GEO SAR time-varying ionospheric error compensation method based on maximum contrast self-focusing

Abstract

The application discloses a GEO SAR time-varying ionosphere error compensation method based on maximum contrast self-focusing, and belongs to the technical field of GEO SAR (Geosynchronous Earth Orbit Synthetic Aperture Radar). The method selects distance line signals from a GEO SAR image, the distance line signals are the signals with the same distance time in the azimuth direction, the average power of each distance line signal in the image is calculated, a part of the distance line signals are selected, then the contrast of the SAR image is used to iteratively estimate the quadratic phase error coefficient, the cubic phase error coefficient is iteratively estimated based on the quadratic phase error coefficient, and finally the obtained quadratic and cubic phase error coefficients are used for phase compensation of the original SAR image, so that the SAR image affected by the time-varying ionosphere is accurately compensated. Experiments prove that the contrast of the compensated SAR image is improved by the method, and the compensated image is good, and is close to the image not affected by the time-varying ionosphere.

Description

Technical Field

[0001] This invention relates to the field of ionospheric error compensation for spaceborne synthetic aperture radar, specifically to a time-varying ionospheric error compensation method for geostationary Earth Orbit Synthetic Aperture Radar (GEO SAR). Background Technology

[0002] Synthetic Aperture Radar (SAR) is a high-resolution microwave imaging system with features such as all-weather, all-day, and wide-area Earth observation. Therefore, SAR systems have unique advantages in disaster monitoring, environmental monitoring, marine monitoring, resource exploration, and military applications.

[0003] Currently, the vast majority of SAR satellites are low-Earth orbit (LEO) SAR satellites. Their long revisit times, narrow mapping bands, and small coverage areas are no longer sufficient to meet the requirements for continuous mapping of specific areas. Therefore, GEO SAR has emerged. A single GEO SAR satellite can cover one-third of the Earth's surface, and its revisit time is even less than one day. Based on its appropriate orbital position, it can conduct continuous reconnaissance and surveillance of a designated geographical area. Due to its extremely high orbital altitude, GEO SAR has a very long synthetic aperture time, typically reaching 10^6 seconds. 2 ~10 3 The ionosphere exhibits strong time-varying characteristics within the synthetic aperture time, causing azimuth phase errors in GEO SAR and thus affecting imaging. Secondary and tertiary phase errors can cause defocusing, resulting in decreased contrast in the defocused image.

[0004] On June 27, 2017, CN106896349A disclosed a two-dimensional space-varying phase error compensation method for inverse synthetic aperture radar (ISAR) of maneuvering targets based on maximum contrast. By establishing a phase error model, the parameters of the compensation term for the space-varying phase error corresponding to maximizing image contrast are solved by the cyclic gradient method, and the solved compensation term is used to compensate for the two-dimensional space-varying phase error of ISAR for maneuvering targets.

[0005] The invention patent application with publication number CN116243258A disclosed on June 9, 2023, an adaptive error estimation and compensation method for GEO SAR. The method involves two-dimensional block division and full synthetic aperture division. Each sub-aperture and sub-block is imaged using the spectral analysis algorithm (SPECAN). Each image is discretely windowed. Each image after discrete windowing is corrected for amplitude and phase errors. Then, the method of extracting the envelope of strong points is used to correct the amplitude error, and the phase gradient subfocusing algorithm (PGA) is used to correct the phase error.

[0006] In existing technologies, the maximum contrast autofocus algorithm is used to compensate for the secondary phase error caused by the background ionosphere. A SAR image can be viewed as the product of the target scattering coefficient and the point spread function (PSF). The PSF is a sinc function; under the influence of dispersion, the PSF broadens due to the phase error, resulting in reduced image contrast. In defocused images, the difference between the target brightness and the surrounding background brightness is small, leading to low contrast. The maximum contrast autofocus algorithm estimates and compensates for this secondary phase error based on this, finding a suitable matched filter function to achieve image focusing.

[0007] Currently, the time-varying ionosphere causes secondary and tertiary phase errors in the GEO SAR azimuth direction, leading to image defocusing, thus requiring compensation. However, existing technologies have the following problems: the established phase error models comprehensively consider spatially varying phase errors, or only primarily consider phase error compensation caused by the background ionosphere, without further research on the secondary and tertiary phase errors in the GEO SAR azimuth direction caused by the time-varying ionosphere; furthermore, the maximum contrast autofocus algorithm used in the range direction only compensates for the secondary phase error, not the tertiary phase error; and existing compensation schemes for the GEO SAR azimuth error caused by the time-varying ionosphere are insufficient and lack accuracy. Summary of the Invention

[0008] The second phase error in the azimuth direction of GEO SAR caused by the time-varying ionosphere can cause image defocusing, and the third phase error also affects SAR imaging. However, existing technologies do not adequately consider this issue, resulting in insufficient compensation accuracy. To address this problem, this invention provides a GEO SAR time-varying ionospheric error compensation method based on maximum contrast autofocus. By utilizing the contrast of the SAR image, the second and third phase error coefficients are iteratively estimated, thereby achieving accurate compensation for the SAR image affected by the time-varying ionosphere.

[0009] This invention provides a time-varying ionospheric error compensation method for GEO SAR based on maximum contrast autofocus, comprising the following steps:

[0010] Step 1) Select range line signals from the SAR image acquired by GEO SAR; the range line signals refer to azimuth signals with the same distance and time. Calculate the average power of each range line signal and sort them from largest to smallest according to the power value. Select the range line signal that is sorted first according to a preset ratio a. At the same time, set the initial values ​​of the secondary phase error coefficient k2, the cubic phase error coefficient k3, and the iteration step size Δk2 and Δk3.

[0011] Step 2) Perform secondary phase error compensation on the azimuth signal, including: (2.1) Decompress the azimuth of the acquired range line signal; (2.2) Perform secondary phase error compensation on the decompressed signal using k2; (2.3) Compress the azimuth of the compensated signal; (2.4) Adjust the iteration step size Δk2 according to the image contrast before and after compensation, and update k2; (2.5) If the updated k2 is less than the set threshold, stop the iteration and continue to step 3, otherwise continue to step 2.1 for iteration; wherein, the image contrast is calculated by the selected range line signal; the initial value of the image contrast during secondary phase error compensation is calculated based on the selected range line signal in the original image;

[0012] Step 3) Perform tertiary phase error compensation on the azimuth signal after secondary phase error compensation, including: (3.1) Decompress the azimuth of the range line signal selected in the current image; (3.2) Perform tertiary phase error compensation on the decompressed signal using k3; (3.3) Compress the compensated signal in azimuth; (3.4) Adjust the iteration step size Δk3 according to the image contrast before and after compensation, and update k3; (3.5) If the updated k3 is less than the set threshold, stop the iteration; otherwise, continue to step 3.1 for iteration; wherein, the initial value of the image contrast when performing tertiary phase error compensation is calculated based on the range line signal selected in the image after secondary phase error compensation.

[0013] Step 4) Use the final secondary phase error coefficient obtained in Step 2 iteration and the final tertiary phase error coefficient obtained in Step 3 iteration to perform secondary and tertiary phase error compensation on the original SAR image obtained in Step 1.

[0014] Compared with existing technologies, the advantages and positive effects of the method of this invention are as follows: This method utilizes the principle of optimal contrast to simultaneously compensate for the second and third phase errors in the azimuth direction of GEO SAR caused by the time-varying ionosphere, achieving accurate error compensation for SAR images affected by the time-varying ionosphere. Experimental simulations have demonstrated that the method of this invention can improve the contrast of the compensated SAR image, and the compensated image quality is good, approaching that of images unaffected by the time-varying ionosphere. Attached Figure Description

[0015] Figure 1 This is a flowchart of the GEO SAR time-varying ionospheric compensation method according to an embodiment of the present invention;

[0016] Figure 2 The following are experimental results of urban scenes in embodiments of the present invention: (a) is a figure unaffected by the time-varying ionosphere, (b) is a figure affected by the time-varying ionosphere, and (c) is a figure after compensating for the time-varying ionosphere error using the method of the present invention.

[0017] Figure 3 The experimental results of the mountain scene in the embodiments of the present invention are shown in Figure (a), which is unaffected by the time-varying ionosphere; Figure (b), which is affected by the time-varying ionosphere; and Figure (c), which is after compensating for the time-varying ionosphere error using the method of the present invention. Detailed Implementation

[0018] To facilitate understanding and implementation of the present invention by those skilled in the art, the present invention will be further described in detail below with reference to the accompanying drawings and embodiments.

[0019] First, this invention analyzes the variation of GEO SAR image contrast with azimuth secondary and tertiary phase errors. It finds that when the tertiary phase error is less than 600°, the SAR image contrast monotonically decreases with increasing azimuth secondary phase error; and when the secondary phase error is less than 180°, the SAR image contrast monotonically decreases with increasing azimuth tertiary phase error. Based on this, this invention provides a GEO SAR time-varying ionospheric error compensation method based on maximum contrast autofocus. Through iteration, this method optimizes the contrast of images whose contrast is reduced due to azimuth secondary and tertiary phase errors.

[0020] According to the ionospheric signal propagation theory, when a signal passes through the ionosphere, the SAR azimuth signal experiences a phase error due to the ionospheric effect. for:

[0021]

[0022] Where TEC(t) is the total electron content of the ionosphere, and the unit is TECU, 1 TECU = 10 16 m -2 ; t is the azimuth time; K is a constant, K = 40.28; f c is the carrier frequency; c is the speed of light.

[0023] Polynomial expansion of TEC(t) yields TEC(t) = TEC0 + k1t + k2t 2 +k3t 3 +..., where TEC0 is the constant total number of electrons in the ionosphere, k i It is the phase error coefficient of the i-th time.

[0024] The GEOSAR time-varying ionospheric error compensation method of this invention, as shown in the embodiments, is as follows: Figure 1 As shown, the specific steps are as follows:

[0025] Step 1: Select the range line signal from the SAR image acquired by GEO SAR.

[0026] SAR images affected by the time-varying ionosphere are acquired from GEO SAR and analyzed. Range line signals in the images refer to azimuth signals with the same range-time. The average power of each range line signal in the image is calculated; the average power is the mathematical expectation of the azimuth signal power along the entire range line. All range line signals in the SAR image are sorted from largest to smallest average power, and then the range line signals with the highest average power values ​​are selected.

[0027] Set the initial quadratic phase error coefficient k2, the cubic phase error coefficient k3, and the iteration step size Δk2 and Δk3.

[0028] It should be noted that when selecting distance line signals in this invention, the quantity can be selected within the range of 5%-20%. Selecting a proportion of distance line signals within this range is beneficial for highlighting the target and eliminating interference information.

[0029] Step 2: Azimuth Decompression. In the first iteration, a Fourier transform is performed on the range line signal obtained in Step 1. The resulting signal is multiplied by a decompression factor to complete azimuth decompression, followed by an inverse Fourier transform. In subsequent iterations, a Fourier transform is performed on the range line signal obtained in Step 4. The resulting signal is multiplied by a decompression factor to complete azimuth decompression, followed by an inverse Fourier transform.

[0030] Step 3: Perform secondary phase error compensation on the signal that has undergone inverse Fourier transform in Step 2.

[0031] The formula for using k2 to perform secondary phase error compensation is as follows:

[0032]

[0033] Step 4: Azimuth Compression. Perform an azimuth-to-Fourier transform on the compensated signal, multiply the resulting signal by the azimuth compression factor, and then perform an inverse Fourier transform.

[0034] Step 5: Contrast comparison and iteration.

[0035] The image contrast C is defined as follows:

[0036]

[0037] Where I is the amplitude of the image, I 2 Let E() represent the power of the image, and E(I) represent the expected value. 2 ) represents the mathematical expectation of the image power. This indicates the calculation of the standard deviation of the image.

[0038] Compare the contrast C of the currently compensated image. iThe contrast C of the image before compensation, i.e., after the previous iteration. i-1 In this embodiment of the invention, the image contrast is calculated based on the selected distance line signal. Let the initial image contrast be C0, where C0 is the contrast calculated from the power of the selected original distance line signal. The quadratic phase error coefficient k2 is updated based on the comparison result. If the contrast increases, the iteration step size Δk2 remains unchanged, and coefficient k2 is updated using this iteration step size. If the contrast decreases, the iteration step size Δk2 is halved and its inverse is taken, and coefficient k2 is updated again. Steps two through five are repeated until the quadratic phase error coefficient is less than a pre-defined threshold (i.e., the threshold value), at which point the iteration stops. The quadratic phase error coefficient used in the last iteration is saved.

[0039] Step Six: Azimuth Decompression. Perform a Fourier transform on the range line signal obtained after the second phase error compensation in Step Five, multiply the resulting signal by the decompression factor to complete the azimuth decompression, and then perform an inverse Fourier transform.

[0040] Step 7: Perform triple phase error compensation using k3. The triple phase error compensation formula is as follows:

[0041]

[0042] Step 8: Azimuth Compression. Perform an azimuth-to-Fourier transform on the compensated signal, multiply the resulting signal by the azimuth compression factor, and then perform an inverse Fourier transform.

[0043] Step 9: Contrast Comparison and Iteration. Compare the contrast C of the current image. i Contrast C of the image from the previous iteration i-1 The initial contrast ratio compared after the first iteration is labeled C. 0,s C 0,s To compensate for the contrast of the distance line signal after the second phase error, if the contrast increases, keep the iteration step size Δk3 unchanged and update the coefficient k3 by Δk3. If the contrast decreases, take half of the original iteration step size Δk3 and its opposite, then update k3. Repeat steps six through nine until the third phase error coefficient k3 is less than a given threshold, then stop the iteration. Save the third phase error coefficient used in the last iteration.

[0044] Step 10: Original Image Compensation. Using the finally obtained secondary phase error coefficient k2 and cubic phase error coefficient k3, compensate the original image obtained in Step 1 according to the formulas given in Steps 3 and 7.

[0045] For different acquired GEO SAR images, the optimal secondary phase error coefficient and the third phase error coefficient are obtained through steps one to nine above. Then, the obtained two error coefficients are used to compensate for the original SAR image.

[0046] This invention uses ALOS PALSAR2 urban and mountain scene data for simulation verification, introducing time-varying ionospheric errors through simulation. The parameter f is set... c =1250MHz, T s =415s, T s The time for synthesizing the aperture is given. In the simulation experiments of this invention, two different time-varying ionospheric error scenarios are introduced to demonstrate the second and third phase error coefficients obtained using the method of this invention under the two scenarios, as well as the phase error results, image contrast, etc., as shown in Tables 1-4.

[0047] Table 1 Phase Error in Urban Scenarios

[0048] Urban Scene <![CDATA[k2(TECU / s 2 )]]> <![CDATA[k3(TECU / s 3 )]]> <![CDATA[k2(TECU / s 2 )]]> <![CDATA[k3(TECU / s 3 ) <!-- 4 -->]]> original <![CDATA[1*10 -5 ]]> <![CDATA[5*10 -8 ]]> <![CDATA[5*10 -6 ]]> <![CDATA[5*10 -9 ]]> estimate <![CDATA[1.07*10 -5 ]]> <![CDATA[4.79*10 -8 ]]> <![CDATA[4.96*10 -6 ]]> <![CDATA[5.33*10 -9 ]]> Original phase error 332.99° 345.47° 166.49° 34.55° Residual phase error 23.31° 14.51° 1.33° 2.28°

[0049] Table 2 Phase Error in Mountain Scenes

[0050] Mountain Scene <![CDATA[k2(TECU / s 2 )]]> <![CDATA[k3(TECU / s 3 )]]> <![CDATA[k2(TECU / s 2 )]]> <![CDATA[k3(TECU / s 3 )]]> original <![CDATA[1*10 -5 ]]> <![CDATA[5*10 -8 ]]> <![CDATA[5*10 -6 ]]> <![CDATA[5*10 -9 ]]> estimate <![CDATA[1.02*10 -5 ]]> <![CDATA[5.13*10 -8 ]]> <![CDATA[5.3*10 -6 ]]> <![CDATA[5*10 -9 ]]> Original phase error 332.99° 345.47° 166.49° 34.55° Residual phase error 6.659° 8.982° 10.988° 0

[0051] Tables 1 and 2 present the estimated phase error coefficients and residual phase error results for urban and mountain scenes under different quadratic and cubic phase error coefficients, respectively. Generally, when the quadratic phase error is less than 45° and the cubic phase error is less than 22.5°, the phase error can be ignored; therefore, the compensated residual phase error meets the requirements. In the tables, the "original" row refers to the preset values ​​during simulation, and the "estimated" row refers to the values ​​calculated by this invention. The original phase error refers to the phase error of the image before compensation, and the residual phase error is the phase error after compensation using the method of this invention.

[0052] Table 3 Image contrast before and after phase error compensation in urban scenes.

[0053] Urban Scene <![CDATA[k2=1*10 -5 ,k3=5*10 -8 ]]> <![CDATA[k2=5*10 -6 ,k3=5*10 -9 ]]> Original image contrast 244.17 255.28 Contrast after compensating for quadratic phase error 259.80 266.43 Contrast after compensating for second and third phase errors 265.02 266.44

[0054] Table 4 Image contrast before and after phase error compensation in mountain scenes

[0055] Mountain Scene <![CDATA[k2=1*10 -5 ,k3=5*10 -8 ]]> <![CDATA[k2=5*10 -6 ,k3=5*10 -9 ]]> Original image contrast 101.87 104.01 Contrast after compensating for quadratic phase error 103.74 105.05 Contrast after compensating for second and third phase errors 105.06 105.07

[0056] Tables 3 and 4 show the changes in image contrast before and after compensation under two sets of phase error coefficients in two different scenarios. From the contrast results in Tables 3 and 4, it can be seen that the image contrast is improved after compensation.

[0057] like Figure 2 (a) and Figure 3 As shown in (a), the images are of a city and a mountain that are not affected by the time-varying ionosphere, respectively. The size is 800 pixels in the azimuth direction and 400 pixels in the range direction. The horizontal direction is the range direction and the vertical direction is the azimuth direction. Figure 2 (b) and (c) show urban scenes affected by the time-varying ionosphere (k2 = 1 * 10⁻⁶). -5 k3 = 5 * 10 -8 The images affected by the time-varying ionospheric error and the images after compensation show that the compensated images are refocused. Figure 3 In the image, (b) and (c) represent the mountain scene affected by the time-varying ionosphere (k2 = 1 * 10⁻⁶). -5 k3 = 5 * 10 -8 The image affected by the time-varying ionospheric error and the image after compensation for the time-varying ionospheric error are shown. Similarly, the compensated image is refocused.

[0058] Except for the technical features described in the specification, all other technologies are known to those skilled in the art. Descriptions of well-known components and technologies are omitted in this invention to avoid redundancy and unnecessary limitation. The embodiments described above do not represent all embodiments consistent with this application. Various modifications or variations that can be made by those skilled in the art without creative effort based on the technical solutions of this invention are still within the protection scope of this invention.

Claims

1. A method for compensating time-varying ionospheric errors in GEO SAR based on maximum contrast autofocus, characterized in that, Includes the following steps: First, we analyzed the variation of GEO SAR image contrast with azimuth secondary and tertiary phase errors. We found that when the tertiary phase error is less than 600°, the SAR image contrast decreases monotonically with the increase of the azimuth secondary phase error. When the secondary phase error is less than 180°, the SAR image contrast decreases monotonically with the increase of the azimuth tertiary phase error. Then perform the following steps: 1) Range line signals are selected from SAR images acquired by GEO SAR; the range line signals refer to azimuth signals with the same distance and time. The average power of each range line signal is calculated and sorted from largest to smallest power value. The range line signal with the highest power value is selected according to a preset ratio 'a'. At the same time, a secondary phase error coefficient is set. Third phase error coefficient and iteration step size and The initial value; 2) Perform secondary phase error compensation on the azimuth signal, including: (2.1) Decompressing the azimuth of the acquired range line signal; (2.2) Using the decompressed signal... Perform secondary phase error compensation; (2.3) Perform azimuth compression on the compensated signal; (2.4) Adjust the iteration step size according to the image contrast before and after compensation. ,renew (2.5) If the updated If the value is less than the set threshold, stop the iteration and continue to step 3; otherwise, continue to step 2.1 for iteration. The image contrast is calculated from the selected distance line signal; the initial value of the image contrast during secondary phase error compensation is calculated based on the selected distance line signal in the original image. 3) Perform tertiary phase error compensation on the azimuth signal after secondary phase error compensation, including: (3.1) performing azimuth decompression on the range line signal selected in the current image; (3.2) using the azimuth decompressed signal... Perform three phase error compensations; (3.3) Perform azimuth compression on the compensated signal; (3.4) Adjust the iteration step size according to the image contrast before and after compensation. ,renew (3.5) If the updated If the value is less than the set threshold, stop the iteration; otherwise, continue to step 3.1 for iteration. The initial value of image contrast during the third phase error compensation is calculated based on the distance line signal selected in the image after the second phase error compensation. 4) Use the final secondary phase error coefficient obtained in step 2 iteration and the final tertiary phase error coefficient obtained in step 3 iteration to perform secondary and tertiary phase error compensation on the original SAR image obtained in step 1.

2. The method according to claim 1, characterized in that, In step 1, the value of the ratio 'a' is set to be between 5% and 20%.

3. The method according to claim 1, characterized in that, In steps 2 and 3, azimuth decompression of the distance line signal refers to first performing an azimuth-to-Fourier transform on the distance line signal, then multiplying it by a decompression factor, and finally performing an inverse Fourier transform on the resulting signal; azimuth compression of the compensated signal refers to first performing an azimuth-to-Fourier transform on the compensated signal, then multiplying it by an azimuth compression factor, and finally performing an inverse Fourier transform on the resulting signal.

4. The method according to claim 1, characterized in that, In step 2, the formula for secondary phase error compensation is as follows: ； In step 3, the formula for performing three phase error compensations is as follows: ； in, The phase error of the azimuth signal in the SAR image caused by the ionosphere is represented by a constant K = 40.

28. It is a direction in time. It's the speed of light. For carrier frequency.

5. The method according to claim 1, characterized in that, In steps 2 and 3, the iteration step size is adjusted. or The method is as follows: compare the image contrast before and after compensation; if the contrast increases, keep the iteration step size unchanged and update the quadratic phase error coefficient. or third phase error coefficient Increase or ; If the contrast decreases, update the iteration step size to half of the current iteration step size and take the inverse, then update with the updated iteration step size. or .

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