A centimeter-level high-precision calibration method for multi-angle SAR slant range error based on Luneberg sphere reflector

Abstract

The present invention proposes a centimeter-level high-precision calibration method for multi-angle SAR slant range error based on Luneberg sphere reflectors, which includes deploying Luneberg sphere radar reflectors; taking multi-angle SAR images of the calibration site; obtaining the image coordinates of the Luneberg sphere reflectors on the multi-angle SAR images; calculating the RD model parameters of each Luneberg sphere reflector on each SAR image; performing slant range correction on the Luneberg sphere reflector so that the strong scattering center of the Luneberg sphere reflector is equivalent to the center of the sphere; using the corrected slant range, taking the slant range error, the equivalent Doppler center frequency error, and the three-dimensional coordinates of each Luneberg sphere reflector as unknown quantities, establishing a slant range error joint calibration model based on a unified dimension RD model; solving the slant range error, the equivalent Doppler center frequency error, and the three-dimensional coordinates of each Luneberg sphere in the multi-angle SAR slant range error joint calibration model. The present invention does not require field measurement of the Luneberg sphere reflector, and can achieve robust, centimeter-level high-precision joint calibration of the slant range error using multi-angle SAR data.

Description

Technical Field

[0001] The invention relates to a synthetic aperture radar three-dimensional positioning and geometric calibration technology, and in particular to a centimeter-level high-precision calibration method and device for a multi-angle SAR slant range error based on a Luneberg sphere reflector. Background Art

[0002] SAR geometric calibration can eliminate the errors of satellite-borne or airborne SAR imaging systems and improve the geometric positioning accuracy of SAR images. It is a key link in achieving SAR high-precision positioning and subsequent interferometric processing and three-dimensional imaging processing. The traditional geometric calibration method requires the use of a large number of corner reflectors to build a geometric calibration field, and the high-precision three-dimensional geographic coordinates of the corner reflectors need to be measured as control points, and then the SAR geometric calibration model is established and the least squares adjustment is performed to solve the errors of slant range, azimuth time, etc.

[0003] However, in the calibration of geometric errors based on corner reflectors, in order to make the corner reflectors have better imaging effects, it is usually necessary to manually measure the angles, adjust the attitude and angle of the corner reflectors with the vertex of the corner reflectors as the center, and make the incident direction of the electromagnetic wave consistent with its normal direction. In addition, since the trihedral corner reflector is not omnidirectional, for SAR with multi-angle observation, in order to obtain good imaging effects in different directions, it is necessary to deploy multiple trihedral corner reflectors at the same time, and the vertices of each corner reflector need to be highly overlapped to be used as effective connection points for slant range error calibration. This places high operational requirements on the deployment of trihedral corner reflectors and increases the error sources, making it difficult to achieve centimeter-level high-precision slant range error calibration requirements.

[0004] Unlike corner reflectors, Luneberg sphere radar reflectors are spherically symmetrical optical systems. Figure 1 As shown in the figure, no matter from which direction the electromagnetic wave is incident, it can converge the incident electromagnetic wave to the other end of the diameter perpendicular to the plane wavefront. Therefore, all points on the surface of the Luneburg sphere reflector can be used as the focus of convergence, and it is a device with consistent isotropic scattering characteristics. However, at different incident angles, the focal position of the electromagnetic wave on the Luneburg sphere reflector is not the same. As a result, the actual scattering position corresponding to the strong scattering center on the SAR image at different angles is not the same, which in turn affects the calibration accuracy of the slant range error of the multi-angle SAR image.

[0005] At present, the existing technology mainly uses a trihedral corner reflector and accurately measures the position of its vertex to achieve SAR slant range error calibration, and the calibration accuracy is mainly at the meter level, and can reach the decimeter level at most, so it is not very sensitive to the error of the calibrator. This technology uses the method of obtaining multi-angle observation data from the Luneberg sphere in the same scene, without measuring the position of the calibrator, and can achieve centimeter-level accuracy calibration of the SAR system's slant range error. Summary of the invention

[0006] The purpose of the present invention is to provide a centimeter-level high-precision calibration method and device for multi-angle SAR slant range error based on Luneberg sphere reflector.

[0007] The technical solution to achieve the purpose of the present invention is: a centimeter-level high-precision calibration method for multi-angle SAR slant range error based on Luneberg sphere reflector, comprising the following steps:

[0008] The first step is to deploy Luneberg sphere radar reflectors at the calibration site;

[0009] The second step is to take multi-angle SAR images of the calibration site;

[0010] The third step is to obtain the image coordinates of the Luneberg sphere reflector on the multi-angle SAR image;

[0011] The fourth step is to calculate the RD model parameters of each Luneburg sphere reflector on each SAR image;

[0012] The fifth step is to perform slant range correction on the Luneburg sphere reflector so that the strong scattering center of the Luneburg sphere reflector is equivalent to the center of the sphere;

[0013] The sixth step is to use the corrected slant range, take the slant range error, equivalent Doppler center frequency error, and the three-dimensional coordinates of each Luneberg sphere reflector as unknown quantities, and establish a slant range error joint calibration model based on the unified dimension RD model;

[0014] The seventh step is to solve the slant range error, equivalent Doppler center frequency error, and three-dimensional coordinates of each Luneberg sphere in the multi-angle SAR slant range error joint calibration model.

[0015] Furthermore, in the second step, the intersection angle of the captured multi-angle SAR images should not be less than 10°.

[0016] Furthermore, in the fourth step, the slant range correction is performed on the Luneberg sphere reflector. The specific method is as follows:

[0017]

[0018] Where R' is the corrected slope distance, d is the diameter of the Luneberg sphere, and v air is the propagation speed of electromagnetic waves in air, v vacuo is the propagation speed of electromagnetic waves in vacuum, ε r is the equivalent relative dielectric constant of the Luneberg sphere.

[0019] Furthermore, in the sixth step, a slant range error joint calibration model based on the unified dimension RD model is established, specifically:

[0020]

[0021] Where i = 1, 2, ..., n is the number of the n multi-angle SAR images, j = 1, 2, ..., m is the number of the j Luneberg spheres deployed, and f ij1 and f ij2 are the distance equation and Doppler equation under unified dimension established for the j-th Luneberg sphere in the i-th SAR image, (X j , Y j , Z j ) is the three-dimensional coordinate of the j-th Luneberg sphere to be solved, (X sij , Y Sij , Z Sij ) is the phase center position of the radar antenna corresponding to the jth Luneberg sphere in the i-th SAR image, V ij (V Xij , V Yij , V Zij ) is the radar antenna phase center velocity corresponding to the jth Luneberg sphere in the i-th SAR image, R′ ij is the slant range corrected by the j-th Luneberg sphere in the i-th SAR image, R b is the slope range error to be calibrated, f Dij is the Doppler center frequency corresponding to the jth Luneberg sphere in the i-th SAR image, f Db is the equivalent Doppler center frequency error to be calibrated, and λ is the wavelength of the electromagnetic wave emitted by the radar.

[0022] In the seventh step, the Gauss-Newton iteration method is used to solve the multi-angle SAR slant range error joint calibration model. The specific method is as follows:

[0023] In each iteration, the slant range error joint calibration model based on the unified dimension RD model is linearized to obtain the following linearized equations:

[0024] Jx=b

[0025] x=[x 1 ...x m ΔR b Δf Db ] T , b=[b 1 ...b m ] T

[0026]

[0027]

[0028] Among them, the matrix J is the Jacobian matrix of the nonlinear equation system, the x vector contains the correction values ​​of the three-dimensional coordinates of the calibrator, the slant range error, and the equivalent Doppler center frequency error, and the b vector is the residual vector;

[0029] According to the least squares principle, the least squares solution is:

[0030] x (k )=(J T J) -1 J T b

[0031] So, the calculated result x (k) , add the calibrator's three-dimensional coordinates, slant range error, and equivalent Doppler center frequency error to obtain the updated value, and determine the correction vector x (k) Is the modulus greater than 0.00001? If so, proceed to the next iteration; otherwise, the iteration ends and the slope distance error of the last iteration is output as the calibration value.

[0032] A centimeter-level high-precision calibration system for multi-angle SAR slant range error based on a Luneberg sphere reflector realizes centimeter-level high-precision calibration of multi-angle SAR slant range error based on a Luneberg sphere reflector based on the centimeter-level high-precision calibration method for multi-angle SAR slant range error.

[0033] A computer device comprises a memory, a processor and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, based on the centimeter-level high-precision calibration method for the multi-angle SAR slant range error, centimeter-level high-precision calibration of the multi-angle SAR slant range error based on a Luneberg sphere reflector is achieved.

[0034] A computer-readable storage medium stores a computer program. When the computer program is executed by a processor, based on the centimeter-level high-precision calibration method for the multi-angle SAR slant range error, a centimeter-level high-precision calibration of the multi-angle SAR slant range error based on a Luneberg sphere reflector is achieved.

[0035] Compared with the prior art, the present invention has the following significant advantages: 1) a Luneberg sphere radar reflector is used as a calibrator, and the Luneberg sphere scattering position is equivalent to the center of the sphere through a slant range correction method, so that the Luneberg sphere scattering position during the joint calibration of multi-angle SAR data is equivalent to the same point in the geographic space, thereby achieving high-precision calibration of centimeter-level slant range errors; 2) a multi-angle SAR slant range error joint calibration method based on a unified dimension RD model is adopted, which does not require measuring the geographic coordinates of the Luneberg sphere reflector, and is more convenient and quick; at the same time, the unified dimension RD model can achieve robust calibration of slant range errors under multi-angle SAR data. BRIEF DESCRIPTION OF THE DRAWINGS

[0036] Figure 1 This is the structure and principle diagram of the Luneburg sphere lens reflector.

[0037] Figure 2 It is a flow chart of the present invention.

[0038] Figure 3 Schematic diagram of the calibration site, calibrator position and flight trajectory in the embodiment. DETAILED DESCRIPTION

[0039] In order to make the purpose, technical solution and advantages of the present application more clearly understood, the present application is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present application and are not used to limit the present application.

[0040] The present invention provides a centimeter-level high-precision calibration method and system for multi-angle SAR slant range error based on Luneberg sphere reflectors, and proposes a method for slant range correction of Luneberg sphere corner reflectors under multi-angle SAR data conditions, which solves the problem of different scattering positions of Luneberg sphere reflectors under SAR data at different angles. Further, a multi-angle SAR slant range error joint calibration method based on a unified dimension RD model is proposed, which does not require field measurement of the Luneberg sphere reflector, and can achieve robust, centimeter-level high-precision joint calibration of slant range error using multi-angle SAR data. The specific implementation process is as follows: Figure 2 As shown, the main steps are:

[0041] 1) Install the Luneburg sphere reflector device at the calibration site:

[0042] The Luneberg sphere reflector is best placed on open flat ground, away from areas prone to overlap, shadows, etc. After placement, there is no need to measure the geographical coordinates of the Luneberg sphere.

[0043] 2) Take multi-angle SAR images of the calibration site and obtain the image coordinates of the Luneburg sphere on the multi-angle SAR images:

[0044] Since the error calibration method of the present invention is based on the principle of stereo SAR, the intersection angle of the SAR image should not be less than 10°.

[0045] 3) Calculate the RD model parameters of each Luneburg sphere reflector corresponding to each SAR image:

[0046] For each Luneberg sphere reflector, the corresponding slant range R, Doppler center frequency f, and D , radar wavelength λ, position S and velocity V of the radar antenna phase center. The calculation method is an existing method and will not be repeated here.

[0047] 4) Slant range correction for the Luneburg sphere reflector:

[0048] like Figure 1 As shown in the figure, since the actual scattering position of the electromagnetic wave incident on the Luneberg sphere is at the other end F of the perpendicular diameter to the plane wavefront, when the incident angle of the electromagnetic wave is different, the geographical coordinates corresponding to the strong scattering center positions on different SAR images are actually different. In addition, the relative dielectric constant of the material inside the Luneberg sphere is different from that of the air, which will also cause errors in the slant range. In order to make the strong scattering center of the Luneberg sphere reflector equivalent to the center of the sphere, the following formula needs to be used to correct the slant range R calculated in the previous step:

[0049]

[0050] Where R' is the corrected slope distance, d is the diameter of the Luneberg sphere, and v air is the propagation speed of electromagnetic waves in air, v vacuo is the propagation speed of electromagnetic waves in vacuum, ε r is the equivalent relative dielectric constant of the Luneberg sphere;

[0051] 5) Establish a joint calibration model for multi-angle SAR slant range error based on a unified dimension RD model:

[0052] Using the corrected slope distance R′ and other RD model parameters, the slope distance error R b , equivalent Doppler center frequency error f Db The three-dimensional coordinates of each Luneberg sphere reflector are unknown quantities, and the following slant range error joint calibration model based on the unified dimension RD model is established:

[0053]

[0054] Wherein, i=1, 2, ..., n is the number of n multi-angle SAR images, j=1, 2, ..., m is the number of j Luneberg spheres, and f ij1 and f ij2 are the distance equation and Doppler equation under unified dimension established for the j-th Luneberg sphere in the i-th SAR image, (X j , Y j , Z j ) is the three-dimensional coordinate of the j-th Luneberg sphere to be solved, (X Sij , Y Sij , Z Sij ) is the phase center position of the radar antenna corresponding to the jth Luneberg sphere in the i-th SAR image, V ij (V Xij , V Yij , V Zij ) is the radar antenna phase center velocity corresponding to the jth Luneberg sphere in the i-th SAR image, R′ ij is the slant range corrected by the j-th Luneberg sphere in the i-th SAR image, Rb is the slope range error to be calibrated, f Dij is the Doppler center frequency corresponding to the jth Luneberg sphere in the i-th SAR image, f Db is the equivalent Doppler center frequency error to be calibrated, and λ is the wavelength of the electromagnetic wave emitted by the radar.

[0055] Among them, R b It can be a polynomial about the distance coordinate c, that is, formula (3).

[0056] R b =R b0 +R b1 c+R b2 c 2 +...+R bn c n (3)

[0057] Among them, R bi , i = 0, 1, ..., n are polynomial coefficients. In most cases, only the constant term is considered.

[0058] 6) Solve the slant range error, equivalent Doppler center frequency error and three-dimensional coordinates of each Luneberg sphere reflector in the multi-angle SAR slant range error joint calibration model:

[0059] The system of equations established in the previous step contains 2mn equations, and the unknown number is R b 、f Db and (X j , Y j , Z j ), the least square solution of the equation group is the slope range error calibration result. The solution method can be the Gauss-Newton iteration method. In each iteration, the slope range error joint calibration model based on the unified dimension RD model in the previous step (Equation (2)) needs to be linearized to obtain the following linearized equation group:

[0060] J·x=b

[0061] x=[x 1 ...x m ΔR b Δf Db ] T , b=[b 1 ...b m ] T

[0062]

[0063]

[0064] Among them, the matrix J is the Jacobian matrix of the nonlinear equation group (2), the x vector contains the correction values ​​of the calibrator's three-dimensional coordinates, slant range error, and equivalent Doppler center frequency error, and the b vector is the residual vector.

[0065] According to the least squares principle, the least squares solution of formula (4) is:

[0066] x (k) =(J T J) -1 J T b (5)

[0067] Therefore, the calculation result x of formula (5) is (k) , add it to the calibrator's three-dimensional coordinates, slant range error, and equivalent Doppler center frequency error to get the updated value. And determine the correction vector x (k) Is the modulus greater than 0.00001? If so, proceed to the next iteration; otherwise, the iteration ends and the slope distance error of the last iteration is output as the calibration value.

[0068] The present invention also proposes a centimeter-level high-precision calibration system for multi-angle SAR slant range error based on a Luneburg sphere reflector. Based on the centimeter-level high-precision calibration method for multi-angle SAR slant range error, centimeter-level high-precision calibration of multi-angle SAR slant range error based on a Luneburg sphere reflector is achieved.

[0069] A computer device comprises a memory, a processor and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, based on the centimeter-level high-precision calibration method for the multi-angle SAR slant range error, centimeter-level high-precision calibration of the multi-angle SAR slant range error based on a Luneberg sphere reflector is achieved.

[0070] A computer-readable storage medium stores a computer program. When the computer program is executed by a processor, based on the centimeter-level high-precision calibration method for the multi-angle SAR slant range error, a centimeter-level high-precision calibration of the multi-angle SAR slant range error based on a Luneberg sphere reflector is achieved.

[0071] Example

[0072] This embodiment uses a miniature Ku-band SAR system carried by an unmanned aerial vehicle to conduct image capture and slant range calibration experiments in the Binhai New Area of ​​Tianjin. The image resolution of the SAR system is 6 cm, and the track measurement accuracy is better than 5 cm, which creates conditions for centimeter-level slant range error calibration accuracy. In order to achieve centimeter-level calibration accuracy, it is necessary to deploy a Luneburg sphere reflector device at the calibration site, and use the method of the present invention to calibrate the slant range error.

[0073] Therefore, a total of 4 Luneberg sphere reflectors were deployed in the calibration site, numbered L1 to L4. At the same time, a total of 4 corner reflectors were deployed as a control group, numbered J1 to J4. The location of the deployed calibrators and the schematic diagram of the flight trajectory are shown in the figure below. Figure 3 As shown in the figure, the calibrators are evenly distributed in an open area. The center of the Luneburg sphere calibrator and the vertex of the corner reflector are measured by GPS to obtain the reference three-dimensional coordinates of each calibrator for subsequent three-dimensional positioning accuracy verification. Subsequently, the drone flew along the red dotted line and captured SAR images at eight angles, numbered ID01 to ID08, and upsampled to obtain the image coordinates of each calibrator.

[0074] The method proposed in the present invention is used to calculate the RD model parameters of each calibrator. The slant distance of the Luneberg sphere reflector is corrected according to formula (1), and the slant distance correction value is 25.17 cm. Among them, the radius of the Luneberg sphere is 15 cm, and the transmission delay of the electromagnetic wave inside the Luneberg sphere is 10.17 cm. After the slant distance correction of the Luneberg sphere, the actual scattering positions of the electromagnetic waves incident on the Luneberg sphere from multiple angles can all be equivalent to the center of the sphere.

[0075] Subsequently, using images ID01-ID08 as the SAR data for joint calibration, a multi-angle SAR slant range error joint calibration model based on a unified dimension RD model is constructed. The slant range error, equivalent Doppler center frequency error, and three-dimensional position of the calibrator in the model are all unknown quantities, and the least squares solution is performed. The slant range error in this embodiment is set as a first-order polynomial of the range coordinate c. Finally, the following slant range error calibration value is obtained.

[0076] Table 1 Slant range error calibration results

[0077]

[0078]

[0079] At the same time, the three-dimensional coordinates of the calibrator obtained by subtracting the three-dimensional coordinates of the calibrator obtained by GPS field measurement are used to obtain the three-dimensional positioning accuracy of the calibrator. This accuracy can reflect the three-dimensional positioning accuracy after the slope range error calibration. At the same time, the three-dimensional positioning accuracy obtained by the traditional forward intersection method is compared and calculated as the positioning accuracy before error calibration. The results are shown in the following table.

[0080] Table 2 3D coordinate solution results of the calibrator (unit: cm)

[0081]

[0082] It can be seen that the three-dimensional positioning accuracy of the slant range error calibration method based on the Luneburg sphere reflector proposed in the present invention is 2.9 cm, which is significantly improved compared with the slant range error before calibration. At the same time, since this method is based on the structural characteristics of the Luneburg sphere reflector, the slant range of the Luneburg sphere reflector is corrected, so that SAR data with different incident angles can have the same and clear scattering position on the Luneburg sphere reflector. Therefore, the positioning accuracy obtained by this method is better than the calibration method using the corner reflector device, and it is a centimeter-level high-precision slant range error calibration method.

[0083] The technical features of the above embodiments may be combined arbitrarily. To make the description concise, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0084] The above-described embodiments only express several implementation methods of the present application, and the descriptions thereof are relatively specific and detailed, but they cannot be understood as limiting the scope of the present application. It should be pointed out that, for a person of ordinary skill in the art, several variations and improvements can be made without departing from the concept of the present application, and these all belong to the protection scope of the present application. Therefore, the protection scope of the present application shall be subject to the attached claims.

Claims

1. A centimeter-level high-precision calibration method for multi-angle SAR slant range error based on Luneberg sphere reflector. It is characterized in that The steps include: The first step is to deploy Luneberg sphere radar reflectors at the calibration site; The second step is to take multi-angle SAR images of the calibration site; The third step is to obtain the image coordinates of the Luneberg sphere reflector on the multi-angle SAR image; The fourth step is to calculate the RD model parameters of each Luneburg sphere reflector on each SAR image; The fifth step is to perform slant range correction on the Luneburg sphere reflector so that the strong scattering center of the Luneburg sphere reflector is equivalent to the center of the sphere; The sixth step is to use the corrected slant range, take the slant range error, equivalent Doppler center frequency error, and the three-dimensional coordinates of each Luneberg sphere reflector as unknown quantities, and establish a slant range error joint calibration model based on the unified dimension RD model; Step 7: Solve the slant range error, equivalent Doppler center frequency error, and three-dimensional coordinates of each Luneberg sphere in the multi-angle SAR slant range error joint calibration model; Among them, the slant range correction of the Luneberg sphere reflector is performed as follows: Where R′ is the corrected slope distance, d is the diameter of the Luneberg sphere, and v air is the propagation speed of electromagnetic waves in air, v vacuo is the propagation speed of electromagnetic waves in vacuum, ε r is the equivalent relative dielectric constant of the Luneberg sphere.

2. According to the method for centimeter-level high-precision calibration of multi-angle SAR slant range error based on Luneberg sphere reflector according to claim 1, It is characterized in that In the second step, the intersection angle of the multi-angle SAR images taken should not be less than 10°.

3. According to the method for centimeter-level high-precision calibration of multi-angle SAR slant range error based on Luneberg sphere reflector in claim 1, It is characterized in that The sixth step is to establish a slant range error joint calibration model based on the unified dimension RD model, specifically: Where i = 1, 2, ..., n is the number of the n multi-angle SAR images, j = 1, 2, ..., m is the number of the j Luneberg spheres deployed, and f ij1 and f ij2 are the distance equation and Doppler equation under unified dimension established for the j-th Luneberg sphere in the i-th SAR image, (X j ,Y j ,Z j ) is the three-dimensional coordinate of the j-th Luneberg sphere to be solved, (X Sij ,Y Sij ,Z Sij ) is the phase center position of the radar antenna corresponding to the jth Luneberg sphere in the i-th SAR image, V ij (V Xij ,V Yij ,V Zij ) is the radar antenna phase center velocity corresponding to the jth Luneberg sphere in the i-th SAR image, R′ ij is the slant range corrected by the j-th Luneberg sphere in the i-th SAR image, R b is the slope range error to be calibrated, f Dij is the Doppler center frequency corresponding to the jth Luneberg sphere in the i-th SAR image, f Db is the equivalent Doppler center frequency error to be calibrated, and λ is the wavelength of the electromagnetic wave emitted by the radar.

4. According to the method for centimeter-level high-precision calibration of multi-angle SAR slant range error based on Luneberg sphere reflector according to claim 3, It is characterized in that The seventh step is to use the Gauss-Newton iteration method to solve the multi-angle SAR slant range error joint calibration model. The specific method is: In each iteration, the slant range error joint calibration model based on the unified dimension RD model is linearized to obtain the following linearized equations: Among them, the matrix J is the Jacobian matrix of the nonlinear equation system, the x vector contains the correction values ​​of the three-dimensional coordinates of the calibrator, the slant range error, and the equivalent Doppler center frequency error, and the b vector is the residual vector; According to the least squares principle, the least squares solution is: x (k) =(J T J) -1 J T b So, the calculated result x (k) , add the calibrator's three-dimensional coordinates, slant range error, and equivalent Doppler center frequency error to obtain the updated value, and determine the correction vector x (k) Is the modulus greater than 0.00001? If so, proceed to the next iteration; otherwise, the iteration ends and the slope distance error of the last iteration is output as the calibration value.

5. A centimeter-level high-precision calibration system for multi-angle SAR slant range error based on Luneberg sphere reflector. It is characterized in that Based on the centimeter-level high-precision calibration method for the multi-angle SAR slant range error according to any one of claims 1 to 4, the centimeter-level high-precision calibration of the multi-angle SAR slant range error based on the Luneberg sphere reflector is achieved.

6. A computer device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein when the processor executes the computer program, based on the centimeter-level high-precision calibration method for the multi-angle SAR slant range error according to any one of claims 1 to 4, centimeter-level high-precision calibration of the multi-angle SAR slant range error based on a Luneberg sphere reflector is realized.

7. A computer-readable storage medium having a computer program stored thereon, wherein when the computer program is executed by a processor, based on the centimeter-level high-precision calibration method for the multi-angle SAR slant range error according to any one of claims 1 to 4, a centimeter-level high-precision calibration of the multi-angle SAR slant range error based on a Luneberg sphere reflector is implemented.

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