Optimization method for imaging swath of space-borne SAR non-azimuthally curved imaging mode

Abstract

The application provides a spaceborne SAR non-azimuth bending imaging mode imaging strip optimization method, can solve the problems of difficult multi-target observation imaging strip design and large target point deviation in the spaceborne SAR non-azimuth bending imaging mode with beam maneuvering constraints, and realizes multi-target observation imaging strip optimization. The application firstly plans the observation sequence of the non-azimuth distributed target points, then firstly gives the analytical expression of the beam attitude angle and the high-order derivative, and on this basis, proposes the wave foot tracking algorithm and the minimum deviation point criterion to design and generate the optimal non-azimuth imaging strip conforming to the beam maneuvering constraints, solves the problems of difficult multi-target observation imaging strip design and large target point deviation in the spaceborne SAR non-azimuth bending imaging mode with beam maneuvering constraints, avoids the large loss of computing resources generated by the simulation calculation of the attitude angle, and realizes the multi-target observation imaging strip optimization of the spaceborne SAR non-azimuth bending imaging mode.

Description

Technical Field

[0001] This invention relates to the field of Synthetic Aperture Radar (SAR) technology, specifically to a method for optimizing the imaging band of a non-track bending imaging mode in spaceborne SAR. Background Technology

[0002] Non-track imaging is a unique operating mode of spaceborne SAR. Compared to traditional spaceborne SAR, non-track SAR generates mapping strips directly along the target terrain by continuously adjusting the beam pointing in the elevation and azimuth dimensions, instead of generating mapping strips along the satellite orbit as in the traditional method. This fundamentally reduces echo data redundancy when imaging certain "non-track scenarios" such as seismic zones and coastlines, significantly improving the observation efficiency of spaceborne SAR for narrow scenes, and has unique advantages.

[0003] During data acquisition, satellites typically conduct observations by controlling the beam attitude angle. Since the orientation of "oblique scenes" is often irregular, it's necessary to simultaneously design the beam attitude angle and its higher-order derivatives during data acquisition to generate irregular mapping strips. Simultaneously, the satellite payload also imposes constraints on the beam attitude angle and its higher-order derivatives to ensure the satellite's safe and stable operation. Therefore, how to plan mapping strips along the scene under given beam attitude angle and higher-order derivative constraints has become a crucial problem for non-track imaging modes. Traditional methods, lacking theoretical guidance and relevant algorithmic support, generally do not consider beam maneuvering during the design phase, instead determining whether the constraints are met after the design is complete. This leads to problems such as difficulty in imaging strip planning and large target point deviations. Summary of the Invention

[0004] In view of this, the present invention proposes an imaging band optimization method for spaceborne SAR non-track bending imaging mode, which can solve the problem of difficult design of multi-target observation imaging band when there are beam maneuver constraints in spaceborne SAR non-track bending imaging mode, and realize multi-target observation imaging band optimization.

[0005] To achieve the above objectives, the present invention provides a method for optimizing the imaging band of a spaceborne SAR non-track bending imaging mode, comprising the following steps:

[0006] Step 1: Plan the input set of target points and generate several sequences of target points;

[0007] Step 2: Establish a coordinate system to obtain the analytical expression of the beam attitude angle and its higher-order derivatives;

[0008] Step 3: Input the target point sequence and solve the feasible wave foot trajectory under the beam attitude angle constraint according to the wave foot optimization algorithm. The wave foot optimization algorithm is as follows: Input the satellite power-on time and the target point sequence generated in Step 1. Calculate the position, velocity, and acceleration of the wave foot's optional motion direction at the next moment from the current point. Calculate the wave foot attitude angle and its higher-order derivatives for each optional direction based on the analytical expression of the beam attitude angle and its higher-order derivatives obtained in Step 2. Filter the wave foot motion direction at the next moment based on the attitude constraint. Then determine whether to traverse all target points. If yes, output the wave foot trajectory. Otherwise, determine whether to switch the tracking target point. If yes, set the next target point as the tracking target and return to recalculate the position, velocity, and acceleration of the wave foot's optional motion direction at the next moment. Otherwise, directly return to recalculate the position, velocity, and acceleration of the wave foot's optional motion direction at the next moment until all target points are traversed and the wave foot trajectory is output.

[0009] Step 4: Change the judgment threshold in the target switching criterion, iterate the relevant parameters in the wave foot optimization algorithm, and select the optimal wave foot trajectory according to the minimum target point deviation criterion.

[0010] The analytical relationship between the beam attitude angle and the observation configuration characteristic angle is as follows:

[0011]

[0012] Where β is the downward viewing angle, β′ is the downward viewing angle containing left and right viewing information, when viewing from the right β′=β, when viewing from the left β′=-β; γ is the projection of the oblique viewing angle onto the Earth's tangent plane where the nadir point is located; η is the beam projection angle, used to characterize the rotation angle of the projection ellipse, which can be set by the user during observation to balance swath width and azimuth resolution; β, γ, and η are collectively referred to as the observation configuration characteristic angle; θ is the roll angle, θ is the pitch angle, and ψ is the yaw angle, collectively referred to as the beam attitude angle;

[0013] Taking the first and second derivatives of the analytical relationship between the beam attitude angle and the observation configuration characteristic angle, respectively, yields the higher-order forms of the beam attitude angle, which are:

[0014]

[0015]

[0016] The wave foot optimization algorithm specifically includes the following steps:

[0017] First, input the target point sequence and satellite startup time parameters generated in step one, and then calculate the possible motion directions of the wave foot:

[0018]

[0019] Where Pfoot.f (i) represents the position of the wave foot ground-solid system at time i, p i It is its unit vector; P T (j) represents the fixed position of the j-th tracking target, satisfying j∈[1,2,…,M], where M is the number of target points; the normal vector of the plane containing the two vectors is n. ij ;v ij For the Earth's surface from P foot.f (i) to P T (j) is the unit direction vector; ||·||2 is the 2-norm operator; v i Let k be the unit vector of the wave foot velocity in the ground-solid system at time i; ij For v ij With v i The angle between the two sides; N is the number of possible motion directions for the wave foot, n is the index of the possible motion direction, satisfying n∈[1,2,…,N], and k(n) is the angle between the nth possible direction; v′ ij (n) represents the unit vector of the nth optional direction for the j-th target in the Earth-fixed system at time i, H Y (θ) represents rotating the coordinate axis by θ degrees along the positive direction of the right-hand rule with the positive direction of the Y-axis as the axis;

[0020]

[0021]

[0022] V′ ij (n) represents the velocity of the j-th target in the Earth-fixed system at time i in the n-th optional direction; a′ ij (n) indicates the use of V′ ij (n) The acceleration of the j-th target in the Earth-fixed system at time i; P′ ij (n) indicates the use of V′ ij (n) and a′ ij (n) The coordinates of the wave foot in the ground-fixed system at the (i+1)th time after the wave foot, V foot.f (i) represents the velocity of the wave at time i, and dt is the time derivative;

[0023]

[0024] P′ ij (n), V′ ij (n), a′ ij (n) Substituting the analytical expression obtained in step two, we can directly calculate the attitude angles and their first and second derivatives for each selectable direction, and then... Select the index n of the optimal direction that meets the satellite attitude angle constraints. iWhere F(·) is the attitude angle constraint, G(·) is the attitude angle change rate constraint, and H(·) is the attitude angle change acceleration constraint, the acceleration at time i is determined, and the position and velocity of the wave foot in the Earth-solid system at time i+1 are determined.

[0025] The switching criterion for the tracking target is as follows:

[0026]

[0027] Where P foot.f (i) represents the position of the wave foot ground-solid system at time i, P T (j) represents the fixed position of the j-th tracking target, satisfying j∈[1,2,...,M], where M is the number of target points; v ij For the Earth's surface from P foot.f (i) to P T (j) is the unit direction vector; ||·||2 is the 2-norm operator; R set The set length threshold has a value range within a distance width; v i Let H be the unit vector of the wave foot-ground-solid system velocity at time i, with the superscript H indicating transpose.

[0028] The target point planning method includes target point clustering and target sequence partitioning; the specific steps of target point clustering are as follows:

[0029] Step 11: Label all points in the set as 1, 2, ..., M, and calculate the distance from each point in the target point set to all points. Compare the distance with the clustering threshold. If the distance is less than the threshold, it is judged as 1, otherwise it is 0. Put the results into an M×M matrix according to the target point index to generate the target distance matrix.

[0030] Step 12: Starting from the first row, find the column numbers i, j, k, ... corresponding to the elements with a value of 1 in the matrix, record the index, and set all elements in the i, j, k, ... rows and the i, j, k, ... columns to 0;

[0031] Step 13: Repeat step 12 M times, traversing all rows of the target distance matrix, and recording all the indexes are the points to be clustered;

[0032] The specific steps for dividing the target sequence are as follows:

[0033] Step 21: Sort all target points after clustering from low to high dimensionality. Let the point set be T = {T1, T2, ..., T...} N};

[0034] Step 22, let S1(1) = T1, i = 1, j = 2, based on the following judgment conditions:

[0035]

[0036] If the condition is met, then let S1(i+1) = T. j If the condition is not met, let j = j + 1, where S1(i) is the i-th target point of the first sequence divided; repeat the above operation until j = N, and the divided target sequence S1 can be obtained;

[0037] Step 23: Let T1 = T - S1. Perform step 22 on T1 to obtain S2 and T2. Repeat step 22 until... Then output the k target sequences that have been divided.

[0038] The criterion for minimizing the target point deviation is as follows:

[0039]

[0040] Among them, L′ foot.f (R set () represents the fitted wave foot trajectory. The optimal threshold is obtained based on this criterion, and inf(·) is used to find the infimum of the function.

[0041] Beneficial effects:

[0042] This invention first plans the observation sequence of non-track-distributed target points, and then, for the first time, provides analytical expressions for the beam attitude angle and its higher-order derivatives. Based on this, it proposes a wave foot tracking algorithm and a minimum deviation point criterion to design and generate the optimal non-track-distributed imaging band that meets the beam maneuvering constraints. This solves the problems of difficult multi-target observation imaging band design and large target point deviation in the non-track-distributed curved imaging mode of spaceborne SAR when there are beam maneuvering constraints. At the same time, it avoids the large loss of computing resources caused by simulating the attitude angle, and realizes the optimization of multi-target observation imaging band in the non-track-distributed curved imaging mode of spaceborne SAR. Attached Figure Description

[0043] Figure 1 This is a flowchart of the multi-target observation imaging band optimization method for spaceborne SAR non-track bending imaging mode described in this invention.

[0044] Figure 2 This is a flowchart of the target point planning method described in this invention.

[0045] Figure 3 This is a schematic diagram of the observation configuration of the non-track bending imaging mode of spaceborne SAR described in this invention.

[0046] Figure 4 This is a flowchart of the wave-foot optimization algorithm described in this invention.

[0047] Figure 5This refers to the planning results and target coverage of the methods described in this invention and traditional methods in the embodiments of this invention.

[0048] Figure 6 This is a comparison diagram of the beam attitude angle and its first and second derivatives between the method described in this invention and the traditional method in this embodiment of the invention.

[0049] Figure 7 The error between the analytical expressions of the beam attitude angle and its first and second derivatives used in the embodiments of this invention and the simulation results of the code is due to the discrepancy between them. Detailed Implementation

[0050] The present invention will now be described in detail with reference to the accompanying drawings and embodiments.

[0051] In spaceborne SAR non-track bending imaging modes, traditional imaging strait design methods do not consider beam maneuver constraints during the design phase, often resulting in designs that fail to meet actual beam maneuver constraints and are therefore unusable. Furthermore, these designs often deviate significantly from the target point, making it easy to lose the target during data acquisition. The method proposed in this invention first plans the mission objectives, then obtains the wave foot trajectory that satisfies the beam maneuver constraints based on the proposed wave foot optimization algorithm, and finally iteratively provides the optimal multi-target observation imaging strait design result based on the minimum deviation criterion. This solves the problems of difficult design implementation and large target point deviation in traditional methods. The flowchart of the multi-target observation imaging strait optimization method for spaceborne SAR non-track bending imaging modes described in this invention is as follows: Figure 1 As shown, the present invention includes the following steps:

[0052] Step 1: Plan the input set of target points and generate several sequences of target points;

[0053] The target point planning method process is as follows: Figure 2 As shown, this includes target point clustering and target sequence partitioning. The specific steps for target point clustering are as follows:

[0054] Step 11: Label all points in the set as 1, 2, ..., M (M is the total number of target points) and calculate the distance from each point in the target point set to all other points. Compare this distance with a clustering threshold; if the distance is less than the threshold, classify it as 1; otherwise, classify it as 0. Store the results in an M×M matrix according to the target point index to generate the target distance matrix.

[0055] Step 12: Starting from the first row, find the column numbers i, j, k, ... corresponding to the elements with a value of 1 in the matrix, record the index, and set all elements in the i, j, k, ... rows and the i, j, k, ... columns to 0;

[0056] Step 13: Repeat step 12 M times, traversing all rows of the target distance matrix, and recording all the indexes are the points to be clustered.

[0057] The specific steps for dividing the target sequence are as follows:

[0058] Step 21: Sort all target points after clustering from low to high dimensionality. Let the point set be T = {T1, T2, ..., T...} N}

[0059] Step 22, let S1(1) = T1, i = 1, j = 2. According to the judgment condition given in equation (1), if it is satisfied, let S1(i+1) = T1. j If the condition is not met, let j = j + 1, where S1(i) is the i-th target point of the first divided sequence. Repeat the above operation until j = N to obtain the divided target sequence S1.

[0060] Step 23: Let T1 = T - S1. Performing step 22 on T1 will yield S2 and T2. Repeat step 22 until... Then output the k target sequences that have been divided.

[0061]

[0062] Step 2: Establish a coordinate system to obtain the analytical expression of the beam attitude angle and its higher-order derivatives. The specific process is as follows:

[0063] 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 velocity; the Z-axis vector is in the satellite orbit plane and points towards the Earth's center; the Y-axis is solved according to the right-hand rule; In the SAR antenna coordinate system, the positive X-axis direction is in the same direction as the satellite's motion, the XOZ plane is the antenna's cross-section along the azimuth direction; the Z-axis is the direction of the antenna beam center.

[0064] The beam attitude angle is a general term for yaw, pitch, and roll angles, used to describe the relative relationship between the satellite beam pointing and the satellite body, that is, to describe the transfer matrix from the satellite orbit coordinate system to the SAR antenna coordinate system. As shown in equation (2), a 3-2-1 transfer sequence (yaw-pitch-roll) is adopted, where Let θ(t) be the roll angle, θ(t) be the pitch angle, and ψ(t) be the yaw angle. X (θ) represents rotating the coordinate axis by θ degrees along the positive direction of the right-hand rule, with the positive X-axis as the axis. Y (θ) and H Z The definition of (θ) is similar.

[0065]

[0066] Similarly, the relative relationship between the satellite orbit coordinate system and the SAR antenna coordinate system can be derived from... Figure 3The satellite-borne SAR observation configuration shown 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 angle, γ is the projection of the oblique angle onto the Earth's tangent plane (parallel to the XOY plane) where the nadir point is located, and η is the angle formed by the intersection of the Y-axis with the antenna range plane and the XOZ plane, 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 observation configuration characteristic angles. The analytical relationship between the beam attitude angle and the observation configuration characteristic angle is shown in Equation (3), where β′ is the downward angle containing left and right viewing information. When looking to the right, β′ = β, and when looking to the left, β′ = -β.

[0067]

[0068] Taking the first and second order derivatives of equation (3) respectively, we can obtain the higher order forms of the beam attitude angle, as shown in equations (4) and (5).

[0069]

[0070]

[0071] In equation (3), η can be set by the user during the observation period to balance swath width and azimuth resolution; the analytical expressions for β and γ are given by equation (6), where k1, k2, and k3 are the unit column vectors of the three coordinate axes of the satellite orbit system in the Earth inertial frame; L3 is the position vector of the satellite to the wave foot. The first and second derivatives of β and γ are given by equations (7) and (8).

[0072]

[0073]

[0074]

[0075] The first and second derivatives of k1, k2, k3 and L3 in equations (7) and (8) are shown in equations (9) to (11), where ω is the average angular velocity of the satellite orbit; w e P is the Earth's rotational angular velocity. foot (t) and P sat (t) represents the position coordinates of the wave foot and the satellite in Earth's inertial system at time t, respectively. sat (t) represents the ground inertial acceleration at the wave foot; ||·||2 is the L2 norm operator; P ⊥Z P is the projection matrix of the XOY plane; foot.f (t), V foot.f (t), a foot.f (t) represents the position of the lower wave foot of the Earth-solid system; H ecef2eci(t) is the transfer matrix from the Earth-fixed frame to the Earth-inertial frame at time t.

[0076]

[0077]

[0078]

[0079] According to equations (3) to (11), the beam attitude angle (yaw, pitch, roll) and its first and second derivatives can be directly obtained from the position, velocity, and acceleration of the ground-fixed wave foot at a certain instant, thus providing support for the planning of the surveying zone.

[0080] Step 3: Input the target point sequence and solve the feasible wave foot trajectory under the beam attitude angle constraint according to the wave foot optimization algorithm.

[0081] The flowchart of the wave-foot optimization algorithm is as follows: Figure 4 As shown, the specific steps include the following:

[0082] First, input the target point sequence and satellite startup time generated in step one, and then calculate the selectable motion direction of the wave foot, as shown in equations (12) to (14). Where P foot.f (i) represents the position of the wave foot ground-solid system at time i, p i It is its unit vector; P T (j) represents the fixed position of the j-th tracking target, satisfying j∈[1,2,...,M], where M is the number of target points; the normal vector of the plane containing the two vectors is n. ij ;v ij For the Earth's surface from P foot.f (i) to P T (j) is the unit direction vector; ||·||2 is the 2-norm operator.

[0083]

[0084] v i Let k be the unit vector of the wave foot velocity in the ground-solid system at time i; ij For v ij With v i The angle between the two sides; N is the number of possible motion directions for the wave foot, n is the index of the possible motion direction, satisfying n∈[1,2,...,N], and k(n) is the angle between the nth possible direction; v′ ij (n) represents the unit vector of the nth optional direction for the jth target in the Earth-fixed system at time i.

[0085]

[0086]

[0087] V′ ij (n) represents the velocity of the j-th target in the Earth-fixed system at time i in the n-th optional direction; a′ ij (n) indicates the use of V′ ij (n) The acceleration of the j-th target in the Earth-fixed system at time i; P′ ij (n) indicates the use of V′ ij (n) and a′ ij (n) The coordinates of the wave foot in the ground-fixed system at the (i+1)th time after the wave foot, V foot.f (i) represents the velocity of the wave foot on the solid system at time i.

[0088]

[0089] P′ in equation (15) ij (n), V′ ij (n), a′ ij Substituting (n) into step two, we can directly calculate the attitude angles and their first and second derivatives for each selectable direction. Then, based on equation (16), we select the index n of the optimal direction that meets the satellite attitude angle constraints. i , where F(·) is the attitude angle constraint, G(·) is the attitude angle change rate constraint, and H(·) is the attitude angle change acceleration constraint. Thus, the acceleration at time i and the position and velocity of the wave foot in the ground-solid system at time i+1 are determined, as shown in equation (17).

[0090]

[0091]

[0092] The criterion for switching the tracking target is shown in equation (18). Switching the tracking target can be performed if any condition of this equation is met, where R... set The set length threshold has a range of values ​​within a distance width.

[0093]

[0094] Step 4: Iterate through the relevant parameters in the wave-foot optimization algorithm, and select the optimal wave-foot trajectory based on the criterion of minimizing the target point deviation, as follows:

[0095] Let L foot.f (R set The length threshold R in equation (18) is used. set The wave foot trajectory obtained by tracking. In practical applications, the attitude angles need to be further fitted with a polynomial to facilitate onboard command transmission and control. Based on the fitted attitude angles, the fitted wave foot trajectory L′ can be calculated. foot.f (R set ). For Rset By iterating, and then using the minimum target point deviation criterion in equation (19), the optimal wave foot trajectory can be selected. in The optimal threshold is obtained based on this criterion, and inf(·) is used to find the infimum of the function.

[0096]

[0097] Simulation Experiment: Simulation parameters for mapping zone planning in spaceborne SAR non-track bending imaging mode are shown in Table 1.

[0098] Table 1. List of Simulation Parameters for Mapping Strip Planning in Spaceborne SAR Non-Trajectory Curved Imaging Mode

[0099]

[0100] First, to verify the advantages of the multi-target observation imaging strait optimization method in the non-track bending imaging mode of spaceborne SAR in solving the problem of difficult design of multi-target observation imaging straits along the scene under beam maneuver constraints, a set of target points (29 in total) were planned for observation tasks using the traditional imaging strait design method (i.e., the method of directly fitting the point target positions) under the parameters in Table 1. These were divided into two target sequences, as follows: Figure 5 As shown in (a). Next, we will take the target sequence on the left as an example (i.e. Figure 5 (b) The 21 target points indicated by "*" are used to design the wave foot for this set of target sequences. The satellite maneuver constraints for this simulation are: beam attitude angle less than or equal to 45 degrees, attitude angular velocity less than or equal to 0.8 degrees / s, and attitude angular acceleration less than or equal to 0.08 degrees / s. 2 .exist Figure 5 (b) shows the wave feet planned using the conventional method (dashed line) and the method proposed in this invention (solid line), respectively; Figure 5 (c) The shortest distances from the 21 target points to the wave foot centers of the two mapping zones are given. "o" represents the traditional method, where 7 targets are outside the observation range; "*" represents the method proposed in this invention, where only 1 target is outside the observation range. The true values ​​of the attitude angles and their velocities and accelerations for both methods are shown below. Figure 6 As shown, the solid line represents the result generated by the algorithm proposed in this invention. It can be seen that both algorithms satisfy the satellite maneuver constraints, but this algorithm has more relaxed requirements for maneuver constraints, meaning it covers more targets and has lower requirements for beam maneuvering, which has significant advantages. Furthermore, to verify the correctness of the analytical expressions for the beam attitude angle and its first and second derivatives... Figure 7 The analytical expressions for the beam attitude angle and its first and second derivatives proposed in this invention are given, along with the errors obtained from code simulation. It can be seen that the beam attitude angle error is within 10... -13The error of its first and second derivatives is on the order of magnitude of 10. -4 The degree is on the order of magnitude, much smaller than the true values ​​of the beam attitude angle and its first and second derivatives, verifying the correctness of the analytical expression proposed in this invention.

[0101] In summary, the above are merely preferred embodiments of the present invention and are not intended to limit the scope of protection of the present invention. 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 optimizing the imaging swath of a space-borne SAR non-streaked squinted imaging mode, characterized in that, It comprises the following steps: Step one, planning input target point set, generating several target point sequences; Step two, establishing coordinate system, obtaining analytical expression of beam attitude angle and its high order derivative; wherein, analytical relation of beam attitude angle and observation configuration characteristic angle is as follows: where β is the lower viewing angle, β' is the lower viewing angle containing the right and left viewing information, β' = β when right viewing and β' = -β when left viewing; γ is the projection of the oblique viewing angle on the Earth's tangent plane where the subsolar point is located; η is the beam projection angle, which is used to represent the rotation angle of the projection ellipse and can be set during observation to balance the width and azimuth resolution; β, γ, and η are collectively referred to as observation configuration characteristic angles; is the roll angle, θ is the pitch angle, and ψ is the yaw angle, collectively referred to as the beam attitude angle; First and second order differential of analytical relation of beam attitude angle and observation configuration characteristic angle is obtained, which is high order form of beam attitude angle, respectively as follows: Step three, input target point sequence, solving feasible wave foot trajectory under beam attitude angle constraint according to wave foot optimization algorithm process; the wave foot optimization algorithm process is: input satellite start time and target point sequence generated in step one, calculating position, velocity and acceleration of wave foot optional motion direction at next time from current point, calculating wave foot attitude angle and its high order derivative based on analytical expression of beam attitude angle and its high order derivative obtained in step two, selecting wave foot motion direction at next time based on attitude constraint, then judging whether all target points are traversed, if yes, outputting wave foot trajectory, otherwise, judging whether to switch tracking target point, if yes, setting next target point as tracking target, then returning to recalculate position, velocity and acceleration of wave foot optional motion direction at next time, otherwise, directly returning to recalculate position, velocity and acceleration of wave foot optional motion direction at next time, until all target points are traversed, outputting wave foot trajectory; Step four, changing judgment threshold in tracking target switching criterion, iterating relevant parameters in wave foot optimization algorithm, selecting optimal wave foot trajectory according to minimum target point deviation criterion.

2. The method of claim 1, wherein, The wave foot optimization algorithm specifically comprises the following steps: First, input target point sequence generated in step one and satellite start time parameter, then calculate wave foot optional motion direction: where P foot.f (i) is the wave foot ground-fixed position, p i is its unit vector; P T (j) is the jth tracking target station fixed position, satisfying j ∈ [1, 2, K, M], M is the number of target points; the normal vector of the plane where the two vectors lie is n ij ; v ij is the unit direction vector from P foot.f (i) to P T (j) on the earth's surface; ||·||2 is the two-norm operator; v i is the unit vector of the wave foot earth-fixed velocity at the ith moment; k ij is the angle between v ij and v i ; N is the number of wave foot selectable motion directions, n is the selectable motion direction serial number, satisfying n ∈ [1, 2, K, N], k(n) is the angle opposite the nth selectable direction; v′ ij (n) represents the unit vector of the nth selectable direction of the jth target in the earth-fixed coordinate system at the ith moment, H Y (θ) represents rotating the coordinate axis by θ degrees along the positive direction of the right-hand rule with the positive direction of the Y axis as the axis; V' ij (n) represents the velocity of the jth target in the earth-fixed frame in the nth alternative direction at the ith time; a' ij (n) represents the velocity of the jth target in the earth-fixed frame in the nth alternative direction at the ith time using V' ij (n) represents the acceleration of the jth target in the earth-fixed frame after using V' P' ij (n) represents the use of V' ij (n) and a' ij (n) the i+1 time wave foot body-fixed coordinate, V foot.f (i) is the i time wave foot body-fixed velocity, dt is the time differential P′ ij (n), V′ ij (n), a′ ij (n) into the analytical expression obtained in step two, directly solve the attitude angle of each selectable direction and its first and second order derivatives, and then determine the optimal direction according to the sequence number n of the optimal direction that meets the satellite attitude angle constraint i where F(·) is the attitude angle constraint, G(·) is the attitude angle change speed constraint, and H(·) is the attitude angle change acceleration constraint, thereby determining the acceleration at the i th moment, the position and velocity of the wave foot in the ground-based system at the i+1 th moment 3. The method of claim 1, wherein, The tracking target switching criterion is: where P foot.f (i) is the i-th time wave foot body-fixed position, P T (j) is the j-th tracking target body-fixed position, satisfying j ∈ [1, 2, K, M], M is the number of target points; v ij is the unit direction vector of the earth's surface from P foot.f (i) to P T (j); ||·||2 is the two-norm operator; R set is the set length threshold, which is within a distance range; v i is the unit vector of the i-th time wave foot body-fixed velocity, and the superscript H represents the transpose.

4. The method according to any one of claims 1 to 3, characterized in that, Target point planning method process comprises target point clustering and target sequence division; wherein, specific steps of target point clustering are as follows: Step 11, marking all points in set as 1, 2, K, M, calculating distance of each point in target point set to all points, and comparing with clustering threshold, if less than the threshold, judging as 1, otherwise as 0; putting result into MxM matrix according to target point serial number, generating target distance matrix; Step 12, starting from first row, finding column number i, j, k, K of matrix element with value 1, recording the serial number and setting all elements of i, j, k, K row and i, j, k, K column as 0; Step 13, repeating step 12 M times to traverse all rows of target distance matrix, recording all serial numbers as clustered points; Specific steps of target sequence division are as follows: Step 21: Sort all target points after clustering from low to high dimensionality. Let the point set be T = {T1, T2, K, T...} N }; Step 22, setting S1(1) = T1, i = 1, j = 2, according to following judgment condition: If yes, then S1(i+1) = T j If no, then j = j + 1, where S1(i) is the ith target point of the first divided sequence; repeat the above operation until j = N, and the divided target sequence S1 is obtained. Step 23, set T1 = T - S1, perform step 22 on T1 to get S2 and T2, repeat step 22 until Then output the divided k target sequences.

5. The method of claim 3, wherein, The minimum target point deviation criterion is: where L' = L - L0 foot.f (R set ) is the fitted wave foot trajectory, is the best threshold value based on the criterion, and inf(·) is the infimum of the function.

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