CN104931058B - A kind of Lunar satellite orbit precision positioning method and system improving libration parameter - Google Patents

Abstract

Improve Lunar satellite orbit precision positioning method and the system of libration parameter, input primary data, with the initial coordinate of lander approximate coordinates for lander position; Calculate the theoretical observed reading of time delay observed quantity of VLBI according to the initial coordinate of lander position for every bar baseline, calculation delay observed quantity forms matrix of coefficients to the partial derivative of lander position with to lunar libration parameter partial derivative, model is built for lander position and lunar libration parametric joint, least-squares calculation is carried out for model parameter vector, and judge whether to reach the condition of convergence to result of calculation, if then Output rusults, if not then again iteration until reach the condition of convergence.The present invention is on the observation model basis setting up VLBI observation data, propose first and set up the new model that one estimates reference frame Connecting quantity (physical libration of the moon) and lander positional parameter simultaneously, significantly improving the positioning precision of Lunar satellite orbit.

Description

A kind of Lunar satellite orbit precision positioning method and system improving libration parameter

Technical field

The invention belongs to Lunar satellite orbit location and deep-space detection field, particularly relate to a kind of Lunar satellite orbit precision positioning method and the system of improving libration parameter.

Background technology

For moon exploration program, Lunar satellite orbit positional information is most important, and therefore the determination of Lunar satellite orbit position is the gordian technique of whole engineering project is also difficulties.Obtain lander positional information related track control is carried out to lander accurately, directly have influence on Lunar satellite orbit and whether can enter predetermined design track according to plan, and generation material impact is carried out to follow-up various predetermined scientific experiment.

In China's moon exploration program project, use VLBI (verylongbaselineinterferometry, very long baseline interferometry(VLBI technology) as main lander location technology means.

VLBI ultimate principle see Fig. 1, wherein survey station 1 coordinate S ₁(X ₁, Y ₁, Z ₁) and survey station 2 coordinate S ₂(X ₂, Y ₂, Z ₂) be the solid ITRF2000 coordinate of ground heart; S (X _s, Y _s, Z _s) be lander J2000.0 month heart celestial coordinate system coordinate. for basic lineal vector, that is:

$\stackrel{\→}{B}=S_2-S_1={\left[\begin{array}{c}{X}_2-X_1\\ Y_2-Y_1\\ Z_2-Z_1\end{array}\right]}^T---\left(1\right)$

represent limited source sense vector, mathematic(al) representation is:

$\stackrel{\→}{K}=\frac{{2R}_M{\left[\begin{array}{c}{X}_S\\ Y_S\\ Z_S\end{array}\right]}^T-R_E{\left[\begin{array}{c}{X}_1+X_2\\ Y_1+Y_2\\ Z_1+Z_2\end{array}\right]}^T}{|2R_M{\left[\begin{array}{c}{X}_S\\ Y_S\\ Z_S\end{array}\right]}^T-R_E{\left[\begin{array}{c}{X}_1+X_2\\ Y_1+Y_2\\ Z_1+Z_2\end{array}\right]}^T|}---\left(2\right)$

Therefore VLBI time delay observed quantity τ can be expressed as:

$\mathrm{\τ}=-\frac{1}{c}{R}_E{\left[\begin{array}{c}{X}_2-X_1\\ Y_2-Y_1\\ Z_2-Z_1\end{array}\right]}^T\·\frac{{2R}_M{\left[\begin{array}{c}{X}_S\\ Y_S\\ Z_S\end{array}\right]}^T-R_E{\left[\begin{array}{c}{X}_1+X_2\\ Y_1+Y_2\\ Z_1+Z_2\end{array}\right]}^T}{|2R_M{\left[\begin{array}{c}{X}_S\\ Y_S\\ Z_S\end{array}\right]}^T-R_E{\left[\begin{array}{c}{X}_1+X_2\\ Y_1+Y_2\\ Z_1+Z_2\end{array}\right]}^T|}---\left(3\right)$

In above-mentioned formula, c represents the light velocity, matrix R _mrepresent that the moon is tied to the rotation matrix of J2000.0 month heart celestial coordinate system admittedly, matrix R _erepresent that ground is tied to the rotation matrix of J2000.0 month heart celestial coordinate system admittedly.

In addition, namely physical libration of the moon is the space swing of moon necessary being.Lunar libration not only plays key effect in the mutual transfer process of moon spherical coordinate system, it also acts on lunar craters by with the form of moon Nonspherical Gravitational Potential, perturbation is produced to the track of moonik, determining that work brings impact to Lunar satellite orbit track, is describe the important physical parameter of the moon.Lunar libration information carried out observing primarily of LLR (LunarLaserRanging, Lunar LASER Ranging) and provided with ephemeris form by JPL (JetPropulsionLaboratory, U.S. jet propulsion laboratory) present stage.By determining the position of lander under moon spherical coordinate system, resolving libration simultaneously, to follow-up moon exploration program, there is certain reference.

But, in the observation model to each observation technology of Lunar satellite orbit, relate to the prior imformation of a lot of geometry and physical model statistic property, if directly utilize and do not improve the precision of its prior imformation, will propagate in determined Lunar satellite orbit position.Connecting quantity (the libration parameter in the present invention) in current observation model between different reference frame directly adopts the prior imformation that beyond this recording geometry, recording geometry provides, and its precision level also can affect Lunar satellite orbit positioning precision.

Summary of the invention

For prior art defect, the invention provides a kind of Lunar satellite orbit precision positioning method and the system of improving libration parameter.

Technical solution of the present invention provides a kind of Lunar satellite orbit precision positioning method improving libration parameter, comprises the following steps,

Step 1, input lunar libration parameter (Ω, i, μ) initial value, lander approximate coordinates (X ₀, Y ₀, Z ₀), the time delay observed quantity τ of EOP data and each bar baseline, with lander approximate coordinates (X ₀, Y ₀, Z ₀) be lander position (X _s, Y _s, Z _s) initial coordinate;

Step 2, for every bar baseline according to formula one according to lander position (X _s, Y _s, Z _s) initial coordinate calculate the theoretical observed reading of time delay observed quantity τ of VLBI, according to formula two, formula three according to lander position (X _s, Y _s, Z _s) initial coordinate and the observed quantity of lunar libration parameter (Ω, i, μ) calculation of initial value time delay to the partial derivative of lander position and libration parameter;

$\mathrm{\τ}=-\frac{1}{c}{R}_E{\left[\begin{array}{c}{X}_2-X_1\\ Y_2-Y_1\\ Z_2-Z_1\end{array}\right]}^T\·\frac{{2R}_M{\left[\begin{array}{c}{X}_S\\ Y_S\\ Z_S\end{array}\right]}^T-R_E{\left[\begin{array}{c}{X}_1+X_2\\ Y_1+Y_2\\ Z_1+Z_2\end{array}\right]}^T}{|2R_M{\left[\begin{array}{c}{X}_S\\ Y_S\\ Z_S\end{array}\right]}^T-R_E{\left[\begin{array}{c}{X}_1+X_2\\ Y_1+Y_2\\ Z_1+Z_2\end{array}\right]}^T|}$ Formula one

Wherein, (X ₁, Y ₁, Z ₁) be the coordinate of survey station 1, (X ₂, Y ₂, Z ₂) be the coordinate of survey station 2, lander position (X _s, Y _s, Z _s) adopting lander J2000.0 month heart celestial coordinate system coordinate, c represents the light velocity, matrix R _mrepresent that the moon is tied to the rotation matrix of J2000.0 month heart celestial coordinate system admittedly, matrix R _erepresent that ground is tied to the rotation matrix of J2000.0 month heart celestial coordinate system admittedly;

Time delay observed quantity is to lander position (X _s, Y _s, Z _s) partial derivative be,

${\left(\begin{array}{c}\frac{\∂\mathrm{\τ}}{\∂X_S}\\ \frac{\∂\mathrm{\τ}}{\∂Y_S}\\ \frac{\∂\mathrm{\τ}}{\∂Z_S}\end{array}\right)}^T={\left(\begin{array}{c}{B}_1\\ B_2\\ B_3\end{array}\right)}^T=-\frac{2}{c}\frac{R_E{\left[\begin{array}{c}{X}_1-X_2\\ Y_1-Y_2\\ Z_1-Z_2\end{array}\right]}^T{R}_M}{|2R_M{\left[\begin{array}{c}{X}_0\\ Y_0\\ Z_0\end{array}\right]}^T-R_E{\left[\begin{array}{c}{X}_1+X_2\\ Y_1+Y_2\\ Z_1+Z_2\end{array}\right]}^T|}$ Formula two

The partial derivative of time delay observed quantity to lunar libration parameter (Ω, i, μ) is,

formula three

Wherein, coefficient B ₁, B ₂, B ₃represent the partial derivative of time delay observed quantity to lander position, coefficient B ₄, B ₅, B ₆represent the partial derivative of time delay observed quantity to lunar libration parameter (Ω, i, μ);

Step 3, performs step 2 according to this and forms matrix of coefficients B=(B to the partial derivative that each baseline calculates ₁, B ₂, B ₃, B ₄, B ₅, B ₆), if model parameter vector X=is (X _s, Y _s, Z _s, Ω, i, μ) ^t, model parameter approximate value is X ⁰, x is parameter correction, represents approximate value X ⁰and the corrected value between parameter true value, l represents the difference between observed reading and approximate treatment value, least-squares calculation is carried out according to formula four, formula five, and judge whether to reach the condition of convergence to result of calculation, if then enter step 4, if not then with this compensating computation gained lander position (X _s, Y _s, Z _s) and lunar libration parameter (Ω, i, μ) as new lander position (X _s, Y _s, Z _s) initial coordinate and lunar libration parameter (Ω, i, μ) initial value, return step 2 again iteration until reach the condition of convergence;

$(B^T{P}_{\mathrm{\Δ}}B+{\mathrm{\σ}}_0^2{\mathrm{\σ}}_x^{-2}{P}_{\hat{x}})\hat{x}=B^T{P}_{\mathrm{\Δ}}l+{\mathrm{\σ}}_0^2{\mathrm{\σ}}_x^{-2}{P}_{\hat{x}}{l}_{\hat{x}}$ Formula four

$\hat{x}={(B^T{P}_{\mathrm{\Δ}}B+{\mathrm{\σ}}_0^2{\mathrm{\σ}}_x^{-2}{P}_{\hat{x}})}^{-1}{B}^T{P}_{\mathrm{\Δ}}l$ Formula five

Wherein, P _Δrepresent observed reading power battle array, represent observed reading variance of unit weight, represent that parameter weighs variance surely, for the adjusted value of x, represent expect, represent adjusted value corresponding parameter power battle array;

Step 4, according to final model parameter vector X=(X _s, Y _s, Z _s, Ω, i, μ) ^texport lander location parameter and lunar libration parameter extraction result.

And in step 3, the condition of convergence is, the mould of parameter correction x is less than 1 centimetre.

And in step 1, lunar libration parameter (Ω, i, μ) initial value is provided by JPL ephemeris.

And, in step 2, matrix R _mthered is provided lunar libration parameter (Ω, i, μ) calculation of initial value to obtain by JPL ephemeris, described EOP data are provided numerical value, matrix R by EOPC04_08 sequence _eobtained by EOPC04_08 numerical evaluation that sequence provides.

The present invention is also corresponding provides a kind of Lunar satellite orbit Precision Position Location System improving libration parameter, comprises with lower module,

Initialization module, for inputting lunar libration parameter (Ω, i, μ) initial value, lander approximate coordinates (X ₀, Y ₀, Z ₀), the time delay observed quantity τ of EOP data and each bar baseline, with lander approximate coordinates (X ₀, Y ₀, Z ₀) be lander position (X _s, Y _s, Z _s) initial coordinate;

Theoretical observed reading and partial derivative ask for module, for for every bar baseline according to formula one according to lander position (X _s, Y _s, Z _s) initial coordinate calculate the theoretical observed reading of time delay observed quantity τ of VLBI, according to formula two, formula three according to lander position (X _s, Y _s, Z _s) initial coordinate and the observed quantity of lunar libration parameter (Ω, i, μ) calculation of initial value time delay to the partial derivative of lander position and libration parameter;

$\mathrm{\τ}=-\frac{1}{c}{R}_E{\left[\begin{array}{c}{X}_2-X_1\\ Y_2-Y_1\\ Z_2-Z_1\end{array}\right]}^T\·\frac{{2R}_M{\left[\begin{array}{c}{X}_S\\ Y_S\\ Z_S\end{array}\right]}^T-R_E{\left[\begin{array}{c}{X}_1+X_2\\ Y_1+Y_2\\ Z_1+Z_2\end{array}\right]}^T}{|2R_M{\left[\begin{array}{c}{X}_S\\ Y_S\\ Z_S\end{array}\right]}^T-R_E{\left[\begin{array}{c}{X}_1+X_2\\ Y_1+Y_2\\ Z_1+Z_2\end{array}\right]}^T|}$ Formula one

Wherein, (X ₁, Y ₁, Z ₁) be the coordinate of survey station 1, (X ₂, Y ₂, Z ₂) be the coordinate of survey station 2, lander position (X _s, Y _s, Z _s) adopting lander J2000.0 month heart celestial coordinate system coordinate, c represents the light velocity, matrix R _mrepresent that the moon is tied to the rotation matrix of J2000.0 month heart celestial coordinate system admittedly, matrix R _erepresent that ground is tied to the rotation matrix of J2000.0 month heart celestial coordinate system admittedly;

Time delay observed quantity is to lander position (X _s, Y _s, Z _s) partial derivative be,

${\left(\begin{array}{c}\frac{\∂\mathrm{\τ}}{\∂X_S}\\ \frac{\∂\mathrm{\τ}}{\∂Y_S}\\ \frac{\∂\mathrm{\τ}}{\∂Z_S}\end{array}\right)}^T={\left(\begin{array}{c}{B}_1\\ B_2\\ B_3\end{array}\right)}^T=-\frac{2}{c}\frac{R_E{\left[\begin{array}{c}{X}_2-X_1\\ Y_2-Y_1\\ Z_2-Z_1\end{array}\right]}^T{R}_M}{|2R_M{\left[\begin{array}{c}{X}_0\\ Y_0\\ Z_0\end{array}\right]}^T-R_E{\left[\begin{array}{c}{X}_1+X_2\\ Y_1+Y_2\\ Z_1+Z_2\end{array}\right]}^T|}$ Formula two

The partial derivative of time delay observed quantity to lunar libration parameter (Ω, i, μ) is,

formula three

Wherein, coefficient B ₁, B ₂, B ₃represent the partial derivative of time delay observed quantity to lander position, coefficient B ₄, B ₅, B ₆represent the partial derivative of time delay observed quantity to lunar libration parameter (Ω, i, μ);

Positioning calculation model, for asking for the partial derivative composition matrix of coefficients B=(B that this execution work of module calculates each baseline according to theoretical observed reading and partial derivative ₁, B ₂, B ₃, B ₄, B ₅, B ₆), if model parameter vector X=is (X _s, Y _s, Z _s, Ω, i, μ) ^t, model parameter approximate value is X ⁰, x is parameter correction, represents approximate value X ⁰and the corrected value between parameter true value, l represents the difference between observed reading and approximate treatment value, least-squares calculation is carried out according to formula four, formula five, and judge whether to reach the condition of convergence to result of calculation, if then command result output module work, if not then with this compensating computation gained lander position (X _s, Y _s, Z _s) and lunar libration parameter (Ω, i, μ) as new lander position (X _s, Y _s, Z _s) initial coordinate and lunar libration parameter (Ω, i, μ) initial value, order theoretical observed reading and partial derivative ask for module again iteration work until reach the condition of convergence;

$(B^T{P}_{\mathrm{\Δ}}B+{\mathrm{\σ}}_0^2{\mathrm{\σ}}_x^{-2}{P}_{\hat{x}})\hat{x}=B^T{P}_{\mathrm{\Δ}}l+{\mathrm{\σ}}_0^2{\mathrm{\σ}}_x^{-2}{P}_{\hat{x}}{l}_{\hat{x}}$ Formula four

$\hat{x}={(B^T{P}_{\mathrm{\Δ}}B+{\mathrm{\σ}}_0^2{\mathrm{\σ}}_x^{-2}{P}_{\hat{x}})}^{-1}{B}^T{P}_{\mathrm{\Δ}}l$ Formula five

Wherein, P _Δrepresent observed reading power battle array, represent observed reading variance of unit weight, represent that parameter weighs variance surely, for the adjusted value of x, represent expect, represent adjusted value corresponding parameter power battle array;

Result output module, for according to final model parameter vector X=(X _s, Y _s, Z _s, Ω, i, μ) ^texport lander location parameter and lunar libration parameter extraction result.

And in positioning calculation model, the condition of convergence is, the mould of parameter correction x is less than 1 centimetre.

And in initialization module, lunar libration parameter (Ω, i, μ) initial value is provided by JPL ephemeris.

And theoretical observed reading and partial derivative are asked in module, matrix R _mthered is provided lunar libration parameter (Ω, i, μ) calculation of initial value to obtain by JPL ephemeris, described EOP data are provided numerical value, matrix R by EOPC04_08 sequence _eobtained by EOPC04_08 numerical evaluation that sequence provides.

The invention provides the Lunar satellite orbit precision positioning method and system that improve libration parameter, establish a kind of improvement simultaneously in conjunction with the new model of reference frame Connecting quantity involved in Lunar satellite orbit One-Point Location model, lander location parameter, the priori precision of these parameters can be improved by this model and observation data, improve the positioning precision of Lunar satellite orbit.The present invention completes under state natural sciences fund support, has important actual promotional value and application prospect, has very important effect to the development of national economy and the raising of living standards of the people.

Accompanying drawing explanation

Fig. 1 is the VLBI One-Point Location schematic diagram of prior art.

Fig. 2 is the process flow diagram of the embodiment of the present invention.

Embodiment

Below in conjunction with drawings and Examples, technical solution of the present invention is described in detail.

During different reference frame in unified model, have employed the reference frame Connecting quantity priori value that this recording geometry provides with external system at present, its precision level will affect the precision of Lunar satellite orbit location.How improving the priori precision of these geometry and physical model statistic property, is the key issue that current Lunar satellite orbit precision positioning faces.Solution of the present invention is exactly propose a kind of improvement simultaneously in conjunction with the new model of reference frame Connecting quantity (physical libration of the moon) involved in Lunar satellite orbit One-Point Location model, lander location parameter.Namely on the observation model basis setting up VLBI observation data, propose first and set up the new model that one estimates reference frame Connecting quantity (physical libration of the moon), lander positional parameter simultaneously, avoid the priori precision directly quoting these geometry and physical model statistic property in existing model to the defect of lander location precision, improve the positioning precision of Lunar satellite orbit.

Embodiment concrete scheme with " goddess in the moon No. three " moon exploration program for background, based on VLBI technology derivation Lunar satellite orbit One-Point Location model.On the basis of VLBI One-Point Location, account for foundation and the connectivity problem of moon spherical coordinate system, lunar libration Eulerian angle of having derived parameter calculation mathematical model, and with measured data, libration predicted value given by DE421 ephemeris is improved.

Being implemented as follows of embodiment:

1. set up the VLBI geometry observation equation of lander and ground survey station, and derive the partial derivative of VLBI observed quantity to lander coordinate.

By formula 3 VLBI observed quantity of can deriving to the partial derivative of lander position be:

${\left(\begin{array}{c}\frac{\∂\mathrm{\τ}}{\∂X_S}\\ \frac{\∂\mathrm{\τ}}{\∂Y_S}\\ \frac{\∂\mathrm{\τ}}{\∂Z_S}\end{array}\right)}^T={\left(\begin{array}{c}{B}_1\\ B_2\\ B_3\end{array}\right)}^T=-\frac{2}{c}\frac{R_E{\left[\begin{array}{c}{X}_2-X_1\\ Y_2-Y_1\\ Z_2-Z_1\end{array}\right]}^T{R}_M}{|2R_M{\left[\begin{array}{c}{X}_0\\ Y_0\\ Z_0\end{array}\right]}^T-R_E{\left[\begin{array}{c}{X}_1+X_2\\ Y_1+Y_2\\ Z_1+Z_2\end{array}\right]}^T|}---\left(4\right)$

Wherein, coefficient B ₁, B ₂, B ₃represent the partial derivative of VLBI observed quantity to lander position, (X ₀, Y ₀, Z ₀) be (X _s, Y _s, Z _s) initial coordinate, generally adopt approximate coordinates.

2. set up the transfer equation that Lunar satellite orbit J2000.0 agreement moon heart celestial coordinates is tied to moon heart moon solid coordinate system, and derive the partial derivative of rotation of coordinate matrix to libration Eulerian angle parameter (Ω, i, μ).

R in formula 3 _mthree rotation matrixs around X-axis rotate can be expressed as be multiplied, that is:

R _M＝R _Z(-Ω)R _X(-i)R _Z(-μ)(5)

In formula, R _z(-Ω) represents the rotation matrix rotating-Ω around Z axis, R _x(-i) represents the rotation matrix rotating-i around X-axis, R _z(-μ) represents the rotation matrix rotating-μ around Z axis.

In order to more convenient expression, now first ask above-mentioned rotation matrix to the local derviation matrix of anglec of rotation θ expression is as follows:

$\left\{\begin{array}{c}{\stackrel{\·}{R}}_X\left(\mathrm{\θ}\right)=\left[\begin{array}{ccc}0& 0& 0\\ 0& -\sin \mathrm{\θ}& \cos \mathrm{\θ}\\ 0& -\cos \mathrm{\θ}& -\sin \mathrm{\θ}\end{array}\right]\\ {\stackrel{\·}{R}}_Z\left(\mathrm{\θ}\right)=\left[\begin{array}{ccc}-\sin \mathrm{\θ}& \cos \mathrm{\θ}& 0\\ -\cos \mathrm{\θ}& -\sin \mathrm{\θ}& 0\\ 0& 0& 0\end{array}\right]\end{array}\right.---\left(6\right)$

According to formula 5R _m=R _z(-Ω) R _x(-i) R _z(-μ), so:

$\left\{\begin{array}{c}\frac{\∂R_M}{\∂\mathrm{\Ω}}=-{\stackrel{\·}{R}}_Z(-\mathrm{\Ω})R_X(-i)R_Z(-\mathrm{\μ})\\ \frac{\∂R_M}{\∂i}=-R_Z(-\mathrm{\Ω}){\stackrel{\·}{R}}_X(-i)R_Z(-\mathrm{\μ})\\ \frac{\∂R_M}{\∂\mathrm{\μ}}=-R_Z(-\mathrm{\Ω})R_X(-i){\stackrel{\·}{R}}_Z(-\mathrm{\μ})\end{array}\right.---\left(7\right)$

3. the partial derivative of VLBI observed quantity to (Ω, i, μ) parameter can be derived by said process:

4. utilize least square adjustment method to resolve lander location parameter and lunar libration Eulerian angle (Ω, i, μ) parameter simultaneously.

Matrix of coefficients B=(the B of each parameter after note model linearization ₁, B ₂, B ₃, B ₄, B ₅, B ₆), model parameter vector X=(X _s, Y _s, Z _s, Ω, i, μ) ^t, L is observation vector, then formula 3 can be expressed as:

L＝BX+Δ(9)

In formula, Δ is error vector.

If model parameter approximate value is X ⁰, order

$\left\{\begin{array}{c}X=X^0+x\\ l=L-{\mathrm{BX}}^0\end{array}\right.---\left(10\right)$

In formula, x represents approximate value X ⁰and the corrected value between parameter true value; L represents the difference between observed reading and approximate treatment value.

In " goddess in the moon No. three " Lunar satellite orbit location compute process, libration Eulerian angle are very little compared to location parameter magnitude, therefore directly carry out adjustment and resolve there will be because normal equation morbid state that the parameter that causes cannot solve or the situation of calculation accuracy extreme difference.In order to head it off, the present invention adopts the method for Weighted Parameter Adjustment to carry out unknown parameter and resolves.

Take following probabilistic model into account:

$\left\{\begin{array}{c}E\left(\mathrm{\Δ}\right)=0\\ E\left(x\right)=0\\ \mathrm{cov}(\mathrm{\Δ},\mathrm{\Δ})={\mathrm{\σ}}_0^2{P}_{\mathrm{\Δ}}^{-1}\\ \mathrm{cov}(x,x)={\mathrm{\σ}}_x^2{P}_x^{-1}\\ \mathrm{cov}(\mathrm{\Δ},x)=0\end{array}\right.---\left(11\right)$

In formula, E (Δ) represents that error is expected, E (x) represents that parameter correction is expected, cov (Δ, Δ) represents error covariance matrix, cov (x, x) parameter correction variance matrix is represented, (Δ x) represents error and parameter correction covariance matrix, P to cov _Δrepresent observed reading power battle array, represent observed reading variance of unit weight, P _xrepresent parameter power battle array, represent that parameter weighs variance surely.

Based on above-mentioned analysis, introduce virtual observation error equation e representation unit battle array, represent the adjusted value of parameter x, represent expect, and error equation is rewritten:

$\left[\begin{array}{c}{V}_x\\ V\end{array}\right]=\left[\begin{array}{c}E\\ B\end{array}\right]\hat{x}-\left[\begin{array}{c}{l}_{\hat{x}}\\ l\end{array}\right]---\left(12\right)$

Under criterion of least squares, method of adjustment equation can be obtained:

$(B^T{P}_{\mathrm{\Δ}}B+{\mathrm{\σ}}_0^2{\mathrm{\σ}}_x^{-2}{P}_{\hat{x}})\hat{x}=B^T{P}_{\mathrm{\Δ}}l+{\mathrm{\σ}}_0^2{\mathrm{\σ}}_x^{-2}{P}_{\hat{x}}{l}_{\hat{x}}---\left(13\right)$

Therefore the adjusted value of x can be obtained for:

$\hat{x}={(B^T{P}_{\mathrm{\Δ}}B+{\mathrm{\σ}}_0^2{\mathrm{\σ}}_x^{-2}{P}_{\hat{x}})}^{-1}{B}^T{P}_{\mathrm{\Δ}}l---\left(14\right)$

In formula represent adjusted value corresponding parameter power battle array.

Parameter adjustment value variance for:

${\widehat{\mathrm{\σ}}}_0^2=\frac{V^T{P}_{\mathrm{\Δ}}V}{r}=\frac{l^T{P}_{\mathrm{\Δ}}l-{\left(B^T{P}_{\mathrm{\Δ}}l\right)}^T\hat{x}}{r}---\left(15\right)$

In formula, r represents redundant observation number.

During concrete enforcement, software mode can be adopted to realize VLBI and to improve one's methods automatic operational scheme for Lunar satellite orbit location and lunar libration, see Fig. 2, the realization flow of embodiment is as follows:

1., after starting, input primary data, comprises lunar libration parameter (Ω, i, μ) initial value, lander approximate coordinates (X ₀, Y ₀, Z ₀), the time delay observed quantity τ of EOP data and each bar baseline (embodiment is 6), with lander approximate coordinates (X ₀, Y ₀, Z ₀) be lander position (X _s, Y _s, Z _s) initial coordinate.

During concrete enforcement, lander approximate coordinates (X ₀, Y ₀, Z ₀) can preset, subsequent operation of the present invention can correct the error as far as a few km; Lunar libration parameter (Ω, i, μ) initial value can be provided by JPL ephemeris.Step matrix is required R 2. _mthered is provided lunar libration parameter (Ω, i, μ) calculation of initial value to obtain by JPL ephemeris, described EOP data are provided numerical value, matrix R by EOPC04_08 sequence _eobtained by EOPC04_08 numerical evaluation that sequence provides.

2. for every bar baseline according to formula 3 according to lander position (X _s, Y _s, Z _s) initial coordinate calculate the theoretical observed reading of time delay observed quantity τ of VLBI, according to formula 4, formula 8 according to lander position (X _s, Y _s, Z _s) initial coordinate and the partial derivative of lunar libration parameter (Ω, i, μ) calculation of initial value VLBI observed quantity, comprise VLBI observed quantity to lander position (X _s, Y _s, Z _s) partial derivative and VLBI observed quantity to the partial derivative of lunar libration parameter (Ω, i, μ).

3. perform step 2 according to this and matrix of coefficients B=(B is formed to the partial derivative that each baseline calculates ₁, B ₂, B ₃, B ₄, B ₅, B ₆), for model parameter vector X=(X _s, Y _s, Z _s, Ω, i, μ) ^t, carry out least-squares calculation according to formula 13, formula 14, and judge whether to reach the condition of convergence to result of calculation, if then enter step 4., if not then with this compensating computation gained lander position (X _s, Y _s, Z _s) and lunar libration parameter (Ω, i, μ) as new lander position (X _s, Y _s, Z _s) initial coordinate and lunar libration parameter (Ω, i, μ) initial value, return step 2. again iteration until reach the condition of convergence.

During concrete enforcement, those skilled in the art can preset the condition of convergence voluntarily.In embodiment, the condition of convergence is, the mould of parameter correction x is less than 1 centimetre.

4. according to final model parameter vector X=(X _s, Y _s, Z _s, Ω, i, μ) ^texport lander location parameter and lunar libration parameter extraction result, process flow operation terminates.

During concrete enforcement, modular mode also can be adopted to provide a kind of Lunar satellite orbit Precision Position Location System improving libration parameter, and the system of embodiment comprises with lower module,

Initialization module, for inputting lunar libration parameter (Ω, i, μ) initial value, lander approximate coordinates (X ₀, Y ₀, Z ₀), the time delay observed quantity τ of EOP data and each bar baseline, with lander approximate coordinates (X ₀, Y ₀, Z ₀) be lander position (X _s, Y _s, Z _s) initial coordinate;

Theoretical observed reading and partial derivative ask for module, for for every bar baseline according to formula 3 according to lander position (X _s, Y _s, Z _s) initial coordinate calculate the theoretical observed reading of time delay observed quantity τ of VLBI, according to formula 4, formula 8 according to lander position (X _s, Y _s, Z _s) initial coordinate and the observed quantity of lunar libration parameter (Ω, i, μ) calculation of initial value time delay treat the partial derivative asking parameter;

Positioning calculation model, for asking for the partial derivative composition matrix of coefficients B=(B that this execution work of module calculates each baseline according to theoretical observed reading and partial derivative ₁, B ₂, B ₃, B ₄, B ₅, B ₆), if model parameter vector X=is (X _s, Y _s, Z _s, Ω, i, μ) ^t, model parameter approximate value is X ⁰, x is parameter correction, represents approximate value X ⁰and the corrected value between parameter true value, l represents the difference between observed reading and approximate treatment value, least-squares calculation is carried out according to formula 13, formula 14, and judge whether to reach the condition of convergence to result of calculation, if then command result output module work, if not then with this compensating computation gained lander position (X _s, Y _s, Z _s) and lunar libration parameter (Ω, i, μ) as new lander position (X _s, Y _s, Z _s) initial coordinate and lunar libration parameter (Ω, i, μ) initial value, order theoretical observed reading and partial derivative ask for module again iteration work until reach the condition of convergence;

Result output module, for according to final model parameter vector X=(X _s, Y _s, Z _s, Ω, i, μ) ^texport lander location parameter and lunar libration parameter extraction result.

Above embodiment is used for illustrative purposes only, but not limitation of the present invention, person skilled in the relevant technique, without departing from the spirit and scope of the present invention, various conversion or modification can also be made, therefore all equivalent technical schemes also should belong within category of the present invention, should be limited by each claim.

Claims (8)

1. improve a Lunar satellite orbit precision positioning method for libration parameter, it is characterized in that: comprise the following steps,

Step 1, input lunar libration parameter (Ω, i, μ) initial value, lander approximate coordinates (X ₀, Y ₀, Z ₀), the time delay observed quantity τ of EOP data and each bar baseline, with lander approximate coordinates (X ₀, Y ₀, Z ₀) be lander position (X _s, Y _s, Z _s) initial coordinate;

Step 2, for every bar baseline according to formula one according to lander position (X _s, Y _s, Z _s) initial coordinate calculate the theoretical observed reading of time delay observed quantity τ of VLBI, according to formula two, formula three according to lander position (X _s, Y _s, Z _s) initial coordinate and the observed quantity of lunar libration parameter (Ω, i, μ) calculation of initial value time delay to the partial derivative of lander position and libration parameter;

$\mathrm{\τ}=-\frac{1}{c}{R}_E{\left[\begin{array}{c}{X}_2-X_1\\ Y_2-Y_1\\ Z_2-Z_1\end{array}\right]}^T\·\frac{{2R}_M{\left[\begin{array}{c}{X}_S\\ Y_S\\ Z_S\end{array}\right]}^T-R_E{\left[\begin{array}{c}{X}_1+X_2\\ Y_1+Y_2\\ Z_1+Z_2\end{array}\right]}^T}{|{2R}_M{\left[\begin{array}{c}{X}_S\\ Y_S\\ Z_S\end{array}\right]}^T-R_E{\left[\begin{array}{c}{X}_1+X_2\\ Y_1+Y_2\\ Z_1+Z_2\end{array}\right]}^T|}$ Formula one

Wherein, (X ₁, Y ₁, Z ₁) be the coordinate of survey station 1, (X ₂, Y ₂, Z ₂) be the coordinate of survey station 2, lander position (X _s, Y _s, Z _s) adopting lander J2000.0 month heart celestial coordinate system coordinate, c represents the light velocity, matrix R _mrepresent that the moon is tied to the rotation matrix of J2000.0 month heart celestial coordinate system admittedly, matrix R _erepresent that ground is tied to the rotation matrix of J2000.0 month heart celestial coordinate system admittedly;

Time delay observed quantity is to lander position (X _s, Y _s, Z _s) partial derivative be,

${\left(\begin{array}{c}\frac{\∂\mathrm{\τ}}{{\∂X}_s}\\ \frac{\∂\mathrm{\τ}}{{\∂Y}_s}\\ \frac{\∂\mathrm{\τ}}{{\∂Z}_s}\end{array}\right)}^T={\left(\begin{array}{c}{B}_1\\ B_2\\ B_3\end{array}\right)}^T=-\frac{2}{c}\frac{R_E{\left[\begin{array}{c}{X}_2-X_1\\ Y_2-Y_1\\ Z_2-Z_1\end{array}\right]}^T{R}_M}{|{2R}_M{\left[\begin{array}{c}{X}_0\\ Y_0\\ Z_0\end{array}\right]}^T-R_E{\left[\begin{array}{c}{X}_1+X_2\\ Y_1+Y_2\\ Z_1+Z_2\end{array}\right]}^T|}$ Formula two

The partial derivative of time delay observed quantity to lunar libration parameter (Ω, i, μ) is,

formula three

Wherein, coefficient B ₁, B ₂, B ₃represent the partial derivative of time delay observed quantity to lander position, coefficient B ₄, B ₅, B ₆represent the partial derivative of time delay observed quantity to lunar libration parameter (Ω, i, μ);

Step 3, performs step 2 according to this and forms matrix of coefficients B=(B to the partial derivative that each baseline calculates ₁, B ₂, B ₃, B ₄, B ₅, B ₆), if model parameter vector X=is (X _s, Y _s, Z _s, Ω, i, μ) ^t, model parameter approximate value is X ⁰, x is parameter correction, represents approximate value X ⁰and the corrected value between parameter true value, l represents the difference between observed reading and approximate treatment value, least-squares calculation is carried out according to formula four, formula five, and judge whether to reach the condition of convergence to result of calculation, if then enter step 4, if not then with this compensating computation gained lander position (X _s, Y _s, Z _s) and lunar libration parameter (Ω, i, μ) as new lander position (X _s, Y _s, Z _s) initial coordinate and lunar libration parameter (Ω, i, μ) initial value, return step 2 again iteration until reach the condition of convergence;

$(B^T{P}_{\mathrm{\Δ}}B+{\mathrm{\σ}}_0^2{\mathrm{\σ}}_x^{-2}{P}_{\hat{x}})\hat{x}=B^T{P}_{\mathrm{\Δ}}l+{\mathrm{\σ}}_0^2+{\mathrm{\σ}}_x^{-2}{P}_{\hat{x}}{l}_{\hat{x}}$ Formula four

$\hat{x}={(B^T{P}_{\mathrm{\Δ}}B+{\mathrm{\σ}}_0^2{\mathrm{\σ}}_x^{-2}{P}_{\hat{x}})}^{-1}{B}^T{P}_{\mathrm{\Δ}}l$ Formula five

Wherein, P _Δrepresent observed reading power battle array, represent observed reading variance of unit weight, represent that parameter weighs variance surely, for the adjusted value of x, represent expect, represent adjusted value corresponding parameter power battle array;

Step 4, according to final model parameter vector X=(X _s, Y _s, Z _s, Ω, i, μ) ^texport lander location parameter and lunar libration parameter extraction result.

2. improve the Lunar satellite orbit precision positioning method of libration parameter according to claim 1, it is characterized in that: in step 3, the condition of convergence is, the mould of parameter correction x is less than 1 centimetre.

3. according to claim 1 or 2, improve the Lunar satellite orbit precision positioning method of libration parameter, it is characterized in that: in step 1, lunar libration parameter (Ω, i, μ) initial value is provided by JPL ephemeris.

4. improve the Lunar satellite orbit precision positioning method of libration parameter according to claim 3, it is characterized in that: in step 2, matrix R _mthered is provided lunar libration parameter (Ω, i, μ) calculation of initial value to obtain by JPL ephemeris, described EOP data are provided numerical value, matrix R by EOPC04_08 sequence _eobtained by EOPC04_08 numerical evaluation that sequence provides.

5. improve a Lunar satellite orbit Precision Position Location System for libration parameter, it is characterized in that: comprise with lower module,

Initialization module, for inputting lunar libration parameter (Ω, i, μ) initial value, lander approximate coordinates (X ₀, Y ₀, Z ₀), the time delay observed quantity τ of EOP data and each bar baseline, with lander approximate coordinates (X ₀, Y ₀, Z ₀) be lander position (X _s, Y _s, Z _s) initial coordinate;

Theoretical observed reading and partial derivative ask for module, for for every bar baseline according to formula one according to lander position (X _s, Y _s, Z _s) initial coordinate calculate the theoretical observed reading of time delay observed quantity τ of VLBI, according to formula two, formula three according to lander position (X _s, Y _s, Z _s) initial coordinate and the observed quantity of lunar libration parameter (Ω, i, μ) calculation of initial value time delay to the partial derivative of lander position and libration parameter;

$\mathrm{\τ}=-\frac{1}{c}{R}_E{\left[\begin{array}{c}{X}_2-X_1\\ Y_2-Y_1\\ Z_2-Z_1\end{array}\right]}^T\·\frac{{2R}_M{\left[\begin{array}{c}{X}_S\\ Y_S\\ Z_S\end{array}\right]}^T-R_E{\left[\begin{array}{c}{X}_1+X_2\\ Y_1+Y_2\\ Z_1+Z_2\end{array}\right]}^T}{|{2R}_M{\left[\begin{array}{c}{X}_S\\ Y_S\\ Z_S\end{array}\right]}^T-R_E{\left[\begin{array}{c}{X}_1+X_2\\ Y_1+Y_2\\ Z_1+Z_2\end{array}\right]}^T|}$ Formula one

Wherein, (X ₁, Y ₁, Z ₁) be the coordinate of survey station 1, (X ₂, Y ₂, Z ₂) be the coordinate of survey station 2, lander position (X _s, Y _s, Z _s) adopting lander J2000.0 month heart celestial coordinate system coordinate, c represents the light velocity, matrix R _mrepresent that the moon is tied to the rotation matrix of J2000.0 month heart celestial coordinate system admittedly, matrix R _erepresent that ground is tied to the rotation matrix of J2000.0 month heart celestial coordinate system admittedly;

Time delay observed quantity is to lander position (X _s, Y _s, Z _s) partial derivative be,

${\left(\begin{array}{c}\frac{\∂\mathrm{\τ}}{{\∂X}_s}\\ \frac{\∂\mathrm{\τ}}{{\∂Y}_s}\\ \frac{\∂\mathrm{\τ}}{{\∂Z}_s}\end{array}\right)}^T={\left(\begin{array}{c}{B}_1\\ B_2\\ B_3\end{array}\right)}^T=-\frac{2}{c}\frac{R_E{\left[\begin{array}{c}{X}_2-X_1\\ Y_2-Y_1\\ Z_2-Z_1\end{array}\right]}^T{R}_M}{|{2R}_M{\left[\begin{array}{c}{X}_0\\ Y_0\\ Z_0\end{array}\right]}^T-R_E{\left[\begin{array}{c}{X}_1+X_2\\ Y_1+Y_2\\ Z_1+Z_2\end{array}\right]}^T|}$ Formula two

The partial derivative of time delay observed quantity to lunar libration parameter (Ω, i, μ) is,

formula three

Wherein, coefficient B ₁, B ₂, B ₃represent the partial derivative of time delay observed quantity to lander position, coefficient B ₄, B ₅, B ₆represent the partial derivative of time delay observed quantity to lunar libration parameter (Ω, i, μ);

Positioning calculation model, for asking for the partial derivative composition matrix of coefficients B=(B that this execution work of module calculates each baseline according to theoretical observed reading and partial derivative ₁, B ₂, B ₃, B ₄, B ₅, B ₆), if model parameter vector X=is (X _s, Y _s, Z _s, Ω, i, μ) ^t, model parameter approximate value is X ⁰, x is parameter correction, represents approximate value X ⁰and the corrected value between parameter true value, l represents the difference between observed reading and approximate treatment value, least-squares calculation is carried out according to formula four, formula five, and judge whether to reach the condition of convergence to result of calculation, if then command result output module work, if not then with this compensating computation gained lander position (X _s, Y _s, Z _s) and lunar libration parameter (Ω, i, μ) as new lander position (X _s, Y _s, Z _s) initial coordinate and lunar libration parameter (Ω, i, μ) initial value, order theoretical observed reading and partial derivative ask for module again iteration work until reach the condition of convergence;

$(B^T{P}_{\mathrm{\Δ}}B+{\mathrm{\σ}}_0^2{\mathrm{\σ}}_x^{-2}{P}_{\hat{x}})\hat{x}=B^T{P}_{\mathrm{\Δ}}l+{\mathrm{\σ}}_0^2+{\mathrm{\σ}}_x^{-2}{P}_{\hat{x}}{l}_{\hat{x}}$ Formula four

$\hat{x}={(B^T{P}_{\mathrm{\Δ}}B+{\mathrm{\σ}}_0^2{\mathrm{\σ}}_x^{-2}{P}_{\hat{x}})}^{-1}{B}^T{P}_{\mathrm{\Δ}}l$ Formula five

Wherein, P _Δrepresent observed reading power battle array, represent observed reading variance of unit weight, represent that parameter weighs variance surely, for the adjusted value of x, represent expect, represent adjusted value corresponding parameter power battle array;

Result output module, for according to final model parameter vector X=(X _s, Y _s, Z _s, Ω, i, μ) ^texport lander location parameter and lunar libration parameter extraction result.

6. improve the Lunar satellite orbit Precision Position Location System of libration parameter according to claim 5, it is characterized in that: in positioning calculation model, the condition of convergence is, the mould of parameter correction x is less than 1 centimetre.

7. according to claim 5 or 6, improve the Lunar satellite orbit Precision Position Location System of libration parameter, it is characterized in that: in initialization module, lunar libration parameter (Ω, i, μ) initial value is provided by JPL ephemeris.

8. improve the Lunar satellite orbit Precision Position Location System of libration parameter according to claim 7, it is characterized in that: theoretical observed reading and partial derivative are asked in module, matrix R _mthered is provided lunar libration parameter (Ω, i, μ) calculation of initial value to obtain by JPL ephemeris, described EOP data are provided numerical value, matrix R by EOPC04_08 sequence _eobtained by EOPC04_08 numerical evaluation that sequence provides.