CN115639556A - Optimizing method of imaging zone in non-track-curved imaging mode of spaceborne SAR - Google Patents

Abstract

The present invention proposes a method for optimizing the imaging zone of the spaceborne SAR non-track-curving imaging mode, which can solve the problems of difficult design of multi-target observation imaging zone and large target point deviation when there are beam maneuver constraints in the space-borne SAR non-track-curving imaging mode. To solve the problem, realize the optimization of multi-objective observation imaging zone. The invention firstly plans the observation order of the target points not distributed along the track, and then gives the analytical expression of the beam attitude angle and its high-order derivative for the first time, and proposes the wave foot tracking algorithm and the minimum deviation point criterion on this basis. Design and generate the optimal non-along-track imaging zone that conforms to the beam maneuvering constraints, and solve the problems of difficult design of multi-target observation imaging zone and large target point deviation when there are beam maneuvering constraints in the spaceborne SAR non-along-track bending imaging mode. A large amount of computing resources are consumed by the simulation calculation of the attitude angle, and the optimization of the multi-target observation imaging zone of the spaceborne SAR non-along-track bending imaging mode is realized.

Description

Optimizing method of imaging zone in non-track-curved imaging mode of spaceborne SAR

technical field

The invention relates to the technical field of Synthetic Aperture Radar (SAR for short), in particular to a method for optimizing an imaging zone of a spaceborne SAR non-along-track curved imaging mode.

Background technique

The non-track imaging mode is a unique working mode of spaceborne SAR. Compared with the traditional space-borne SAR, the space-borne off-track SAR can directly generate the mapping strip along the target terrain by continuously adjusting the beam pointing in the elevation dimension and the azimuth dimension, instead of the traditional generation of the mapping strip along the satellite orbit, which makes it useful for certain Some "non-satellite track scenarios" such as seismic belts and coastline imaging fundamentally reduce the redundancy of echo data, and significantly improve the observation efficiency of spaceborne SAR for narrow and long scenes, which has unique advantages.

During data acquisition, satellites generally make observations by controlling the beam attitude angle. Since the direction of the "oblique scene" is mostly irregular, it is necessary to simultaneously design the beam attitude angle and its higher-order derivatives during data acquisition to generate irregular swaths. At the same time, the satellite load will also impose constraints on the beam attitude angle and its high-order derivatives to ensure the safe and stable operation of the satellite. Therefore, how to realize the swath planning along the scene under the given beam attitude angle and its higher-order derivative constraints has become an important problem to be solved in the non-track imaging mode. However, due to the lack of theoretical guidance and related algorithm support, the traditional methods generally do not consider beam maneuvering in the design, but judge whether the constraints are met after the design is completed, resulting in problems such as difficult imaging zone planning and large deviation of target points.

Contents of the invention

In view of this, the present invention proposes a method for optimizing the imaging zone of the spaceborne SAR non-curving along the track imaging mode, which can solve the problem of difficult design of the imaging zone for multi-object observation when there are beam maneuver constraints in the non-curving along the track imaging mode of the spaceborne SAR , to realize the optimization of multi-objective observation imaging band.

In order to achieve the above object, a method for optimizing the imaging zone of a spaceborne SAR non-along-track curved imaging mode of the present invention comprises the following steps:

Step 1. Plan the input target point set and generate several target point sequences;

Step 2, establish a coordinate system, and obtain the analytical expression of the beam attitude angle and its higher-order derivatives;

Step 3: Input the sequence of target points, and solve the feasible wave foot trajectory that meets the constraints of the beam attitude angle according to the wave foot optimization algorithm flow; the wave foot optimization algorithm flow is: input the satellite startup time and the target points generated in step Sequence, starting from the current point to calculate the position, velocity and acceleration of the optional movement direction of the wave foot at the next moment, according to the analytical expression of the beam attitude angle and its high-order derivative obtained in step 2, calculate the wave foot attitude angle and Its high-order derivative, based on the attitude constraints, screens out the movement direction of the wave foot at the next moment, and then judges whether to traverse all the target points, if so, outputs the wave foot trajectory, otherwise judges whether to switch the tracking target point, and if so, the next target point Set it as the tracking target, and then return to recalculate the position, velocity and acceleration of the optional movement direction of the wave foot at the next moment, otherwise directly return to recalculate the position, velocity and acceleration of the optional movement direction of the wave foot at the next moment, until all Target point, output wave foot trajectory;

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

Among them, the analytical relationship between the beam attitude angle and the observation configuration characteristic angle is as follows:

为滚转角，θ为俯仰角，ψ为偏航角，统称为波束姿态角；Wherein β is the downward angle of view, and β' is the downward angle of view that includes the information of the left and right views, when the right view is β'=β, and when the left view is β'=-β; η is the beam projection angle, which is used to represent the rotation angle of the projected ellipse, which can be set during the observation period to balance the width and azimuth resolution; β, γ, and η are collectively referred to as the observation configuration characteristic angle;

is the roll angle, θ is the pitch angle, and ψ is the yaw angle, collectively referred to as the beam attitude angle;

The high-order form of the beam attitude angle is obtained by taking the first-order and second-order differentials of the analytical relational expressions of the beam attitude angle and the observation configuration characteristic angle, respectively:

Wherein, the wave-foot-based optimization algorithm specifically includes the following steps:

First input the target point sequence generated in step 1 and the satellite start-up time and other parameters, and then calculate the optional movement direction of the wave foot:

where P _foot.f (i) is the fixed position of the wave foot at the i-th moment, and p _i is its unit vector; P _T (j) is the fixed position of the jth tracking target, satisfying j∈[1,2 ,...,M], M is the number of target points; the normal vector of the plane where the two vectors are located is n _ij ; v _ij is the unit direction vector from P _foot.f (i) to P _T (j) on the surface of the earth; ||·|| ₂ is the two-norm operator; v _i is the unit vector of the ground-solid velocity of the wave foot at the i-th moment; k _ij is the angle between v _ij and v _i ; N is the number of optional motion directions of the wave foot , n is the serial number of the optional motion direction, satisfying n∈[1,2,…,N], k(n) is the angle opposite to the nth optional direction; v′ _ij (n) represents the The unit vector of the n-th optional direction of the j-th target in the solid system, H _Y (θ) represents the positive direction of the Y-axis as the axis, and rotates the coordinate axis by θ degrees along the positive direction of the right-hand rule;

V' _ij (n) represents the speed of the nth optional direction of the jth target in the ground-fixed system at the _i -th moment; a' _ij (n) represents the ground-fixed The acceleration of the jth target in the system; P′ _ij (n) represents the ground-solid system coordinates of the wave foot at the i+1th moment after using V′ _ij (n) and a′ _ij (n), V _foot.f (i) is the velocity of the wave-foot ground solid system at the i-th moment, and dt is the time differential;

选出符合卫星姿态角约束下的最优方向的序号n_i，其中F(·)为姿态角约束，G(·)为姿态角变化速度约束，H(·)为姿态角变化加速度约束，进而确定第i时刻的加速度，第i+1时刻波足在地固系的位置、速度

Put P′ _ij (n), V′ _ij (n), a′ _ij (n) into the analytical expression obtained in step 2, and directly calculate the attitude angle and its first and second order derivatives in each optional direction, and then according to

Select the serial number n _i that meets the optimal direction under the satellite attitude angle constraint, where F( ) is the attitude angle constraint, G( ) is the attitude angle change speed constraint, H( ) is the attitude angle change acceleration constraint, and then Determine the acceleration at the i-th moment, the position and velocity of the wave foot on the ground at the i+1th moment

Wherein, the switching criterion of the tracking target is:

where P _foot.f (i) is the fixed position of the wave foot at the i-th moment, and P _T (j) is the fixed position of the jth tracking target, satisfying j∈[1,2,...,M] , M is the number of target points; 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; R _set is the setting The length threshold of , and its value range is within a distance width; v _i is the unit vector of the wave-foot ground-solid velocity at the i-th moment, and the superscript H represents transposition.

Among them, the target point planning method process includes target point clustering and target sequence division; wherein, the specific steps of target point clustering are:

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, and compare it with the clustering threshold, if it is less than the threshold, it will be judged as 1 , otherwise it is 0; put the result into an M×M matrix according to the target point number to generate the target distance matrix;

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 serial number and put the i, j, k, ... row and the All elements of i,j,k,... columns are set to 0;

Step 13, repeating step 12 M times, traversing all the rows of the target distance matrix, and all the serial numbers recorded are the clustered points;

The specific steps of target sequence division are as follows:

Step 21, sort all target points after clustering from low latitude to high latitude, set point set as T={T ₁ , T ₂ ,...,T _N };

Step 22, set S ₁ (1)=T ₁ , i=1, j=2, according to the following judgment conditions:

If it is satisfied, set S ₁ (i+1)=T _j , if it is not satisfied, set j=j+1, where S ₁ (i) is the i-th target point of the first sequence divided; repeat the above operations Until j=N, the divided target sequence S ₁ can be obtained;

则输出所划分出的k个目标序列。Step 23, set T ₁ =TS ₁ , perform step 22 on T ₁ to obtain S ₂ and T ₂ , repeat step 22 until

Then output the divided k target sequences.

Wherein, the minimum criterion of the target point deviation is:

为基于该准则得到的最佳阈值，inf(·)为求函数下确界.Among them, L′ _foot.f (R _set ) is the fitted wave foot trajectory,

is the optimal threshold obtained based on this criterion, and inf( ) is the infimum of the function.

Beneficial effect:

The invention firstly plans the observation order of the target points not distributed along the track, and then gives the analytical expression of the beam attitude angle and its high-order derivative for the first time, and on this basis, proposes the wave foot tracking algorithm and the minimum deviation point criterion to Design and generate the optimal non-along-track imaging zone that conforms to the beam maneuvering constraints, and solve the problems of difficult design of multi-target observation imaging zone and large target point deviation when there are beam maneuvering constraints in the spaceborne SAR non-along-track bending imaging mode. A large amount of computing resources are consumed by the simulation calculation of the attitude angle, and the optimization of the multi-target observation imaging zone of the spaceborne SAR non-along-track bending imaging mode is realized.

Description of drawings

Fig. 1 is a flow chart of the method for optimizing the multi-target observation imaging zone in the spaceborne SAR non-along-track curved imaging mode of the present invention.

Fig. 2 is a flow chart of the target point planning method of the present invention.

Fig. 3 is a schematic diagram of the observation configuration of the spaceborne SAR non-track-curving imaging mode according to the present invention.

Fig. 4 is a flow chart of wave foot optimization algorithm in the present invention.

Fig. 5 shows the planning results and target coverage of the method of the present invention and the traditional method in the embodiment of the present invention.

Fig. 6 is a comparison diagram of the beam attitude angle and its first and second order derivatives between the method of the present invention and the traditional method in the embodiment of the present invention.

Fig. 7 is the error of the analytical expression of the beam attitude angle and its first and second order derivatives and the code simulation results used in the embodiment of the present invention.

Detailed ways

The present invention will be described in detail below with reference to the accompanying drawings and examples.

In the non-track-curving imaging mode of spaceborne SAR, the traditional imaging zone design method does not consider the beam maneuvering constraints in the design, and the design results often do not meet the actual beam maneuvering constraints and cannot be used; in addition, the design results are far from the target point. Large, it is easy to lose the target during data acquisition. The method proposed in the present invention first plans the mission target, then obtains the wave foot trajectory satisfying the beam maneuvering constraints based on the proposed wave foot optimization algorithm, and then iteratively gives the optimal multi-object observation imaging zone design based on the minimum deviation point criterion As a result, the problems of difficult design and realization and large deviation of target points in traditional methods are solved. The flow chart of the method for optimizing the multi-target observation imaging zone of the space-borne SAR non-along-track curved imaging mode described in the present invention is shown in Figure 1, and the present invention includes the following steps:

Step 1. Plan the input target point set and generate several target point sequences;

The process flow of the target point planning method is shown in Figure 2, including target point clustering and target sequence division. Among them, the specific steps of target point clustering are:

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 points, and compare with the clustering threshold, if less than The threshold is judged as 1, otherwise it is 0. Put the result into an M×M matrix according to the target point number to generate a target distance matrix;

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 serial number and put the i, j, k, ... row and the All elements of i,j,k,... columns are set to 0;

Step 13, repeating step 12 M times, traversing all the rows of the target distance matrix, and all the serial numbers recorded are the points to be clustered.

The specific steps of target sequence division are as follows:

Step 21, sort all target points after clustering from low latitude to high latitude, and set the point set as T={T ₁ , T ₂ , . . . , T _N }.

Step 22, set S ₁ (1)=T ₁ , i=1, j=2, according to the judgment condition given by formula (1), if it is satisfied, then set S ₁ (i+1)=T _j , if not Then let j=j+1, wherein S ₁ (i) is the i-th target point of the first divided sequence. By repeating the above operations until j=N, the divided target sequence S ₁ can be obtained.

则输出所划分出的k个目标序列。Step 23, set T ₁ =TS ₁ , execute step 22 on T ₁ to obtain S ₂ and T ₂ , repeat step 22 until

Then output the divided k target sequences.

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:

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 motion velocity; the Z-axis vector is in the satellite orbit plane and points to the center of the earth; the Y-axis follows the right-hand rule Solution: In the SAR antenna coordinate system, the positive direction of the X-axis is in the same direction as the satellite motion direction, and the XOZ plane is the section of the antenna along the azimuth direction; the Z-axis is the center pointing of the antenna beam.

为滚转角，θ(t)为俯仰角，ψ(t)为偏航角，H_X(θ)代表以X轴正方向为轴，沿着右手定则的正方向将坐标轴旋转θ度,H_Y(θ)和H_Z(θ)的定义与之类似。Beam attitude angle is a general term for yaw, pitch, and roll angles, which is used to describe the relative relationship between the satellite beam pointing to 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 formula (2), a 3-2-1 rotation sequence (yaw-pitch-roll) is adopted, where

is the roll angle, θ(t) is the pitch angle, ψ(t) is the yaw angle, H _X (θ) represents the positive direction of the X-axis as the axis, and rotates the coordinate axis by θ degrees along the positive direction of the right-hand rule, H _Y (θ) and H _Z (θ) are defined similarly.

Similarly, the relative relationship between the satellite orbit coordinate system and the SAR antenna coordinate system can be obtained from the spaceborne SAR observation configuration shown in Figure 3, where the satellite orbit coordinate system is XYZ, and the SAR antenna coordinate system is r ₁ -r ₂ -r ₃ ; the antenna distance plane is r ₂ -or ₃ ; the antenna azimuth plane is r ₁ -or ₃ ; β is the downward angle of view; η is the angle formed by the Y-axis and the intersection line of the antenna distance plane and XOZ, which is called the beam projection angle, and is used to represent the rotation angle of the projected ellipse; β, γ, and η are collectively called the observation configuration characteristic angle. The analytical relationship between the beam attitude angle and the observation configuration characteristic angle is shown in formula (3), where β' is the downward viewing angle including the left and right view information, and β'=β for the right view, and β'=-β for the left view.

The high-order form of the beam attitude angle can be obtained by taking the first-order and second-order differentials of equation (3), as shown in equations (4) and (5).

In Equation (3), η can be set during the observation period to balance the width and azimuth resolution; the analytical expressions of β and γ are given by Equation (6), where k ₁ , k ₂ , and k ₃ are satellite orbit systems The unit column vector of the three coordinate axes in the geo-inertial system; L ₃ is the position vector from the satellite to the wave foot. The first and second derivatives of β and γ are given by formulas (7) and (8).

The first and second derivatives of k ₁ , k ₂ , k ₃ and L ₃ in formulas (7) and (8) are shown in formulas (9) to (11), where ω is the average angular velocity of the satellite orbit; w _e is the earth’s Angular velocity of rotation; P _foot (t) and P _sat (t) are the position coordinates of the wave foot and the satellite’s inertial system at time t respectively, a _sat (t) is the acceleration of the ground inertial system of the wave foot; ||·|| ₂ is two Norm operator; P _⊥Z is the XOY plane projection matrix; P _foot.f (t), V _foot.f (t), a _foot.f (t) are the wave foot positions under the ground-solid system; H _ecef2eci (t ) is the transfer matrix from the fixed system to the inertial system at time t.

According to formulas (3)-(11), the value of the beam attitude angle (yaw, pitch, roll) and its first and second orders can be obtained directly by using the position, velocity, and acceleration of the ground wave foot at a certain instant. Derivatives, thus providing support for swath planning.

Step 3: Input the target point sequence, and solve the feasible wave foot trajectory under the constraints of the beam attitude angle according to the wave foot follow-through algorithm process;

The flow chart of wave foot optimization algorithm is shown in Figure 4, which specifically includes the following steps:

First input the target point sequence generated in step 1 and the satellite start-up time and other parameters, and then calculate the optional movement direction of the wave foot, as shown in equations (12)-(14). where P _foot.f (i) is the fixed position of the wave foot at the i-th moment, and p _i is its unit vector; P _T (j) is the fixed position of the jth tracking target, satisfying j∈[1,2 ,...,M], M is the number of target points; the normal vector of the plane where the two vectors are located is n _ij ; v _ij is the unit direction from P _foot.f (i) to P _T (j) on the surface of the earth Vector; ||·|| ₂ is a two-norm operator.

v _i is the unit vector of the ground-solid velocity of the wave foot at the i-th moment; k _ij is the angle between v _ij and v _i ; N is the number of optional movement directions of the wave foot, and n is the number of the optional movement direction, satisfying n∈[ 1,2,...,N], k(n) is the angle opposite to the nth optional direction; v′ _ij (n) represents the nth Unit vector for optional orientation.

V' _ij (n) represents the speed of the nth optional direction of the jth target in the ground-fixed system at the _i -th moment; a' _ij (n) represents the ground-fixed The acceleration of the jth target in the system; P′ _ij (n) represents the ground-solid system coordinates of the wave foot at the i+1th moment after using V′ _ij (n) and a′ _ij (n), V _foot.f (i) is the fixed velocity of wave feet at the i-th moment.

Bringing P′ _ij (n), V′ _ij (n), and a′ _ij (n) in formula (15) into step 2 can directly calculate the attitude angle and its first and second order derivatives in each optional direction, and then According to formula (16), select the sequence number n _i that meets the optimal direction under the satellite attitude angle constraint, where F(·) is the attitude angle constraint, G(·) is the attitude angle change speed constraint, H(·) is the attitude angle Vary acceleration constraints. Furthermore, the acceleration at the i-th moment is determined, and the position and velocity of the wave foot at the ground-solid system at the i+1th moment are shown in formula (17).

The switching criterion of the tracking target is shown in formula (18). The tracking target can be switched if any condition of the formula is satisfied, where R _set is the set length threshold, and its value range is within a distance width .

Step 4. Iterate the relevant parameters in the wave foot optimization algorithm, and select the optimal wave foot trajectory according to the minimum deviation criterion of the target point, as follows:

其中

为基于该准则得到的最佳阈值，inf(·)为求函数下确界。Let L _foot.f (R _set ) be the wave foot track obtained by using the length threshold R _set in formula (18). In practical applications, it is necessary to perform polynomial fitting on the attitude angle to facilitate on-board command transmission and control, and the fitted wave foot trajectory L′ _foot.f (R _set ) can be calculated according to the fitted attitude angle. Iterate on R _set , and then select the optimal wave foot trajectory according to the minimum criterion of the target point deviation in formula (19)

in

is the optimal threshold obtained based on this criterion, and inf(·) is the infimum of the function.

Simulation experiment: Table 1 shows the simulation parameters of the surveying zone planning in the non-along-track curved imaging mode of spaceborne SAR.

Table 1. Simulation parameter list of mapping zone planning in spaceborne SAR non-along-track curved imaging mode

First of all, in order to verify the advantages of the multi-target observation imaging zone optimization method of spaceborne SAR non-along-track curved imaging mode in solving the problem of difficult design of multi-target observation imaging zone along the scene under the constraint of beam maneuvering, the traditional The imaging zone design method (that is, the method of directly fitting the point target position) performs observation task planning on a set of target points (29 in total), which are divided into two target sequences, as shown in Fig. 5(a). Next, we take the target sequence on the left as an example (that is, the 21 target points represented by "*" in Figure 5(b)), and conduct wave foot design on this group of target sequences. The satellite maneuvering constraints for this simulation are: the beam attitude angle is less than or equal to 45deg, the attitude angular velocity is less than or equal to 0.8deg/s, and the attitude angular acceleration is less than or equal to 0.08deg/s ² . In Fig. 5(b), the wave feet planned by the traditional method (dotted line) and the method proposed by the present invention (solid line) are shown respectively; Fig. 5(c) provides 21 target points respectively to the above two surveying and mapping The shortest distance with the center of the wave foot, where "o" represents that with the traditional method, a total of 7 targets are beyond the observation range, and "*" represents that with the method proposed by the present invention, only 1 target is beyond the observation range. The true value of the attitude angle and its velocity and acceleration of the two methods are shown in Figure 6. The solid line represents the results generated by the proposed algorithm of the present invention. It can be seen that the above two algorithms all meet the satellite maneuver constraints, but the algorithm does not require the maneuver constraints. The requirements are looser, that is, to cover more targets and have lower requirements for beam maneuvering, which has significant advantages. In addition, in order to verify the correctness of the analytical expressions of the beam attitude angle and its first and second derivatives. Fig. 7 has provided the error that adopts the beam attitude angle that the present invention proposes and its first, second order derivative analytical expression and code emulation seek, visible beam attitude angle error is on the order of magnitude of ^10-13 degree, and its first, second order derivative The error is on the order of 10 ^-4 degrees, which is far smaller than the true value of the beam attitude angle and its first and second order derivatives, which verifies the correctness of the analytical expression proposed by the present invention.

To sum up, the above are only preferred embodiments of the present invention, and are not intended to limit the protection scope of the present invention. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principles of the present invention shall be included within the protection scope of the present invention.

Claims (6)

1. a space-borne SAR non-along-track curved imaging mode imaging band optimization method, is characterized in that, comprises the steps: Step 1. Plan the input target point set and generate several target point sequences; Step 2, establish a coordinate system, and obtain the analytical expression of the beam attitude angle and its higher-order derivatives; Step 3: Input the sequence of target points, and solve the feasible wave foot trajectory that meets the constraints of the beam attitude angle according to the wave foot optimization algorithm flow; the wave foot optimization algorithm flow is: input the satellite startup time and the target points generated in step Sequence, starting from the current point to calculate the position, velocity and acceleration of the optional movement direction of the wave foot at the next moment, according to the analytical expression of the beam attitude angle and its high-order derivative obtained in step 2, calculate the wave foot attitude angle and Its high-order derivative, based on the attitude constraints, screens out the movement direction of the wave foot at the next moment, and then judges whether to traverse all the target points, if so, outputs the wave foot trajectory, otherwise judges whether to switch the tracking target point, and if so, the next target point Set it as the tracking target, and then return to recalculate the position, velocity and acceleration of the optional movement direction of the wave foot at the next moment, otherwise directly return to recalculate the position, velocity and acceleration of the optional movement direction of the wave foot at the next moment, until all Target point, output wave foot trajectory; Step 4: Change the judgment threshold in the switching criterion of the tracking target, iterate the relevant parameters in the wave foot tracking optimization algorithm, and select the optimal wave foot trajectory according to the minimum deviation criterion of the target point. 2. the method for claim 1, is characterized in that, the analytic relation of beam attitude angle and observation configuration characteristic angle is as follows:

Wherein β is the downward angle of view, and β' is the downward angle of view that includes the information of the left and right views, when the right view is β'=β, and when the left view is β'=-β; η is the beam projection angle, which is used to represent the rotation angle of the projected ellipse, which can be set during the observation period to balance the width and azimuth resolution; β, γ, and η are collectively referred to as the observation configuration characteristic angle;

is the roll angle, θ is the pitch angle, and ψ is the yaw angle, collectively referred to as the beam attitude angle; The high-order form of the beam attitude angle is obtained by taking the first-order and second-order differentials of the analytical relational expressions of the beam attitude angle and the observation configuration characteristic angle, respectively:

3. method as claimed in claim 2, is characterized in that, described wave foot search algorithm specifically comprises the steps: First input the target point sequence generated in step 1 and the satellite start-up time and other parameters, and then calculate the optional movement direction of the wave foot:

where P _foot.f (i) is the fixed position of the wave foot at the i-th moment, and p _i is its unit vector; P _T (j) is the fixed position of the jth tracking target, satisfying j∈[1,2 ,...,M], M is the number of target points; the normal vector of the plane where the two vectors are located is n _ij ; v _ij is the unit direction from P _foot.f (i) to P _T (j) on the surface of the earth vector; ||·|| ₂ is the two-norm operator; v _i is the unit vector of the ground-solid velocity of the wave foot at the i-th moment; k _ij is the angle between v _ij and v _i ; N is the optional movement of the wave foot The number of directions, n is the serial number of the optional movement direction, satisfying n∈[1,2,...,N], k(n) is the angle opposite to the nth optional direction; v′ _ij (n) represents the The unit vector of the n-th optional direction of the j-th target in the ground-fixed system at time i, H _Y (θ) represents the positive direction of the Y-axis as the axis, and rotates the coordinate axis by θ degrees along the positive direction of the right-hand rule ;

V' _ij (n) represents the speed of the nth optional direction of the jth target in the ground-fixed system at the _i -th moment; a' _ij (n) represents the ground-fixed The acceleration of the jth target in the system; P′ _ij (n) represents the ground-solid system coordinates of the wave foot at the i+1th moment after using V′ _ij (n) and a′ _ij (n), V _foot.f (i) is the velocity of the wave-foot ground solid system at the i-th moment, and dt is the time differential;

Put P′ _ij (n), V′ _ij (n), a′ _ij (n) into the analytical expression obtained in step 2, and directly calculate the attitude angle and its first and second order derivatives in each optional direction, and then according to

Select the serial number n _i that meets the optimal direction under the satellite attitude angle constraint, where F( ) is the attitude angle constraint, G( ) is the attitude angle change speed constraint, H( ) is the attitude angle change acceleration constraint, and then Determine the acceleration at the i-th moment, the position and velocity of the wave foot on the ground at the i+1th moment

4. The method according to claim 1, wherein the switching criterion of the tracking target is:

where P _foot.f (i) is the fixed position of the wave foot at the i-th moment, and P _T (j) is the fixed position of the jth tracking target, satisfying j∈[1,2,...,M] , M is the number of target points; 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; R _set is the setting The length threshold of , and its value range is within a distance width; v _i is the unit vector of the wave-foot ground-solid velocity at the i-th moment, and the superscript H represents transposition. 5. The method according to any one of claims 1-4, wherein the target point planning method flow includes target point clustering and target sequence division; wherein, the specific steps of target point clustering are: 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, and compare it with the clustering threshold, if it is less than the threshold, it will be judged as 1 , otherwise it is 0; put the result into an M×M matrix according to the target point number to generate the target distance matrix; 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 serial number and put the i, j, k, ... row and the All elements of i,j,k,... columns are set to 0; Step 13, repeating step 12 M times, traversing all the rows of the target distance matrix, and all the serial numbers recorded are the clustered points; The specific steps of target sequence division are as follows: Step 21, sort all target points after clustering from low latitude to high latitude, set point set as T={T ₁ , T ₂ ,...,T _N }; Step 22, set S ₁ (1)=T ₁ , i=1, j=2, according to the following judgment conditions:

If it is satisfied, set S ₁ (i+1)=T _j , if it is not satisfied, set j=j+1, where S ₁ (i) is the i-th target point of the first sequence divided; repeat the above operations Until j=N, the divided target sequence S ₁ can be obtained; Step 23, set T ₁ =TS ₁ , perform step 22 on T ₁ to obtain S ₂ and T ₂ , repeat step 22 until

Then output the divided k target sequences. 6. method as claimed in claim 4, is characterized in that, described target point deviation minimum criterion is:

Among them, L′ _foot.f (R _set ) is the fitted wave foot trajectory,

is the optimal threshold obtained based on this criterion, and inf(·) is the infimum of the function.

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