CN102591343B - 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 be subject to the impact 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 whole world covers or realize strict track mesh spacing requirement without crack when carrying out Track desigh, the track that therefore must carry out satellite is kept control, otherwise satellite freely drift about without the control state under the operation a period of time after, 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 not to the forecast of upper atmosphere density, so that the parameter such as the theoretical control cycle that calculates, rail control amount and actual conditions can have greater difference.Therefore, the formulation of rail control parameter should be in conjunction with adding up and predicted in the variation of rail at that time, and this just need to have corresponding true orbital data source.In 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 regional limits, interface are coordinated, personnel take, energy drops into and the restriction of the objective condition such as data confidentiality, so that long-term, the stable data of obtaining satellite orbit measuring unit become loaded down with trivial details, even non-traffic aided unit is difficult to obtain, and the scope of obtaining is only for national satellite, and can't follow the tracks of analysis with Specifications 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 definite value, this with the uncertain and factor that accounts for leading role as input, tool is calculated in track drift forecast and control disturbs.Because satellite orbit measuring unit has specific orbital data advantage, therefore there is sufficient sample can supply to analyze to the attenuation of satellite orbit, can directly add up the semi-major axis variation of Kepler's six roots of sensation number, although verify at rail that through satellite this forecasting mode based on the true track six roots of sensation of satellite number still has the limitation such as stronger use object, satellite ownership.

Summary of the invention

Technology of the present invention is dealt with problems and is: overcome the deficiencies in the prior art, provide a kind of and based on disclosed two row radical data the satellite that has ground trace to keep requirement has been carried out orbit prediction and control method, overcome with rough atmosphere density and inputted the error effect that brings as calculating, improved reliability, accuracy that forecast and control are calculated.

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

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

(2) judge that according to the latitude argument value of satellite 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 the geographical longitude and latitude of the sub-satellite point 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 relatively sampling moment in the formula, y is the alternate position spike of the relative nominal trajectory of sub-satellite point ground trace;

(4) obtain by the up-to-date sample poor Δ a of satellite orbit semi-major axis actual value and nominal value constantly according to the coefficient calculations of polynomial fitting _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 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 next time rail control T on opportunity _cWith controlled quentity controlled variable Δ a _f, $T_c=\frac{-B+\sqrt{{\mathrm{<figure-callout\; id="2"\; label="B"\; filenames="HSA00000667929600022.png"\; state="\{\{state\}\}">B</figure-callout>}}^2+4C\&CenterDot;\mathrm{\&Delta;}{L}_{\max }}}{2C},$ ${\mathrm{\&Delta;a}}_f=2\sqrt{\frac{2a\stackrel{\&CenterDot;}{a}}{{3\mathrm{\&pi;R}}_E}{\mathrm{\&Delta;L}}_{\max }};$

(6) at rail control moment T _cAdopt corresponding controlled quentity controlled variable Δ a _fTrack to satellite is controlled so that 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 takes full advantage of disclosed two row radical data, is not subjected to the condition restriction such as satellite orbit type, nationality's ownership, can serve easily satellite orbit and keep the control forecast.By the 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 next time rail control parameter 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 for the ocean, can according to ground trace drift about the sample inverting track control frequency and precision, obtain satellite orbit control index and sea level grid dividing precision; Perhaps by 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 designing more, subsequent satellites provides reference near truth in the rail environmental analysis.

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, adopt the disclosed two row radical data of satellite, determine 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) resolve position and the speed of this moment satellite under the terrestrial equator rotating coordinate system that obtains; obtain accordingly the geographical longitude and latitude of sub-satellite point, and judge that by latitude argument value satellite is in rail lift or falls the rail segmental arc.Because the impact of the factors such as model recursion error and space environment, the satellite position error constantly nearer apart from two row radical orbit determination is less, 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.

During the geographical longitude and latitude of Calculation of Satellite substar, because two row radicals are felt concerned about S with using instantaneous true equator _c, therefore utilize the SGP4 track determine model resolve obtain position and velocity after, be transformed into again terrestrial equator rotating coordinate system S _eLower getting final product.

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

The track drift is made 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,

Ideally, 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 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 strengthen continuously, 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 may 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 by constantly newly-increased sample cluster pair

Carry out real-time update, and be used for the calculating of follow-up ground trace forecast and orbit control quantity.

According to equation (1), ground trace drift figure is the quafric curve of opening upwards, and as shown in Figure 2, 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 next time rail control 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 determined 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, work A=0 when floating after 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 twice curve fitting method obtains in period, according to next time rail control of the range of drift decision-making opportunity of setting, and corresponding rail control amount.

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

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 is obtained by formula (5)

Scale and timeliness with observation sample change, and can reflect satellite reality in the semi-major axis average attenuation situation of rail, and introduce equation (2) and can carry out the forecast of follow-up some days ground track position, and pass through to constantly update

With relative nominal trajectory range of drift [Δ L _Max, Δ L _Max], determine next time rail control opportunity by 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 as follows:

To equation (1), when The time, maximum value is measured in the next time drift before the circle, arrival east:

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

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 Gravitational coefficient of the Earth, 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.

In the abundant situation of sample, above-mentioned result of calculation can be tolerated 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

Drift episode uses MATLAB software as example before take certain satellite that track keeps requirement, certain control once being arranged, the actual path position of contrast satellite and the track position of match, and the opportunity on boundary is in the east got back in forecast again.The result as shown in Figure 3, therefore the consistance of two row radical True Ground Tracks and matched curve is better, is used for forecasting that next time rail control 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 as shown in Figure 4.Fig. 4 illustrates 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 that is not described 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 as follows:

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

(2) judge that according to the latitude argument value of satellite 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 the geographical longitude and latitude of the sub-satellite point 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 relatively sampling moment in the formula, y is the alternate position spike of the relative nominal trajectory of sub-satellite point ground trace;

(4) obtain by the up-to-date sample poor Δ a of satellite orbit semi-major axis actual value and nominal value constantly according to the coefficient calculations of polynomial fitting _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 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 next time rail control T on opportunity _cWith controlled quentity controlled variable Δ a _f, $T_c=\frac{-B+\sqrt{B^2+4C\&CenterDot;\mathrm{\&Delta;}{L}_{\max }}}{2C},$ ${\mathrm{\&Delta;a}}_f=2\sqrt{\frac{2a\stackrel{\&CenterDot;}{a}}{{3\mathrm{\&pi;R}}_E}{\mathrm{\&Delta;L}}_{\max }};$

(6) at rail control moment T _cAdopt corresponding controlled quentity controlled variable Δ a _fTrack to satellite is controlled so that 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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