CN102591343A - Satellite orbit maintenance and control method based on two lines of radicals - Google Patents

Abstract

The invention relates to a satellite orbit maintenance and control method based on two lines of radicals, which comprises the following steps of: calculating two lines of radical data disclosed by a satellite by utilizing a SGP4 orbit determination model, calculating and obtaining a geographical latitude and a geographical longitude of a sub-satellite point of the satellite and comparing with an agreed ground nominal track. Through taking the duration of a first sample opposite to an orbit epoch moment as an independent variable and taking the ground track distance difference as a variable, all samples are subjected to quadratic curve fitting by using an average method; the difference delta at between an actual value of a satellite orbit semi-major axis and a nominal value by a latest sample moment as well as the average attenuation rate of the satellite orbit semi-major axis within the time interval of the sample are calculated and obtained through a fitting polynomial coefficient; and finally, the next orbit control time Tc as well as the control quantity delta af required to be used are predicted and obtained by utilizing a fitted secondary curve and an allowable drift range [-delta Lmax and delta Lmax] to ensure that the position of an actual ground track within the satellite next drift period opposite to a ground nominal track is within the allowrable drift range.

Description

Satellite orbit based on two row radicals is kept control method

Technical field

The present invention relates to a kind of satellite orbit and keep control method.

Background technology

Satellite owing to receive the influence of atmospherical drag, causes the sub-satellite track of satellite to drift about during rail.For survey high satellite such as the detailed survey cartographic satellite that does not possess the side-sway function or the radar that has specific ground orbit interval to require for; Must make it can realize that within set recursion period the no crack in the whole world covers or realize strict track mesh spacing requirement when carrying out orbit Design; The track that therefore must carry out satellite is kept control; Otherwise satellite is after operation a period of time under the no control state that freely drifts about; Rail spacing will change, and causes covering crack occurring or orbit interval is jumped out the grid requirement.

Because the uncertainty of solar activity and space environment is still accurate inadequately to the forecast of upper atmosphere density, make the parameter such as control cycle, rail control amount and the actual conditions of Theoretical Calculation to have greater difference.Therefore, the formulation of rail control parameter should combine at that time to add up and predict that this just needs corresponding true orbital data source in the variation of rail.Under the situation of generally having ready conditions; Can be by the orbital tracking of calculating satellite orbit measuring unit every day as input; But because the restriction of objective condition such as region restriction, interface are coordinated, personnel take, energy input and data confidentiality; Make long-term, the stable data of obtaining satellite orbit measuring unit become loaded down with trivial details; Even non-professional relevant unit is difficult to obtain, and the scope of obtaining is only for national satellite, and can't follow the tracks of the analysis with the correlation technique index to other countries' Vanguard satellite in the world.

At present, the analysis of carrying out satellite ground trace drift in a certain period both at home and abroad all is based on the hypothesis that atmospheric density is a definite value, this with the uncertain and factor that accounts for leading role as input, track drift forecast and control calculated have bigger interference.Because satellite orbit measuring unit has specific orbital data advantage; Therefore the attenuation to satellite orbit has sufficient sample can supply to analyze; Can directly add up the semi-major axis variation of Kepler's six roots of sensation number; Though verify at rail that through satellite this forecasting mode based on the true track six roots of sensation of satellite number still has limitation such as stronger use object, satellite ownership.

Summary of the invention

Technology of the present invention is dealt with problems and is: the deficiency that overcomes prior art; Provide a kind of and the satellite that has ground trace to keep requirement has been carried out orbit prediction and control method based on disclosed two row radical data; Overcome with rough atmosphere density and imported the error effect that brings, improved forecast and control computation's reliability, accuracy as calculating.

Technical solution of the present invention is: the satellite orbit based on two row radicals is kept control method, and step is following:

(1) utilizes the SGP4 track to confirm that model resolves satellite two capable radical data, obtain the satellite two capable radical epoch of position and speed constantly under the terrestrial equator rotating coordinate system, obtain the geographical longitude and latitude of sub-satellite point thus;

(2) satellite-based latitude argument value judges that satellite is in the rail lift segmental arc or falls the rail segmental arc; The longitude of same latitude in the segmental arc data under the ground nominal trajectory of geographical longitude and latitude of the sub that obtains in the step (1) and agreement is made comparisons, and alternate position spike is as the result of each relative ground of sample nominal trajectory;

(3) adopt the method for average that all samples that step (2) obtains are carried out conic fitting, obtain polynomial fitting y=A+Bx+Cx ², x is the moment of sampling relatively in the formula, y is the alternate position spike of the relative nominal trajectory of sub-satellite point ground trace;

(4) coefficient calculations according to polynomial fitting obtains the poor Δ a by up-to-date sample moment satellite orbit semi-major axis actual value and nominal value _t, and the satellite orbit semi-major axis average attenuation rate in the sample time interval of living in

Wherein

R _EBe the terrestrial equator radius, a is a satellite orbit semi-major axis nominal value;

(5) according to permission range of drift [the Δ L of the relative nominal trajectory of satellite actual path _Max, Δ L _Max], obtain the T on opportunity of rail control next time _cWith controlled quentity controlled variable Δ a _f, $T_c=\frac{-B+\sqrt{{\mathrm{<figure-callout\; id="2"\; label="B"\; filenames="HSA00000667929600022.png"\; state="\{\{state\}\}">B</figure-callout>}}^2+4C\&CenterDot;\mathrm{\&Delta;}{L}_{\mathrm{Max}}}}{2C},$ ${\mathrm{\&Delta;\; a}}_f=2\sqrt{\frac{2a\stackrel{\&CenterDot;}{a}}{{3\mathrm{\&pi;\; R}}_E}{\mathrm{\&Delta;\; L}}_{\mathrm{Max}}};$

(6) at rail control moment T _cAdopt control corresponding amount Δ a _fTrack to satellite is controlled, make satellite next time the range of drift of the relative nominal trajectory of actual path in the drift episode be positioned at [Δ L _Max, Δ L _Max] within.

The present invention's advantage compared with prior art is: the inventive method has made full use of disclosed two row radical data, does not receive condition restriction such as satellite orbit type, nationality's ownership, can serve satellite orbit easily and keep the control forecast.Through processing to true orbital data, inverting the actual attenuation situation of observation sample track, avoided introducing rough atmosphere density and calculated the error effect that causes, the track position of forecast and the parameter of rail control next time all have higher accuracy.The inventive method has the value of further deeply using, for the technical indicator inverting of carrying out external Vanguard satellite is truly offered help in the space environment storehouse of rail with improving.For example survey high satellite to the ocean, can obtain satellite orbit controlling index and sea level grid dividing precision according to ground trace drift about the sample inverting track control frequency and precision; Perhaps through to all tracking of emission space target both at home and abroad, obtain on the multiple orbital attitudes atmosphere to the contribution of orbital decay, for subsequent satellites design carries out more in the rail environmental analysis reference being provided near truth.

Description of drawings

Fig. 1 is the process flow diagram of the inventive method;

Fig. 2 is ground trace drift schematic diagram;

Fig. 3 is satellite actual path position and forecast match track position comparison diagram;

Fig. 4 is the ground trace compare error figure that the inventive method and orbit measurement unit's orbit determination obtain.

Embodiment

As shown in Figure 1; The inventive method is kept control based on two row radicals to satellite orbit, adopts the disclosed two row radical data of satellite, confirms model (Hoots via the SGP4 track; Felix R.and Lane; Max H., " General Perturbations Theories Derived from the 1965 Lane DragTheory ", Asrrodynamics-SR-2; Dec 1979; Aerospace Defense Command Peterson AFB CO Office of Asrrodynamics) resolves and obtain position and the speed of this moment satellite under the terrestrial equator rotating coordinate system, obtain the geographical longitude and latitude of sub-satellite point in view of the above, and judge that through latitude argument value satellite is in rail lift or falls the rail segmental arc.Because the influence of factors such as model recursion sum of errors space environment; The satellite position error constantly near more apart from two row radical orbit determination is more little; Therefore adopt two row radical track epoch constantly the position of the relative nominal trajectory of sub-satellite points as this ground trace, can close satellite at rail actual position state.At last, the sample that all two row radicals are produced carries out curve fitting, and carries out the forecast analysis of ground trace drift situation.

When calculating the geographical longitude and latitude of sub-satellite point, because two row radicals are felt concerned about S with using instantaneous true equator _c, therefore utilize the SGP4 track confirm model resolve obtain position and velocity after, be transformed into terrestrial equator rotating coordinate system S again _eGet final product down.

Said process obtains the moment and the substar positional information of a sample, and the longitude that same latitude in the rail segmental arc data perhaps falls in its ground nominal trajectory rail lift segmental arc with agreement is made comparisons, and range difference is as the result of the relative ground of this time sample nominal trajectory.

The track drift is made up of two parts: the track drift value Δ L that t moment semi-major axis of orbit and nominal value deviation delta a cause ₁Cause semi-major axis to decay to atmospherical drag perturbation

The track drift value Δ L that causes ₂

$\mathrm{\&Delta;L}={\mathrm{\&Delta;<figure-callout\; id="1"\; label="L"\; filenames="HSA00000667929600022.png"\; state="\{\{state\}\}">L</figure-callout>}}_1+{\mathrm{\&Delta;<figure-callout\; id="2"\; label="L"\; filenames="HSA00000667929600022.png"\; state="\{\{state\}\}">L</figure-callout>}}_2=3{\mathrm{\&pi;R}}_E\frac{\mathrm{\&Delta;a}}{a}t+\frac{3}{2}{\mathrm{\&pi;R}}_E\frac{\stackrel{\&CenterDot;}{a}}{a}{t}^2---\left(1\right)$

Wherein, R _EBe the terrestrial equator radius, a is the nominal value of satellite orbit semi-major axis design,

Under the ideal situation, semi-major axis just in time dropped to nominal value when track floated to the circle, west, thereby turned to the east drift.Following formula supposes that in advance the rate of change of semi-major axis is a constant, and actual conditions are really not so.Satellite is in the equal difference to some extent of the damping capacity of rail every day, if rough atmosphere density continues to strengthen, ground trace can be when also floating to the circle, west just then drift eastwards causes the time interval of orbit maneuver to shorten; On the other hand, weakening also possibly appear in rough atmosphere density also will cross the border and continue the west and float when causing the ground trace west to float to the border, and final track departs from the scope of setting.Therefore analyze satellite reality when the semi-major axis decay of rail; Need

to be carried out real-time update, and be used for the calculating of follow-up ground trace forecast and orbit control quantity through constantly newly-increased sample cluster.

According to equation (1), ground trace drift figure is the quafric curve that opening makes progress, and is as shown in Figure 2, and the horizontal ordinate initial value is track moment epoch of first sample, and ordinate is the position of relative ground nominal trajectory, [Δ L _Max, Δ L _Max] expression ground trace permission range of drift, T _cRepresent rail control next time opportunity.The employing method of average is carried out conic fitting to all samples, gets polynomial expression and is:

y＝A+Bx+Cx ² (2)

A, B, C can be confirmed by following ternary linear function group:

$\left\{\begin{array}{c}\frac{1}{n}\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{y}_i=A+B\left(\frac{1}{n}\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{x}_i\right)+C\left(\frac{1}{n}\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{x}_i^2\right)\\ \frac{1}{n-1}\underset{i=1}{\overset{n-1}{\mathrm{\&Sigma;}}}{y}_i=A+B\left(\frac{1}{n-1}\underset{i=1}{\overset{n-1}{\mathrm{\&Sigma;}}}{x}_i\right)+C\left(\frac{1}{n-1}\underset{i=1}{\overset{n-1}{\mathrm{\&Sigma;}}}{x}_i^2\right)\\ \frac{1}{n-2}\underset{i=1}{\overset{n-2}{\mathrm{\&Sigma;}}}{y}_i=A+B\left(\frac{1}{n-2}\underset{i=1}{\overset{n-2}{\mathrm{\&Sigma;}}}{x}_i\right)+C\left(\frac{1}{n-2}\underset{i=1}{\overset{n-2}{\mathrm{\&Sigma;}}}{x}_i^2\right)\end{array}\right.---\left(3\right)$

Only consider that in the east the boundary does track and keep and can reduce the control frequency, generally speaking, A=0 when floating is worked in the back of boundary's control in the east.Float the position not in the east during the boundary when satellite rises, A has represented to float the position displacement on boundary relatively in the east.

Inner orbit average attenuation situation and follow-up track reference position in this of using that the conic fitting method obtains in period, according to the range of drift decision-making rail control next time opportunity of setting, and corresponding rail control amount.The value of

is calculated by the sample data of following the tracks of in up-to-date one period; And, do not go out the circle, west to guarantee ground trace as far as possible according to slightly inching of variation tendency.

Equation (1) and (2) are compared, can be by the poor Δ a of up-to-date sample moment semi-major axis and nominal value _t, and the semi-major axis average attenuation rate in the sample time interval of living in

${\mathrm{\&Delta;a}}_t=\frac{a}{3{\mathrm{\&pi;R}}_E}B---\left(4\right)$

$\stackrel{\&CenterDot;}{a}=\frac{2a}{3{\mathrm{\&pi;R}}_E}C---\left(5\right)$

The semi-major axis attenuation rate that obtains by formula (5)

Scale and timeliness with observation sample change, and can reflect the semi-major axis average attenuation situation of satellite reality at rail, and introduce equation (2) and can carry out the forecast of follow-up some days ground track position, and pass through to bring in constant renewal in With relative nominal trajectory range of drift [Δ L _Max, Δ L _Max], confirm rail control next time opportunity through counter solving an equation (2).

$T_c=\frac{-B+\sqrt{B^2+4C\&CenterDot;{\mathrm{\&Delta;L}}_{\max }}}{2C}---\left(6\right)$

Following formula Δ L _MaxSet by the covering overlap joint surplus of agreement or the requirement of track drift control enclosure.

At rail control T on opportunity _cControlled quentity controlled variable Δ a _f, derivation is following:

To equation (1); During as

, maximum value is measured in the drift before the circle, arrival east next time:

$-{\mathrm{\&Delta;L}}_{\max }={3\mathrm{\&pi;R}}_E\frac{1}{a}(-\frac{{\left(\mathrm{\&Delta;a}\right)}^2}{\stackrel{\&CenterDot;}{a}}+\frac{1}{2}\frac{{\left(\mathrm{\&Delta;a}\right)}^2}{\stackrel{\&CenterDot;}{a}})---\left(7\right)$

Corresponding semi-major axis deviation:

$\mathrm{\&Delta;a}=\sqrt{\frac{2a\stackrel{\&CenterDot;}{a}}{{3\mathrm{\&pi;R}}_E}{\mathrm{\&Delta;L}}_{\max }}---\left(8\right)$

Since generally speaking only in the east the boundary do track and keep, so controlled quentity controlled variable Δ a _fFor:

${\mathrm{\&Delta;a}}_f=2\mathrm{\&Delta;a}=2\sqrt{\frac{2a\stackrel{\&CenterDot;}{a}}{{3\mathrm{\&pi;R}}_E}{\mathrm{\&Delta;L}}_{\max }}---\left(9\right)$

According to formula (9), can calculate respectively velocity pulse, Fuel Consumption and engine ignition duration (Yang Jiachi etc. spacecraft orbit dynamics and control [M]. Beijing: Yuhang Publishing House .61-75 in 2002):

$\mathrm{\&Delta;v}=\frac{1}{\mathrm{<figure-callout\; id="2"\; label="a"\; filenames="HSA00000667929600022.png"\; state="\{\{state\}\}">a</figure-callout>}}\sqrt{\frac{2\mathrm{\&mu;}\stackrel{\&CenterDot;}{a}}{{3\mathrm{\&pi;R}}_E}{\mathrm{\&Delta;L}}_{\max }}---\left(10\right)$

$\mathrm{\&Delta;m}=M(1-e^{-\frac{1}{\mathrm{<figure-callout\; id="2"\; label="aIg"\; filenames="HSA00000667929600022.png"\; state="\{\{state\}\}">aIg</figure-callout>}}\sqrt{\frac{2\mathrm{\&mu;}\stackrel{\&CenterDot;}{a}}{{3\mathrm{\&pi;R}}_E}{\mathrm{\&Delta;L}}_{\max }}})---\left(11\right)$

$\mathrm{\&Delta;t}=\frac{\mathrm{<figure-callout\; id="2"\; label="M\; aF"\; filenames="HSA00000667929600022.png"\; state="\{\{state\}\}">M</figure-callout>}}{\mathrm{aF}}\sqrt{\frac{2\mathrm{\&mu;}\stackrel{\&CenterDot;}{a}}{{3\mathrm{\&pi;R}}_E}{\mathrm{\&Delta;L}}_{\max }}---\left(12\right)$

Wherein, μ is the terrestrial gravitation constant, and M is whole star quality, and I is the specified vacuum specific impulse of engine, and F becomes the rail average thrust for this.

Under the abundant situation of sample, aforementioned calculation result can tolerate the wrong individual samples of orbit determination in the two row radicals, and the accuracy of the forecast of its ground trace position and rail control calculation of parameter is unaffected.

Embodiment

Have with certain that drift episode is an example before satellite that track keeps requirement, certain control once, use MATLAB software, the actual path position and the track position of match of contrast satellite, and the opportunity on circle, east is got back in forecast once more.The result is as shown in Figure 3, and the consistance of two row radical True Ground Tracks and matched curves is better, so is used to forecast that rail control next time has higher accuracy opportunity.

The substar ground trace that the present invention calculates with resolve the ground trace that obtains based on the orbit determination result of satellite measuring unit, carry out the relative position error contrast, the result is as shown in Figure 4.Fig. 4 explains that two row radicals resolve the ground trace that obtains track moment epoch; Result with satellite measuring unit orbit determination data solver; Error in this drift episode is less than 3%, proves that two row radicals can keep the input data source that control is calculated as satellite orbit.

The content of not doing to describe in detail in the instructions of the present invention belongs to those skilled in the art's known technology.

Claims (1)

1. keep control method based on the satellite orbit of two row radicals, it is characterized in that step is following:

(1) utilizes the SGP4 track to confirm that model resolves satellite two capable radical data, obtain the satellite two capable radical epoch of position and speed constantly under the terrestrial equator rotating coordinate system, obtain the geographical longitude and latitude of sub-satellite point thus;

(2) satellite-based latitude argument value judges that satellite is in the rail lift segmental arc or falls the rail segmental arc; The longitude of same latitude in the segmental arc data under the ground nominal trajectory of geographical longitude and latitude of the sub that obtains in the step (1) and agreement is made comparisons, and alternate position spike is as the result of each relative ground of sample nominal trajectory;

(3) adopt the method for average that all samples that step (2) obtains are carried out conic fitting, obtain polynomial fitting y=A+Bx+Cx ², x is the moment of sampling relatively in the formula, y is the alternate position spike of the relative nominal trajectory of sub-satellite point ground trace;

(4) coefficient calculations according to polynomial fitting obtains the poor Δ a by up-to-date sample moment satellite orbit semi-major axis actual value and nominal value _t, and the satellite orbit semi-major axis average attenuation rate in the sample time interval of living in

Wherein

R _EBe the terrestrial equator radius, a is a satellite orbit semi-major axis nominal value;

(5) according to permission range of drift [the Δ L of the relative nominal trajectory of satellite actual path _Max, Δ L _Max], obtain the T on opportunity of rail control next time _cWith controlled quentity controlled variable Δ a _f, $T_c=\frac{-B+\sqrt{B^2+4C\&CenterDot;\mathrm{\&Delta;}{L}_{\mathrm{Max}}}}{2C},$ ${\mathrm{\&Delta;\; a}}_f=2\sqrt{\frac{2a\stackrel{\&CenterDot;}{a}}{{3\mathrm{\&pi;\; R}}_E}{\mathrm{\&Delta;\; L}}_{\mathrm{Max}}};$

(6) at rail control moment T _cAdopt control corresponding amount Δ a _fTrack to satellite is controlled, make satellite next time the range of drift of the relative nominal trajectory of actual path in the drift episode be positioned at [Δ L _Max, Δ L _Max] within.

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