Bistatic SAR receiver flight trajectory planning method, electronic equipment and storage medium

Abstract

This invention belongs to the field of synthetic aperture radar (SAR) technology, and relates to a method for planning the flight trajectory of a bistatic SAR receiver, electronic equipment, and storage medium. The method includes: establishing motion models of the transmitter, moving target, and receiver; establishing a three-dimensional proportional guidance model, and establishing the differential equation of motion of the receiver under the enhanced proportional guidance law as the guided flight trajectory; establishing a mixed-integer nonlinear programming model with the optimal approximation of the guided flight trajectory as the objective function, and taking imaging constraints, guidance terminal constraints, flight dynamics constraints, and system communication constraints as constraints; solving the mixed-integer nonlinear programming model to obtain the optimal flight trajectory of the receiver that satisfies both guidance and imaging constraints. This invention can guarantee guidance accuracy with a small miss distance against maneuvering targets in the terminal guidance phase; it balances terminal guidance performance and SAR imaging quality, greatly expands the feasible solution space, and improves the feasibility and optimization performance of trajectory planning under complex constraints.

Description

Technical Field

[0001] This invention belongs to the field of synthetic aperture radar technology, specifically relating to a flight trajectory planning method for a bistatic SAR receiver, electronic equipment, and storage medium. Background Technology

[0002] Synthetic Aperture Radar (SAR) provides high-resolution imaging capabilities in all weather conditions and at all times, making it an important tool for Earth observation and target identification. Bistatic SAR systems, by separating the transmitter and receiver onto different platforms, offer greater flexibility and overcome the limitations of monostatic SAR in forward-looking imaging.

[0003] However, while the separate transmission and reception configuration of bistatic SAR introduces configurational freedom, it also brings new problems: On the one hand, imaging performance is highly dependent on the bistatic geometry. If the receiver flight trajectory is optimized only according to guidance requirements, it can easily lead to bistatic geometry deterioration, causing a decrease in range resolution, Doppler resolution, and azimuth ambiguity, thus affecting continuous target tracking and identification. On the other hand, targets are usually maneuvering targets with uncertain and nonlinear motion characteristics. The guided aircraft needs to complete large maneuver adjustments within a limited time to ensure that the miss distance meets the performance requirements, while also satisfying communication and flight envelope constraints. Traditional trajectory planning methods that only consider stationary targets or only flight dynamics constraints are difficult to directly apply to this type of terminally guided bistatic SAR cooperative scenario.

[0004] In existing technologies, there are two main approaches to bistatic SAR flight trajectory planning:

[0005] (1) The bistatic SAR flight configuration planning problem is abstracted into a set of nonlinear equations for optimal configuration parameters, and the configuration parameters are obtained by numerical solution. Such methods generally assume that the imaging scene and the target state are relatively static, and the solution is a static configuration. They are not adaptable to the rapid changes in the target state and dynamic adjustment of the configuration during the terminal guidance stage.

[0006] (2) The imaging constraints and flight dynamics constraints are modeled as a multi-objective optimization problem, and the receiver trajectory is planned using heuristic search or intelligent optimization algorithms. However, such studies are mostly aimed at stationary or slow-moving targets, and do not fully incorporate the guidance constraints brought about by target maneuvering, making it difficult to guarantee the ability to accurately seek targets in terminal guidance scenarios.

[0007] In terminal guidance applications for maneuvering targets, the receiver flight trajectory must not only meet the imaging performance constraints of the bistatic SAR system (such as range resolution, Doppler resolution, and gradient angle constraints), but also ensure the terminal miss distance index based on the guidance law. This requires that the following factors be considered simultaneously during trajectory planning: the moving target state estimation results (such as position, velocity, and acceleration), the constraints of the Augmented Proportional Navigation (APN) guidance law on the receiver acceleration and navigation ratio, the complex nonlinear constraints of bistatic SAR imaging performance as the configuration changes, and engineering constraints such as flight dynamics, flight envelope, and communication range.

[0008] There is currently a lack of a receiver flight trajectory planning method that integrates enhanced proportional guidance constraints and bistatic SAR imaging constraints in the context of terminal guidance of maneuvering targets, and comprehensively optimizes the trajectory using variable navigation ratio and variable number of discrete points. Summary of the Invention

[0009] To address the aforementioned technical problems, the present invention provides a solution. The present invention provides a bistatic SAR receiver flight trajectory planning method, electronic equipment, and storage medium.

[0010] In a first aspect, the present invention provides a method for planning the flight trajectory of a bistatic SAR receiver, including:

[0011] Acquire initial system parameters and target state information, and establish motion models of the transmitter, moving target, and receiver; initial system parameters include the initial position, velocity, and state transition matrix of the transmitting node, as well as the initial position, velocity, trajectory inclination angle, and trajectory deflection angle of the receiving node; target state information includes the initial position, velocity, acceleration, and state transition matrix of the maneuvering target;

[0012] Calculate the relative position vector and relative velocity vector between the receiver and the moving target, establish a three-dimensional proportional guidance model, introduce a target acceleration compensation term to construct an enhanced proportional guidance law, obtain the command acceleration in the ground coordinate system, transform the command acceleration to the receiver ballistic coordinate system through the attitude transformation matrix, and establish the motion differential equation of the receiver under the drive of the enhanced proportional guidance law as the guided flight trajectory.

[0013] Based on the equation of motion, the entire flight time interval of the receiver is discretized into several segments, each containing the number of trajectory points for adaptive optimization. Within each segment, the navigation ratio parameter is used as a continuous optimization variable, the number of discrete trajectory points is used as an integer variable, and the acceleration sequence is used as a continuous control variable. A mixed integer nonlinear programming model is established with the objective function of best approximating the guided flight trajectory. Imaging constraints, guidance terminal constraints, flight dynamics constraints, and system communication constraints are used as constraints of the mixed integer nonlinear programming model.

[0014] A hierarchical solution strategy is employed to solve the mixed-integer nonlinear programming model, yielding the optimal flight trajectory of the receiver that satisfies both guidance and imaging constraints, including:

[0015] The branch and bound method is used to process the integer variable of the number of trajectory segment points in the mixed integer nonlinear optimization model, and the mixed integer nonlinear optimization problem is decomposed into multiple continuous nonlinear optimization subproblems.

[0016] For each continuous nonlinear optimization subproblem, the guidance and imaging constraints are decoupled by introducing auxiliary variables equivalent to the acceleration sequence, an augmented Lagrangian function is constructed to handle the constraints, and the navigation ratio parameter and acceleration sequence are optimized hierarchically and solved by using the alternating direction multiplier method.

[0017] The Lagrange multipliers and penalty parameters that satisfy the imaging constraints, terminal constraints, and flight envelope constraints are updated until the receiver reaches the terminal guidance region, thus obtaining the optimal flight trajectory of the receiver that satisfies both guidance and imaging constraints.

[0018] Secondly, this invention provides an electronic device, the electronic device comprising:

[0019] At least one processor; and,

[0020] A memory communicatively connected to the at least one processor; wherein,

[0021] The memory stores instructions that can be executed by the at least one processor, which, when executed by the at least one processor, enables the at least one processor to perform the bistatic SAR receiver flight trajectory planning method.

[0022] Thirdly, the present invention provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the bistatic SAR receiver flight trajectory planning method.

[0023] In some optional embodiments, the enhanced proportional guidance law includes a target acceleration compensation term; the target acceleration compensation term consists of the target acceleration given in real time by the target state estimation algorithm.

[0024] In some optional embodiments, the navigation ratio parameter takes values ​​within a preset continuous interval, and the number of trajectory segment points takes values ​​within a preset integer interval. By using the navigation ratio parameter and the number of trajectory segment points together as optimization variables, a family of guiding trajectories with navigation ratio and discrete point number as parameters is constructed.

[0025] In some optional embodiments, imaging constraints include range resolution constraints, Doppler resolution constraints, and range-Doppler gradient angle constraints;

[0026] A local two-dimensional grid search region is constructed on the ground plane with the predicted target position as the center, and then discretized.

[0027] Based on the spatial position and velocity of the transmitter and receiver at each discrete moment, calculate the bistatic distance resolution, Doppler resolution, and the angle between the distance gradient and the Doppler gradient at each grid point;

[0028] An imaging constraint threshold is set for the imaging performance of the region near the moving target, and an imaging performance measurement function is established that includes range resolution constraint, Doppler resolution constraint and gradient angle constraint.

[0029] In some optional embodiments, the guidance terminal is constrained to the point that the terminal distance error between the receiving node and the maneuvering target is less than a preset miss distance.

[0030] In some alternative embodiments, flight dynamics constraints include maximum acceleration, minimum negative acceleration, maximum flight altitude, and maximum flight speed constraints.

[0031] In some optional embodiments, the mixed-integer nonlinear optimization problem is decomposed into multiple continuous nonlinear optimization subproblems, including:

[0032] The whole trajectory planning problem is decomposed into piecewise iterative optimization subproblems by rolling time-domain optimization, with the terminal state of each optimization segment serving as the initial state of the next segment; the branch and bound method is used to handle integer variables, fixing the number of segment points to integer values, and transforming the mixed integer nonlinear optimization model into a continuous nonlinear optimization subproblem.

[0033] In some optional embodiments, the navigation ratio parameter and acceleration sequence are optimized hierarchically and solved using the alternating direction multiplier method, including: decomposing the continuous optimization subproblem into low-dimensional and high-dimensional subproblems using the alternating direction multiplier method; optimizing the navigation ratio with a fixed acceleration sequence in the low-dimensional subproblem and solving it using the golden section method or Bayesian optimization; optimizing the acceleration sequence with a fixed navigation ratio in the high-dimensional subproblem and solving it as a constrained nonlinear least squares problem; and solving the acceleration sequence using a global optimization algorithm.

[0034] In some optional embodiments, whether to apply terminal constraints is determined based on the instantaneous distance between the receiver and the target. When the distance is greater than a threshold, no terminal constraints are applied, and when the distance is less than the threshold, the weight of the terminal constraints is increased.

[0035] The beneficial effects of this invention are:

[0036] This invention achieves true integrated imaging-guidance trajectory planning by introducing maneuvering target guidance constraints. It explicitly introduces an enhanced proportional guidance law into the trajectory planning process and incorporates the target acceleration into the guidance model, ensuring that the receiver trajectory always follows the homing constraint of the maneuvering target during the optimization process. Unlike existing bistatic SAR trajectory planning methods that only target stationary or slowly moving targets, this invention can guarantee guidance accuracy with a small miss distance for maneuvering targets in the terminal guidance stage.

[0037] This invention achieves unified modeling by combining guidance and imaging constraints, taking into account both terminal guidance performance and SAR imaging quality. By introducing constraints on range resolution, Doppler resolution, and range-Doppler gradient angle into the trajectory planning model, it ensures that the receiver can meet guidance constraints without compromising the high-resolution imaging performance of the bistatic SAR system in the vicinity of the target, thus providing reliable imaging support for target identification in the terminal guidance phase.

[0038] This invention expands the degrees of freedom in trajectory optimization by using a variable navigation ratio and a variable number of trajectory points, breaking through the limitation of the uniqueness of proportional guidance trajectories under traditional fixed navigation ratios. It treats the navigation ratio parameter as a continuous optimization variable and the number of trajectory segment points as an integer optimization variable, constructing a family of guidance trajectories with the navigation ratio and the number of discrete points as parameters. By optimizing the selection of trajectories from this family, the feasible solution space is greatly expanded, improving the feasibility and optimization performance of trajectory planning under complex constraints.

[0039] This invention employs a hybrid solution architecture combining rolling time domain and branch-bound, alternating direction multiplier method, and augmented Lagrange multiplier method, achieving excellent real-time performance and computational efficiency. By controlling the rolling time domain, the entire problem is distributed across multiple short time intervals for solution. Combined with branch-bound, the mixed integer problem is transformed into a continuous optimization subproblem. The alternating direction multiplier method is then used to process low-dimensional navigation ratio optimization and high-dimensional acceleration sequence optimization in a hierarchical manner. The augmented Lagrange multiplier method is introduced to unify constraint processing, enabling high solution efficiency even under complex high-dimensional non-convex feasible sets. This invention is suitable for high dynamic response requirements in terminal guidance scenarios.

[0040] This invention extends bistatic SAR receiver trajectory planning from traditional stationary or slow-moving target scenarios to terminal guidance scenarios for maneuvering targets, expanding the application scope of bistatic SAR trajectory planning. It can be widely applied to collaborative terminal guidance systems for high-altitude fixed illumination platforms (such as UAVs and satellites), providing theoretical and methodological support for the engineering implementation of next-generation distributed SAR guidance systems. Attached Figure Description

[0041] Figure 1 This is a flowchart illustrating the flight trajectory planning method for a bistatic SAR receiver provided in Embodiment 1 of the present invention.

[0042] Figure 2This is a schematic diagram of the relative motion relationship between the flight platform and the moving target in Embodiment 1 of the present invention;

[0043] Figure 3 This is a schematic diagram of an electronic device provided in Embodiment 3 of the present invention.

[0044] Icons: 30 - Electronic device; 310 - Processor; 320 - Bus; 330 - Memory; 340 - Transceiver. Detailed Implementation

[0045] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. The components of the embodiments of the present invention described and shown in the accompanying drawings can generally be arranged and designed in various different configurations.

[0046] Example 1

[0047] As an example, to address the problems existing in the prior art, this embodiment provides a bistatic SAR receiver flight trajectory planning method. Based on fully considering the state of the moving target and the enhanced proportional guidance constraint, this method introduces a variable navigation ratio and trajectory point number adaptive partitioning mechanism. It models the receiver flight trajectory optimization as an optimal approximation problem of an ideal guidance trajectory family, while simultaneously satisfying bistatic SAR imaging performance constraints as well as engineering constraints such as flight and communication, thereby achieving stable homing and continuous high-quality imaging of maneuvering targets.

[0048] The following is a detailed description of the implementation details of the method described in this embodiment. The following content is only for the convenience of understanding and is not necessary for implementing this solution.

[0049] The bistatic SAR receiver flight trajectory planning method of this embodiment can be applied to electronic devices with communication, computing, and data storage capabilities. (See attached...) Figure 1 As shown, the method provided in this embodiment includes the following steps:

[0050] Step 110: Obtain the initial system parameters and target state information, and establish motion models of the transmitter, moving target and receiver; the initial system parameters include the initial position, velocity and state transition matrix of the transmitting node and the initial position, velocity, trajectory tilt angle and trajectory deflection angle of the receiving node; the target state information includes the initial position, velocity, acceleration and state transition matrix of the maneuvering target.

[0051] Assuming the launching node is a high-altitude illumination platform, its flight trajectory is pre-planned and considered known during the trajectory planning process. The launching platform typically flies in a uniform straight line or along a stable trajectory. In this embodiment, the state of the moving target has been estimated by the detection system (such as radar and filters), including its position, velocity, and acceleration.

[0052] To ensure the universality of the receiver node's motion model, it is assumed that the receiver node can perform arbitrary three-dimensional motion in space. At any given moment, the position vector of the flight platform's velocity is... The flight speed vector is The position of the moving ground target is The target's velocity vector is .

[0053] set up This is the time interval for state transitions; the target's state transition matrix is... ,but:

[0054] .

[0055] The state of the moving target at the previous moment is The current state of the moving target is ,but: .

[0056] Step 120: Calculate the relative position vector and relative velocity vector between the receiver and the moving target, establish a three-dimensional proportional guidance model, introduce a target acceleration compensation term to construct an enhanced proportional guidance law, obtain the command acceleration in the ground coordinate system, transform the command acceleration to the receiver ballistic coordinate system through the attitude transformation matrix, and establish the motion differential equation of the receiver under the enhanced proportional guidance law as the guided flight trajectory.

[0057] In some optional embodiments, the enhanced proportional guidance law includes a target acceleration compensation term; the target acceleration compensation term consists of the target acceleration given in real time by the target state estimation algorithm.

[0058] In some optional embodiments, a ground coordinate system is established, with the origin fixed to a point on the ground. The OX axis points to the initial heading, the OY axis is perpendicular to the local horizontal plane and points upwards, and the OZ axis is determined according to the right-hand rule, perpendicular to the OXY plane and pointing to the right. The origin is the center of mass of the flight platform, the velocity direction of the flight platform is the OX2 axis, the unit vector perpendicular to the OX2 axis and located in the vertical plane is the OY2 axis, and the OZ2 axis is perpendicular to the OX2Y2 plane and points to the right. The OX2Y2Z2 coordinate system is called the ballistic coordinate system, which is a moving coordinate system. The attitude changes between the ballistic coordinate system and the ground coordinate system are described by two angles: the ballistic inclination angle. and ballistic deflection Ballistic inclination angle It is the velocity vector of the flight platform. The angle with the horizontal plane, the velocity vector points upwards. Angle is positive, and vice versa. The range is from -90° to +90°. Ballistic deflection angle It is the velocity vector of the flight platform. The angle between the projection component on the ground and the OX axis of the ground coordinate system is positive if the projection is to the left and negative if it is to the right. The range is from -180° to +180°.

[0059] Appendix Figure 2 In the schematic diagram showing the relative motion relationship between the flight platform and the moving target, and The two dashed arrows represent two vectors parallel to the horizontal plane. With flight platform speed as well as The projection components on the ground lie in the same vertical plane. Taking the reference point of the receiving node, the position vector of the moving target relative to the flight platform, i.e., the relative position vector, is... Relative position vector If the direction is from the center of mass of the flight platform to the center of mass of the moving target, then:

[0060] ;

[0061] The speed of the moving target relative to the flight platform is ,but: .

[0062] Will The endpoint of the vector is placed at the center of mass of the moving target on the ground, and its direction is as shown in the attached diagram. Figure 2 As shown. At any given time, the relative position vector... and relative velocity vector The plane on which the line of sight is transferred is the plane of the line of sight transfer. This is because the line of sight vector is the relative position vector. During guidance, the relative position vector The direction of rotation is the relative velocity vector. Direction, relative position vector and relative velocity vector The relative relationship determines the design of the guidance law; if the relative position vectors and relative velocity vector If they are parallel, the line-of-sight vector will translate in space without rotating. If they are not parallel, in order to achieve guidance, an acceleration of a perpendicular relative velocity vector is needed to make the line-of-sight vector rotate.

[0063] In the line-of-sight transition plane, the relative velocity vector Decomposition yields: one is relative position vector projection components , The approach speed, also known as the speed at which the relative position of the flight platform and the target changes, is another factor. Vertical projection component , The presence of the velocity component is the reason for the rotation of the line-of-sight vector.

[0064] In the line-of-sight plane analysis of the guidance law, the command acceleration for proportional guidance should be applied perpendicular to the line-of-sight vector, and its magnitude should be proportional to the approach velocity. The product of magnitude and line-of-sight angular velocity, let's assume... This is a navigation constant, typically taking a value of 3 to 5. If the line-of-sight angular velocity is given, then the expression for the command acceleration is:

[0065] .

[0066] According to the vector projection decomposition theorem, the approach velocity is equal to:

[0067] .

[0068] line-of-sight angular velocity It is a vector that causes the line-of-sight vector to rotate, its direction perpendicular to the line-of-sight transfer plane. Its magnitude causes the flight platform to generate a lateral velocity component perpendicular to the line-of-sight vector, and this velocity is proportional to the vertical velocity component. This makes the relative velocity in the vertical velocity direction zero, the line-of-sight vector does not rotate, and the relative velocity is reduced to only the approximate velocity. This allows the flight platform to seek out moving targets.

[0069] Let the mass of the moving ground target be... , If the momentum is that of the moving platform, then the momentum of the moving target relative to the flying platform is:

[0070] ;

[0071] Let the angular momentum of the moving target relative to the center of mass of the flight platform be... ,but:

[0072] ;

[0073] Let the moment of inertia of the moving target relative to the flight platform be... ,but:

[0074] ;

[0075] Let the relative position vector The rotational angular velocity is Then the rotational angular momentum of the moving target can also be expressed as:

[0076] ;

[0077] Therefore, the following equation can be obtained:

[0078] ;

[0079] Then the line-of-sight angular velocity is equal to:

[0080] ;

[0081] Command Acceleration The magnitude of is such that, according to the cross product rule, its direction is equal to .

[0082] ;

[0083] The command acceleration is:

[0084] ;

[0085] In an ideal three-dimensional proportional navigation law that neglects the acceleration of a moving target, if the target acceleration can be estimated in real time by the tracking system (e.g., through a Kalman filter or other state estimator), ignoring the target acceleration will lead to decreased guidance accuracy and increased miss distance. To effectively handle maneuvering targets, Augmented Proportional Navigation (APN) is needed, adding target acceleration as a compensation term to the overload command. Let... The first goal of the movement The acceleration at any given time is obtained from the platform system. The enhanced proportional guidance law considering the target acceleration is derived from the following formula:

[0086] .

[0087] This invention achieves true integrated imaging-guidance trajectory planning by introducing guidance constraints for maneuvering targets. It explicitly introduces an enhanced proportional guidance law into the trajectory planning process and incorporates the target acceleration into the guidance model, ensuring that the receiver trajectory always follows the homing constraint of the maneuvering target during the optimization process. Unlike existing bistatic SAR trajectory planning methods that only target stationary or slowly moving targets, this invention can guarantee guidance accuracy with a small miss distance for maneuvering targets in the terminal guidance stage.

[0088] In some optional embodiments, the guidance terminal is constrained to the point that the terminal distance error between the receiving node and the maneuvering target is less than a preset miss distance.

[0089] The differential equations of motion for nodes are generally expressed in the ballistic coordinate system; therefore, it is necessary to transform the commanded acceleration from the ground coordinate system to the ballistic coordinate system. Based on the ballistic inclination and deflection angles in the ballistic and ground coordinate systems at any given time, a coordinate transformation from the ground coordinate system to the ballistic coordinate system is constructed. Let... It is the local gravitational acceleration. It is the trajectory angle. It is the ballistic deflection angle. It is a transformation matrix, and the transformation matrix has the following form:

[0090] .

[0091] The command overload form in the ballistic coordinate system is as follows:

[0092] .

[0093] Let the ballistic coordinate system be represented as , yes Directional acceleration, yes Directional acceleration, yes Directional acceleration, It is the ballistic coordinate system receiving platform in The position of direction, It is the ballistic coordinate system receiving platform in The position of direction, It is the ballistic coordinate system receiving platform in The position of direction, Indicates to Differentiate, Indicates to Differentiate, Indicates to Taking the derivative, the differential equation of motion of the receiving node in the ballistic coordinate system driven by the guidance law is expressed as:

[0094] .

[0095] Step 130: Discretize the receiver's entire flight time interval into several segments based on the motion differential equations. Each segment contains the number of trajectory points for adaptive optimization. Within each segment, use the navigation ratio parameter as a continuous optimization variable, the number of discrete trajectory points as an integer variable, and the acceleration sequence as a continuous control variable. Establish a mixed integer nonlinear programming model with the objective function of best approximating the guided flight trajectory. Use imaging constraints, guidance terminal constraints, flight dynamics constraints, and system communication constraints as constraints of the mixed integer nonlinear programming model.

[0096] In some optional embodiments, the navigation ratio parameter takes values ​​within a preset continuous interval, and the number of trajectory segment points takes values ​​within a preset integer interval. By using the navigation ratio parameter and the number of trajectory segment points together as optimization variables, a family of guiding trajectories with navigation ratio and discrete point number as parameters is constructed.

[0097] By expanding the degrees of freedom in trajectory optimization through variable navigation ratio and variable number of trajectory points, this approach overcomes the limitation of uniqueness of proportional guidance trajectories under traditional fixed navigation ratios. The navigation ratio parameter is treated as a continuous optimization variable, and the number of trajectory segment points is treated as an integer optimization variable, constructing a family of guidance trajectories with navigation ratio and discrete point count as parameters. Optimizing the selection of trajectories from this family significantly expands the feasible solution space and improves the feasibility and optimization performance of trajectory planning under complex constraints.

[0098] In some alternative embodiments, imaging constraints include range resolution constraints, Doppler resolution constraints, and range-Doppler gradient angle constraints.

[0099] set up It is a given distance resolution constraint function. It is a given Doppler resolution constraint function. It is a given gradient angle constraint function. The function is an imaging performance metric function; if If the imaging performance is extremely poor at any given time, then the imaging performance metric function is... This indicates that the imaging performance is too poor and does not meet the constraints. Define an imaging performance metric function:

[0100] ;

[0101] set up It is the imaging constraint function. It is the number of trajectory segments. If the number of points is the trajectory segment, then the imaging performance constraints are:

[0102] ;

[0103] This is an equality constraint that requires any... At any given moment, the imaging performance's range resolution, Doppler resolution, and gradient angle must all satisfy the given constraints.

[0104] A local two-dimensional grid search region is constructed on the ground plane with the predicted target position as the center, and then discretized.

[0105] Based on the spatial position and velocity of the transmitter and receiver at each discrete moment, calculate the bistatic distance resolution, Doppler resolution, and the angle between the distance gradient and the Doppler gradient at each grid point;

[0106] An imaging constraint threshold is set for the imaging performance of the region near the moving target, and an imaging performance measurement function is established that includes range resolution constraint, Doppler resolution constraint and gradient angle constraint.

[0107] By unifying the modeling of guidance and imaging constraints, and taking into account both terminal guidance performance and SAR imaging quality, constraints of range resolution, Doppler resolution, and range-Doppler gradient angle are introduced into the trajectory planning model. This ensures that the receiver can meet the guidance constraints without compromising the high-resolution imaging performance of the bistatic SAR system in the vicinity of the target, thus providing reliable imaging support for target identification in the terminal guidance phase.

[0108] In some alternative embodiments, flight dynamics constraints include maximum acceleration, minimum negative acceleration, maximum flight altitude, and maximum flight speed constraints.

[0109] Given the transmitter trajectory, target state estimation, and system parameters, by optimizing the navigation ratio parameter, the number of trajectory discrete points, and the acceleration control sequence for each rolling segment, the receiver trajectory achieves optimal approximation of the ideal guidance trajectory generated by enhanced proportional guidance, while satisfying constraints such as imaging performance, terminal guidance, acceleration and flight envelope, and communication range.

[0110] Step 140: Use a hierarchical solution strategy to solve the mixed integer nonlinear programming model to obtain the optimal flight trajectory of the receiver that satisfies both guidance and imaging constraints.

[0111] Step 150: The integer variable of the number of trajectory segment points in the mixed integer nonlinear optimization model is processed by the branch and bound method, and the mixed integer nonlinear optimization problem is decomposed into multiple continuous nonlinear optimization subproblems.

[0112] Step 160: For each continuous nonlinear optimization subproblem, decouple the guidance and imaging constraints by introducing auxiliary variables equivalent to the acceleration sequence, construct an augmented Lagrangian function to handle the constraints, and use the alternating direction multiplier method to optimize the navigation ratio parameter and acceleration sequence in layers and solve them.

[0113] set up An acceleration sequence, For the acceleration sequence of the ideal guided trajectory, It is the first one that actually satisfies the constraints. Step acceleration sequence, For the first Segmented navigation ratio optimization parameters The actual position vector of the target. For position vectors that only satisfy imaging constraints, To satisfy the entire constraint of the flight velocity vector, For velocity vectors that only satisfy imaging constraints, For acceleration vectors that only satisfy imaging constraints, Given imaging constraints, a weighted constraint function is used to transform multi-objective imaging constraints into single-objective constraints through weighting. This is an additional term derived from the constraint conditions through a penalty function. It is a Lagrange multiplier vector. for The transpose vector, To compensate for the penalty coefficients of the augmented Lagrange term, we construct the augmented Lagrange function, which has the following form:

[0114] ;

[0115] It is an additional term transformed from the constraint condition through a penalty function, in the form of:

[0116] ;

[0117] Although the introduction of auxiliary variables increased the dimensionality of the solution, due to In reality, the dimensions are the same, but when optimizing the trajectory, the interference of imaging constraints can be ignored, thus decoupling the guidance trajectory tracking error from the imaging constraints. Through the alternating direction multiplier method distribution optimization and coordination mechanism, the problem of high and low dimension mixed optimization of navigation ratio and acceleration sequence can be effectively handled.

[0118] The optimization problem is solved using the alternating direction multiplier method, with the following steps:

[0119] (1) Since it is an unconstrained optimization and the objective function is complex, a genetic algorithm is used for optimization, which can obtain a better global optimization result and obtain an ideal acceleration sequence that satisfies the imaging constraints. And based on ideal acceleration sequences Computational theory and ;

[0120] (2) Set the initial navigation ratio , acceleration sequence , ride Number of iterations , express;

[0121] (3) Fixed navigation ratio and auxiliary variables Optimize the acceleration sequence and optimize the objective function value. The objective function at this point is:

[0122] ;

[0123] in, and as well as It is by The corresponding variables of the calculated ideal guidance trajectory; It is the first one that actually satisfies the constraints. Step-by-step position sequence, It is the k-th step velocity sequence that actually satisfies the constraints. It is the optimized first The number of points in the segment, It is an additional term transformed from the constraint condition through the penalty function. It is the coefficient of the penalty function.

[0124] (4) Since this problem is an unconstrained optimization problem, a genetic algorithm is used to solve it and obtain the optimal sequence. ;

[0125] (5) Fixed acceleration sequence and auxiliary variables Optimize navigation ratio parameters The objective function is optimized as follows:

[0126] ;

[0127] (6) The optimal navigation ratio parameter is directly searched using the golden section method. ;

[0128] (7) Update the auxiliary variables, with the following update rules:

[0129] ;

[0130] (8) Update the Lagrange multipliers, and update the result as follows:

[0131] ;

[0132] (9) Dynamically adjust the penalty coefficient The adjustment rule is: if the degree of constraint violation does not decrease, increase... Otherwise, maintain or reduce;

[0133] (10) Convergence judgment: When the residual And the objective function variable If the condition is met, the iteration terminates; otherwise, continue evaluating the iteration variable. Is it greater than the maximum number of iterations? If it is less, then... Jump to step (3);

[0134] (11) Determine if the condition is met. If not, continue the branch. Determine whether to exit the target. If not, recalculate the distance from the receiving node to the target and perform a terminal miss constraint rule judgment. If the condition is met, proceed to the next step.

[0135] (12) Update the number of iterations in segments. Determine if the process has ended; if it has, exit the current process; otherwise, proceed to the rolling time-domain optimization step, initialize the rolling iteration variables, and use branch and bound for each subproblem to be optimized.

[0136] Step 170: Update the Lagrange multipliers and penalty parameters that satisfy the imaging constraints, terminal constraints, and flight envelope constraints until the receiver reaches the terminal guidance region, and obtain the receiver's optimal flight trajectory that satisfies both guidance and imaging constraints.

[0137] In some optional embodiments, the mixed-integer nonlinear optimization problem is decomposed into multiple continuous nonlinear optimization subproblems, including:

[0138] The whole trajectory planning problem is decomposed into piecewise iterative optimization subproblems by rolling time-domain optimization, with the terminal state of each optimization segment serving as the initial state of the next segment; the branch and bound method is used to handle integer variables, fixing the number of segment points to integer values, and transforming the mixed integer nonlinear optimization model into a continuous nonlinear optimization subproblem.

[0139] The terminal state of each optimized trajectory segment is used as the initial value for the next segment optimization. This process is repeated until the entire trajectory segment is obtained. Each segment of the rolling optimization can be designed with a distance threshold. If the distance is greater than the distance threshold, the terminal guidance constraint can be disregarded.

[0140] The presence of integer variables representing the number of segment points complicates the problem. There are two typical approaches: one is to relax the integer variables, making... Relaxation can be performed on continuous variables, but this method is unsuitable for the problem itself and does not reduce dimensionality. Another approach is to use branch search on integer variables. When branching on integer variables, the parameters are fixed, and the optimization problem becomes a continuous subproblem, which is easier to solve and reduces the dimensionality of the problem itself. Therefore, this paper uses branch and bound to handle integer variables, further transforming the subproblem into a continuous subproblem. The efficiency of branch and bound is related to the number of branches. Here, the number of points in each segment is constrained to a small number, such as between 10 and 20, to improve the efficiency of solving the subproblem.

[0141] In some optional embodiments, the navigation ratio parameter and acceleration sequence are optimized hierarchically and solved using the alternating direction multiplier method, including: decomposing the continuous optimization subproblem into low-dimensional and high-dimensional subproblems using the alternating direction multiplier method; optimizing the navigation ratio with a fixed acceleration sequence in the low-dimensional subproblem and solving it using the golden section method or Bayesian optimization; optimizing the acceleration sequence with a fixed navigation ratio in the high-dimensional subproblem and solving it as a constrained nonlinear least squares problem; and solving the acceleration sequence using a global optimization algorithm.

[0142] With the integer variables fixed, the optimization problem becomes a continuous problem. However, considering the properties of the optimization variables, the navigation ratio and acceleration sequence can still be divided into two layers: the inner layer is the navigation ratio parameter, and the outer layer is the acceleration sequence. This layering is feasible because the navigation ratio parameter and the acceleration sequence are independent. However, simple layering results in a large computational burden because the navigation ratio is a continuous variable. Solving the acceleration sequence with a fixed navigation ratio parameter, combined with the previous branch and bound method, leads to an excessive number of iterations and low efficiency. Therefore, this invention uses the alternating direction multiplier method to solve the continuous optimization subproblem after branch and bound, decomposing the continuous optimization subproblem into low-dimensional and high-dimensional subproblems. The low-dimensional subproblem optimizes the navigation ratio parameter by fixing the acceleration sequence. Since it is a one-dimensional optimization problem, efficient search algorithms such as the golden section method and Bayesian optimization can be used. The high-dimensional subproblem corresponds to a fixed navigation ratio, transforming the problem into a constrained nonlinear least squares problem, which can also be solved using efficient algorithms. Then, alternating iterative optimization is performed to obtain the solution to the final continuous subproblem.

[0143] This invention employs a hybrid solution architecture combining rolling time domain and branch-bound, alternating direction multiplier method, and augmented Lagrange multiplier method, achieving excellent real-time performance and computational efficiency. By controlling the rolling time domain, the entire problem is distributed across multiple short time intervals for solution. Combined with branch-bound, the mixed integer problem is transformed into a continuous optimization subproblem. The alternating direction multiplier method is then used to process low-dimensional navigation ratio optimization and high-dimensional acceleration sequence optimization in a hierarchical manner. The augmented Lagrange multiplier method is introduced to unify constraint processing, enabling high solution efficiency even under complex high-dimensional non-convex feasible sets. This invention is suitable for high dynamic response requirements in terminal guidance scenarios.

[0144] The augmented Lagrange method is employed to handle constraints. This includes addressing the constraints after decomposing the objective function. Since the feasible set contains imaging, dynamic, and terminal constraints, it is a typical high-dimensional non-convex set, increasing the complexity of the algorithm. To adapt to the alternating direction multiplier method, the augmented Lagrange method is chosen to handle constraints. A variable equal to the acceleration sequence is introduced as an auxiliary variable to decouple guidance and imaging constraints. Simultaneously, augmented Lagrange terms and Lagrange multipliers coordinate the alternating optimization of the navigation ratio and acceleration sequence. Furthermore, terminal and dynamic constraints are converted into additional terms in the objective function, simplifying the solution of subproblems during alternating optimization.

[0145] In some optional embodiments, whether to apply terminal constraints is determined based on the instantaneous distance between the receiver and the target. When the distance is greater than a threshold, no terminal constraints are applied, and when the distance is less than the threshold, the weight of the terminal constraints is increased.

[0146] By extending bistatic SAR receiver trajectory planning from traditional stationary or slow-moving target scenarios to terminal guidance scenarios for maneuvering targets, the application scope of bistatic SAR trajectory planning is expanded. It can be widely applied to collaborative terminal guidance systems for high-altitude fixed illumination platforms (such as UAVs and satellites), providing theoretical and methodological support for the engineering implementation of next-generation distributed SAR guidance systems.

[0147] This invention takes into account the motion of the target. For the target motion, guidance constraints for the moving target are added to the trajectory planning. Enhanced proportional guidance modeling is used to track and guide the moving target, which meets the imaging guidance requirements of the terminal guidance for the moving target.

[0148] This invention considers the complexity of the flight trajectory planning model after the guidance constraints of the moving target, and proposes a corresponding numerical solution method. It reduces the dimensionality and decouples the problem, which can adapt to the high dynamic response requirements of trajectory planning in complex dynamic environments of terminal guidance, and has high computational efficiency.

[0149] This invention breaks through the limitations of existing bistatic SAR flight trajectory planning, extending from stationary targets to moving targets, and providing a typical paradigm for bistatic SAR terminal guidance flight trajectory planning.

[0150] Example 2

[0151] Based on the same principle as the bistatic SAR receiver flight trajectory planning method shown in the embodiments of the present invention, the embodiments of the present invention also provide electronic equipment, as shown in the appendix. Figure 3 As shown, the electronic device may include, but is not limited to: a processor and a memory; the memory for storing computer programs; and the processor for executing the bistatic SAR receiver flight trajectory planning method shown in any embodiment of the present invention by calling the computer program.

[0152] In one alternative embodiment, an electronic device is provided, with... Figure 3 The illustrated electronic device 30 includes a processor 310 and a memory 330. The processor 310 and the memory 330 are connected, for example, via a bus 320.

[0153] Optionally, the electronic device 30 may further include a transceiver 340, which can be used for data interaction between the electronic device and other electronic devices, such as sending and / or receiving data. It should be noted that in practical applications, the transceiver 340 is not limited to one type, and the structure of the electronic device 30 does not constitute a limitation on the embodiments of the present invention.

[0154] Processor 310 may be a CPU (Central Processing Unit), a general-purpose processor, a DSP (Digital Signal Processor), an ASIC (Application-Specific Integrated Circuit), an FPGA (Field-Programmable Gate Array), or other programmable logic devices, hardware components, or any combination thereof. Processor 310 may also be a combination that implements computing functions, such as including one or more microprocessor combinations, or a combination of a DSP and a microprocessor.

[0155] Bus 320 may include a pathway for transmitting information between the aforementioned components. Bus 320 may be a PCI peripheral component interconnect standard bus or an EISA extended industry standard architecture bus, etc. Bus 320 can be divided into control bus, data bus, address bus, etc. For ease of illustration, see attached... Figure 3 The character is represented by a single thick line, but this does not mean that there is only one bus or a type of bus.

[0156] The memory 330 may be a ROM read-only memory or other type of static storage device capable of storing static information and instructions, RAM random access memory or other type of dynamic storage device capable of storing information and instructions, or an EEPROM electrically erasable programmable read-only memory, a CD-ROM read-only optical disc or other optical disc storage, optical disc storage (including optical discs, laser discs, compressed optical discs, digital universal optical discs, etc.), a disk storage medium, or any other medium capable of carrying or storing desired program code in the form of instructions or data structures and accessible by a computer, but not limited thereto.

[0157] The memory 330 is used to store application code (computer program) for executing the present invention, and its execution is controlled by the processor 310. The processor 310 is used to execute the application code stored in the memory 330 to implement the content shown in the aforementioned embodiment of the bistatic SAR receiver flight trajectory planning method.

[0158] Example 3

[0159] Another embodiment of this application relates to a computer-readable storage medium storing a computer program. When executed by a processor, the computer program implements an embodiment of the bistatic SAR receiver flight trajectory planning method.

[0160] That is, those skilled in the art will understand that all or part of the steps in the methods of the above embodiments can be implemented by a program instructing related hardware. This program is stored in a storage medium and includes several instructions to cause a device (which may be a microcontroller, chip, etc.) or processor to execute all or part of the steps of the methods described in the various embodiments of this application. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0161] In some embodiments of this application, a computer program product is also provided, including a computer program that, when executed by a processor, implements the steps of the bistatic SAR receiver flight trajectory planning method described in the above embodiments.

[0162] Those skilled in the art will understand that the above embodiments are specific embodiments for implementing this application, and in practical applications, various changes can be made to them in form and detail without departing from the spirit and scope of this application.

[0163] The above are merely preferred embodiments of the present invention and are not intended to limit the present invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for planning the flight trajectory of a bistatic SAR receiver, characterized in that, include: Acquire initial system parameters and target state information, and establish motion models of the transmitter, moving target, and receiver; The initial parameters of the system include the initial position, velocity, and state transition matrix of the launching node, as well as the initial position, velocity, trajectory inclination angle, and trajectory deflection angle of the receiving node; Target state information includes the initial position, velocity, acceleration, and state transition matrix of the maneuvering target; Calculate the relative position vector and relative velocity vector between the receiver and the moving target, establish a three-dimensional proportional guidance model, introduce a target acceleration compensation term to construct an enhanced proportional guidance law, obtain the command acceleration in the ground coordinate system, transform the command acceleration to the receiver ballistic coordinate system through the attitude transformation matrix, and establish the motion differential equation of the receiver under the drive of the enhanced proportional guidance law as the guided flight trajectory. Based on the equation of motion, the receiver's entire flight time interval is discretized into several segments, each containing the number of adaptively optimized trajectory points. Within each segment, the navigation ratio parameter is used as a continuous optimization variable, the number of discrete trajectory points is used as an integer variable, and the acceleration sequence is used as a continuous control variable. A mixed-integer nonlinear programming model is established with the goal of minimizing the mean square error of the guided flight trajectory. Imaging constraints, guidance terminal constraints, flight dynamics constraints, and system communication constraints are used as constraints of the mixed-integer nonlinear programming model. A hierarchical solution strategy is employed to solve the mixed-integer nonlinear programming model, yielding the optimal flight trajectory of the receiver that satisfies both guidance and imaging constraints, including: The branch and bound method is used to process the integer variable of the number of trajectory segment points in the mixed integer nonlinear optimization model, and the mixed integer nonlinear optimization problem is decomposed into multiple continuous nonlinear optimization subproblems. For each continuous nonlinear optimization subproblem, the guidance and imaging constraints are decoupled by introducing auxiliary variables equivalent to the acceleration sequence, an augmented Lagrangian function is constructed to handle the constraints, and the navigation ratio parameter and acceleration sequence are optimized hierarchically and solved by using the alternating direction multiplier method. The Lagrange multipliers and penalty parameters that satisfy the imaging constraints, terminal constraints, and flight envelope constraints are updated until the receiver reaches the terminal guidance region, thus obtaining the optimal flight trajectory of the receiver that satisfies both guidance and imaging constraints.

2. The bistatic SAR receiver flight trajectory planning method according to claim 1, characterized in that, The enhanced proportional guidance law includes a target acceleration compensation term; the target acceleration compensation term is composed of the target acceleration given in real time by the target state estimation algorithm.

3. The bistatic SAR receiver flight trajectory planning method according to claim 2, characterized in that, The navigation ratio parameter takes values ​​within a preset continuous interval, and the number of trajectory segment points takes values ​​within a preset integer interval. By using the navigation ratio parameter and the number of trajectory segment points together as optimization variables, a family of guiding trajectories with navigation ratio and discrete point number as parameters is constructed.

4. The bistatic SAR receiver flight trajectory planning method according to claim 1, characterized in that, Imaging constraints include range resolution constraints, Doppler resolution constraints, and range-Doppler gradient angle constraints; A local two-dimensional grid search region is constructed on the ground plane with the predicted target position as the center, and then discretized. Based on the spatial position and velocity of the transmitter and receiver at each discrete moment, calculate the bistatic distance resolution, Doppler resolution, and the angle between the distance gradient and the Doppler gradient at each grid point; An imaging constraint threshold is set for the imaging performance of the region near the moving target, and an imaging performance measurement function is established that includes range resolution constraint, Doppler resolution constraint and gradient angle constraint.

5. The bistatic SAR receiver flight trajectory planning method according to claim 1, characterized in that, The guidance terminal constraint is that the terminal distance error between the receiving node and the maneuvering target is less than the preset miss distance.

6. The bistatic SAR receiver flight trajectory planning method according to claim 1, characterized in that, Flight dynamics constraints include maximum acceleration, minimum negative acceleration, maximum flight altitude, and maximum flight speed constraints.

7. The bistatic SAR receiver flight trajectory planning method according to claim 1, characterized in that, The mixed-integer nonlinear optimization problem is decomposed into multiple continuous nonlinear optimization subproblems, including: The whole trajectory planning problem is decomposed into piecewise iterative optimization subproblems by rolling time-domain optimization, with the terminal state of each optimization segment serving as the initial state of the next segment; the branch and bound method is used to handle integer variables, fixing the number of segment points to integer values, and transforming the mixed integer nonlinear optimization model into a continuous nonlinear optimization subproblem.

8. The bistatic SAR receiver flight trajectory planning method according to claim 1, characterized in that, The navigation ratio parameter and acceleration sequence are optimized hierarchically and solved using the alternating direction multiplier method. This includes: decomposing the continuous optimization subproblem into low-dimensional and high-dimensional subproblems using the alternating direction multiplier method; optimizing the navigation ratio with a fixed acceleration sequence in the low-dimensional subproblem and solving it using the golden section method or Bayesian optimization; optimizing the acceleration sequence with a fixed navigation ratio in the high-dimensional subproblem and solving it as a constrained nonlinear least squares problem; and solving the acceleration sequence using a global optimization algorithm.

9. An electronic device, characterized in that, The electronic device includes: At least one processor; and, A memory communicatively connected to the at least one processor; wherein, The memory stores instructions that can be executed by the at least one processor to enable the at least one processor to perform the bistatic SAR receiver flight trajectory planning method as described in any one of claims 1 to 8.

10. A computer-readable storage medium, characterized in that, The storage medium stores a computer program, which, when executed by a processor, implements the bistatic SAR receiver flight trajectory planning method according to any one of claims 1 to 8.

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