Joint design and optimization method of satellite-ground configuration for off-track multi-target imaging of spaceborne SAR

Abstract

The present invention discloses a joint design and optimization method for satellite-ground configuration of spaceborne SAR non-along-track multi-target imaging, comprising: first, establishing a coordinate system, and performing parameterized modeling of azimuth resolution and range width; second, inputting a target point sequence, a satellite orbit, and an observation start time, adding real-time control of azimuth resolution to a wave foot tracking algorithm process, and solving a feasible wave foot trajectory; third, establishing a cost function, and calculating fitness based on the target point deviation, azimuth resolution, range width, and slant range variation of the wave foot trajectory described in step two; fourth, based on a particle swarm algorithm, and taking the minimum cost function as a criterion when the satellite orbit and the target point sequence are determined, obtaining the optimal wave foot trajectory of the spaceborne SAR non-along-track curved imaging mode; the present invention can solve the problems of high configuration freedom and high design difficulty in the spaceborne SAR non-along-track curved imaging mode, and realize high-efficiency and high-quality observation of non-along-track curved scenes.

Description

Technical Field

[0001] The present invention belongs to the technical field of synthetic aperture radar (SAR), and in particular relates to a satellite-ground configuration joint design and optimization method for spaceborne SAR non-along-track multi-target imaging. Background Art

[0002] The ability to acquire multi-target information is a key indicator of spaceborne SAR reconnaissance capabilities. Traditional spaceborne SAR imaging modes have a single imaging swath, aligned with the satellite's orbit. However, many hotspot JS areas, such as borders, coastlines, railways, and highways, have diverse and non-satellite-orbital orientations. This single, orbit-aligned imaging swath of traditional modes has limited multi-target imaging capabilities, significantly limiting spaceborne SAR's multi-target imaging capabilities. Simply put, spaceborne SAR satellites have a single orbital orientation, while the geographical distribution of targets is diverse and complex. Acquiring as much multi-target information as possible using a single satellite orbit is a key requirement.

[0003] To enhance the multi-target imaging capabilities of spaceborne SAR for Earth reconnaissance, a new spaceborne SAR off-track imaging mode has emerged. This mode utilizes beam control to perform "target-customized" continuous two-dimensional scanning, generating an imaging swath that follows the target's geographic distribution rather than mechanically following the satellite's orbit. This upgrades the traditional SAR satellite imaging mode from "on-track continuous one-dimensional scanning" to "off-track continuous two-dimensional scanning." By adding a new dimension of observation freedom, multi-target imaging capabilities are significantly enhanced. Specifically, the imaging swath of spaceborne SAR off-track imaging mode can be either linear or curved, depending on the geographic orientation of the target area.

[0004] The geometric configuration of a SAR satellite during data acquisition determines imaging performance indicators such as range swath and azimuth resolution. In conventional imaging modes, the direction of the imaging swath is determined by orbital parameters, requiring only the satellite beam pointing to be designed on a fixed orbit. However, the off-track curved mode of a SAR satellite generates a curved imaging swath that matches the geographic orientation of the scene. Compared to conventional imaging modes, this geometric configuration increases the design freedom of the one-dimensional imaging swath's geographic orientation, requiring consideration of the impact of both the satellite orbit and the imaging swath shape on imaging performance when designing the geometric configuration. Furthermore, the irregular extension of the imaging swath in the off-track curved mode of a SAR satellite places more precise requirements on the control accuracy, range, and rate of beam pointing, which must be considered in the geometric configuration to meet the beam maneuvering constraints of the satellite platform. Therefore, it is necessary to deeply analyze the satellite-ground geometric relationship of the off-track curved mode of a SAR satellite, study the impact of satellite beam pointing and the ground imaging swath shape on imaging performance indicators, and conduct research on joint optimization methods for the satellite-ground geometric configuration. Summary of the Invention

[0005] In view of this, the present invention provides a joint design and optimization method of satellite-ground configuration for spaceborne SAR non-along-track multi-target imaging, which can solve the problems of high configuration freedom and high design difficulty in the non-along-track curved imaging mode of spaceborne SAR, and realize high-efficiency and high-quality observation of non-along-track curved scenes.

[0006] The technical solutions for implementing the present invention are as follows:

[0007] The joint design and optimization method of satellite-ground configuration for spaceborne SAR non-along-track multi-target imaging includes the following steps:

[0008] Step 1: Establish a coordinate system and perform parametric modeling of the orientation resolution and range width;

[0009] Step 2: Input the target point sequence, satellite orbit, and observation start time, add real-time control of the orientation resolution to the wave foot tracking algorithm process, and solve the feasible wave foot trajectory;

[0010] Step 3: Establish a cost function and calculate the fitness based on the target point deviation, azimuth resolution, range width, and slant range change of the wave foot trajectory described in step 2;

[0011] Step 4: Based on the particle swarm optimization (PSO) algorithm, when the satellite orbit and target point sequence are determined, the optimal wave foot trajectory of the spaceborne SAR non-along-track curved imaging mode is obtained with the minimum cost function as the criterion.

[0012] Furthermore, the azimuth resolution ρ a The expression is:

[0013]

[0014]

[0015]

[0016] Among them, V Sat.f is the satellite velocity in the ground-fixed system, B a is the accumulated Doppler bandwidth, R E is the radius of the Earth, H is the orbital height, ||·||2 is the two-norm operator; R(t)″ is the second derivative of the slant range, λ is the wavelength, V foot.f is the wave foot velocity under the ground fixed system, l res is the intercept of the half-power projection ellipse on the ground along the wave foot direction; ω represents the ground wave foot velocity V in the earth's inertial system foot With k a The angle, l r and l a Represents the projected ellipse along k r and k a The length of the two axes, θe k r and k a The angle, k r and k a They are respectively the distance and azimuth profiles of the antenna beam in the Earth inertial system and the intersection lines of the Earth's tangent plane.

[0017] Furthermore, the distance width W r That is, the intercept along the orthogonal direction of the wave foot in the half-power projection ellipse, and its expression is:

[0018]

[0019] Where ω represents the ground wave foot velocity V in the Earth inertial system foot With k a The angle, l r and l a Represents the projected ellipse along k r and k a The length of the two axes, θ e k r and k a The angle, k r and k a They are respectively the distance and azimuth profiles of the antenna beam in the Earth inertial system and the intersection lines of the Earth's tangent plane.

[0020] Furthermore, step 2 specifically includes the following steps:

[0021] Step 2.1. Input the target point sequence to be observed, satellite orbit, and observation start time t0, and set the first observation target point as the wave foot starting point P foot.f (1) , the second target is set to the current tracking target point P T (1);

[0022] Step 2.2: Assume that the position of the wave foot under the ground fixed system during the tracking step i is P foot.f (i) , the wave foot speed is V foot.f (i) , Bozu P foot.f (i) To the current tracking target point P T The direction vector of (j) is v ij , in V foot.f (i) and v ij Set n direction vectors v uniformly in the angle between i ' j (n), called the optional direction of the wave foot, where V ij '(n) is the velocity vector in the optional direction, and the position P' in each optional direction is calculated ij (n), speed V′ij (n), acceleration a′ ij (n),

[0023] Step 2.3: Calculate the azimuth resolution ρ for each optional direction a (n), then update the velocity of the optional direction of the wave foot using formula (12) and jump to step 2.2 until the calculated azimuth resolution is consistent with the expected resolution ρ a0 The residuals between them are small enough;

[0024]

[0025] Step 2.4, based on yaw angle ψ, pitch angle θ, roll angle and its high-order differential analytical expression, calculate the maneuverability of each feasible direction, and select the feasible direction number n according to the criterion shown in formula (13) i , where F(·) is the attitude angle range constraint, G(·) is the attitude angular velocity constraint, H(·) is the attitude angular acceleration constraint, and ζ is the weight factor; in formula (14), a and b are constants and a<<1, b<0.5, L foot is the distance between the wave foot and the previous tracking target, L T is the distance between the two tracking targets; then, n i The corresponding position and speed are taken as the wave foot position P of the i+1th step foot.f (i+1) , wave foot speed V foot.f (i+1) , the acceleration is the wave foot acceleration a of step i foot.f (i+1) ;

[0026]

[0027]

[0028] Step 2.5: After each iteration, it is necessary to judge whether the tracking target needs to be switched. The judgment criterion is shown in formula (17). If any condition of the formula is met, the tracking target can be switched. That is, let j = j + 1, where R set is the length threshold set, and its value range is within a distance width, v foot.f (i) is the velocity direction vector of the wave foot at step i;

[0029]

[0030] Step 2.6: Repeat steps 2.2 to 2.5 until the entire target point sequence is traversed and the wave foot trajectory is output.

[0031] Furthermore, the cost function is shown in Equation (18), where N is the total number of target points to be observed, k = 1, 2, ..., N, λ1, λ2, λ3 are weight factors, satisfying λ1 + λ2 + λ3 = 1; Q0 is the quality factor of the conventional system, which is about 10 4 ρ a (k) and W r (k) is the azimuth resolution and range width at each target point; Δl(k) is the deviation distance between the designed wave foot trajectory and the observed target point; ΔR is the change in slant range during data acquisition; S is the total length of the imaging band along the wave foot direction.

[0032]

[0033] Beneficial effects:

[0034] 1. The present invention solves the problems of high configuration freedom and great design difficulty in the non-along-track curved imaging mode of spaceborne SAR, and can achieve high-efficiency and high-quality observation of non-along-track curved scenes.

[0035] 2. Step 1 of the present invention provides an analytical expression for the azimuth resolution and range width under this mode, which solves the problem that traditional resolution and range width expressions are not applicable when imaging non-track scenes, and lays a research foundation for subsequent designs.

[0036] 3. In step 2 of the present invention, real-time control of azimuth resolution is added to the original wave foot tracking algorithm, which can achieve uniform azimuth resolution while satisfying the satellite's maneuverability constraints.

[0037] 4. Step 3 of the present invention provides a fitness function under the comprehensive optimal imaging performance, which provides a consistent evaluation criterion for measuring the quality of imaging indicators, and ultimately realizes the observation configuration design that optimizes the imaging performance indicators when the satellite orbit and observation target are determined. BRIEF DESCRIPTION OF THE DRAWINGS

[0038] Figure 1 This is a flow chart of the joint design and optimization method of satellite-ground configuration for spaceborne SAR non-along-track multi-target imaging described in the present invention.

[0039] Figure 2 It is a schematic diagram of the observation configuration of the non-along-track curved imaging mode of the spaceborne SAR according to the present invention.

[0040] Figure 3 This is a flow chart of the improved wave foot tracking algorithm described in the present invention.

[0041] Figure 4 It is the flow chart of particle swarm (PSO) algorithm.

[0042] Figure 5Figure 1 shows the wave foot trajectory and target point deviations for the proposed method and conventional method in the examples. (a) Wave foot trajectory for the conventional method, (b) Wave foot trajectory for the proposed method, (c) Target point deviation for the conventional method, and (d) Target point deviation for the proposed method.

[0043] Figure 6 The azimuth resolution and range width of the method described in the present invention and the conventional method at each target point in the examples are shown in Figure 1. (a) Azimuth resolution of the conventional method, (b) Azimuth resolution of the method described in the present invention, (c) Range width of the conventional method, and (d) Range width of the method described in the present invention.

[0044] Figure 7 Figure 1 shows the beam attitude angles and their first- and second-order simulation results for the method described in the present invention and the conventional method in the examples. (a) Conventional method attitude angle, (b) Conventional method attitude angular velocity, (c) Conventional method attitude angular acceleration, (d) Conventional method attitude angle, (e) Conventional method attitude angular velocity, (f) Conventional method attitude angular acceleration. DETAILED DESCRIPTION

[0045] The present invention is described in detail below with reference to the accompanying drawings and embodiments.

[0046] The flowchart of the satellite-ground configuration joint design and optimization method for spaceborne SAR non-along-track multi-target imaging of the present invention is as follows: Figure 1 As shown, the present invention includes the following steps:

[0047] Step 1: Establish a coordinate system and perform parametric modeling of the orientation resolution and range width;

[0048] First, establish the satellite orbit coordinate system and the SAR coordinate system, which are defined as follows: In the satellite orbit coordinate system, the X-axis direction is the direction of the satellite's motion velocity; the Z-axis vector is in the satellite orbit plane and points to the center of the earth; the Y-axis is solved according to the right-hand rule. In the SAR antenna coordinate system, the positive direction of the X-axis is the same as the direction of the satellite's motion, the XOZ plane is the cross-section of the antenna along the azimuth direction; the Z-axis is the direction of the antenna beam center. The relative relationship between the satellite orbit coordinate system and the SAR antenna coordinate system can be obtained by Figure 2 The spaceborne SAR observation configuration shown in the figure is obtained, where the satellite orbit coordinate system is XYZ, the SAR antenna coordinate system is r1-r2-r3; the antenna range plane is r2-o-r3; the antenna azimuth plane is r1-o-r3; β is the downward viewing angle; γ is the projection of the oblique viewing angle on the earth tangent plane (parallel to the XOY plane) at the sub-satellite point; η is the angle formed by the intersection of the Y axis and the antenna range plane and the XOZ, called the beam projection angle, which is used to characterize the rotation angle of the projection ellipse; β, γ, and η are collectively referred to as the characteristic angles of the observation configuration.

[0049] Azimuth resolution ρ in spaceborne SAR aThe expression is shown in formula (1), where V Sat.f is the satellite velocity in the ground-fixed system, B a is the accumulated Doppler bandwidth, R E is the radius of the Earth, H is the orbital height, and ||·||2 is the two-norm operator. B a The analytical expression of is also given in Equation (2), where R(t)″ is the second derivative of the slant range, λ is the wavelength, and V foot.f is the wave foot velocity under the ground fixed system, l res is the intercept of the half-power projection ellipse on the ground along the wave foot.

[0050]

[0051]

[0052] In order to obtain the Doppler bandwidth B a The analytical expression of l is given by equations (3) to (7). res The solution method is: k in formula (3) and (4) r and k a are the distance of the antenna beam in the earth inertial system, the intersection of the azimuth profile and the earth tangent plane, β ec is the geocentric angle, β′ ec is the geocentric angle that includes left and right viewing information. When looking right, β′ ec =β ec , β when looking left e ' c =-β ec , H X (θ) represents the rotation of the coordinate axis by θ degrees along the positive direction of the right-hand rule with the positive direction of the X axis as the axis. Y (θ) and H Z The definition of (θ) is similar to that of the projection ellipse. Equations (5) and (6) give the projection ellipse along k. r and k a The length of the two axes l r and l a , where θ e k r and k a The angle, σ r and σ a L3 and k r 、k a The angles are respectively, L3 is the satellite position P in the Earth inertial system sat.i To the ground wave foot position P foot.i The vector of are the distance and azimuth beam width of the beam respectively. In formula (7), ω represents the ground wave foot velocity V in the earth inertial system. foot With k aThe angle between . Combining equations (3) to (7) we can get l res The analytical expression of is shown in formula (8).

[0053]

[0054]

[0055]

[0056]

[0057]

[0058]

[0059] Formula (9) gives the analytical expression of R(t)″, where V foot.f 、a foot.f denote the velocity and acceleration of the wave foot under the ground-fixed system, dL3 and d 2 L3 is the first and second order differentials of L3 with respect to time.

[0060]

[0061] In the non-tracking imaging mode of spaceborne SAR, the range direction is perpendicular to the wave foot direction, so its range width W r That is, it is the intercept along the orthogonal direction of the wave foot in the half-power projection ellipse. Its expression can be directly obtained based on formula (8), as shown in formula (10):

[0062]

[0063] Step 2: Input the target point sequence, satellite orbit, and observation start time, add real-time control of the orientation resolution to the wave foot tracking algorithm process, and solve the feasible wave foot trajectory;

[0064] The wave foot tracking algorithm uses the analytical expression of the yaw, pitch, roll angles and their high-order differentials that describe the beam attitude, and iterates the wave foot trajectory point by point to achieve the "growth" of the wave foot, thus obtaining a wave foot trajectory that satisfies the platform constraints and covers all target points as much as possible. The algorithm flow chart is shown in the figure below. Figure 3 As shown, it is divided into the following six steps:

[0065] (1) Input the target point sequence to be observed, satellite orbit, and observation start time t0, and set the first observation target point as the wave foot starting point P foot.f (1) , the second target is set to the current tracking target point P T (1);

[0066] (2) Assume that the position of the wave foot under the ground fixed system during the tracking step i is P foot.f (i) , the wave foot speed is V foot.f (i) , Bozu P foot.f (i) To the current tracking target point P T The direction vector of (j) is v ij , in V foot.f (i) and v ij Set n direction vectors v uniformly in the angle between i ' j (n), called the optional direction of the wave foot, where V′ ij (n) is the velocity vector in the optional direction. Calculate the position P′ in each optional direction ij (n), speed V′ ij (n), acceleration a′ ij (n), as shown in formula (11), where dt is the time differential;

[0067]

[0068] (3) Calculate the azimuth resolution ρ of each optional direction according to equations (1) to (9): a (n), then update the velocity of the optional direction of the wave foot using formula (12) and jump to step (2) until the calculated azimuth resolution is consistent with the expected resolution ρ a0 The residuals between them are small enough;

[0069]

[0070] (4) Based on yaw angle ψ, pitch angle θ, roll angle and its high-order differential analytical expression, calculate the maneuverability of each feasible direction, and select the feasible direction number n according to the criterion shown in formula (13) i , where F(·) is the attitude angle range constraint, G(·) is the attitude angular velocity constraint, H(·) is the attitude angular acceleration constraint, and ζ is the weight factor; in formula (14), a and b are constants and a<<1, b<0.5, L foot is the distance between the wave foot and the previous tracking target, L T is the distance between the two tracking targets. i The corresponding position and speed are taken as the wave foot position P of the i+1th step foot.f (i+1) , wave foot speed V foot.f (i+1) , the acceleration is the wave foot acceleration a of step i foot.f (i+1) , as shown in formula (16);

[0071]

[0072]

[0073]

[0074]

[0075] (5) After each iteration, it is necessary to judge whether the tracking target needs to be switched. The judgment criterion is shown in formula (17). If any condition of the formula is met, the tracking target can be switched. That is, let j = j + 1, where R set is the length threshold set, and its value range is within a distance width, v foot.f (i) is the velocity direction vector of the wave foot at step i;

[0076]

[0077] (6) Repeat steps (2) to (5) until the entire target point sequence is traversed and the wave foot trajectory is output.

[0078] The above algorithm solves the problem of difficult non-track wave foot design and large deviation of wave foot trajectory under the constraints of satellite platform, and performs real-time control of azimuth resolution on the basis of the original algorithm to solve the problem of non-uniformity of expected azimuth resolution. In addition, since Equation (2) is used to calculate the accumulated Doppler bandwidth B, a When the instantaneous value at the center of the synthetic aperture is used instead of the integral value, if the wave foot near the target point has a large curvature, the actual synthetic aperture integration time will be different from that in the formula, resulting in an error in the theoretical azimuth resolution calculation. To this end, a weight factor is added to formula (13) in step (4) to make the wave foot trajectory near the target point approximate to a straight line.

[0079] Step 3: Establish a cost function and calculate the fitness based on the target point deviation, azimuth resolution, range width, and slant range change of the wave foot trajectory in step 2.

[0080] The cost function established is shown in Equation (18), where N is the total number of target points to be observed, λ1, λ2, and λ3 are weight factors, satisfying λ1+λ2+λ3=1; Q0 is the quality factor of the conventional system, which is about 10 4 ρ a (k) and W r(k) represents the azimuth resolution and range width at each target point; Δl(k) represents the deviation between the designed wave foot trajectory and the observed target point; ΔR represents the change in slant range during data acquisition; and S represents the total length of the imaging swath along the wave foot. This cost function comprehensively considers metrics such as azimuth resolution, range width, wave foot deviation, and total slant range change. A fitness cost is calculated for each wave foot trajectory to comprehensively describe the imaging performance.

[0081]

[0082] Step 4: Based on the particle swarm optimization (PSO) algorithm, when the satellite orbit and target point sequence are determined, the optimal wave foot trajectory of the spaceborne SAR non-along-track curved imaging mode is obtained with the minimum cost function as the criterion.

[0083] According to the conventional wave foot tracking algorithm, it can only obtain the wave foot design result when the observation start time t0 is determined, that is, it only designs the ground wave foot, lacking the overall optimization of the observation configuration between the satellite and ground wave foot and the evaluation of the imaging performance index. At the same time, the wave foot tracking threshold R in the algorithm set The rotation angle η relative to the projected ellipse must be specified, which significantly affects the design results. Therefore, we employ a particle swarm optimization (PSO) algorithm to optimize the wave foot tracking algorithm, minimizing the cost function in step 3. This results in optimal wave foot trajectory design for the non-along-track curved imaging mode of spaceborne SAR.

[0084] The PSO algorithm flow chart is as follows Figure 4 The specific steps are as follows:

[0085] (1) Initialize the particle swarm, including the number of particles, number of iterations, initial position and velocity, inertia weight and other parameter values, where the initial value of the position vector x of the qth particle is q (0) , the vector length is 3, and the value ranges of its three elements are the observation start time t0, the wave foot tracking threshold R set , is the range of the projected ellipse rotation angle η; the initial velocity of the particle is the zero vector.

[0086] (2) Evaluate the initial fitness value of each particle based on formula (18) in step 3.

[0087] (3) The initial fitness value is used as the local optimal solution of each particle, and the optimal position of each particle is saved as pbest q (0) . And find the optimal value among them as the initial value gbest of the global optimal solution (0) , and record its location.

[0088] (4) Update the velocity and position of each particle based on equations (19) and (20), where c1 is the individual learning factor, c2 is the social learning factor, w is the inertia weight of the velocity, r1 and r2 are random numbers, g is the constraint factor, and d is the current number of iterations.

[0089]

[0090]

[0091] (5) Calculate the fitness value of the updated particles, update the local optimal value of each particle and the global optimal value of the entire particle swarm.

[0092] (6) Repeat steps (4) and (5) until the maximum number of iterations is reached or the optimal position found by the particle swarm satisfies the minimum allowable error of the objective function. Output the value at this time. The optimized observation start time t0 is obtained, which is the wave foot tracking threshold R set , is the rotation angle η of the projection ellipse.

[0093] Simulation experiment: The simulation parameters of the parametric configuration design of the non-along-track curved imaging mode of spaceborne SAR are shown in Table 1.

[0094] Table 1 List of simulation parameters for parametric configuration design of spaceborne SAR non-along-track curved imaging mode

[0095]

[0096] To verify the advantages of the joint satellite-ground configuration design and optimization method for off-track multi-target imaging in spaceborne SAR, which addresses the high degree of configuration freedom and high design difficulty in off-track curved imaging mode, a set of 22 target points were designed using both the off-track mode configuration design method described in this invention and the conventional method under the parameters in Table 1.

[0097] exist Figure 5 The wave foot trajectory and the deviation between the target point and the wave foot trajectory planned by the method proposed in this invention and the conventional method are given in the figure, where Figure 5 (a) and (b) are the wave foot trajectories designed by the two methods. Figure 5 (c) and (d) are the deviations between the wave foot trajectory and the observed target point. Obviously, the deviation of the method described in the present invention is significantly smaller than that of the conventional wave foot tracking method, and it fits the direction of the target scene more closely. Figure 6 The imaging performance indicators of the two methods at each target point are given. Figure 6 (a) and (b) are the azimuth resolutions designed by the two methods, Figure 6(c) and (d) are the designed range widths. It can be seen that the resolution of each target point in the conventional method varies significantly, affecting the visibility of the final image. However, the azimuth resolution of the method described in this invention is consistently 0.5m, ensuring resolution uniformity. Furthermore, the average range width for each point in the conventional method is 4.26km, while that of the method described in this invention is 6km. These results demonstrate that the method described in this invention significantly outperforms the conventional method, achieving a globally optimal configuration design. Figure 7 The range of attitude angles of the two methods is given ( Figure 7 (a) and (d)), angular velocity ( Figure 7 (b) and (e)), angular acceleration ( Figure 7 (c) and (f)), the satellite maneuver constraints of this simulation are: beam attitude angle ≤ 45 degrees, attitude angle velocity ≤ 0.8 degrees / s, attitude angle acceleration ≤ 0.08 degrees / s 2 , it can be seen that both methods can realize the design of non-tracking imaging mode under given platform maneuvering constraints.

[0098] In summary, the above are only preferred embodiments of the present invention and are not intended to limit the scope of protection of the present invention. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A joint design and optimization method for satellite-ground configuration of spaceborne SAR non-along-track multi-target imaging, characterized by: The following steps are involved: Step 1: Establish a coordinate system and perform parametric modeling of the orientation resolution and range width; Step 2: Input the target point sequence, satellite orbit, and observation start time, add real-time control of the orientation resolution to the wave foot tracking algorithm process, and solve the feasible wave foot trajectory; including the following steps: Step 2.

1. Input the target point sequence to be observed, satellite orbit, and observation start time t0, and set the first observation target point as the wave foot starting point P foot.f (1) , the second target is set to the current tracking target point P T (1); Step 2.2: Assume that the position of the wave foot under the ground fixed system during the tracking step i is P foot.f (i) , the wave foot speed is V foot.f (i) , Bozu P foot.f (i) To the current tracking target point P T The direction vector of (j) is v ij , in V foot.f (i) and v ij Set n direction vectors v′ uniformly in the angle between ij (n), called the optional direction of the wave foot, where V′ ij (n) is the velocity vector in the optional direction, and the position P′ in each optional direction is calculated. ij (n), speed V′ ij (n), acceleration a′ ij (n), Step 2.3: Calculate the azimuth resolution ρ for each optional direction a (n), then update the velocity of the optional direction of the wave foot using formula (12) and jump to step 2.2 until the calculated azimuth resolution is consistent with the expected resolution ρ a0 The residuals between them are small enough; Step 2.4, based on yaw angle ψ, pitch angle θ, roll angle and its high-order differential analytical expression, calculate the maneuverability of each feasible direction, and select the feasible direction number n according to the criterion shown in formula (13) i , where F(·) is the attitude angle range constraint, G(·) is the attitude angular velocity constraint, H(·) is the attitude angular acceleration constraint, and ζ is the weight factor; in formula (14), a and b are constants and a<<1, b<0.5, L foot is the distance between the wave foot and the previous tracking target, L T is the distance between the two tracking targets; then, n i The corresponding position and speed are taken as the wave foot position P of the i+1th step foot.f (i+1) , wave foot speed V foot.f (i+1) , the acceleration is the wave foot acceleration a of step i foot.f (i+1) ; Step 2.5: After each iteration, it is necessary to judge whether the tracking target needs to be switched. The judgment criterion is shown in formula (17). If any condition of the formula is met, the tracking target can be switched. That is, let j = j + 1, where R set is the length threshold set, and its value range is within a distance width, v foot.f (i) is the velocity direction vector of the wave foot at step i; Step 2.6: Repeat steps 2.2 to 2.5 until the entire target point sequence is traversed and the wave foot trajectory is output; Step 3: Establish a cost function and calculate the fitness based on the target point deviation, azimuth resolution, range width, and slant range change of the wave foot trajectory described in step 2; Step 4: Based on the particle swarm optimization algorithm, when the satellite orbit and target point sequence are determined, the optimal wave foot trajectory of the spaceborne SAR non-along-track curved imaging mode is obtained with the minimum cost function as the criterion.

2. The method for joint satellite-ground configuration design and optimization for spaceborne SAR off-track multi-target imaging according to claim 1, characterized in that: The azimuth resolution ρ a The expression is: Among them, V Sat.f is the satellite velocity in the ground-fixed system, B a is the accumulated Doppler bandwidth, R E is the radius of the Earth, H is the orbital height, ||·||2 is the two-norm operator; R(t)″ is the second derivative of the slant range, λ is the wavelength, V foot.f is the wave foot velocity under the ground fixed system, l res is the intercept of the half-power projection ellipse on the ground along the wave foot direction; ω represents the ground wave foot velocity V in the earth's inertial system foot With k a The angle, l r and l a Represents the projected ellipse along k r and k a The length of the two axes, θ e k r and k a The angle, k r and k a They are respectively the distance and azimuth profile of the antenna beam in the Earth inertial system and the intersection line of the Earth's tangent plane.

3. The satellite-ground configuration joint design and optimization method for spaceborne SAR non-along-track multi-target imaging according to claim 1 or 2, characterized in that: Distance width W r That is, the intercept along the orthogonal direction of the wave foot in the half-power projection ellipse, and its expression is: Where ω represents the ground wave foot velocity V in the Earth inertial system foot With k a The angle, l r and l a Represents the projected ellipse along k r and k a The length of the two axes, θ e k r and k a The angle, k r and k a They are respectively the distance and azimuth profile of the antenna beam in the Earth inertial system and the intersection line of the Earth's tangent plane.

4. The method for joint satellite-ground configuration design and optimization for spaceborne SAR non-along-track multi-target imaging according to claim 1, wherein: The cost function is shown in Equation (18), where N is the total number of target points to be observed, k = 1, 2, ..., N, λ1, λ2, λ3 are weight factors, satisfying λ1 + λ2 + λ3 = 1; Q0 is the quality factor of the conventional system, which is 10 4 ; ρ a (k) and W r (k) is the azimuth resolution and range width at each target point; Δl(k) is the deviation distance between the designed wave foot trajectory and the observed target point; ΔR is the change in slant distance during data acquisition; S is the total length of the imaging band along the wave foot direction;

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