CN102682201A - 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 real-time method of scanning area over the ground of satellite that obtains

Technical field

The invention belongs to aerospace measurement and control application, relate to a kind of real-time method of scanning area over the ground of satellite that obtains, be applicable to the calculating of scanning area over the ground in flight course of ERTS and remote sensing satellite.

Background technology

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

Summary of the invention

The technical matters that solves

Weak point for fear of prior art; The present invention proposes a kind of real-time method of scanning area over the ground of satellite that obtains; Provided the satellite equation of scanning area calculating over the ground according to the space geometry relation; And obtained this equation of analysis and separate, compare with numerical method, analytic approach is much better than numerical method on counting yield.This result can be used in the calculating of ERTS and remote sensing satellite earth observation.

Technical scheme

A kind of real-time method of scanning area over the ground of satellite that obtains, it is characterized in that: with ground is to be reference frame admittedly, and the position vector in a certain moment of satellite 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 be designated as a=(x, y, z); Concrete steps are following:

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

Step 2: calculate satellite and point to the vector in the earth's core and the angle theta that satellite points to the vector of 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: the relational expression when two scanning end points are vertical with the 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, find the solution satellite over the ground the 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:

is earth mean radius;

expression the earth's core distance, θ is the maximum side-sway angle of satellite;

Cycle repeats step 1～step 3 obtains the zone that satellite scans in real time over the ground.

Beneficial effect

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

(1) provides the satellite earth observation equation based on the space geometry relation.This method provides the system of equations that satellite earth observation satisfies from how much observations, and the demand of earth observation during the adaptation satellite side-sway.

(2) provide the expression formula of separating of analytic approach.Provide the analytical solution of satellite earth observation according to observation equation.

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

Description of drawings

Fig. 1: satellite and geospace geometric relationship synoptic diagram

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

The reverse synoptic diagram of Fig. 3: v3 and satellite motion

Embodiment

Combine embodiment, accompanying drawing that the present invention is further described at present:

Satellite is the equation of scanning area calculating over the ground

We get reference frame and are the solid system in ground, and the position vector of establishing a certain moment of satellite 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 be designated as a=(x, y, z).The space geometry relation of the satellite and the earth is like Fig. 1.

Calculate an a, it need satisfy equation:

Two end points can get all at the earth's surface

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

Angle is θ between end points and satellite line and satellite and the earth's core line, can get

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

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

v _x(x-x ₀)+v _y(y-y ₀)+v _z(z-z ₀)＝0

Promptly need satisfy 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 the following formula;

is earth mean radius;

expression the earth's core distance, θ is the maximum side-sway angle of satellite.

Satellite is the numerical solution of scanning area calculating over the ground:

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

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

The objective definition function does

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

Then the computation process of gradient method is following:

(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 finishes; Otherwise continue.

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

$\frac{\∂F}{{\∂x}_i}=2\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{f}_j\frac{{\∂f}_j}{{\∂x}_i},$ i＝1，2，L，n

Calculate again

$D=\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{\left(\frac{\∂F}{{\∂x}_j}\right)}^2$

(5) calculate

$x_i-\mathrm{\λ}\frac{\∂F}{{\∂x}_i}\⇒x_i,$ i＝1，2，A，n

Wherein, λ=F/D

From (2) beginning double counting, till satisfying accuracy requirement.

Satellite is the analytical solution of scanning area calculating over the ground:

Because the numerical solution computing velocity is slow, we directly derive x, y, the method for 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 of specifically setting up expression formula is following:

If xx ₀+ yy ₀+ zz ₀=S subtracts second equationization in the equation of constraint group, 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 are that example is obtained analytical expression with (1), and follow the prescribed rules (2).

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，

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

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

Through obtaining after the arrangement: $z_{\mathrm{1,2}}=\frac{-l\±\sqrt{l^2-4\mathrm{Km}}}{2k}$

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).

Equally (2) are found the solution like method, obtaining in addition, two endpoint locations are:

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

Can predict; When satellite is arrived on the earth air to surface scanning by plane; The plane of scanning motion and sphere intersection have only one; So have only two end points, bring top four satellite side-sway substar position vectors in the equation of constraint

check eliminating.Obtain two end points and be designated as position1, position2.So far confirmed satellite scanning boundary over the ground, calculating finishes.

Sometimes need confirm left and right sides end points with respect to the satellite motion direction.We remember the velocity vector v=(v of satellite motion _x, v _y, v _z), remember that it is v1 that two end points and satellite position are made the vector of difference, v2.With v1, the v2 multiplication cross obtains v3, when v3 and satellite velocities in the same way the time, can confirm that right endpoint is the end points that produces v1, and left end point is for producing the end points of v2; When v3 and satellite velocities are reverse, can confirm that left end point is the end points that produces v1, right endpoint is for producing the end points of v2, and concrete condition is as shown in Figure 2.

Two kinds of examples and comparison:

Getting certain a certain satellite position speed of the moment does

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

With two kinds of methods it is carried out the scanning area position calculation respectively.The result is following:

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

Table 1 turns to longitude and latitude with the scanning area endpoint location

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. one kind obtains the real-time method of scanning area over the ground of satellite, and it is characterized in that: with ground is to be reference frame admittedly,

The position vector in a certain moment of satellite is w=(x ₀, y ₀, z ₀), velocity vector is v=(v _x, v _y, v _z); The satellite scanning plane

With the coordinate unification of two end points of earth surface intersection be designated as a=(x, y, z); Concrete steps are following:

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

Step 2: calculate satellite and point to the vector in the earth's core and the angle theta that satellite points to the vector of 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: the relational expression when two scanning end points are vertical with the 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, find the solution satellite over the ground the 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: is earth mean radius;

expression the earth's core distance, θ is the maximum side-sway angle of satellite; Cycle repeats step 1～step 3 obtains the zone that satellite scans in real time over the ground.

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