SAR (Synthetic Aperture Radar) imaging compensation method based on motion error of mobile terminal

Abstract

The invention discloses an SAR (Synthetic Aperture Radar) imaging compensation method based on a motion error of a mobile terminal, which comprises the following steps of: establishing an xyz coordinate system, and generating moving tracks Rx, Ry and Rz of the mobile terminal according to the moving speeds vx, vy and vz of the mobile terminal in each frame; according to Rx, Ry and Rz, echo signals Sr formed after signals emitted by the mobile terminal are reflected by all the point targets are obtained, and the radial speed and distance of the mobile terminal relative to each preset corner reflector target in each frame are solved according to Sr; fitting the distance of the mobile terminal relative to each preset corner reflector target in the mth frame, substituting the fitted distance into the non-linear programming model, and determining the search range of the non-limited programming model based on the coordinate of the mobile terminal in the (m-1) th frame and the radial speed of the mobile terminal relative to each preset corner reflector target, obtaining the coordinates of the mobile terminal in the mth frame; coordinates of the mobile terminal in all the frames are obtained, and actual movement tracks Rxx, Ryy and Rzz of the mobile terminal are generated for backward projection imaging.

Description

Technical Field

[0001] The invention belongs to the technical field of SAR imaging, and in particular relates to a SAR imaging compensation method based on mobile terminal motion error. Background Art

[0002] With the rapid development of mobile communication technology, mobile base stations and terminal equipment have become widely popular. Radio waves not only transmit information, but also have the ability to perceive information. The sixth generation of mobile communication technology (6G) not only focuses on large-bandwidth communication, but also has detection and perception capabilities to achieve the integration of communication and perception.

[0003] At present, the industry's research on ISAC (Integrated Sensing And Communications) perception imaging is mainly focused on base station real aperture perception imaging. In this mode, the transmission and reception process of perception signals can be completed through a single base station. It has advantages in signal transmission and reception synchronization, can greatly improve perception accuracy, and the networking of a single base station is more convenient, flexible and easy to implement. However, since the base station antenna is fixed and has a small aperture, it can only perform real aperture imaging, and its long-distance resolution is low, which makes it difficult to meet the requirements of perception imaging in many application scenarios.

[0004] As two parties in mobile communication, the base station and the mobile terminal can form a dual-base perception imaging system, that is, a base station-mobile terminal dual-base imaging system. The mobility of the terminal enables it to form a longer virtual aperture through the user's handheld movement, thereby effectively improving the azimuth resolution of the imaging, solving the problem of insufficient resolution of the base station's real aperture in long-distance perception imaging, and improving the ISAC perception imaging performance to meet the needs of more application scenarios. However, due to the fluctuation and offset of the center of gravity caused by human body movement, the movement trajectory of the mobile terminal will be unsatisfactory, which will adversely affect the imaging performance. Therefore, it is necessary to provide a suitable motion compensation method to achieve high-resolution imaging.

[0005] For base station-mobile terminal dual-base imaging, there is a motion compensation method based on image entropy iteration in the prior art, which mainly includes three steps: first, a BP (Back Projection) algorithm is used to perform coarse imaging of the target scene. At this time, the imaging performance is deteriorated due to the displacement of the center of gravity of the user holding the mobile terminal; then, the human body motion parameters are jointly estimated and an error correction model is established; finally, motion compensated imaging is performed based on the error correction model. When the error correction model continuously approaches the real human body motion trajectory, it can compensate for the human body motion error and obtain the imaging result after focus compensation.

[0006] The above method only stays in the simulation stage, only assuming that the human body motion model is a simple sine function, and can only solve the scenario of human body uniform motion, without considering the speed information. However, research shows that the human body motion trajectory model is actually the superposition of multiple sine functions. If the above motion compensation method based on image entropy iteration is used, multiple initial phases and amplitude parameters need to be iterated, resulting in a huge amount of computation, and the parameters cannot be fitted to the optimal state, ultimately leading to poor compensation focusing effect. Summary of the Invention

[0007] In order to solve the above problems existing in the prior art, the present invention provides a SAR imaging compensation method based on the motion error of a mobile terminal. The technical problems to be solved by the present invention are realized through the following technical solutions:

[0008] The present invention provides a SAR imaging compensation method based on the motion error of a mobile terminal, including:

[0009] Establish an xyz coordinate system, and generate the moving trajectories R x 、R y 、R z of the mobile terminal in the x-axis, y-axis, and z-axis directions according to the moving speeds v x 、v y 、v z of the mobile terminal in each frame;

[0010] According to the moving trajectories R x 、R y 、R z , obtain the echo signal Sr formed after the signal emitted by the mobile terminal is reflected by all point targets, and calculate the radial velocity and distance of the mobile terminal relative to each preset corner reflector target in each frame according to the echo signal Sr;

[0011] Fit the distance of the mobile terminal relative to each preset corner reflector target in the mth frame, substitute the fitted distance into the nonlinear programming model, and determine the search range of the non-restricted programming model based on the coordinates of the mobile terminal and its radial velocity relative to each preset corner reflector target in the (m - 1)th frame, to obtain the coordinates of the mobile terminal in the mth frame; where m = 2, 3,..., M, and M represents the number of frames;

[0012] Obtain the coordinates of the mobile terminal in all frames, and generate the actual moving trajectories R xx 、R yy and R zz of the mobile terminal in the x-axis, y-axis, and z-axis for back-projection imaging.

[0013] In an embodiment of the present invention, the number of the preset corner reflector targets is at least three.

[0014] In an embodiment of the present invention, an xyz coordinate system is established, and according to the moving speeds v x 、v y 、v z of the mobile terminal in the x-axis, y-axis, and z-axis directions in each frame, the moving trajectories R x 、R y 、R z of the mobile terminal in the x-axis, y-axis, and z-axis directions are generated. The steps include:

[0015] Establish an xyz coordinate system, and randomly generate the moving speeds v x 、v y 、v z of the mobile terminal in the x-axis, y-axis, and z-axis directions in each frame;

[0016] Calculate the coordinates of the mobile terminal in each frame to obtain the moving trajectories R x 、R y 、R z of the mobile terminal in the x-axis, y-axis, and z-axis directions.

[0017] In an embodiment of the present invention, the steps of resolving the radial velocity and distance of the mobile terminal relative to each preset corner reflector target in each frame according to the echo signal Sr include:

[0018] Perform a two-dimensional fast Fourier transform on the echo signal Sr to obtain a signal Sr';

[0019] Perform a maximum value search on the signal Sr' to obtain the radial velocity and distance of the mobile terminal relative to each preset corner reflector target in each frame.

[0020] In an embodiment of the present invention, before the step of fitting the distance of the mobile terminal relative to each preset corner reflector target in the m-th frame, substituting the fitted distance into a non-linear programming model, and determining the search range of the non-linear programming model based on the coordinates of the mobile terminal and its radial velocity relative to each preset corner reflector target in the (m - 1)-th frame to obtain the coordinates of the mobile terminal in the m-th frame, it further includes:

[0021] Estimate the coordinates of the mobile terminal in the first frame according to the distance of the mobile terminal relative to each preset corner reflector target in the first frame.

[0022] In an embodiment of the present invention, the steps of fitting the distance of the mobile terminal relative to each preset corner reflector target in the m-th frame, substituting the fitted distance into a non-linear programming model, and determining the search range of the non-linear programming model based on the coordinates of the mobile terminal and its radial velocity relative to each preset corner reflector target in the (m - 1)-th frame to obtain the coordinates of the mobile terminal in the m-th frame include:

[0023] Estimate the actual velocities v x1 , v y1 and v z1 of the mobile terminal in the x-axis, y-axis, and z-axis directions in the (m - 1)-th frame according to the radial velocity of the mobile terminal relative to each preset corner reflector target in the (m - 1)-th frame;

[0024] Determine the search range of the non-restricted programming model corresponding to the m-th frame according to the coordinates of the mobile terminal in the (m - 1)-th frame and the actual velocities and of the mobile terminal in the x-axis, y-axis, and z-axis directions in the (m - 1)-th frame;

[0025] Fit the distances of the mobile terminal relative to each preset corner reflector target in the m-th frame, substitute the fitted distances into the non-linear programming model, and determine the coordinates of the mobile terminal in the m-th frame in combination with the search range of the non-restricted programming model corresponding to the m-th frame.

[0026] In an embodiment of the present invention, the step of estimating the actual velocities and of the mobile terminal in the x-axis, y-axis, and z-axis directions in the (m - 1)-th frame according to the radial velocity of the mobile terminal relative to each preset corner reflector target in the (m - 1)-th frame includes:

[0027] Calculate the relative azimuth angle and relative elevation angle of the mobile terminal relative to each of the preset corner reflector targets in the (m - 1)-th frame:

[0028]

[0029] wherein, θ m-1,p , respectively represent the relative azimuth angle and relative elevation angle of the mobile terminal relative to the p-th preset corner reflector target in the (m - 1)-th frame, (X m-1 , Y m-1 , Z m-1 ) represent the coordinates of the mobile terminal in the (m - 1)-th frame, and (x p , y p , z p ) represent the coordinates of the p-th preset corner reflector target;

[0030] Project the radial velocity of the mobile terminal relative to each of the preset corner reflector targets in the (m - 1)-th frame onto the x-axis, y-axis, and z-axis respectively according to the relative azimuth angle θ m-1,p and the relative elevation angle to obtain the velocity components of the mobile terminal relative to each preset corner reflector target in the x-axis direction, y-axis direction, and z-axis direction in the (m - 1)-th frame:

[0031]

[0032]

[0033] In the formula, vv m-1,p represents the radial velocity of the mobile terminal relative to the p-th preset corner reflector target in the (m-1)-th frame, respectively represent the velocity components of the mobile terminal relative to the p-th preset corner reflector target in the x-axis direction, y-axis direction, and z-axis direction in the (m-1)-th frame;

[0034] The average values of the velocity components of the mobile terminal relative to each preset corner reflector target in the x-axis direction, y-axis direction, and z-axis direction in the (m-1)-th frame are respectively taken to obtain the actual velocities of the mobile terminal in the x-axis direction, y-axis direction, and z-axis direction in the (m-1)-th frame and

[0036] In an embodiment of the present invention, the search range of the non-linear programming model corresponding to the m-th frame is expressed as:

[0037]

[0038] In the formula, T r is the frame interval of the signal transmitted by the mobile terminal.

[0039] In an embodiment of the present invention, the non-linear programming model is expressed as:

[0040]

[0041] In the formula, (x p , y p , z p ) represents the coordinates of the p-th preset corner reflector target, R m,p represents the distance after fitting of the mobile terminal relative to the p-th preset corner reflector target in the m-th frame, and P represents the number of preset corner reflector targets.

[0042] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0043] The present invention provides a SAR imaging compensation method based on the motion error of a mobile terminal. By using the velocity information, angle information, and three-dimensional distance information of the mobile terminal in the previous frame, the coordinates of the mobile terminal in the current frame are estimated without considering how many sine function sets are specifically included in the human motion model. Since the position estimation result of the mobile terminal in each frame is related to the position estimation result of the mobile terminal in the previous frame and its average velocity in the previous frame, the present invention has better generalization and improves the azimuth compensation effect.

[0044] In addition, compared with the prior art, the present invention adds the velocity information of the mobile terminal during the imaging compensation process, and performs non-linear programming fitting through distance entropy to obtain the actual motion trajectory of the mobile terminal, and finally completes the compensated focused imaging result, overcoming the problems of missing velocity information, low image entropy iteration efficiency, and unsatisfactory parameter iteration effect in the prior art.

[0045] The present invention will be further described in detail below in conjunction with the drawings and embodiments. Description of the Drawings

[0046] Figure 1a It is a schematic diagram of the model of the human body's horizontal motion trajectory provided by an embodiment of the present invention;

[0047] Figure 1b It is a schematic diagram of the model of the human body's vertical motion trajectory provided by an embodiment of the present invention;

[0048] Figure 2 It is a schematic diagram of the non-ideal motion model of a person holding a mobile terminal provided by an embodiment of the present invention.

[0049] Figure 3 It is a flowchart of a SAR imaging compensation method based on the motion error of a mobile terminal provided by an embodiment of the present invention. Detailed Embodiment

[0050] The present invention will be further described in detail below in conjunction with specific embodiments, but the embodiments of the present invention are not limited thereto.

[0051] Nowadays, in the field of 6G communication technology, the research on integrated sensing and communication (ISAC) has been continuously heating up. By using a mobile terminal device to transmit communication signals to realize the perception of the surrounding environment, this research direction is expected to bring major changes to fields such as smart life and the Internet of Things. However, in actual applications, when using a handheld mobile terminal for environmental perception, due to the inevitable shift of the center of gravity of the human body during movement, the motion trajectory of the mobile terminal is difficult to reach an ideal state.

[0052] Figure 1aIt is a schematic model diagram of the human body's horizontal movement trajectory provided by an embodiment of the present invention. Figure 1b It is a schematic model diagram of the human body's vertical movement trajectory provided by an embodiment of the present invention. Figure 2 It is a schematic diagram of a non-ideal motion model of a human holding a mobile terminal provided by an embodiment of the present invention. Next, in combination with Figure 1a , Figure 1b and Figure 2 , the human body motion characteristics are modeled and the errors are analyzed.

[0053] First, the human body motion trajectory is decomposed into horizontal and vertical directions, and a base station-mobile terminal geometric model is established. The position of the base station is (0, 0, Z r ), and the mobile terminal moves along the y-axis direction. At a certain azimuth moment η, its ideal position is (X t , Y t + V t ·η, Z t ). However, in reality, due to the offset of the human body's motion center of gravity, the mobile terminal will deviate from the ideal straight-line trajectory, and its actual position is (Xt + Δx(η), Yt + Vt·η, Zt + Δz(η)). Δx(η) and Δz(η) are the motion error components of the mobile terminal in the x-axis direction and z-axis direction at a certain azimuth moment, that is, the undulation offset amount in the human body motion model.

[0054] The position of any point target in the scene is denoted as (X p , Y p , 0). The motion error components mainly come from the non-ideality of the user's movement of holding the mobile terminal. Therefore, the slant range history between the user's hand-held mobile terminal and the target in the real situation is:

[0055]

[0056] Expanding the above formula gives:

[0057]

[0058] Among them,

[0059] For the convenience of derivation, it is defined as In general motion relationships, the following formula always holds:

[0060]

[0061] The above formula can be further simplified to:

[0062]

[0063] The second term in the above formula is expanded by the first-order Taylor expansion with R t0 as the independent variable to obtain:

[0064]

[0065] Define the following variables:

[0066]

[0067] θ is the instantaneous oblique view angle of the mobile terminal to the target, and the final oblique distance from the mobile terminal to the target is:

[0068]

[0069] where Δr(η,α) = Δx(η)·sinα(R t0 ) + Δz(η)·cosα(R t0 ) represents the motion error caused by the fluctuation and offset of the human body center of gravity when the user holds the mobile terminal. This motion error will bring about an error in the echo phase, and finally lead to azimuth defocusing after imaging.

[0070] It can be seen that the non-ideal motion trajectory of the mobile terminal will cause the azimuth defocusing problem, seriously affecting the accuracy of perception and the imaging quality.

[0071] In view of this, the embodiment of the present invention provides a SAR imaging compensation method based on the motion error of the mobile terminal.

[0072] Figure 3 is a flowchart of a SAR imaging compensation method based on the motion error of the mobile terminal provided by the embodiment of the present invention. As Figure 3 shown, the embodiment of the present invention provides a SAR imaging compensation method based on the motion error of the mobile terminal, including:

[0073] S1. Establish an xyz coordinate system, and generate the motion trajectories R x , R y , R z of the mobile terminal in the x-axis, y-axis, and z-axis directions according to the moving speeds v x , R y , R z in each frame.

[0074] Specifically, step S1 includes:

[0075] S101. Establish an xyz coordinate system, and randomly generate the moving speeds v x , v y , v z of the mobile terminal in the x-axis, y-axis, and z-axis directions in each frame;

[0076] S102. Calculate the coordinates of the mobile terminal in each frame to obtain the motion trajectories Rx , R y , R z .

[0077] It should be noted that when establishing the xyz coordinate system in this embodiment, there is no need to limit the position of the origin o, and the directions indicated by the x-axis, y-axis, and z-axis can be referred to Figure 1a , 1b .

[0078] S2. According to the movement trajectory R x , R y , R z , obtain the echo signal Sr formed by the signal emitted by the mobile terminal after being reflected by all point targets, and calculate the radial velocity and distance of the mobile terminal relative to each preset corner reflector target in each frame according to the echo signal Sr.

[0079] In this embodiment, the number of preset corner reflector targets is at least three. Optionally, the step of calculating the radial velocity and distance of the mobile terminal relative to each preset corner reflector target in each frame according to the echo signal Sr in step S2 includes:

[0080] Perform a two-dimensional fast Fourier transform on the echo signal Sr to obtain the signal Sr';

[0081] Perform a maximum value search on the signal Sr' to obtain the radial velocity and distance of the mobile terminal relative to each preset corner reflector target in each frame.

[0082] S3. Fit the distances of the mobile terminal relative to each preset corner reflector target in the m-th frame, substitute the fitted distances into the nonlinear programming model, and determine the search range of the non-restricted programming model based on the coordinates of the mobile terminal in the (m - 1)-th frame and its radial velocity relative to each preset corner reflector target, to obtain the coordinates of the mobile terminal in the m-th frame; where m = 2, 3,..., M, and M represents the number of frames.

[0083] It should be noted that before executing step S3, the coordinates of the mobile terminal in the first frame can be estimated first according to the distances of the mobile terminal relative to each preset corner reflector target in the first frame.

[0084] Optionally, step S3 includes:

[0085] S301. According to the radial velocities of the mobile terminal relative to each preset corner reflector target in the (m - 1)-th frame, estimate the actual velocities v x1 , v y1 and v z1 of the mobile terminal in the x-axis, y-axis, and z-axis directions in the (m - 1)-th frame;

[0086] S302. Determine the search range of the non - restricted planning model corresponding to the m - th frame according to the coordinates of the mobile terminal in the (m - 1) - th frame and the actual velocities of the mobile terminal in the x - axis, y - axis, and z - axis directions in the (m - 1) - th frame and determine the search range of the non - restricted planning model corresponding to the m - th frame;

[0087] S303. Fit the distances between the mobile terminal in the m - th frame and each preset corner reflector target, substitute the fitted distances into the non - linear planning model, and determine the coordinates of the mobile terminal in the m - th frame in combination with the search range of the non - restricted planning model corresponding to the m - th frame.

[0088] Specifically, in step S301, estimate the actual velocities of the mobile terminal in the x - axis, y - axis, and z - axis directions in the (m - 1) - th frame according to the radial velocities of the mobile terminal relative to each preset corner reflector target in the (m - 1) - th frame and The steps include:

[0089] First, calculate the relative azimuth angle and relative pitch angle of the mobile terminal relative to each preset corner reflector target in the (m - 1) - th frame:

[0090]

[0091] In the formula, θ m-1,p , respectively represent the relative azimuth angle and relative pitch angle of the mobile terminal relative to the p - th preset corner reflector target in the (m - 1) - th frame, (X m-1 , Y m-1 , Z m-1 ) represent the coordinates of the mobile terminal in the (m - 1) - th frame, (x p , y p , z p ) represent the coordinates of the p - th preset corner reflector target.

[0092] Next, project the radial velocities of the mobile terminal relative to each preset corner reflector target in the (m - 1) - th frame onto the x - axis, y - axis, and z - axis respectively according to the relative azimuth angle θ m-1,p and the relative pitch angle to obtain the velocity components of the mobile terminal relative to each preset corner reflector target in the x - axis direction, y - axis direction, and z - axis direction in the (m - 1) - th frame:

[0093]

[0094] In the formula, vv m-1,p represents the radial velocity of the mobile terminal relative to the p - th preset corner reflector target in the (m - 1) - th frame, respectively represent the velocity component of the mobile terminal relative to the p-th preset corner reflector target in the x-axis direction, the velocity component in the y-axis direction, and the velocity component in the z-axis direction in the (m - 1)-th frame.

[0095] Finally, the average values of the velocity components of the mobile terminal relative to each preset corner reflector target in the x-axis direction, the y-axis direction, and the z-axis direction in the (m - 1)-th frame are taken respectively to obtain the actual velocities of the mobile terminal in the x-axis direction, the y-axis direction, and the z-axis direction in the (m - 1)-th frame and

[0096] Optionally, the non-linear programming model in this embodiment is expressed as:

[0097]

[0098] In the formula, (x p , y p , z p ) represents the coordinates of the p-th preset corner reflector target, R m,p represents the distance after fitting of the mobile terminal relative to the p-th preset corner reflector target in the m-th frame, and P represents the number of preset corner reflector targets.

[0099] Correspondingly, the search range of the non-restricted programming model corresponding to the m-th frame is expressed as:

[0100]

[0101] In the formula, T r is the frame interval of the signal transmitted by the mobile terminal.

[0102] S4. Obtain the coordinates of the mobile terminal in all frames, and generate the actual movement trajectories R xx , R yy and R zz of the mobile terminal on the x-axis, y-axis, and z-axis for back-projection imaging.

[0103] Specifically, after obtaining the coordinates of the mobile terminal in all frames, the actual movement trajectories R xx , R yy and R zz of the mobile terminal on the x-axis, y-axis, and z-axis can be formed, and R xx and R yy are selected from them for back-projection imaging.

[0104] As can be seen from the above embodiments, the beneficial effects of the present invention are:

[0105] The present invention provides a SAR imaging compensation method based on the motion error of a mobile terminal. By using the velocity information, angle information, and three-dimensional distance information of the mobile terminal in the previous frame, the coordinates of the mobile terminal in the current frame are estimated without considering how many sine function sets are specifically included in the human motion model. Since the position estimation result of the mobile terminal in each frame is related to the position estimation result of the mobile terminal in the previous frame and its average velocity within the previous frame, the present invention has better generalization and improves the azimuth compensation effect.

[0106] In addition, compared with the prior art, the present invention adds the velocity information of the mobile terminal during the imaging compensation process, and performs non-linear programming fitting through distance entropy to obtain the actual motion trajectory of the mobile terminal, and finally completes the compensated focused imaging result, overcoming the problems of missing velocity information, low image entropy iteration efficiency, and unsatisfactory parameter iteration effect in the prior art.

[0107] In the description of the present invention, the description referring to terms such as "one embodiment", "some embodiments", "example", "specific example", or "some examples" means that the specific features, structures, materials, or characteristics described in connection with the embodiment or example are included in at least one embodiment or example of the present invention. In this specification, the schematic representations of the above terms do not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials, or characteristics described can be combined in any one or more embodiments or examples in a suitable manner. In addition, those skilled in the art can combine and combine the different embodiments or examples described in this specification.

[0108] Although the present application has been described in conjunction with various embodiments herein, however, in the process of implementing the claimed present application, those skilled in the art can understand and realize other variations of the disclosed embodiments by viewing the accompanying drawings, the disclosed content, and the appended claims.

[0109] The above content is a further detailed description of the present invention in combination with specific preferred embodiments, and it cannot be determined that the specific implementation of the present invention is only limited to these descriptions. For those of ordinary skill in the technical field to which the present invention pertains, without departing from the concept of the present invention, several simple deductions or substitutions can still be made, and all should be regarded as belonging to the protection scope of the present invention.

Claims

1. A SAR imaging compensation method based on mobile terminal motion error, characterized in that: include: Establish an xyz coordinate system, based on the moving speed v of the mobile terminal in the x-axis, y-axis and z-axis directions in each frame x 、v y 、v z , generate the moving trajectory R of the mobile terminal in the x-axis, y-axis and z-axis directions x , R y , R z ; According to the moving trajectory R x , R y , R z , obtaining an echo signal Sr formed after the signal emitted by the mobile terminal is reflected by all point targets, and calculating the radial speed and distance of the mobile terminal relative to each preset corner reflector target in each frame according to the echo signal Sr; Fitting the distance of the mobile terminal relative to each preset corner reflector target in the mth frame, substituting the fitted distance into the nonlinear programming model, and determining the search range of the non-limited programming model based on the coordinates of the mobile terminal in the m-1th frame and its radial velocity relative to each preset corner reflector target, to obtain the coordinates of the mobile terminal in the mth frame; wherein m=2, 3, ..., M, and M represents the number of frames; Get the coordinates of the mobile terminal in all frames and generate the actual movement trajectory R of the mobile terminal on the x-axis, y-axis and z-axis xx , R yy and R zz For back projection imaging.

2. The SAR imaging compensation method based on mobile terminal motion error according to claim 1, characterized in that: The number of the preset corner reflector targets is at least three.

3. The SAR imaging compensation method based on mobile terminal motion error according to claim 1, characterized in that: Establish an xyz coordinate system, based on the moving speed v of the mobile terminal in the x-axis, y-axis and z-axis directions in each frame x 、v y 、v z , generate the moving trajectory R of the mobile terminal in the x-axis, y-axis and z-axis directions x , R y , R z The steps include: Establish an xyz coordinate system and randomly generate the moving speed v of the mobile terminal in the x-axis, y-axis and z-axis directions in each frame x 、v y 、v z ; Calculate the coordinates of the mobile terminal in each frame to obtain the moving trajectory R of the mobile terminal in the x-axis, y-axis and z-axis directions x , R y , R z .

4. The SAR imaging compensation method based on mobile terminal motion error according to claim 2, characterized in that: The step of calculating the radial speed and distance of the mobile terminal relative to each preset corner reflector target in each frame according to the echo signal Sr comprises: Performing a two-dimensional fast Fourier transform on the echo signal Sr to obtain a signal Sr'; The signal Sr' is searched for a maximum value to obtain the radial speed and distance of the mobile terminal relative to each preset corner reflector target in each frame.

5. The SAR imaging compensation method based on mobile terminal motion error according to claim 1, characterized in that: Fitting the distance of the mobile terminal relative to each preset corner reflector target in the m-th frame, substituting the fitted distance into the nonlinear programming model, and determining the search range of the unrestricted programming model based on the coordinates of the mobile terminal in the m-1-th frame and its radial velocity relative to each preset corner reflector target, before obtaining the coordinates of the mobile terminal in the m-th frame, the method further includes: The coordinates of the mobile terminal in the first frame are estimated according to the distance of the mobile terminal in the first frame relative to each preset corner reflector target.

6. The SAR imaging compensation method based on mobile terminal motion error according to claim 5, characterized in that: The step of fitting the distance of the mobile terminal relative to each preset corner reflector target in the mth frame, substituting the fitted distance into the nonlinear programming model, and determining the search range of the unrestricted programming model based on the coordinates of the mobile terminal in the m-1th frame and its radial velocity relative to each preset corner reflector target, and obtaining the coordinates of the mobile terminal in the mth frame includes: According to the radial velocity of the mobile terminal relative to each preset corner reflector target in the m-1th frame, the actual velocity v of the mobile terminal in the x-axis, y-axis and z-axis directions in the m-1th frame is estimated. x1 、v y1 and v z1 ; According to the coordinates of the mobile terminal in the m-1th frame and the actual speed v of the mobile terminal in the x-axis, y-axis and z-axis directions in the m-1th frame x1m-1 、v y1m-1 and v z1m-1 , determine the search range of the unrestricted planning model corresponding to the mth frame; The distance of the mobile terminal relative to each preset corner reflector target in the mth frame is fitted, and the fitted distance is substituted into the nonlinear programming model, and the coordinates of the mobile terminal in the mth frame are determined in combination with the search range of the non-limited planning model corresponding to the mth frame.

7. The SAR imaging compensation method based on mobile terminal motion error according to claim 6, characterized in that: According to the radial velocity of the mobile terminal in the m-1th frame relative to each preset corner reflector target, estimate the actual velocity of the mobile terminal in the x-axis, y-axis and z-axis directions in the m-1th frame The steps include: Calculate the relative azimuth angle and relative elevation angle of the mobile terminal relative to each of the preset corner reflector targets in the m-1th frame: In the formula, θ m-1,p , They represent the relative azimuth and relative elevation of the mobile terminal relative to the pth preset corner reflector target in the m-1th frame, respectively. (X m-1 ,Y m-1 ,Z m-1 ) represents the coordinates of the mobile terminal in the m-1th frame, (x p ,y p ,z p ) represents the coordinates of the pth preset corner reflector target; According to the relative azimuth angle θ m-1,p and relative pitch angle The radial velocity of the mobile terminal relative to each of the preset corner reflector targets in the m-1th frame is projected onto the x-axis, y-axis and z-axis respectively, and the velocity component of the mobile terminal relative to each of the preset corner reflector targets in the m-1th frame in the x-axis direction, the velocity component of the y-axis direction and the velocity component of the z-axis direction are obtained: In the formula, vv m-1,p represents the radial velocity of the mobile terminal relative to the pth preset corner reflector target in the m-1th frame, They respectively represent the velocity component of the mobile terminal in the x-axis direction, the y-axis direction and the z-axis direction relative to the p-th preset corner reflector target in the m-1-th frame; The speed components of the mobile terminal in the x-axis direction, the y-axis direction, and the z-axis direction relative to each of the preset corner reflector targets in the m-1th frame are averaged to obtain the actual speed of the mobile terminal in the x-axis direction, the y-axis direction, and the z-axis direction in the m-1th frame.

8. The SAR imaging compensation method based on mobile terminal motion error according to claim 7, characterized in that: The search range of the non-restricted planning model corresponding to the mth frame is expressed as: Where, T r It is the frame interval for transmitting signals by mobile terminals.

9. The SAR imaging compensation method based on mobile terminal motion error according to claim 8, characterized in that: The nonlinear programming model is expressed as: In the formula, (x p ,y p ,z p ) represents the coordinates of the pth preset corner reflector target, R m,p represents the distance after fitting of the mobile terminal to the pth preset corner reflector target in the mth frame, and P represents the number of preset corner reflector targets.

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