Beam space synchronization design method and system under zero doppler constraint of same-track bistatic sar

Abstract

The application provides a same-orbit bistatic SAR zero Doppler constraint beam space synchronization design method and system, comprising the following steps: calculating an average baseline length according to initial orbit parameters of same-orbit front and rear SAR satellites; calculating a beam offset azimuth angle according to the average baseline length; establishing a zero Doppler line model and a geostationary coordinate; constructing an antenna beam pointing surface and converting to a geostationary system; establishing an attitude optimization function with minimum distance optimization target, and solving to obtain a three-axis attitude guide rule. The application solves the technical problem of lacking a beam space synchronization design method which simultaneously considers zero Doppler frequency shift constraint and three-axis attitude guide in a bistatic SAR system.

Description

Technical Field

[0001] This invention relates to the field of synthetic aperture radar technology, and more specifically, to a method and system for beam spatial synchronization design under zero-Doppler constraints in co-orbit bistatic SAR. Background Technology

[0002] Bistatic SAR refers to a synthetic aperture radar system with separate transmitter and receiver satellites, acquiring reflected signals from ground targets. Compared to traditional monostatic SAR, bistatic SAR offers the following advantages: it can obtain the non-backscattering coefficients of ground objects; different observation geometries help identify and classify targets from different angles, thus enhancing target recognition capabilities; interferometric processing using multiple bistatic SARs with different baselines enables ground moving target detection (SAR-GMTI), digital elevation measurement (DEM), ocean current measurement, and improved imaging resolution; the system boasts good concealment, strong anti-jamming capabilities, and high survivability. With the development of miniaturized, lightweight, and low-cost satellite technologies, bistatic SAR has become more flexible and adaptable to different acquisition scenarios, making it a key technology direction for development in various countries.

[0003] The paper "Numerical Calculation of Doppler Steering Laws in Bi- and Multistatic SAR" (J. Mittermayer, G. Krieger, Fellow et al. IEEE TRANSACTIONS ONGROSCIENCE AND REMOTE SENSING LETTERS. 2022, 60) proposes a dual-base station zero-Doppler frequency shift correction method based on zero-Doppler geometry. This method estimates the yaw and elevation angles of the satellite using numerical methods to minimize the azimuth deviation between the beam coverage and the zero-Doppler geometry. Based on the optimization of the yaw and elevation angles, the roll angle is further optimized to minimize the deviation of the beam coverage in the direction of the ground area.

[0004] The paper "Interferometric SAR Satellite Formation Beam Synchronization Method" (He Donglei; Cao Xibin et al., *China Space Science and Technology*, 2010, 05.) combines the satellite-to-ground and inter-satellite positional relationships and uses coordinate transformation to plan the satellite attitude that enables the system to meet beam synchronization requirements. Considering the shortcomings of this method, such as abstract modeling and cumbersome solutions, a beam synchronization method based on Euler rotation is proposed. This method does not consider the constraint of zero Doppler shift.

[0005] The paper "Research on Attitude Guidance Method for S-band SAR Satellites in Low-Earth Orbit with Small Elliptical Orbit" (Zheng Zexing; Liu Yang et al. Space Electronics Technology, 2019, 05) proposes yaw guidance and two-dimensional attitude guidance methods for S-band synthetic aperture radar satellites in low-Earth orbit with small eccentricity, as well as simplified implementations using different orbit models. The paper analyzes the compensation effects of different compensation methods and the influence of antenna pointing accuracy on the compensation effect. This method is only applicable to monostatic two-dimensional attitude guidance.

[0006] The paper "A Novel Two-Dimensional Attitude Guidance Method for Fast Zero-Doppler Centering in GEOSAR" (Zhao Bingji; Zhang Qingjun et al., Journal of Electronics and Information Technology, 2019, 04) proposes a novel two-dimensional pitch-roll attitude guidance method for geostationary orbit synthetic aperture radar. This method effectively solves the problem of large yaw angles when using traditional two-dimensional yaw guidance methods for GEOSAR, and is more suitable for GEOSAR satellites with high power, large antennas, and large rotational inertia. When applied to GEOSAR satellites, this method does not require adjustment of the yaw angle; only the pitch and roll angles, not exceeding ±8°, need to be adjusted to achieve positive side-looking. This method is not applicable to low-Earth orbit bistatic SAR.

[0007] The paper "A Three-Dimensional Spatial Synchronization Method for Bistatic Radar Transmit and Receive Beams" (Song Sisheng; Zhang Xing et al. Science and Technology Innovation and Application, 2019, 23.) proposes a three-dimensional spatial synchronization calculation method for bistatic radar beams based on coordinate transformation technology. This method can quickly generate a three-dimensional synchronization intersection table of the range, azimuth, and elevation of the bistatic radar transmit and receive beams. However, this method does not consider the constraint of zero Doppler shift.

[0008] There are numerous studies on attitude maneuvers for monostatic SAR satellites under zero Doppler shift constraints, both domestically and internationally, and these studies have been validated in orbit. Although these studies have provided valuable insights into beam spatial synchronization for bistatic SAR systems, there are relatively few studies on achieving spatial synchronization by combining beam and three-axis attitude guidance for bistatic SAR satellites, and these studies have certain limitations. Summary of the Invention

[0009] To address the shortcomings of existing technologies, the purpose of this invention is to provide a method and system for beam spatial synchronization design under zero-Doppler constraint in co-track bistatic SAR.

[0010] According to one aspect of the present invention, a method for beam spatial synchronization design under zero Doppler constraint in co-orbit bistatic SAR is characterized by comprising the following steps: Step S1: Calculate the average baseline length based on the initial orbital parameters of the SAR satellites before and after orbital alignment; Step S2: Calculate the dual-satellite SAR beam offset azimuth angle based on the average baseline length; Step S3: Establish a bistatic zero-Doppler line model based on the distance equation, Doppler equation, and Earth ellipsoid model; Step S4: Based on the distance range corresponding to the SAR beam, calculate the coordinates of multiple points on the bistatic zero Doppler line in the Earth-fixed coordinate system; Step S5: Based on the SAR beam offset azimuth angle, establish the beam pointing surface in the SAR antenna coordinate system; Step S6: Based on the spatial relationship, establish a transformation matrix from the SAR antenna coordinate system to the Earth-fixed coordinate system, and transform the beam pointing plane to the Earth-fixed coordinate system; Step S7: Based on the beam pointing surface and the point on the zero Doppler line, with the minimum distance from the point on the zero Doppler line to the beam pointing surface as the optimization objective, establish the satellite three-axis attitude optimization function; Step S8: Perform satellite three-axis attitude optimization and solution based on the attitude optimization function; Step S9: Output the three-axis attitude guidance law of the whole orbit bistatic SAR satellite.

[0011] Preferably, step S1 specifically includes: Based on the orbital parameters of the preceding and following stars in the same orbit, and using a high-precision ephemeris or Kepler orbital model, the position and velocity sequences of the preceding and following stars within one orbit are generated, and the average baseline length is calculated. The orbital parameters include the semi-major axis, eccentricity, and inclination.

[0012] Preferably, step 2 specifically includes: determining and allocating the SAR beam offset azimuth angles of the preceding and following satellites based on the average baseline length of the co-orbit bistatic SAR system. The beam offset azimuth angles remain fixed during the whole-orbit imaging process and are time-invariant parameters.

[0013] Preferably, step 3 specifically includes: A bistatic zero-Doppler line model is constructed in the Earth fixed coordinate system. The bistatic zero-Doppler line satisfies both the bistatic distance-Doppler constraint equation and the Earth ellipsoidal geometric model.

[0014] Preferably, in step 4, the near-range, medium-range, and far-range imaging areas are covered according to the range range corresponding to SAR imaging. Multiple bistatic zero-Doppler constraint points are selected along the range direction on the bistatic zero-Doppler line, and the spatial coordinates of each bistatic zero-Doppler point in the Earth-fixed coordinate system are calculated.

[0015] Preferably, in step 5, based on the determined azimuth angle of the beam, a beam pointing surface is constructed in the SAR antenna coordinate system by presetting the range angles of the two antenna beams. The beam pointing surface is determined by the two beam pointing vectors and the corresponding satellite positions, forming a geometric plane.

[0016] Preferably, step S7 includes: By jointly adjusting the satellite's three-axis attitude angles, including yaw, pitch, and roll, the centerline of the beam pointing surface is spatially aligned as much as possible at the zero-Doppler points corresponding to multiple bistatic zero-Doppler lines. Based on this, according to the spatial geometric relationship between the beam pointing surface and each zero-Doppler point, the satellite's three-axis attitude optimization function is constructed with the minimum distance from the zero-Doppler point to the beam pointing surface as the optimization objective.

[0017] Preferably, step S8 specifically includes: An optimization algorithm is used to solve the three-degree-of-freedom attitude optimization problem, thereby completing the joint optimization and calculation of the satellite's yaw angle, pitch angle, and roll angle.

[0018] Preferably, step S9 specifically includes: Using the position information of the preceding and following satellites at each moment within the orbital period, the satellite attitude angles under the corresponding bistatic zero Doppler line constraint conditions are solved; the obtained attitude angle sequence is processed by low-pass filtering or spline interpolation to ensure the continuity and smoothness of attitude changes; and the attitude parameters of yaw angle, pitch angle and roll angle changing with time are stored in tabular form for use in calling and executing by the onboard attitude control system.

[0019] According to another aspect of the present invention, a beam space synchronization design system under zero-Doppler constraint for co-orbit bistatic SAR includes: Module M1: Calculates the average baseline length based on the initial orbital parameters of SAR satellites before and after orbital alignment; Module M2: Calculates the azimuth angle of the dual-satellite SAR beam offset based on the average baseline length; Module M3: Establish a bistatic zero-Doppler line model based on the distance equation, Doppler equation, and Earth ellipsoid model; Module M4: Calculates the coordinates of multiple points on the bistatic zero-Doppler line in the Earth-fixed coordinate system based on the distance range corresponding to the SAR beam; Module M5: Establish the beam pointing surface in the SAR antenna coordinate system based on the SAR beam offset azimuth angle; Module M6: Based on spatial relationships, establish a transformation matrix from the SAR antenna coordinate system to the Earth-fixed coordinate system, and transform the beam pointing plane to the Earth-fixed coordinate system; Module M7: Based on the beam pointing surface and the point on the zero Doppler line, with the minimum distance from the point on the zero Doppler line to the beam pointing surface as the optimization objective, establish a satellite three-axis attitude optimization function; Module M8: Performs satellite three-axis attitude optimization and solution based on the attitude optimization function; Module M9: Outputs the three-axis attitude guidance rules for bistatic SAR satellites with the same orbit.

[0020] Compared with the prior art, the present invention has the following beneficial effects: By leveraging the co-orbit bistatic SAR beam scanning capability and satellite three-axis attitude control capability, a fixed beam azimuth offset angle and satellite three-axis attitude angle can be calculated through joint control. On-orbit spatial synchronization of co-orbit bistatic SAR satellite beams can be achieved, and the zero Doppler frequency shift requirement for imaging is met. The algorithm is efficient and easy to implement on-orbit.

[0021] The beam spatial synchronization design method of bistatic SAR under zero Doppler constraint of the present invention can calculate the yaw angle, pitch angle and roll angle of the preceding and following satellites as well as the fixed offset angle of SAR beam azimuth. By jointly controlling the satellite attitude and beam electronic scanning angle, zero Doppler frequency shift and beam spatial synchronization coverage of bistatic SAR can be achieved. The beam spatial synchronization design method of the present invention under zero Doppler constraint for co-orbit bistatic SAR not only satisfies zero Doppler frequency shift at the beam center, but also satisfies zero Doppler frequency shift as much as possible at the entire beam center, and satisfies the requirement of synchronous coverage of the dual-satellite SAR beam space as much as possible. The beam spatial synchronization design method for co-track bistatic SAR under zero Doppler constraint of the present invention is simple, reliable and stable, widely applicable, and has good application and market prospects. Attached Figure Description

[0022] Other features, objects, and advantages of the present invention will become more apparent from the following detailed description of non-limiting embodiments with reference to the accompanying drawings: Figure 1 This is the process for designing beam spatial synchronization under zero-Doppler constraint for co-track bistatic SAR according to the present invention.

[0023] Figure 2 This is a schematic diagram of the geometric relationship of the dual-base SAR satellite for Earth observation according to the present invention.

[0024] Figure 3 This is a schematic diagram illustrating the geometric relationship between the bistatic SAR satellite and ground points according to the present invention.

[0025] Figure 4 This is a schematic diagram of the zero Doppler line, zero Doppler point, and beam space plane of the present invention.

[0026] Figure 5 This is a three-dimensional schematic diagram of the spatial synchronization results of the bistatic SAR beam of the present invention.

[0027] Figure 6 This is a two-dimensional schematic diagram of the bistatic SAR beam spatial ground projection and zero Doppler point of the present invention. Detailed Implementation

[0028] The present invention will now be described in detail with reference to specific embodiments. These embodiments will help those skilled in the art to further understand the present invention, but do not limit the invention in any way. It should be noted that those skilled in the art can make several changes and improvements without departing from the concept of the present invention. These all fall within the protection scope of the present invention.

[0029] Example 1: According to the present invention, a method for beam spatial synchronization design under zero-Doppler constraint in co-orbit bistatic SAR is provided, such as... Figure 1 As shown, the method includes the following steps: Step 1: Calculate the average baseline length based on the initial orbital parameters of the SAR satellites before and after co-orbiting. Step 2: Calculate the dual-satellite SAR beam offset azimuth angle based on the average baseline length; Step 3: Establish a bistatic zero-Doppler line model based on the distance equation, Doppler equation, and Earth ellipsoid model; Step 4: Calculate the coordinates of multiple points on the bistatic zero-Doppler line in the Earth-fixed coordinate system based on the distance range corresponding to the SAR beam. Step 5: Based on the SAR beam offset azimuth angle, establish the beam pointing surface in the SAR antenna coordinate system; Step 6: Based on the spatial relationship, establish the transformation matrix from the SAR antenna coordinate system to the Earth-fixed coordinate system, and transform the beam pointing plane to the Earth-fixed coordinate system. Step 7: Based on the beam pointing surface and the point on the zero Doppler line, with the minimum distance from the point on the zero Doppler line to the beam pointing surface as the optimization objective, establish the satellite three-axis attitude optimization function; Step 8: Perform satellite three-axis attitude optimization and solution based on the attitude optimization function; Step 9 finally yields the three-axis attitude guidance rules for a bistatic SAR satellite with a complete orbit.

[0030] Furthermore, in step 1, based on the orbital parameters (semi-major axis, eccentricity, inclination, etc.) of the preceding and following stars in the same orbit, and using a high-precision ephemeris or Kepler orbital model, a sequence of positions and velocities within the orbit of the preceding and following stars is generated. , .

[0031] The length of the baseline along the heading within a single track is calculated by the following formula:

[0032] Where, ‖·‖along-track represents the length along the heading baseline; The average baseline length is calculated by the following formula:

[0033] in T For orbital period.

[0034] like Figure 2 The diagram shown is a schematic representation of the geometric relationship of the dual-base SAR satellite for Earth observation according to the present invention.

[0035] like Figure 3 The diagram shown illustrates the geometric relationship between the bistatic SAR satellite and ground points according to the present invention.

[0036] Furthermore, in step 2, the average baseline length of the bistatic orbit is used as the basis. The SAR beam offset azimuth angles of the preceding and following satellites are allocated and remain constant throughout the orbit, without changing over time. They are calculated using the following formula.

[0037] SAR beam offset azimuth of the preceding satellite:

[0038] SAR beam offset azimuth angle of the later satellite:

[0039] in For the orbital height, It is the equatorial radius.

[0040] like Figure 4 The diagram shown is a schematic representation of the zero Doppler line, zero Doppler point, and beam space plane of the present invention.

[0041] like Figure 5 The figure shown is a three-dimensional schematic diagram of the spatial synchronization result of the bistatic SAR beam of the present invention.

[0042] like Figure 6 The figure shown is a two-dimensional schematic diagram of the bistatic SAR beam spatial ground projection and the zero Doppler point of the present invention.

[0043] Furthermore, in step 3, as Figure 3 As shown, a bistatic zero-Doppler line is defined in the Earth-fixed coordinate system, satisfying the bistatic distance-Doppler equation. It is assumed that the first satellite is the transmitting satellite and the second satellite is the receiving satellite.

[0044] Distance equation:

[0045] In the formula, and These are the phase center position vectors of the SAR antennas of the launching and receiving satellites, respectively. For the target position vector, At the speed of light, This represents the signal propagation delay. R is the distance from the satellite to the Earth's surface, and ||·|| represents the vector distance.

[0046] Doppler equations:

[0047] In the formula, and These are the phase center velocity vectors of the SAR antennas of the launching and receiving satellites, respectively. For wavelength, For Doppler center.

[0048]

[0049] in , The line-of-sight vector for launching and receiving satellites to the target. , The velocity of the launching and receiving satellites in the Earth-fixed coordinate system. The Doppler frequency of the target point.

[0050] Earth ellipsoid model:

[0051] In the formula, P T,X ,P T,Y ,P T,Z These are the x, y, and z coordinates of the target point in the Earth-fixed coordinate system, respectively. The radius is the equatorial radius. Ground elevation, The polar radius is .

[0052] Furthermore, in step 4, as Figure 4 As shown, according to ,in and To determine the minimum and maximum distances corresponding to the near and far ends of the beam distance relative to the detection angle, N optimization points are selected along the bistatic zero-Doppler line. Calculate the coordinates of the bistatic zero Doppler points of N points, denoted as . It covers the near, middle and far regions.

[0053] Furthermore, in step 5, as Figure 4 As shown, the calculated beam azimuth angle , Based on this, by assuming the range-direction angle of the two antenna beams... , Establish the beam pointing plane under the SAR antenna coordinate system. The beam pointing plane is a plane composed of two beam vectors and the satellite position.

[0054] The antenna pointing vector in the SAR antenna coordinate system is:

[0055]

[0056] in This is the offset of the antenna scanning elevation angle.

[0057] in, These are the transformation matrices around the Y-axis and X-axis, respectively.

[0058] Furthermore, in step 6, a transformation matrix is ​​established from the SAR antenna coordinate system (T-frame) to the Earth-fixed coordinate system (EF-frame) to transform the beam spatial pointing plane to the Earth-fixed coordinate system:

[0059] in This is the transformation matrix from the SAR antenna coordinate system (T-frame) to the Earth-fixed coordinate system (EF-frame), which includes the satellite's three-axis attitude angles (yaw). , looking up ,scroll The calculation formula is:

[0060] in, , and These are the precession, nutation, and polar motion matrices, respectively. The Earth rotation matrix; Right ascension of the ascending node, For track inclination, Argument of latitude; This refers to the angle at which the satellite flies.

[0061] Furthermore, in step 7, by jointly adjusting the three-axis attitude angle of the satellite, the center line of the beam pointing surface is aligned as much as possible with the points on the N zero-Doppler lines. Therefore, based on the beam pointing surface and the zero-Doppler points, the satellite three-axis attitude optimization function is established with the minimum distance from the zero-Doppler points to the beam pointing surface as the optimization objective.

[0062] Find the minimum distance from all zero Doppler points to the beam pointing plane:

[0063] in, Let K be the position coordinates of the k-th bistatic zero-Doppler point in the Earth-fixed coordinate system. These are the satellite's position coordinates in the Earth-fixed coordinate system. The weighting can be adjusted based on the importance of the zero Doppler point.

[0064] Furthermore, in step 8, an optimization algorithm (such as the least squares method) is used to solve the three-degree-of-freedom optimization problem to optimize and solve the satellite's three-axis attitude angles.

[0065] Furthermore, in step 9, each within the orbital period T is utilized. The positions of the preceding and following stars at that moment , Solve for the attitude angles under the corresponding zero Doppler line constraints. Low-pass filtering or spline interpolation is applied to the attitude angle sequence to ensure continuous and smooth attitude changes. Storage. The time-varying table is available for use by the onboard attitude control system.

[0066] Example 2: This invention provides a method for beam spatial synchronization design under zero-Doppler constraint in co-orbit bistatic SAR, comprising the following steps: Step 1: Calculate the average baseline length based on the initial orbital parameters of the SAR satellites before and after co-orbiting. Step 2: Calculate the dual-satellite SAR beam offset azimuth angle based on the average baseline length; Step 3: Establish a bistatic zero-Doppler line model based on the distance equation, Doppler equation, and Earth ellipsoid model; Step 4: Calculate the coordinates of multiple points on the bistatic zero-Doppler line in the Earth-fixed coordinate system based on the distance range corresponding to the SAR beam. Step 5: Based on the SAR beam offset azimuth angle, establish the beam pointing surface in the SAR antenna coordinate system; Step 6: Based on the spatial relationship, establish the transformation matrix from the SAR antenna coordinate system to the Earth-fixed coordinate system, and transform the beam pointing plane to the Earth-fixed coordinate system. Step 7: Based on the beam pointing surface and the point on the zero Doppler line, with the minimum distance from the point on the zero Doppler line to the beam pointing surface as the optimization objective, establish the satellite three-axis attitude optimization function; Step 8: Perform satellite three-axis attitude optimization and solution based on the attitude optimization function; Step 9 finally yields the three-axis attitude guidance rules for a bistatic SAR satellite with a complete orbit.

[0067] In step 1, the simulation started at 12:00:00 UTC on July 1, 2007. The orbital parameters of the preceding and following satellites were: semi-major axis 6978.14 km, eccentricity 0.001, inclination 97.7924°, perigee argument 90°, right ascension of ascending node 189.163°, and mean perigee angles of 0° and 356°, respectively. The average baseline length was calculated. The length is 487.26 km.

[0068] In step 2, the SAR beam offset azimuth angles of the preceding and following satellites. , The values ​​are -20.241° and 20.241° respectively.

[0069] In step 4, five optimization points are selected along the bistatic zero-Doppler line according to R=700km:10km:750km, and the bistatic zero-Doppler coordinates of the six points are calculated. The following distances are: (631.807,227.292,6321.480), (605.649,227.147,6324.028), (581.587,227.010,6326.276), (559.121,226.880,6328.292), (537.920,226.755,6330.122), and (517.751,226.634,6331.796) km.

[0070] In step 5, it is assumed that the range angle of the two antenna beams is... , With 0° and -45° respectively, the beam pointing plane of the SAR antenna coordinate system is established. Taking the previous satellite as an example, the two beam unit vectors of the beam pointing plane of the previous satellite are calculated to be (-0.3460, 0, 0.9382) and (-0.2446, 0.7071, 0.6634), and the satellite position is (945.728, 6.695, 6906.708) km.

[0071] In step 6, a transformation matrix is ​​established from the SAR antenna coordinate system (T system) to the Earth-fixed coordinate system (EF system).

[0072] In step 7, distance functions from six zero Doppler points to the beam pointing surface are established.

[0073] In step 8, the three-axis attitude angles of the foreplane are obtained using the least squares method: yaw. -1.3623°, pitch 0.2513°, rolling -0.4225°. Rear-axis attitude angles: Yaw. 1.4487°, pitch -0.2686°, rolling It is -1.4507°.

[0074] Furthermore, please refer to Figures 1-6 .

[0075] This embodiment can be seen as a specific implementation scenario of embodiment 1.

[0076] This invention also provides a beam spatial synchronization design system under zero-Doppler constraint for co-track bistatic SAR. The beam spatial synchronization design system under zero-Doppler constraint for co-track bistatic SAR can be implemented by executing the process steps of the beam spatial synchronization design method under zero-Doppler constraint for co-track bistatic SAR. That is, those skilled in the art can understand the beam spatial synchronization design method under zero-Doppler constraint for co-track bistatic SAR as a preferred embodiment of the beam spatial synchronization design system under zero-Doppler constraint for co-track bistatic SAR.

[0077] Those skilled in the art will understand that, besides implementing the system and its various devices, modules, and units provided by this invention in the form of purely computer-readable program code, the same functions can be achieved entirely through logical programming of the method steps, making the system and its various devices, modules, and units of this invention function in the form of logic gates, switches, application-specific integrated circuits, programmable logic controllers, and embedded microcontrollers. Therefore, the system and its various devices, modules, and units provided by this invention can be considered as a hardware component, and the devices, modules, and units included therein for implementing various functions can also be considered as structures within the hardware component; alternatively, the devices, modules, and units for implementing various functions can be considered as both software modules implementing the method and structures within the hardware component.

[0078] Specific embodiments of the present invention have been described above. It should be understood that the present invention is not limited to the specific embodiments described above, and those skilled in the art can make various changes or modifications within the scope of the claims, which do not affect the essence of the present invention. Unless otherwise specified, the embodiments and features described in this application can be arbitrarily combined with each other.

Claims

1. A method for beam spatial synchronization design under zero-Doppler constraint in co-orbit bistatic SAR, characterized in that, Includes the following steps: Step S1: Calculate the average baseline length based on the initial orbital parameters of the SAR satellites before and after orbital alignment; Step S2: Calculate the dual-satellite SAR beam offset azimuth angle based on the average baseline length; Step S3: Establish a bistatic zero-Doppler line model based on the distance equation, Doppler equation, and Earth ellipsoid model; Step S4: Based on the distance range corresponding to the SAR beam, calculate the coordinates of multiple points on the bistatic zero Doppler line in the Earth-fixed coordinate system; Step S5: Based on the SAR beam offset azimuth angle, establish the beam pointing surface in the SAR antenna coordinate system; Step S6: Based on the spatial relationship, establish a transformation matrix from the SAR antenna coordinate system to the Earth-fixed coordinate system, and transform the beam pointing plane to the Earth-fixed coordinate system; Step S7: Based on the beam pointing surface and the point on the zero Doppler line, with the minimum distance from the point on the zero Doppler line to the beam pointing surface as the optimization objective, establish the satellite three-axis attitude optimization function; Step S8: Perform satellite three-axis attitude optimization and solution based on the attitude optimization function; Step S9: Output the three-axis attitude guidance law of the whole orbit bistatic SAR satellite.

2. The beam spatial synchronization design method under zero-Doppler constraint for co-orbit bistatic SAR according to claim 1, characterized in that, Step S1 specifically includes: Based on the orbital parameters of the preceding and following stars in the same orbit, and using a high-precision ephemeris or Kepler orbital model, the position and velocity sequences of the preceding and following stars within one orbit are generated, and the average baseline length is calculated. The orbital parameters include the semi-major axis, eccentricity, and inclination.

3. The beam spatial synchronization design method under zero-Doppler constraint for co-orbit bistatic SAR according to claim 1, characterized in that, Step 2 specifically includes: determining and allocating the SAR beam offset azimuth angles of the preceding and following satellites based on the average baseline length of the bistatic SAR system. The beam offset azimuth angles remain fixed during the whole-track imaging process and are time-invariant parameters.

4. The beam spatial synchronization design method under zero-Doppler constraint for co-orbit bistatic SAR according to claim 1, characterized in that, Step 3 specifically includes: A bistatic zero-Doppler line model is constructed in the Earth fixed coordinate system. The bistatic zero-Doppler line satisfies both the bistatic distance-Doppler constraint equation and the Earth ellipsoidal geometric model.

5. The beam spatial synchronization design method under zero-Doppler constraint for co-orbit bistatic SAR according to claim 1, characterized in that, In step 4, the near-range, medium-range, and far-range imaging areas are covered according to the range range corresponding to SAR imaging. Multiple bistatic zero-Doppler constraint points are selected along the range direction on the bistatic zero-Doppler line, and the spatial coordinates of each bistatic zero-Doppler point in the Earth-fixed coordinate system are calculated.

6. The beam spatial synchronization design method under zero-Doppler constraint for co-orbit bistatic SAR according to claim 1, characterized in that, In step 5, based on the determined azimuth angle of the beam, a beam pointing surface is constructed in the SAR antenna coordinate system by presetting the range angles of the two antenna beams. The beam pointing surface is determined by the two beam pointing vectors and the corresponding satellite positions, forming a geometric plane.

7. The beam spatial synchronization design method under zero-Doppler constraint for co-orbit bistatic SAR according to claim 1, characterized in that, Step S7 includes: By jointly adjusting the satellite's three-axis attitude angles, including yaw, pitch, and roll, the centerline of the beam pointing surface is spatially aligned as much as possible at the zero-Doppler points corresponding to multiple bistatic zero-Doppler lines. Based on this, according to the spatial geometric relationship between the beam pointing surface and each zero-Doppler point, the satellite's three-axis attitude optimization function is constructed with the minimum distance from the zero-Doppler point to the beam pointing surface as the optimization objective.

8. The beam spatial synchronization design method under zero-Doppler constraint for co-orbit bistatic SAR according to claim 1, characterized in that, Step S8 specifically includes: An optimization algorithm is used to solve the three-degree-of-freedom attitude optimization problem, thereby completing the joint optimization and calculation of the satellite's yaw angle, pitch angle, and roll angle.

9. The beam spatial synchronization design method under zero-Doppler constraint for co-orbit bistatic SAR according to claim 1, characterized in that, Step S9 specifically includes: Using the position information of the preceding and following satellites at each moment within the orbital period, the satellite attitude angles under the corresponding bistatic zero Doppler line constraint conditions are solved; the obtained attitude angle sequence is processed by low-pass filtering or spline interpolation to ensure the continuity and smoothness of attitude changes; and the attitude parameters of yaw angle, pitch angle and roll angle changing with time are stored in tabular form for use in calling and executing by the onboard attitude control system.

10. A beam spatial synchronization design system for co-orbit bistatic SAR under zero Doppler constraint, characterized in that, include: Module M1: Calculates the average baseline length based on the initial orbital parameters of SAR satellites before and after orbital alignment; Module M2: Calculates the azimuth angle of the dual-satellite SAR beam offset based on the average baseline length; Module M3: Establish a bistatic zero-Doppler line model based on the distance equation, Doppler equation, and Earth ellipsoid model; Module M4: Calculates the coordinates of multiple points on the bistatic zero-Doppler line in the Earth-fixed coordinate system based on the distance range corresponding to the SAR beam; Module M5: Establish the beam pointing surface in the SAR antenna coordinate system based on the SAR beam offset azimuth angle; Module M6: Based on spatial relationships, establish a transformation matrix from the SAR antenna coordinate system to the Earth-fixed coordinate system, and transform the beam pointing plane to the Earth-fixed coordinate system; Module M7: Based on the beam pointing surface and the point on the zero Doppler line, with the minimum distance from the point on the zero Doppler line to the beam pointing surface as the optimization objective, establish a satellite three-axis attitude optimization function; Module M8: Performs satellite three-axis attitude optimization and solution based on the attitude optimization function; Module M9: Outputs the three-axis attitude guidance rules for bistatic SAR satellites with the same orbit.

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