CN103226660B - Spacecraft powered phase track method of estimation - Google Patents

Abstract

The present invention proposes spacecraft powered phase track method of estimation, described method utilizes big-dipper satellite to obtain object space aircraft in powered phase initial position message, set up object space aircraft powered phase and simplify the equation of motion and point solve an equation, thereby set up the estimation model of the equation of motion model of its spacecraft orbit and the spacecraft orbit based on three rank polynomial repressentations; Estimation model to set up track solves, and draws estimated position and the estimating speed of object space aircraft at each time point of powered phase. The present invention can carry out more accurately the spacecraft of powered phase, more reliably, more independently track is estimated, can be intended to provide better Information base with flight for the classification that judge object space aircraft, the method is simple, practicality is extremely strong.

Description

Spacecraft powered phase track method of estimation

Technical field

The invention belongs to spacecraft track estimation technique field, especially relate to spacecraft powered phase railChannel estimation method.

Background technology

Beidou satellite navigation system is the global navigation satellite system of the independent research implemented of China, independent operatingSystem, it can be user round-the-clock, the high precision of round-the-clock, highly reliable positioning service is provided. Big-dipper satellite is ledBoat system is made up of vacant terminal, ground surface end and user side three parts. Beidou satellite navigation system is to promoting that China defendsThe development of star navigator fix cause, the needs that meet China's military affairs and national economy have great strategy and economicMeaning. But Beidou satellite navigation system can only carry out location constantly to destination object, but can not carry out it and not send outThe location in raw moment and track are estimated.

Spacecraft refers to the cosmic space beyond earth atmosphere, substantially according to the rule of celestial mechanicsAll kinds of aircraft of operation. Some country can transmitting specific purposes spacecraft, as ballistic missile etc.And being implemented to track, the inimical spacecraft of tool of other country's transmitting estimates, monitors and make fast reaction, toolThere is important strategic importance.

Spacecraft track generally can be divided into three sections, is followed successively by: by rocket-propelled powered phase, outside the earthAttack section after inertial flight phase and the atmospheric reentry of sheaf space. Powered phase is pushed away in succession by multistep rocket conventionallyEnter, previous stage rocket comes off after completing propelling, by rear one-stage rocket relay. Inertial flight phase is at the air drag utmost pointUnpowered coasting flight is done by the speed obtaining before final-stage rocket shutdown in little exoatmosphere on elliptic orbit.Attack Duan Ze according to mission requirements, controlled rear atmospheric reentry, target. Wherein, by rocket-propelledPowered phase is a more crucial link.

For traditional spacecraft track method of estimation, institute's object space aircraft is being flown in powered phaseIn the acquisition process of interior initial position message of row a period of time, the general normal employing infrared optics of traditional detection modeDetector is surveyed and is obtained, and it receives only the infra-red radiation information of target, orientable but can not find range, andBe subject to climatic effect and cloud noise, reliability is good not, and its initial position message of obtaining is with detectionThe positional information that the observation coordinate of satellite motion is fastened, so just need to carry out being tied to base coordinate from observation coordinateThe coordinate transform of system, it converts complicated, and operand is large. In addition traditional spacecraft track method of estimation,Also exist the initial position message obtained not accurately, unknown variable is too much in track estimation procedure, computing is complicated,The high not weak point of estimated accuracy.

Summary of the invention

Technical problem to be solved by this invention is to overcome the deficiencies in the prior art, has proposed spacecraft masterMoving section track method of estimation.

For solving the problems of the technologies described above, the technical solution adopted in the present invention is:

Spacecraft powered phase track method of estimation, comprises the steps:

Steps A, utilize big-dipper satellite obtain object space aircraft within boosting flight a period of time on basisInitial position message under coordinate system;

Step B, because the revolution of the earth cycle is much larger than the observation segmental arc duration of spacecraft, therefore in the short timeInside think that this base coordinate is inertial coodinate system, it is not with earth rotation, according to the power of variable mass particleLearn, set up the simplification equation of motion of the powered phase of object space aircraft under base coordinate system:

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

Wherein, vectorThe external force acceleration sum that representation space aircraft is suffered,Represent what rocket producedThrust acceleration, m (t) is instantaneous mass;It is mass change;For spacecraft is on basisPosition vector under coordinate system;RepresentTo the second dervative of time t, i.e. acceleration;GetThe jet velocity of fuel with respect to rocket afterbody spout, G_mFor Gravitational coefficient of the Earth, x_c(t)、y_c(t)、z_c(t)For the position of t moment object space aircraft under base coordinate system;

Step C, decomposes the simplification equation of motion of object space aircraft, is decomposed into following equation group:

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

Wherein,For the speed of t moment object space aircraft under base coordinate system;

Step D, gets the nonnegative function that m (t) is strictly monotone decreasing, chooses m (t) model and is:

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

Wherein, m₀For target initial mass;

Be the jet velocity of fuel with respect to rocket afterbody spout, getDirection and the speed of aircraftThe reverse conllinear of degree direction, its size is stable, choosesModel is:

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

Wherein,For the speed of aircraft;

Step e, by the simplification equation of motion of object space aircraft with point solve an equation and m (t) model,Model carries out combination, sets up the equation of motion model of its 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 taking into account system error, on the equation of motion model basis of spacecraft orbit,Set up the estimation model of the spacecraft orbit based on three rank polynomial repressentations:

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

Wherein, a₁、a₂…a₁₂Be respectively parameter to be estimated;

Step G, utilizes the object space aircraft that big-dipper satellite obtains flying powered phase under base coordinate systemInitial position message data, parameter to be estimated in model is solved, obtain definite spacecraftThe estimation model of orbit, thus draw the estimated position of object space aircraft at each time point of powered phaseAnd speed, the track of realize target spacecraft is estimated.

The invention has the beneficial effects as follows: the present invention proposes spacecraft powered phase track method of estimation, described inMethod utilizes big-dipper satellite to obtain object space aircraft in powered phase initial position message, sets up object space and fliesRow device powered phase is simplified the equation of motion and is divided and solve an equation, thereby sets up the motion side of its spacecraft orbitThe estimation model of journey model and the spacecraft orbit based on three rank polynomial repressentations; To set up railThe estimation model in road solves, draw object space aircraft in the estimated position of each time point of powered phase andEstimating speed. The present invention can carry out more accurately the spacecraft of powered phase, more reliably, track more independentlyEstimate, can provide better Information base, the method with flight intention for the classification that judges object space aircraftSimple, practicality is extremely strong.

Brief description of the drawings

Fig. 1 is the schematic diagram of object space aircraft powered phase track.

Fig. 2 is the track schematic diagram of the object space aircraft powered phase that estimates of specific embodiment middle orbit.

Detailed description of the invention

Below in conjunction with accompanying drawing, the spacecraft powered phase track method of estimation that the present invention is proposed is said in detailBright:

As shown in Figure 1, be the schematic diagram of object space aircraft powered phase track. If powered phase can be subdivided into againDry subsegment: vertical lifting section, the tiltedly section of flying of program turning section and gravity. Press optimal trajectory design, for saving fuel,Rocket body should pass dense atmosphere as early as possible, therefore the general first Vertical Launch of rocket. If A point is ground launch point, ABFor vertical lifting section, BC segmental arc is program turning section, and CD segmental arc is the tiltedly section of flying of gravity, and DE segmental arc is oval railRoad. Program turning section connects vertical lifting section and the tiltedly section of flying of gravity, makes outside rocket body turn over necessarily under Torque ControlAngle, after this section completes, applied moment is cancelled, and enters the state that tiltedly flies. Mother missile is born " vertical section conventionallyThe tiltedly leading portion of the section of flying of+program turning section (adding moment of face)+gravity " propelling (depending on the characteristic of engine), heavyThe power tiltedly rear Cheng Ze of the section of flying completes in succession by second, third grade of rocket. Owing to tiltedly flying under state terrestrial gravitation and pushing awayPower is 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 object space aircraft, need to set up its base coordinate system, its base coordinate be withThe coordinate system of the earth's core translation, gets earth center O_cFor initial point, earth's axis is taken as z axle, and directed north is for justTo, x axle is by O_cPoint to 0 meridian in zero moment, then determine y axle by right-handed system, sit thereby set up its basisMark is O_c-X_cY_cZ_c。

The specific embodiment of the invention provides for object space aircraft, carries out spacecraft powered phase railChannel estimation method, its concrete implementation step is:

Steps A, utilize big-dipper satellite obtain object space aircraft within boosting flight a period of time on basisCoordinate system O_c-X_cY_cZ_cUnder initial position message;

Step B, because the revolution of the earth cycle is much larger than the observation segmental arc duration of object space aircraft, therefore shortIn time, think that this base coordinate is inertial coodinate system, it is with earth rotation, according to variable mass particleDynamics, set up the simplification equation of motion of the powered phase of object space aircraft under base coordinate system:

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

Wherein, vectorRepresent the suffered external force acceleration sum of object space aircraft,Represent that rocket producesRaw thrust acceleration, m (t) is instantaneous mass;It is mass change;For object space flightThe position vector of device under base coordinate system;RepresentTo the second dervative of time t, i.e. acceleration;What get is the jet velocity of fuel with respect to rocket afterbody spout, G_mFor Gravitational coefficient of the Earth, x_c(t)、y_c(t)、z_c(t) be the position of t moment object space aircraft;

Step C, decomposes the simplification equation of motion of object space aircraft, is decomposed into following equation group:

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

Wherein,For the speed of t moment object space aircraft;

Step D, gets the nonnegative function that m (t) is strictly monotone decreasing, chooses suitable m (t) model and is:

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

Wherein, m₀For target initial mass;

Be the jet velocity of fuel with respect to rocket afterbody spout, getDirection and the speed of aircraftThe reverse conllinear of degree direction, its size is stable, and it is suitable to chooseModel is:

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

Wherein,For the speed of aircraft;

Step e, by the simplification equation of motion of object space aircraft with point solve an equation and m (t) model,MouldType carries out combination, sets up the equation of motion model of its object space aircraft 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 taking into account system error, on the equation of motion model basis of object space aircraft orbitUpper, the estimation model of the object space aircraft orbit of foundation based on three rank polynomial repressentations:

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

Wherein, x_c(t)、y_c(t)、z_c(t) be the position of t moment object space aircraft,For the speed of t moment object space aircraft, a₁、a₂…a₁₂For parameter to be estimated;

Step G, uses SPSS software, utilizes the object space aircraft that big-dipper satellite obtains to fly in powered phaseRow a period of time, inherent base coordinate was O_c-X_cY_cZ_cUnder initial position message data, estimate waiting in modelParameter solve, the estimation model that obtains definite object space aircraft orbit is:

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

Thereby draw estimated position and the speed of object space aircraft at each time point of powered phase, asWhen 100.0s, location estimation value is (0.874932 × 10⁶m,6.74695×10⁶m,2.58814×10⁶M), velocity estimationValue is (1145.4m/s, 1879.54m/s, 5718m/s), thereby carries out track estimation, the powered phase that it estimatesTrack as shown in Figure 2.

Claims (1)

1. a spacecraft powered phase track method of estimation, is characterized in that, comprises the steps:

Steps A, utilize big-dipper satellite obtain object space aircraft within boosting flight a period of time on basisInitial position message under coordinate system;

Step B, according to the dynamics of variable mass particle, sets up object space aircraft under the base coordinate systemThe simplification equation of motion of powered phase:

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

Wherein, vectorThe external force acceleration sum that representation space aircraft is suffered,Represent what rocket producedThrust acceleration, m (t) is instantaneous mass;It is mass change;For spacecraft is on basisPosition vector under coordinate system; r_c(t) beAbsolute valueRepresentation space aircraft is at base coordinateThe lower distance to the origin of coordinates of system;RepresentTo the second dervative of time t, i.e. acceleration;BeFuel is with respect to the jet velocity of rocket afterbody spout, G_mFor Gravitational coefficient of the Earth, x_c(t)、y_c(t)、z_c(t)For the position of t moment object space aircraft under base coordinate system;

Step C, decomposes the simplification equation of motion of object space aircraft, is decomposed into following equation group:

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

Wherein,For the speed of t moment object space aircraft under base coordinate system;

Step D, gets the nonnegative function that m (t) is strictly monotone decreasing, chooses m (t) model and is:

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

Wherein, m₀For target initial mass;

Be the jet velocity of fuel with respect to rocket afterbody spout, getDirection and the speed of aircraftThe reverse conllinear of degree direction, its size is stable, choosesModel is:

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

Wherein,For the speed of aircraft;

Step e, by the simplification equation of motion of object space aircraft with point solve an equation and m (t) model,Model carries out combination, sets up the equation of motion model of its spacecraft orbit:

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

Step F, not taking into account system error, on the equation of motion model basis of spacecraft orbit,Set up the estimation model of the spacecraft orbit based on three rank polynomial repressentations:

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

Wherein, a₁、a₂…a₁₂Be respectively parameter to be estimated;

Step G, utilizes the object space aircraft that big-dipper satellite obtains flying powered phase under base coordinate systemInitial position message data, parameter to be estimated in model is solved, obtain definite spacecraftThe estimation model of orbit, thus draw the estimated position of object space aircraft at each time point of powered phaseAnd speed, the track of realize target spacecraft is estimated.