CN101893712A - Weight selection fitting method for precise orbit determination of geostationary satellite - Google Patents

Abstract

The invention discloses a weight selection fitting method for precise orbit determination of a geostationary satellite, which relates to a solution for ill-posed problems in the precise orbit determination of the geostationary satellite. The method comprises the following steps of: calculating a corresponding prior weight matrix by using prior information, obtaining a linear observation equation according to an observation data and a parameter approximate value of the geostationary satellite, applying restraint to 3 to 5 orbit parameters in 6 orbit parameters, and calculating the orbit parameters by a weight selection fitting formula to obtain a parameter assessment value of the precise orbit determination of the geostationary satellite. The method has the advantages that: the ill-posed property of the precise orbit determination equation of the geostationary satellite is improved by reasonably using the prior information of parameters, discriminating the parameters with different prior information and selecting the number of a part of orbits with small variation range to apply the restraint; and shown by graphs, the orbit parameter, the clock correction and the orbit kinetic parameter assessment value calculated by using the weight selection fitting formula have higher stability and higher precision compared with the results obtained by the prior art.

Description

The choosing power approximating method that is used for the geostationary satellite precise orbit determination

Technical field

The present invention relates to satellite precise orbit determination, relate in particular to pathosis way to solve the problem in the geostationary satellite precise orbit determination.

Background technology

Geostationary satellite has this unique track characteristic of relative geostationary, makes geostationary satellite be widely used in communication, meteorology, scouting, navigator fix, time service, tracking and fields such as data relaying and scientific research.The geostationary satellite Precise Orbit must satisfy all kinds of satellite business to strict demands such as " space reference " availability, continuity and consistance, and this has also determined the exploitation and the expansion of the potential application market of geostationary satellite simultaneously.Therefore, precise orbit determination method and Study on Technology always are one of focuses of geostationary satellite development and utilization.Geostationary satellite plays an important role in China's new generation satellite navigation positioning system.For realizing the design performance of new generation satellite navigation positioning system, guarantee its availability, need high-precision geostationary satellite ephemeris.

Compare with other classification of track satellite, the geostationary satellite Precise Orbit determines to exist big difficulty, mainly show: 1) since geostationary satellite orbit apart from ground 30,000 6 thousand km, it is less relatively that tracking station lays scope, makes observation geometry intensity difference to geostationary satellite; 2) geostationary satellite is relative with the ground tracking station position static, and the variation of the star geometry of standing is very little, and the quantity of information that the increase observation time brings is limited, makes some systematic errors (as clock correction and survey station deviation etc.) be difficult to resolve and separate.3) for the relative geostationary in holding position, geostationary satellite needs the frequent motor-driven control of implementing, this gives determining of geostationary satellite Precise Orbit and forecast brings than burden, if handle bad then can have a strong impact on the performance and the system availability of new generation satellite navigation system.

The difficulty that aforementioned geostationary satellite orbit is determined mainly is seriously morbid state of normal equation that track resolves.If linearizing error equation by kinetics equation and observation equation fusion

v＝Ax-l，

Wherein, v is the observation residual error, and A is design matrix (factor arrays), and x is for waiting to estimate orbital tracking and kinetic parameter, and l is an observation vector.The angle that between the survey station direction of visual lines, forms hour, design battle array A column vector is near linear dependence.

In geostationary satellite orbit determination, satellite field angle over the ground is less, and less than 18 °, during surface-based observing station observation geostationary satellite, the angle between its sight line is very little, makes design matrix A linear dependence characteristic outstanding, causes normal equation factor arrays N=A ^TPA is morbid state seriously, and conditional number reaches 10 ¹²～10 ¹⁴

By least square method obtain x separate into

$\hat{x}={\left(A^T\mathrm{PA}\right)}^{-1}{A}^T\mathrm{Pl}$

Wherein, P is an observed reading power battle array.

May exist more greatly with true value and to depart from, by orbit integration, there is bigger deviation in the geostationary satellite orbit that obtains.

In the method that solves this class difficult problem, lucky big vast promise husband regularization (Tikhonov) method is used more extensive.But this method retrains all parameters, the prior imformation of all parameters of equivalent processes, and in fact some wait to estimate the prior imformation of parameter may be inaccurate, will cause parameter estimation to depart from true value.Therefore, there is deficiency in actual applications in the lucky big vast promise husband method of regularization that all parameters are retrained.

Geodetic surveying data handle and geophysics inverting research in, the prior imformation that also has a partial parameters is situation more accurately, can adopt choosing power fitting process to prior imformation parameter additional constraint accurately.

Choosing power fitting process is that the method for the solution ill-conditioning problem of Ou Jikun proposition (is seen " mapping journal " 2004 33 the 4th phases of volume, pp283-288).This method fully takes into account the difference that the parameter prior imformation exists, and the method for employing is different with lucky big vast promise husband method of regularization, and parameter estimation is

$\hat{x}={(A^T\mathrm{PA}+\mathrm{\α}{P}_x)}^{-1}{A}^T\mathrm{Pl}$

Wherein, α is a smoothing factor; P _xBe the constraint weight matrix, can determine according to the priori weight matrix of parameter and the conditions such as parameter that need restraint.

In geostationary satellite orbit determination, the acquisition methods of the priori power battle array of parameter priori value and parameter is: according to the observation data of geostationary satellite, adopt dynamic method or simplify dynamic method to obtain the priori value X that geostationary satellite does not have singular orbit radical, clock correction and kinetic parameter, obtain corresponding variance-covariance battle array ∑ simultaneously _X, the priori power battle array of no singular orbit parameter

$P_X={\mathrm{\Σ}}_X^{-1}$

Wherein, P _XBe the parameter priori power battle array of n rank square formation, n is a number of waiting to estimate parameter, comprises the number of number, clock correction and the kinetic parameter of orbit parameter.

The linearization observation equation that obtains according to the observation data and the parameter approximate value of geostationary satellite:

l＝Ax-v

Wherein: l is the poor of geostationary satellite observed reading O and its observation calculated value C, l=O-C, and C is by waiting that estimating the parameter approximation calculation obtains;

Be the observation design matrix, treat the partial derivative of estimating parameter by observed quantity and waiting that estimating parameter approximate value place obtains that x is parameter to be estimated.

Summary of the invention

The objective of the invention is: a kind of choosing power approximating method that is used for the geostationary satellite precise orbit determination is provided, this method adopts the comparatively accurate and little parameter of parameter estimation variation range of choosing power approximating method constraint portions prior imformation, improve the pathosis that geostationary satellite orbit resolves normal equation in the process, improved geostationary satellite orbit accuracy of parameter estimation and accuracy.

For achieving the above object, the present invention has adopted following technical scheme:

The choosing power approximating method that is used for the geostationary satellite precise orbit determination comprises the following step:

A, according to the observation data of geostationary satellite, adopt dynamic method or simplify dynamic method to obtain the priori value X that geostationary satellite does not have singular orbit radical, clock correction and kinetic parameter, obtain corresponding variance-covariance battle array ∑ simultaneously _X, the priori power battle array of no singular orbit parameter

$P_X={\mathrm{\Σ}}_X^{-1}$

Wherein, P _XBe the parameter priori power battle array of n rank square formation, n is a number of waiting to estimate parameter, comprises the number of number, clock correction and the kinetic parameter of orbit parameter;

B, the linearization observation equation that obtains according to the observation data and the parameter approximate value of geostationary satellite:

l＝Ax-v

Wherein: l is the poor of geostationary satellite observed reading O and its observation calculated value C, l=O-C, and C is by waiting that estimating the parameter approximation calculation obtains;

Be the observation design matrix, treat the partial derivative of estimating parameter by observed quantity and waiting that estimating parameter approximate value place obtains that x is parameter to be estimated;

C, the m in other five orbit parameters except that semi-major axis of orbit a is imposed restriction, 3≤m≤5, the selection of parameter method is: at parameter priori value corresponding variance-covariance matrix ∑ _XIn, sort according to the size of diagonal element numerical value, select m parameter from small to large; Wait that the constraint matrix of estimating the parameter correspondence is obtained by following formula:

P _x＝TP _XT

Wherein, T is n rank square formations, and n is a number of waiting to estimate parameter,

T ⁽¹⁾

Be 6 rank square formations, its element

I parameter is elected to be constraint condition; T ⁽²⁾Be n-6 rank square formation, its element is 0 entirely, P _XBe the priori power battle array of parameter, T ' is the transposed matrix of T;

D, calculate, obtain the parameter estimation of geostationary satellite precise orbit determination with following choosing power fitting process formula:

$\hat{x}={(A^{\′}\mathrm{PA}+\mathrm{\α}{P}_x)}^{-1}{A}^{\′}\mathrm{Pl}$

${\mathrm{\Σ}}_{\hat{x}}={(A^{\′}\mathrm{PA}+\mathrm{\α}{P}_c)}^{-1}$

Wherein, A ' is the transposed matrix of A, and α is a smoothing factor, in geostationary satellite orbit determination, gets α=1.

Advantage of the present invention is: the prior imformation of rationally utilizing parameter, parameter with different prior imformations is treated with a certain discrimination, select the less orbital tracking of part variation range to impose restriction, improved the pathosis of geostationary satellite precise orbit determination normal equation, the orbit parameter, clock correction and the dynamics of orbits parameter estimation that calculate with choosing power fitting process formula are stronger than the stability as a result that prior art obtains, and precision is higher.

Description of drawings

Fig. 1 track that to be the orbit parameter calculated by additional parameter prior imformation not obtain with the orbit parameter of additional parameter prior imformation calculating and track true value poor.

Embodiment

Below in conjunction with accompanying drawing, the present invention is described in further detail.

Embodiment one

The choosing power approximating method that is used for the geostationary satellite precise orbit determination comprises the following step:

A, according to the observation data of geostationary satellite, adopt dynamic method or simplify dynamic method to obtain the priori value X that geostationary satellite does not have singular orbit radical, clock correction and kinetic parameter, obtain corresponding variance-covariance battle array ∑ simultaneously _X, the priori power battle array of no singular orbit parameter

$P_X={\mathrm{\Σ}}_X^{-1}$

Wherein, P _XBe the parameter priori power battle array of n rank square formation, n is a number of waiting to estimate parameter, comprises the number of number, clock correction and the kinetic parameter of orbit parameter;

B, the linearization observation equation that obtains according to the observation data and the parameter approximate value of geostationary satellite:

l＝Ax-v

Wherein: l is the poor of geostationary satellite observed reading O and its observation calculated value C, l=O-C, and C is by waiting that estimating the parameter approximation calculation obtains;

Be the observation design matrix, treat the partial derivative of estimating parameter by observed quantity and waiting that estimating parameter approximate value place obtains that x is parameter to be estimated;

C, the m in other five orbit parameters except that semi-major axis of orbit a is imposed restriction, 3≤m≤5, the selection of parameter method is: at parameter priori value corresponding variance-covariance matrix ∑ _XIn, sort according to the size of diagonal element numerical value, select m parameter from small to large; Wait that the constraint matrix of estimating the parameter correspondence is obtained by following formula:

P _x＝TP _XT′

Wherein, T is n rank square formations, and n is a number of waiting to estimate parameter,

T ⁽¹⁾

Be 6 rank square formations, its element

I parameter is elected to be constraint condition; T ⁽²⁾Be n-6 rank square formation, its element is 0 entirely, P _XBe the priori power battle array of parameter, T ' is the transposed matrix of T;

D, calculate, obtain the parameter estimation of geostationary satellite precise orbit determination with following choosing power fitting process formula:

$\hat{x}={(A^{\′}\mathrm{PA}+\mathrm{\α}{P}_x)}^{-1}{A}^{\′}\mathrm{Pl}$

${\mathrm{\Σ}}_{\hat{x}}{(A^{\′}\mathrm{PA}+\mathrm{\α}{P}_c)}^{-1}$

Wherein, A ' is the transposed matrix of A, and α is a smoothing factor, in geostationary satellite orbit determination, gets α=1.

Embodiment two

The application of choosing power fitting process in the geostationary satellite precise orbit determination

Two of emulation are distributed in east longitude 50 respectively and spend to the geostationary satellite and synchronous (IGSO) satellite of the inclined plane earth in the sky, equator of 160 degree, are labeled as GEO1, GEO6 and IGSO; Emulation five ground monitoring stations and South Pole survey station within Chinese territory.Prior imformation when using IGSO satellite orbit parameter that the poor method of list of GEO1 and IGSO satellite dynamic method resolves as the poor orbit determination of list of GEO6 and IGSO satellite dynamic method, the step of employing embodiment one obtains the parameter estimation of GEO6 geostationary satellite precise orbit determination when GEO6 and IGSO satellite list difference orbit determination, parameter estimation is carried out orbit integration, obtain geostationary satellite orbit, the result as shown in Figure 1.

The last figure of Fig. 1 is the orbit parameter calculated of additional parameter prior imformation not, and orbit parameter is carried out the poor of the track of the geostationary satellite that the dynamics integration obtains and track true value.

Figure below of Fig. 1 is the orbit parameter that the additional parameter prior imformation is calculated, and orbit parameter is carried out the poor of the track of the geostationary satellite that the dynamics integration obtains and track true value.

Horizontal ordinate is the time among Fig. 1, and ordinate is the poor of track calculated value and true value.

Contrast up and down from Fig. 1, the satellite orbit that the difference of using the GEO6 satellite orbit that resolves after the prior imformation and true value is as can be known resolved when not using prior imformation and the difference of true value are little.Hence one can see that, adopts choosing power fitting process when the geostationary satellite precise orbit determination, can improve the orbit determination accuracy of geostationary satellite.

Claims (1)

1. be used for the choosing power fitting process of geostationary satellite precise orbit determination, this method comprises the following step:

A, according to the observation data of geostationary satellite, adopt dynamic method or simplify dynamic method to obtain the priori value X that geostationary satellite does not have singular orbit radical, clock correction and kinetic parameter, obtain corresponding variance-covariance battle array ∑ simultaneously _X, geostationary satellite does not have the priori power battle array of singular orbit radical, clock correction and kinetic parameter

$P_X={\mathrm{\Σ}}_X^{-1}$

Wherein, P _XBe the parameter priori power battle array of n rank square formation, n is a number of waiting to estimate parameter, comprises the number of number, clock correction and the kinetic parameter of orbit parameter;

B, the linearization observation equation that obtains according to the observation data and the parameter approximate value of geostationary satellite:

l＝Ax-v

Wherein: l is the poor of geostationary satellite observed reading O and its observation calculated value C, l=O-C, and C is by waiting that estimating the parameter approximation calculation obtains;

Be the observation design matrix, treat the partial derivative of estimating parameter by observed quantity and waiting that estimating parameter approximate value place obtains that x is parameter to be estimated;

It is characterized in that choosing power fitting process also comprises the following step:

C, the m in other five orbit parameters except that semi-major axis of orbit a is imposed restriction, 3≤m≤5, the selection of parameter method is: at parameter priori value corresponding variance-covariance matrix ∑ _XIn, sort according to the size of diagonal element numerical value, select m parameter from small to large;

Wait that the constraint matrix of estimating the parameter correspondence is obtained by following formula:

P _x＝TP _XT

Wherein, T is n rank square formations, and n is a number of waiting to estimate parameter,

T ⁽¹⁾Be 6 rank square formations, its element I parameter is elected to be constraint condition; T ⁽²⁾Be n-6 rank square formation, its element is 0 entirely, P _XBe the priori power battle array of parameter, T ' is the transposed matrix of T;

D, calculate, obtain the parameter estimation of geostationary satellite precise orbit determination with following choosing power fitting process formula:

$\hat{x}={(A^{\′}\mathrm{PA}+\mathrm{\α}{P}_x)}^{-1}{A}^{\′}\mathrm{Pl}$

${\mathrm{\Σ}}_{\hat{x}}={(A^{\′}\mathrm{PA}+\mathrm{\α}{P}_c)}^{-1}$

Wherein, A ' is the transposed matrix of A, and α is a smoothing factor, in geostationary satellite orbit determination, gets α=1.

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