Dual-baseline SAR ship imaging time window optimization method based on imaging projection plane analysis

Abstract

The application discloses a dual-baseline SAR ship imaging time window optimization method based on imaging projection plane analysis. Firstly, short-time Fourier transform is performed on the echo of a strong scattering point in a ship target to obtain time-frequency information, then the position and rotation parameters of the target scattering point are estimated by using a differential evolution method to obtain the change of the imaging projection plane, the time when the target presents a front / side / normal view is selected, and finally the optimal imaging time length is selected by comparing the image contrast and entropy of different time lengths, so that the optimal time period of dual-baseline SAR ship target imaging under high sea conditions is selected. The method combines imaging projection plane analysis and imaging time window optimization, does not require prior parameters such as sea wave and target motion parameters, can accurately select the optimal time period when the target presents a front / side / normal view, and solves the problem that the existing imaging time window optimization method cannot overcome the imaging defocus caused by the irregular three-dimensional swing of the sea surface moving target under high sea conditions and the problem of obtaining excellent imaging views without prior conditions.

Description

Technical Field

[0001] This invention belongs to the field of radar technology, specifically relating to a method for optimizing the imaging time window of a bistatic SAR ship based on imaging projection plane analysis. Background Technology

[0002] Synthetic Aperture Radar (SAR) is an advanced high-resolution radar system renowned for its excellent stealth capabilities, all-weather, and long-range detection. SAR constructs a virtual array system by capturing echo signals from antennas at different locations, utilizing the relative motion between the radar platform and the target. This technology has wide applications in maritime target monitoring, and holds significant economic value, especially for major maritime powers like China.

[0003] In ship target imaging, selecting the optimal imaging time period is crucial. The characteristic of maritime target imaging is that the target's angular motion caused by wave fluctuations can be used to obtain the required lateral resolution. Furthermore, extending the imaging time can expand the cumulative imaging angle, thereby improving azimuth resolution to some extent. However, excessively long imaging times can lead to unstable target rotation, complicating the signal phase within the imaging time and causing repeated superposition of imaging projection planes, ultimately affecting the clarity of the imaging result. Existing methods for optimizing the imaging time window generally select the period of most stable target motion for imaging, but these methods suffer from problems such as poor target view, difficulty in obtaining prior information, and the requirement for the target to exhibit specific motion, failing to meet the requirements for high-quality imaging of ship targets on the sea surface under complex sea conditions. Summary of the Invention

[0004] To address the aforementioned technical problems, this invention provides a method for optimizing the imaging time window of a bi-base SAR ship based on imaging projection plane analysis, which solves the problem that existing methods cannot simultaneously guarantee imaging resolution and excellent imaging view without prior conditions.

[0005] The technical solution adopted in this invention is: a method for optimizing the imaging time window of a bi-static SAR ship based on imaging projection plane analysis, the specific steps of which are as follows:

[0006] Step 1: Establish the bistatic SAR and ship target geometry, and complete parameter initialization;

[0007] In a Cartesian coordinate system, O-XYZ is the reference coordinate system, and O-UVW is the ship target's own rotation coordinate system. The U-axis, V-axis, and W-axis correspond to the target's roll, pitch, and yaw, respectively.

[0008] Let T represent the transmitting platform and R represent the receiving platform. Initially, the two coordinate systems coincide, and the target center is located at the origin O [0,0,0].T , [·] T This represents the matrix transpose operation; the initial coordinates of the bistatic radar's transmitting platform are r. T =[X T ,Y T Z T ] T The speed is The initial coordinates of the receiving platform are r R =[X R ,Y R Z R ] T The speed is

[0009] The three-dimensional oscillation of a ship target caused by the influence of ocean waves is considered as simple harmonic motion, and its three-dimensional rotation angle expression in the O-UVW coordinate system is as follows:

[0010]

[0011] Where η represents slow time, θ i (η) represents the rotation angles around the UVW axes, respectively, where i = u, v, w represent rotations around the U-axis, V-axis, and W-axis, respectively; A i Indicates the amplitude of oscillation, Ω i φ represents the angular frequency of the oscillation. i Indicates the initial phase of the swing.

[0012] Step 2: Obtain the bistatic distance history of scattering points on the ship target;

[0013] Let the initial coordinates of a scattering point p be [x p ,y p ,z p ] T The speed is [v] x ,v y ,v z ] T Then the instantaneous coordinate r of the scattering point in the O-XYZ coordinate system p The expression for (η) is as follows:

[0014]

[0015] in, The rotation matrix about the center point O in UVW axis order is shown below:

[0016]

[0017]

[0018] in, Represents rotation θ around the U-axisu Rotation matrix of angle, Represents rotation θ around the V-axis v Rotation matrix of angle, Indicates rotation θ around the W axis w Rotation matrix of angle.

[0019] Then the corresponding rotational angular velocity ω of the scattering point p in the O-XYZ coordinate system rot The expression is as follows:

[0020]

[0021] The bistatic distance history R(η) of scattering point p is the distance from the ship target to the receiver R. R (η) and transmitter R T The sum of distances (η) is expressed as:

[0022]

[0023] Step 3: Acquire bistatic SAR echoes of ship targets and perform range pulse compression;

[0024] The echo reflected from scattering point p, after range-direction pulse compression, has the following two-dimensional time-domain expression:

[0025]

[0026] Where t and η represent fast time and slow time, respectively, and T a λ represents the pulse accumulation time. c c and σ represent wavelength and speed of light, respectively, B represents bandwidth, and σ represents speed of light. η This represents the scattering coefficient of the target.

[0027] Step 4: Obtain the STFT time-frequency analysis of the scattering point, and interpolate and smooth the STFT curve;

[0028] s PC The expression for the short-time Fourier transform (STFT) of (t,η) is as follows:

[0029] STFT{s Pc (t,η)}=∫s PC (t,η)w(η-τ)e -jωη dη

[0030] Where w(η-τ) represents the window function, ω represents the frequency, and τ represents the time offset.

[0031] Then, the STFT curves of the scattering points are interpolated, and the moving average method is used to smooth the STFT time-frequency curves.

[0032] Step 5: Search for the target rotation parameters and scattering point positions using the differential evolution method;

[0033] The expression for the Doppler frequency at scattering point p is as follows:

[0034]

[0035] Three strong scattering points were selected on the target and labeled A, B, and C. Their echoes were extracted for STFT time-frequency analysis. Then, based on these three STFT curves, the finite difference evolution method was used to search for the rotation parameter A. i Ω i (i = u, v, w) and the position of the scattering point r p (p=A,B,C), then the objective function expression of the differential evolution method is as follows:

[0036]

[0037] Among them, MSE(f D () represents a three-row matrix, where each row represents a strong scattering point. The Doppler frequency is calculated by searching for rotation parameters using the differential evolution method. The mean square error between the actual STFT value STFT(n) at the scattering point throughout the entire pulse accumulation time is expressed as follows:

[0038]

[0039] Where n represents the number of discrete time points and N represents the total number of time points.

[0040] Δ represents another three-row matrix, where each row represents the bibase distance history R calculated from the parameters obtained by the differential evolution method for a strong scattering point. cal The absolute value of the difference between (η) and the actual data R(η) at the center time is expressed as follows:

[0041] ΔR=|R cal (η)-R(η)|

[0042] Here, ||·|| represents the magnitude of the vector. When the value of oj approaches 0, the search parameters are considered the optimal solution, i.e., the estimated target rotation parameters and scattering point position coordinates.

[0043] Step 6: Combine bistatic SAR with monostatic SAR to obtain the radar line-of-sight (RLOS) direction;

[0044] Set r T r R r E Let i represent the initial positions of the transmitting, receiving, and synthesizing single-base platforms, respectively, with their unit direction vectors relative to the center point O being i, i, and i, respectively. T iR i E0 After a period of time η, the positions of the three platforms become r. T ′, r R ′ and r E ′, the unit direction vectors are i T (η), i R (n) and i E (η).

[0045] Assuming the translational component of the ship target relative to the radar has already been compensated during the echo preprocessing stage, the motion of the transmitting and receiving platforms is considered as rotation relative to the center point. Therefore, the direction vector expression for the transmitting platform is as follows:

[0046]

[0047] in, Let θ represent the rotation matrix. T Indicates the rotation angle. The velocity V of the launch platform. T Tangential component V T Its rotational angular velocity vector ω T The expression is as follows:

[0048]

[0049] Where × represents the cross product. ω T Direction of vector This represents the axis of rotation of the launch platform, with the rotation angle determined by ω. T The magnitude of a vector, i.e., θ T =‖ω T ‖η.

[0050] Derived using Rodriguez's rotation formula The expression is as follows:

[0051]

[0052] Where I represents the identity matrix, [·] × The antisymmetric matrix representing the vector. The rotation matrix of the receiving platform. and rotation angle θ R They have the same structure.

[0053] Similarly, the initial orientation of the synthetic single-base platform is Its instantaneous direction vector i E (η) represents the RLOS direction of a single-base SAR system, expressed as follows:

[0054]

[0055] in, Represents the composite rotation matrix, with structure and Similarly, the expression is as follows:

[0056]

[0057] Where, k E θ represents the rotation axis of the synthetic single-base SAR. E The rotation angle is expressed as follows:

[0058]

[0059]

[0060] Step 7: Obtain the valid rotation vector;

[0061] The imaging projection plane IPP is parallel to RLOS and perpendicular to the effective rotation vector. The target rotation angular velocity ω can be calculated by estimating the parameters. rot Then subtract the component ω parallel to RLOS from it. || , thus obtaining vector ω ⊥ It is both the effective rotation vector and the normal vector of the IPP.

[0062] Step 8: Select the optimal time for imaging the ship's top / side / front view;

[0063] Select the optimal top-view imaging time, i.e., when ω ⊥ When the IPP approaches parallel to the Z-axis, it appears as an approximately horizontal plane, resulting in a ship image resembling a top-down view. The optimal time for side-view imaging is selected when ω... ⊥ When the IPP approaches parallel to the Y-axis, it appears as an approximately vertical plane, and the ship's image at this point resembles a side view. The optimal time for frontal view imaging is selected when ω... ⊥ When it approaches parallel to the X-axis, the IPP appears as an approximately vertical plane, and the ship image is a near-frontal view.

[0064] Step 9: Select the optimal imaging time length;

[0065] At the optimal time for imaging the ship's top / side / front views, images of different time lengths are compared. The optimal imaging time length is determined by analyzing the contrast and entropy values ​​of each image. At these optimal times, imaging is performed using the selected optimal time length to obtain the clearest and most accurate top, side, and front views of the ship.

[0066] The beneficial effects of this invention are as follows: The method of this invention first performs a short-time Fourier transform on the echoes of strong scattering points in the ship target to obtain time-frequency information. Then, it uses the differential evolution method to estimate the position and rotation parameters of the target scattering points to obtain the changes in the imaging projection plane, selects the time when the target is in a top / side / front view, and then compares the image contrast and entropy of images from different time lengths to select the optimal imaging time length, thus completing the selection of the optimal time period for imaging ship targets under high sea states using bistatic SAR. This invention combines imaging projection plane analysis and imaging time window optimization, requiring no prior parameters such as sea waves and target motion parameters. It can accurately select the optimal time period for the target to be in a top / side / front view, solving the problem that existing imaging time window optimization methods cannot overcome the imaging defocusing problem caused by the irregular three-dimensional oscillation of moving targets on the sea surface under high sea states and the problem of obtaining excellent imaging views when no prior conditions are available. Attached Figure Description

[0067] Figure 1 This is a flowchart of a bi-base SAR ship imaging time window optimization method based on imaging projection plane analysis according to the present invention.

[0068] Figure 2 This is a diagram of the bistatic SAR geometry used in an embodiment of the present invention.

[0069] Figure 3 This is a schematic diagram of the ship target used in an embodiment of the present invention.

[0070] Figure 4 This is the interpolated and smoothed STFT curve after step four in this embodiment of the invention.

[0071] Figure 5 This is a geometric structure diagram of the synthesized single-base SAR after step six in an embodiment of the present invention.

[0072] Figure 6 This is a schematic diagram of the three-dimensional size of the effective rotation vector after step seven in an embodiment of the present invention.

[0073] Figure 7 This is a schematic diagram of the IPP plane after step eight in an embodiment of the present invention.

[0074] Figure 8 This is the optimal top / side / front view of the ship target imaging after step nine in this embodiment of the invention. Detailed Implementation

[0075] This embodiment uses simulation experiments for verification, and the simulation verification platform is Matlab2022b. The method of the present invention will be further described below with reference to the accompanying drawings and embodiments.

[0076] like Figure 1The flowchart of a bi-base SAR ship imaging time window optimization method based on imaging projection plane analysis of the present invention is shown below. The specific steps are as follows:

[0077] Step 1: Establish the bistatic SAR and ship target geometry, and complete parameter initialization;

[0078] In a Cartesian coordinate system, O-XYZ is the reference coordinate system, and O-UVW is the ship target's own rotation coordinate system. The U-axis, V-axis, and W-axis correspond to the target's roll, pitch, and yaw, respectively.

[0079] Let T represent the transmitting platform and R represent the receiving platform. Initially, the two coordinate systems coincide, and the target center is located at the origin O [0,0,0]. T , [·] T This represents the matrix transpose operation; the initial coordinates of the bistatic radar's transmitting platform are r. T =[X T ,Y T Z T ] T The speed is The initial coordinates of the receiving platform are r R =[X R ,Y R Z R ] T The speed is The three-dimensional sway of a ship target caused by the influence of ocean waves can be regarded as simple harmonic motion, and its three-dimensional rotation angle expression in the O-UVW coordinate system is as follows:

[0080]

[0081] Where η represents slow time, θ i (η) represents the rotation angles around the UVW axes, respectively, where i = u, v, w represent rotations around the U-axis, V-axis, and W-axis, respectively; A i Indicates the amplitude of oscillation, Ω i φ represents the angular frequency of the oscillation. i This represents the initial phase of the swing. Since the initial phase has a relatively small impact on the imaging results, it is usually not considered during the analysis.

[0082] In this embodiment, the bistatic SAR geometry used is as follows: Figure 2 As shown in Table 1, the parameters of the bistatic SAR system used are as follows, and the target scattering point modeling (i.e., the ship target used) is as follows. Figure 3 As shown in Table 2, the ship target rotation parameters used are as follows.

[0083] Table 1

[0084]

[0085] Table 2

[0086]

[0087] Step 2: Obtain the bistatic distance history of scattering points on the ship target;

[0088] Let the initial coordinates of a scattering point p be [x p ,y p ,z p ] T The speed is [v] x ,v y ,v z ] T Then the instantaneous coordinate r of the scattering point in the O-XYZ coordinate system p The expression for (η) is as follows:

[0089]

[0090] in, The rotation matrix about the center point O in UVW axis order is shown below:

[0091]

[0092]

[0093] in, Represents rotation θ around the U-axis u Rotation matrix of angle, Represents rotation θ around the V-axis v Rotation matrix of angle, Indicates rotation θ around the W axis w Rotation matrix of angle.

[0094] Then the corresponding rotational angular velocity ω of the scattering point p in the O-XYZ coordinate system rot The expression is as follows:

[0095]

[0096] The bistatic distance history R(η) of scattering point p is the distance from the ship target to the receiver R. R (η) and transmitter R T The sum of distances (η) is expressed as:

[0097]

[0098] Step 3: Acquire bistatic SAR echoes of ship targets and perform range pulse compression;

[0099] The echo reflected from scattering point p, after range-direction pulse compression, has the following two-dimensional time-domain expression:

[0100]

[0101] Where t and η represent fast time and slow time, respectively, and T a λ represents the pulse accumulation time. c c and σ represent wavelength and speed of light, respectively, B represents bandwidth, and σ represents speed of light. η This represents the scattering coefficient of the target.

[0102] Step 4: Obtain the STFT (Short-Time Fourier Transform) time-frequency analysis of the scattering points, and interpolate and smooth the STFT curve;

[0103] s PC The expression for the short-time Fourier transform (STFT) of (t,η) is as follows:

[0104] STFT{s PC (t,η)}=∫s PC (t,η)w(η-τ)e -jωη dη

[0105] Where w(η-τ) represents the window function, ω represents the frequency, and τ represents the time offset.

[0106] Because of the trade-off between time and frequency resolution caused by window function sliding during the STFT process, interpolation is required for the STFT curves at the scattering points. Furthermore, to reduce jitter when extracting echoes from strong scattering points, a moving average method is needed to smooth the STFT time-frequency curves. The interpolated and smoothed STFT curves obtained in step four are as follows: Figure 4 As shown.

[0107] Step 5: Search for the target rotation parameters and scattering point positions using the Differential Evolution (DE) method;

[0108] The expression for the Doppler frequency at scattering point p is as follows:

[0109]

[0110] In actual operation, the Doppler frequency f at the scattering point D (η) can be obtained by performing STFT on the echo at point p, which is the result after step four.

[0111] Three strong scattering points were selected on the target and labeled A, B, and C. Their echoes were extracted for STFT time-frequency analysis. Then, based on these three STFT curves, the finite difference evolution method was used to search for the rotation parameter A.i Ω i (i = u, v, w) and the position of the scattering point r p (p=A,B,C), then the objective function expression of the differential evolution method is as follows:

[0112]

[0113] Among them, MSE(f D () represents a three-row matrix, where each row represents a strong scattering point. The Doppler frequency is calculated by searching for rotation parameters using the differential evolution method. The mean square error between the actual STFT value STFT(n) at the scattering point throughout the entire pulse accumulation time is expressed as follows:

[0114]

[0115] Where n represents the number of discrete time points and N represents the total number of time points.

[0116] Δ represents another three-row matrix, where each row represents the bibase distance history R calculated from the parameters obtained by the differential evolution method for a strong scattering point. cal The absolute value of the difference between (η) and the actual data R(η) at the center time is expressed as follows:

[0117] ΔR=|R cal (η)-R(η)|

[0118] Where ||·|| represents the magnitude of the vector. When the value of oj approaches 0, the searched parameters are considered the optimal solution, i.e., the estimated target rotation parameters and scattering point position coordinates. The target parameter estimates after step five are shown in Table 3. It can be seen that the rotation parameter estimation errors are all within 5%, and the scattering point position estimation errors are all within 3m.

[0119] Table 3

[0120]

[0121] Step 6: Combine bistatic SAR with monostatic SAR to obtain the radar line of sight (RLOS) direction;

[0122] Set r T r R r E Let i represent the initial positions of the transmitting, receiving, and synthesizing single-base platforms, respectively, with their unit direction vectors relative to the center point O being i, i, and i, respectively. T i R i E0 After a period of time η, the positions of the three platforms become r. T ′, rR ′ and r E ′, the unit direction vectors are i T (η), i R (n) and i E (η).

[0123] Assuming the translational component of the ship target relative to the radar has already been compensated during the echo preprocessing stage, the motion of the transmitting and receiving platforms is considered as rotation relative to the center point. Therefore, the direction vector expression for the transmitting platform is as follows:

[0124]

[0125] in, Let θ represent the rotation matrix. T Indicates the rotation angle. The velocity V of the launch platform. T Tangential component V T Its rotational angular velocity vector ω T The expression is as follows:

[0126]

[0127] Where × represents the cross product. ω T Direction of vector This represents the axis of rotation of the launch platform, with the rotation angle determined by ω. T The magnitude of a vector, i.e., θ T =‖ω T ‖η.

[0128] Derived using Rodriguez's rotation formula The expression is as follows:

[0129]

[0130] Where I represents the identity matrix, [·] × The antisymmetric matrix representing the vector. The rotation matrix of the receiving platform. and rotation angle θ R It also has the same structure.

[0131] Similarly, the initial orientation of the synthetic single-base platform is Its instantaneous direction vector i E (η) represents the RLOS direction of a single-base SAR system, expressed as follows:

[0132]

[0133] in, Represents the composite rotation matrix, with structure and Similarly, the expression is as follows:

[0134]

[0135] Where, k E θ represents the rotation axis of the synthetic single-base SAR. E The rotation angle is expressed as follows:

[0136]

[0137]

[0138] In this embodiment, the synthesized monopole SAR geometry after step six is ​​as follows: Figure 5 As shown.

[0139] Step 7: Obtain the valid rotation vector;

[0140] Since the imaging projection plane IPP is parallel to RLOS and perpendicular to the effective rotation vector, the target rotation angular velocity ω can be calculated by estimating the parameters. rot Subtract the component ω parallel to RLOS from it. || The resulting vector ω ⊥ It is both the effective rotation vector and the normal vector of the IPP. The three-dimensional size of the effective rotation vector after step seven is as follows: Figure 6 As shown.

[0141] Step 8: Select the optimal time for imaging the ship's top / side / front view;

[0142] Select the optimal top-view imaging time, i.e., when ω ⊥ When the IPP approaches parallel to the Z-axis, it appears as an approximately horizontal plane, resulting in a ship image resembling a top-down view. The optimal time for side-view imaging is selected when ω... ⊥ When the IPP approaches parallel to the Y-axis, it appears as an approximately vertical plane, and the ship's image at this point resembles a side view. The optimal time for frontal view imaging is selected when ω... ⊥ When it approaches parallel to the X-axis, the IPP appears as an approximately vertical plane, and the ship image is a near-frontal view.

[0143] In this embodiment, the IPP after step eight is as follows: Figure 7 As shown, Figure 7 (a) is the top view of the imaging IPP, with the imaging center time at 2.8265s; Figure 7 (b) is the imaging side view IPP, with the imaging center time at 3.1405s; Figure 7 (c) is the front view of the imaging IPP, with the imaging center time being 1.9828s.

[0144] Step 9: Select the optimal imaging time length;

[0145] At the optimal time for imaging the ship's top / side / front view, images of different time lengths are compared. The optimal imaging time length is determined by analyzing the contrast and entropy values ​​of each image. At these optimal times, images are taken using the selected optimal time length, thereby obtaining the clearest and most accurate top, side, and front views of the ship.

[0146] In this embodiment, the optimal top / side / front view imaging results of the ship after step nine are as follows: Figure 8 As shown, Figure 8 (a) is a top view of the ship, with an imaging time of [2.7590, 2.8940] s; Figure 8 (b) is a side view of the ship, with an imaging time of [3.0543, 3.2268] s; Figure 8 (c) is a frontal view of the ship, with an imaging time of [1.9578, 2.0078] s.

[0147] In summary, as can be seen from this embodiment, the method of the present invention combines imaging projection plane analysis and imaging time window optimization, without requiring prior parameters such as sea waves and target motion parameters. It can accurately select the optimal time period for the target to be imaged in top / side / front view, solving the problem that existing imaging time window optimization methods cannot overcome the problem of imaging defocus and obtaining excellent imaging views caused by irregular three-dimensional swaying of moving targets on the sea surface under high sea conditions when there are no prior conditions.

[0148] Those skilled in the art will recognize that the embodiments described herein are intended to help the reader understand the principles of the invention, and should be understood that the scope of protection of the invention is not limited to such specific statements and embodiments. Various modifications and variations can be made to the invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the invention should be included within the scope of the claims of the invention.

Claims

1. A method for optimizing the imaging time window of a ship based on imaging projection plane analysis, the specific steps of which are as follows: Step 1: Establish the bistatic SAR and ship target geometry, and complete parameter initialization; Set in a rectangular coordinate system, As a reference coordinate system, Let be the ship's own rotating coordinate system, where axis, axis, The axes correspond to the target's roll, pitch, and yaw respectively; set up Indicates the launch platform. This indicates that, at the initial moment, the two coordinate systems coincide on the receiving platform, and the target center is located at the origin. Place , This represents the matrix transpose operation; the initial coordinates of the bistatic radar's transmitting platform are... The speed is The initial coordinates of the receiving platform are The speed is ; The three-dimensional oscillation of a ship target caused by the influence of ocean waves is considered as simple harmonic motion. The expression for a three-dimensional rotation angle in a coordinate system is as follows: ； in, Indicates slow time. Indicates the rotation angles about the UVW axes, respectively. Indicates to circling separately axis, axis, Axis rotation; Indicates the amplitude of the swing. Indicates the angular frequency of the oscillation. Indicates the initial phase of the swing; Step 2: Obtain the bistatic distance history of scattering points on the ship target; Set a scattering point Initial coordinates are The speed is Then the scattering point is at Instantaneous coordinates in a coordinate system The expression is as follows: ； in, Indicates around the center Tap The rotation matrix for axis order is as follows: ； ； in, Indicates circling Axis rotation Rotation matrix of angle, Indicates circling Axis rotation Rotation matrix of angle, Indicates circling Axis rotation Angle rotation matrix; Then the scattering point exist The corresponding rotational angular velocity in the coordinate system The expression is as follows: ； Scattering point Bibase distance history For ship targets to receiver and transmitter The sum of distances is expressed as: ； Step 3: Acquire bistatic SAR echoes of ship targets and perform range pulse compression; Scattering point The reflected echo, after range-direction pulse compression, is expressed in the two-dimensional time domain as follows: ； in, and They represent fast time and slow time, respectively. Indicates the pulse accumulation time. and These represent wavelength and speed of light, respectively. Indicates bandwidth. Represents the scattering coefficient of the target; Step 4: Obtain the STFT time-frequency analysis of the scattering point, and interpolate and smooth the STFT curve; The expression for the Short-Time Fourier Transform (STFT) is as follows: ； in, Represents the window function. Indicates frequency, Indicates time offset; Then, the STFT curve of the scattering point is interpolated, and the STFT time-frequency curve is smoothed using the moving average method. Step 5: Search for the target rotation parameters and scattering point positions using the differential evolution method; Scattering point The expression for the Doppler frequency is as follows: ； Select three strong scattering points on the target and mark them as follows: , and The points are used to extract their echoes for STFT time-frequency analysis. Then, based on these three STFT curves, the differential evolution method is used to search for rotation parameters. , ( and scattering point location ( Then, the objective function expression of the differential evolution method is as follows: ； in, This represents a three-row matrix, where each row represents a strong scattering point. The Doppler frequency is calculated by searching for rotation parameters using the finite difference evolution method. The actual STFT value of the scattering point throughout the entire pulse accumulation time. The mean square error between them is expressed as follows: ； Where n represents the number of discrete time points, and N represents the total number of time points; This represents another three-row matrix, where each row represents the bibase distance history calculated from parameters obtained through the differential evolution method for a strong scattering point. Actual data at the center time The absolute value of the difference between them is expressed as follows: ； in, Represents the magnitude of a vector; when The value approaches the When the search parameters are considered as the optimal solution, that is, the estimated target rotation parameters and scattering point position coordinates are obtained; Step 6: Combine bistatic SAR with monostatic SAR to obtain the radar line-of-sight (RLOS) direction; set up , , These represent the initial positions of the transmitting, receiving, and synthesizing single-base platforms, respectively, relative to the center point. The unit direction vectors are respectively , , After a period of time Afterwards, the positions of the three platforms changed , and The unit direction vectors are respectively , and ; Assuming the translational component of the ship target relative to the radar has already been compensated during the echo preprocessing stage, and the motion of the transmitting and receiving platforms is considered as rotation relative to the center point; then the expression for the direction vector of the transmitting platform is as follows: ； in, Represents the rotation matrix. Indicates the rotation angle; speed via the launch platform. tangential component Its rotational angular velocity vector The expression is as follows: ； in, Indicates cross product; Direction of vector The axis of rotation of the launch platform is indicated by the rotation angle. The magnitude representation of a vector, i.e. ; Derived using Rodriguez's rotation formula The expression is as follows: ； in, Represents the identity matrix. The antisymmetric matrix representing a vector; the rotation matrix of the receiving platform. and rotation angle They have the same structure; Similarly, the initial orientation of the synthetic single-base platform is Its instantaneous direction vector This refers to the RLOS direction of a single-base SAR system, expressed as follows: ； in, Represents the composite rotation matrix, with structure and Similarly, the expression is as follows: ； in, Indicates the rotation axis of the synthetic single-base SAR. The rotation angle is expressed as follows: ； ； Step 7: Obtain the valid rotation vector; The imaging projection plane IPP is parallel to RLOS and perpendicular to the effective rotation vector. The target rotation angular velocity can be calculated by estimating the parameters. Then subtract the component parallel to RLOS from it. , to obtain vector It is both the effective rotation vector and the normal vector of the IPP; Step 8: Select the optimal time for imaging the ship's top / side / front view; Select the optimal top-view imaging time, i.e. when Approaching and When the axes are parallel, the IPP is approximately horizontal, and the ship image is similar to a top view; the optimal time for side view imaging is selected when... Approaching and When the axes are parallel, the IPP is approximately perpendicular to the plane, and the ship image is similar to a side view; the optimal time for frontal view imaging is selected, i.e., when... Approaching and When the axes are parallel, the IPP is approximately perpendicular to the plane, and the ship image is a near-frontal view. Step 9: Select the optimal imaging time length; At the optimal time for imaging the ship's top / side / front view, images of different time lengths are compared, and the optimal imaging time length is determined by analyzing the contrast and entropy values ​​of each image. At these optimal times, the selected optimal time length is used for imaging to obtain the clearest and most accurate top, side, and front views of the ship.

Images