CN112508227B - Regional target visible window rapid calculation method for remote sensing satellite complex conical view field - Google Patents
Regional target visible window rapid calculation method for remote sensing satellite complex conical view field Download PDFInfo
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Abstract
The invention discloses a regional target visible window rapid calculation method of a remote sensing satellite complex conical view field, wherein the calculation efficiency is improved by 10 times of magnitude in comparison with the conventional tracking propagation calculation method in terms of visibility judgment, and is improved by 10 times of magnitude in terms of global visible window calculation in comparison with the conventional method. Meanwhile, the relative error of the calculation precision compared with the STK is within 0.1 percent, and the calculation precision meets the engineering practical requirement; according to the method, satellite orbit information is obtained through Lagrange interpolation, the calculation process is independent from an orbit model, and any orbit model can be met, so that the algorithm has wider applicability; the boundary of the regional target is described as a large arc, so that the size of the regional target has no influence on the method. Compared with the traditional algorithm, the method has higher calculation efficiency and better precision under the large-area target.
Description
Technical Field
The invention belongs to the technical field of remote sensing satellite imaging, and particularly relates to a method for rapidly calculating a region target visible window of a complex conical view field of a remote sensing satellite.
Background
From existing research, the visibility problem is at the earliest focused on the visibility of satellite-to-point targets. The most common method is called a propagation algorithm, namely judging one by traversing discrete time steps, and the method has accurate calculation, but low calculation efficiency and is often used as a comparison algorithm in the literature. The subsequent research mainly aims at improving the problem of excessive calculation amount. The visibility of satellite-satellite and satellite-point targets is firstly judged by using a visual function method by Lawton, so that the calculation efficiency is greatly improved, but the method is only suitable for the satellite-point track under one period by using a large circular arc approximate orbit by AliI and the like, the model is simplified, the calculation efficiency is high, the method is only suitable for low-orbit satellites, mai Y and the like consider that the satellite can perform visible window calculation under the attitude maneuver, han C and the like adopt a Hermit interpolation method on the calculation of the visual function, and Zhang Jinxiu and the like propose a rough search method for the satellite with variable step length at low latitude and Gao Wei degrees.
However, the above researches are all calculation methods of satellite point-to-point target visible windows, for regional targets, the existing researches are less, and the original methods cannot be directly popularized because the field type has a large influence on the regional target visibility. Some studies exist that are still based on an extension of the point target, mainly sampling the region interior or region boundaries to approximate the solution, but this approach results in a significant increase in computation. Such as Song Zhiming, directly discretizing the regional target boundaries into point targets and then summing up their visible windows without regard to the satellite field of view. Wang Rongfeng, etc. take into account the case of overlay information at the same time in the calculation process. Some studies have considered how to increase the coarse search range during the calculation process, the henbane et al propose to use dichotomy to perform the exact search to increase the initial search step. As can be seen, there is no more general and efficient algorithm for the visibility calculation of the regional target at present, and the field type involved in the above study is only cone and rectangular fields. It is therefore necessary to propose an accurate and efficient method for complex conical fields of view.
Disclosure of Invention
Aiming at the problem, the invention provides a semi-analytic rapid calculation method for the visual window of the regional target based on a complex conical view field, which can rapidly determine the precise visual window of the regional target.
A method for calculating a region target visible window of a remote sensing satellite complex conical view field comprises the following steps:
step 1, establishing mathematical description of a complex conical view field: the projections of the circles corresponding to the inner half cone angles and the outer half cone angles of the complex cone view field on the surface of the earth are two common circular arcs, and the projections of the two sides corresponding to the minimum clock angle and the maximum clock angle on the surface of the earth sphere are two large circular arcs; wherein the center of the large arc coincides with the center of the sphere, and the circumference is on the surface of the earth; the common circular arc is any circular arc except a large circular arc, the circumference of which is on the earth;
step 2, establishing mathematical description of the regional target: the regional target is a closed convex polygon on the surface of the earth, and each side of the convex polygon is a large arc on the sphere of the earth;
step 3, judging whether an overlapping area exists between a visual area A projected on the earth surface and an area B where an area target is located by the complex cone view field at each moment, specifically:
(81) Judging whether the area A is within the area B:
(811) Traversing each side of the area B, and calculating the limit point of the area A relative to the side; wherein, the limit point refers to the point on the boundary of the area A, which is most likely to be outside the area B; each boundary edge of the region B corresponds to a group of limit points;
(812) Judging whether the corresponding limit points are all on the inner side of each side of the area B, if one limit point is not on the inner side of each side, exiting, returning to NO, and entering the step (82);
(813) If all the limit points on the area A are on the inner side of each side of the corresponding area B, the time area A is in the area B;
(82) Judging whether at least one intersection point exists at the boundary of the area A and the area B, if so, the two areas have intersection points; if not, the method exits, returns to NO, and enters the step (83);
(83) Judging whether the area B is within the area A:
sequentially judging whether each boundary point of the area target B is in the projection area A of the complex conical view field, and if all the points are met, the area B is in the area A; otherwise, if one point is not satisfied, exiting, and returning to 'no';
for a certain moment, if one of the three conditions (81), (82) and (83) is met, the field of view is visible to the regional target at the moment; if all three conditions are not satisfied, the field of view is invisible to the regional target at the moment;
and 4, determining a visible window of the complex conical view field on the region target B according to the position relation between the region A and the region B at each moment calculated in the step 3.
Preferably, in the step (811), the method for calculating the limit point is as follows:
firstly, calculating the half cone angle of the earth corresponding to the half angle of the inner cone and the outer cone of the complex cone view fieldAnd->Wherein D represents the distance of the satellite from the sphere center of the earth, R represents the radius of the earth, θ represents the half cone angle of the field of view of the satellite, +.>Representing the half cone angle of the earth to satellite field of view: />
Next, calculate "limit points": taking the limit points as at most 6 in one judgment, wherein the points 1,2,3 and 4 are 4 boundary points of the area A, and the points 5 and 6 are calculated according to the condition of the target boundary of the area, and the specific steps are as follows:
calculating a unit vector n of the unitized speed and the reverse angular speed x ,n y The unit direction vector corresponding to each clock edge is obtained through the definition of the clock angle, taking the clock edge where 1 and 3 points are located as an example, and the unit direction vector v 1,3 The expression is as follows:
representing a minimum clock angle;
the position vector of the center of the circle where the projection area of the complex conical view field is positioned is directed to v by using a rotation method 1,3 Direction of rotation respectivelyCorner (s)/or(s)>The angle obtains the position vector of 1 point and the position vector of 3 points, and the position vectors of 2 and 4 points are obtained by the method;
calculating 5 th and 6 th limit points which can exist in the projection area A of the complex conical field relative to the boundary line of the area B: wherein, when the difference between the maximum and minimum clock half angles is less than 180 degrees, there may be a 5 th limit point; when greater than 180 degrees, there are 5 th and 6 th limit points;
for possible 5 th and 6 th limit points on the boundary of the area A, taking the normal vector of the target boundary of the area as the direction vector, and calculating the position vector of the possible limit points by adopting a calculation method of the points 1,2,3 and 4; then it is determined whether the possible limit point is in region a according to the following formula:
if the above formula is satisfied, the possible limit point is proved to be in the field of view, namely the limit point exists, otherwise the limit point does not exist;
wherein; p is p 5 For the position vector of the possible limit points, the norm function represents the unitization, and the expression of the f function is as follows:
representing a maximum clock angle; v 1/2 ＝f(norm(v 1,3 +v 2,4 ) A) a midpoint vector representing region a; v 2,4 The unit direction vector of the "clock edge" where the 2,4 points are located.
Preferably, the rotation method specifically comprises the following steps:
the vector p ' after the vector p is rotated by α to the unit vector v ' is represented by p ' =cos (α) p+sin (α) v as follows * Wherein v is * =norm (v ' - (v ' ·p) v '), norm (·) representing the unitization of the vector; the unit vector v' represents a unit direction vector of a large circular arc or a normal circular arc.
Preferably, in the step (812), the method for determining whether the corresponding limit points are all inside the edge is as follows:
let v denote the normal vector on each side of region B, let p denote the position vector of a point, if pV.gtoreq.0, vector p is on the same side as the normal vector on that side, otherwise, on the outside of the normal vector on that side.
Preferably, in the step (82), when determining whether the intersection exists between the area a and the area B, determining whether the intersection exists between the large arc where the target boundary of each area is located and the large arc projected by the largest and small clock angles of the complex conical view field by the following method is specifically:
the intersection point Q of the two large arcs is calculated by the following formula to judge whether Q is in the large arc d or not 1 d 2 In the internal part, it is necessary to determine whether (d) is satisfied 1 ×Q)·(Q×d 2 ) More than or equal to 0 and Q (d) 1 +d 2 ) And if the Q is not less than 0, proving that Q is in the large arc, namely the two large arcs have intersection points.
Preferably, in the step (82), when determining whether the intersection exists between the area a and the area B, determining whether the intersection exists between the large arc of the target boundary of each area and the common arc of the inner cone projection and the outer cone projection of the complex cone field of view by the following method is specifically:
setting the intersection point of the common arc and the large arc as Q ', and setting the included angle of the unit vectors v and v' as beta; v and v' are respectively the unit normal vector of the plane where the large arc is located and the unit normal vector of the plane where the common arc is located;
if beta+θ=90°, the normal arc is tangent to the major arc; θ represents the half cone angle of the satellite view field corresponding to the common circular arc;
if beta+theta is more than 90 degrees, the common circular arc is intersected with the large circular arc;
if beta+theta is smaller than 90 degrees, the common arc and the large arc have no intersection point;
wherein β is calculated as β=arccoso (|v·v' |) as follows;
when the intersection point is judged, the vector is required to be calculated: let the intersection point Q' and the current projection plane have an angle γ, then cos (γ) =cos (θ)/sin (β); at this time, the in-plane direction vector is constructed to be v // Unit vector v in vertical plane =norm (v '- (v' ·v) v) ⊥ ＝norm(v’×v)；
The intersection point Q' is determined according to the following equation: q' =cos (γ) v // ±sin(γ)v ⊥ ；
Finally, whether the intersection points are in the large circular arc and the common circular arc or not needs to be judged, Q' is projected onto the common circular plane first, and then judgment is carried out according to whether the intersection points are between the circles or not.
Preferably, the specific method in the step 4 is as follows:
firstly, judging the visibility of a remote sensing satellite to an area target at the moment according to discrete step length; then, arranging the visibility under each step length according to the time sequence and determining the range of the visible starting time and the visible ending time of each visible window; and obtaining the fine moment of each visible window through binary search, and finally summarizing and outputting the information of each precise visible window.
Preferably, the satellite orbit information used in the binary search is obtained by Lagrange interpolation.
The invention has the following beneficial effects:
firstly, a calculation method of a visual window of a regional target aiming at a complex conical view field is provided;
compared with the traditional tracking propagation calculation method, the calculation speed of the calculation efficiency is improved by 10 times by the magnitude of 3 in the aspect of visibility judgment, and the calculation speed of the calculation efficiency is improved by 10 times by the magnitude of 5 in the aspect of global visible window calculation. Meanwhile, the relative error of the calculation precision is within 0.1 percent compared with that of the STK, and the calculation precision meets the engineering practical requirements;
according to the method, satellite orbit information is obtained through Lagrange interpolation, the calculation process is independent from an orbit model, and any orbit model can be satisfied, so that the algorithm has wider applicability;
the boundary of the regional target is described as a large arc, so that the size of the regional target has no influence on the method. Compared with the traditional algorithm, the method has higher calculation efficiency and better precision under the large-area target.
Drawings
FIG. 1 is a schematic diagram of complex cone field imaging;
FIG. 2 is a schematic diagram of a large circle and a common circle;
FIG. 3 is a schematic diagram of intersection points of a large arc with a normal arc;
FIG. 4 is a half cone angle of the earth versus satellite field of view;
FIG. 5 is a schematic diagram showing the meaning of "limit points";
FIG. 6 is a schematic diagram of a complex cone field of view "limit point" solution;
FIG. 7 is a complex conical field of view unit vector;
fig. 8 is a flowchart of the overall program algorithm.
Detailed Description
The invention will now be described in detail by way of example with reference to the accompanying drawings.
The implementation steps of the invention are as follows:
step 1, establishing mathematical description of complex cone view field
An imaging schematic diagram of a complex conical field of view is shown in fig. 1, and the shape and size of the field of view are represented by four parameters, namely, a inner conical half angle, an outer conical half angle, a minimum clock angle and a maximum clock angle. It should be clear that, under the assumption of the sphere of the earth, the projections of the circle corresponding to the inner half cone angle and the circle corresponding to the outer half cone angle of the complex cone field of view on the surface of the earth are two common circular arcs, and the projections of the two sides corresponding to the minimum and large clock angles on the surface of the earth are two large circular arcs.
The big circle in the previous section is a circle with the center of the circle coincident with the center of the sphere and the circumference on the surface of the sphere. The large circle is also called geodesic because the two points on the sphere have the shortest distance along the geodesic on the sphere. The common circle refers to any circle with the circumference on the ball, and for convenience of distinction, the common circle described later in the invention does not contain a large circle unless specified.
Step 2, establishing mathematical description of the regional target
The regional target is a closed convex polygon of the earth's surface, each edge of the convex polygon being a large arc on the earth's sphere, i.e., geodesic. Conventionally, the initial description of the boundary points of the regional target is described in terms of (longitude, latitude, sea-going) in the geodetic coordinate system.
Step 3, describing visibility problem of complex conical view field of satellite on regional target
The visible window of the satellite on the regional target refers to the time range in which the carried load view field can observe the regional target. From the mathematical descriptions of step 1 and step 2, the visibility problem of the complex conical field of view of the satellite to the regional target can be expressed as: the complex conical field of view of the satellites projects in a visible region of the earth's surface with or without overlapping regions of the regional target.
Step 4, in order to reduce the calculation amount of the problem of judging whether one area is in another area, a thought of calculating a limit point is provided.
For a projection view field area A and an area target B with complex shapes, the conventional method for judging whether the area A is in the inner part of the area B is as follows: and traversing all points of the area A according to the boundary of the area B in sequence, and judging whether all points are inside each side of the area B. Such a processing method is computationally intensive. Therefore, the present invention proposes the concept of "limit point", which essentially includes finding a point most likely not satisfying the situation that "region a is located inside region B", and determining whether the positional relationship between the two regions satisfies the situation that "region a is located inside region B" by determining the positional relationship between the "limit point" and region B, by referring to this point as "limit point". The meaning of which is shown in figure 5. That is, whether the illustrated area a is on one side in the arrow direction is determined by verifying only one point shown in the drawing, which is the "limit point" described in the present invention, and the principle is similar for the case of a three-dimensional sphere. It should be noted that the position of the "limit point" is related to the direction of the boundary of the area B (i.e., the arrow direction in fig. 5), and therefore, the "limit point" of the area a corresponding to each side of the area target B should be calculated independently.
And 5, establishing a vector geometric basic algorithm model for calculating the overlapping problem of the two areas of the sphere.
By converting the problem into a sphere two-region overlapping problem, the calculation amount is obviously reduced by using sphere space vector calculation, and for this purpose, the invention provides the following five vector geometry basic algorithms for rapidly calculating relevant required information:
(51) Solving a vector of a spherical surface one-bit vector rotated by an angle along a certain direction;
the algorithm is designed to solve for the "limit points" of the complex conical field of view relative to the target boundaries of each region. As shown in fig. 2, when a vector p 'rotated by α is obtained from p to v' (unit vector), p 'may be represented by the following formula p' =cos (α) p+sin (α) v * Wherein v is * =norm (v ' - (v ' ·p) v '), norm (·) represents the unitization of the vector.
(52) Judging whether a point on the spherical surface is on one side of a great circle or not;
the algorithm is designed for judging the relation between each point and each regional target boundary. As shown in fig. 2. If it is determined that p is on one side of the large circle 2. If p.v is greater than or equal to 0, p is on the same side of the normal vector of the large circle 2, otherwise, on the outer side of the normal vector of the large circle "
(53) Judging whether one point of the spherical surface is on one side of a common circle;
the algorithm is designed for judging the common circular relationship between the target boundary points of each region and the inner cone projection and the outer cone projection of the complex cone view field. As shown in fig. 2. If p is to be judged to be on one side of the normal circle. Similarly, the magnitude of p.v' is calculated. If p.v.gtoreq.cos (θ), p is said to be "on the same side of normal vector" as the normal circle, whereas p is said to be "on the outside of normal vector" as the circle.
(54) Judging whether the two sections of large arcs have intersection points or not;
the algorithm is designed for judging whether the intersection points exist between the target boundaries of all areas and the large circles projected by the maximum and small clock angles of the complex conical view field. The overall idea of judging whether the two sections of large arcs have intersection points can be summarized into the following two points: firstly, calculating the intersection point of two large circles; next, it is determined whether the point is on two large arcs.
Taking fig. 2 as an example, first, the intersection point Q of the great circle 2 and the great circle 1 may be calculated as q= ±norm (v×v') according to the following formula, and since there are two intersection points, there are positive and negative cases in the formula. Then, judge whether Q is in the large arc d 1 d 2 Inside, at this time, judgment (d 1 ×Q)·(Q×d 2 ) More than or equal to 0 and Q (d) 1 +d 2 ) Not less than 0, if the two conditions are satisfied, prove that Q is in the large circular arc d 1 d 2 Inside.
(55) Judging whether an intersection point exists between a large arc and a common arc.
The algorithm is designed for judging whether the intersection points exist between the target boundaries of all areas and the common circles projected by the inner cone and the outer cone of the complex cone view field. The calculation process is the same as algorithm (54) and is described in detail below with respect to the side view of fig. 2 perpendicular to the v and v' directions. As shown in fig. 3. Wherein the intersection point of the common circle and the great circle 2 is Q ', and the included angle between v and v' is beta.
Similarly, the intersection point Q' is required first, but it is necessary to determine whether or not there are intersection points first, because there are three possibilities of intersection points of a normal circle and a great circle.
If beta+θ=90°, the normal circle is tangent to the large circle;
if β+θ >90 °, the normal circle intersects the large circle.
If beta+theta is smaller than 90 degrees, the common circle and the great circle have no intersection point.
Where β is calculated as β=arccos (|v·v' |) in the following manner, which is both cases where the large circle normal vector is considered positive and negative.
When it is determined that there is an intersection, its vector needs to be calculated. Let the intersection point Q' and the current projectionThe angle of the planes is γ, cos (γ) =cos (θ)/sin (β). At this time, the in-plane direction vector is constructed to be v // Unit vector v in vertical plane =norm (v '- (v' ·v) v) ⊥ ＝norm(v’×v)。
The intersection point Q' can be found as follows: q' =cos (γ) v // ±sin(γ)v ⊥
Finally, it is necessary to determine whether the intersection point is in two circular arcs, and only Q' is projected onto the common circular plane first, and then the thought and algorithm (54) remain consistent, which is not described herein.
Step 6, preprocessing an algorithm:
(61) Normal vector calculation of regional target boundary
In order to facilitate subsequent calculation, boundary points of the regional targets are sequenced anticlockwise, coordinates of the boundary points are converted into a ground-solid system, the boundary points can be conveniently converted by definition, and normalization processing is carried out to obtain the DN 1 ,DΝ 2 ,...,DΝ n (DistrictNode)。
The obtained coordinates DN 1 ,DΝ 2 ,...,DΝ n And (5) mutually cross multiplying according to the front-back sequence to obtain normal vectors of all boundaries. To obtain the geodesic formed by boundary points of two adjacent areas, the vector of the boundary points is needed to be multiplied by the vector of the boundary points to obtain the normal vector, and the expression is that
And normalization processing:
obtaining the normal vector of the area boundary as NV 1 ,NV 2 ,...,NV n 。
(62) The half cone angle of the earth corresponding to the inner and outer cones of the satellite field of view is calculated.
In the process of "limiting", it is necessary to use the half cone angle of the earth to the satellite field of view, whereas for a general earth-observing satellite, its eccentricity is close to zero. The half cone angle of the earth's field of view remains almost unchanged throughout the satellite's operation. In order to reduce the calculation amount, the algorithm calculates the half cone angle in advance in the preprocessing process of the regional target.
The half cone angle of the earth to the satellite field of view may be represented as in fig. 4. Where D represents the distance of the satellite from the center of the earth, R represents the radius of the earth, θ represents the half cone angle of the satellite's field of view,the calculated half cone angle of the earth to the satellite field of view is shown in fig. 4.
For a complex conical field of view, the half cone angle of the earth corresponding to the half cone angles inside and outside needs to be calculatedAnd->
Step 7, calculating limit points of complex cone projection view field "
For the complex cone view field, because the boundary of the projection area is complex, in order to facilitate the subsequent unified processing, the invention combines the shape of the projection area, and takes the limit points as at most 6 in one judgment, wherein the points 1,2,3 and 4 are 4 boundary points of the projection area A of the complex cone view field, and the points 5 and 6 are calculated (possibly not exist) according to the condition of the target boundary of the area. A schematic of its "limit point" is shown in fig. 6.
(71) First, the earth half cone angle corresponding to the inner cone angle and the outer cone angle is calculatedAnd->The specific algorithm is shown in the step 6, namely the half cone angle of the inner cone and the outer cone of the satellite view field corresponding to the earth is calculated;
(72) Next, the "limit points" 1,2,3,4,5,6 of the complex conical field of view projection area in fig. 7 are calculated.
Calculating a unit vector n of the unitized speed and the reverse angular speed x ,n y As a unit vector of this plane, fig. 7 shows.
After obtaining the unit vector, the unit direction vector v corresponding to each clock edge is obtained by defining the clock angle, taking the clock edge where 1 and 3 points are located in fig. 7 as an example 1,3 The expression is as follows
The position vector of the center of the circle where the projection area of the complex conical view field is positioned is directed to v 1,3 Direction of rotation respectivelyAngle(s),The angle can obtain a position vector of 1 point and a position vector of 3 points, and the rotation method is shown in the algorithm (51) in the step 5 for solving the vector of the spherical surface one-bit vector rotated by an angle along a certain direction. The bit vectors of 1,2,3,4 points can be obtained according to the above method.
The calculation method is the same for the 5,6 points that may be present, except that its direction vector is the normal vector to the target boundary of the region. It should be noted that, since the projection area of the complex conical field of view is not a complete circle, the point rotated by the above method may not exist in the effective visible area of the complex conical field of view, and thus it is necessary to determine the existence thereof.
First, a midpoint vector v of the projection region is calculated 1/2 The calculation formula is as follows:
v 1/2 ＝f(norm(v 1,3 +v 2,4 ))
wherein norm functions represent the unitization, and the expression of f functions is as follows:
if the 5-point bit vector obtained according to the original algorithm is p 5 If it satisfies the following relation, it proves that the point is within the field of view, i.e. the point is present, otherwise the point is not present.
Step 8, judging whether the two areas have overlapping areas at a certain moment according to a visibility judging and analyzing algorithm
One of the bases for solving the visibility window is to be able to judge the visibility to the area target at each moment. According to the proposed vector geometric basic algorithm, the invention provides a mathematical model aiming at the problem, wherein the visual situation is divided into three situations, whether the situation is met or not is judged in sequence according to each situation, and if one situation is met, the situation can be judged to be visible at the moment. If the visual area of the complex conical field of view projected on the earth's surface is called area a and the area target is called area B, then the three cases are: (a) A is in B, (B) A and B boundary have intersection point, and (c) B is in A. The algorithm flow for these three cases is as follows:
(81) Judging whether the condition (a) is met, namely judging whether the conical view field is positioned in the regional target:
(811) Traversing each side of the area target B, and calculating the limit point of the area A relative to the side. The specific method for calculating the limit point is shown in the step 7;
(812) For each side of the area target, judging whether all limit points are inside the side, and the specific method for judging whether the points are inside the side is shown in the algorithm (52) in the step 5 to judge whether one point on the spherical surface is on one side of a great circle. If there is a limit point that is not inside a certain edge, the process exits, returns to NO, and proceeds to step (82).
(813) If all the limit points are inside each edge after traversing each edge, return to "yes".
The "limit point" of the complex cone view field is a special point found in the judgment case (a), and the purpose of the limit point is to obtain the relative position relationship between the projection area of the complex cone view field and the target area by proving the position relationship between the points and the target area so as to reduce the calculated amount. In addition to the presence of 4 points on the boundary of the projection area of the complex conical field of view, the "limit points" can be divided into two categories depending on whether the difference between the maximum and minimum clock half angles is greater than 180 degrees, as shown in fig. 7. When the angle is smaller than 180 degrees, judging whether the 5 th point exists according to the condition of the regional target boundary; and when the angle is larger than 180 degrees, judging whether 5 points and 6 points exist according to the condition of the regional target boundary.
(82) Judging whether the complex conical view field projection area belongs to the condition (b), namely judging whether an intersection point exists between the complex conical view field projection area and the target area or not:
sequentially judging whether each boundary of the regional target and the boundary of the complex cone view field in the earth projection region have an intersection point, if so, satisfying the condition (b), and returning to yes; if not, return to "no". The specific method for judging whether the intersection point exists is shown in the algorithm (54) in the step 5, whether the intersection point exists between two large arcs or not is shown in the algorithm (55), and whether the intersection point exists between one large arc and one common arc or not is shown in the algorithm.
(83) Judging whether the condition (c) is met, namely judging whether the target area is positioned in the complex conical field projection area:
sequentially judging whether boundary points of each regional target are inside a projection region of the complex conical view field, if all points are met, meeting the condition (c), and returning to yes; if there is a point that is not satisfied, return to "no". The specific algorithm is shown in the algorithm (52) of the step 5, which is used for judging whether one point on the sphere is on one side of the great circle, and the algorithm (53) which is used for judging whether one point on the sphere is on one side of the common circle.
Wherein, being located inside the projection area of the complex cone field of view means being located on the "normal vector opposite side" of the normal circle projected by the inner cone, and on the "normal vector same side" of the normal circle projected by the outer cone and the other projection boundary.
Step 9, semi-analytic determination of the visible window of the complex conical field of view
And obtaining a semi-resolution method for finally determining the visible window through the visibility judging and resolving algorithm. Firstly, judging the visibility at the moment according to the discrete step length; then, arranging the visibility under each step length according to the time sequence and determining the range of the visible starting time and the visible ending time of each visible window; obtaining fine time of each visible window through binary search, wherein satellite orbit information used in binary search is obtained through Lagrange interpolation; and finally, summarizing and outputting the information of each accurate visible window. The overall flow of the operation can be described in terms of a flowchart as shown in fig. 8.
In summary, the above embodiments are only preferred embodiments of the present invention, and are not intended to limit the scope of the present invention. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention should be included in the protection scope of the present invention.
Claims (8)
1. A method for calculating a region target visible window of a remote sensing satellite complex conical view field is characterized by comprising the following steps:
step 1, establishing mathematical description of a complex conical view field: the projections of the circles corresponding to the inner half cone angles and the outer half cone angles of the complex cone view field on the surface of the earth are two common circular arcs, and the projections of the two sides corresponding to the minimum clock angle and the maximum clock angle on the surface of the earth are two large circular arcs; wherein the center of the large arc coincides with the center of the sphere, and the circumference is on the surface of the earth; the common circular arc is any circular arc except a large circular arc, the circumference of which is on the earth;
step 2, establishing mathematical description of the regional target: the regional target is a closed convex polygon on the surface of the earth, and each side of the convex polygon is a large arc on the sphere of the earth;
step 3, judging whether an overlapping area exists between a visual area A projected on the earth surface and an area B where an area target is located in the complex cone view field at each moment, specifically:
(81) Judging whether the area A is within the area B:
(811) Traversing each side of the area B, and calculating the limit point of the area A relative to the side; wherein, the limit point refers to the point on the boundary of the area A, which is most likely to be outside the area B; each boundary edge of the region B corresponds to a group of limit points;
(812) Judging whether the corresponding limit points are all on the inner side of each side of the area B, if one limit point is not on the inner side of each side, exiting, returning to NO, and entering the step (82);
(813) If all the limit points on the area A are on the inner side of each side of the corresponding area B, the time area A is in the area B;
(82) Judging whether at least one intersection point exists at the boundary of the area A and the area B, if so, the two areas have intersection points; if not, the method exits, returns to NO, and enters the step (83);
(83) Judging whether the area B is within the area A:
sequentially judging whether each boundary point of the area target B is in the projection area A of the complex conical view field, and if all the points are met, the area B is in the area A; otherwise, if one point is not satisfied, exiting, and returning to 'no';
for a certain moment, if one of the three conditions (81), (82) and (83) is met, the field of view is visible to the regional target at the moment; if all three conditions are not satisfied, the field of view is invisible to the regional target at the moment;
and 4, determining a visible window of the complex conical view field on the region target B according to the position relation between the region A and the region B at each moment calculated in the step 3.
2. The method for calculating the area target visible window of the complex conical field of view of the remote sensing satellite according to claim 1, wherein in the step (811), the method for calculating the limit point is as follows:
firstly, calculating the half cone angle of the earth corresponding to the half angle of the inner cone and the outer cone of the complex cone view fieldAnd->Wherein D represents the distance of the satellite from the sphere center of the earth, R represents the radius of the earth, θ represents the half cone angle of the field of view of the satellite, +.>Representing the half cone angle of the earth to satellite field of view required:
next, calculate "limit points": taking the limit points as at most 6 in one judgment, wherein the points 1,2,3 and 4 are 4 boundary points of the area A, and the points 5 and 6 are calculated according to the condition of the target boundary of the area, and the specific steps are as follows:
calculating a unit vector n of the unitized speed and the reverse angular speed x ,n y The unit direction vector corresponding to each clock edge is obtained through the definition of the clock angle, taking the clock edge where 1 and 3 points are located as an example, and the unit direction vector v 1,3 The expression is as follows:
representing a minimum clock angle;
the position vector of the center of the circle where the projection area of the complex conical view field is positioned is directed to v by using a rotation method 1,3 Direction of rotation respectivelyCorner (s)/or(s)>The angle obtains the position vector of 1 point and the position vector of 3 points by the same method, and the position vectors of 2 and 4 points are obtained by the method;
calculating 5 th and 6 th limit points which can exist in the projection area A of the complex conical field relative to the boundary line of the area B: wherein, when the difference between the maximum and minimum clock half angles is less than 180 degrees, there may be a 5 th limit point; when greater than 180 degrees, there are 5 th and 6 th limit points;
for possible 5 th and 6 th limit points on the boundary of the area A, taking the normal vector of the target boundary of the area as the direction vector, and calculating the position vector of the possible limit points by adopting a calculation method of the points 1,2,3 and 4; then it is determined whether the possible limit point is in region a according to the following formula:
if the above formula is satisfied, the possible limit point is proved to be in the field of view, namely the limit point exists, otherwise the limit point does not exist;
wherein; p is p 5 For the position vector of the possible limit points, the norm function represents the unitization, and the expression of the f function is as follows:
representing a maximum clock angle; v 1/2 ＝f(norm(v 1,3 +v 2,4 ) A) a midpoint vector representing region a; v 2,4 The unit direction vector of the "clock edge" where the 2,4 points are located.
3. The method for calculating the region target visible window of the complex conical field of view of the remote sensing satellite according to claim 2, wherein the rotation method is specifically as follows:
the vector p ' after the vector p is rotated by α to the unit vector v ' is represented by p ' =cos (α) p+sin (α) v as follows * Wherein v is * =norm (v ' - (v ' ·p) v '), norm (·) representing the unitization of the vector; the unit vector v' represents a unit direction vector of a large circular arc or a normal circular arc.
4. The method for calculating the area target visible window of the complex conical field of view of the remote sensing satellite according to claim 1, wherein in the step (812), the method for judging whether the corresponding limit points are all inside the edge is as follows:
let v denote the normal vector on each side of region B, let p denote the position vector of a point, if pV.gtoreq.0, vector p is on the same side as the normal vector on that side, otherwise, on the outside of the normal vector on that side.
5. The method for calculating the region target visible window of the complex conical view field of the remote sensing satellite according to claim 1, wherein in the step (82), when judging whether the intersection point exists between the region a and the region B, judging whether the intersection point exists between the large circular arc where the boundary of each region target is located and the large circular arc projected by the maximum and the small clock angles of the complex conical view field by the following method is specifically:
the intersection point Q of the two large arcs is calculated by the following formula to judge whether Q is in the large arc d or not 1 d 2 Inside, at this time, it is necessary to determine whether (d) is satisfied 1 ×Q)·(Q×d 2 ) More than or equal to 0 and Q (d) 1 +d 2 ) And if the Q is not less than 0, proving that Q is inside the large circular arc, namely the two large circular arcs have intersection points.
6. The method for calculating the visible window of the regional target of the complex conical view field of the remote sensing satellite according to claim 1, wherein in the step (82), when judging whether the intersection point exists between the region a and the region B, judging whether the intersection point exists between the large circular arc of the boundary of each regional target and the common circular arc projected by the inner cone and the outer cone of the complex conical view field by the following method is specifically:
setting the intersection point of the common arc and the large arc as Q ', and setting the included angle of the unit vectors v and v' as beta; v and v' are respectively the unit normal vector of the plane where the large arc is located and the unit normal vector of the plane where the common arc is located;
if beta+θ=90°, the normal arc is tangent to the major arc; θ represents the half cone angle of the satellite view field corresponding to the common circular arc;
if beta+theta is more than 90 degrees, the common circular arc is intersected with the large circular arc;
if beta+theta is smaller than 90 degrees, the common arc and the large arc have no intersection point;
wherein β is calculated as β=arccoso (|v·v' |) as follows;
when the intersection point is judged, the vector is required to be calculated: let the intersection point Q' and the current projection plane have an angle γ, then cos (γ) =cos (θ)/sin (β); at this time, the in-plane direction vector is constructed to be v // Unit vector v in vertical plane =norm (v '- (v' ·v) v) ⊥ ＝norm(v′×v)；
The intersection point Q' is determined according to the following equation: q' =cos (γ) v // ±sin(γ)v ⊥ ；
Finally, whether the intersection points are in the large circular arc and the common circular arc or not needs to be judged, Q' is projected onto the common circular plane first, and then judgment is carried out according to whether the intersection points exist between the circles or not.
7. The method for calculating the region target visible window of the complex conical field of view of the remote sensing satellite according to claim 1, wherein the specific method in the step 4 is as follows:
firstly, judging the visibility of a remote sensing satellite to an area target at the moment according to discrete step length; then, arranging the visibility under each step length according to the time sequence and determining the range of the visible starting time and the visible ending time of each visible window; and obtaining the fine moment of each visible window through binary search, and finally summarizing and outputting the information of each precise visible window.
8. The method of claim 7, wherein the satellite orbit information used in the binary search is obtained by lagrangian interpolation.
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