Smoothing Window Design Method for Ionospheric Scintillation Error Compensation in Spaceborne Full-Polarimetric SAR

Abstract

The present invention provides a method for designing a smoothing window in the compensation of ionospheric scintillation errors for spaceborne full-polarization SAR, including the following steps: Step 1: Decompress to the ionospheric height; Step 2: Estimate the magnitude of the Faraday rotation angle; Step 3: Estimate the ionospheric scintillation phase; Step 4: Compensate the scintillation errors of the original image; Step 5: Select the best result of mean filtering; Step 6: Design a parallelogram filtering window; Step 7: Compensate the scintillation errors of the original image; Step 8: Select the best result. The present invention considers the correlation of spatially-varying scintillation phases, designs a parallelogram filtering window, improves the estimation accuracy of the scintillation phase, and achieves a better effect of compensating ionospheric scintillation errors.

Description

Technical Field

[0001] The present invention provides a method for designing a smoothing window in ionospheric scintillation error compensation of spaceborne full-polarization SAR, belonging to the field of synthetic aperture radar imaging. Background Art

[0002] Synthetic Aperture Radar (SAR for short) is a microwave active imaging radar that can achieve two-dimensional high resolution all day and all weather. Due to different frequencies of radio waves, the penetration capabilities of electromagnetic signals vary greatly. Electromagnetic wave signals working in the low frequency band have better penetration performance for vegetation and soil, and are effective means for detecting hidden targets covered by shallow surface vegetation, ice and snow, etc.

[0003] However, due to the inherent characteristics of low-frequency band electromagnetic wave signals and the altitude of spaceborne SAR, the signal transmission process will inevitably be severely affected by the ionosphere, resulting in a decline in imaging quality. When radio signals propagate through the ionosphere, the existence of small-scale irregularities in the ionosphere will cause fluctuations in the Total Electron Content (TEC for short), resulting in irregular changes in the phase of azimuth signals, and ultimately leading to defocusing of the azimuth pulse compression waveform, that is, the ionospheric scintillation phenomenon. Since the electron density of small-scale irregularities in the ionosphere fluctuates randomly, the additional phase introduced into the SAR azimuth receiving signal is also random. Therefore, the research on scintillation phase compensation methods is more complex.

[0004] The full-polarization spaceborne SAR system transmits and receives electromagnetic waves with different polarization modes through two channels, and finally measures four groups of data HH, HV, VH, VV (representing the horizontal polarization transmitting and horizontal polarization receiving channel, horizontal polarization transmitting and vertical polarization receiving channel, vertical polarization transmitting and horizontal polarization receiving channel, vertical polarization transmitting and vertical polarization receiving channel respectively). Compared with traditional SAR, full-polarization SAR greatly improves the ability to obtain target scattering information. However, when electromagnetic waves pass through the ionosphere, in addition to being affected by the ionospheric scintillation effect, the polarization plane will also deflect, causing the polarization SAR scattering matrix to be distorted, that is, there is a Faraday rotation effect. The angle of polarization plane deflection is the Faraday rotation angle. The calculation formula of the Faraday rotation angle Ω is as follows:

[0005]

[0006] Where Q is a constant, and Q = 2.365×10 4 , the unit is A·m 2 / kg; f cis the carrier frequency; θ represents the angle between the direction of the Earth's magnetic field and the propagation direction of the radar electromagnetic wave (i.e., the direction of the antenna beam); B represents the Earth's magnetic field strength, with the unit of Wb / m 2 ; TEC is the total electron content on the path, representing the integral of the electron density along the propagation path of the electromagnetic wave, with the unit of TECU, and 1 TECU = 10 16 m -2 For the compensation of ionospheric scintillation errors, a scintillation error compensation method based on the estimation of the Faraday rotation angle can be adopted. First, use the relationship between the Faraday rotation angle and the total electron content of the ionosphere as shown in Equation (1) to calculate TEC. Then, estimate the ionospheric scintillation phase according to the relationship between the scintillation phase and TEC as shown in Equation (2), and further compensate for the ionospheric scintillation error.

[0007]

[0008] where K is a constant, K = 40.28; c is the speed of light in vacuum.

[0009] In the existing scintillation error compensation method based on the estimation of the Faraday rotation angle, the method proposed by Bickel & Bates is used to estimate the Faraday rotation angle first, and then use the relationship between the Faraday rotation angle and TEC to estimate TEC, and then estimate the ionospheric scintillation phase to compensate for the ionospheric scintillation error. Due to the system noise in the polarization system, noise suppression is required during the estimation of the Faraday rotation angle. In the traditional Bickel & Bates method, mean filtering is used to suppress noise, and a rectangular filtering window is used in the filtering process.

[0010] This method uses a rectangular window for mean filtering to suppress the noise in the estimation of the Faraday rotation angle. The shape and size of the filtering window are both restricted to a certain extent. Taking a larger filtering window can reduce the estimation error caused by noise, but the change in the scintillation phase itself will increase the estimation error; taking a smaller filtering window can reduce the error caused by the change in the scintillation phase, but the influence of noise increases. Eventually, it will lead to a certain deviation in the estimation of the Faraday rotation angle, affecting the estimation result of the ionospheric scintillation phase. Summary of the Invention

[0011] Aiming at the above technical problems, the present invention provides a design of a parallelogram filtering window to suppress the noise in the estimation process of the Faraday rotation angle, improve the compensation accuracy of the ionospheric scintillation error, and obtain a better compensation effect.

[0012] The specific technical solution is as follows:

[0013] A smoothing window design method for ionospheric scintillation error compensation in spaceborne full-polarization SAR, including the following steps:

[0014] Step 1: Decompress to the ionospheric altitude

[0015] Perform azimuth Fourier transform on the image data of each polarization channel, and multiply by the decompressed phase in the azimuth frequency domain.

[0016]

[0017] Among them, λ represents the wavelength, f a represents the azimuth frequency, V ref represents the equivalent velocity of the spaceborne radar, and R iono represents the slant range corresponding to the ionospheric height, that is:

[0018]

[0019] Among them, H iono represents the height where the ionosphere is located, θ represents the beam center viewing angle, Nr represents the number of range samples, Δr represents the range sampling point spacing, and i = 0, 1,..., Nr - 1;

[0020] Then perform inverse azimuth Fourier transform to obtain the azimuth time-domain signal at the ionospheric height.

[0021] Step 2: Estimate the magnitude of the Faraday rotation angle;

[0022] The full-polarization spaceborne SAR data is represented in the form of the following observation matrix Among them, M HH is the data obtained from the horizontal polarization transmit and horizontal polarization receive channels; M HV is the data obtained from the horizontal polarization transmit and vertical polarization receive channels; M VH is the data obtained from the vertical polarization transmit and horizontal polarization receive channels; M VV is the data obtained from the vertical polarization transmit and vertical polarization receive channels;

[0023] Convert the observation matrix from the linear polarization channel to the circular polarization basis, that is, calculate Z according to (4) 11 、Z 12 、Z 21 、Z 22 :

[0024]

[0025] Then calculate Z 21 Z 12 * , where * represents taking the complex conjugate, and process the Z 21 Z 12 * image using the mean filtering method of the traditional rectangular window to suppress noise;

[0026] Calculate the estimated value of the Faraday rotation angle using the processed result, and the formula is as follows:

[0027]

[0028] Obtain the estimated value of the Faraday rotation angle;

[0029] Step 3: Estimate the ionospheric scintillation phase. As can be seen from formula (1):

[0030]

[0031] Substitute the estimated value of the Faraday rotation angle obtained in the previous step into formula (6) to obtain the estimated value of TEC;

[0032] Then estimate the ionospheric scintillation phase according to formula (2).

[0033] Step 4: Compensate the original image scintillation error

[0034] Use the estimated value of the ionospheric scintillation phase obtained in the previous step to compensate the original images of the four channels; perform azimuth Fourier transform on the original image data of the four channels respectively, multiply by the compression phase Then perform inverse azimuth Fourier transform to obtain the compensated image; calculate the image entropy of the HH channel image after compensation; the formula for calculating the image entropy is as follows:

[0035]

[0036] where S(m,n) is the value at the position of pixel (m,n), the image size is M×N, m = 0, 1, … M - 1, n = 0, 1, … N - 1, and I is the total energy of the image, and the calculation formula is as follows:

[0037]

[0038] Step 5: Select the best result of mean filtering

[0039] Adjust the size of the mean filtering rectangular filter window, repeat steps 2 to 4, and select the rectangular window value when the image entropy after compensation is the smallest; calculate the two-dimensional autocorrelation function of the estimated value of the ionospheric scintillation phase under this condition.

[0040] Step 6: Design a parallelogram filter window

[0041] According to the graph when the autocorrelation function value in step 5 is 0.7, take the connection lines of the upper and lower, left and right endpoints as the two axes, and the angle passed by the axis of the connection line of the upper and lower endpoints rotating counterclockwise to the axis of the connection line of the left and right endpoints is the deflection angle. Take the deflection angle as the angle from the vertical side to the hypotenuse of the parallelogram filter window in the counterclockwise direction, take the axis length of the connection line of the upper and lower endpoints as the initial value of the vertical side length of the parallelogram filter window, and take the axis length of the connection line of the left and right endpoints as the initial value of the hypotenuse length of the parallelogram filter window.

[0042] Step 7: Compensate the original image flicker error

[0043] Repeat Step 2, estimate the Faraday rotation angle using Equation (5), and use the parallelogram filtering window obtained in the previous step to perform mean filtering on the Z 21 Z 12 * image to suppress noise;

[0044] Repeat Step 3, calculate the TEC according to Equation (6), and then estimate the ionospheric scintillation phase according to Equation (2);

[0045] Repeat Step 4 to compensate for the ionospheric scintillation error, perform compression processing on the compensated image to obtain the time-domain image after compensating for the scintillation error. Finally, calculate the image entropy of the compensated HH-channel image according to Equation (7).

[0046] Step 8: Select the best result;

[0047] Adjust the sizes of both sides of the parallelogram filtering window, and repeat Steps 2 to 4 to select the compensation result with the minimum image entropy of the compensated image as the final result.

[0048] The present invention considers the correlation of spatially varying scintillation phases, designs a parallelogram filtering window, improves the estimation accuracy of scintillation phases, and achieves a better ionospheric scintillation error compensation effect. Description of the Drawings

[0049] Figure 1 The full-polarization image of the rainforest scene ALOS PALSAR2 for the embodiment;

[0050] Figure 2 Schematic diagram of the value of 0.7 for the scintillation phase autocorrelation function of the present invention;

[0051] Figure 3 Schematic diagram of the parallelogram filtering window of the present invention;

[0052] Figure 4 Simulation result of the value of 0.7 for the scintillation phase autocorrelation function of the embodiment;

[0053] Figure 5 Simulation result of the parallelogram filtering window of the embodiment. Detailed Embodiment

[0054] The specific technical solution of the present invention is described in combination with the embodiment.

[0055] Use the full-polarization data of ALOS PALSAR2, and the selected scene is the rainforest scene. The scene image is as Figure 1 shown, and the image size is 800×400.

[0056] Introduce ionospheric scintillation phase, Faraday rotation angle, and polarization channel noise through simulation. Among them, three different data are used for the two-dimensional ionospheric scintillation phase, and the angles between the upper and lower axes and the left and right axes of its autocorrelation function are 18°, 154°, and 113° respectively; the signal-to-noise ratios of the polarization channels are 20 dB, 30 dB, and 40 dB respectively; before introducing the polarization system noise, make the VH channel data equal to the HV channel data and remove the original data noise. Next, use the method of the present invention to compensate the ionospheric scintillation error for the above simulation data.

[0057] Step 1: Decompress to the ionospheric altitude. Use the matrix to represent the simulation results of the four channels. Perform azimuthal Fourier transform on M HH 、M HV 、M VH 、M VV respectively, multiply by the decompression phase in the azimuthal frequency domain and then perform inverse azimuthal Fourier transform to obtain the azimuthal time-domain signals of the four channels at the ionospheric altitude.

[0058] Step 2: Estimate the magnitude of the Faraday rotation angle. Use formula (4) to transform the simulation image from the linear polarization channel to the circular polarization basis. Calculate Z 21 Z 12 * , and process Z 21 Z 12 * using the mean filtering method of the traditional rectangular window to suppress noise. Estimate the Faraday rotation angle according to the processed result using formula (5).

[0059] Step 3: Estimate the ionospheric scintillation phase. Substitute the estimated value of the Faraday rotation angle obtained in Step 2 into formula (6) to estimate the TEC. Estimate the ionospheric scintillation phase according to the relationship between TEC and the scintillation phase using formula (2).

[0060] Step 4: Compensate the scintillation error of the original image. Use the ionospheric scintillation phase estimated in Step 3 to compensate the simulation image. Perform azimuthal Fourier transform on the compensated four-channel data respectively, multiply by the compression phase and then perform inverse azimuthal Fourier transform to obtain the time-domain image after compensating the scintillation error. Calculate the image entropy of the HH channel image after compensation using formula (7).

[0061] Step 5: Select the best result of mean filtering. Adjust the size of the mean filtering rectangular filter window, and repeat Steps 2 to 4. Select the data with the minimum image entropy of the HH channel image after compensation, and calculate the two-dimensional autocorrelation function of the ionospheric scintillation phase estimated under this condition.

[0062] Step 6: Design a parallelogram filter window. Based on the graph when the autocorrelation function value is 0.7 in Step 5, take the connection lines of the upper and lower endpoints and the left and right endpoints as the two axes. The angle passed by rotating the axis of the connection line of the upper and lower endpoints counterclockwise to the axis of the connection line of the left and right endpoints is the deflection angle. Take the deflection angle as the angle from the vertical side to the hypotenuse of the parallelogram filter window counterclockwise, take the length of the axis of the connection line of the upper and lower endpoints as the initial value of the length of the vertical side of the parallelogram filter window, and take the length of the axis of the connection line of the left and right endpoints as the initial value of the length of the hypotenuse of the parallelogram filter window.

[0063] The schematic diagram of this step is shown in the attached drawings of the specification. Figure 2 It is a schematic diagram when the autocorrelation function value of the scintillation phase is 0.7, where ∠1 is the included angle between the two axes, i.e., the deflection angle. Figure 3 It is a schematic diagram of the parallelogram filter window, where ∠2 = ∠1, A1B1 = AB, and A1C1 = CD.

[0064] In this embodiment, taking the simulation results of the ionospheric two-dimensional scintillation phase with the included angle between the two axes of the autocorrelation function being 154° and the polarization channel noise with a signal-to-noise ratio of 30 dB as an example, Figure 4 the simulation results when the two-dimensional autocorrelation function value of the ionospheric scintillation phase estimated in Step 5 is 0.7 are given. Figure 5 The simulation results of the designed parallelogram filter window are given.

[0065] Step 7: Compensate the scintillation error of the original image. Repeat Step 2, use formula (5) to estimate the Faraday rotation angle, and use the parallelogram filter window obtained in the previous step to perform mean filtering on the Z 21 Z 12 * image to suppress noise. Repeat Step 3, calculate the TEC according to formula (6), and then estimate the ionospheric scintillation phase according to formula (2). Repeat Step 4 to compensate for the ionospheric scintillation error, and perform compression processing on the compensated image to obtain the time-domain image after compensating for the scintillation error. Finally, calculate the image entropy of the HH channel image after compensation according to formula (7).

[0066] Step 8: Select the best result. Adjust the sizes of the two sides of the parallelogram filter window, and repeat Steps 2 to 4 to select a set of data with the minimum image entropy after compensation as the final result.

[0067] The two-axis angles of the two-dimensional autocorrelation function of the original ionospheric scintillation phase introduced in the simulation process are 18°, 154°, and 113° respectively. When system noise with a signal-to-noise ratio of 20 dB is introduced, the two-axis angles of the two-dimensional autocorrelation function of the best-estimated ionospheric scintillation phase in step five are 40°, 150°, and 105° respectively; when system noise with a signal-to-noise ratio of 30 dB is introduced, the two-axis angles are 20°, 155°, and 110° respectively; when system noise with a signal-to-noise ratio of 40 dB is introduced, the two-axis angles are 18°, 155°, and 112° respectively. Under each condition, it is necessary to calculate the correlation coefficient between the HH-channel image of the best compensation result based on the rectangular filter window in step five and the original HH-channel image, and the correlation coefficient between the HH-channel image of the best compensation result based on the parallelogram filter window in step eight and the original HH-channel image. By comparing the two correlation coefficients, the effects of the ionospheric scintillation error compensation methods based on the two filter windows are compared. The comparison results are shown in the following table:

[0068] Table 1 Experimental results at a signal-to-noise ratio of 20 dB

[0069]

[0070] Table 2 Experimental results at a signal-to-noise ratio of 30 dB

[0071]

[0072] Table 3 Experimental results at a signal-to-noise ratio of 40 dB

[0073]

[0074]

[0075] As can be seen from the above table, under the same conditions, compared with the traditional rectangular window mean filtering, the scintillation phase error compensation method based on the parallelogram filter window has a smaller image entropy after final compensation and a larger correlation coefficient between the compensated image and the original image.

Claims

1. A smoothing window design method for ionospheric scintillation error compensation in spaceborne full-polarimetric SAR, characterized in that, It includes the following steps: Step 1: Decompress to the ionospheric height; Perform azimuth Fourier transform and inverse azimuth Fourier transform on the image data of each polarization channel to obtain the azimuth time-domain signal at the ionospheric height; Step 2: Estimate the magnitude of the Faraday rotation angle; Convert the observation matrix from the linear polarization channel to the circular polarization basis, and process the image using the mean filtering method with a rectangular window to suppress noise; Calculate the estimated value of the Faraday rotation angle; Step 3: Estimate the ionospheric scintillation phase; Obtain the TEC estimated value using the estimated value of the Faraday rotation angle; then estimate the ionospheric scintillation phase according to the scintillation phase calculation formula; Step 4: Compensate the original image scintillation error; Compensate the original images of the four channels using the estimated value of the ionospheric scintillation phase. Perform azimuth Fourier transform on the original image data of the four channels respectively, multiply by the compression phase, and then perform inverse azimuth Fourier transform to obtain the compensated images; calculate the image entropy of the compensated HH channel image; Step 5: Select the best result of mean filtering; Adjust the size of the mean filtering rectangular filter window, repeat Steps 2 to 4, and select the rectangular window value when the image entropy of the compensated image is the smallest; Calculate the two-dimensional autocorrelation function of the estimated value of the ionospheric scintillation phase under this condition; Step 6: Design a parallelogram filter window; According to the graph when the autocorrelation function value in Step 5 is 0.7, take the connection line of the upper and lower, left and right endpoints as the two axes. The angle through which the axis of the connection line of the upper and lower endpoints rotates counterclockwise to the axis of the connection line of the left and right endpoints is the deflection angle; use the deflection angle as the angle from the vertical side to the hypotenuse of the parallelogram filter window counterclockwise. Take the axis length of the connection line of the upper and lower endpoints as the initial value of the vertical side length of the parallelogram filter window, and take the axis length of the connection line of the left and right endpoints as the initial value of the hypotenuse length of the parallelogram filter window; Step 7: Compensate the original image scintillation error; Repeat Step 2 to estimate the Faraday rotation angle. During the estimation process, use the parallelogram filter window obtained in the previous step to perform mean filtering on the image to suppress noise; Repeat Step 3 to calculate the TEC and then estimate the ionospheric scintillation phase; Repeat Step 4 to compensate the ionospheric scintillation error, perform compression processing on the compensated image to obtain the time-domain image after compensating the scintillation error; finally calculate the image entropy of the compensated HH channel image; Step 8: Select the best result; Adjust the sizes of the two sides of the parallelogram filter window, repeat Steps 2 to 4, and select the compensation result with the smallest image entropy of the compensated image as the final result.

2. The smoothing window design method in the ionospheric scintillation error compensation of the spaceborne full-polarization SAR according to claim 1, characterized in that The specific method of Step 1 is: Perform azimuth Fourier transform on the image data of each polarization channel; Multiply by the decompression phase in the azimuth frequency domain where λ represents the wavelength, f a represents the azimuth frequency, V ref represents the equivalent velocity of the spaceborne radar, R iono represents the slant range corresponding to the ionospheric height, i.e.: where H iono represents the height where the ionosphere is located, θ represents the beam center viewing angle, Nr represents the number of points in the range direction, △r represents the range sampling point spacing, and i = 0, 1, …, Nr-1; Then perform inverse azimuth Fourier transform to obtain the azimuth time-domain signal at the ionospheric height.

3. The smoothing window design method in the spaceborne full-polarization SAR ionospheric scintillation error compensation according to claim 2, characterized in that The specific method of Step 2 is: The full-polarization spaceborne SAR data is expressed in the form of the following observation matrix where M HH is the data obtained from the horizontal polarization transmission and horizontal polarization reception channel; M HV is the data obtained from the horizontal polarization transmission and vertical polarization reception channel; M VH is the data obtained from the vertical polarization transmission and horizontal polarization reception channel; M VV is the data obtained from the vertical polarization transmission and vertical polarization reception channel; Transform the observation matrix from the linear polarization channels to the circular polarization basis, i.e., calculate \(Z\) according to (2). 11 , \(Z\) 12 , \(Z\) 21 , \(Z\) 22 : Calculate Z again 21 Z 12 * , where * represents taking the complex conjugate, and process Z using the mean filtering method of the traditional rectangular window 21 Z 12 * image to suppress noise; Calculate the estimated value of the Faraday rotation angle using the processed result. The formula is as follows: Obtain the estimated value of the Faraday rotation angle.

4. The smoothing window design method in the ionospheric scintillation error compensation for spaceborne full-polarimetric SAR according to claim 3, wherein The specific method of Step 3 is: According to the calculation formula (4) of the Faraday rotation angle Among them, Q is a constant, and Q = 2.365×10 4 , with the unit of A·m 2 / kg; f c is the carrier frequency; θ represents the angle between the direction of the Earth's magnetic field and the propagation direction of the radar electromagnetic wave; B represents the Earth's magnetic field strength, with the unit of Wb / m 2 ; TEC is the total electron content on the path, representing the integral of the electron density along the propagation path of the electromagnetic wave, with the unit of TECU, 1 TECU = 10 16 m -2 ; It can be known that: Substitute the estimated value of the Faraday rotation angle obtained in the previous step into formula (5) to obtain the TEC estimated value; Then estimate the ionospheric scintillation phase according to the scintillation phase calculation formula (6); Where K is a constant, K = 40.28; c is the speed of light in vacuum.

5. The smoothing window design method in the spaceborne full-polarimetric SAR ionospheric scintillation error compensation according to claim 4, wherein The specific method of Step 4 is: Compensate the original images of the four channels with the ionospheric scintillation phase estimation values obtained in the previous step; perform azimuth Fourier transforms on the original image data of the four channels respectively, and multiply by the compression phase Then perform inverse azimuth Fourier transform to obtain the compensated images; calculate the image entropy of the HH channel image after compensation; the formula for calculating the image entropy is as follows: Where S(m,n) is the value at the position of pixel (m,n), the image size is M×N, m = 0, 1, … M-1, n = 0, 1, … N-1, I is the total energy of the image, and the calculation formula is as follows:

6. The smoothing window design method in the ionospheric scintillation error compensation of spaceborne full-polarimetric SAR according to claim 5, wherein The specific method of Step Seven is as follows: Repeat step 2, estimate the Faraday rotation angle using formula (3), and use the parallelogram filter window obtained in the previous step to perform mean filtering on the Z 21 Z 12 * image to suppress noise; Repeat Step Three, calculate the TEC estimated value according to formula (5), and then estimate the ionospheric scintillation phase according to formula (6); Repeat Step Four, compensate for the ionospheric scintillation error, perform compression processing on the compensated image to obtain the time-domain image after compensating for the scintillation error; finally, calculate the image entropy of the HH channel image after compensation according to formula (7).

Images