A vehicle-mounted SAR imaging self-focusing method based on Rényi entropy

Abstract

The application discloses a kind of vehicle-mounted SAR imaging self-focusing methods based on Rényi entropy, it is related to vehicle-mounted synthetic aperture radar imaging technical field, vehicle-mounted SAR motion compensation is realized in the case without inertial navigation equipment;The method comprises: obtaining vehicle-mounted SAR original data, and the sub-aperture division is carried out to vehicle-mounted SAR echo data;For each sub-aperture, first, imaging is carried out using Omega-K algorithm, then, the Rényi entropy of SAR image is defined, and a self-focusing method based on Rényi entropy is designed to optimize image quality;SAR subgraph imaging is realized by sub-aperture iteration, and sub-aperture splicing is carried out according to the division principle, to obtain wide vehicle-mounted SAR image with high precision.The present application can be directly applied to existing vehicle-mounted FMCW-SAR system, and the performance of SAR system can be more accurately measured using Rényi entropy, to further optimize the self-focusing algorithm, significantly improve the vehicle-mounted SAR imaging quality and system applicability, and provide technical support for the development of vehicle-mounted SAR technology.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of vehicle-mounted SAR imaging, and particularly relates to a vehicle-mounted SAR imaging self-focusing method based on Rényi entropy. BACKGROUND

[0002] Autonomous driving is an important vision for human society in the future. In recent years, the industry and academia have achieved intelligent perception and decision-making in the automotive environment by using multi-modal data sets. The accuracy of these data sets essentially determines the correctness and reliability of perception and decision-making. The automotive multi-modal data set is mainly obtained through sensors such as lidar, camera and millimeter wave radar. Compared with lidar and camera, millimeter wave radar has the advantages of all-weather operation, miniaturization, high integration and low cost. Therefore, automotive millimeter wave radar has become a research hotspot for many manufacturers and scholars.

[0003] Automotive millimeter wave radar working in W-band (76-81GHz) can provide multi-dimensional information, including range, velocity and angle. In terms of imaging, compared with point cloud imaging which is limited by the size of the antenna and has low angular resolution, SAR imaging forms a virtual aperture through the relative motion between the platform and the target, achieving higher azimuth resolution, thereby providing more accurate perception data for the autonomous driving system.

[0004] In theory, SAR imaging requires accurate estimation of the relative geometric relationship between the imaging scene and the radar trajectory. This geometric information can be provided by motion sensors such as global positioning system (GPS) and inertial navigation system (INS). However, these sensors are either too expensive or cannot provide the wavelength-level navigation accuracy required for high-resolution SAR imaging, especially in the W-band. At the same time, the high mobility of vehicles and the complexity of the automotive environment often lead to radar trajectory deviations and velocity instability. This will introduce additional motion errors and eventually lead to defocusing. Therefore, motion compensation (MoCo) is an important process in automotive SAR (Auto-SAR) imaging and is a key supplement to motion sensors.

[0005] MoCo methods can be mainly divided into sensor-based and data-based estimation, where the latter extracts motion information directly from raw data, and the self-focusing method is widely used due to its flexibility and robustness. The self-focusing method can be divided into parametric and non-parametric types. Parametric methods estimate parameters by establishing a motion error model, but lack flexibility in high-resolution imaging; non-parametric methods directly extract phase information from raw data to achieve more accurate motion compensation.

[0006] The non-parametric methods mainly include two types of dominant point based (DPB) and image optimization based (IOB). As an effective DPB method, standard phase gradient autofocus (PGA) has been widely used in various scenarios, such as improved versions like PWE-PGA and WPGA. However, the DPB method needs isolated dominant points to extract the integral phase information in the imaging scene, otherwise it will fail. On the contrary, the IOB method does not depend on these points and has less dependence on the scene. Therefore, the IOB method has better robustness and universality than the DPB method. The IOB method estimates the phase error by optimizing the global metric of the image, including the minimum entropy algorithm (MEA), the maximum contrast algorithm (MCA) and the minimum Rényi entropy algorithm (MREA) and the like. Specifically, the MCA method is only applicable to scenes with strong isolated points, and its performance is low for other scenes; the MEA measures the SAR image quality based on Shannon entropy, which cannot comprehensively measure all SAR images, especially the vehicle-mounted SAR system with complex and changeable application scenarios; for the MREA, although it has been applied to ISAR systems, it is only used as a measurement index for iterative optimization, and the theoretical derivation of the self-focusing method has not been carried out, and the application potential of Rényi entropy in SAR systems has not been explored, and its application value is even greater for complex vehicle-mounted scenarios. SUMMARY

[0007] The purpose of the present application is to provide a vehicle-mounted SAR imaging self-focusing method based on Rényi entropy, which solves the robustness problem of the current vehicle-mounted SAR self-focusing method based on image index optimization, theoretically derives the iterative optimization process of the self-focusing method, and improves its stability and applicability in complex vehicle-mounted application scenarios.

[0008] Technical scheme: In order to achieve the above-mentioned purpose, the present application adopts the following technical scheme:

[0009] A vehicle-mounted SAR imaging self-focusing method based on Rényi entropy, comprising:

[0010] Sub-aperture division is performed on the vehicle-mounted SAR raw echo data;

[0011] SAR imaging is performed on each sub-aperture SAR raw FMCW signal using the Omega-K algorithm;

[0012] According to the definition of Rényi entropy, the phase error is estimated sub-aperture by sub-aperture using the MREA method based on Rényi entropy, the phase error is compensated, and the sub-aperture high-precision SAR image is obtained by continuously iterating through the fixed point (FP) method;

[0013] Sub-aperture splicing is performed to obtain a full-aperture high-precision SAR image.

[0014] Further, in the sub-aperture division, a length range of the sub-aperture is determined based on a difference between a minimum distance and a maximum distance of the imaging area, in combination with an antenna beam angle and a proportion constraint of system design.

[0015] Further, the SAR imaging of each sub-aperture SAR original FMCW signal by using the Omega-K algorithm comprises: residual video phase compensation and intra-pulse motion compensation on the received signal; and SAR imaging of the signal subjected to the residual video phase compensation and the intra-pulse motion compensation by using the Omega-K algorithm to obtain a coarse-precision SAR image.

[0016] Further, the SAR imaging of the signal subjected to the residual video phase compensation and the intra-pulse motion compensation by using the Omega-K algorithm comprises consistent compensation function compensation and Stolt interpolation, and the consistent compensation function H rfm (K a ,K r ) is expressed as wherein K r , K a and R0 respectively represent a distance wave number, an azimuth wave number and a reference distance, The Stolt interpolation kernel is expressed as K y =K r -K rc represents a distance wave number, K rc =4π / λ represents a reference distance wave number, and λ represents a signal wavelength.

[0017] Further, the expression of the Rényi entropy is defined as η>0andη≠1, wherein, Different selection of η values has an influence on the self-focusing result, and the selection is based on experimental effect, s(m,n) represents an mth column and nth row element of the SAR image, M represents an azimuth sampling point number, and N represents a distance sampling point number.

[0018] Further, the MREA method based on the Rényi entropy comprises: first derivative solving of the Rényi entropy with respect to a phase error, iterative formula solving of the phase error by using the FP method, phase error estimation and iterative phase correction.

[0019] Further, the FP method is used to solve the minimum Rényi entropy problem, and the first derivative of the Rényi entropy with respect to the phase error is

[0020]

[0021] wherein k represents a Doppler frequency point, φ(k) represents an estimated phase error at k, denotes the true phase error at k, Im{} denotes the imaginary part operator, u(k, n) denotes the element of the kth column and nth row of the range-doppler domain data,

[0022] Further, the iteration process of the FP-MREA is represented as

[0023]

[0024] wherein, u (l) (k, n), s (l) (m, n) correspond to the phase error, range-doppler domain data and SAR image data of the lth iteration, respectively; the iteration is continuously carried out until the Rēnyi entropy threshold values of the two iterations before and after are within the set error range.

[0025] The application further provides a computer system, comprising a memory, a processor and a computer program stored on the memory and capable of running on the processor, wherein the computer program, when executed by the processor, implements the steps of the Rēnyi entropy-based vehicle-mounted SAR imaging autofocusing method.

[0026] The application further provides a computer program product, comprising a computer program, wherein the computer program, when executed by a processor, implements the steps of the Rēnyi entropy-based vehicle-mounted SAR imaging autofocusing method.

[0027] Beneficial effects: the application can be directly applied to the existing vehicle-mounted FMCW-SAR system, the Rēnyi entropy can more accurately represent the vehicle-mounted SAR image, and the iteration convergence process of the accelerated autofocusing method is accelerated through theoretical derivation, thereby improving the stability and applicability of the vehicle-mounted application scenario, and providing technical support for the development of future vehicle-mounted SAR technology. BRIEF DESCRIPTION OF DRAWINGS

[0028] In order to more clearly illustrate the technical solutions in the embodiments of the application or the prior art, the following will briefly introduce the drawings needed to be used in the embodiments or the prior art description. Obviously, the drawings in the following description only constitute some embodiments of the application, and for those skilled in the art, other drawings can also be obtained without creative labor on the basis of these drawings.

[0029] Figure 1 The flowchart of the method of the embodiments of the application is shown in the figure;

[0030] Figure 2 The sub-aperture division schematic diagram of the vehicle-mounted SAR is shown in the figure;

[0031] Figure 3This is a schematic diagram of sub-aperture stitching for a vehicle-mounted SAR.

[0032] Figure 4 This is a geometric model diagram of a vehicle-mounted SAR.

[0033] Figure 5 Optical images of the experimental scene and coarse-precision full-aperture SAR images stitched together from sub-aperture images;

[0034] Figure 6 The images show the experimental results, where (a) is the original SAR image; (b) is the SAR image processed by the FP-MEA method; (c) is the SAR image processed by the MCA method; (d) is the SAR image processed by the WPGA method; and (e) is the SAR image processed by the method of this invention.

[0035] Figure 7 The figures show a comparison of experiments using different self-focusing methods, where (a) is a comparison of Shannon entropy iterations and (b) is a comparison of Rényi entropy iterations. Detailed Implementation

[0036] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0037] This invention provides a vehicle-mounted SAR imaging autofocusing method based on Rényi entropy, the specific process of which is as follows: Figure 1 As shown, the specific steps include the following:

[0038] Step 1, Sub-aperture segmentation, which involves segmenting the original echo data into sub-apertures using the equivalent focusing principle; specifically including:

[0039] (1.a) Determine a reasonable range for the sub-aperture length. In the equivalent spotting mode of vehicle-mounted synthetic aperture radar (SAR), the sub-aperture L is determined based on the difference between the minimum and maximum distances in the imaging area, i.e., the imaging range distance difference, and in conjunction with the antenna beam angle and the proportional constraints of the system design. sub Reasonable length range (generally, L) sub ≤2m);

[0040] (1.b) Select a suitable value L within the range of sub-aperture lengths. sub Set the overlap ratio α (1≤α≤2) between sub-apertures to divide the original echo data into n aSub-apertures, sub-aperture length is aL sub , sub-aperture division schematic diagram as Figure 2 shown, wherein the zero-padded data matrix is marked with light gray, the full-aperture data matrix is marked with yellow, and the sub-aperture data matrix is marked with dark blue, and the zero-padded full-aperture data matrix is formed into a sample data matrix with a length of L a +2L zp , wherein L a represents the original data aperture length, L zp represents the zero-padded data length, and is divided into n a sub-apertures according to the above-mentioned overlapping sub-aperture length, and the segmented overlapping processing of the aperture data can be realized by this method.

[0041] Step 2, vehicle-mounted sub-aperture SAR coarse imaging, wherein after the residual video phase compensation and intra-pulse motion compensation of each sub-aperture SAR original frequency modulation continuous wave (FMCW) signal in step 1, the SAR imaging is performed by using the Omega-K algorithm; specifically including:

[0042] (2.a) Establish a vehicle-mounted millimeter wave FMCW-SAR signal model, and the geometric model of the vehicle-mounted SAR is as shown in Figure 4 , assuming that the automobile radar works in a strip imaging mode, the motion distance along the X axis is vT a , v is the reference speed of the automobile, T a is the synthetic aperture time, the radar reference height is H, the beam width is , the reference slant range is R0, the reference point is P(x0, y0, z0), the instantaneous squint angle is θ, and the actual instantaneous position of the SAR is C[X(t a +τ)+Δx(t a ),Δy(t a ),H+Δz(t a )], wherein X(t a +τ)=v(t a +τ), and [Δx(t a ),Δy(t a ),Δz(t a )] represents the deviation of the actual trajectory from the ideal trajectory on the coordinate axis.

[0043] The reference slant range vector can be expressed as

[0044]

[0045] , wherein θ0 is the reference squint angle.

[0046] Considering a target Q(Δx n +R0sinθ0-Δy nR = R

[0047] R = R i R = R e

[0048] R = R i = (Δx n + R0sinθ0- X, -Δy n - R0cosθ0, 0) e = [Δx(t a ), Δy(t a ), Δz(t a )] represents the instantaneous slant-range error vector, Δx n and Δy n represent the offset of the target Q relative to the reference point P in the X and Y axis directions.

[0049] The received signal after De-chirped processing can be expressed as

[0050] s if (t a , τ) = A · σ(x n , y0, z0) · rect[(τ-Δτ) / T-1 / 2] · g(t a )

[0051] × exp[j2π(f c + γτ)Δτ - jτγΔτ 2 ],

[0052] where A is the signal amplitude, t a and τ represent the slow time and fast time, respectively, T is the signal transmission time width, σ(x n , y0, z0) is the target complex reflection coefficient, (x n , y0, z0) represents the X, Y, Z axis coordinates of the target in the Cartesian coordinate system, rect[(τ-Δτ) / T-1 / 2] and g(t a ) are the distance dimension envelope and the antenna pattern of the received signal after De-chirped processing, respectively, f c and γ represent the carrier frequency and the frequency modulation rate of the transmitted signal, respectively, Δτ = 2|R| / c is the target two-way time delay, |·| is the modulus operator; at this time, the signal is in the distance wavenumber domain-azimuth time domain.

[0053] (2.b) residual video phase compensation and intra-pulse motion compensation are performed on the received signal. The signal after residual video phase compensation is expressed as

[0054] s(X, K r ) = W r(K r )·g(X)·exp[-jK r (|R i |+ΔR)],

[0055] where X=vt a denotes azimuth spatial sampling point, W r (K r ) denotes range wave number domain envelope, g(X) denotes azimuth antenna pattern, K r =4π(f c +γτ) / c denotes range total wave number; intra-pulse motion compensation function H im (K a ,K r ) is expressed as

[0056]

[0057] where, K a =2πf a / v denotes azimuth wave number, f a denotes Doppler frequency. Two-dimensional wave number spectrum of compensated signal is expressed as

[0058]

[0059] where, denotes azimuth wave number domain motion error, K a denotes azimuth wave number, x n =Δx n +R0sinθ0 denotes X-axis coordinate of target Q, y n = -Δy n -R0cosθ0 denotes Y-axis coordinate of target Q.

[0060] (2.c) using Omega-K algorithm to perform SAR imaging on the signal obtained in step (1.b), to obtain a sub-aperture coarse-precision SAR image, including consistent compensation function compensation and Stolt interpolation; specifically, the consistent compensation function H rfm (K a ,K r ) is expressed as

[0061]

[0062] Here, H rfm (K a ,K r ) is directly multiplied with the signal S(K a ,K r ), then Stolt interpolation is performed on each range cell, and the Stolt interpolation kernel is expressed as where K y = K r - K rc denotes the range wavenumber, K rc = 4π / λ denotes the reference range wavenumber, and λ denotes the signal wavelength. Finally, a two-dimensional inverse Fourier transform is applied to the signal to achieve focusing, and a subaperture coarse accuracy SAR image is obtained.

[0063] The range Doppler signal is

[0064]

[0065] where K a denotes the azimuth wavenumber, and r denotes the range cell index, denotes the phase error in the azimuth wavenumber domain, B r denotes the transmitted signal bandwidth.

[0066] The subaperture coarse accuracy SAR image is

[0067]

[0068] where B a denotes the Doppler bandwidth, denotes the phase error in the azimuth time domain.

[0069] Step 3, subaperture SAR self-focusing, according to the definition of Rènyi entropy, the phase error is estimated subaperture by subaperture using the MREA method based on Rēnyi entropy, and then the phase error is compensated through the structural characteristics of the phase, and the iteration is continuously performed to obtain a subaperture high-precision SAR image. Specifically, it includes: solving the first derivative of Rényi entropy with respect to the phase error, obtaining the phase error iteration formula by the fixed point (Fixed Point, FP) method, phase error estimation and iterative phase correction:

[0070] After the subaperture image described in step 2 is discretized in two-dimensional time domain and range time domain-azimuth Doppler domain, the relationship between the two can be obtained

[0071]

[0072] where u(k,n), s(m,n) respectively denote the range Doppler domain data and the SAR image, M denotes the number of azimuth sampling points, k denotes the Doppler frequency, denotes the phase error at k.

[0073] The expression of Rényi entropy is defined as

[0074]

[0075] where N denotes the distance sampling point number, and |·| is the amplitude operator. Different selection of η value will affect the self-focusing result, and η is taken as 1.2 through experiment.

[0076] The FP method is used to solve the minimum Rényi entropy problem, and the first-order derivative of the Rényi entropy with respect to the phase error is obtained as

[0077]

[0078] wherein,

[0079]

[0080] Let the first-order derivative be 0, and can be obtained wherein, angle[·] is a complex amplitude angle function.

[0081] At this point, the iterative process of FP-MREA is obtained as

[0082]

[0083] wherein, u (l) (k,n), s (l) (m,n) correspond to the phase error of the lth iteration, the range-doppler domain and the SAR image respectively.

[0084] Iteration is continuously carried out until the Rényi entropy thresholds of the previous and the next two iterations are within a certain error range, and the specific expression is

[0085]

[0086] Step 4: According to the sub-aperture division principle of step 1, the sub-aperture splicing is carried out, and the full-aperture high-precision SAR image is obtained, and the sub-aperture splicing schematic diagram is as shown in Figure 3 wherein, L mos represents the splicing aperture length selected by each sub-aperture.

[0087] The effectiveness of the present application can be further illustrated by the following experiment.

[0088] (I) Data and experimental scene description

[0089] The radio frequency system of the vehicle-mounted SAR selects TI AWR2243 radar development board, and the vehicle-mounted SAR experimental parameters are as shown in Table 1. The size of the finally obtained vehicle-mounted SAR original echo data is 1024*112000 (range*azimuth). The experimental scene selects a parking lot scene, and more than ten vehicles are parked.

[0090] Table 1 Vehicle-borne SAR experiment parameters

[0091]

[0092] (II) SAR coarse imaging results

[0093] The optical image of the experimental scene and the full-aperture SAR contrast image after sub-aperture coarse-precision imaging and splicing are shown in Fig. 1, and the scene size is about 15 m x 40 m (range x azimuth), wherein the SAR image is divided into five red box regions, each of which corresponds to an optical image; the whole image mainly contains more than ten vehicles, and the outline of each vehicle is relatively clear. However, it is obvious that due to the existence of vehicle motion error, defocusing exists in the imaging result, and therefore motion compensation is needed to obtain a SAR image with good focusing. Figure 5

[0094] (II) SAR self-focusing results

[0095] In this experiment, 27 sub-aperture coarse-precision SAR images are obtained after sub-aperture division. After image optimization by the self-focusing method, the full-aperture high-precision vehicle-borne SAR image is obtained after sub-aperture splicing.

[0096] 1. Comparison of different self-focusing methods

[0097] Here, the results of different self-focusing methods are compared, and the comparison methods include the FP-MEA method, the MCA method, the WPGA method and the method of the embodiment of the present application; Figure 6 The comparison results are shown in Fig. 2, wherein (a) is the original SAR image; (b) is the SAR image processed by the FP-MEA method; (c) is the SAR image processed by the MCA method; (d) is the SAR image processed by the WPGA method; and (e) is the SAR image processed by the method of the embodiment of the present application. It can be seen that the self-focusing method is effective in the vehicle-borne scene, wherein the method of the embodiment of the present application significantly improves the SNR and quality of the SAR image while retaining the details, and has the best performance.

[0098] Quantitative analysis is performed to statistically analyze the performance indicators of the self-focusing methods, including Shannon entropy, Rényi entropy and contrast, and the results are shown in Table 2. It can be seen that for the three indicators, the performance indicators of the method of the embodiment of the present application are the best, which fully illustrates the superiority of the method of the embodiment in complex scenes.

[0099] Table 2 Performance indicators of different self-focusing methods

[0100] Method Shannon entropy Rènyi entropy Contrast Original image 14.0452 13.7222 2.1374 FP-MEA method 13.7893 13.3652 2.3403 MCA method 13.8825 13.3819 2.3516 WPGA method 13.9443 13.5824 2.2454 The method of the invention 13.5254 12.9147 2.5566

[0101] 2. Comparison of convergence of different self-focusing methods

[0102] ​Here, the convergence performance of different autofocusing methods in the B region of the original imaging scene is compared, and the comparison methods are the FP-MEA method, the MCA method, the WPGA method and the method of the embodiment of the present application. Figure 7 (a) gives the comparison results of different autofocusing methods on the Shannon entropy index, Figure 7 (b) gives the comparison results of different autofocusing methods on the Rényi entropy index, and the method of the embodiment of the present application has a faster convergence speed and can converge to the lowest index among the above-mentioned methods.

[0103] In summary, the present application provides a vehicle-mounted SAR imaging autofocusing method based on Rényi entropy for complex vehicle-mounted scenes, which can more accurately represent vehicle-mounted SAR images using Rényi entropy, and theoretically derives the iterative optimization process of the autofocusing method, thereby improving the stability and applicability of SAR imaging in complex vehicle-mounted application scenarios.

[0104] The embodiment of the present application also provides a computer system, which comprises a memory, a processor and a computer program stored on the memory and executable on the processor, and the computer program is executed by the processor to realize the steps of the vehicle-mounted SAR imaging autofocusing method based on Rényi entropy.

[0105] The embodiment of the present application also provides a computer program product comprising a computer program, and the computer program is executed by the processor to realize the steps of the vehicle-mounted SAR imaging autofocusing method based on Rényi entropy.

[0106] The program code for implementing the method of the present application can be written in any combination of one or more programming languages. The program code can be provided to a processor or controller of a general purpose computer, a special purpose computer, or other programmable data processing apparatus, such that the program code, when executed by the processor or controller, causes the steps of the method of the present application to be implemented. The program code can be executed entirely on a machine, partially on a machine, partially on a machine as a separate software package and partially on a remote machine, or entirely on a remote machine or server. The present application does not detail what is known to those skilled in the art.

[0107] The preferred embodiments of the present application are described in detail above. It should be understood that those skilled in the art can make many modifications and changes without creative labor based on the concept of the present application. Therefore, any technical solution obtained by logical analysis, reasoning or limited experiments based on the prior art according to the concept of the present application shall be within the protection scope defined by the claims.

Claims

1. A method for vehicle-borne SAR imaging autofocusing based on Rényi entropy, characterized in that, The application relates to a vehicle-mounted SAR imaging method based on Rényi entropy. The vehicle-mounted SAR raw echo data are divided into sub-apertures; Each sub-aperture SAR raw FMCW signal is subjected to SAR imaging by using an Omega-K algorithm; According to the definition of Rényi entropy, the phase error is estimated sub-aperture by sub-aperture using the MREA method based on the minimum Rényi entropy, the phase error is compensated, and the sub-aperture high-precision SAR image is obtained through the fixed point FP method and iteration; the expression of the Rényi entropy is defined as wherein, The selection of different η values has an impact on the self-focusing result, and based on the experimental effect, η is selected as The element of the mth column and the nth row of the SAR image is represented, M represents the number of azimuth sampling points, and N represents the number of range sampling points. Full-aperture high-precision SAR images are obtained by sub-aperture splicing.

2. The Rényi entropy-based self-focusing method for vehicular SAR imaging according to claim 1, wherein, In the sub-aperture division, the length range of the sub-aperture is determined based on the difference between the minimum distance and the maximum distance of the imaging area, in combination with the antenna beam angle and the proportional constraint of system design.

3. The Rényi entropy-based self-focusing method for vehicular SAR imaging according to claim 1, wherein, The SAR imaging of each sub-aperture SAR raw FMCW signal by using the Omega-K algorithm comprises: residual video phase compensation and intra-pulse motion compensation of the received signal; and SAR imaging of the signal subjected to the residual video phase compensation and the intra-pulse motion compensation by using the Omega-K algorithm, so as to obtain a coarse-precision SAR image.

4. The Rényi entropy-based self-focusing method for vehicular SAR imaging according to claim 3, characterized in that, The SAR imaging of the signal compensated for residual video phase and intra-pulse motion using the Omega-K algorithm includes consistent compensation function compensation and Stolt interpolation, the consistent compensation function is expressed as , , and respectively represent the distance wave number, the azimuth wave number and the reference distance, ; the Stolt interpolation kernel is expressed as , represents the distance wave number, represents the reference distance wave number, represents the signal wavelength.

5. The Rényi entropy-based self-focusing method for vehicular SAR imaging according to claim 1, wherein, The MREA method based on the minimum Rényi entropy comprises: solving the first-order derivative of the Rényi entropy with respect to the phase error, obtaining an iterative formula of the phase error by using an FP method, phase error estimation and iterative phase correction.

6. The Rényi entropy-based vehicular SAR imaging self-focusing method according to claim 5, characterized in that, The minimum Rényi entropy problem is solved using the FP method, yielding the Rényi entropy with respect to the phase error. The first derivative is ； where k denotes a Doppler frequency point, denotes the estimated phase error at k, denotes the true phase error at k, denotes the imaginary part operator, denotes the element in the nth row and kth column of the range-Doppler domain data, .

7. The Rényi entropy-based vehicular SAR imaging self-focusing method according to claim 6, characterized in that, The iterative process of the FP-MREA is represented as ； wherein, , , respectively correspond to the phase error, the range-doppler domain data and the SAR image data of the lth iteration; the iteration is continuously carried out until the Rényi entropy thresholds of the two adjacent iterations are within the set error range.

8. A computer system comprising a memory, a processor, and a computer program stored on the memory and executable on the processor, characterized in that, The computer program is executed by the processor to realize the steps of the vehicle-mounted SAR imaging self-focusing method based on the Rényi entropy according to any one of claims 1-7.

9. A computer program product comprising a computer program, characterized in that, The computer program is executed by the processor to realize the steps of the vehicle-mounted SAR imaging self-focusing method based on the Rényi entropy according to any one of claims 1-7.

Images