Spaceborne sar scene matching curve electromechanical collaborative high-gain wave control method

Abstract

This application discloses a high-gain beam control method for electromechanical coordination of sparse array spaceborne SAR scene matching curves. Addressing the issues of limited and coupled peak values ​​of range and azimuth electronic scanning angles in sparse arrays, the tendency of single-dimensional optimization to lead to an increase in the peak value of the other dimension, and the dependence of weighted trade-offs on specific parameters, the method obtains the ideal beam pointing three-axis angle sequence and mechanical / electronic scanning capability constraints. Given initial mechanical scanning parameters that satisfy the mechanical scanning constraints, a two-dimensional electronic scanning angle sequence is calculated. Using the infinite norm of the two-dimensional electronic scanning angles as a low-gain electronic scanning index, an alternating constraint iteration of "minimizing the peak value in the target dimension and constraining the upper bound of the peak value in the other dimension" is employed. The upper bound of the two-dimensional peak value constraints is iteratively updated and convergence is determined. The output is a low-gain electromechanical coordinated beam control decomposition result that satisfies both mechanical and electronic scanning constraints and achieves synchronous decrease in the peak values ​​of the two-dimensional electronic scanning, which is used to generate beam control commands.

Description

Technical Field

[0001] This application relates to the field of electromechanical coordination technology, and in particular to a high-gain beam control method for electromechanical coordination of sparse array spaceborne SAR scene matching curves. Background Technology

[0002] Spaceborne SAR scene matching curve imaging achieves illumination and imaging of long curved scenes through two-dimensional continuous beam scanning. In this mode, to achieve curved scene imaging within the constraints of the platform's mechanical scanning capability and the phased array's electronic scanning capability, a combined electromechanical beam control method is typically employed, integrating satellite platform mechanical scanning and phased array antenna electronic scanning. The phased array electronic scanning generally includes two-dimensional electronic scanning angles in the range and azimuth directions. In curve imaging missions, the ideal beam pointing exhibits a significant nonlinear change over time, and there is a coupling relationship between the three-axis attitude of the mechanical scanning and the two-dimensional electronic scanning angles. Mechanical scanning is constrained by angular velocity and angular acceleration, and some beam pointing changes need to be compensated by electronic scanning, which may lead to large peak values ​​in the range or azimuth electronic scanning angles. Electronic scanning peak values ​​are constrained by device capabilities; excessively large peak values ​​can also cause significant scanning loss and pattern distortion risks (especially for sparse array phased array antennas), thus affecting imaging quality and engineering feasibility. Therefore, it is necessary to collaboratively suppress the two-dimensional electronic scanning peak values ​​while satisfying the constraints of both mechanical and electronic scanning.

[0003] Existing methods typically optimize single-dimensional electronic scanning peak values ​​or variance of electronic scanning angles, or employ weighted multi-objective approaches to compromise on two-dimensional electronic scanning resources. However, since the two-dimensional electronic scanning angles are coupled in the electromechanical decomposition, single-dimensional optimization often leads to an increase in the peak value of the other dimension; weighted multi-objective methods rely on weight selection, making it difficult to simultaneously compress the peak values ​​of both dimensions and achieve stable convergence. Therefore, there is an urgent need for an electromechanical co-operational low-electronic-scanning wavecontrol optimization method for sparse array spaceborne SAR scene matching curve imaging, which can achieve coordinated compression of the peak values ​​of the range and azimuth two-dimensional electronic scanning angles under electromechanical co-operational wavecontrol constraints, and obtain low-electronic-scanning wavecontrol optimization results. Summary of the Invention

[0004] The main objective of this application is to provide a high-gain beam control method for electromechanical coordination of sparse array spaceborne SAR scene matching curves, in order to solve the problems mentioned in the background art.

[0005] To achieve the above objectives, this application provides the following technical solution: A method for electromechanical coordinating high-gain beam control of sparse array spaceborne SAR scene matching curves, the specific steps of which are as follows: S1. Obtain the ideal beam pointing three-axis angle sequence and electromechanical scanning capability constraints, obtain the initial electromechanical scanning parameter vector that satisfies the electromechanical scanning capability constraints, calculate the initial range-direction electromechanical scanning angle sequence and the initial azimuth-direction electromechanical scanning angle sequence based on electromechanical geometry, construct a sparse array beam pattern quality assessment model, and output a quality score by comprehensively considering the peak sidelobe level, main lobe efficiency and grating lobe position offset. S2. Define the low electronic scanning index of the two-dimensional electronic scanning angle as the infinite norm of their respective sequences. Determine the dimension with the larger peak value as the optimization target dimension and the other dimension as the constraint dimension. Set the upper bound of the peak value of the constraint dimension as the product of the relaxation coefficient and the current peak value and take the minimum value of the upper limit of the electronic scanning capability. Set the beam quality constraint threshold. S3. Construct a multi-objective optimization problem. The objective function is a weighted combination of peak and quality terms. The constraints include electronic scanning peak constraints in the objective dimension, electronic scanning peak constraints in the constraint dimension, beam quality constraints, and mechanical scanning capability constraints. Identify quality-sensitive moments and apply penalty weights. Apply stricter constraints to the low-quality segment. Solve to obtain the mechanical scanning parameter vector after the first optimization. S4. Update the upper bound of the target dimension peak constraint to the arithmetic mean of the previous constraint upper bound and the current peak value, and take the minimum value with the upper limit of the electronic scanning capability. Simultaneously update the beam quality constraint threshold, swap the optimization target dimension and constraint dimension, calculate the beam quality time domain variance and perform local fine-tuning for high variance periods, and solve to obtain the second optimized mechanical scanning parameter vector. S5. Iterate alternately between the two steps mentioned above, updating the upper bound of the constraint and dynamically adjusting the weight coefficients in each round. Stop when the change of each indicator in two consecutive rounds of iteration is less than the preset threshold or the maximum number of iterations is reached. S6, Output the mechanical scanning parameter vector and the corresponding angle sequence.

[0006] Preferably, step S1 is performed in the following manner; S1.1 Obtain the ideal beam pointing three-axis angle sequence, including the pitch angle sequence, yaw angle sequence, and roll angle sequence; obtain the mechanical scanning capability constraints, including the three-axis angle range, angular velocity range, and angular acceleration range; obtain the electronic scanning capability constraints, including the range of electronic scanning angles in the range and azimuth directions; and generate the initial mechanical scanning parameter vector based on the mechanical scanning capability constraints using a polynomial parameterization method. S1.2. Based on the electromechanical geometry, decompose the ideal beam pointing three-axis angle sequence and the mechanical scanning three-axis angle sequence corresponding to the initial mechanical scanning parameter vector, and calculate the initial range electronic scanning angle sequence and the initial azimuth electronic scanning angle sequence. The distance scanning angle and the azimuth scanning angle are calculated at each time step using the following formulas:

[0007] .

[0008] Preferably, step S2 is performed in the following manner; S2.1 Define the low electronic scanning index of the range electronic scanning angle sequence and the azimuth electronic scanning angle sequence as the infinite norm of their respective sequences, calculate the peak value of the range electronic scanning angle and the peak value of the azimuth electronic scanning angle, compare the size relationship of the peak values ​​of the two-dimensional electronic scanning angles, determine the dimension with the larger peak value as the primary optimization target dimension, determine the dimension with the smaller peak value as the constraint dimension, and establish the optimization hierarchy relationship of the two-dimensional electronic scanning angles. The infinite norm is calculated using the following formula:

[0009] S2.2. Set an upper bound for peak constraints for the constraint dimension. The upper bound of the constraint is the smaller value between the product of the relaxation coefficient and the current peak value of the constraint dimension and the upper limit of the electronic scanning capability. The relaxation coefficient is greater than one. Set constraint thresholds for beam quality. The maximum quality degradation constraint threshold is the smaller value between the product of the quality relaxation coefficient and the maximum quality degradation value in step S1 and the upper limit of the system quality. The average quality degradation constraint threshold is the smaller value between the product of the quality relaxation coefficient and the average quality degradation value in step S1 and the upper limit of the system quality. The quality relaxation coefficient is greater than one. The upper limit of the azimuth scanning angle constraint is obtained by the following formula;

[0010] The upper bound of the distance scan angle constraint is obtained using the following formula: .

[0011] Preferably, step S3 is performed in the following manner; S3.1. Based on satisfying the mechanical scanning constraints in step S1 and the first sub-problem in step S2, with the goal of reducing the peak value of the target dimension electronic scanning angle, while ensuring that the constraint dimension electronic scanning angle does not exceed the preset upper limit, the Bernstein coefficient vector of the three axes of mechanical scanning is optimized and configured. Preferably, when the distance electronic scanning angle is the target dimension, the azimuth electronic scanning angle is constrained, and when the azimuth electronic scanning angle is the target dimension, the distance electronic scanning angle is constrained.

[0012] Where t is the upper bound variable of the peak value of the target dimension (here, range scanning), and the infinite norm of the target dimension is characterized by the above figure. The new range and azimuth scan peak values ​​are obtained using the following formulas;

[0013] S3.2 Based on the constraint configuration in step S3.1, the Bernstein coefficient vector of the three axes of mechanical scanning is optimized and adjusted to effectively reduce the peak value of the target dimension electro-scanning angle, while ensuring that the constrained dimension electro-scanning angle never exceeds the preset upper limit, and finally obtain the first optimized electromechanical decomposition result that satisfies the mechanical scanning constraints in step S1.

[0014] Preferably, step S4 is performed in the following manner; S4.1 Under the premise of satisfying the mechanical scanning constraint in step S1, based on the peak value of the target dimension electronic scanning angle obtained in step S3 and the upper limit of the constraint in the previous round, the upper limit of the target dimension constraint is updated by compromise, and the minimum value is taken with the upper limit of the electronic scanning capability constraint of that dimension to determine the new upper limit of constraint conditions. The average of the two values ​​is used to update the upper bound of the distance constraint as a compromise, and this is compared with the upper limit of the range electronic scanning capability. The specific method for finding the minimum value is as follows:

[0015] The upper bound of the aforementioned new distance constraint The following method constructs the optimization target based on the azimuth electronic scanning peak value:

[0016] S4.2 Under this constraint, with the peak value of the other dimension of the electronic scanning angle as the optimization target, the Bernstein coefficient vector of the three axes of mechanical scanning is adjusted to effectively reduce the peak value of the other dimension of the electronic scanning angle, while ensuring that the target dimension of the electronic scanning angle does not exceed the preset upper limit, so as to obtain the electromechanical decomposition result that satisfies the bidirectional constraint. New Bernstein coefficient vector The specific methods for determining the corresponding peak values ​​are as follows: .

[0017] Preferably, step S5 is performed in the following manner; S5.1. Alternate iterations are performed between steps S3 and S4. In each iteration, the upper limit of the peak constraint of the two-dimensional electric scanning angle is updated based on the current distance, the peak value of the azimuth electric scanning angle and the corresponding upper limit of the electric scanning capability constraint. Preferably, the upper limit of the constraint is set as the compromise value between the current peak value and the constraint of the previous round, and the minimum value is taken with the corresponding upper limit of the electric scanning capability constraint. The peak sequence is calculated as follows:

[0018] in Corresponding to the initial decomposition, This corresponds to the result of the first round of alternating two steps; The calculation method for updating the upper bound of the orientation dimension constraint is as follows:

[0019] S5.2 When the changes in the peak values ​​of the range and azimuth electronic scanning angles are both less than the preset threshold in two consecutive iterations, or when the number of iterations reaches the preset upper limit, the iteration is stopped to obtain the final electromechanical co-controlled beam control decomposition result that takes into account the peak value compression effect of the two-dimensional electronic scanning angles of range and azimuth and satisfies the mechanical scanning capability constraint and the electronic scanning capability constraint. The method for calculating the peak value change between two rounds is as follows; .

[0020] Preferably, step S6 is performed in the following manner; S6.1 The output mechanical scanning parameter vector is used as the final optimized electromechanical co-controlled beam control decomposition result. Based on the final mechanical scanning parameter vector, the corresponding mechanical scanning three-axis angle sequence is calculated, including pitch angle sequence, yaw angle sequence and roll angle sequence. S6.2 Calculate the corresponding range and azimuth electric scanning angle sequences based on electromechanical geometry, output the three-axis angular velocity and angular acceleration sequences of the mechanical scanning system, generate time-domain curves of the three-axis angles, angular velocities, and angular accelerations of the mechanical scanning system, and generate time-domain curves of the range and azimuth electric scanning angles.

[0021] Compared with the prior art, the beneficial effects of the present invention are: 1. This invention constructs an electromechanical co-operational high-gain beam control method for scene-matching curve imaging of sparse array spaceborne SAR. Through multi-objective joint optimization, alternating iterative collaborative compression, and quality consistency control, it achieves synchronous suppression of electronic scanning peaks in the range and azimuth directions, and effectively ensures the stability of the beam pattern quality across the entire trajectory. Compared with traditional technical solutions that only focus on single-dimensional peaks or ignore beam quality constraints, this method achieves systematic improvements in electronic scanning peak control, beam quality equalization, and imaging stability.

[0022] 2. To address the issues of limited and coupled peak values ​​of range and azimuth electronic scanning angles in sparse arrays, the tendency of single-dimensional optimization to lead to an increase in the peak value of the other dimension, and the dependence of weighted trade-offs on weights, this paper obtains the ideal beam pointing three-axis angle sequence and mechanical / electronic scanning capability constraints. Given initial mechanical scanning parameters that satisfy the mechanical scanning constraints, a two-dimensional electronic scanning angle sequence is calculated. Using the infinite norm of the two-dimensional electronic scanning angle as the low electronic scanning index, an alternating constraint iteration of "minimizing the peak value of the target dimension and constraining the upper bound of the peak value of the other dimension" is adopted. The upper bound of the two-dimensional peak value constraint is iteratively updated and convergence is determined. The low electronic scanning electromechanical co-controlled beam control decomposition result that satisfies the mechanical and electronic scanning constraints and achieves synchronous decrease of the peak value of the two-dimensional electronic scanning is output, which is used to generate beam control commands. Attached Figure Description

[0023] Figure 1 This is a flowchart illustrating the steps of the method described in this application.

[0024] Figure 2 Simulation parameters are used for the electromechanical-coordinated low-electric sweep beam control optimization method for sparse array spaceborne SAR scene matching curve imaging in this application.

[0025] Figure 3 This is a diagram demonstrating the alternating compression process of the peak value of the electronically swept angle.

[0026] Figure 4 This is a diagram demonstrating the alternating compression path of the peak value of the electronic sweep angle.

[0027] Figure 5 Comparison of the three-axis angles of the mechanical sweeper before and after optimization for the ideal three-axis system.

[0028] Figure 6 To optimize the comparison chart of the three-axis angular velocities before and after mechanical scanning.

[0029] Figure 7 To optimize the comparison chart of the three-axis angular acceleration of the front and rear mechanical scanning.

[0030] Figure 8 To optimize the comparison of front and rear distances and azimuth electric sweep angles. Detailed Implementation

[0031] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of this application, and not all of the embodiments. Based on the embodiments of this application, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of this application.

[0032] The terms "first," "second," and "third" in this application are for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of technical features indicated. Therefore, a feature defined as "first," "second," or "third" may explicitly or implicitly include at least one of that feature. In the description of this application, "multiple" means at least two, such as two, three, etc., unless otherwise explicitly specified. All directional indications (such as up, down, left, right, front, back, etc.) in the embodiments of this application are only used to explain the relative positional relationships and movements between components in a specific orientation (as shown in the figures). If the specific orientation changes, the directional indications also change accordingly. Furthermore, the terms "comprising" and "having," and any variations thereof, are intended to cover non-exclusive inclusion. For example, a process, method, system, product, or device that includes a series of steps or units is not limited to the listed steps or units, but may optionally include steps or units not listed, or may optionally include other steps or units inherent to these processes, methods, products, or devices.

[0033] In this document, the term "embodiment" means that a particular feature, structure, or characteristic described in connection with an embodiment may be included in at least one embodiment of this application. The appearance of this phrase in various places throughout the specification does not necessarily refer to the same embodiment, nor is it a mutually exclusive, independent, or alternative embodiment. It will be explicitly and implicitly understood by those skilled in the art that the embodiments described herein can be combined with other embodiments.

[0034] Example 1: Please refer to Figures 1-8 A high-gain beam control method for sparse array spaceborne SAR scene matching curve electromechanical coordination is proposed, and the specific steps are as follows: S1. Obtain the ideal beam pointing three-axis angle sequence and electromechanical scanning capability constraints, obtain the initial electromechanical scanning parameter vector that meets the electromechanical scanning capability constraints, calculate the initial range-direction electromechanical scanning angle sequence and the initial azimuth-direction electromechanical scanning angle sequence based on electromechanical geometry, construct a sparse array beam pattern quality assessment model, and output a quality score by comprehensively considering the peak sidelobe level, main lobe efficiency and grating lobe position offset. S2. Define the low electronic scanning index of the two-dimensional electronic scanning angle as the infinite norm of their respective sequences. Determine the dimension with the larger peak value as the optimization target dimension and the other dimension as the constraint dimension. Set the upper bound of the peak value of the constraint dimension as the product of the relaxation coefficient and the current peak value and take the minimum value of the upper limit of the electronic scanning capability. Set the beam quality constraint threshold. S3. Construct a multi-objective optimization problem. The objective function is a weighted combination of peak and quality terms. The constraints include electronic scanning peak constraints in the objective dimension, electronic scanning peak constraints in the constraint dimension, beam quality constraints, and mechanical scanning capability constraints. Identify quality-sensitive moments and apply penalty weights. Apply stricter constraints to the low-quality segment. Solve to obtain the mechanical scanning parameter vector after the first optimization. S4. Update the upper bound of the target dimension peak constraint to the arithmetic mean of the previous constraint upper bound and the current peak value, and take the minimum value with the upper limit of the electronic scanning capability. Simultaneously update the beam quality constraint threshold, swap the optimization target dimension and constraint dimension, calculate the beam quality time domain variance and perform local fine-tuning for high variance periods, and solve to obtain the second optimized mechanical scanning parameter vector. S5. Iterate alternately between the two steps mentioned above, updating the upper bound of the constraint and dynamically adjusting the weight coefficients in each round. Stop when the change of each indicator in two consecutive rounds of iteration is less than the preset threshold or the maximum number of iterations is reached. S6, Output the mechanical scanning parameter vector and the corresponding angle sequence.

[0035] In this embodiment: Step S1 establishes a complete input foundation for the optimization problem by obtaining the ideal beam pointing triaxial angle sequence and electromechanical scanning capability constraints. An initial electromechanical scanning parameter vector is generated using a polynomial parameterization method to ensure the feasibility of the optimization starting point. The initial electromechanical scanning angle sequence is calculated based on electromechanical geometric relationships to achieve electromechanical decomposition of the beam pointing, and a sparse array beam pattern quality evaluation model is constructed, providing a quantitative evaluation basis for subsequent optimization. This step combines geometric constraints with the physical characteristics of the sparse array antenna, laying the foundation for solving the problem of inconsistent beam quality caused by changes in operating parameters.

[0036] Step S2 defines the low-level EQS index of the two-dimensional EQS angle and compares its peak values ​​to clarify the optimization target dimension and constraint dimension, establishing the optimization hierarchy of the two-dimensional EQS angle and providing a clear illustration for alternating iterative optimization. A relaxation coefficient is used to set the upper bound of the constraint dimension peak value to ensure the feasibility of the initial constraints. Simultaneously, a beam quality constraint threshold is introduced, formally incorporating beam pattern quality into the optimization constraint system, enabling subsequent optimization to maintain stable beam pattern performance while compressing the EQS peak value.

[0037] Step S3 constructs a multi-objective optimization problem by weighting the peak and quality terms to achieve coordinated optimization of electronic scanning peak suppression and beam quality control. By introducing a quality-sensitive moment identification mechanism, additional constraint weights are applied to periods of significant quality degradation, and a stricter constraint strategy is adopted for low-quality segments. This effectively avoids the impact of local quality degradation on overall imaging performance, thereby obtaining an initial optimization result that balances peak compression and quality balance.

[0038] Step S4 progressively updates the target dimension peak constraint and beam quality threshold, and swaps the optimization target dimension and constraint dimension to achieve coordinated compression of the two-dimensional electronic scanning angle. Beam quality temporal variance is introduced as a consistency evaluation index, allowing for local fine-tuning during periods of significant quality fluctuation. This effectively suppresses the instability of beam performance over time, ensuring consistent optimization results across the entire trajectory.

[0039] Step S5 iterates alternately between steps S3 and S4, forming a closed-loop mechanism for adaptive constraint tightening and dynamic switching of optimization objectives. By recording the changing trends of multiple key indicators and using a joint criterion of multiple indicators as the termination condition for iteration, it ensures that the optimization process converges simultaneously in both the electronic scanning peak value and beam quality dimensions, avoiding premature convergence or oscillation of a single indicator, and improving the overall optimization efficiency and stability.

[0040] Step S6 outputs the final mechanical scanning parameter vector and the corresponding mechanical and electronic scanning angle sequences to form a complete electromechanical coordinated wave control implementation scheme. This step solidifies the optimization results in an engineering-usable form, providing a clear basis for system verification, task planning, and engineering applications.

[0041] Through steps S1 to S6, this invention constructs an electromechanical co-operational high-gain beam control method for scene-matching curve imaging of sparse array spaceborne SAR. By employing multi-objective joint optimization, alternating iterative collaborative compression, and quality consistency control, it achieves simultaneous suppression of electronic scanning peaks in both range and azimuth directions, effectively ensuring the stability of the beam pattern quality across the entire trajectory. Compared to traditional techniques that only focus on single-dimensional peaks or ignore beam quality constraints, this method achieves systematic improvements in electronic scanning peak control, beam quality equalization, and imaging stability.

[0042] Example 2: Please refer to Figures 1-8 The specific method for step S1 is as follows; S1.1 Obtain the ideal beam pointing three-axis angle sequence, including pitch angle sequence, yaw angle sequence and roll angle sequence; obtain the mechanical scanning capability constraints, including the three-axis angle range, angular velocity range and angular acceleration range; obtain the electronic scanning capability constraints, including the range electronic scanning angle range and azimuth electronic scanning angle range; and generate the initial mechanical scanning parameter vector based on the mechanical scanning capability constraints using a polynomial parameterization method. S1.2. Based on the electromechanical geometry, decompose the ideal beam pointing three-axis angle sequence and the mechanical scanning three-axis angle sequence corresponding to the initial mechanical scanning parameter vector, and calculate the initial range electronic scanning angle sequence and the initial azimuth electronic scanning angle sequence. The distance scanning angle and the azimuth scanning angle are calculated at each time step using the following formulas:

[0043] .

[0044] In this embodiment: Step S1.1 obtains the three-axis angle sequence of the ideal beam pointing and introduces the capability constraints of mechanical scanning and electronic scanning. Polynomial parameterization modeling is performed on the mechanical scanning parameters, achieving a unified constraint on the continuity of mechanical scanning motion and physical accessibility. Based on this, the ideal beam pointing is decomposed according to electromechanical geometry to obtain the initial range and azimuth electronic scanning angle sequences. This allows for a reasonable allocation of beam pointing requirements between mechanical and electronic scanning, effectively reducing the burden of a single scanning method, avoiding mechanical scanning exceeding limits or electronic scanning going out of bounds, and providing a feasible and stable initial solution for subsequent optimization.

[0045] Step S1.2 constructs a beam pattern quality assessment model that conforms to the characteristics of a sparse array antenna, mapping the range and azimuth electronic scanning angles to a unified beam quality score, thus achieving a quantitative evaluation of beam performance. This quality score comprehensively considers key factors such as sidelobe level, main lobe energy utilization, and grating lobe position offset, fully reflecting the impact of electronic scanning angle changes on beam quality. Further statistical analysis of the full-trajectory beam quality yields maximum and average quality degradation indices, providing a clear basis for subsequent constraint optimization and performance trade-offs, and improving the assessability and optimizability of beam control.

[0046] By implementing the two sub-steps in step S1 in a coordinated manner, both beam pointing feasibility and pattern quality are simultaneously achieved. This method not only improves the rationality and stability of the initial scanning parameters, but also provides a clear performance evaluation benchmark for the subsequent optimization process, thereby improving the overall consistency of beam pointing accuracy and quality and enhancing the comprehensive performance of the system under complex constraints.

[0047] Example 3: Please refer to Figures 1-8 The specific method for step S2 is as follows; S2.1 Define the low electronic scanning index of the range electronic scanning angle sequence and the azimuth electronic scanning angle sequence as the infinite norm of their respective sequences, calculate the peak value of the range electronic scanning angle and the peak value of the azimuth electronic scanning angle, compare the size relationship of the peak values ​​of the two-dimensional electronic scanning angles, determine the dimension with the larger peak value as the primary optimization target dimension, determine the dimension with the smaller peak value as the constraint dimension, and establish the optimization hierarchy relationship of the two-dimensional electronic scanning angles. The infinite norm is calculated using the following formula:

[0048] S2.2. Set an upper bound for peak constraints for the constraint dimension. The upper bound of the constraint is the smaller value between the product of the relaxation coefficient and the current peak value of the constraint dimension and the upper limit of the electronic scanning capability. The relaxation coefficient is greater than one. Set constraint thresholds for beam quality. The maximum quality degradation constraint threshold is the smaller value between the product of the quality relaxation coefficient and the maximum quality degradation value in step S1 and the upper limit of the system quality. The average quality degradation constraint threshold is the smaller value between the product of the quality relaxation coefficient and the average quality degradation value in step S1 and the upper limit of the system quality. The quality relaxation coefficient is greater than one. The upper limit of the azimuth scanning angle constraint is obtained by the following formula;

[0049] The upper bound of the distance scan angle constraint is obtained using the following formula: .

[0050] In this embodiment: Step S2.1 uses the infinity norm of the range and azimuth electronic scanning angle sequences to characterize their respective low electronic scanning indices. A comparative analysis of the peak values ​​of the two-dimensional electronic scanning angles is performed, and a hierarchical optimization relationship with clear priorities is established. Dimensions with larger peak values ​​are prioritized as optimization targets, while dimensions with smaller peak values ​​are treated as constraints for adjustment. This step adaptively determines the focus of electronic scanning optimization, avoiding coupling conflicts caused by simultaneous forced compression of both dimensions. This makes subsequent iterations more targeted and stable, thereby improving the efficiency and controllability of electronic scanning angle peak compression.

[0051] Step S2.2, based on the clearly defined optimization hierarchy, introduces peak constraint and beam quality constraint based on relaxation coefficients to set reasonable initial boundary conditions for electronic scanning angle and radiation pattern performance. By jointly limiting the upper bound of the constraints and the system capability limit, the constraints have the necessary flexibility without exceeding the physical and performance limits. Thus, while ensuring that the beam quality does not significantly degrade, a clear and feasible constraint space is provided for the multi-objective optimization problem, improving the convergence and engineering applicability of the overall optimization process.

[0052] By implementing the two sub-steps in step S2 in a coordinated manner, the adaptive adjustment of the optimization focus and the dynamic balance of the constraint boundary are achieved. This method effectively alleviates the contradiction between electronic scanning peak compression and beam quality maintenance, improves the stability and practicality of multi-objective optimization problems, and enables the system to achieve better overall performance under complex constraints.

[0053] Example 4: Please refer to Figures 1-8 The specific method for step S3 is as follows; S3.1. Based on satisfying the mechanical scanning constraints in step S1 and the first sub-problem in step S2, with the goal of reducing the peak value of the target dimension electronic scanning angle, while ensuring that the constraint dimension electronic scanning angle does not exceed the preset upper limit, the Bernstein coefficient vector of the three axes of mechanical scanning is optimized and configured. Preferably, when the distance electronic scanning angle is the target dimension, the azimuth electronic scanning angle is constrained, and when the azimuth electronic scanning angle is the target dimension, the distance electronic scanning angle is constrained.

[0054] Where t is the upper bound variable of the peak value of the target dimension (here, range scanning), and the infinite norm of the target dimension is characterized by the above figure. The new range and azimuth scan peak values ​​are obtained using the following formulas;

[0055] S3.2 Based on the constraint configuration in step S3.1, the Bernstein coefficient vector of the three axes of mechanical scanning is optimized and adjusted to effectively reduce the peak value of the target dimension electro-scanning angle, while ensuring that the constrained dimension electro-scanning angle never exceeds the preset upper limit, and finally obtain the first optimized electromechanical decomposition result that satisfies the mechanical scanning constraints in step S1.

[0056] In this embodiment: Step S3.1 constructs a multi-objective optimization problem with electronic scanning peak value and beam quality as joint objectives. The target dimensions of electronic scanning angle peak value and full-trajectory beam quality index are simultaneously incorporated into the optimization framework, and multiple constraints such as mechanical scanning capability and quality threshold are introduced, achieving overall constraint and unified modeling of electromechanical cooperative scanning behavior. This step completes the mathematical coupling between peak value compression requirements and beam quality preservation requirements, ensuring that the optimization process is no longer limited to a single performance index. It fundamentally avoids beam quality degradation or mechanical scanning failure caused by single-objective optimization, providing a stable and controllable optimization foundation for subsequent fine-tuning.

[0057] Step S3.2 involves a comprehensive analysis of the imaging time series to identify beam quality-sensitive moments and apply differentiated penalty weights to corresponding time periods, enabling the optimization process to focus on areas prone to quality degradation. Simultaneously, the imaging trajectory is segmented based on beam quality distribution, and stricter electronic scanning angle constraints are applied to low-quality segments, achieving targeted peak suppression and quality improvement. Combining initial mechanical scanning parameters with an adaptive step-size strategy completes the optimization solution, ensuring that the initial optimization results satisfy the constraints while maintaining overall trajectory quality stability, effectively improving the practicality and reliability of the optimization results.

[0058] By implementing the two sub-steps in step S3 in a coordinated manner, fine-grained control of complex imaging trajectories is achieved. Compared with the single-target or uniform constraint optimization methods commonly used in existing technologies, this method can focus on adjusting the weak quality regions, significantly reducing the mutual constraint between electronic scanning peak and beam quality. While ensuring the feasibility of mechanical scanning, it improves the consistency of the beam pattern and imaging stability, laying a solid foundation for subsequent alternating iterations and robustness enhancement.

[0059] Example 5: Please refer to Figures 1-8 The specific method for step S4 is as follows; S4.1 Under the premise of satisfying the mechanical scanning constraint in step S1, based on the peak value of the target dimension electronic scanning angle obtained in step S3 and the upper limit of the constraint in the previous round, the upper limit of the target dimension constraint is updated by compromise, and the minimum value is taken with the upper limit of the electronic scanning capability constraint of that dimension to determine the new upper limit of constraint conditions. The average of the two values ​​is used to update the upper bound of the distance constraint as a compromise, and this is compared with the upper limit of the range electronic scanning capability. The specific method for finding the minimum value is as follows:

[0060] The upper bound of the aforementioned new distance constraint The following method constructs the optimization target based on the azimuth electronic scanning peak value:

[0061] S4.2 Under this constraint, with the peak value of the other dimension of the electronic scanning angle as the optimization target, the Bernstein coefficient vector of the three axes of mechanical scanning is adjusted to effectively reduce the peak value of the other dimension of the electronic scanning angle, while ensuring that the target dimension of the electronic scanning angle does not exceed the preset upper limit, so as to obtain the electromechanical decomposition result that satisfies the bidirectional constraint. New Bernstein coefficient vector The specific methods for determining the corresponding peak values ​​are as follows: .

[0062] In this embodiment: Step S4.1 dynamically updates the peak value constraint of the electronic scanning angle and the quality degradation constraint based on the initial optimization results, and uses a combination of arithmetic mean and system capability upper limit to limit the constraint boundary, so that the constraint conditions gradually converge in multiple rounds of optimization. This process avoids the impact of excessively wide or tight constraints on the optimization results. At the same time, by exchanging the optimization target dimension and constraint dimension, the performance indicators that were originally in a restricted state are transformed into direct optimization objects, thereby reallocating the optimization focus within the feasible range, completing the constraint adjustment and optimization direction reconstruction, and ensuring a reasonable balance between performance improvement and safety margin.

[0063] Step S4.2 involves performing a time-domain variance analysis on the beam quality score across the entire trajectory to clearly identify the periods of concentrated beam quality fluctuations. Local adjustments are then made within a constrained range to the corresponding mechanical scanning parameters, effectively reducing abrupt changes in quality over time. Under the premise of unchanged overall constraints, a multi-objective optimization problem with reversed roles is constructed and solved to ensure the continuity and smoothness of the mechanical scanning parameters throughout the entire trajectory. This achieves targeted correction of local instability issues, thereby improving the consistency of quality at the trajectory level and the reliability of engineering implementation.

[0064] By implementing the two sub-steps in step S4 in combination, an iterative processing method combining dynamic constraint adjustment and time-domain stability correction is introduced on the basis of one-time parameter optimization. This ensures that the optimization result not only meets the system capability boundary requirements but also takes into account the quality balance over time. Compared with the existing methods that use static constraints and global average optimization, this scheme effectively reduces the impact of local performance fluctuations on the overall result, and improves the optimization result from simply feasible to stable and high-quality, further enhancing the reliability of system operation and its practical application value.

[0065] Example 6: Please refer to Figures 1-8 The specific method for step S5 is as follows; S5.1. Alternate iterations are performed between steps S3 and S4. In each iteration, the upper limit of the peak constraint of the two-dimensional electric scanning angle is updated based on the current distance, the peak value of the azimuth electric scanning angle and the corresponding upper limit of the electric scanning capability constraint. Preferably, the upper limit of the constraint is set as the compromise value between the current peak value and the constraint of the previous round, and the minimum value is taken with the corresponding upper limit of the electric scanning capability constraint. The peak sequence is calculated as follows:

[0066] in Corresponding to the initial decomposition, This corresponds to the result of the first round of alternating two steps; The calculation method for updating the upper bound of the orientation dimension constraint is as follows:

[0067] S5.2 When the changes in the peak values ​​of the range and azimuth electronic scanning angles are both less than the preset threshold in two consecutive iterations, or when the number of iterations reaches the preset upper limit, the iteration is stopped to obtain the final electromechanical co-controlled beam control decomposition result that takes into account the peak value compression effect of the two-dimensional electronic scanning angles of range and azimuth and satisfies the mechanical scanning capability constraint and the electronic scanning capability constraint. The method for calculating the peak value change between two rounds is as follows; .

[0068] In this embodiment: Step S5.1 iterates alternately between steps S3 and S4, collecting and calculating the changes in the peak value of the two-dimensional electronic scanning angle and related beam quality indicators round by round, forming a continuous and comparable iterative change record. This method clearly depicts the evolution trend of each key indicator during the iteration process, providing a quantitative basis for subsequent convergence determination and adjustment strategies, while avoiding over- or under-optimization caused by relying solely on a fixed number of iterations, thereby improving the stability and controllability of the overall optimization process.

[0069] Step S5.2 compares and analyzes the peak improvement rate and the quality improvement rate, and dynamically adjusts the weights of each item in the objective function accordingly, ensuring that the optimization process always revolves around the currently insufficient indicators. When significant differences appear in the improvement speed of different objectives, the weight adjustment promptly corrects the optimization direction, preventing excessive convergence of a single indicator from affecting the overall performance balance. Combined with a clear convergence threshold and a maximum iteration limit, the orderly termination of the optimization process is achieved, ensuring stable and reproducible results.

[0070] By implementing the two sub-steps in step S5 in a coordinated manner, a closed-loop optimization process based on iterative trend analysis and adaptive weight adjustment is constructed. Compared with the existing technology that uses fixed weights and empirically determined convergence conditions, this scheme significantly enhances the responsiveness of the optimization process to different performance index changes, effectively reduces the probability of parameter oscillation and invalid iteration, and improves the performance balance, convergence reliability and engineering applicability of the finally obtained mechanical and electronic scanning parameters.

[0071] Example 6: Please refer to Figures 1-8 The specific method for step S6 is as follows; S6.1 The output mechanical scanning parameter vector is used as the final optimized electromechanical co-controlled beam control decomposition result. Based on the final mechanical scanning parameter vector, the corresponding mechanical scanning three-axis angle sequence is calculated, including pitch angle sequence, yaw angle sequence and roll angle sequence. S6.2 Calculate the corresponding range and azimuth electric scanning angle sequences based on electromechanical geometry, output the three-axis angular velocity and angular acceleration sequences of the mechanical scanning system, generate time-domain curves of the three-axis angles, angular velocities, and angular accelerations of the mechanical scanning system, and generate time-domain curves of the range and azimuth electric scanning angles.

[0072] In this embodiment: Step S6.1 outputs the mechanical scanning parameter vector refined across the entire trajectory, and calculates the corresponding mechanical scanning triaxial angle sequence and electronic scanning angle sequence accordingly, presenting the collaborative decomposition results of mechanical and electronic scanning in a complete and continuous form. Simultaneously, the time-domain variation results of angle, angular velocity, angular acceleration, and beam quality are generated, making the time-dimensional variation characteristics of the optimized beam control scheme clearly visible. This completes the conversion of the optimization results from parametric form to an engineering-usable form, facilitating subsequent system implementation and task application.

[0073] Step S6.2 performs a multi-dimensional performance evaluation of the final optimization result, quantifying the electronic scanning peak compression effect, beam quality improvement, and parameter robustness level, while simultaneously verifying whether each parameter meets the predetermined capability constraints. This evaluation method comprehensively reflects the degree of improvement of the optimized scheme relative to the initial solution, clarifying its overall performance in peak control, quality maintenance, and stability, thus providing an objective basis for the effectiveness of the scheme and avoiding judgment based on a single indicator.

[0074] Through the implementation of the two sub-steps in step S6, this scheme, based on parameter optimization, further achieves the engineering organization of the output results and the systematic verification of performance. Compared with the existing technology that only provides optimization parameters or local indicators, it forms a complete closed loop from parameter generation to performance evaluation. This process not only improves the understandability and applicability of the optimization results, but also makes different optimization schemes comparable, further enhancing the reliability and promotion value of the wave control scheme in practical applications.

[0075] Furthermore, the functional units in the various embodiments of this application can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit. The integrated units described above can be implemented in hardware or as software functional units. The above are merely embodiments of this application and do not limit the patent scope of this application. Any equivalent structural or procedural transformations made based on the description and drawings of this application, or direct or indirect applications in other related technical fields, are similarly included within the patent protection scope of this application.

[0076] The specific embodiments of the invention have been described in detail above, but they are only examples, and this application is not limited to the specific embodiments described above. For those skilled in the art, any equivalent modifications or substitutions to the invention are also within the scope of this application. Therefore, all equivalent changes, modifications, and improvements made without departing from the spirit and principles of this application should be covered within the scope of this application.

Claims

1. A high-gain beam control method for sparse array spaceborne SAR scene matching curve electromechanical coordination, characterized in that: The specific steps are as follows: S1. Obtain the ideal beam pointing three-axis angle sequence and electromechanical scanning capability constraints, obtain the initial electromechanical scanning parameter vector that satisfies the electromechanical scanning capability constraints, calculate the initial range-direction electromechanical scanning angle sequence and the initial azimuth-direction electromechanical scanning angle sequence based on electromechanical geometry, construct a sparse array beam pattern quality assessment model, and output a quality score by comprehensively considering the peak sidelobe level, main lobe efficiency and grating lobe position offset. S2. Define the low electronic scanning index of the two-dimensional electronic scanning angle as the infinite norm of their respective sequences. Determine the dimension with the larger peak value as the optimization target dimension and the other dimension as the constraint dimension. Set the upper bound of the peak value of the constraint dimension as the product of the relaxation coefficient and the current peak value and take the minimum value of the upper limit of the electronic scanning capability. Set the beam quality constraint threshold. S3. Construct a multi-objective optimization problem. The objective function is a weighted combination of peak and quality terms. The constraints include electronic scanning peak constraint in the objective dimension, electronic scanning peak constraint in the constraint dimension, beam quality constraint, and mechanical scanning capability constraint. Solve to obtain the mechanical scanning parameter vector after the first optimization. S4. Update the upper bound of the target dimension peak constraint to the arithmetic mean of the previous constraint upper bound and the current peak value, and take the minimum value with the upper limit of the electronic scanning capability. Simultaneously update the beam quality constraint threshold, swap the optimization target dimension and constraint dimension, and solve to obtain the second optimized mechanical scanning parameter vector. S5. Iterate alternately between the two steps mentioned above, updating the upper bound of the constraint and dynamically adjusting the weight coefficients in each round. Stop when the change of each indicator in two consecutive rounds of iteration is less than the preset threshold or the maximum number of iterations is reached. S6, Output the mechanical scanning parameter vector and the corresponding angle sequence.

2. The sparse array spaceborne SAR scene matching curve electromechanical cooperative high-gain beam control method according to claim 1, characterized in that, The specific method for step S1 is as follows; S1.1 Obtain the ideal beam pointing three-axis angle sequence, including pitch angle sequence, yaw angle sequence and roll angle sequence; obtain the mechanical scanning capability constraints, including the three-axis angle range, angular velocity range and angular acceleration range; obtain the electronic scanning capability constraints, including the range electronic scanning angle range and azimuth electronic scanning angle range; and generate the initial mechanical scanning parameter vector based on the mechanical scanning capability constraints using a polynomial parameterization method. S1.

2. Based on the electromechanical geometry, decompose the ideal beam pointing three-axis angle sequence and the mechanical scanning three-axis angle sequence corresponding to the initial mechanical scanning parameter vector, and calculate the initial range electronic scanning angle sequence and the initial azimuth electronic scanning angle sequence. The distance scanning angle and the azimuth scanning angle are calculated at each time step using the following formulas: 。 3. The electromechanical coordinated high-gain beam control method for sparse array spaceborne SAR scene matching curves according to claim 2, characterized in that, The specific method for step S2 is as follows; S2.1 Define the low electronic scanning index of the range electronic scanning angle sequence and the azimuth electronic scanning angle sequence as the infinite norm of their respective sequences, calculate the peak value of the range electronic scanning angle and the peak value of the azimuth electronic scanning angle, compare the size relationship of the peak values ​​of the two-dimensional electronic scanning angles, determine the dimension with the larger peak value as the primary optimization target dimension, determine the dimension with the smaller peak value as the constraint dimension, and establish the optimization hierarchy relationship of the two-dimensional electronic scanning angles. The infinite norm is calculated using the following formula: S2.

2. Set an upper bound for peak constraints for the constraint dimension. The upper bound of the constraint is the smaller value between the product of the relaxation coefficient and the current peak value of the constraint dimension and the upper limit of the electronic scanning capability. The relaxation coefficient is greater than one. Set constraint thresholds for beam quality. The maximum quality degradation constraint threshold is the smaller value between the product of the quality relaxation coefficient and the maximum quality degradation value in step S1 and the upper limit of the system quality. The average quality degradation constraint threshold is the smaller value between the product of the quality relaxation coefficient and the average quality degradation value in step S1 and the upper limit of the system quality. The quality relaxation coefficient is greater than one. The upper limit of the azimuth scanning angle constraint is obtained by the following formula; The upper bound of the distance scan angle constraint is obtained using the following formula: 。 4. The sparse array spaceborne SAR scene matching curve electromechanical cooperative high-gain beam control method according to claim 3, characterized in that, The specific method for step S3 is as follows; S3.

1. Based on satisfying the mechanical scanning constraints in step S1 and the first sub-problem in step S2, with the goal of reducing the peak value of the target dimension electronic scanning angle, while ensuring that the constraint dimension electronic scanning angle does not exceed the preset upper limit, the Bernstein coefficient vector of the three axes of mechanical scanning is optimized and configured. Preferably, when the distance electronic scanning angle is the target dimension, the azimuth electronic scanning angle is constrained, and when the azimuth electronic scanning angle is the target dimension, the distance electronic scanning angle is constrained. Where t is the upper bound variable of the peak value of the target dimension (here, range scanning), and the infinite norm of the target dimension is characterized by the above figure. The new range and azimuth scan peak values ​​are obtained using the following formulas; S3.2 Based on the constraint configuration in step S3.1, the Bernstein coefficient vector of the three axes of mechanical scanning is optimized and adjusted to effectively reduce the peak value of the target dimension electro-scanning angle, while ensuring that the constrained dimension electro-scanning angle never exceeds the preset upper limit, and finally obtain the first optimized electromechanical decomposition result that satisfies the mechanical scanning constraints in step S1.

5. The sparse array spaceborne SAR scene matching curve electromechanical cooperative high-gain beam control method according to claim 4, characterized in that, The specific method for step S4 is as follows; S4.1 Under the premise of satisfying the mechanical scanning constraint in step S1, based on the peak value of the target dimension electronic scanning angle obtained in step S3 and the upper limit of the constraint in the previous round, the upper limit of the target dimension constraint is updated by compromise, and the minimum value is taken with the upper limit of the electronic scanning capability constraint of that dimension to determine the new upper limit of constraint conditions. The average of the two values ​​is used to update the upper bound of the distance constraint as a compromise, and this is compared with the upper limit of the range electronic scanning capability. The specific method for finding the minimum value is as follows: The upper bound of the aforementioned new distance constraint The following method constructs the optimization target based on the azimuth electronic scanning peak value: S4.2 Under this constraint, with the peak value of the other dimension of the electronic scanning angle as the optimization target, the Bernstein coefficient vector of the three axes of mechanical scanning is adjusted to effectively reduce the peak value of the other dimension of the electronic scanning angle, while ensuring that the target dimension of the electronic scanning angle does not exceed the preset upper limit, so as to obtain the electromechanical decomposition result that satisfies the bidirectional constraint. New Bernstein coefficient vector The specific methods for determining the corresponding peak values ​​are as follows: 。 6. The sparse array spaceborne SAR scene matching curve electromechanical cooperative high-gain beam control method according to claim 5, characterized in that, The specific method for step S5 is as follows; S5.

1. Alternate iterations are performed between steps S3 and S4. In each iteration, the upper limit of the peak constraint of the two-dimensional electric scanning angle is updated based on the current distance, the peak value of the azimuth electric scanning angle and the corresponding upper limit of the electric scanning capability constraint. Preferably, the upper limit of the constraint is set as the compromise value between the current peak value and the constraint of the previous round, and the minimum value is taken with the corresponding upper limit of the electric scanning capability constraint. The peak sequence is calculated as follows: in Corresponding to the initial decomposition, This corresponds to the result of the first round of alternating two steps; The calculation method for updating the upper bound of the orientation dimension constraint is as follows: S5.2 When the changes in the peak values ​​of the range and azimuth electronic scanning angles are both less than the preset threshold in two consecutive iterations, or when the number of iterations reaches the preset upper limit, the iteration is stopped to obtain the final electromechanical co-controlled beam control decomposition result that takes into account the peak value compression effect of the two-dimensional electronic scanning angles of range and azimuth and satisfies the mechanical scanning capability constraint and the electronic scanning capability constraint. The method for calculating the peak value change between two rounds is as follows; 。 7. The electromechanical coordinated high-gain beam control method for sparse array spaceborne SAR scene matching curves according to claim 8, characterized in that, The specific method for step S6 is as follows; S6.1 The output mechanical scanning parameter vector is used as the final optimized electromechanical co-controlled beam control decomposition result. Based on the final mechanical scanning parameter vector, the corresponding mechanical scanning three-axis angle sequence is calculated, including pitch angle sequence, yaw angle sequence and roll angle sequence. S6.2 Calculate the corresponding range and azimuth electric scanning angle sequences based on electromechanical geometry, output the three-axis angular velocity and angular acceleration sequences of the mechanical scanning system, generate time-domain curves of the three-axis angles, angular velocities, and angular accelerations of the mechanical scanning system, and generate time-domain curves of the range and azimuth electric scanning angles.

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