High-orbit sar time-varying ionospheric effect error correction method based on faraday rotation estimation

Abstract

A method for correcting time-varying ionospheric error in high-orbit SAR based on Faraday rotation estimation is proposed. The method first performs zero-padding of the azimuth signal, then calculates the azimuth decompression phase, reconstructs the azimuth echo, estimates the time-varying ionospheric error phase, performs time-varying ionospheric error correction, acquires the corrected full image data, and finally obtains the final corrected image data. This invention utilizes the Faraday rotation error caused by the time-varying ionosphere in the fully circularly polarized signal wave of high-orbit SAR. By employing azimuth echo reconstruction and Faraday rotation angle estimation inversion, it can achieve high-precision correction of the time-varying ionospheric error in high-orbit SAR images. Its phase correction accuracy is better than 0.01 rad, and the correlation between the corrected image and the original image is as high as 99%. The system is simple and low-cost.

Description

Technical Field

[0001] This invention belongs to the field of signal processing technology, specifically relating to a method for correcting errors of time-varying ionospheric effects in high-orbit SAR based on Faraday rotation estimation. Background Technology

[0002] High-orbit synthetic aperture radar (SAR), as a novel spaceborne remote sensing Earth observation system, possesses the capability to conduct long-term monitoring of specific areas and achieve ultra-wide swath coverage of thousands of kilometers. Leveraging the advantages of high revisit time and wide coverage of high-orbit SAR, it can be applied to various fields such as marine environment, glacier dynamics, and geographic mapping. However, due to the extremely long synthetic aperture time of high-orbit SAR, the ionosphere undergoes significant changes during the radar echo coherence accumulation time. High-orbit SAR echo signals are severely affected by time-varying ionospheric effects during space transmission, leading to severe distortion of the radar echo signal and consequently affecting the quality of the acquired radar images. Therefore, achieving error correction for time-varying ionospheric effects in high-orbit SAR is of significant scientific importance and application value for space environment science research and the development of spaceborne remote sensing Earth observation systems.

[0003] Existing methods for correcting time-varying ionospheric effects in high-orbit SAR include: transmitting dual-band signals via a radar-mounted dual-frequency system and employing correlation processing algorithms to correct time-varying ionospheric effect errors (Bruno, D.; Hobbs SERadarImagingFromGeosynchronous Orbit:Temporal Decorrelation Aspects.IEEE Transactions on Geoscience & Remote Sensing. 2010, 48, 2924-2929.); and calculating corresponding ionospheric effect errors using total electron content (TEC) data obtained from actual measurements by Global Navigation Satellite Systems (GNSS) to achieve correction (Long, T.; Hu, C.; Ding, Z.; Dong, X.; Tian, ​​W.; Zeng, T.Geosynchronous SAR:System and Signal). Processing; Springer: Singapore, 2018); Based on the affected SAR image itself, an autofocusing processing algorithm is used to estimate the received time-varying ionospheric additional phase to achieve error correction (Li, Z.; Quegan, S.; Chen, J.; Rogers, NC Performance Analysis of Phase Gradient Autofocus for Compensating Ionospheric Phase Scintillation in BIOMASS P-Band SAR Data. IEEE Geoscience & Remote Sensing Letters. 2015, 12, 1367-1371.). However, the above correction method has problems such as using a complex transceiver system, requiring a complex additional measurement system, and the correction accuracy being limited by the scattering characteristics of ground objects, resulting in a complex system, high cost, and limited correction accuracy. Summary of the Invention

[0004] In order to overcome the shortcomings of the prior art, the present invention aims to propose a time-varying ionospheric effect error correction method for high-orbit SAR based on Faraday rotation estimation, which can achieve high-precision correction of time-varying ionospheric effect errors on high-orbit SAR images. Its phase correction accuracy is better than 0.01 rad, and the correlation between the corrected image and the original image is as high as 99%. The system is simple and low-cost.

[0005] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0006] A time-varying ionospheric effect error correction method for high-orbit SAR based on Faraday rotation estimation utilizes the Faraday rotation effect error caused by the time-varying ionosphere on the fully circularly polarized signal wave acquired by a fully circularly polarized high-orbit SAR system. Error correction is achieved through azimuth echo reconstruction and Faraday rotation angle estimation inversion, including the following steps:

[0007] Step 1, azimuth signal zero-padding: Calculate the number of synthetic aperture points N in the azimuth direction based on the radar system parameters. syn To this end, zeros are padded at the beginning and end of each column of the four polarization channel data matrices, with the number of zeros padded being [number missing]. Obtain the preprocessed data S of the four polarization channels RR_temp S RL_temp S LR_temp S LL_temp ;

[0008] Step 2, Calculate the azimuth decompression phase: Based on the radar system parameters, calculate the reference slant range R corresponding to each range gate (each column). ref The decompression phase φ of the azimuth signal is calculated accordingly. d ;

[0009] Step 3, Azimuth Echo Reconstruction: Based on the four polarization channel data preprocessed in Step 1, perform a Fast Fourier Transform (FFT) along each range gate (column) to obtain the azimuth spectrum data of the preprocessed signal. Multiply this by the azimuth decompression phase φ. d The azimuth reconstructed echo spectrum data is obtained, and then an inverse fast Fourier transform (IFFT) is performed along each range gate (column) to obtain the azimuth reconstructed echo data E. RR E RL E LR E LL ;

[0010] Step 4, Time-varying ionospheric effect error phase estimation: Based on the azimuth reconstructed echo data E calculated in Step 3 RR E LL The argument FR is obtained by multiplying the conjugates. temp , for FR temp The Faraday rotation angle estimate FR is obtained by smoothing, and the time-varying ionospheric effect error phase φ is calculated by combining it with radar system parameters. iono ;

[0011] Step 5, Time-varying ionospheric effect error correction: Based on the azimuth reconstructed echo data of the four polarization channels calculated in Step 3, perform Fast Fourier Transform (FFT) along each azimuth sampling time (by row) to obtain the reconstructed echo range spectrum data, and multiply it by the time-varying ionospheric effect error phase φ. ionoAfter obtaining the corrected and reconstructed echo range spectrum data, perform a fast inverse Fourier transform (IFFT) along each azimuth sampling time (row by row) to obtain the corrected and reconstructed echo data E. RR_corr E RL_corr E LR_corr E LL_corr ;

[0012] Step 6: Obtain the corrected full image data: Based on the corrected reconstructed echo data from Step 5, perform a Fast Fourier Transform (FFT) along each range gate (column-wise) to obtain the corrected reconstructed echo azimuth spectrum data. Multiply this by the azimuth decompression phase φ. d After obtaining the corrected full-image azimuth spectrum data, perform a Fast Inverse Fourier Transform (IFFT) along each range gate (column-wise) to obtain the corrected full-image data M. RR_temp M RL_temp M LR_temp M LL_temp ;

[0013] Step 7: Obtain the final corrected image data: Based on the azimuth synthetic aperture point number N calculated in Step 1. syn This is used to crop the beginning and end of each column of the full image data matrix after correction in the four polarization channels. Line data, obtain the final corrected image data M RR M RL M LR M LL Both of them are of size N a ×N r A two-dimensional complex matrix.

[0014] The advantages of this invention are:

[0015] (1) This invention has the feature of high accuracy in correcting time-varying ionospheric effect errors in high-orbit SAR. Due to the use of an error estimation model based on Faraday rotation angle, it has higher accuracy than existing correction methods (the correlation between the corrected image and the original image is as high as 99%).

[0016] (2) The present invention has the feature of high accuracy in estimating the phase of time-varying ionospheric effect error. Due to the use of azimuth echo reconstruction processing, it breaks through the limitation of loss of azimuth time sampling information caused by synthetic aperture processing. Compared with existing correction methods, it can achieve accurate estimation of the phase of time-varying ionospheric effect error (the accuracy of the phase estimation of time-varying ionospheric effect error is better than 0.01 rad).

[0017] (3) The present invention has the characteristics of simple and convenient time-varying ionospheric effect error correction equipment. It utilizes a fully circular polarized spaceborne SAR system. Compared with existing correction methods, it does not require additional measurement equipment (e.g., dual-frequency transmitter, global navigation satellite system, etc.). It only uses the fully polarized data obtained by high-orbit SAR to perform time-varying ionospheric effect error phase inversion, which greatly reduces the system load complexity and facilitates engineering implementation.

[0018] (4) The present invention has the characteristics of high robustness of time-varying ionospheric effect error correction effect. Due to the adoption of a fully polarized working mode, compared with the existing correction methods, it uses the Faraday rotation angle to achieve accurate estimation of ionospheric effect error, and the error phase estimation result is not limited by the type of ground object scene.

[0019] (5) The present invention has the feature of real-time correction of time-varying ionospheric effect error. Since the error correction is achieved by using fully polarized high-orbit SAR data, compared with the existing correction methods, the time-varying ionospheric effect error can be achieved by processing the acquired SAR image through on-board real-time processing equipment. Attached Figure Description

[0020] Figure 1 This is a flowchart of the present invention.

[0021] Figure 2 This is a schematic diagram of the image data of the original four polarization channels in an embodiment of the present invention.

[0022] Figure 3 This is a schematic diagram of the time-varying ionospheric effect error phase added to the four polarization channel signals in an embodiment of the present invention.

[0023] Figure 4 This is a schematic diagram of the estimated time-varying ionospheric effect error phase in an embodiment of the present invention.

[0024] Figure 5 This is a schematic diagram of the image data of the four polarization channels after correction in an embodiment of the present invention. Detailed Implementation

[0025] The present invention will now be described in further detail with reference to the accompanying drawings.

[0026] A time-varying ionospheric effect error correction method for high-orbit SAR based on Faraday rotation estimation is proposed. This method utilizes the data from the four polarization channels of the fully circularly polarized signal wave acquired by a fully circularly polarized high-orbit SAR system, represented as S... RR S RL S LR S LL Both of them are of size N a ×N rA two-dimensional complex matrix; for each polarization channel data matrix, its matrix has a one-dimensional representation of the azimuth direction, and N... a There are 3 sampling points, each corresponding to a different azimuth time. The time interval between two adjacent sampling times is 1. Where PRF represents the radar pulse repetition frequency; the other dimension of the matrix represents the range direction, and N r Each sampling point represents a sampling time in each azimuth direction at a sampling rate f. s The radar pulse signal is sampled, and each range pulse sample contains N. r One sampling point.

[0027] like Figure 1 As shown, a method for correcting errors in time-varying ionospheric effects in high-orbit SAR based on Faraday rotation estimation includes the following steps:

[0028] Step 1, azimuth signal zero-padding: Calculate the number of synthetic aperture points N in the azimuth direction based on the radar system parameters. syn Therefore, zeros are padded at the beginning and end of each column of the four polarization channel data matrices, with the number of zeros padded being [number missing]. Obtain the preprocessed data S of the four polarization channels RR_temp S RL_temp S LR_temp S LL_temp Specifically, it means:

[0029] Let S be the data from the four polarization channels acquired by high-orbit SAR. RR S RL S LR S LL They are respectively:

[0030]

[0031]

[0032]

[0033]

[0034] In the formula, This represents the value at coordinate (1,1) in the RR channel data matrix. Represents the coordinates (1, N) in the RR channel data matrix. r The value of ) Represents the coordinates (N) in the RR channel data matrix. a The value of ,1). Represents the coordinates (N) in the RR channel data matrix. a N r The value of ); This represents the value at coordinate (1,1) in the RL channel data matrix. Represents the coordinates (1, N) in the RL channel data matrix. r The value of ) Represents the coordinates (N) in the RL channel data matrix a The value of ,1). Represents the coordinates (N) in the RL channel data matrix a N r The value of ); This represents the value at coordinate (1,1) in the LR channel data matrix. Represents the coordinates (1, N) in the LR channel data matrix. r The value of ) Represents the coordinates (N) in the LR channel data matrix a The value of ,1). Represents the coordinates (N) in the LR channel data matrix a N r The value of ); This represents the value at coordinate (1,1) in the LL channel data matrix. Represents the coordinates (1, N) in the LL channel data matrix r The value of ) Represents the coordinates (N) in the LL channel data matrix a The value of ,1). Represents the coordinates (N) in the LL channel data matrix a N r The value of );

[0035] 1.1) Calculate the number of azimuth synthetic aperture points N based on radar system parameters. syn :

[0036]

[0037] In the formula, λ represents the operating wavelength of the radar system, R represents the reference slant range at the center point of the radar illumination scene, and L... a V represents the azimuth antenna length. g Represents the radar ground velocity; round[x] represents the operation of taking the largest even number not greater than x;

[0038] 1.2) Based on the number N of synthetic aperture points in the azimuth direction syn Zeros are padded at the beginning and end of each column of the four polarization channel data matrices, with the number of zeros padded being [number missing]. Obtain the preprocessed data S of the four polarization channels RR_temp S RL_temp S LR_temp S LL_temp They are all expanded to size N a_temp ×Nr A two-dimensional complex matrix, and They are respectively:

[0039]

[0040]

[0041]

[0042]

[0043] In the formula, This represents the coordinates in the RR channel data matrix after zero padding. The value, This represents the coordinates in the RR channel data matrix after zero padding. The value, This represents the coordinates in the RR channel data matrix after zero padding. The value, This represents the coordinates in the RR channel data matrix after zero padding. The value; This represents the coordinates in the RL channel data matrix after zero-padding. The value, This represents the coordinates in the RL channel data matrix after zero-padding. The value, This represents the coordinates in the RL channel data matrix after zero-padding. The value, This represents the coordinates in the RL channel data matrix after zero-padding. The value; This represents the coordinates in the LR channel data matrix after zero padding. The value, This represents the coordinates in the LR channel data matrix after zero padding. The value, This represents the coordinates in the LR channel data matrix after zero padding. The value, This represents the coordinates in the LR channel data matrix after zero padding. The value; This represents the coordinates in the LL channel data matrix after zero padding. The value, This represents the coordinates in the LL channel data matrix after zero padding. The value, This represents the coordinates in the LL channel data matrix after zero padding. The value, This represents the coordinates in the LL channel data matrix after zero padding. The value;

[0044] Step 2, Calculate the azimuth decompression phase: Based on the radar system parameters, calculate the reference slant range R corresponding to each range gate (each column). ref The decompression phase φ of the azimuth signal is calculated accordingly. d Specifically, it means:

[0045] 2.1) Based on the radar system parameters, calculate the reference slant range R corresponding to each range gate (each column). ref :

[0046]

[0047] In the formula, c represents the speed of light;

[0048] 2.2) Calculate the azimuth signal frequency f after zero-padding. a :

[0049]

[0050] 2.3) Calculate the decompression phase φ of the azimuth signal d :

[0051]

[0052] In the formula, Indicates the azimuth signal frequency f a The first frequency value in a one-dimensional array, Indicates the azimuth signal frequency f a The Nth element in a one-dimensional array a_temp One frequency value, Indicates the reference slope distance R ref The slope distance at coordinate (1,1) in a two-dimensional matrix. Indicates the reference slope distance R ref Coordinates (1, N) in a two-dimensional matrix r The slope distance value, Indicates the reference slope distance R ref Coordinates in a two-dimensional matrix (N) a_temp The slope distance value of ,1). Indicates the reference slope distance R ref Coordinates in a two-dimensional matrix (N) a_temp N r The slope distance value;

[0053] Step 3, Azimuth Echo Reconstruction: Based on the four polarization channel data preprocessed in Step 1, perform a Fast Fourier Transform (FFT) along each range gate (column-wise) to obtain the azimuth spectrum data of the preprocessed signal. Multiply this by the azimuth decompression phase φ. dThe azimuth reconstructed echo spectrum data is obtained, and then an inverse fast fourier transform (IFFT) is performed along each range gate (column) to obtain the azimuth reconstructed echo data E. RR E RL E LR E LL Specifically, it means:

[0054] 3.1) Preprocessing the four polarization channel data S RR_temp S RL_temp S LR_temp S LL_temp Perform a Fast Fourier Transform (FFT) along each distance gate (column-wise) to obtain the azimuth spectrum data of the preprocessed signal.

[0055]

[0056]

[0057]

[0058]

[0059] In the formula, This represents the value of coordinate (1,1) in the azimuth spectrum data of the RR channel preprocessed signal. This represents the coordinates (1, N) in the azimuth spectrum data of the RR channel preprocessed signal. r The value of ) This represents the coordinates (N) in the azimuth spectrum data of the RR channel preprocessed signal. a_temp The value of ,1). Represents the coordinates (N) of the RR channel distance in the spectral data. a_temp N r The value of ); This represents the value of coordinate (1,1) in the azimuth spectrum data of the RL channel preprocessed signal. This represents the coordinates (1, N) in the azimuth spectrum data of the RL channel preprocessed signal. r The value of ) Represents the coordinates (N) in the azimuth spectrum data of the RL channel preprocessed signal. a_temp The value of ,1). Represents the coordinates (N) of the RL channel distance in the spectral data. a_temp N r The value of ); This represents the value of coordinate (1,1) in the azimuth spectrum data of the LR channel preprocessed signal. This represents the coordinates (1, N) in the azimuth spectrum data of the LR channel preprocessed signal. r The value of ) This represents the coordinates (N) in the azimuth spectrum data of the LR channel preprocessed signal. a_temp The value of ,1). Represents the coordinates (N) in the LR channel distance spectrum data. a_temp N r The value of ); This represents the value of coordinate (1,1) in the azimuth spectrum data of the LL channel preprocessed signal. This represents the coordinates (1, N) in the azimuth spectrum data of the LL channel preprocessed signal. r The value of ) This represents the coordinates (N) in the azimuth spectrum data of the LL channel preprocessed signal. a_temp The value of ,1). This represents the coordinates (N) in the azimuth spectrum data of the LL channel preprocessed signal. a_temp N r The value of ); FFT a (·) indicates performing a Fast Fourier Transform on each column of data in a two-dimensional matrix;

[0060] 3.2) Direct the preprocessed signal to the spectral data Multiply by the azimuth decompression phase φ d Obtain azimuth reconstructed echo spectrum data

[0061]

[0062]

[0063]

[0064]

[0065] In the formula, Indicates the phase φ of the azimuth signal decompression. d The value of the coordinate (1,1) in a two-dimensional matrix. Indicates the phase φ of the azimuth signal decompression. d Coordinates (1, N) in a two-dimensional matrix r The value of ) Indicates the phase φ of the azimuth signal decompression. d Coordinates in a two-dimensional matrix (N) a_temp The value of ,1). Indicates the phase φ of the azimuth signal decompression. d Coordinates in a two-dimensional matrix (N) a_temp N rThe value of ); j ​​represents the imaginary unit, i.e.

[0066] 3.3) Reconstructing echo spectrum data in the orientation direction Performing an inverse fast Fourier transform (IFFT) along each distance gate (column-wise) yields the azimuth reconstructed echo data E. RR E RL E LR E LL :

[0067]

[0068]

[0069]

[0070]

[0071] In the formula, This represents the value of coordinate (1,1) in the azimuth reconstruction echo data of the RR channel. This indicates the coordinates (1, N) in the RR channel azimuth reconstruction echo data. r The value of ) This indicates the coordinates (N) in the azimuth reconstruction echo data of the RR channel. a_temp The value of ,1). This indicates the coordinates (N) in the azimuth reconstruction echo data of the RR channel. a_temp N r The value of ); This represents the value of coordinate (1,1) in the azimuth reconstruction echo data of the RL channel. This represents the coordinates (1, N) in the RL channel azimuth reconstruction echo data. r The value of ) This represents the coordinates (N) in the RL channel azimuth reconstruction echo data. a_temp The value of ,1). This represents the coordinates (N) in the RL channel azimuth reconstruction echo data. a_temp N r The value of ); This represents the value of coordinate (1,1) in the azimuth reconstruction echo data of the LR channel. This represents the coordinates (1, N) in the LR channel azimuth reconstruction echo data. r The value of ) This indicates the coordinates (N) in the LR channel azimuth reconstruction echo data. a_temp The value of ,1). This indicates the coordinates (N) in the LR channel azimuth reconstruction echo data. a_temp N r The value of ); This represents the value of coordinate (1,1) in the azimuth reconstruction echo data of the LL channel. This represents the coordinates (1, N) in the LL channel azimuth reconstruction echo data. r The value of ) This indicates the coordinates (N) in the LL channel azimuth reconstruction echo data. a_temp The value of ,1). This indicates the coordinates (N) in the LL channel azimuth reconstruction echo data. a_temp N r The value of ); IFFT a (·) indicates performing a fast inverse Fourier transform on each column of a two-dimensional matrix;

[0072] For details on Fast Fourier Transform (FFT) and Inverse Fast Fourier Transform (IFFT), please refer to pages 18-19 of the book "Synthetic Aperture Radar Imaging - Algorithms and Implementation" by Ian G Cumming et al., published by Electronic Industry Press in June 2012 and translated by Hong Wen et al.

[0073] Step 4, Time-varying ionospheric effect error phase estimation: Based on the azimuth reconstructed echo data E calculated in Step 3 RR E LL The argument FR is obtained by multiplying the conjugates. temp , for FR temp The Faraday rotation angle estimate FR is obtained by smoothing, and the time-varying ionospheric effect error phase φ is calculated by combining it with radar system parameters. iono Specifically, it means:

[0074] 4.1) Perform conjugate multiplication on the azimuth reconstructed echo data of the RR and LL channels to obtain the argument angle FR. temp :

[0075]

[0076] In the formula, the argument FR temp The size is N a_temp ×N r A two-dimensional real matrix, * Indicates conjugation, and angle(x) is the argument operation for taking the complex number x;

[0077] 4.2) The argument FR calculated above temp Using a rectangular smoothing window for FR temp After smoothing, the estimated Faraday rotation angle FR is obtained, and the result is of size N. a_temp ×N r Two-dimensional real matrix:

[0078] FR = <FR temp > (26)

[0079] In the formula, <x>This indicates that a smoothing window function with a window size of (2A+1, 2A+1) is applied to x, centered at the coordinates (p, q) of x (where 1 ≤ p ≤ N). a_temp , 1≤q≤N r Let x be the mean of all values ​​in rows pA to p+A and columns qA to q+A surrounding the FR column; temp Elements on the edge of a two-dimensional matrix, i.e., pA≤0, p+A≥N. a_temp qA≤0, q+A≥N r At this point, the element is not smoothed and the calculated x value is used directly as the result at that coordinate.

[0080] 4.3) Calculate the range signal frequency f r :

[0081]

[0082] 4.4) Using the Faraday rotation angle estimate FR obtained from the above calculation and the range signal frequency f r Based on the radar system and geomagnetic field parameters, the time-varying ionospheric effect error phase φ is calculated. iono :

[0083]

[0084] In the formula, Indicates the range signal frequency f r The first frequency value in a one-dimensional array, Indicates the range signal frequency The Nth element in a one-dimensional array r One frequency value, FR 11 This represents the angle value at coordinate (1,1) in the two-dimensional matrix of the phase error FR of the time-varying ionospheric effect. This represents the coordinates (1, N) in the reference slant distance FR two-dimensional matrix. r ) angle value, Represents the coordinates (N) in the reference slant distance FR two-dimensional matrix. a_temp ,1) Angle value, Represents the coordinates (N) in the reference slant distance FR two-dimensional matrix. a_temp N r The angle value of ), where K is a constant and K = 40.28, K Ω is a constant and B represents the geomagnetic field strength parallel to the radar beam direction, measured in tons (T).

[0085] Step 5, Time-varying ionospheric effect error correction: Based on the azimuth reconstructed echo data of the four polarization channels calculated in Step 3, perform Fast Fourier Transform (FFT) along each azimuth sampling time (by row) to obtain the reconstructed echo range spectrum data, and multiply it by the time-varying ionospheric effect error phase φ. iono After obtaining the corrected and reconstructed echo range spectrum data, perform a fast inverse Fourier transform (IFFT) along each azimuth sampling time (row by row) to obtain the corrected and reconstructed echo data E. RR_corr E RL_corr E LR_corr E LL_corr Specifically, it means:

[0086] 5.1) Reconstruct the echo data E from the azimuth direction of the four polarization channels. RR E RL E LR E LL Perform a Fast Fourier Transform (FFT) along each azimuth sampling time (row by row) to obtain the reconstructed echo range spectrum data.

[0087]

[0088]

[0089]

[0090]

[0091] In the formula, This represents the value at coordinate (1,1) in the reconstructed echo range spectrum data of the RR channel. This represents the coordinates (1, N) in the reconstructed echo distance spectrum data of the RR channel. r The value of ) This represents the coordinates (N) in the reconstructed echo distance spectrum data of the RR channel. a_temp The value of ,1). This represents the coordinates (N) in the reconstructed echo distance spectrum data of the RR channel. a_temp N r The value of ); This represents the value at coordinate (1,1) in the reconstructed echo range spectrum data of the RL channel. This represents the coordinates (1, N) in the reconstructed echo distance spectrum data of the RL channel. r The value of ) This represents the coordinates (N) in the reconstructed echo distance spectrum data of the RL channel. a_temp The value of ,1). This represents the coordinates (N) in the reconstructed echo distance spectrum data of the RL channel. a_temp N r The value of ); This represents the value of coordinate (1,1) in the reconstructed echo range spectrum data of the LR channel. This represents the coordinates (1, N) in the reconstructed echo distance spectrum data of the LR channel. r The value of ) This represents the coordinates (N) in the reconstructed echo distance spectrum data of the LR channel. a_temp The value of ,1). This represents the coordinates (N) in the reconstructed echo distance spectrum data of the LR channel. a_temp N r The value of ); This represents the value at coordinate (1,1) in the reconstructed echo range spectrum data of the LL channel. This represents the coordinates (1, N) in the reconstructed echo distance spectrum data of the LL channel. r The value of ) This represents the coordinates (N) in the reconstructed echo distance spectrum data of the LL channel. a_temp The value of ,1). This represents the coordinates (N) in the reconstructed echo distance spectrum data of the LL channel. a_temp N r The value of ); FFT r (·) indicates performing a Fast Fourier Transform on each row of data in a two-dimensional matrix;

[0092] 5.2) Reconstruct the echo range spectrum data Multiply by the time-varying ionospheric effect error phase φ iono After correction, the echo range spectrum data is reconstructed.

[0093]

[0094]

[0095]

[0096]

[0097] In the formula, The time-varying ionospheric effect error phase φ iono The value of the coordinate (1,1) in a two-dimensional matrix. The time-varying ionospheric effect error phase φ iono Coordinates (1, N) in a two-dimensional matrix r The value of ) The time-varying ionospheric effect error phase φ iono Coordinates in a two-dimensional matrix (N) a_temp The value of ,1). The time-varying ionospheric effect error phase φ iono Coordinates in a two-dimensional matrix (N) a_temp N r The value of );

[0098] 5.3) Reconstructing the echo range spectrum data after correction Perform an inverse fast Fourier transform (IFFT) along each azimuth sampling time (row by row) to obtain the corrected and reconstructed echo data E. RR_corr E RL_corr E LR_corr E LL_corr :

[0099]

[0100]

[0101]

[0102]

[0103] In the formula, This represents the value of coordinate (1,1) in the reconstructed echo data after RR channel correction. This indicates the coordinates (1, N) in the reconstructed echo data after RR channel correction. r The value of ) This indicates the coordinates (N) in the reconstructed echo data after RR channel correction. a_temp The value of ,1). This indicates the coordinates (N) in the reconstructed echo data after RR channel correction. a_temp N r The value of ); This represents the value of coordinate (1,1) in the reconstructed echo data after RL channel correction. This indicates the coordinates (1, N) in the reconstructed echo data after RL channel correction. r The value of ) This indicates the coordinates (N) in the reconstructed echo data after RL channel correction. a_temp The value of ,1). This indicates the coordinates (N) in the reconstructed echo data after RL channel correction. a_temp N r The value of ); This represents the value of coordinate (1,1) in the reconstructed echo data after LR channel correction. This indicates the coordinates (1, N) in the reconstructed echo data after LR channel correction. r The value of ) This indicates the coordinates (N) in the reconstructed echo data after LR channel correction. a_temp The value of ,1). This indicates the coordinates (N) in the reconstructed echo data after LR channel correction. a_temp N r The value of ); This represents the value of coordinate (1,1) in the reconstructed echo data after LL channel correction. This indicates the coordinates (1, N) in the reconstructed echo data after LL channel correction. r The value of ) This indicates the coordinates (N) in the reconstructed echo data after LL channel correction. a_temp The value of ,1). This indicates the coordinates (N) in the reconstructed echo data after LL channel correction. a_temp N r The value of ); IFFT r (·) indicates performing a fast inverse Fourier transform on each row of a two-dimensional matrix;

[0104] Step 6: Obtain the corrected full image data: Based on the corrected reconstructed echo data from Step 5, perform a Fast Fourier Transform (FFT) along each range gate (column-wise) to obtain the corrected reconstructed echo azimuth spectrum data. Multiply this by the azimuth decompression phase φ. d After obtaining the corrected full-image azimuth spectrum data, perform a Fast Inverse Fourier Transform (IFFT) along each range gate (column-wise) to obtain the corrected full-image data M. RR_temp M RL_temp M LR_temp M LL_temp Specifically, it means:

[0105] 6.1) For the corrected reconstructed echo data E RR_corr E RL_corr E LR_corr E LL_corr Perform a Fast Fourier Transform (FFT) along each distance gate (column-wise) to obtain the corrected and reconstructed echo azimuth spectrum data.

[0106]

[0107]

[0108]

[0109]

[0110] In the formula, This represents the value of coordinate (1,1) in the reconstructed echo azimuth spectrum data after RR channel correction. This indicates the coordinates (1, N) in the reconstructed echo azimuth spectrum data after RR channel correction. r The value of ) This indicates the coordinates (N) in the reconstructed echo azimuth spectrum data after RR channel correction. a_temp The value of ,1). Represents the coordinates (N) of the RR channel distance in the spectral data. a_temp N r The value of ); This represents the value of coordinate (1,1) in the reconstructed echo azimuth spectrum data after RL channel correction. This represents the coordinates (1, N) in the reconstructed echo azimuth spectrum data after RL channel correction. r The value of ) This represents the coordinates (N) in the reconstructed echo azimuth spectrum data after RL channel correction. a_temp The value of ,1). Represents the coordinates (N) of the RL channel distance in the spectral data. a_temp N r The value of ); This represents the value of coordinate (1,1) in the reconstructed echo azimuth spectrum data after LR channel correction. This represents the coordinates (1, N) in the reconstructed echo azimuth spectrum data after LR channel correction. r The value of ) This indicates the coordinates (N) in the reconstructed echo azimuth spectrum data after LR channel correction. a_temp The value of ,1). Represents the coordinates (N) in the LR channel distance spectrum data. a_temp N r The value of ); This represents the value of coordinate (1,1) in the reconstructed echo azimuth spectrum data after LL channel correction. This represents the coordinates (1, N) in the reconstructed echo azimuth spectrum data after LL channel correction. r The value of ) This represents the coordinates (N) in the reconstructed echo azimuth spectrum data after LL channel correction. a_temp The value of ,1). This represents the coordinates (N) in the reconstructed echo azimuth spectrum data after LL channel correction. a_temp N r The value of ); FFT a (·) indicates performing a Fast Fourier Transform on each column of data in a two-dimensional matrix;

[0111] 6.2) Reconstruct the corrected echo azimuth spectrum data Inverse multiplication by azimuth decompression phase φ d Obtain the corrected full-image azimuth spectrum data

[0112]

[0113]

[0114]

[0115]

[0116] 6.3) The azimuth spectrum data of the corrected full image Perform an Inverse Fast Fourier Transform (IFFT) along each distance gate (column-wise) to obtain the corrected full image data M. RR_temp M RL_temp M LR_temp M LL_temp :

[0117]

[0118]

[0119]

[0120]

[0121] In the formula, This represents the value at coordinate (1,1) in the full image data after RR channel correction. This represents the coordinates (1, N) in the full image data after RR channel correction. r The value of ) Represents the coordinates (N) in the full image data after RR channel correction. a_temp The value of ,1). Represents the coordinates (N) in the full image data after RR channel correction. a_temp N r The value of ); This represents the value at coordinate (1,1) in the full image data after RL channel correction. This represents the coordinates (1, N) in the full image data after RL channel correction. r The value of ) Represents the coordinates (N) in the full image data after RL channel correction. a_temp The value of ,1). Represents the coordinates (N) in the full image data after RL channel correction. a_temp N r The value of ); This represents the value at coordinate (1,1) in the full image data after LR channel correction. This represents the coordinates (1, N) in the full image data after LR channel correction. r The value of ) Represents the coordinates (N) in the full image data after LR channel correction. a_temp The value of ,1). Represents the coordinates (N) in the full image data after LR channel correction. a_temp N r The value of ); This represents the value at coordinate (1,1) in the full image data after LL channel correction. This represents the coordinates (1, N) in the full image data after LL channel correction. r The value of ) Represents the coordinates (N) in the full image data after LL channel correction. a_temp The value of ,1). Represents the coordinates (N) in the full image data after LL channel correction. a_temp N r The value of ); IFFT a (·) indicates performing a fast inverse Fourier transform on each column of a two-dimensional matrix;

[0122] Step 7: Obtain the final corrected image data: Based on the azimuth synthetic aperture point number N calculated in Step 1. syn This is used to crop the beginning and end of each column of the full image data matrix after correction in the four polarization channels. Line data, obtain the final corrected image data M RR M RL M LR M LL Both of them are of size N a ×N r A two-dimensional complex matrix; specifically represented as:

[0123]

[0124]

[0125]

[0126]

[0127] In the formula, Represents the coordinates in the full image data matrix after RR channel correction. The value, Represents the coordinates in the full image data matrix after RR channel correction. The value, Represents the coordinates in the full image data matrix after RR channel correction. The value, Represents the coordinates in the full image data matrix after RR channel correction. The value; Represents the coordinates in the full image data matrix after RL channel correction. The value, Represents the coordinates in the full image data matrix after RL channel correction. The value, Represents the coordinates in the full image data matrix after RL channel correction. The value, Represents the coordinates in the full image data matrix after RL channel correction. The value; Represents the coordinates in the full image data matrix after LR channel correction. The value, Represents the coordinates in the full image data matrix after LR channel correction. The value, Represents the coordinates in the full image data matrix after LR channel correction. The value, Represents the coordinates in the full image data matrix after LR channel correction. The value; Represents the coordinates in the full image data matrix after LL channel correction. The value, Represents the coordinates in the full image data matrix after LL channel correction. The value, Represents the coordinates in the full image data matrix after LL channel correction. The value, Represents the coordinates in the full image data matrix after LL channel correction. The value.

[0128] Through the above seven steps, the error of time-varying ionospheric effect was accurately corrected by using the fully circularly polarized high-orbit SAR signal and estimating the Faraday rotation angle.

[0129] The present invention will now be described in further detail with reference to the embodiments.

[0130] Since it is currently impossible to obtain high-orbit SAR satellite data in orbit, and the radar image data acquired by existing spaceborne SAR systems are all affected by ionospheric effects, this embodiment uses simulated fully circularly polarized high-orbit SAR images, such as... Figure 2 As shown, a time-varying ionospheric effect error phase is added to the four polarization channel signals, as follows: Figure 3 As shown in Table 1, the parameters involved in the processing are as follows:

[0131] Table 1 Parameters of the Example

[0132]

[0133]

[0134] A method for correcting errors of time-varying ionospheric effects in high-orbit SAR based on Faraday rotation estimation includes the following steps:

[0135] Step 1, Azimuth Signal Zero Padding: Based on the radar system parameters, the number of synthetic aperture points in the azimuth direction is calculated to be 15620. Zeros are then padded at the beginning and end of each column of the four polarization channel data matrix, with 7810 zeros padded in each column. This yields the preprocessed data S from the four polarization channels. RR_temp S RL_temp S LR_temp S LL_temp Specifically, let S be the data from the four polarization channels acquired by the high-orbit SAR. RR S RL S LR S LL All of them are two-dimensional complex matrices of size 224×323;

[0136] 1.1) Based on the radar system parameters, the number of azimuth synthetic aperture points is calculated as 15620 according to formula (5);

[0137] 1.2) Based on the azimuth synthesized aperture point count of 15620, zeros are padded at the beginning and end of each column of the four polarization channel data matrix according to equations (6), (7), (8), and (9), with a zero-padding count of 7810 in each column, to obtain the preprocessed four polarization channel data S. RR_temp S RL_temp S LR_temp S LL_temp They are all two-dimensional complex matrices of size 15844×323;

[0138] Step 2, calculate the azimuth decompression phase:

[0139] 2.1) Based on the radar system parameters, calculate the reference slant range R corresponding to each range gate (each column) according to formula (10). ref It is a two-dimensional real matrix of size 15844×323;

[0140] 2.2) Calculate the zero-padded azimuth signal frequency f according to formula (11). a It is a two-dimensional real matrix of size 15844×1;

[0141] 2.3) Calculate the decompression phase φ of the azimuth signal according to formula (12). d It is a two-dimensional real matrix of size 15844×323;

[0142] Step 3, azimuth echo reconstruction:

[0143] 3.1) Preprocessing the four polarization channel data S RR_temp S RL_temp S LR_temp S LL_temp Perform Fast Fourier Transform (FFT) along each distance gate (column) according to equations (13), (14), (15), and (16) to obtain the azimuth spectrum data of the preprocessed signal. They are all two-dimensional complex matrices of size 15844×323;

[0144] 3.2) Direct the preprocessed signal to the spectral data Multiply by the azimuth decompression phase φ according to equations (17), (18), (19), and (20). d Obtain azimuth reconstructed echo spectrum data They are all two-dimensional complex matrices of size 15844×323;

[0145] 3.3) Reconstructing echo spectrum data in the orientation direction Perform a fast inverse Fourier transform (IFFT) along each distance gate (column-wise) according to equations (21), (22), (23), and (24) to obtain the azimuth reconstructed echo data E. RR E RL E LR E LL They are all two-dimensional complex matrices of size 15844×323;

[0146] Step 4, Time-varying ionospheric effect error phase estimation:

[0147] 4.1) Perform conjugate multiplication on the azimuth reconstructed echo data of the RR and LL channels according to equation (25) and take the argument angle FR. temp It is a two-dimensional real matrix of size 15844×323;

[0148] 4.2) The argument value FR obtained above. temp According to formula (26), a rectangular smooth window of size (2A+1=129, 2A+1=129) is used to smooth the FR. temp Perform smoothing, i.e., use FR temp Centered on the coordinate (p, q) element in the matrix (where 1 ≤ p ≤ 15844, 1 ≤ q ≤ 323), calculate the mean of all values ​​within rows p-64 to p+64 and columns q-64 to q+64, and use this as the value of the coordinate (p, q) element. For values ​​close to FR... temp The elements at the edges of the two-dimensional matrix, namely all elements in rows 1 to 64, rows 15780 to 15844, columns 1 to 64, and columns 259 to 323, are used to directly calculate the argument value FR without smoothing. temp As a result at this coordinate, the estimated Faraday rotation angle FR is obtained, which is a two-dimensional real matrix of size 15844×323;

[0149] 4.3) Calculate the range signal frequency f according to formula (27). r It is a two-dimensional real matrix of size 1×323;

[0150] 4.4) Using the Faraday rotation angle estimate FR obtained from the above calculation and the range signal frequency f r Based on the radar system and geomagnetic field parameters, the time-varying ionospheric effect error phase φ is calculated according to equation (28). iono It is a two-dimensional real matrix of size 15844×323, such as Figure 4 As shown;

[0151] Step 5, Time-varying ionospheric effect error correction:

[0152] 5.1) Reconstruct the echo data E from the azimuth direction of the four polarization channels. RR E RL E LR E LL Perform Fast Fourier Transform (FFT) along each azimuth sampling time (row-by-row) according to equations (29), (30), (31), and (32) to obtain the reconstructed echo range spectrum data. They are all two-dimensional complex matrices of size 15844×323;

[0153] 5.2) Reconstruct the echo range spectrum data Multiply by the time-varying ionospheric effect error phase φ according to equations (33), (34), (35), and (36). iono After correction, the echo range spectrum data is reconstructed. They are all two-dimensional complex matrices of size 15844×323;

[0154] 5.3) Reconstructing the echo range spectrum data after correction Perform a fast inverse Fourier transform (IFFT) along each azimuth sampling time (row-by-row) according to equations (37), (38), (39), and (40) to obtain the corrected reconstructed echo data E. RR_corr E RL_corr E LR_corr E LL_corr , They are all two-dimensional complex matrices of size 15844×323;

[0155] Step 6: Obtain the corrected full image data:

[0156] 6.1) For the corrected reconstructed echo data E RR_corr E RL_corr E LR_corr E LL_corr Perform Fast Fourier Transform (FFT) along each distance gate (column) according to equations (41), (42), (43), and (44) to obtain the corrected reconstructed echo azimuth spectrum data. They are all two-dimensional complex matrices of size 15844×323;

[0157] 6.2) Reconstruct the corrected echo azimuth spectrum data Multiply by the azimuth decompression phase φ using equations (45), (46), (47), and (48). d Obtain the corrected full-image azimuth spectrum data They are all two-dimensional complex matrices of size 15844×323;

[0158] 6.3) The azimuth spectrum data of the corrected full image Perform a Fast Inverse Fourier Transform (IFFT) along each distance gate (column-wise) according to equations (49), (50), (51), and (52) to obtain the corrected full image data M. RR_temp M RL_temp M LR_temp M LL_temp They are all two-dimensional complex matrices of size 15844×323;

[0159] Step 7: Obtain the final corrected image data: Based on the azimuth synthetic aperture point count of 15620 calculated in Step 1, 7810 rows of data are cropped from the beginning and end of each column of the full image data matrix after correction in the four polarization channels to obtain the final corrected image data M. RR M RL M LR M LL They are all two-dimensional complex matrices of size 224×323, such as Figure 5 As shown.

[0160] contrast Figure 2 The original image data of the four polarization channels shown is compared with the data corrected according to this embodiment. Figure 5 The image data of the four polarization channels after correction shown can be seen to have very similar image quality, with a correlation coefficient of 0.9987. Further comparison... Figure 3 The time-varying ionospheric effect error phase added in the simulation shown is different from that calculated using this embodiment. Figure 4 The estimated time-varying ionospheric effect error phase shown is extremely close to the distribution results of the two methods. The calculated root mean square error of the time-varying ionospheric effect error phase is 0.0085 rad, meaning that this invention can achieve a time-varying ionospheric effect error phase correction accuracy of better than 0.01 rad for high-orbit SAR. In summary, the above embodiments demonstrate that the time-varying ionospheric effect error correction method for high-orbit SAR based on Faraday rotation estimation can achieve high-precision correction of time-varying ionospheric effect errors in high-orbit SAR.< / x>

Claims

1. A high orbit SAR time-varying ionospheric effect error correction method based on Faraday rotation estimation, characterized in that: The error influence of the Faraday rotation effect caused by the time-varying ionosphere on the full-circular polarization signal wave obtained by using a full-circular polarization high-orbit SAR system is corrected by using azimuth echo reconstruction and Faraday rotation angle estimation inversion, including the following steps: Step one, azimuth signal zero padding: according to the radar system parameters, the azimuth synthetic aperture point number is calculated , and the number of zero padding is , respectively in the head and tail of each column of the four polarization channel data matrix, and the number of zero padding is , , , ; Step two, calculate the azimuth decompression phase: according to the radar system parameters, calculate the reference slant range corresponding to each distance gate each column , and calculate the azimuth signal decompression phase ; Step three, azimuth echo reconstruction: according to the four polarization channel data after pre-processing in step one, fast Fourier transform (FFT) is performed along each distance gate by column to obtain pre-processed signal azimuth spectrum data, and the azimuth spectrum data is multiplied by the azimuth decompression phase to obtain azimuth reconstruction echo spectrum data, and inverse fast Fourier transform (IFFT) is performed along each distance gate by column to obtain azimuth reconstruction echo data 、 、 、 ; Step four, time-varying ionospheric effect error phase estimation: according to the reconstructed echo data in the azimuth direction calculated in step three , , the argument is obtained by conjugate multiplication , , the Faraday rotation angle estimation value is obtained by smoothing , combined with the radar system parameters, the time-varying ionospheric effect error phase is calculated ; The step four is specifically: 4.1) Conjugate multiplication of azimuthally reconstructed echo data for RR and LL channels to take the argument : (25) where the argument is a two-dimensional real matrix of size , denotes the conjugate, is the argument operation taking complex numbers; denotes the RR channel azimuthal direction reconstructed echo data, denotes the LL channel azimuthal direction reconstructed echo data; 4.2) The argument obtained from the above calculation Using a rectangular smooth window to Smoothing is performed to obtain the estimated Faraday rotation angle. The result is the size Two-dimensional real matrix: (26) In the formula, Indicates to Use a window size of ( , Smoothing is performed using a smoothing window function, i.e., using... Coordinates of location ( , Centered on ), , , find the surrounding number Arrive Okay, number List to The mean of all values ​​in the column is used as For those near The elements on the edge of a two-dimensional matrix, i.e. , , , At this point, the element is calculated directly without smoothing. The value is used as the result at that coordinate. 4.3) Calculate the range bin signal frequency : (27) fs is the sampling rate; 4.4) Using the calculated Faraday rotation angle estimate and the distance to the signal frequency , the time-varying ionospheric effect error phase is calculated : (28) wherein denotes the distance-wise signal frequency the 1st frequency value in the one-dimensional array, denotes the distance-wise signal frequency the 1st frequency value in the one-dimensional array, the 1st frequency value in the one-dimensional array, denotes the time-varying ionospheric effect phase error the angle value at coordinate (1,1) in the two-dimensional matrix, denotes the reference slant range the angle value at coordinate (1,1) in the two-dimensional matrix, the angle value at coordinate (1,1) in the two-dimensional matrix, the angle value at coordinate (1,1) in the two-dimensional matrix, the angle value at coordinate (1,1) in the two-dimensional matrix, the angle value at coordinate (1,1) in the two-dimensional matrix, the angle value at coordinate (1,1) in the two-dimensional matrix, the angle value at coordinate (1,1) in the two-dimensional matrix, the angle value at coordinate (1,1) in the two-dimensional matrix, the angle value at coordinate (1,1) in the two-dimensional matrix, is a constant and , is a constant and , denotes the geomagnetic field strength parallel to the radar beam direction, in units of ; Step five, time-varying ionospheric effect error correction: according to the four polarization channel data azimuth direction reconstruction echo data calculated in step three, the fast Fourier transform (FFT) is performed along each azimuth sampling time by row to obtain the reconstruction echo range direction spectrum data, and the time-varying ionospheric effect error phase is multiplied by the reconstruction echo range direction spectrum data to obtain the corrected reconstruction echo range direction spectrum data The inverse fast Fourier transform (IFFT) is performed along each azimuth sampling time by row to obtain the corrected reconstruction echo data 、 、 、 ; Step six, obtaining corrected full image data: according to the reconstructed echo data corrected in step five, performing fast Fourier transform (FFT) along columns in each distance gate to obtain corrected reconstructed echo azimuth spectrum data, and multiplying the corrected reconstructed echo azimuth spectrum data by azimuth decompression phase in reverse obtaining corrected full image azimuth spectrum data, performing inverse fast Fourier transform (IFFT) along columns in each distance gate to obtain corrected full image data 、 、 、 ; Step seven, obtaining final corrected image data: according to the azimuth synthetic aperture point number calculated in step one , respectively cutting off the head and tail of each column of the four-polarization-channel-corrected full image data matrix , Obtaining final corrected image data , , , , which are all two-dimensional complex number matrices with a size of .

2. The method of claim 1, wherein, The step one is specifically: Four polarimetric channels data acquired by high orbit SAR , , , respectively: (1) (2) (3) (4) wherein represents the value of the coordinate (1,1) in the RR channel data matrix, represents the value of the coordinate (1, ) in the RR channel data matrix, represents the value of the coordinate ( ,1) in the RR channel data matrix, represents the value of the coordinate ( , ) in the RR channel data matrix; represents the value of the coordinate (1,1) in the RL channel data matrix, represents the value of the coordinate (1, ) in the RL channel data matrix, represents the value of the coordinate ( ,1) in the RL channel data matrix, represents the value of the coordinate ( , ) in the RL channel data matrix; represents the value of the coordinate (1,1) in the LR channel data matrix, represents the value of the coordinate (1, ) in the LR channel data matrix, represents the value of the coordinate ( ,1) in the LR channel data matrix, represents the value of the coordinate ( , ) in the LR channel data matrix; represents the value of the coordinate (1,1) in the LL channel data matrix, represents the value of the coordinate (1, ) in the LL channel data matrix, represents the value of the coordinate ( ,1) in the LL channel data matrix, represents the value of the coordinate ( , ) in the LL channel data matrix; 1.1) Calculation of the number of azimuth synthetic aperture points from the radar system parameters : (5) wherein denotes the radar system operating wavelength, denotes the reference slant range of the radar to the center point of the scene, denotes the azimuth antenna length, denotes the radar ground speed; denotes the maximum even number operation taking not greater than the maximum even number operation taking not greater than 1.2) The number of azimuth synthetic aperture points , zero-padded in the head and tail of each column of the four-polarization channel data matrix, respectively, and the number of zero-padded is , obtaining the pre-processed four-polarization channel data 、 、 、 , which are all expanded into two-dimensional complex matrices with a size of , and , respectively: (6) (7) (8) (9) In the formula, represents the value of the coordinate (m, 1) in the RR channel data matrix after zero padding, represents the value of the coordinate (m, 1) in the RR channel data matrix after zero padding, represents the value of the coordinate (m, 1) in the RR channel data matrix after zero padding, represents the value of the coordinate (m, 1) in the RR channel data matrix after zero padding, represents the value of the coordinate (m, 1) in the RR channel data matrix after zero padding; represents the value of the coordinate (m, 1) in the RL channel data matrix after zero padding, represents the value of the coordinate (m, 1) in the RL channel data matrix after zero padding, represents the value of the coordinate (m, 1) in the RL channel data matrix after zero padding, represents the value of the coordinate (m, 1) in the RL channel data matrix after zero padding, represents the value of the coordinate (m, 1) in the RL channel data matrix after zero padding; represents the value of the coordinate (m, 1) in the LR channel data matrix after zero padding, represents the value of the coordinate (m, 1) in the LR channel data matrix after zero padding, represents the value of the coordinate (m, 1) in the LR channel data matrix after zero padding, represents the value of the coordinate (m, 1) in the LR channel data matrix after zero padding, represents the value of the coordinate (m, 1) in the LR channel data matrix after zero padding; represents the value of the coordinate (m, 1) in the LL channel data matrix after zero padding, represents the value of the coordinate (m, 1) in the LL channel data matrix after zero padding, represents the value of the coordinate (m, 1) in the LL channel data matrix after zero padding, represents the value of the coordinate (m, 1) in the LL channel data matrix after zero padding, represents the value of the coordinate (m, 1) in the LL channel data matrix after zero padding.​​​​​​​​​​​​​​​​​​​​ 3. The method of claim 2, wherein, The step two is specifically: 2.1) Calculate the reference slant range corresponding to each column of each range gate according to the radar system parameters : (10) wherein denotes the speed of light; 2.2) Calculate the frequency of the zero-padded azimuth signal : (11) 2.3) Calculate azimuth signal decompression phase : (12) wherein represents azimuth signal frequency 1st frequency value in one-dimensional array, represents azimuth signal frequency 1st frequency value in one-dimensional array, represents azimuth signal frequency represents reference slant range slant range value at coordinate (1, 1) in two-dimensional matrix, represents reference slant range slant range value at coordinate (1, ) in two-dimensional matrix, represents reference slant range slant range value at coordinate (1, ) in two-dimensional matrix, represents reference slant range slant range value at coordinate (1, , ) in two-dimensional matrix.

4. The method of claim 3, wherein, The step three is specifically: 3.1) On the four pre-processed polarization channel data , , , , along each range gate by column to get the pre-processed signal azimuth spectrum data , , , : (13) (14) (15) (16) wherein represents the value of the coordinate (1,1) in the azimuth spectrum data of the RR channel pre-processed signal, represents the value of the coordinate (1, ) in the azimuth spectrum data of the RR channel pre-processed signal, represents the value of the coordinate ( ,1) in the azimuth spectrum data of the RR channel pre-processed signal, represents the value of the coordinate ( , ) in the range spectrum data of the RR channel; represents the value of the coordinate (1,1) in the azimuth spectrum data of the RL channel pre-processed signal, represents the value of the coordinate (1, ) in the azimuth spectrum data of the RL channel pre-processed signal, represents the value of the coordinate ( ,1) in the azimuth spectrum data of the RL channel pre-processed signal, represents the value of the coordinate ( , ) in the range spectrum data of the RL channel; represents the value of the coordinate (1,1) in the azimuth spectrum data of the LR channel pre-processed signal, represents the value of the coordinate (1, ) in the azimuth spectrum data of the LR channel pre-processed signal, represents the value of the coordinate ( ,1) in the azimuth spectrum data of the LR channel pre-processed signal, represents the value of the coordinate ( , ) in the range spectrum data of the LR channel; represents the value of the coordinate (1,1) in the azimuth spectrum data of the LL channel pre-processed signal, represents the value of the coordinate (1, ) in the azimuth spectrum data of the LL channel pre-processed signal, represents the value of the coordinate ( ,1) in the azimuth spectrum data of the LL channel pre-processed signal, represents the value of the coordinate ( , ) in the range spectrum data of the LL channel; represents performing a fast Fourier transform on each column of data of the two-dimensional matrix; 3.2) multiply the pre-processed signal azimuthal spectral data , , , by the azimuthal decompression phase to obtain the azimuthal reconstructed echo spectral data , , , : (17) (18) (19) (20) wherein the azimuthal signal decompression phase the value of the coordinate (1,1) in the two-dimensional matrix, the azimuthal signal decompression phase the value of the coordinate (1, ) in the two-dimensional matrix, the azimuthal signal decompression phase the value of the coordinate ( ,1) in the two-dimensional matrix, the azimuthal signal decompression phase the value of the coordinate ( , ) in the two-dimensional matrix; j denotes the imaginary unit, i.e. ; 3.3) Azimuth reconstruction of the echo spectrum data , , , , along each range gate, a fast inverse Fourier transform (IFFT) is performed by column to obtain the azimuth reconstructed echo data , , , : (21) (22) (23) (24) wherein represents the value of the coordinate (1,1) in the RR channel azimuthally reconstructed echo data, represents the value of the coordinate (1, ) in the RR channel azimuthally reconstructed echo data, represents the value of the coordinate ( ,1) in the RR channel azimuthally reconstructed echo data, represents the value of the coordinate ( , ) in the RR channel azimuthally reconstructed echo data; represents the value of the coordinate (1,1) in the RL channel azimuthally reconstructed echo data, represents the value of the coordinate (1, ) in the RL channel azimuthally reconstructed echo data, represents the value of the coordinate ( ,1) in the RL channel azimuthally reconstructed echo data, represents the value of the coordinate ( , ) in the RL channel azimuthally reconstructed echo data; represents the value of the coordinate (1,1) in the LR channel azimuthally reconstructed echo data, represents the value of the coordinate (1, ) in the LR channel azimuthally reconstructed echo data, represents the value of the coordinate ( ,1) in the LR channel azimuthally reconstructed echo data, represents the value of the coordinate ( , ) in the LR channel azimuthally reconstructed echo data; represents the value of the coordinate (1,1) in the LL channel azimuthally reconstructed echo data, represents the value of the coordinate (1, ) in the LL channel azimuthally reconstructed echo data, represents the value of the coordinate ( ,1) in the LL channel azimuthally reconstructed echo data, represents the value of the coordinate ( , ) in the LL channel azimuthally reconstructed echo data; represents performing a fast inverse Fourier transform on each column of a two-dimensional matrix.

5. The method of claim 4, wherein, The step five is specifically: 5.1) Azimuthal reconstruction of echo data for the four polarized channels 、 、 、 , along each azimuthal sampling instant, a fast Fourier transform (FFT) is performed in rows to obtain reconstructed echo range spectral data 、 、 、 : (29) (30) (31) (32) wherein, represents the value of the RR channel-reconstructed echo range profile data at coordinate (1, 1), represents the value of the RR channel-reconstructed echo range profile data at coordinate (1, ), represents the value of the RR channel-reconstructed echo range profile data at coordinate ( , 1), represents the value of the RR channel-reconstructed echo range profile data at coordinate ( , ), represents the value of the RL channel-reconstructed echo range profile data at coordinate (1, 1), represents the value of the RL channel-reconstructed echo range profile data at coordinate (1, ), represents the value of the RL channel-reconstructed echo range profile data at coordinate ( , 1), represents the value of the RL channel-reconstructed echo range profile data at coordinate ( , ), represents the value of the LR channel-reconstructed echo range profile data at coordinate (1, 1), represents the value of the LR channel-reconstructed echo range profile data at coordinate (1, ), represents the value of the LR channel-reconstructed echo range profile data at coordinate ( , 1), represents the value of the LR channel-reconstructed echo range profile data at coordinate ( , ), represents the value of the LL channel-reconstructed echo range profile data at coordinate (1, 1), represents the value of the LL channel-reconstructed echo range profile data at coordinate (1, ), represents the value of the LL channel-reconstructed echo range profile data at coordinate ( , 1), represents the value of the LL channel-reconstructed echo range profile data at coordinate ( , ), represents performing a fast Fourier transform on each row of data of a two-dimensional matrix; 5.2) multiply the reconstructed echo range profile data , , , by the time-varying ionospheric effect error phase to obtain corrected reconstructed echo range profile data , , , : (33) (34) (35) (36) wherein representing the time-varying ionospheric effect error phase the value of the coordinate (1,1) in the two-dimensional matrix, representing the time-varying ionospheric effect error phase the value of the coordinate (1, ) in the two-dimensional matrix, representing the time-varying ionospheric effect error phase the value of the coordinate ( ,1) in the two-dimensional matrix, representing the time-varying ionospheric effect error phase the value of the coordinate ( , ) in the two-dimensional matrix; 5.3) Reconstructing the corrected echo range profile data 、 、 、 , performing inverse fast Fourier transform (IFFT) on each row of the corrected echo range profile data to obtain the corrected echo data 、 、 、 : (37) (38) (39) (40) wherein represents the value of the coordinate (1,1) in the reconstructed echo data after correction of the RR channel, represents the value of the coordinate (1, ) in the reconstructed echo data after correction of the RR channel, represents the value of the coordinate ( ,1) in the reconstructed echo data after correction of the RR channel, represents the value of the coordinate ( , ) in the reconstructed echo data after correction of the RR channel; represents the value of the coordinate (1,1) in the reconstructed echo data after correction of the RL channel, represents the value of the coordinate (1, ) in the reconstructed echo data after correction of the RL channel, represents the value of the coordinate ( ,1) in the reconstructed echo data after correction of the RL channel, represents the value of the coordinate ( , ) in the reconstructed echo data after correction of the RL channel; represents the value of the coordinate (1,1) in the reconstructed echo data after correction of the LR channel, represents the value of the coordinate (1, ) in the reconstructed echo data after correction of the LR channel, represents the value of the coordinate ( ,1) in the reconstructed echo data after correction of the LR channel, represents the value of the coordinate ( , ) in the reconstructed echo data after correction of the LR channel; represents the value of the coordinate (1,1) in the reconstructed echo data after correction of the LL channel, represents the value of the coordinate (1, ) in the reconstructed echo data after correction of the LL channel, represents the value of the coordinate ( ,1) in the reconstructed echo data after correction of the LL channel, represents the value of the coordinate ( , ) in the reconstructed echo data after correction of the LL channel; represents a fast inverse Fourier transform of each row of a two-dimensional matrix.

6. The method of claim 5, wherein, The step six is specifically: 6.1) Reconstructing the corrected echo data 、 、 、 , along each range gate, a fast Fourier transform (FFT) is performed on the columns to obtain the corrected reconstructed echo azimuthal spectral data 、 、 、 : (41) (42) (43) (44) In the formula, represents the value of the coordinate (1, 1) in the azimuth direction spectral data of the reconstructed echo after RR channel correction, represents the value of the coordinate (1, ) in the azimuth direction spectral data of the reconstructed echo after RR channel correction, represents the value of the coordinate ( , 1) in the azimuth direction spectral data of the reconstructed echo after RR channel correction, represents the value of the coordinate ( , ) in the range direction spectral data of the reconstructed echo after RR channel correction; represents the value of the coordinate (1, 1) in the azimuth direction spectral data of the reconstructed echo after RL channel correction, represents the value of the coordinate (1, ) in the azimuth direction spectral data of the reconstructed echo after RL channel correction, represents the value of the coordinate ( , 1) in the azimuth direction spectral data of the reconstructed echo after RL channel correction, represents the value of the coordinate ( , ) in the range direction spectral data of the reconstructed echo after RL channel correction; represents the value of the coordinate (1, 1) in the azimuth direction spectral data of the reconstructed echo after LR channel correction, represents the value of the coordinate (1, ) in the azimuth direction spectral data of the reconstructed echo after LR channel correction, represents the value of the coordinate ( , 1) in the azimuth direction spectral data of the reconstructed echo after LR channel correction, represents the value of the coordinate ( , ) in the range direction spectral data of the reconstructed echo after LR channel correction; represents the value of the coordinate (1, 1) in the azimuth direction spectral data of the reconstructed echo after LL channel correction, represents the value of the coordinate (1, ) in the azimuth direction spectral data of the reconstructed echo after LL channel correction, represents the value of the coordinate ( , 1) in the azimuth direction spectral data of the reconstructed echo after LL channel correction, represents the value of the coordinate ( , ) in the range direction spectral data of the reconstructed echo after LL channel correction; represents performing fast Fourier transform on each column of data of the two-dimensional matrix; 6.2) Reconstruct the corrected echo azimuthal spectral data , , , , multiply by the azimuthal decompression phase to obtain the corrected full image azimuthal spectral data , , , : (45) (46) (47) (48) 6.3) On the corrected full image azimuthal spectral data 、 、 、 , a fast inverse Fourier transform IFFT is performed along each range gate by column to obtain corrected full image data 、 、 、 : (49) (50) (51) (52) wherein represents the value of the coordinate (1,1) in the full image data after correction of the RR channel, represents the value of the coordinate (1, ) in the full image data after correction of the RR channel, represents the value of the coordinate ( ,1) in the full image data after correction of the RR channel, represents the value of the coordinate ( , ) in the full image data after correction of the RR channel; represents the value of the coordinate (1,1) in the full image data after correction of the RL channel, represents the value of the coordinate (1, ) in the full image data after correction of the RL channel, represents the value of the coordinate ( ,1) in the full image data after correction of the RL channel, represents the value of the coordinate ( , ) in the full image data after correction of the RL channel; represents the value of the coordinate (1,1) in the full image data after correction of the LR channel, represents the value of the coordinate (1, ) in the full image data after correction of the LR channel, represents the value of the coordinate ( ,1) in the full image data after correction of the LR channel, represents the value of the coordinate ( , ) in the full image data after correction of the LR channel; represents the value of the coordinate (1,1) in the full image data after correction of the LL channel, represents the value of the coordinate (1, ) in the full image data after correction of the LL channel, represents the value of the coordinate ( ,1) in the full image data after correction of the LL channel, represents the value of the coordinate ( , ) in the full image data after correction of the LL channel; represents a fast inverse Fourier transform of each column of the two-dimensional matrix.

7. The method of claim 6, wherein, The step seven is specifically: (53) (54) (55) (56) In the formula, represents the value of the coordinate (i, 1) in the full image data matrix after correction of the RR channel, represents the value of the coordinate (i, 1) in the full image data matrix after correction of the RR channel, represents the value of the coordinate (i, 1) in the full image data matrix after correction of the RR channel, represents the value of the coordinate (i, 1) in the full image data matrix after correction of the RR channel, represents the value of the coordinate (i, 1) in the full image data matrix after correction of the RR channel, represents the value of the coordinate (i, 1) in the full image data matrix after correction of the RL channel, represents the value of the coordinate (i, 1) in the full image data matrix after correction of the RL channel, represents the value of the coordinate (i, 1) in the full image data matrix after correction of the RL channel, represents the value of the coordinate (i, 1) in the full image data matrix after correction of the RL channel, represents the value of the coordinate (i, 1) in the full image data matrix after correction of the RL channel, represents the value of the coordinate (i, 1) in the full image data matrix after correction of the LR channel, represents the value of the coordinate (i, 1) in the full image data matrix after correction of the LR channel, represents the value of the coordinate (i, 1) in the full image data matrix after correction of the LR channel, represents the value of the coordinate (i, 1) in the full image data matrix after correction of the LR channel, represents the value of the coordinate (i, 1) in the full image data matrix after correction of the LR channel, represents the value of the coordinate (i, 1) in the full image data matrix after correction of the LL channel, represents the value of the coordinate (i, 1) in the full image data matrix after correction of the LL channel, represents the value of the coordinate (i, 1) in the full image data matrix after correction of the LL channel, represents the value of the coordinate (i, 1) in the full image data matrix after correction of the LL channel, represents the value of the coordinate (i, 1) in the full image data matrix after correction of the LL channel, ​​​​​​​​​​​​​​​​​​​​

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