps: Step S31: Through an airborne Ka-band along-track interferometric SAR experiment, collect data from multiple spatial sub-regions within the observation area and register them spatially and temporally with GNSS drifting buoy observations and CMEMS wind field data; Step S32: Using the current velocity observed by the GNSS drifting buoy as a reference, compare the observed values ​​of each sub-region with the reference values ​​to obtain the wave error observations for each sub-region, and record the corresponding wind field information and radar observation parameters; Step S33: The modulation transfer function parameters are calibrated using the weighted nonlinear least squares method, and the calibration results are evaluated using statistical indicators such as root mean square error, deviation, and correlation coefficient. The optimal parameter set is then selected for model calibration.

6. The method for correcting the flow velocity of Luojia-2 SAR based on Bragg orbit velocity according to claim 5, characterized in that, In step S33, the calibration of the modulation transfer function parameters using the weighted nonlinear least squares method specifically involves: a) Within the airborne Ka-band along-track interferometric SAR imaging area, select several spatial sub-regions that are synchronously registered with the wind field and GNSS drifting buoys, and invert the radial surface velocity using the interferometric phase difference Δφ. ,Right now: ； in, For platform speed, For interference phase, Radar wave number, The length of the baseline along the track. The radar incident angle; b) Define wave error observations for each sub-region. for: ； in, Radial surface velocity measured by a GNSS drifting buoy; c) Introduce tilt and hydrodynamic modulation transfer functions into the Bragg wave modulation term in the wave error correction model, with the parameter vector as follows: ; Model output for the first The sub-regions are: ； in, The wave error predicted by the model for the i-th observation point. The angle between the radar line of sight and the wind direction. The wind speed is at a depth of 10 meters above the sea surface. The radar incident angle, The parameter to be determined; Weighted nonlinear least squares fitting is used, and the objective function is... for: ； in, As weight; To observe the error of ocean waves; The Levenberg-Marquardt iterative algorithm is used to optimize the parameter vector p, and the parameter update formula is as follows: ； in, For Jacobian matrices, For the residual vector, The damping factor, It is a diagonal weight matrix. As a unit array, This is the transpose of the Jacobian matrix; Update parameters iteratively: Continue until the convergence condition is met; d) The calibrated modulation transfer function parameter set is evaluated using root mean square error, bias and correlation coefficient, and the parameter uncertainty is estimated by residuals.

7. The method for correcting the current velocity of Luojia-2 SAR based on Bragg orbit velocity according to claim 1, characterized in that, Step S4 specifically includes: Step S41: Apply the calibrated wave error correction model to the in-orbit interferometric SAR data of Luojia-2 satellite, and perform current velocity inversion and wind field registration for each resolution unit of the observation area. Step S411: Perform standardized interferometric processing on the raw satellite data, including registration, removal of flat phase, interferogram generation, and dividing the entire observation area into regular geographic grids, i.e., resolution units; Step S412: Based on the interference phase difference Δ Using the basic principles of in-orbit interferometric SAR, the uncorrected radial surface velocity of each resolution cell was initially inverted. ; Step S42: Calculate the wave error using the correction model for each resolution unit and compare it with the observation results from the Luojia-2 satellite; For each resolvable unit: Step S421: Extract the wind speed and the angle between the radar line of sight and the wind direction for this unit; Step S422: Substitute the environmental parameters and radar geometric parameters from step S421 into the calibrated WBCM model to calculate the velocity deviation caused by wave motion in this element, i.e., the wave error. ; Step S423: Subtract the error from the initially inverted flow velocity to obtain the corrected true radial surface flow velocity: ； Step S43: Format the calculation results as a raster data product to obtain two core layers: the corrected radial surface velocity field, i.e. Spatial distribution; wave error field, i.e. Spatial distribution.

8. The method for correcting the current velocity of Luojia-2 SAR based on Bragg orbit velocity according to claim 1, characterized in that, Step S5 specifically includes: Step S51: Within the satellite observation area, a reference flow field is generated using assimilated GDP drift buoy and Copernicus Current data, and registered in time and space with the Luojia-2 in-orbit interferometric SAR observation data, and interpolated to a grid consistent with the satellite according to the resolution unit. Step S52: On each resolution unit, compare the wave error calculated by the model with the satellite observation results, calculate the root mean square error, deviation and correlation coefficient statistical indicators, and evaluate and verify the effectiveness of the wave error correction model.

9. The method for correcting the current velocity of Luojia-2 SAR based on Bragg orbit velocity according to claim 1, characterized in that, Step S6 specifically includes: Step S61: Using the unit-level error sequence registered with the reference data, establish a statistical evaluation system, wherein the evaluation indicators include root mean square error, bias and correlation coefficient; Step S62: Under the condition of consistency with the space and time of the satellite observation area, generate unit-level wave error sequences using the wave error correction model and the KaDOP model respectively, and compare and evaluate them with the reference error; Step S63: Quantify the performance improvement, specifically the improvement rate, using root mean square error as the primary indicator. Defined as: ； in, denoted as the root mean square error of the KaDOP model. This represents the root mean square error of the wave error correction model.

10. The method for correcting the current velocity of Luojia-2 SAR based on Bragg orbit velocity according to claim 1, characterized in that, In step S7, visualizing the wave error simulation results specifically includes: Step S71: Based on the corrected radial surface velocity product obtained in step S4, generate a two-dimensional spatial distribution map, use color mapping to represent the velocity magnitude, and overlay coastline, contour lines and scale elements. Step S72: Based on the wave error field data separated in step S4, generate a wave error spatial distribution map, use a diverging color scheme to distinguish positive and negative error values, and mark the maximum and minimum error areas; Step S73: Based on the comparative evaluation results of step S6, generate statistical comparison charts, including: (1) Scatter plot of flow velocity before and after correction versus reference value; (2) Error distribution histograms of the WBCM model and the KaDOP model; (3) Comparison table of performance indicators of each model in different wind speed ranges; Step S74: Generate a comprehensive evaluation report that includes raw observation data quality assessment indicators, root mean square error, bias and correlation coefficient statistics before and after model correction, correction effect analysis under different sea state conditions, and quantitative indicators of performance improvement of the KaDOP model. Step S75: Integrate the spatial distribution map, statistical charts, and evaluation report into a visualization product, output it in a standardized format, and support loading and interactive querying on the GIS platform.

Images