A PFA imaging and motion error compensation method for unmanned airborne SAR

Abstract

The application discloses a UAV-borne SAR PFA imaging and motion error compensation method and belongs to the technical field of UAV-borne synthetic aperture radar imaging, and mainly solves the phase error coupling effect caused by the attitude disturbance of a UAV platform to improve the accuracy and reliability of SAR imaging results. The method comprises the following steps: processing strip signals to realize conversion from a strip mode to a quasi-burst mode; then implementing a polar format algorithm (PFA) to perform distance frequency modulation, distance cell migration linearization and wedge transformation; then acquiring residual distance cell migration (RCM) through cross-correlation estimation to construct a rough compensation term to reduce most of the motion errors; then performing fine compensation of the motion errors by using a minimum entropy autofocus algorithm (MEA); and finally generating a SAR image through two-dimensional fast Fourier transform (FFT).

Description

Technical Field

[0001] This invention relates to the field of unmanned aerial vehicle (UAV)-borne synthetic aperture radar (SAR) imaging technology, specifically to a method for PFA imaging and motion error compensation of UAV-borne SAR. Background Technology

[0002] Synthetic Aperture Radar (SAR), as a high-resolution active microwave remote sensing method, occupies an important position in military reconnaissance and land resource monitoring due to its all-weather and long-range imaging advantages. In recent years, with the integrated development of UAV platforms and SAR technology, UAV-borne SAR systems have demonstrated significant technological advantages: SAR operates in the 0.1-10THz frequency band, and its unique millimeter-level wavelength characteristics provide the physical basis for achieving centimeter-level ultra-high resolution imaging, while the UAV platform endows the system with stronger mobility and adaptability to complex terrain.

[0003] Currently, SAR imaging faces two major challenges: First, while the polar coordinate format algorithm (PFA), as a classic imaging algorithm, can effectively match the narrow-angle scanning characteristics of SAR, its traditional design is geared towards spotlight mode SAR. When applied to strip mode, it suffers from wavefront curvature compensation mismatch, leading to imaging geometric distortion. Second, the wavelength characteristics of SAR increase the system's sensitivity to platform micro-motion errors by orders of magnitude. Traditional motion compensation methods based on range-Doppler algorithms have theoretical limitations when dealing with two-dimensional spatially varying errors, especially under ultra-high resolution conditions where the spatially varying error effect is more significant.

[0004] In existing technologies, PFA improvements for striped SAR often employ wavenumber domain reconstruction, but fail to fully consider the phase error coupling effect caused by attitude disturbances of the UAV platform. Regarding motion compensation, conventional envelope alignment methods struggle to meet the sub-millimeter accuracy requirements of SAR, while image-domain-based autofocus algorithms are limited by the spatially varying azimuth characteristics of the striped mode. Particularly noteworthy is that when the resolution is better than 5 cm, the coupled phase error generated by motion errors in the range and azimuth directions can reach tens of wavelengths, directly leading to image defocusing and geometric positioning deviations.

[0005] Therefore, how to design a PFA imaging and error compensation method for UAV-borne SAR to overcome the above limitations and improve the accuracy and reliability of imaging results is an important issue that urgently needs to be addressed. Summary of the Invention

[0006] The purpose of this invention is to provide a method for PFA imaging and motion error compensation in UAV-borne SAR. This method focuses on solving imaging problems caused by poor stability during UAV flight. By accurately measuring the motion error of the UAV platform and combining it with echo data for real-time compensation, the accuracy and quality of SAR imaging are significantly improved. This invention can effectively compensate for motion errors, improve image focusing, and thus enhance the all-weather remote sensing capabilities of UAVs under complex weather conditions, meeting the high-precision imaging needs of fields such as urban construction surveying, agricultural surveys, and disaster monitoring.

[0007] The technical specifications for achieving the objectives of this invention are as follows: This invention provides a method for PFA imaging and motion error compensation of unmanned aerial vehicle (UAV)-borne SAR, comprising the following key steps:

[0008] S1: First, process the strip signal, select clustered regions, and use specific phase compensation functions and azimuth Decirp functions to convert the data from strip mode to clustered mode, laying the foundation for subsequent processing.

[0009] S2: Implement the polar coordinate format algorithm (PFA), first perform distance frequency modulation to change the signal frequency structure, then linearize the distance cell migration, and finally perform wedge transformation to complete the two-dimensional decoupling of the signal and eliminate the two-dimensional coupling of the signal.

[0010] S3: Perform coarse compensation for motion errors. Use cross-correlation estimation to obtain residual distance cell migration (RCM), derive the total phase error based on its linear relationship with azimuth phase error (APE), construct a coarse compensation term, process the preprocessed signal, and reduce most of the motion errors.

[0011] S4: After completing PFA, since residual errors can cause image defocusing, fine motion error compensation is performed. The Minimum Entropy Autofocus (MEA) algorithm is used to further compensate for errors based on overall image quality optimization.

[0012] S5: Perform a two-dimensional fast Fourier transform (FFT) on the signal that has undergone the above series of processing to obtain the compressed image, which is the final terahertz strip SAR image.

[0013] Furthermore, the specific processing method for the original strip signal in S1 is as follows:

[0014] To simulate a real-world application scenario, it is assumed that the radar platform moves along a non-ideal trajectory. An XYZ coordinate system is constructed, with the scene center O as the origin, where the x-axis, y-axis, and z-axis correspond to the range, azimuth, and altitude directions, respectively. In this coordinate system, the instantaneous position of the radar antenna phase center is denoted as (xa, ya, za), and the corresponding instantaneous elevation and azimuth angles are denoted as... And θ. Taking the center of the synthetic aperture as the origin of the azimuth slow time, the corresponding instantaneous pitch angle is taken as the reference pitch angle, denoted as θ. For a point target (xp, yp) in the scene, the instantaneous distance from the radar antenna phase center to that point is denoted as Rp, Rc represents the instantaneous tilt distance from the radar platform to the scene center, and Rref represents the reference tilt distance from the radar platform reference point to the scene center.

[0015] When a radar transmits a linear frequency modulated (LFM) signal to a detection scene, this signal can be represented as:

[0016]

[0017] Where fc is the carrier frequency of the transmitted LFM signal, which determines the radar's operating frequency band; Kr is the frequency modulation frequency, which plays a crucial role in range resolution; τ = t - nPRF represents the fast time in the range direction, t is the slow time in the azimuth direction, n represents the nth pulse, and PRF is the pulse repetition frequency, which affects the radar imaging frame rate; C is the speed of light, a fundamental physical constant; and A represents the intensity amplitude of the transmitted signal, reflecting the magnitude of the transmitted signal energy.

[0018] 1) When selecting the clustering region, in strip SAR detection, when the strip azimuth accumulation length La is greater than the equivalent clustering azimuth accumulation length Ls, a common detection region ωa exists, where λ is the wavelength. Based on radar detection geometry, the beamwidth β and azimuth resolution ρa satisfy:

[0019]

[0020] The equivalent beamwidth is:

[0021]

[0022] The echo data from this region can be used as cluster beam detection data.

[0023] 2) Then perform phase compensation. The function used for phase compensation is:

[0024]

[0025] Where Ra(t) is the function of the distance from the phase center of the radar antenna to the center of the scene as a function of time.

[0026] 3) The function to implement azimuth de-chirp is:

[0027]

[0028] After phase compensation and azimuth dechirp, the two-dimensional dechirp signal of the beamforming conversion is:

[0029]

[0030] Furthermore, the specific method of the polar coordinate format algorithm in S2 is as follows:

[0031] 1) Range-frequency modulation, defined as:

[0032] f r =δ r f r +f c (δ r -1)

[0033] in It is a frequency scaling standard. It is the reference pitch angle. θ is the instantaneous pitch angle, and θ is the azimuth angle; fc(δr-1) ​​represents the offset in Ssignal2(n,τ). The modulated signal is:

[0034]

[0035] Where Re(t) is the distance error term.

[0036] 2) Range cell migration linearization: In the format conversion of the signal in the azimuth dimension, RCM linearization is a simple transformation from azimuth angle to azimuth time, that is, let:

[0037]

[0038] The signal at this time is:

[0039]

[0040] Where Ω = Va / Rc represents the angular velocity of the radar platform, Va is the platform velocity, and:

[0041]

[0042] 3) Perform a wedge transformation, let Perform a wedge transform on the signal to achieve two-dimensional decoupling of the signal:

[0043]

[0044] In the formula Represents the two-dimensional error of the signal in the spatial frequency domain:

[0045]

[0046] Furthermore, the specific steps for coarse motion error compensation in S3 are as follows:

[0047] 1) Perform cross-correlation estimation of residuals (RCM). At each azimuth time step, estimate the misalignment of adjacent range profiles using fast zonal interferometry. Based on the signal structure in the azimuth dimension:

[0048]

[0049] Extracting sub-timebands of the signal to construct distance sub-signals:

[0050]

[0051] The frequency shift caused by the differential motion error dδ of adjacent azimuth units is:

[0052] Δf=2K r dδ / C

[0053] The signals of adjacent azimuth units are as follows:

[0054]

[0055] The differential motion error dδ is obtained through calculation:

[0056] [S a1 (f)·S a2 (f)*]·[S b1 (f)·S b2 (f)*]=exp[j2π(t ca -t cb )Δf]

[0057]

[0058] The error is obtained by integrating each term:

[0059]

[0060] 2) Construct and process the coarse compensation term. Based on the error term, construct the coarse compensation term H(t):

[0061]

[0062] Perform coarse compensation on the preprocessed signal (Ssignal2) to obtain the coarse compensation signal:

[0063]

[0064] Rb(t) is the basic term of the differential distance, and Re(t) is the distance error term. The remaining error after coarse compensation is:

[0065]

[0066] ΔR(t)=R c -R p =R b (t)+R e (t)

[0067] Furthermore, the specific details of MEA motion error fine compensation in S4 are as follows:

[0068] After completing PFA, the Minimum Entropy Autofocus (MEA) algorithm is used for fine compensation. MEA uses image entropy as the optimization criterion, and the formula for calculating image entropy E is:

[0069]

[0070] Where M and N are the number of rows and columns of the image, respectively, and pij is the normalized probability of the pixel value at position (i,j). By adjusting the phase error parameter to minimize the image entropy, further compensation for residual errors is achieved, thus optimizing the image focusing quality.

[0071] Furthermore, the final step in S5 to generate the image is as follows:

[0072] Perform a two-dimensional Fast Fourier Transform (FFT) on the signal that has undergone the above series of processing steps, that is, perform a two-dimensional Fast Fourier Transform (FFT) on the S signal. A2 Perform a two-dimensional FFT on (t,fr) to obtain the compressed image, and generate the final terahertz strip SAR image:

[0073] I(x, y) = FFT 2D {S A2 (t,f r )}

[0074] Where x and y represent the azimuth and range coordinates of the image, respectively. Attached Figure Description

[0075] Figure 1 This is a flowchart illustrating the implementation of the PFA imaging and motion error compensation method for UAV-borne SAR as described in this invention. Detailed Implementation

[0076] This invention relates to a method for PFA imaging and motion error compensation of unmanned aerial vehicle (UAV)-borne SAR, the specific steps of which are as follows:

[0077] S1: First, process the strip signal, select clustered regions, and use specific phase compensation functions and azimuth Decirp functions to convert the data from strip mode to clustered mode, laying the foundation for subsequent processing.

[0078] S2: Implement the polar coordinate format algorithm (PFA), first perform distance frequency modulation to change the signal frequency structure, then linearize the distance cell migration, and finally perform wedge transformation to complete the two-dimensional decoupling of the signal and eliminate the two-dimensional coupling of the signal.

[0079] S3: Perform coarse compensation for motion errors. Use cross-correlation estimation to obtain residual distance cell migration (RCM), derive the total phase error based on its linear relationship with azimuth phase error (APE), construct a coarse compensation term, process the preprocessed signal, and reduce most of the motion errors.

[0080] S4: After completing PFA, since residual errors can cause image defocusing, fine motion error compensation is performed. The Minimum Entropy Autofocus (MEA) algorithm is used to further compensate for errors based on overall image quality optimization.

[0081] S5: Perform a two-dimensional fast Fourier transform (FFT) on the signal that has undergone the above series of processing to obtain the compressed image, which is the final terahertz strip SAR image.

[0082] In this embodiment, step S1 specifically includes the following:

[0083] S11: Select the clustering region. When the strip azimuth accumulation length La is greater than the equivalent clustering azimuth accumulation length Ls, determine the common detection region ωa as the clustering detection data, where the width of the equivalent clustering region satisfies a specific formula:

[0084]

[0085] in λ is the wavelength;

[0086] S12: Perform phase compensation. The function used for phase compensation is:

[0087]

[0088] Where Ra(t) is the function of time as a function of the distance from the phase center of the radar antenna to the center of the scene;

[0089] S13: Achieve azimuth de-chirp. After phase compensation and azimuth de-chirp, a two-dimensional de-chirp signal with beamforming is obtained. The function of azimuth de-chirp is:

[0090]

[0091] In this embodiment, step S2 specifically includes the following:

[0092] S21: Distance frequency modulation, the modulation formula is:

[0093] f r =δ r f r +f c (δ r -1)

[0094] in It is a frequency scaling standard. It is the reference pitch angle. It is the instantaneous pitch angle, θ is the azimuth angle, and fc(δr-1) ​​represents the offset in Ssignal2(n,τ);

[0095] S22: Linearization of distance cell migration, by letting... Perform an azimuth angle to azimuth time transformation, and the transformed signal satisfies the formula:

[0096]

[0097] Where Ω = Va / Rc represents the angular velocity of the radar platform, Va is the platform velocity, and

[0098] S23: Perform a wedge transformation, let A wedge transform is performed on the signal to achieve two-dimensional decoupling. The decoupled signal satisfies the formula:

[0099]

[0100] in

[0101] In this embodiment, step S3 specifically includes the following:

[0102] S31: Perform cross-correlation estimation of residual RCM. At each azimuth time, use the fast zonal signal interferometry to estimate the inaccuracy of adjacent distance profiles. Obtain the differential motion error dδ through specific calculations and integrate the results term by term to obtain the error.

[0103] S32: Construct and process the coarse compensation term. Based on the error term, construct the coarse compensation term H(t), and perform coarse compensation on the preprocessed signal to obtain the coarse compensation signal. The remaining error after coarse compensation satisfies the formula:

[0104] ΔR(t)=R c -R p =R b (t)+R e (t)

[0105] Where Rb(t) is the basic term of the differential distance, and Re(t) is the distance error term;

[0106] In this embodiment, step S4 specifically includes the following:

[0107] The Minimum Entropy Autofocus (MEA) algorithm is employed, using image entropy as the optimization criterion. By adjusting the phase error parameter, the image entropy is minimized, thereby further compensating for residual errors. The formula for calculating image entropy E is:

[0108]

[0109] Where M and N are the number of rows and columns of the image, respectively, and pij is the normalized probability of the pixel value at position (i,j) in the image;

[0110] In this embodiment, step S5 specifically includes the following:

[0111] Perform a two-dimensional Fast Fourier Transform (FFT) on the signal that has undergone the above series of processing steps, that is, perform a two-dimensional Fast Fourier Transform (FFT) on the S signal. A2 Performing a two-dimensional FFT on (t,fr) yields a compressed image, generating the final terahertz strip SAR image. The image coordinates satisfy a specific formula:

[0112] I(x, y) = FFT 2D {S A2 (t,f r )}

[0113] Where x and y represent the azimuth and range coordinates of the image, respectively.

Claims

1. A polar coordinate format algorithm (PFA) imaging and motion error compensation method for UAV-borne SAR, characterized in that, Includes the following steps: S1: Process the strip signal, select clustered regions, and convert the data from strip mode to clustered mode using a specific phase compensation function and azimuth de-chirp function; this includes the following steps: S11: Select clustering regions, when the cumulative length of the strip orientation L... a Greater than the equivalent azimuth accumulation length L s At that time, the common detection area ω is determined. a As beam-like detection data, the equivalent beam-spotting region width satisfies a specific formula: ,in λ is the wavelength; S12: Perform phase compensation. The function used for phase compensation is: ， Where R a (t) is a function of time that represents the distance from the phase center of the radar antenna to the center of the scene. S13: Achieve azimuth de-chirp. After phase compensation and azimuth de-chirp, a two-dimensional de-chirp signal with beamforming is obtained. The function of azimuth de-chirp is: ; S2: Implement PFA, first perform range frequency modulation, then linearize the range cell migration, and finally perform wedge transformation to complete the two-dimensional decoupling of the signal; S3: Perform coarse compensation for motion errors, use cross-correlation estimation to obtain the migration of residual distance cells, derive the total phase error based on its linear relationship with the azimuth phase error, construct a coarse compensation term, and process the preprocessed signal; S4: After completing PFA, the minimum entropy self-focusing algorithm is used to perform fine compensation for motion errors; S5: Perform a two-dimensional fast Fourier transform on the signal that has undergone the above series of processing to obtain the compressed image and generate the final terahertz strip SAR image.

2. The polar coordinate format algorithm PFA imaging and motion error compensation method for UAV-borne SAR according to claim 1, characterized in that, S2 includes the following sub-steps: S21: Distance frequency modulation, the modulation formula is: ， in It is a frequency scaling scale, φ ref φ is the reference pitch angle, θ is the instantaneous pitch angle, and f is the azimuth angle. c (δ r -1) represents S signal2 The offset in (n, τ); S22: Range cell migration linearization is achieved by transforming the azimuth angle to azimuth time. The transformed signal satisfies the formula: ， Where Ω = V a / R c V represents the angular velocity of the radar platform. a For platform speed, and ; S23: Perform a wedge transformation to complete the signal's wedge transformation, achieving two-dimensional decoupling of the signal. The decoupled signal satisfies the formula: , in .

3. The polar coordinate format algorithm PFA imaging and motion error compensation method for UAV-borne SAR according to claim 2, characterized in that, S3 includes the following sub-steps: S31: Perform cross-correlation estimation of residual distance cell migration. At each azimuth time, use the fast zonal signal interferometry to estimate the inaccuracy of adjacent distance profiles. Obtain the differential motion error dδ through specific calculations and integrate the errors term by term. S32: Construct and process the coarse compensation term. Based on the error term, construct the coarse compensation term H(t), and perform coarse compensation on the preprocessed signal to obtain the coarse compensation signal. The remaining error after coarse compensation satisfies the formula: ， ， Where R b (t) is a fundamental term of the difference distance, R e (t) is the distance error term.

4. The polar coordinate format algorithm (PFA) imaging and motion error compensation method for UAV-borne SAR according to claim 3, characterized in that, S4 includes the following sub-steps: The minimum entropy autofocus algorithm is adopted, using image entropy as the optimization criterion. By adjusting the phase error parameter, the image entropy is minimized, thereby achieving further compensation for residual errors. The formula for calculating image entropy E is: ， Where M and N are the number of rows and columns of the image, respectively, p ij It is the normalized probability of the pixel value at position (i, j) in the image.

5. The polar coordinate format algorithm PFA imaging and motion error compensation method for UAV-borne SAR according to claim 4, characterized in that, S5 includes the following sub-steps: Perform a two-dimensional fast Fourier transform on the signal that has undergone the above series of processing steps, that is, on S A2 (t, f r A two-dimensional fast Fourier transform is performed to obtain the compressed image, generating the final terahertz strip SAR image. The image coordinates satisfy a specific formula: ， Where x and y represent the azimuth and range coordinates of the image, respectively.

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