CN112508227A

CN112508227A - Method for rapidly calculating area target visible window of complex conical view field of remote sensing satellite

Info

Publication number: CN112508227A
Application number: CN202011196998.9A
Authority: CN
Inventors: 黄丽霞; 殷建丰; 张众; 鄂智博; 彭妮娜; 王心月; 苗峻; 王博
Original assignee: Beijing Institute of Spacecraft System Engineering
Current assignee: Beijing Institute of Spacecraft System Engineering
Priority date: 2020-10-30
Filing date: 2020-10-30
Publication date: 2021-03-16
Anticipated expiration: 2040-10-30
Also published as: CN112508227B

Abstract

The invention discloses a method for quickly calculating a regional target visible window of a remote sensing satellite complex conical view field, wherein the calculation efficiency is improved by 10^3 times in comparison with the calculation speed of a traditional tracking propagation calculation method in the aspect of visibility judgment, and is improved by 10^5 times in comparison with the traditional method in the aspect of calculation of a global visible window. Meanwhile, the relative error of the calculation precision and the STK is within 0.1 percent, and the actual engineering requirements are met; according to the method, the satellite orbit information is obtained through Lagrange interpolation, the calculation process is independent of the orbit model, and any orbit model can be met, so that the algorithm is wider in applicability; since the boundary of the regional target is described as a great circle arc by the method, 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

Method for rapidly calculating area target visible window of complex conical view field of remote sensing satellite

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 prior studies, the visibility problem was first focused on the visibility of point targets by satellites. The most common method is called as a propagation algorithm, namely, the discrete time step is traversed to carry out judgment one by one, the method is accurate in calculation, but the calculation efficiency is low, and the method is often used as a comparison algorithm in documents. Subsequent studies have focused on improving the problem of excessive calculation. Lawton et al firstly proposes to use a visual function method for judging the visibility of satellite-satellite and satellite-point targets, so that the calculation efficiency is greatly improved, but the method is only suitable for a small eccentricity orbit, AliI et al adopts a great circular arc approximate orbit to obtain a sub-satellite point track in one period, the model is simplified, the calculation efficiency is high but only suitable for a low orbit satellite, Mai Y et al considers that the satellite can perform visible window calculation under attitude maneuver, Han C et al adopts a Hermit interpolation method on the calculation of the visual function, Zhangjin et al proposes a coarse search method for changing the step length of the satellite at low latitude and high latitude.

However, the above researches are all methods for calculating a point target visible window by a satellite, the existing researches are few for regional targets, and the original method cannot be directly popularized due to the fact that the visibility problem of the regional targets is greatly influenced by the field type. Some existing studies are still based on an extension of the point target, mainly sampling the region inside or the region boundary to approximate the solution, but this approach can result in a significant increase in the amount of computation. For example, the method does not consider the satellite field of view, and directly disperses the boundary of the regional target into point targets and then obtains the union of the visible windows of the point targets. Wanglong et al consider the case of coverage information in the calculation process at the same time. Some studies have considered how to increase the coarse search range in the calculation process, and wisdom et al propose to use dichotomy to perform the fine search to increase the initial search step. Therefore, at present, no general and efficient algorithm exists for the visibility calculation problem of the regional target, and the types of the fields related to the research are only conical and rectangular fields. Therefore, it is necessary to provide an accurate and efficient method for complex cone fields.

Disclosure of Invention

Aiming at the problem, the invention provides a semi-analysis rapid calculation method of a regional target visible window based on a complex conical field of view, which can rapidly determine an accurate regional target visible window.

A method for calculating a regional target visible window of a remote sensing satellite complex cone field of view comprises the following steps:

step 1, establishing mathematical description of a complex conical field of view: the projection of the circle corresponding to the inner half cone angle and the projection of the circle corresponding to the outer half cone angle of the complex cone field on the earth surface are two common circular arcs, and the projection of the two sides corresponding to the minimum clock angle and the maximum clock angle on the earth surface are two large circular arcs; wherein, the circle center of the great arc coincides with the sphere center, and the circumference is on the surface of the earth; the common circular arc is any circular arc except a great circular arc 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 edge of the convex polygon is a large circular arc on the sphere of the earth;

step 3, judging whether an overlapping area exists between a visible area A of the projection of the complex cone view field on the earth surface and an area B of the area target at each moment, specifically:

(81) judging whether the area A is in the area B:

(811) traversing each edge of the area B, and calculating the limit point of the area A relative to the edge; wherein the extreme point refers to a point on the boundary of region a that is most likely to be outside region B; each boundary edge of the region B corresponds to a group of limit points;

(812) judging whether the corresponding limit points of each edge of the region B are all positioned at the inner side of the edge or not aiming at each edge of the region B, if one limit point is not positioned at the inner side of the edge, exiting, returning to 'no', and entering the step (82);

(813) if all the limit points on the area A are positioned at the inner side of each side of the corresponding area B, the area A is positioned in the area B at the moment;

(82) judging whether at least one intersection point exists on the boundary of the area A and the area B, if so, determining that the two areas have the intersection point; if not, exiting, returning to 'no', and entering the step (83);

(83) judging whether the area B is in the area A:

sequentially judging whether each boundary point of the regional target B is in the projection region A of the complex cone view field, if all the points are met, the region B is in the region A; otherwise, if one point is not satisfied, quitting and returning to 'no';

for a certain moment, if one of the three conditions (81), (82) and (83) is satisfied, the field of view at the moment is visible for the regional target; if the three conditions are not met, the field of view at the moment is invisible to the regional target;

and 4, determining a visible window of the complex conical view field to the regional target B according to the position relation between the region A and the region B at each moment obtained by calculation in the step 3.

Preferably, in the step (811), the method for calculating the limit point includes:

firstly, calculating the half cone angle of the earth corresponding to the half angles of the inner cone and the outer cone of the complex cone field of view

And

where D represents the distance of the satellite from the center of the earth's sphere, R represents the radius of the earth, θ represents the half cone angle of the satellite's field of view,

represents the half cone angle of the earth to the satellite field of view as found:

next, the "limit point" is calculated: taking the 'limit points' as 6 at most 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 area target boundary, and the specific steps are as follows:

calculating a unit vector n of unitized velocity and inverse angular velocity_x,n_yThe unit direction vector corresponding to each "clock edge" is obtained by defining the clock angle, and taking the "clock edge" where 1,3 points are located as an example, the unit direction vector v is_1,3The expression is as follows:

represents a minimum clock angle;

utilizing a rotation method to vector the position of the center of a circular ring where the complex cone field of view projection area is located to v_1,3Direction is respectively rotated

A corner,

The angle obtains the position vector of 1 point and the position vector of 3 points in the same way, and the position vectors of 2 and 4 points are obtained by the method;

calculating the possible 5 th and 6 th limit points of the boundary line of the projection area A relative to the area B of the complex cone field of view: when the difference between the maximum and minimum clock half angles is less than 180 degrees, a 5 th limit point may exist; when greater than 180 degrees, there are 5 th and 6 th limit points;

regarding the possible 5 th and 6 th limit points on the boundary of the area A, taking the normal vector of the boundary of the area target as the direction vector of the possible 5 th and 6 th limit points, and calculating the position vector of the possible limit points by adopting a calculation method of

points

1,2,3 and 4; it is then determined whether the possible limit point is in the area a according to the following formula:

if the possible limit point meets the formula, 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 a radical of₅For a position vector of possible limit points, the norm function represents a unitization, and the expression of the f-function is as follows:

represents a maximum clock angle; v. of_1/2＝f(norm(v_1,3+v_2,4) Represents a midpoint vector for region a; v. of_2,4A unit direction vector representing the "clock edge" at which the 2,4 points are located.

Preferably, the rotating method specifically comprises the following steps:

obtaining a vector p 'obtained by rotating the vector p by α toward the unit vector v', p 'being represented by the following formula p' ═ cos (α) p + sin (α) v^*Wherein v is^*Norm (v ' - (v ' · p) v ') indicates the unitization of a vector; the unit vector v' represents a unit direction vector of a great circular arc or a general circular arc.

Preferably, in the step (812), the method of determining whether the corresponding limit points are all located inside the edge includes:

let v denote the normal vector of each side of the region B, let p denote the position vector of a certain point, if p · v ≧ 0, the vector p is on the same side as the normal vector of the side, otherwise, it is outside the normal vector of the side.

Preferably, in the step (82), when determining whether the intersection point exists between the area a and the area B, determining whether the intersection point exists between the great arc where the target boundary of each area is located and the great arc of the maximum and small clock angle projection of the complex cone field of view by the following method, specifically:

the intersection Q of the two great arcs is calculated as follows, Q ═ norm (v × v'), and it is determined whether Q is on the great arc d₁d₂Internally, it is necessary to determine whether (d) is satisfied at this time₁×Q)·(Q×d₂) Not less than 0 and Q (d)₁+d₂) And more than or equal to 0, if the two arcs meet the requirement, the Q is proved to be in the large arc, namely the two large arcs have an intersection point.

Preferably, in the step (82), when determining whether the intersection point exists between the area a and the area B, determining whether the intersection point exists between the great arc of the target boundary of each area and the common arc projected by the inner cone and the outer cone of the complex cone field of view by the following method, specifically:

setting the intersection point of the common circular arc and the large circular arc as Q ', and setting the included angle between the unit vector v and the unit vector v' as beta; wherein v and v' are respectively a unit normal vector of a plane where the great circular arc is located and a unit normal vector of a plane where the common circular arc is located;

if the beta + theta is equal to 90 degrees, the common circular arc is tangent to the great circular arc; theta represents a half cone angle of the satellite view field corresponding to the common circular arc;

if the beta + theta is more than 90 degrees, the common circular arc is intersected with the great circular arc;

if the beta + theta is less than 90 degrees, the common circular arc and the large circular arc do not have an intersection point;

wherein β is calculated as follows ═ arccos (| v · v' |);

when the intersection point is judged to exist, the vector needs to be calculated: if the included angle between the intersection point Q' and the current projection plane is γ, cos (γ) ═ cos (θ)/sin (β); at this time, the in-plane direction vector of the structure is v_//Norm (v '- (v'. v) v) and unit vector v in the vertical plane_⊥＝norm(v’×v)；

The intersection point Q' is then found as: q' ═ cos (γ) v_//±sin(γ)v_⊥；

And finally, judging whether the intersection point is in the large arc and the common arc, projecting Q' onto a common circular plane, and judging whether the intersection point exists between circles.

Preferably, the specific method in step 4 is as follows:

firstly, judging the visibility of a remote sensing satellite to a regional target at the moment according to the discrete step length; then arranging the visibility under each step length according to a time sequence and determining the range of the visible starting time and the visible ending time of each visible window; and then obtaining the fine time 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 method for calculating a regional target visible window aiming at a complex conical view field is provided;

the calculation efficiency is improved by 10^3 times in visibility judgment compared with the calculation speed of the traditional tracking propagation calculation method, and is improved by 10^5 times in the calculation of the global visible window compared with the traditional method. Meanwhile, the relative error of the calculation precision and the STK is within 0.1 percent, and the actual engineering requirements are met;

according to the method, the satellite orbit information is obtained through Lagrange interpolation, the calculation process is independent of the orbit model, and any orbit model can be satisfied, so that the algorithm is wider in applicability;

since the boundary of the regional target is described as a great circle arc by the method, 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 view of a complex conical field-of-view imaging;

FIG. 2 is a schematic view of a great circle and a general circle;

FIG. 3 is a schematic diagram of intersection points between a great arc and a common arc;

FIG. 4 is a half cone angle of the earth to the satellite field of view;

FIG. 5 is a schematic representation of the meaning of "limit points";

FIG. 6 is a schematic diagram of the complex cone field of view "limit point" solution;

FIG. 7 is a unit vector of a complex cone field of view;

FIG. 8 is a flowchart of a general program algorithm.

Detailed Description

The invention is described in detail below by way of example with reference to the accompanying drawings.

The invention has the following implementation steps:

step 1, establishing mathematical description of complex conical field of view

The imaging schematic diagram of the complex cone field of view is shown in fig. 1, and the shape and size of the field of view are represented by four parameters, namely an inner cone half angle, an outer cone half angle, a minimum clock angle and a maximum clock angle. It should be clear that, under the assumption of the globe 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 earth surface are two common circular arcs, and the projections of the two sides corresponding to the minimum and large clock angles on the earth surface are two large circular arcs.

The circle center of the great circle in the previous section is coincident with the center of the sphere, and the circumference of the great circle is on the surface of the sphere. The large circle is also called geodesic because two points on the sphere have the shortest distance along the geodesic. The ordinary circle refers to any circle with a circumference on the sphere, and for the sake of convenience in distinguishing, the ordinary circles described later in the invention do not include large circles unless otherwise specified.

Step 2, establishing mathematical description of regional targets

The regional target is a closed convex polygon on the earth surface, and each edge of the convex polygon is a large circular arc on the earth sphere, namely a geodesic line. Conventionally, the initial description of the regional target boundary points is described in terms of (longitude, latitude, altitude) in a geodetic coordinate system.

Step 3, describing visibility problems of the satellite complex cone view field to regional targets

The visible window of the satellite to the regional target refers to the time range in which the loaded field of view carried by the satellite can observe the regional target. According to the mathematical description of the step 1 and the step 2, the visibility problem of the satellite complex cone field of view to the regional target can be expressed as follows: whether the satellite complex cone field of view projects in the visible area of the earth surface and the regional target have overlapping areas.

And 4, in order to reduce the calculation amount of the problem of judging whether one area is in the other area, a thought of calculating a limit point is provided.

For a projection field area a and an area target B with complex shapes, the conventional method for determining whether the area a is inside the area B includes the following steps: and traversing all the points of the area A sequentially according to the boundary of the area B, and judging whether all the points are in each edge of the area B. Such a processing method is computationally expensive. Therefore, the present invention proposes the concept of "limit point", and its essential meaning is to find the point that most probably does not satisfy the condition that "the area a is located inside the area B", and to refer to this point as "limit point", and to judge whether the positional relationship between the two areas satisfies the condition that "the area a is located inside the area B" by judging the positional relationship between the "limit point" and the area B. The meaning is shown in figure 5. That is, whether the area a shown in the figure is on a certain side in the arrow direction is judged, and only one point shown in the figure needs to be verified, wherein the point is the "limit point" of the invention, and the principle is similar to that 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 direction of the arrow in fig. 5), and therefore, the "limit point" of the area a corresponding to each side of the area object B should be calculated independently.

And 5, establishing a vector geometric basic algorithm model for calculating the overlapping problem of two spherical areas.

By converting the problem into the problem of overlapping two spherical areas, the calculation amount is obviously reduced by utilizing the calculation of spherical space vectors, and for this reason, the invention provides the following five vector geometric basic algorithms for quickly calculating the relevant required information:

(51) calculating a vector of the spherical surface after the one-bit vector rotates along a certain direction;

the algorithm is designed to solve the "limit points" of the complex cone field of view relative to the target boundaries of the regions. As shown in fig. 2, when a vector p 'obtained by rotating p by α toward v' (unit vector) is obtained, p 'can be expressed by the following formula p' ═ cos (α) p + sin (α) v^*Wherein v is^*Norm (·) represents the unitization of a vector.

(52) Judging whether one point on the spherical surface is on one side of the great circle or not;

the algorithm is designed to determine the relationship between each point and each region target boundary. As shown in fig. 2. If p is determined to be on one side of the great circle 2. If p.v.gtoreq.0, p is on the same side of the normal vector of the great circle 2, otherwise, p is on the outer side of the normal vector of the great circle "

(53) Judging whether one point of the spherical surface is on one side of the common circle;

the algorithm is designed for judging the common circular relation between the target boundary point of each region and the projection of the inner cone and the outer cone of the complex cone view field. As shown in fig. 2. If p is to be determined to be on one side of the ordinary circle. Similarly, the magnitude of p · v' is calculated. If p · v ≧ cos (θ), it means that p is on the same side as the normal vector of the ordinary circle, whereas p is on the outer side of the normal vector of the circle.

(54) Judging whether the two sections of large arcs have intersection points;

the algorithm is designed for judging whether intersection points exist between the target boundaries of all the areas and the maximum and small clock angle projection great circle of the complex cone view field. The general idea of judging whether two large arcs have an intersection point can be summarized as the following two points: firstly, calculating the intersection point of two great circles; next, it is determined whether the point is on two large arcs.

Taking fig. 2 as an example, first, the intersection Q of the great circle 2 and the great circle 1 may be calculated as follows, where Q is ± norm (v × v'), and there are two positive and negative cases in the formula because there are two intersection points. Then, it is judged whether Q is in the great circle d₁d₂Inside, at which time a judgment is required (d)₁×Q)·(Q×d₂) Not less than 0 and Q (d)₁+d₂) Not less than 0, if the two conditions are met, the Q is proved to be in the large arc d₁d₂Inside.

(55) And judging whether an intersection point exists between one section of the large arc and one section of the common arc.

The algorithm is designed for judging whether intersection points exist between the target boundary of each region and a common circle projected by an inner cone and an outer cone of a complex cone field. The calculation process is the same as the algorithm (54), and is described in detail below with reference to the side view of FIG. 2 perpendicular to the directions v and v'. As shown in fig. 3. Wherein, the intersection point of the common circle and the big circle 2 is Q ', and the included angle between v and v' is beta.

Similarly, the intersection Q' is required first, but it is necessary to determine whether there is an intersection first, because there are three possibilities for the intersection of the ordinary circle and the great circle.

If the beta + theta is equal to 90 degrees, the common circle is tangent to the great circle;

if β + θ >90 °, the ordinary circle intersects the great circle.

If beta + theta is less than 90 degrees, the common circle and the large circle have no intersection point.

Here, β is calculated as follows, taking into account both the positive and negative of the large circular normal vector.

When the intersection point is judged to exist, the vector of the intersection point needs to be calculated. If the angle between the intersection Q' and the current projection plane is γ, cos (γ) is cos (θ)/sin (β). At this time, the in-plane direction vector of the structure is v_//Norm (v '- (v'. v) v) and unit vector v in the vertical plane_⊥＝norm(v’×v)。

The intersection point Q' can be found as follows: q' ═ cos (γ) v_//±sin(γ)v_⊥

And finally, judging whether the intersection point is in two circular arcs, namely projecting Q' to a common circular plane, wherein the idea is consistent with the algorithm (54), and the description is omitted.

Step 6, algorithm pretreatment:

(61) normal vector calculation of regional target boundaries

For convenient subsequent calculation, sequencing boundary points of the regional targets in a counterclockwise manner, converting coordinates of the boundary points into coordinates under a ground fixation system, conveniently converting the coordinates by definition, and performing normalization processing to obtain D N₁,DΝ₂,...,DΝ_n(DistrictNode)。

The obtained coordinates D Ν₁,DΝ₂,...,DΝ_nAnd performing cross multiplication on the normal vectors of the boundaries according to the front and back orders. In order to obtain a geodesic line formed by boundary points of two adjacent areas, the vector of the boundary points needs to be cross-multiplied to obtain a normal vector thereof, and the expression is

And carrying out normalization treatment:

obtaining the normal vector of the boundary of the region as NV₁,NV₂,...,NV_n。

(62) And calculating the half cone angles of the inner cone and the outer cone of the earth corresponding to the satellite field of view.

In the process of solving the limit point, the half cone angle of the earth to the field of view of the satellite needs to be used, and the eccentricity of the general earth observation satellite is close to zero. The half cone angle of the earth to its field of view remains nearly constant 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 area target.

The half-cone angle of the earth to the satellite field of view may be represented by fig. 4. Where D represents the distance of the satellite from the center of the earth's sphere, R represents the radius of the earth, θ represents the half cone angle of the satellite's field of view,

the half cone angle of the earth to the satellite field of view is calculated as shown in fig. 4.

For a complex conical field of view, the half cone angle of the earth corresponding to the half angles of the inner and outer circular cones needs to be calculated

And

step 7, calculating the 'limit point' of the complex cone projection field of view "

For the complex cone visual field, because the boundary of the projection area is complex, in order to facilitate subsequent uniform processing, the invention combines the shape of the projection area, and takes the number of the 'limit points' in one judgment as 6 at most, wherein the

points

1,2,3 and 4 are 4 boundary points of the projection area A of the complex cone visual field, and the

points

5 and 6 are calculated (possibly not existed) according to the condition of the area target boundary. The "limit point" is schematically shown in FIG. 6.

(71) Firstly, calculating the half cone angle of the earth corresponding to the half cone angles of the inner cone angle and the outer cone angle

And

the specific algorithm is detailed in step 6, namely calculating the half cone angle of the inner and outer cones of the satellite view field corresponding to the earth;

(72) next, the "limit points" 1,2,3,4,5,6 of the complex cone field of view projection area in fig. 7 are calculated.

Calculating a unit vector n of unitized velocity and inverse angular velocity_x,n_yFig. 7 shows a unit vector of the plane.

After the unit vector is obtained, the unit direction vector corresponding to each "clock edge" is obtained through the definition of the clock angle, and the unit direction vector v is taken as the "clock edge" where 1 and 3 points are located in fig. 7 as an example_1,3The expression is as follows

The position vector of the center of a circular ring where the projection area of the complex cone field of view is located is directed to v_1,3Direction is respectively rotated

A corner,

The angle can obtain the position vector of 1 point and the position vector of 3 points, and the rotation method is detailed in the algorithm (51) in step 5. According to the method can obtainTo the 1,2,3,4 point.

For the possible 5,6 points, the calculation method is the same, except that the direction vector is the normal vector of the boundary of the regional target. It should be noted that, since the projection area of the complex cone field of view is not a complete circle, the points rotated by the above method may not exist in the effective visible area of the complex cone field of view, and therefore, the existence thereof needs to be determined.

First, a midpoint vector v of the projection region is calculated_1/2The calculation formula is as follows:

v_1/2＝f(norm(v_1,3+v_2,4))

wherein norm function represents unitization, and the expression of f function is as follows:

if the 5-point bit vector obtained according to the original algorithm is p₅If the following relation is satisfied, the point is proved to be in the field of view, namely the point exists, otherwise the point does not exist.

Step 8, judging whether two areas have overlapping areas at a certain moment according to a visibility judgment analysis algorithm

One of the bases for solving the visibility window is to be able to judge the visibility of the regional targets at each instant. According to the proposed vector geometry basic algorithm, the invention provides a mathematical model aiming at the problem, the visible situation is divided into three situations, whether the situation is met or not is judged in sequence aiming at each situation, and if one situation is met, the moment can be judged to be visible. If the visible region of the complex cone field of view projected on the earth's surface is called region a and the regional target is called region B, then the three cases are: a is in B, (B) A and B have an intersection at the boundary, and (c) B is in A. The algorithm flows for these three cases are as follows:

(81) judging whether the situation (a) is satisfied, namely judging whether the conical view field is positioned at the regional target:

(811) and traversing each edge of the regional target B, and calculating a limit point of the region A relative to the edge. The specific method for calculating the limit point is detailed in step 7;

(812) for each edge of the area target, whether all the 'limit points' are located inside the edge is judged, and the specific method for judging whether the point is located inside the edge is detailed in an algorithm (52) in step 5. If a limit point is not in the inner side of the certain edge, the method exits, returns to No and enters the step (82).

(813) If all the limit points are positioned at the inner side of each edge after traversing each edge, then returning to 'yes'.

The 'limit point' of the complex cone field is a special point searched by the judgment condition (a), and the purpose is to obtain the relative position relation between the projection area of the complex cone field and the target area by proving the position relation between the points and the target area so as to reduce the calculation amount. In addition to the presence of 4 points on the boundary of the projection area of the complex cone field of view, the "limit points" can be divided into two categories depending on whether the difference between the maximum and minimum half-clock angles is greater than 180 degrees, as shown in fig. 7. When the angle is less than 180 degrees, judging whether a point 5 exists according to the condition of the boundary of the area target; if the distance is larger than 180 degrees, whether 5 or 6 points exist is judged according to the condition of the boundary of the regional target.

(82) Judging whether the situation (b) is satisfied, namely judging whether the projection area of the complex cone field of view and the target area have an intersection point:

sequentially judging whether each boundary of the region target has an intersection point with the boundary of the complex cone field of view in the earth projection region, if one intersection point exists, meeting the condition (b), and returning to 'yes'; if not, returning to 'no'. The specific method for judging whether the intersection point exists is detailed in the algorithm (54) "judging whether the intersection point exists between the two sections of the large circular arc" in the step 5, and the algorithm (55) "judging whether the intersection point exists between the section of the large circular arc and the section of the common circular arc.

(83) Judging whether the situation (c) is met, namely judging whether the target area is positioned in the projection area of the complex cone field of view:

sequentially judging whether the boundary point of each region target is in the projection region of the complex cone field of view, if all the points are met, meeting the condition (c), and returning to 'yes'; if one point is not satisfied, returning to 'no'. The detailed algorithm is shown in the algorithm (52) in the step 5, whether one point on the spherical surface is on a certain side of the great circle is judged, and (53) whether one point on the spherical surface is on a certain side of the common circle is judged.

The fact that the projection area is located inside the complex cone field of view means that the projection area is located on the opposite side of the normal vector of the ordinary circle projected by the inner cone, and the projection area is located on the same side of the normal vector of the ordinary circle projected by the outer cone and the normal vector of the other projection boundary.

Step 9, determining the visible window of the complex cone view field through semi-analysis

Through the visibility judgment analysis algorithm, a semi-analysis method for finally determining the visible window is obtained. Firstly, judging the visibility at the moment according to the discrete step length; then arranging the visibility under each step length according to a time sequence and determining the range of the visible starting time and the visible ending time of each visible window; then, fine time of each visible window is obtained through binary search, wherein satellite orbit information used in the binary search is obtained through Lagrange interpolation; and finally, summarizing and outputting the information of each accurate visible window. The general flow of the operation can be described by a flow chart shown in fig. 8.

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

1. A method for calculating a regional target visible window of a remote sensing satellite complex cone field of view is characterized by comprising the following steps:

step 3, judging whether an overlapping area exists between a visible area A projected on the earth surface by the complex cone field of view at each moment and an area B where an area target is located, specifically:

(81) judging whether the area A is in the area B:

(811) traversing each edge of the area B, and calculating the limit point of the area A relative to the edge; wherein, the limit point refers to a 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;

(83) judging whether the area B is in the area A:

2. The method for calculating the regional target visible window of the remote sensing satellite complex cone field of view of claim 1, wherein in the step (811), the method for calculating the limit point comprises:

And

next, the "limit point" is calculated: taking the 'limit points' as 6 at most 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 area target boundary, and the specific steps are as follows:

represents a minimum clock angle;

A corner,

The same principle is adopted for the angle to obtain 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;

regarding the possible 5 th and 6 th limit points on the boundary of the area A, taking the normal vector of the boundary of the area target as the direction vector of the possible 5 th and 6 th limit points, and calculating the position vector of the possible limit points by adopting a calculation method of points 1,2,3 and 4; it is then determined whether the possible limit point is in region a according to the following formula:

represents a maximum clock angle; v. of_1/2＝f(norm(v_1,3+v_2,4) Represents a midpoint vector for region a; v. of_2,4The unit direction vector of the "clock edge" where the 2,4 dots are located is indicated.

3. The method for calculating the regional target visible window of the remote sensing satellite complex cone field of view of claim 1, wherein the rotation method is specifically as follows:

4. The method for calculating the regional target visible window of the remote sensing satellite complex cone field of view according to claim 1, wherein in the step (812), the method for judging whether the corresponding limit points are all located inside the edge comprises the following steps:

5. The method for calculating the regional target visible window of the complex conical field of view of the remote sensing satellite according to claim 1, wherein in the step (82), when judging whether the region a and the region B have an intersection, judging whether the orthodrome where the boundary of each regional target is located and the orthodrome of the maximum small-hour-clock-angle projection of the complex conical field of view have an intersection by the following method, specifically:

the intersection Q of the two great arcs is calculated as follows, Q ═ norm (v × v'), and it is determined whether Q is on the great arc d₁d₂Internally, it is necessary to determine whether (d) is satisfied at this time₁×Q)·(Q×d₂) Not less than 0 and Q (d)₁+d₂) And (3) being more than or equal to 0, if the two circular arcs meet the requirement, the Q is proved to be in the large circular arc, namely the two large circular arcs have an intersection point.

6. The method for calculating the regional target visible window of the complex conical field of view of the remote sensing satellite according to claim 1, wherein in the step (82), when judging whether the region a and the region B have an intersection, judging whether the great arc of the boundary of each regional target and the common arc projected by the inner cone and the outer cone of the complex conical field of view have an intersection by the following method, specifically:

wherein β is calculated as follows ═ arccos (| v · v' |);

7. The method for calculating the regional target visible window of the remote sensing satellite complex conical field of view according to claim 1, wherein the specific method in the step 4 is as follows:

8. The method of claim 7, wherein the satellite orbit information used in the binary search is obtained by Lagrangian interpolation.