CN103226660A - Orbit estimation method of space vehicle in active period - Google Patents

Abstract

The invention provides an orbit estimation method of a space vehicle in an active period. The method utilizes a Beidou satellite to acquire information of an objective space vehicle at the initial position in the active period; simplified motion equations and decomposition equations of the objective space vehicle in the active period are built, so that a motion equation model of the orbit of the space vehicle and a represented estimation model, based on a third order polynomial, of the orbit of the space vehicle are built; the built estimation model of the orbit is solved, so that an estimation position and estimation speed of any point in time of the objective space vehicle in the active period are obtained. The method has the advantages that more accurate, more reliable and more independent orbit estimation for the space vehicle in the active period can be realized; better information foundation can be provided for judgment of the category and the flight intention of the objective space vehicle; the method is simple and practicable; and the practicability is strong.

Description

Method for estimating orbit of active section of spacecraft

Technical Field

The invention belongs to the technical field of spacecraft orbit estimation, and particularly relates to a spacecraft active section orbit estimation method.

Background

The Beidou satellite navigation system is an autonomous research and development and independent operation global satellite navigation system which is implemented in China, and can provide all-weather, all-day high-accuracy and high-reliability positioning service for users. The Beidou satellite navigation system consists of a space end, a ground end and a user end. The Beidou satellite navigation system has great strategic and economic significance for promoting the development of the satellite navigation positioning business of China and meeting the needs of military affairs and national economy of China. However, the Beidou satellite navigation system can only perform real-time positioning on a target object, but cannot perform positioning and orbit estimation at the non-occurrence moment.

Spacecraft is a space outside the earth's atmosphere and basically operates according to the laws of celestial mechanics. Some countries launch special purpose space vehicles such as ballistic missiles. And the method has important strategic significance for carrying out orbit estimation, monitoring and making quick response to the spacecraft launched by other countries and having the hostile effect.

Spacecraft orbits can generally be divided into three sections, in turn: an active section propelled by a rocket, an inertial flight section in the earth outer space and an attack section after reentering the atmosphere. The driving section is usually sequentially propelled by a plurality of stages of rockets, the front stage of rocket is thrown off after completing the propelling, and the rear stage of rocket is used for relaying. The inertial flight section does unpowered inertial flight on the elliptical orbit at the speed obtained before the last stage rocket is shut down outside the atmosphere with extremely low air resistance. And the attack section is controlled according to task requirements and then enters the atmosphere to fly to the target. Wherein, the active section which is propelled by the rocket is a more critical link.

For the traditional spacecraft orbit estimation method, in the process of acquiring initial position information of a target spacecraft in a period of active flight, an infrared optical detector is generally adopted in the traditional detection mode to acquire the initial position information, only infrared radiation information of the target is received, the target spacecraft orbit estimation method can be oriented but cannot measure distance, is easily influenced by weather and interfered by cloud layers, is not good enough in reliability, and the acquired initial position information is position information on an observation coordinate system moving along with a detection satellite, so that coordinate transformation from the observation coordinate system to a basic coordinate system is required, the transformation is complex, and the calculation amount is large. In addition, the traditional spacecraft orbit estimation method has the defects of inaccurate acquired initial position information, excessive variables to be solved in the orbit estimation process, complex operation, insufficient estimation precision and the like.

Disclosure of Invention

The invention aims to overcome the defects of the prior art and provides a method for estimating the orbit of the active section of the spacecraft.

In order to solve the technical problems, the technical scheme adopted by the invention is as follows:

the method for estimating the orbit of the active section of the spacecraft comprises the following steps:

a, acquiring initial position information of a target space vehicle in a basic coordinate system within a period of flight of an active segment by using a Beidou satellite;

and step B, as the revolution period of the earth is far longer than the observation arc period of the spacecraft, the basic coordinate system is considered as an inertial coordinate system in a short time, the inertial coordinate system does not rotate along with the earth, and a simplified motion equation of the active section of the target spacecraft in the basic coordinate system is established according to the dynamics of the variable mass particles:

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

wherein the vector

Representing the sum of the external accelerations to which the spacecraft is subjected,

representing the thrust acceleration generated by the rocket, and m (t) is the instantaneous mass;

is the rate of change of mass;

the position vector of the spacecraft under the basic coordinate system is obtained;to represent

The second derivative with respect to time t, i.e. the acceleration;

taking the injection velocity of the fuel relative to the rocket tail nozzle, G_mIs the constant of gravity of the earth, x_c(t)、y_c(t)、z_c(t) the position of the target space vehicle under the basic coordinate system at the moment t;

step C, decomposing the simplified motion equation of the target space vehicle into the following equation sets:

$\left\{\begin{array}{c}\frac{d}{\mathrm{dt}}\left[\begin{array}{c}{\stackrel{\·}{x}}_c\left(t\right)\\ {\stackrel{\·}{y}}_c\left(t\right)\\ {\stackrel{\·}{z}}_c\left(t\right)\end{array}\right]={\stackrel{\→}{F}}_e+{\stackrel{\→}{F}}_T\\ \frac{d}{\mathrm{dt}}\left[\begin{array}{c}{x}_c\left(t\right)\\ y_c\left(t\right)\\ z_c\left(t\right)\end{array}\right]=\left[\begin{array}{c}{\stackrel{\·}{x}}_c\left(t\right)\\ {\stackrel{\·}{y}}_c\left(t\right)\\ {\stackrel{\·}{z}}_c\left(t\right)\end{array}\right]\end{array}\right.$

wherein,

the speed of the target space vehicle at the moment t under the basic coordinate system;

step D, if m (t) is a strictly monotonically decreasing non-negative function, selecting m (t) as a model:

$m\left(t\right)=m_0-\stackrel{\·}{m}\left(t\right)$

wherein m is₀Is a target initial mass;

the injection speed of the fuel relative to the tail nozzle of the rocket is taken

Is in the same direction as the speed direction of the aircraft, and the size of the aircraft is stable, then the direction of the aircraft is selected

The model is as follows:

${\stackrel{\→}{v}}_r\left(t\right)=-\stackrel{\→}{v}\left(t\right)$

wherein,

is the speed of the aircraft;

step E, simplifying the motion equation and the decomposition equation of the target space vehicle and the m (t) model,

Combining the models, and establishing a motion equation model of the spacecraft orbit:

$\left\{\begin{array}{c}{\stackrel{\stackrel{\·\·}{\→}}{r}}_c\left(t\right)={\stackrel{\→}{F}}_e+{\stackrel{\→}{F}}_T=-\frac{G_m}{{\left|{\stackrel{\→}{r}}_c\left(t\right)\right|}^3}{\stackrel{\→}{r}}_c\left(t\right)+{\stackrel{\→}{v}}_r\left(t\right)\frac{\stackrel{\·}{m}\left(t\right)}{m\left(t\right)}\\ \frac{d}{\mathrm{dt}}\left[\begin{array}{c}{x}_c\left(t\right)\\ y_c\left(t\right)\\ z_c\left(t\right)\end{array}\right]=\left[\begin{array}{c}{\stackrel{\·}{x}}_c\left(t\right)\\ {\stackrel{\·}{y}}_c\left(t\right)\\ {\stackrel{\·}{z}}_c\left(t\right)\end{array}\right]\\ \frac{d}{\mathrm{dt}}\left[\begin{array}{c}{\stackrel{\·}{x}}_c\left(t\right)\\ {\stackrel{\·}{y}}_c\left(t\right)\\ {\stackrel{\·}{z}}_c\left(t\right)\end{array}\right]={\stackrel{\→}{F}}_e+{\stackrel{\→}{F}}_T\\ m\left(t\right)=m_0-\stackrel{\·}{m}\left(t\right)\\ {\stackrel{\→}{v}}_r\left(t\right)=-\stackrel{\→}{v}\left(t\right)\\ r_c\left(t\right)=\sqrt{x_c^2\left(t\right)+y_c^2\left(t\right)+z_c^2\left(t\right)}\\ G_m=3.986005\×{10}^{14}\end{array}\right.$

step F, not considering the system error, and establishing an estimation model of the spacecraft orbit based on the third-order polynomial expression on the basis of the motion equation model of the spacecraft orbit:

$\left\{\begin{array}{c}{x}_c\left(t\right)=a_1+a_{2}t+a_3{t}^2+a_4{t}^3\\ y_c\left(t\right)=a_5+a_{6}t+a_7{t}^2+a_8{t}^3\\ z_c\left(t\right)=a_9+a_{10}t+a_{11}{t}^2+a_{12}{t}^3\\ {\stackrel{\·}{x}}_c\left(t\right)=a_2+{2a}_{3}t+{3a}_4{t}^2\\ {\stackrel{\·}{y}}_c\left(t\right)=a_6+{2a}_{7}t+{3a}_8{t}^2\\ {\stackrel{\·}{z}}_c\left(t\right)=a_{10}+{2a}_{11}t+{3a}_{12}{t}^2\end{array}\right.$

wherein, a₁、a₂…a₁₂Respectively are parameters to be estimated;

and G, solving parameters to be estimated in the model by using initial position information data of the target space vehicle in the flight active section under a basic coordinate system, which is acquired by the Beidou satellite, to obtain an accurate estimation model of the running orbit of the space vehicle, so that the estimated position and speed of the target space vehicle at each time point of the active section are obtained, and the orbit estimation of the target space vehicle is realized.

The invention has the beneficial effects that: the invention provides a spacecraft active section orbit estimation method, which utilizes a Beidou satellite to obtain initial position information of a target spacecraft in an active section, and establishes a simplified motion equation and a decomposition equation of the target spacecraft active section, thereby establishing a motion equation model of a spacecraft orbit and an estimation model of the spacecraft orbit based on third-order polynomial expression; and solving the established estimation model of the orbit to obtain the estimated position and the estimated speed of the target space vehicle at each time point of the active period. The method can carry out more accurate, more reliable and more autonomous track estimation on the spacecraft in the active section, can provide a better information basis for judging the category and the flying intention of the target spacecraft, and is simple and easy to implement and extremely high in practicability.

Drawings

FIG. 1 is a schematic diagram of the active segment orbit of a target spacecraft.

Fig. 2 is a schematic diagram of the orbit of the active segment of the target space vehicle estimated by the orbit in the embodiment.

Detailed Description

The following describes in detail a spacecraft active segment orbit estimation method proposed by the present invention with reference to the accompanying drawings:

as shown in fig. 1, a schematic diagram of the orbit of the active segment of the target spacecraft is shown. The active segment can be subdivided into several subsections: a vertical rising section, a program bending section and a gravity inclined flying section. According to the optimal orbit design, in order to save fuel, the rocket body should penetrate through the dense atmosphere as soon as possible, so the rocket is generally vertically launched first. And a point A is set as a ground launching point, an point AB is a vertical ascending section, an arc section BC is a program turning section, an arc section CD is a gravity inclined flying section, and an arc section DE is an elliptical track. The program turning section is connected with the vertical rising section and the gravity inclined flying section, the arrow body is rotated by a certain angle under the control of external moment, and the external moment is cancelled after the section is finished, so that the arrow enters an inclined flying state. The first stage rocket usually bears the propulsion of a vertical section, a program bending section (adding external moment), a front section of a gravity inclined flight section (according to the characteristics of an engine), and the rear section of the gravity inclined flight section is completed by the second stage rocket and the third stage rocket in succession. Because the gravity and the thrust of the ball are not in the same straight line in the inclined flying state, the motion trail of the mass center of the rocket body is a smooth curve with a certain radian.

In order to describe the motion of the target space vehicle, a basic coordinate system needs to be established, wherein the basic coordinate system is a coordinate system which moves along with the translation of the geocenter, and the geocenter O is taken_cAs the origin, the axis of rotation of the earth is taken as the z-axis, pointing to the north pole asPositive direction, x-axis is from O_cPointing to the 0 longitude line of zero time, determining the y axis according to the right hand system, and establishing the basic coordinate system O_c-X_cY_cZ_c。

The specific embodiment of the invention provides a method for estimating the orbit of an active section of a spacecraft aiming at a target spacecraft, which comprises the following specific implementation steps:

step A, acquiring an underlying coordinate system O of the target space vehicle in a period of flight in an active section by utilizing a Beidou satellite_c-X_cY_cZ_cInitial position information of the lower;

and step B, as the revolution period of the earth is far longer than the observation arc period of the target space vehicle, the basic coordinate system is considered as an inertial coordinate system in a short time, the inertial coordinate system does not rotate along with the earth, and a simplified motion equation of the active section of the target space vehicle under the basic coordinate system is established according to the dynamics of the variable mass particles:

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

wherein the vector

Representing the sum of the external accelerations experienced by the target spacecraft,

representing the thrust acceleration generated by the rocket, and m (t) is the instantaneous mass;

is the rate of change of mass;

a position vector of the target space vehicle under a basic coordinate system is obtained;

to representThe second derivative with respect to time t, i.e. the acceleration;

taking the injection velocity of the fuel relative to the rocket tail nozzle, G_mIs the constant of gravity of the earth, x_c(t)、y_c(t)、z_c(t) is the position of the target spacecraft at time t;

step C, decomposing the simplified motion equation of the target space vehicle into the following equation sets:

$\left\{\begin{array}{c}\frac{d}{\mathrm{dt}}\left[\begin{array}{c}{\stackrel{\·}{x}}_c\left(t\right)\\ {\stackrel{\·}{y}}_c\left(t\right)\\ {\stackrel{\·}{z}}_c\left(t\right)\end{array}\right]={\stackrel{\→}{F}}_e+{\stackrel{\→}{F}}_T\\ \frac{d}{\mathrm{dt}}\left[\begin{array}{c}{x}_c\left(t\right)\\ y_c\left(t\right)\\ z_c\left(t\right)\end{array}\right]=\left[\begin{array}{c}{\stackrel{\·}{x}}_c\left(t\right)\\ {\stackrel{\·}{y}}_c\left(t\right)\\ {\stackrel{\·}{z}}_c\left(t\right)\end{array}\right]\end{array}\right.$

wherein,

the speed of the target spacecraft at time t;

step D, if m (t) is a strictly monotonically decreasing non-negative function, selecting a proper m (t) model as follows:

$m\left(t\right)=m_0-\stackrel{\·}{m}\left(t\right)$

wherein m is₀Is a target initial mass;

the injection speed of the fuel relative to the tail nozzle of the rocket is taken

Is in the same direction as the speed direction of the aircraft, and the size of the aircraft is stable, and then the appropriate direction is selectedThe model is as follows:

${\stackrel{\→}{v}}_r\left(t\right)=-\stackrel{\→}{v}\left(t\right)$

wherein,

is the speed of the aircraft;

step E, simplifying the motion equation and the decomposition equation of the target space vehicle and the m (t) model,

Model bindingEstablishing a motion equation model of the target spacecraft orbit:

$\left\{\begin{array}{c}{\stackrel{\stackrel{\·\·}{\→}}{r}}_c\left(t\right)={\stackrel{\→}{F}}_e+{\stackrel{\→}{F}}_T=-\frac{G_m}{{\left|{\stackrel{\→}{r}}_c\left(t\right)\right|}^3}{\stackrel{\→}{r}}_c\left(t\right)+{\stackrel{\→}{v}}_r\left(t\right)\frac{\stackrel{\·}{m}\left(t\right)}{m\left(t\right)}\\ \frac{d}{\mathrm{dt}}\left[\begin{array}{c}{x}_c\left(t\right)\\ y_c\left(t\right)\\ z_c\left(t\right)\end{array}\right]=\left[\begin{array}{c}{\stackrel{\·}{x}}_c\left(t\right)\\ {\stackrel{\·}{y}}_c\left(t\right)\\ {\stackrel{\·}{z}}_c\left(t\right)\end{array}\right]\\ \frac{d}{\mathrm{dt}}\left[\begin{array}{c}{\stackrel{\·}{x}}_c\left(t\right)\\ {\stackrel{\·}{y}}_c\left(t\right)\\ {\stackrel{\·}{z}}_c\left(t\right)\end{array}\right]={\stackrel{\→}{F}}_e+{\stackrel{\→}{F}}_T\\ m\left(t\right)=m_0-\stackrel{\·}{m}\left(t\right)\\ {\stackrel{\→}{v}}_r\left(t\right)=-\stackrel{\→}{v}\left(t\right)\\ r_c\left(t\right)=\sqrt{x_c^2\left(t\right)+y_c^2\left(t\right)+z_c^2\left(t\right)}\\ G_m=3.986005\×{10}^{14}\end{array}\right.$

step F, not considering the system error, and establishing an estimation model of the target spacecraft orbit based on a third-order polynomial expression on the basis of the motion equation model of the target spacecraft orbit:

$\left\{\begin{array}{c}{x}_c\left(t\right)=a_1+a_{2}t+a_3{t}^2+a_4{t}^3\\ y_c\left(t\right)=a_5+a_{6}t+a_7{t}^2+a_8{t}^3\\ z_c\left(t\right)=a_9+a_{10}t+a_{11}{t}^2+a_{12}{t}^3\\ {\stackrel{\·}{x}}_c\left(t\right)=a_2+{2a}_{3}t+{3a}_4{t}^2\\ {\stackrel{\·}{y}}_c\left(t\right)=a_6+{2a}_{7}t+{3a}_8{t}^2\\ {\stackrel{\·}{z}}_c\left(t\right)=a_{10}+{2a}_{11}t+{3a}_{12}{t}^2\end{array}\right.$

wherein x is_c(t)、y_c(t)、z_c(t) is the position of the target spacecraft at time t,

for the speed of the target spacecraft at time t, a₁、a₂…a₁₂Is a parameter to be estimated;

g, using SPSS software, and using the Beidou satellite to obtain the target space vehicle which flies in the active segment for a period of time in the basic coordinate system O_c-X_cY_cZ_cSolving the parameters to be estimated in the model by using the initial position information data to obtain an accurate estimation model of the target space vehicle orbit, wherein the estimation model comprises the following steps:

$\left\{\begin{array}{c}{x}_c\left(t\right)=-0.848+0.001t-8.126\×{10}^{-6}{t}^2-1.734\×{10}^{-8}{t}^3\\ y_c\left(t\right)=6.521+0.003t-4.267\×{10}^{-6}{t}^2-8.902\×{10}^{-9}{t}^3\\ z_c\left(t\right)=1.989+0.006t+2.715\×{10}^{-6}{t}^2-2.750\×{10}^{-8}{t}^3\\ {\stackrel{\·}{x}}_c\left(t\right)=0.001-16.252\×{10}^{-6}t-5.202\×{10}^{-8}{t}^2\\ {\stackrel{\·}{y}}_c\left(t\right)=0.003-8.534\×{10}^{-6}t-26.706\×{10}^{-9}{t}^2\\ {\stackrel{\·}{z}}_c\left(t\right)=0.006+5.43\×{10}^{-6}t-8.250\×{10}^{-8}{t}^2\end{array}\right.$

thereby obtaining the estimated position and speed of the target space vehicle at each time point of the active period, for example, the position estimated value is (-0.874932 multiplied by 10) at 100.0s⁶m,6.74695×10⁶m,2.58814×10⁶m), velocity estimationThe estimated value is (-1145.4m/s,1879.54m/s,5718m/s), so that the orbit estimation is performed, and the estimated orbit of the active segment is shown in FIG. 2.

Claims (1)

1. The method for estimating the orbit of the active segment of the spacecraft is characterized by comprising the following steps of:

a, acquiring initial position information of a target space vehicle in a basic coordinate system within a period of flight of an active segment by using a Beidou satellite;

and step B, establishing a simplified motion equation of the active section of the target space vehicle under a basic coordinate system according to the dynamics of the variable mass particles:

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

wherein the vector

Representing the sum of the external accelerations to which the spacecraft is subjected,

representing the thrust acceleration generated by the rocket, and m (t) is the instantaneous mass;is the rate of change of mass;

the position vector of the spacecraft under the basic coordinate system is obtained;

to represent

The second derivative with respect to time t, i.e. the acceleration;is the injection velocity of the fuel relative to the rocket tail nozzle, G_mIs the constant of gravity of the earth, x_c(t)、y_c(t)、z_c(t) the position of the target space vehicle under the basic coordinate system at the moment t;

step C, decomposing the simplified motion equation of the target space vehicle into the following equation sets:

$\left\{\begin{array}{c}\frac{d}{\mathrm{dt}}\left[\begin{array}{c}{\stackrel{\·}{x}}_c\left(t\right)\\ {\stackrel{\·}{y}}_c\left(t\right)\\ {\stackrel{\·}{z}}_c\left(t\right)\end{array}\right]={\stackrel{\→}{F}}_e+{\stackrel{\→}{F}}_T\\ \frac{d}{\mathrm{dt}}\left[\begin{array}{c}{x}_c\left(t\right)\\ y_c\left(t\right)\\ z_c\left(t\right)\end{array}\right]=\left[\begin{array}{c}{\stackrel{\·}{x}}_c\left(t\right)\\ {\stackrel{\·}{y}}_c\left(t\right)\\ {\stackrel{\·}{z}}_c\left(t\right)\end{array}\right]\end{array}\right.$

wherein,

the speed of the target space vehicle at the moment t under the basic coordinate system;

step D, if m (t) is a strictly monotonically decreasing non-negative function, selecting m (t) as a model:

$m\left(t\right)=m_0-\stackrel{\·}{m}\left(t\right)$

wherein m is₀Is a target initial mass;

the injection speed of the fuel relative to the tail nozzle of the rocket is taken

Is in the same direction as the speed direction of the aircraft, and the size of the aircraft is stable, then the direction of the aircraft is selected

The model is as follows:

${\stackrel{\→}{v}}_r\left(t\right)=-\stackrel{\→}{v}\left(t\right)$

wherein,

is the speed of the aircraft;

step E, simplifying the motion equation and the decomposition equation of the target space vehicle and the m (t) model,

Combining the models, and establishing a motion equation model of the spacecraft orbit:

$\left\{\begin{array}{c}{\stackrel{\stackrel{\·\·}{\→}}{r}}_c\left(t\right)={\stackrel{\→}{F}}_e+{\stackrel{\→}{F}}_T=-\frac{G_m}{{\left|{\stackrel{\→}{r}}_c\left(t\right)\right|}^3}{\stackrel{\→}{r}}_c\left(t\right)+{\stackrel{\→}{v}}_r\left(t\right)\frac{\stackrel{\·}{m}\left(t\right)}{m\left(t\right)}\\ \frac{d}{\mathrm{dt}}\left[\begin{array}{c}{x}_c\left(t\right)\\ y_c\left(t\right)\\ z_c\left(t\right)\end{array}\right]=\left[\begin{array}{c}{\stackrel{\·}{x}}_c\left(t\right)\\ {\stackrel{\·}{y}}_c\left(t\right)\\ {\stackrel{\·}{z}}_c\left(t\right)\end{array}\right]\\ \frac{d}{\mathrm{dt}}\left[\begin{array}{c}{\stackrel{\·}{x}}_c\left(t\right)\\ {\stackrel{\·}{y}}_c\left(t\right)\\ {\stackrel{\·}{z}}_c\left(t\right)\end{array}\right]={\stackrel{\→}{F}}_e+{\stackrel{\→}{F}}_T\\ m\left(t\right)=m_0-\stackrel{\·}{m}\left(t\right)\\ {\stackrel{\→}{v}}_r\left(t\right)=-\stackrel{\→}{v}\left(t\right)\\ r_c\left(t\right)=\sqrt{x_c^2\left(t\right)+y_c^2\left(t\right)+z_c^2\left(t\right)}\\ G_m=3.986005\×{10}^{14}\end{array}\right.$

step F, not considering the system error, and establishing an estimation model of the spacecraft orbit based on the third-order polynomial expression on the basis of the motion equation model of the spacecraft orbit:

$\left\{\begin{array}{c}{x}_c\left(t\right)=a_1+a_{2}t+a_3{t}^2+a_4{t}^3\\ y_c\left(t\right)=a_5+a_{6}t+a_7{t}^2+a_8{t}^3\\ z_c\left(t\right)=a_9+a_{10}t+a_{11}{t}^2+a_{12}{t}^3\\ {\stackrel{\·}{x}}_c\left(t\right)=a_2+{2a}_{3}t+{3a}_4{t}^2\\ {\stackrel{\·}{y}}_c\left(t\right)=a_6+{2a}_{7}t+{3a}_8{t}^2\\ {\stackrel{\·}{z}}_c\left(t\right)=a_{10}+{2a}_{11}t+{3a}_{12}{t}^2\end{array}\right.$

wherein, a₁、a₂…a₁₂Respectively are parameters to be estimated;

and G, solving parameters to be estimated in the model by using initial position information data of the target space vehicle in the flight active section under a basic coordinate system, which is acquired by the Beidou satellite, to obtain an accurate estimation model of the running orbit of the space vehicle, so that the estimated position and speed of the target space vehicle at each time point of the active section are obtained, and the orbit estimation of the target space vehicle is realized.

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