CN115639556A - Imaging band optimization method of satellite-borne SAR non-tracking bending imaging mode - Google Patents
Imaging band optimization method of satellite-borne SAR non-tracking bending imaging mode Download PDFInfo
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Abstract
The invention provides an imaging band optimization method of a satellite-borne SAR non-tracing curved imaging mode, which can solve the problems of difficult design and large target point deviation of a multi-target observation imaging band when beam maneuvering constraint exists in the satellite-borne SAR non-tracing curved imaging mode, and realizes multi-target observation imaging band optimization. The method firstly carries out observation sequence planning on target points distributed along a track, then gives an analytical expression of a beam attitude angle and a high-order derivative of the beam attitude angle for the first time, provides a wave-foot tracking algorithm and a deviation point minimum criterion on the basis to design and generate an optimal non-tracking imaging band conforming to beam maneuver constraints, solves the problems that a multi-target observation imaging band is difficult to design and the target point deviation is large when the beam maneuver constraints exist in a satellite-borne SAR non-tracking curved imaging mode, simultaneously avoids a large amount of loss of computing resources generated by simulating and calculating the attitude angle, and realizes optimization of the multi-target observation imaging band in the satellite-borne SAR non-tracking curved imaging mode.
Description
Technical Field
The invention relates to the technical field of Synthetic Aperture radars (SAR for short), in particular to a satellite-borne SAR non-tracking curved imaging mode imaging band optimization method.
Background
The non-tracking imaging mode is a specific working mode of the satellite-borne SAR. Compared with the traditional satellite-borne SAR, the satellite-borne non-tracking SAR directly generates the mapping band along the target terrain by continuously adjusting the beam pointing direction of the pitch dimension and the azimuth dimension, but not the traditional mapping band generated along the satellite orbit, so that the redundancy of echo data is fundamentally reduced when certain non-tracking satellite scenes such as seismic bands and coastlines are imaged, the observation efficiency of the satellite-borne SAR on long and narrow scenes is remarkably improved, and the method has unique advantages.
During data acquisition, the satellites typically make observations by controlling the beam attitude angle. Since the "oblique scene" trend is mostly irregular, it results in the need to design the beam attitude angle and its higher derivatives simultaneously during data acquisition to generate irregular swaths. Meanwhile, the satellite load also provides constraint on the beam attitude angle and the high-order derivative thereof so as to ensure safe and stable operation of the satellite. Therefore, how to implement swath planning along a scene under the constraint of a given beam attitude angle and its high-order derivatives becomes an important problem to be solved by the non-tracking imaging mode. However, in the conventional methods, because of lack of theoretical guidance and related algorithm support, beam maneuver is generally not considered in design, and whether the beam maneuver meets the constraint or not is judged after the design is completed, so that the problems of difficult imaging band planning, large target point deviation and the like are caused.
Disclosure of Invention
In view of the above, the invention provides an optimization method for imaging strips in a satellite-borne SAR non-tracking curved imaging mode, which can solve the problem that the design of a multi-target observation imaging strip is difficult when beam maneuvering constraints exist in the satellite-borne SAR non-tracking curved imaging mode, and realize the optimization of the multi-target observation imaging strip.
In order to achieve the above object, the imaging band optimization method in the spaceborne SAR non-tracking bending imaging mode of the present invention comprises the following steps:
planning an input target point set to generate a plurality of target point sequences;
establishing a coordinate system to obtain the analytic expression of the beam attitude angle and the high-order derivative thereof;
inputting a target point sequence, and solving the traversable wave foot track conforming to the beam attitude angle constraint according to the wave foot optimization algorithm flow; the wave foot optimization algorithm flow comprises the following steps: inputting satellite starting time and a target point sequence generated in the first step, calculating the position, the speed and the acceleration of a wave foot selectable motion direction at the next moment from the current point, calculating the wave foot attitude angle and the high-order derivative thereof of each selectable direction according to the analytic expression of the wave beam attitude angle and the high-order derivative thereof obtained in the second step, screening out the wave foot motion direction at the next moment based on attitude constraint, judging whether all target points are traversed, outputting wave foot tracks if all target points are traversed, otherwise judging whether tracking target points are switched, setting the next target point as a tracking target if all target points are traversed, returning to recalculate the position, the speed and the acceleration of the wave foot selectable motion direction at the next moment, and directly returning to recalculate the position, the speed and the acceleration of the wave foot selectable motion direction at the next moment until all target points are traversed, and outputting the wave foot tracks;
and step four, changing a judgment threshold value in the switching criterion of the tracking target, iterating relevant parameters in the wave-foot optimization algorithm, and selecting the optimal wave-foot track according to the target point deviation minimum criterion.
The analytic relationship between the beam attitude angle and the observation configuration characteristic angle is as follows:
wherein β is the downward viewing angle, β ' is the downward viewing angle containing left and right view information, β ' = β when viewed right, β ' = - β when viewed left; gamma is the projection of the oblique angle on the section of the earth where the subsatellite point is located; eta is a beam projection angle used for representing the rotation angle of the projection ellipse, and can be set during observation so as to balance the breadth and the azimuth resolution; beta, gamma and eta are collectively called as observation configuration characteristic angles;
is a roll angle, theta is a pitch angle, psi is a yaw angle, and is collectively called a beam attitude angle;
and (3) respectively taking first-order and second-order differentiation on the analytic relational expression of the beam attitude angle and the observation configuration characteristic angle to obtain a high-order form of the beam attitude angle, wherein the high-order form comprises the following steps:
the wave-foot optimization algorithm specifically comprises the following steps:
firstly, inputting parameters such as a target point sequence generated in the step one, satellite starting time and the like, and then calculating the selectable motion direction of the wave foot:
wherein P is foot.f (i) Is the wave foot ground fastening position at the ith time, p i Is its unit vector; p T (j) Satisfies j E [1,2, \8230 ] for the jth tracking target ground fastening position]M is the number of target points; the normal vector of the plane where the two vectors are located is n ij ；v ij From P on the surface of the earth foot.f (i) To P T (j) A unit direction vector of (a); i | · | purple wind 2 Is a two-norm operator; v. of i A unit vector of the wave-foot ground fixation speed at the ith moment; k is a radical of ij Is v is ij And v i The included angle of (c); n is the number of optional moving directions of the wave foot, N is the serial number of the optional moving directions, and N belongs to [1,2, \\ 8230 ], N]K (n) is an included angle subtended by the nth selectable direction; v' ij (n) represents the unit vector of the nth selectable direction of the jth target in the time-to-earth fixation system at the ith time, H Y (theta) represents that the positive direction of the Y axis is taken as an axis, and the coordinate axis is rotated by theta degrees along the positive direction of the right-hand rule;
V′ ij (n) represents the speed of the jth target in the earth fixation system at the ith time in the nth selectable direction; a' ij (n) represents a number of V' ij (n) acceleration of the jth target in the earth-fixed system at the ith moment; p' ij (n) represents a number of V' ij (n) and a' ij (n) th +1 th time wave foot earth-fixed system coordinate, V foot.f (i) The wave foot ground fixation speed at the ith moment is dt is time differential;
p' ij (n)、V′ ij (n)、a′ ij (n) substituting the analytic expression obtained in the second step, directly obtaining the attitude angle and the first derivative and the second derivative of each optional direction, and then obtaining the attitude angle and the first derivative and the second derivative of each optional direction according to the attitude angles
Selecting the sequence number n in accordance with the optimal direction under the constraint of the attitude angle of the satellite i Wherein F (-) is attitude angle constraint, G (-) is attitude angle change velocity constraint, H (-) is attitude angle change acceleration constraint, and further determine acceleration at the ith moment, and position and velocity of the wave foot at the (i + 1) th moment in the earth-fixed system
Wherein the switching criterion of the tracking target is as follows:
wherein P is foot.f (i) Is the wave foot ground fastening position at the ith time point, P T (j) For the jth tracking target ground binding position, satisfy j ∈ [1, 2., M ]]M is the number of target points; v. of ij From P on the earth's surface foot.f (i) To P T (j) A unit direction vector of (a); i | · | purple wind 2 Is twoA norm operator; r set The value range of the set length threshold is within a distance width; v. of i The superscript H represents the transposition for the unit vector of the wave-based ground fastening speed at the ith time.
The target point planning method comprises the steps of clustering target points and dividing target sequences; the specific steps of target point clustering are as follows:
step 11, marking all points in the set as 1, 2.. Multidot.M, calculating the distance from each point in the target point set to all points, comparing the distance with a clustering threshold, judging the distance to be 1 if the distance is smaller than the clustering threshold, otherwise judging the distance to be 0; putting the result into an M multiplied by M matrix according to the sequence number of the target point to generate a target distance matrix;
step 13, repeating the step 12 for M times, traversing all rows of the target distance matrix, and recording all serial numbers as clustered points;
the target sequence division comprises the following specific steps:
step 21, sorting all the clustered target points from low latitude to high latitude, and setting a point set as T = { T = { 1 ,T 2 ,...,T N }；
Step 22, let S 1 (1)＝T 1 I =1, j =2, according to the following judgment conditions:
if satisfied, make S 1 (i+1)＝T j If not, let j = j +1, where S 1 (i) The ith target point which is a first sequence of divisions; repeating the above operation until j = N to obtain the divided target sequence S 1 ；
Step 23, set T 1 ＝T-S 1 To T 1 Step 22 is executed to obtain S 2 And T 2 And repeating step 22 until
The divided k target sequences are output.
Wherein the target point deviation minimum criterion is:
wherein, L' foot.f (R set ) To be the fitted wave foot trajectory,
for an optimal threshold based on this criterion, inf (-) is the function infimum.
Has the beneficial effects that:
the method comprises the steps of firstly carrying out observation sequence planning on target points which are not distributed along the track, then giving out an analytical expression of a beam attitude angle and a high-order derivative of the beam attitude angle for the first time, providing a wave foot tracking algorithm and a deviation point minimum criterion on the basis to design and generate an optimal non-tracking imaging band which accords with beam maneuvering constraints, solving the problems that the design of a multi-target observation imaging band is difficult and the deviation of the target points is large when the beam maneuvering constraints exist in a satellite-borne SAR non-tracking curved imaging mode, avoiding a large amount of loss of computing resources generated by simulating and calculating the attitude angle, and realizing the optimization of the multi-target observation imaging band in the satellite-borne SAR non-tracking curved imaging mode.
Drawings
FIG. 1 is a flow chart of the optimization method of the satellite-borne SAR non-tracking curved imaging mode multi-target observation imaging band.
Fig. 2 is a flowchart of a target point planning method according to the present invention.
FIG. 3 is a schematic diagram of an observation configuration of a spaceborne SAR non-tracking bending imaging mode.
Fig. 4 is a flow chart of the wave-foot optimization algorithm of the invention.
Fig. 5 shows the planning result and the target coverage of the embodiment of the present invention using the method of the present invention and the conventional method.
FIG. 6 is a comparison of beam attitude angles and first and second derivatives thereof for the method of the present invention and a conventional method in accordance with an embodiment of the present invention.
FIG. 7 shows an example of the beam attitude angle and the first and second derivative analytical expressions and the error of the code simulation result.
Detailed Description
The invention is described in detail below by way of example with reference to the accompanying drawings.
In a satellite-borne SAR non-tracking bending imaging mode, beam maneuver constraints are not considered in the design of the traditional imaging band design method, and the design result often cannot meet the actual beam maneuver constraints, so that the imaging band cannot be used; in addition, the design result has large deviation from the target point, and the target is easily lost during data acquisition. The method firstly plans a task target, then obtains a wave-foot track meeting beam maneuvering constraints based on the wave-foot optimization algorithm, and iteratively provides an optimal multi-target observation imaging band design result based on a deviation point minimum criterion, so that the problems of difficult design realization and large target point deviation in the traditional method are solved. The flow chart of the multi-target observation imaging band optimization method in the satellite-borne SAR non-tracing bending imaging mode is shown in figure 1, and the method comprises the following steps:
planning an input target point set to generate a plurality of target point sequences;
the target point planning method flow is shown in fig. 2, and includes target point clustering and target sequence partitioning. The specific steps of target point clustering are as follows:
and 11, marking all points in the set as 1, 2.. Times, M (M is the total number of the target points), calculating the distance from each point in the target point set to all points, comparing the distance with a clustering threshold, judging the distance to be 1 if the distance is smaller than the threshold, and otherwise, judging the distance to be 0. Putting the result into an M multiplied by M matrix according to the sequence number of the target point to generate a target distance matrix;
and step 13, repeating the step 12 for M times, traversing all rows of the target distance matrix, and taking all recorded serial numbers as the clustered points.
The specific steps of the target sequence division are as follows:
step 21, sorting all the clustered target points from low latitude to high latitude, and setting a point set as T = { T = { 1 ,T 2 ,...,T N }。
Step 22, let S 1 (1)＝T 1 I =1, j =2, and if the judgment condition given by the formula (1) is satisfied, S is made 1 (i+1)＝T j If not, let j = j +1, where S 1 (i) The ith target point of the first sequence marked off. Repeating the above operation until j = N, and obtaining the divided target sequence S 1 。
Step 23, set T 1 ＝T-S 1 To T 1 S is obtained by executing step 22 2 And T 2 Repeating step 22 until
The divided k target sequences are output.
Step two, establishing a coordinate system to obtain the analytic expression of the beam attitude angle and the high-order derivative thereof, wherein the specific process is as follows:
firstly, a satellite orbit coordinate system and an SAR coordinate system are established, and the definition is as follows: in a satellite orbit coordinate system, the X-axis direction is the satellite motion speed direction; the Z-axis vector is in the satellite orbit plane and points to the geocentric; solving the Y axis according to a right-hand rule; in an SAR antenna coordinate system, the positive direction of an X axis is the same as the motion direction of a satellite, and an XOZ surface is a section of the antenna along the azimuth direction; the Z-axis is the antenna beam center pointing.
The beam attitude angle is a general term of yaw, pitch and roll angles and is used for describing the relative relation of the satellite beam pointing direction to the satellite body, namely describing the transfer moment from the satellite orbit coordinate system to the SAR antenna coordinate systemAnd (5) arraying. As shown in formula (2), a 3-2-1 turn sequence (yaw-pitch-roll) is adopted, wherein
Theta (t) is the roll angle, theta (t) is the pitch angle, psi (t) is the yaw angle, H X (theta) represents the rotation of the coordinate axis by theta degrees, H, in the positive direction of the right-hand rule with the positive X-axis as the axis Y (theta) and H Z (θ) is defined similarly.
Similarly, the relative relationship between the satellite orbit coordinate system and the SAR antenna coordinate system can be obtained from the satellite-borne SAR observation configuration shown in FIG. 3, wherein the satellite orbit coordinate system is X-Y-Z and the SAR antenna coordinate system is r 1 -r 2 -r 3 (ii) a The distance from the antenna to the plane is r 2 -o-r 3 (ii) a The antenna has an azimuth plane r 1 -o-r 3 (ii) a Beta is a down viewing angle; gamma is the projection of the oblique angle on the earth section (parallel to the X-O-Y plane) where the subsatellite point is located; eta is an included angle formed by the Y axis and the intersection line of the antenna distance direction plane and the X-O-Z, is called as a beam projection angle and is used for representing the rotation angle of the projection ellipse; beta, gamma and eta are collectively called observation configuration characteristic angles. The analytic relation between the beam attitude angle and the observation configuration characteristic angle is shown in formula (3), wherein β ' is a lower view angle containing left and right view information, β ' = β when viewed from the right, and β ' = - β when viewed from the left.
The high-order form of the beam attitude angle can be obtained by taking first-order and second-order differential of the formula (3) respectively, as shown in formulas (4) and (5).
In the formula (3), eta can be set during observation so as to balance the width and the azimuth resolution; the analytical expressions of beta and gamma are given by formula (6), wherein k 1 ,k 2 ,k 3 The unit column vector of the three coordinate axes of the satellite orbital system in the earth inertial system; l is 3 Is the satellite to wave-foot position vector. The first and second derivatives of β, γ are given by equations (7), (8).
K in the formulae (7) and (8) 1 ,k 2 ,k 3 And L 3 The first and second derivatives of (a) are shown in formulas (9) to (11), wherein omega is the satellite orbit average angular velocity; w is a e Is the rotational angular velocity of the earth; p is foot (t) and P sat (t) the position coordinates of the wave foot and the earth inertial system of the satellite at the time t, a sat (t) is the acceleration of the wave-foot earth inertia system; i | · | purple wind 2 Is a two-norm operator; p is ⊥Z Is XOY plane projection matrix; p foot.f (t)、V foot.f (t)、a foot.f (t) represents the position of the lower wave foot of the earth anchor system; h ecef2eci And (t) is a transfer matrix from the ground anchor to the ground inertial system at the time t.
According to the equations (3) - (11), the values of the beam attitude angles (yaw, pitch and roll) at a certain moment and the first derivative and the second derivative thereof can be directly obtained by using the position, the speed and the acceleration of the fixed wave foot at the moment, so that the support is provided for the mapping band planning.
Inputting a target point sequence, and solving the traversable wave foot track conforming to the beam attitude angle constraint according to the wave foot optimization algorithm flow;
the flowchart of the wave-foot optimization-following algorithm is shown in fig. 4, and specifically includes the following steps:
firstly, parameters such as a target point sequence generated in the step one, satellite boot time and the like are input, and then the wave foot selectable motion direction is calculated, as shown in formulas (12) to (14). Wherein P is foot.f (i) Is the wave foot ground fastening position at the ith time, p i Is its unit vector; p T (j) For the jth tracking target ground binding position, satisfy 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 From P on the surface of the earth foot.f (i) To P T (j) The unit direction vector of (2); i | · | purple wind 2 Is a two-norm operator.
v i A unit vector of the wave-foot ground fastening speed at the ith moment; k is a radical of formula ij Is v is ij And v i The included angle of (A); n is the number of the optional movement directions of the wave foot, N is the serial number of the optional movement directions, and N belongs to [1,2]K (n) is an included angle subtended by the nth selectable direction; v' ij And (n) represents the unit vector of the nth selectable direction of the jth target in the time-to-ground fixation system at the ith moment.
V′ ij (n) represents the speed of the jth target in the earth fixation system at the ith time in the nth selectable direction; a' ij (n) represents a number V' ij (n) acceleration of the jth target in the earth-fixed system at the ith moment; p' ij (n) represents a number V' ij (n) and a' ij (n) th +1 th time wave foot earth-fixed system coordinate, V foot.f (i) The wave-based ground-anchoring speed at the i-th time is obtained.
P 'in the formula (15)' ij (n)、V′ ij (n)、a′ ij (n) substituting the second step to directly obtain the attitude angle of each optional direction and the first and second derivatives thereof, and selecting the serial number n meeting the optimal direction under the constraint of the satellite attitude angle according to the formula (16) i Wherein F (-) is attitude angle constraint, G (-) is attitude angle change velocity constraint, and H (-) is attitude angle change acceleration constraint. Further, the acceleration at the i-th time is determined, and the position and the speed of the wave at the i + 1-th time are sufficient to the position and the speed of the earth-fixed system as shown in the formula (17).
The criterion for switching tracking targets is shown in formula (18), and the switching of tracking targets can be performed when any condition of the formula is satisfied, wherein R set The value range of the set length threshold is within a distance width.
And step four, iterating relevant parameters in the wave-foot optimization algorithm, and selecting the optimal wave-foot trajectory according to the minimum deviation criterion of the target point, wherein the method specifically comprises the following steps:
is provided with L foot.f (R set ) To adopt the length threshold value R in the formula (18) set And tracking the obtained wave foot track. In practical application, polynomial fitting needs to be performed on the attitude angle so as to facilitate on-satellite instruction transmission and control, and the fitted wave foot trajectory L 'can be calculated according to the fitted attitude angle' foot.f (R set ). To R is set Iteration is carried out, and the optimal wave foot track can be selected according to the target point deviation minimum criterion in the formula (19)
Wherein
For an optimal threshold based on this criterion, inf (-) is the function infimum.
Simulation experiment: the satellite-borne SAR non-tracking bending imaging mode swath planning simulation parameters are shown in table 1.
TABLE 1 spaceborne SAR non-tracking bending imaging mode swath planning simulation parameter list
Firstly, in order to verify the advantage of the optimization method of the satellite-borne SAR non-tracing-curvature imaging mode multi-target observation imaging band in solving the problem that the design of the non-tracing-curvature imaging band along the scene is difficult under the constraint of beam mobility, a traditional imaging band design method (namely a method for directly fitting the positions of point targets) is used for a group of imaging bands under the parameters of table 1The target points (29 in total) are subjected to observation mission planning, which is divided into two target sequences, as shown in fig. 5 (a). Next, we take the left target sequence as an example (i.e., 21 target points indicated by "+" in fig. 5 (b)), and perform the design of the foothold on the set of target sequences. The satellite maneuvering constraints of the simulation are as follows: the attitude angle of the wave beam 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 . The wave-feet planned by the conventional method (dashed line) and the method proposed by the present invention (solid line) are shown in fig. 5 (b), respectively; fig. 5 (c) shows the shortest distances from the 21 target points to the centers of the two footpads of the swath, where "o" represents that 7 targets are out of the observation range in the conventional method, and "x" represents that only 1 target is out of the observation range in the method of the present invention. The true values of the attitude angles, the speeds and the accelerations of the two methods are shown in fig. 6, and the solid line represents the generated result of the algorithm provided by the invention, so that the two algorithms both meet the satellite maneuvering constraint, but the algorithm has more loose maneuvering constraint requirements, namely more coverage targets and lower beam maneuvering requirements, and has remarkable advantages. In addition, the correctness of the analysis expression of the beam attitude angle and the first derivative and the second derivative is verified. FIG. 7 shows the beam attitude angle and the errors obtained by the analytic expressions of the first and second derivatives and code simulation, which shows that the error of the beam attitude angle is 10 -13 In the order of degrees, the error of the first and second derivatives is 10 -4 The degree magnitude is far smaller than the true values of the beam attitude angle and the first and second derivatives thereof, and the correctness of the analytical expression provided by the invention is verified.
In summary, the above description is only a preferred embodiment of the present invention, and is not intended to limit the scope of the present invention. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the protection scope of the present invention.
Claims (6)
1. A satellite-borne SAR non-tracking bending imaging mode imaging band optimization method is characterized by comprising the following steps:
planning an input target point set to generate a plurality of target point sequences;
establishing a coordinate system to obtain the analytic expression of the beam attitude angle and the high-order derivative thereof;
inputting a target point sequence, and solving the traversable wave foot track conforming to the beam attitude angle constraint according to the wave foot optimization algorithm flow; the wave foot optimization algorithm flow comprises the following steps: inputting satellite starting time and a target point sequence generated in the first step, calculating the position, the speed and the acceleration of the wave foot selectable motion direction at the next moment from the current point, calculating the wave foot attitude angle and the high-order derivative thereof in each selectable direction according to the analytic expression of the wave beam attitude angle and the high-order derivative thereof obtained in the second step, screening out the wave foot motion direction at the next moment based on attitude constraint, judging whether all target points are traversed, outputting wave foot tracks if all target points are traversed, otherwise judging whether tracking target points are switched, setting the next target point as a tracking target if all target points are traversed, returning to recalculate the position, the speed and the acceleration of the wave foot selectable motion direction at the next moment, and directly returning to recalculate the position, the speed and the acceleration of the wave foot selectable motion direction at the next moment until all target points are traversed, and outputting the wave foot tracks;
and step four, changing a judgment threshold value in the switching criterion of the tracking target, iterating relevant parameters in the wave-foot optimization algorithm, and selecting the optimal wave-foot track according to the target point deviation minimum criterion.
2. The method of claim 1, wherein the beam attitude angle is analytically related to the observation configuration feature angle as follows:
wherein β is the downward viewing angle, β ' is the downward viewing angle containing left and right view information, β ' = β when viewed right, β ' = - β when viewed left; gamma is the projection of the oblique angle on the section of the earth where the subsatellite point is located; eta is the beam projection angle, is used for representing the rotation angle of the projection ellipse, and can be set during observationDeciding to balance the width and the azimuth resolution; beta, gamma and eta are collectively called as observation configuration characteristic angles;
is a roll angle, theta is a pitch angle, psi is a yaw angle, and the angles are collectively called as a beam attitude angle;
and (3) respectively taking first-order and second-order differentiation on the analytic relational expression of the beam attitude angle and the observation configuration characteristic angle to obtain a high-order form of the beam attitude angle, wherein the high-order form comprises the following steps:
3. the method of claim 2, wherein the wave-foot optimization algorithm specifically comprises the steps of:
firstly, inputting parameters such as a target point sequence generated in the step one, satellite starting time and the like, and then calculating the optional motion direction of the wave foot:
wherein P is foot.f (i) Is the wave foot ground fastening position at the ith time point, p i Is its unit vector; p T (j) For the jth tracking target ground binding position, satisfy 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 From P on the earth's surface foot.f (i) To P T (j) The unit direction vector of (2); i | · | purple wind 2 Is a two-norm operator; v. of i A unit vector of the wave-foot ground fixation speed at the ith moment; k is a radical of ij Is v ij And v i The included angle of (c); n is the number of optional motion directions of the feet of the wave, and N is the number of optional motion directionsThe sequence number of the moving direction satisfies N belongs to [1,2]K (n) is an included angle subtended by the nth selectable direction; v' ij (n) represents the unit vector of the nth selectable direction of the jth target in the time-to-earth fixation system at the ith time, H Y (theta) represents that the positive direction of the Y axis is taken as an axis, and the coordinate axis is rotated by theta degrees along the positive direction of the right-hand rule;
V′ ij (n) represents the speed of the jth target in the earth fixation system at the ith time in the nth selectable direction; a' ij (n) represents a number of V' ij (n) acceleration of the jth target in the earth-fixed system at the ith moment; p' ij (n) represents a number of V' ij (n) and a' ij (n) th +1 th time wave foot earth-fixed system coordinate, V foot.f (i) The wave foot ground fixation speed at the ith moment is dt is time differential;
p' ij (n)、V′ ij (n)、a′ ij (n) substituting the analytic expression obtained in the second step, directly obtaining the attitude angle of each optional direction and the first derivative and the second derivative thereof, and then obtaining the attitude angle of each optional direction according to the attitude angle and the first derivative and the second derivative
Selecting the sequence number n in accordance with the optimal direction under the constraint of the attitude angle of the satellite i Wherein F (-) is attitude angle constraint, G (-) is attitude angle change velocity constraint, H (-) is attitude angle change acceleration constraint, and further determining acceleration at the ith moment, and the (i + 1) th moment wave foot is at the position and velocity of the earth-fixed system
4. The method of claim 1, wherein the tracking target handover criterion is:
wherein P is foot.f (i) Is the wave foot ground fastening position at the ith time point, P T (j) For the jth tracking target ground binding position, satisfy j ∈ [1, 2., M ]]M is the number of target points; v. of ij From P on the earth's surface foot.f (i) To P T (j) The unit direction vector of (2); i | · | purple wind 2 Is a two-norm operator; r set Setting a length threshold value, wherein the value range of the length threshold value is within a distance width; v. of i The superscript H represents the transposition for the unit vector of the wave-sufficient ground-anchoring velocity at the ith time.
5. The method according to any of claims 1-4, characterized in that the target point planning method flow comprises target point clustering and target sequence partitioning; the specific steps of target point clustering are as follows:
step 11, marking all points in the set as 1, 2.. Multidot.M, calculating the distance from each point in the target point set to all points, comparing the distance with a clustering threshold, judging the distance to be 1 if the distance is smaller than the clustering threshold, and otherwise judging the distance to be 0; putting the result into an M multiplied by M matrix according to the sequence number of the target point to generate a target distance matrix;
step 12, starting from the first row, finding a column number i, j, k,. To which an element with a value of 1 in the matrix corresponds, recording the sequence number, and setting all elements in the ith, j, k,... To the row and the ith, j, k,. To the column as 0;
step 13, repeating the step 12 for M times, traversing all rows of the target distance matrix, and recording all serial numbers as the clustered points;
the specific steps of the target sequence division are as follows:
step 21, all the clustered targetsThe points are sorted from low latitude to high latitude, and the set of the points is set as T = { T = 1 ,T 2 ,...,T N }；
Step 22, let S 1 (1)＝T 1 I =1, j =2, according to the following judgment condition:
if yes, make S 1 (i+1)＝T j If not, let j = j +1, where S 1 (i) The ith target point which is a first sequence of divisions; repeating the above operation until j = N, and obtaining the divided target sequence S 1 ；
Step 23, set T 1 ＝T-S 1 To T 1 Step 22 is executed to obtain S 2 And T 2 Repeating step 22 until
The divided k target sequences are output.
6. The method of claim 4, wherein the target point deviation minimization criteria is:
wherein, L' foot.f (R set ) For the fitted wave foot trajectory,
for the optimal threshold based on this criterion, inf (-) is the function infimum.
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