CN102682201B - Method for acquiring real-time satellite geosynchronous scanning areas - Google Patents

Abstract

The invention relates to a method for acquiring real-time satellite geosynchronous scanning areas. A calculation equation of satellite geosynchronous scanning areas is provided in accordance with space geometry relations, an analytical solution of the equation is obtained, and compared with a numerical method, an analytical method is better than the numerical method in the calculation efficiency. Results can be used in the calculation of geosynchronous observation of earth resources satellites and remote sensing satellites. Compared with traditional calculation methods, the method is characterized in that (1) the method provides a satellite geosynchronous observation equation based on space geometry relations, provides equations sets which meets requirements for satellite geosynchronous observation from geometric observation, and is suitable for requirements of the geosynchronous observation in satellite side swinging; (2) the method provides an expression of a solution of the analytical method and provides the analytical solution of the satellite geosynchronous observation in accordance with the observation equation; and (3) the calculation efficiency and the accuracy of the real-time satellite geosynchronous observation are high. The calculation speed of common numerical methods is slow, and the timeliness of the satellite geosynchronous observation cannot be met well. However, the timeliness problem can be solved well through introduction of the analytical solution.

Description

A kind of method obtaining the real-time scanning area over the ground of satellite

Technical field

The invention belongs to aerospace measurement and control application, relating to a kind of method obtaining the real-time scanning area over the ground of satellite, being applicable to earth resources satellite and the over the ground scanning area calculating of remote sensing satellite in flight course.

Background technology

Along with the fast development of Chinese Space earth observation technology, the demand that satellite scans the ageing of computing technique and accuracy is over the ground also day by day obvious.Earth resources satellite and remote sensing satellite scan ground with certain bandwidth, because satellite orbit has certain inclination angle, cause its scanning strip also to have certain inclination angle, calculate satellite real time scan region and inconvenience.Need to provide the high satellite of a kind of quick precision scanning area computing method over the ground.

Summary of the invention

The technical matters solved

In order to avoid the deficiencies in the prior art part, the present invention proposes a kind of method obtaining the real-time scanning area over the ground of satellite, the satellite equation that calculates of scanning area is over the ground given according to space geometry relation, and obtain the analytical solution of this equation, compared with numerical method, in counting yield, analytic approach is much better than numerical method.This result can be used in the calculating of earth resources satellite and remote sensing satellite earth observation.

Technical scheme

Obtain a method for the real-time scanning area over the ground of satellite, it is characterized in that: be reference frame admittedly with ground, the position vector in satellite a certain moment is w=(x ₀, y ₀, z ₀), velocity vector is v=(v _x, v _y, v _z); The coordinate unification of two end points of satellite scanning plane and earth surface intersection is designated as a=(x, y, z); Concrete steps are as follows:

Step 1 determines the equation that earth surface point meets: two end points of satellite scanning plane and earth surface intersection over the ground meet equation: $x^2+y^2+z^2=R_e^2;$

Step 2: calculate satellite and point to the angle theta that the vector in the earth's core and satellite point to the vector scanning end points

${\mathrm{xx}}_0+{\mathrm{yy}}_0+{\mathrm{zz}}_0=r^2-r\×\cos \left(\mathrm{\θ}\right)\×\sqrt{r^2+R_e^2-2({\mathrm{xx}}_0+{\mathrm{yy}}_0+{\mathrm{zz}}_0)};$

Step 3: relational expression when two scanning end points are vertical with satellite flight direction over the ground according to satellite

v _x(x-x ₀)+v _y(y-y ₀)+v _z(z-z ₀)＝0 ，

                              

Integrating step 1 and step 2, obtain expressing satellite scanning area equation over the ground, solve satellite over the ground scanning area equation obtain satellite scanning coordinate point over the ground:

$\left\{\begin{array}{ccc}{x}^2+y^2+z^2& =& R_e^2\\ {\mathrm{xx}}_0+{\mathrm{yy}}_0+{\mathrm{zz}}_0& =& r^2-r\×\cos \left(\mathrm{\θ}\right)\×\sqrt{r^2+R_e^2-2({\mathrm{xx}}_0+{\mathrm{yy}}_0+{\mathrm{zz}}_0)}\\ v_x(x-x_0)+v_y(y-y_0)+v_z(z-z_0)& =& 0\end{array}\right.$

Wherein: earth mean radius, represent the earth's core distance, θ is the maximum side-sway angle of satellite;

Be cycled to repeat step 1 ~ step 3, obtain the region that satellite scans in real time over the ground.

Beneficial effect

A kind of method obtaining the real-time scanning area over the ground of satellite that the present invention proposes, compared with Traditional calculating methods, the inventive method has following features:

(1) satellite earth observation equation is provided based on space geometry relation.The method from geometry observation, provide satellite earth observation the system of equations that meets, and the demand of earth observation when adapting to satellite side-sway.

(2) solution's expression of analytic approach is provided.The analytical solution of satellite earth observation is provided according to observation equation.

(3) satellite over the ground real-time monitored counting yield and precision high.General numerical method computing velocity is slow, and can not meet the ageing of satellite earth observation very well, the introducing of analytical solution well solves ageing problem.

Accompanying drawing explanation

Fig. 1: satellite and geospace geometric relationship schematic diagram

Fig. 2: v3 and satellite motion schematic diagram in the same way

Fig. 3: v3 and the reverse schematic diagram of satellite motion

Embodiment

Now in conjunction with the embodiments, the invention will be further described for accompanying drawing:

Satellite over the ground scanning area calculate equation

We get reference coordinate with being solid system, if the position vector in satellite a certain moment is w=(x ₀, y ₀, z ₀), velocity vector is v=(v _x, v _y, v _z).The coordinate unification of two end points of satellite scanning plane and earth surface intersection is designated as a=(x, y, z).The space geometry relation of satellite and the earth is as Fig. 1.

Calculate an a, its demand fulfillment following equations:

Two end points all at the earth's surface, can obtain

$x^2+y^2+z^2=R_e^2$

End points and satellite links and between satellite and the earth's core line angle be θ, can obtain

${\mathrm{xx}}_0+{\mathrm{yy}}_0+{\mathrm{zz}}_0=r^2-r\×\cos \left(\mathrm{\θ}\right)\×\sqrt{r^2+R_e^2-2({\mathrm{xx}}_0+{\mathrm{yy}}_0+{\mathrm{zz}}_0)}$

Two end points lines are vertical with satellite working direction, can obtain

v _x(x-x ₀)+v _y(y-y ₀)+v _z(z-z ₀)＝0

Namely need to meet following system of equations

$\left\{\begin{array}{ccc}{x}^2+y^2+z^2& =& R_e^2\\ {\mathrm{xx}}_0+{\mathrm{yy}}_0+{\mathrm{zz}}_0& =& r^2-r\×\cos \left(\mathrm{\θ}\right)\×\sqrt{r^2+R_e^2-2({\mathrm{xx}}_0+{\mathrm{yy}}_0+{\mathrm{zz}}_0)}\\ v_x(x-x_0)+v_y(y-y_0)+v_z(z-z_0)& =& 0\end{array}\right.$

In above formula, earth mean radius, represent the earth's core distance, θ is the maximum side-sway angle of satellite.

Satellite over the ground scanning area calculate numerical solution:

Above-mentioned equation is a Nonlinear System of Equations, and its numerical solution has multiple, has gradient method ^[1], the methods such as the Generalized Quasi method of quasi-Newton method and least square solution, here for gradient method.

If Nonlinear System of Equations is f _i(x ₁, x ₂, L, x _n)=θ, i=1,2, L, n

Objective definition function is

$F=F(x_1,x_2,\mathrm{\Λ},x_n)=\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{f}_i^2$

Then the computation process of gradient method is as follows:

(1) selected one group of initial value x ₁, x ₂, L, x _n

(2) calculating target function value $F=F(x_1,x_2,L,x_n)=\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{f}_i^2$

(3) if F < ε, then X=(x ₁, x ₂, L, x _n) ^tbe one group of real root of system of equations, process terminates; Otherwise continue.

(4) calculating target function is at (x ₁, x ₂, L, x _n) partial derivative put

$\frac{\&PartialD;F}{{\&PartialD;x}_i}=2\underset{j=1}{\overset{n}{\mathrm{\&Sigma;}}}{f}_j\frac{{\&PartialD;f}_j}{{\&PartialD;x}_i},$ i＝1，2，L，n

Calculate again

$D=\underset{j=1}{\overset{n}{\mathrm{\&Sigma;}}}{\left(\frac{\&PartialD;F}{{\&PartialD;x}_j}\right)}^2$

(5) calculate

$x_i-\mathrm{\&lambda;}\frac{\&PartialD;F}{{\&PartialD;x}_i}\&DoubleRightArrow;x_i,$ i＝1，2，A，n

Wherein, λ=F/D

Double counting from (2), until meet accuracy requirement.

Satellite over the ground scanning area calculate analytical solution:

Because numerical solution computing velocity is slow, we directly derive x, the method for y, z expression formula.That is:

$\left\{\begin{array}{ccc}x& =& f(w,v)\\ y& =& f(w,v)\\ z& =& f(w,v)\end{array}\right.$

The process specifically setting up expression formula is as follows:

If xx ₀+ yy ₀+ zz ₀=S, subtracts second carrying out of equation in Constrained equations, calculates S=s1, s2.

So system of equations becomes:

$\left\{\begin{array}{ccc}{x}^2+y^2+z^2& =& R_e^2\\ {\mathrm{xx}}_0+{\mathrm{yy}}_0+{\mathrm{zz}}_0& =& s1\\ v_x(x-x_0)+v_y(y-y_0)+v_z(z-z_0)& =& 0\end{array}\right.---\left(1\right)$

And system of equations

$\left\{\begin{array}{ccc}{x}^2+y^2+z^2& =& R_e^2\\ {\mathrm{xx}}_0+{\mathrm{yy}}_0+{\mathrm{zz}}_0& =& s2\\ v_x(x-x_0)+v_y(y-y_0)+v_z(z-z_0)& =& 0\end{array}\right.---\left(2\right)$

At this, we obtain analytical expression for (1), and (2) follow the prescribed rules.

Because expression formula is comparatively complicated, we introduce variable with the simple analytical expression of acquisition form.

Order:

$x_0+\frac{v_y.y_0.x_0}{v_x}+\frac{v_z.z_0.x_0}{v_x}=a,$ $y_0-\frac{x_0.v_y}{v_x}=b,$ $z_0-\frac{v_z.x_0}{v_x}=c,$ $\frac{{s1}^2}{x_0^2}=d,$

$\frac{y_0^2}{x_0^2}=e,$ $\frac{z_0^2}{x_0^2}=f,$ $\frac{-2.s1.y_0}{x_0^2}=g,$ $\frac{-2.s1.z_0}{x_0^2}=h,$ $\frac{2.y_0.z_0}{x_0^2}=i,$ s1-a＝j，

$\frac{(e+1).c^2}{b^2}-\frac{i.c}{b}+f+1=k,$ $\frac{i.j}{b}+h-\frac{(e+1).2.j.c}{b^2}-\frac{g.c}{b}=l,$

$\frac{(e+1).j^2}{b^2}+\frac{g.j}{b}-R_e^2+d=m$

Obtain after arranging: $z_{\mathrm{1,2}}=\frac{-l\&PlusMinus;\sqrt{l^2-4\mathrm{km}}}{2k}$

Then obtain: $y_{\mathrm{1,2}}=\frac{j-{\mathrm{cz}}_{\mathrm{1,2}}}{b},$ $x_{\mathrm{1,2}}=\frac{s1-y_0{y}_{\mathrm{1,2}}-z_0{z}_{\mathrm{1,2}}}{x_0}$

Like this, obtaining two endpoint locations is: position1=(x ₁, y ₁, z ₁) and position2=(x ₂, y ₂, z ₂).

Solve (2) such as method equally, obtaining another two endpoint locations is:

position3＝(x ₃，y ₃，z ₃)，position4＝(x ₄，y ₄，z ₄).

Can predict, satellite is arrived in by plane on the earth air to surface when scanning, and the plane of scanning motion and sphere intersection only have one, therefore only have two end points, four satellite side-sway substar position vectors will bring equation of constraint into above middle inspection is got rid of.Obtain two end points and be designated as position1, position2.So far determine satellite scanning boundary over the ground, calculate complete.

Sometimes need to determine the left and right end points relative to satellite motion direction.We remember the velocity vector v=(v of satellite motion _x, v _y, v _z), remembering that two end points and satellite position make poor vector is v1, v2.V1, v2 multiplication cross is obtained v3, when v3 and satellite velocities in the same way time, can determine that right endpoint is produce the end points of v1, left end point is the end points producing v2; When v3 and satellite velocities reverse time, can determine that left end point is produce the end points of v1, right endpoint is the end points producing v2, and concrete condition is as shown in Figure 2.

Two kinds of examples and comparing:

Getting certain moment a certain satellite position speed is

/-4922603.581.-3124274.845，5054422.871，5423.294，-1133.058，4576.896/

By two kinds of methods, scanning area position calculation is carried out to it respectively.Result is as follows:

Numerical method result of calculation is:

End points 1-4129249.005-2124321.243 4361903.588

End points 2-3975680.102-3018983.720 3958452.479

Analytic calculation result is:

End points 1-4129249.005-2124321.243 4361903.588

End points 2-3975680.102-3018983.720 3958452.479

Scanning area endpoint location is turned to longitude and latitude by table 1

End points	Geocentric right ascension (degree)	Geocentric latitude (degree)
			End points 1	-152.78	43.21
End points 2	-142.79	38.41

Claims (1)

1. obtain a method for the real-time scanning area over the ground of satellite, it is characterized in that: be reference frame admittedly with ground, the position vector in satellite a certain moment is w=(x ₀, y ₀, z ₀), velocity vector is v=(v _x, v _y, v _z); The coordinate unification of two end points of satellite scanning plane and earth surface intersection is designated as a=(x, y, z); Concrete steps are as follows:

Step 1 determines the equation that earth surface point meets: two end points of satellite scanning plane and earth surface intersection over the ground meet equation: $x^2+y^2+z^2=R_e^2;$

Step 2: calculate satellite and point to the angle theta that the vector in the earth's core and satellite point to the vector scanning end points

${\mathrm{xx}}_0+{\mathrm{yy}}_0+{\mathrm{zz}}_0=r^2-r\&times;\cos \left(\mathrm{\&theta;}\right)\&times;\sqrt{r^2+R_e^2-2({\mathrm{xx}}_0+{\mathrm{yy}}_0+{\mathrm{zz}}_0)};$

Step 3: relational expression when two scanning end points are vertical with satellite flight direction over the ground according to satellite

v _x(x-x ₀)+v _y(y-y ₀)+v _z(z-z ₀)＝0，

Integrating step 1 and step 2, obtain expressing satellite scanning area equation over the ground, solve satellite over the ground scanning area equation obtain satellite scanning coordinate point over the ground:

$\left\{\begin{array}{c}{x}^2+y^2+z^2=R_e^2\\ {\mathrm{xx}}_0+{\mathrm{yy}}_0+{\mathrm{zz}}_0=r^2-r\&times;\cos \left(\mathrm{\&theta;}\right)\&times;\sqrt{r^2+R_e^2-2({\mathrm{xx}}_0+{\mathrm{yy}}_0+{\mathrm{zz}}_0)}\\ v_x(x-x_0)+v_y(y-y_0)+v_z(z-z_0)=0\end{array}\right.$

Wherein: R _eearth mean radius, represent the earth's core distance, θ is the maximum side-sway angle of satellite;

Be cycled to repeat step 1 ~ step 3, obtain the region that satellite scans in real time over the ground.