CN103389098A - Positioning estimation method for spacecraft - Google Patents

Abstract

The invention discloses a positioning estimation method for a spacecraft, first, obtain an initial position and an initial speed of the spacecraft to be observed at a zero hour in an active segment by using the Beidou satellite; Second, build a simplified motion equation of the spacecraft to be observed in the active segment under a basic coordinate system, wherein the simplified motion equation of the spacecraft to be observed is solved, and a non-linear differential equation model which can determine an estimated position of the spacecraft to be observed is then built; at last, carry out solving on the built non-linear differential equation model by using an MATLAB software to obtain the estimated positions of the spacecraft to be observed at all time points in the active segment for positioning estimation. The positioning estimation method for spacecraft can realize the positioning estimation of the spacecraft in the active segment more accurately, reliably and independently and can provide a better basis for judging the positions and flight purposes of the spacecraft to be observed. This method is simple and practicable and has very strong practicability.

Description

The location estimation method of spacecraft

Technical field

The present invention relates to the technical field of aircraft location estimation, especially relate to the location estimation method of spacecraft.

Background technology

Spacecraft refers to the cosmic space beyond earth atmosphere, all kinds of aircraft that basically according to the rule of celestial mechanics, move.Some country can launch the spacecraft of specific purposes, as ballistic missile, reconnaissance satellite etc.And other country's inimical spacecraft of emission tool is implemented location estimation, monitored and make rapid reaction, have important strategic importance.

For traditional spacecraft location estimation method, the spacecraft to required observation by rocket-propelled powered phase zero constantly initial position and during initial velocity surveys acquisition process, the general normal employing infrared optics detector of tradition detection mode is surveyed and is obtained, and it receives only the infrared radiation information of target, orientable but can not find range, and be subject to climate effect and cloud noise, reliability is good not.In addition, traditional spacecraft location estimation method also exist need to carry out coordinate transform, unknown variable is too much, computing is complicated, the high not deficiency of estimated accuracy.

Summary of the invention

The objective of the invention is to overcome the above-mentioned defect that exists in prior art, a kind of location estimation method of spacecraft is provided, that the method can be carried out the spacecraft of powered phase is more accurate, more reliable, location estimation more independently, and the method is simple, and practicality is extremely strong.

To achieve these goals, the invention provides a kind of location estimation method of spacecraft, it comprises the steps:

(1) utilizing big-dipper satellite to obtain needs the spacecraft of observing at powered phase zero initial position and initial velocity constantly, and sets up the equation of its initial position and initial velocity under base coordinate system:

x _c(0)=x ₀,y _c(0)=y ₀,z _c(0)=z ₀

${\stackrel{\·}{x}}_c\left(0\right)=x_{00},$ ${\stackrel{\·}{y}}_c\left(0\right)=y_{00},$ ${\stackrel{\·}{z}}_c\left(0\right)=z_{00}$

Wherein, x _c(0), y _c(0), z _c(0) expression zero needs the initial position of the spacecraft of observation constantly;

Expression zero is the initial velocity of spacecraft constantly; x ₀, y ₀, z ₀, x ₀₀, y ₀₀, z ₀₀For the spacecraft that utilizes the need observation that big-dipper satellite obtains powered phase zero constantly initial position and the initial value of initial velocity;

(2) because of the observation segmental arc duration of revolution of earth cycle much larger than spacecraft, therefore can think that at short notice this base coordinate is inertial coordinates system, it does not rotate with the earth,, according to the dynamics of variable mass particle, can set up the simplification equation of motion of the powered phase of spacecraft under base coordinate system that needs observation:

$\left\{\begin{array}{c}{\stackrel{\·\·}{\stackrel{\→}{r}}}_c\left(t\right)={\stackrel{\→}{F}}_e=-\frac{G_m}{{\left|{\stackrel{\→}{r}}_c\left(t\right)\right|}^3}{\stackrel{\→}{r}}_c\left(t\right)\\ r_c\left(t\right)=\sqrt{x_c^2\left(t\right)+y_c^2\left(t\right)+z_c^2\left(t\right)}\\ G_m=3.986005\×{10}^{14}\end{array}\right.$

Wherein, G _mFor Gravitational coefficient of the Earth, vector

Expression needs the suffered external force acceleration sum of spacecraft of observation;

The position vector of spacecraft under base coordinate system for need observation; Expression

To the second derivative of time t, i.e. acceleration; x _c(t), y _c(t), z _cThe position of the spacecraft that (t) for t, constantly need observe;

The simplification equation of motion of the spacecraft that (3) will observe decomposes, and can be decomposed into following system of equations:

$\left\{\begin{array}{c}{\stackrel{\·\·}{x}}_c\left(t\right)=-\frac{G_m}{r_c{\left(t\right)}^3}{x}_c\left(t\right)\\ {\stackrel{\·\·}{y}}_c\left(t\right)=-\frac{G_m}{r_c{\left(t\right)}^3}{y}_c\left(t\right)\\ {\stackrel{\·\·}{z}}_c\left(t\right)=-\frac{G_m}{r_c{\left(t\right)}^3}{z}_c\left(t\right)\end{array}\right.$

Wherein,

The acceleration of the spacecraft that constantly need observe for t, r _c(t) be

(4) with the simplification equation of motion of the equation of its initial position and initial velocity in conjunction with decomposition, foundation can be determined to the spacecraft of need observation the nonlinear differential equation model of its estimated position:

$\left\{\begin{array}{c}{\stackrel{\·\·}{x}}_c\left(t\right)=-\frac{G_m}{r_c{\left(t\right)}^3}{x}_c\left(t\right)\\ {\stackrel{\·\·}{y}}_c\left(t\right)=-\frac{G_m}{r_c{\left(t\right)}^3}{y}_c\left(t\right)\\ {\stackrel{\·\·}{z}}_c\left(t\right)=-\frac{G_m}{r_c{\left(t\right)}^3}{z}_c\left(t\right)\\ G_m=3.986005\×{10}^{14}\\ r_c\left(t\right)=\sqrt{x_c^2\left(t\right)+y_c^2\left(t\right)+z_c^2\left(t\right)}\\ x_c\left(0\right)=x_0,y_c\left(0\right)=y_0,z_c\left(0\right)=z_0\\ {\stackrel{\·}{x}}_c\left(0\right)=x_{00},{\stackrel{\·}{y}}_c\left(0\right)=y_{00},{\stackrel{\·}{z}}_c\left(0\right)=z_{00}\end{array}\right.$

(5) utilize the Simulink tool box in MATLAB software to carry out the S function programming, the nonlinear differential equation model of setting up is solved, draw the spacecraft of need observation in the estimated position of each time point of powered phase, thereby position estimation.

Compared with prior art, main advantage of the present invention is:

The invention provides a kind of location estimation method of spacecraft, that the present invention can carry out the spacecraft of powered phase is more accurate, more reliable, location estimation more independently, can provide better Information base with the flight intention for judgement needs the position of the spacecraft of observation, the method is simple, and practicality is extremely strong.

Description of drawings

Fig. 1 is for needing the spacecraft boosting flight schematic diagram of observation.

Embodiment

Below in conjunction with accompanying drawing and specific embodiment, the present invention is further illustrated.

As shown in Figure 1, the spacecraft boosting flight schematic diagram of observing for need.Powered phase can be subdivided into some subsegments again: the vertical uplift section, program turning section and gravity is the section of flying tiltedly.Press the optimal trajectory design, be fuel savings, rocket body should pass dense atmosphere as early as possible, therefore the general first Vertical Launch of rocket.If the A point is the ground launching site, AB is the vertical uplift section, and the BC segmental arc is the program turning section, and the CD segmental arc is the tiltedly section of flying of gravity, and the DE segmental arc is elliptical orbit.Program turning section connection vertical uplift section and gravity is the section of flying tiltedly, makes outside rocket body turn over certain angle under Torque Control, and after this section is completed, applied moment is cancelled, and enters the state that tiltedly flies.Mother missile is born the propelling (depending on the characteristic of engine) of " vertical section+program turning section (adding moment of face)+gravity is the leading portion of the section of flying tiltedly " usually, and the gravity tiltedly rear Cheng Ze of the section of flying is completed in succession by second, third grade rocket.Owing to tiltedly flying under state terrestrial gravitation and thrust not at same straight line, so the movement locus of rocket body barycenter is the smooth curve with certain radian.

For describing the motion of the spacecraft that needs observation, need to set up its base coordinate system, its base coordinate is the coordinate system with the earth's core translation, gets earth center O _cFor initial point, earth's axis is taken as the z axle, and directed north is forward, and the x axle is by O _cPointing to 0 meridian in zero moment, then by right-handed system, determine the y axle, is O thereby set up its base coordinate _c-X _cY _cZ _c.

It is (2043922.166765m at powered phase zero initial position constantly that the specific embodiment of the invention provides the known spacecraft of observing that needs, 8186504.631471m, 4343461.714791m) and initial velocity (5379.544693m/s,-407.095342m/s, 3516.052656m/s) time the location estimation method of spacecraft, its concrete implementation step is:

(1) utilizing big-dipper satellite to obtain needs the spacecraft of observing at powered phase zero initial position and initial velocity constantly, and sets up the equation of its initial position and initial velocity under base coordinate system:

x _c(0)=2043922.166765,y _c(0)=8186504.631471,z _c(0)=4343461.714791

${\stackrel{\·}{x}}_c\left(0\right)=-5379.544693,$ ${\stackrel{\·}{y}}_c\left(0\right)=-407.095342,$ ${\stackrel{\·}{z}}_c\left(0\right)=3516.052656$

Wherein, x _c(0), y _c(0), z _c(0) expression zero needs the initial position of the spacecraft of observation constantly;

Expression zero is the initial velocity of spacecraft constantly;

(2) because of the observation segmental arc duration of revolution of earth cycle much larger than spacecraft, therefore can think that at short notice this base coordinate is inertial coordinates system, it does not rotate with the earth,, according to the dynamics of variable mass particle, can set up the simplification equation of motion of the powered phase of spacecraft under base coordinate system that needs observation:

$\left\{\begin{array}{c}{\stackrel{\·\·}{\stackrel{\→}{r}}}_c\left(t\right)={\stackrel{\→}{F}}_e=-\frac{G_M}{{\left|{\stackrel{\→}{r}}_c\left(t\right)\right|}^3}{\stackrel{\→}{r}}_c\left(t\right)\\ r_c\left(t\right)=\sqrt{x_c^2\left(t\right)+y_c^2\left(t\right)+z_c^2\left(t\right)}\\ G_m=3.986005\×{10}^{14}\end{array}\right.$

Wherein, G _mFor Gravitational coefficient of the Earth, vector Expression needs the suffered external force acceleration sum of spacecraft of observation;

The position vector of spacecraft under base coordinate system for need observation;

Expression

To the second derivative of time t, i.e. acceleration; x _c(t), y _c(t), z _cThe position of the spacecraft that (t) for t, constantly need observe;

The simplification equation of motion of the spacecraft that (3) will observe decomposes, and can be decomposed into following system of equations:

$\left\{\begin{array}{c}{\stackrel{\·\·}{x}}_c\left(t\right)=-\frac{G_m}{r_c{\left(t\right)}^3}{x}_c\left(t\right)\\ {\stackrel{\·\·}{y}}_c\left(t\right)=-\frac{G_m}{r_c{\left(t\right)}^3}{y}_c\left(t\right)\\ {\stackrel{\·\·}{z}}_c\left(t\right)=-\frac{G_m}{r_c{\left(t\right)}^3}{z}_c\left(t\right)\end{array}\right.$

Wherein,

The acceleration of the spacecraft that constantly need observe for t, r _c(t) be

(4) with the simplification equation of motion of the equation of its initial position and initial velocity in conjunction with decomposition, foundation can be determined to the spacecraft of need observation the nonlinear differential equation model of its estimated position:

$\left\{\begin{array}{c}{\stackrel{\·\·}{x}}_c\left(t\right)=-\frac{G_m}{r_c{\left(t\right)}^3}{x}_c\left(t\right)\\ {\stackrel{\·\·}{y}}_c\left(t\right)=-\frac{G_m}{r_c{\left(t\right)}^3}{y}_c\left(t\right)\\ {\stackrel{\·\·}{z}}_c\left(t\right)=-\frac{G_m}{r_c{\left(t\right)}^3}{z}_c\left(t\right)\\ G_m=3.986005\×{10}^{14}\\ r_c\left(t\right)=\sqrt{x_c^2\left(t\right)+y_c^2\left(t\right)+z_c^2\left(t\right)}\\ x_c\left(0\right)=2043922.166765,y_c\left(0\right)=8186504.631471,z_c\left(0\right)=4343461.714791\\ {\stackrel{\·}{x}}_c\left(0\right)=-5379.544693,{\stackrel{\·}{y}}_c\left(0\right)=-407.095342,{\stackrel{\·}{z}}_c\left(0\right)=3516.052656{}_{}\end{array}\right.$

(5) utilize the Simulink tool box in MATLAB software to carry out the S function programming, the nonlinear differential equation model of setting up is solved, draw need observation spacecraft in the estimated position of each time point of powered phase, be (1.77381 * 10 as three-dimensional position when the 50.0s ⁶M, 8.16138 * 10 ⁶M, 4.51670 * 10 ⁶M), thus position estimation.

Claims (1)

1. the location estimation method of spacecraft is characterized in that comprising the following steps:

(1) utilizing big-dipper satellite to obtain needs the spacecraft of observing at powered phase zero initial position and initial velocity constantly, and sets up the equation of its initial position and initial velocity under base coordinate system:

x _c(0)=x ₀,y _c(0)=y ₀,z _c(0)=z ₀

${\stackrel{\·}{x}}_c\left(0\right)=x_{00},$ ${\stackrel{\·}{y}}_c\left(0\right)=y_{00},$ ${\stackrel{\·}{z}}_c\left(0\right)=z_{00}$

Wherein, x _c(0), y _c(0), z _c(0) expression zero needs the initial position of the spacecraft of observation constantly;

Expression zero is the initial velocity of spacecraft constantly; x ₀, y ₀, z ₀, x ₀₀, y ₀₀, z ₀₀For the spacecraft that utilizes the need observation that big-dipper satellite obtains powered phase zero constantly initial position and the initial value of initial velocity;

(2) because of the observation segmental arc duration of revolution of earth cycle much larger than spacecraft, therefore can think that at short notice this base coordinate is inertial coordinates system, it does not rotate with the earth,, according to the dynamics of variable mass particle, can set up the simplification equation of motion of the powered phase of spacecraft under base coordinate system that needs observation:

$\left\{\begin{array}{c}{\stackrel{\·\·}{\stackrel{\→}{r}}}_c\left(t\right)={\stackrel{\→}{F}}_e=-\frac{G_m}{{\left|{\stackrel{\→}{r}}_c\left(t\right)\right|}^3}{\stackrel{\→}{r}}_c\left(t\right)\\ r_c\left(t\right)=\sqrt{x_c^2\left(t\right)+y_c^2\left(t\right)+z_c^2\left(t\right)}\\ G_m=3.986005\×{10}^{14}\end{array}\right.$

Wherein, G _mFor Gravitational coefficient of the Earth, vector

Expression needs the suffered external force acceleration sum of spacecraft of observation;

The position vector of spacecraft under base coordinate system for need observation;

Expression

To the second derivative of time t, i.e. acceleration; x _c(t), y _c(t), z _cThe position of the spacecraft that (t) for t, constantly need observe;

The simplification equation of motion of the spacecraft that (3) will observe decomposes, and can be decomposed into following system of equations:

$\left\{\begin{array}{c}{\stackrel{\·\·}{x}}_c\left(t\right)=-\frac{G_m}{r_c{\left(t\right)}^3}{x}_c\left(t\right)\\ {\stackrel{\·\·}{y}}_c\left(t\right)=-\frac{G_m}{r_c{\left(t\right)}^3}{y}_c\left(t\right)\\ {\stackrel{\·\·}{z}}_c\left(t\right)=-\frac{G_m}{r_c{\left(t\right)}^3}{z}_c\left(t\right)\end{array}\right.$

Wherein,

The acceleration of the spacecraft that constantly need observe for t, r _c(t) be

(4) with the simplification equation of motion of the equation of its initial position and initial velocity in conjunction with decomposition, foundation can be determined to the spacecraft of need observation the nonlinear differential equation model of its estimated position:

$\left\{\begin{array}{c}{\stackrel{\·\·}{x}}_c\left(t\right)=-\frac{G_m}{r_c{\left(t\right)}^3}{x}_c\left(t\right)\\ {\stackrel{\·\·}{y}}_c\left(t\right)=-\frac{G_m}{r_c{\left(t\right)}^3}{y}_c\left(t\right)\\ {\stackrel{\·\·}{z}}_c\left(t\right)=-\frac{G_m}{r_c{\left(t\right)}^3}{z}_c\left(t\right)\\ G_m=3.986005\×{10}^{14}\\ r_c\left(t\right)=\sqrt{x_c^2\left(t\right)+y_c^2\left(t\right)+z_c^2\left(t\right)}\\ x_c\left(0\right)=x_0,y_c\left(0\right)=y_0,z_c\left(0\right)=z_0\\ {\stackrel{\·}{x}}_c\left(0\right)=x_{00},{\stackrel{\·}{y}}_c\left(0\right)=y_{00},{\stackrel{\·}{z}}_c\left(0\right)=z_{00}\end{array}\right.$

(5) utilize the Simulink tool box in MATLAB software to carry out the S function programming, the nonlinear differential equation model of setting up is solved, draw the spacecraft of need observation in the estimated position of each time point of powered phase, thereby position estimation.

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