• Acta Photonica Sinica
  • Vol. 49, Issue 10, 1012001 (2020)
Chang-ming LU1、2、3, Xin GAO2, Xi-yu LI2, Mei-lin XIE1, and Zhi-guo LI1
Author Affiliations
  • 1Xi'an Institute of Optics and Precision Mechanics of CAS,Xi'an 710119,China
  • 2Beijing Institute of Track and Telecommunication Technology,Beijing 100094,China
  • 3University of Chinese Academy of Sciences,Beijing 100190,China
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    DOI: 10.3788/gzxb20204910.1012001 Cite this Article
    Chang-ming LU, Xin GAO, Xi-yu LI, Mei-lin XIE, Zhi-guo LI. A Method for Evaluating Medium and High-earth Orbit Object Telescope's Precision by Beidou's Precise Ephemeris[J]. Acta Photonica Sinica, 2020, 49(10): 1012001 Copy Citation Text show less

    Abstract

    In order to solve the lacking of calibration means when working in the field, the Beidou Navigation Satellite System(BDS) is used to evaluate telescopes' astronomy and axis orientation precision, which survey the Medium And High Earth Orbit Objects(MHEO). This research is dedicated to deduce the principle of astronomy and axis orientation, and testify the feasibility of evaluating the electro-optical telescope's accuracy with BDS by analysising the satellites' coverage, orbit pricision and brightness, which has big diameter. Firstly, we interpolate the regular BDS precise ephemeris by Lagrange polynomial, whose data interval is 5 minutes. With coordinate conversion, we get the apparent ascension and apparent declination in the agreement celestial coordinate system, azimuth and pitch in the station coordinate system, which are the true value for astronomy and axis orientation precision evaluation. A MHEO telescope's astronomy orientation precision is superior to 2″ and axis orientation precision is superior to 7″ by this method.
    ξ=cos(δ1)sin(α1-α0)sin(δ1)sin(δ0)+cos(δ1)cos(δ0)cos(α1-α0)ζ=sin(δ1)cos(δ0)-cos(δ1)sin(δ0)cos(α1-α0)sin(δ1)sin(δ0)+cos(δ1)cos(δ0)cos(α1-α0)

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    xs=i,jxi[I(xi,yi)-Ib]i,jI(xi,yi)ys=i,jyi[I(xi,yi)-Ib]i,jI(xi,yi)

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    ξ=a+bxs+cysζ=d+exs+fys

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    ξ=a1+b1xs+c1ys+d1xs2+e1xssys+f1ys2ζ=a2+b2xs+c2ys+d2xs2+e2xsys+f2ys2

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    Es=E0±(ys-y0)SyAs=A0±(xs-x0)Sx/cos(Es)

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    Ai=Ai+fAi(Ai,Ei)Ei=Ei+fEi(Ai,Ei)fAi(Ai,Ei)=Vsin(Ah-Ai)tan(Ei)+ktan(Ei)+csec(Ei)+gfEi(Ai,Ei)=l-Vcos(Ah-Ai)+dcos(Ei)

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    Fθ,λ=l=0Al0Pl0(cosθ)+m=1lAlmcos(mλ)+Blmsin(mλ)Plm(cosθ)

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    fA(A,E)sinE=A0+A1cosE+A2cosAsinE+A3sinAsinE+A4cos2E+A5cosAsinEcosE+A6sinAsinEcosE+A7cos3E+A8cosAsinEcos2E+A9sinAsinEcos2E+A10cos4E+A11cosAsinEcos3E+A12sinAsinEcos3EfB(A,E)sinE=B0+B1cosE+B2cosAsinE+B3sinAsinE+B4cos2E+B5cosAsinEcosE+B6sinAsinEcosE+B7cos3E+B8cosAsinEcos2E+B9sinAsinEcos2E+B10cos4E+B11cosAsinEcos3E+B12sinAsinEcos3E

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    f(x)=i=0nyij=0jinx-xjxi-xj

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    m=1.0-2.5lg(r)-2.5lg(D×L)+5lg(R100)-2.5lg[sin(ϕ)sin(φ)]+Δm(σ)

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    UT1=UTC+ΔUTC

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    T2=T1-t1

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    Rx(θ)=1000cos(θ)sin(θ)0-sin(θ)cos(θ)Ry(θ)=cos(θ)0-sin(θ)010sin(θ)0cos(θ)Rz(θ)=cos(θ)sin(θ)0-sin(θ)cos(θ) 0001

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    XYZt=[Ry(-xp)Rx(-yp)]TXYZ0=(Ep)TXYZ0

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    xyzt=[Rz(GAST)]TXYZt=(ER)TXYZt

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    xyzM=[Rx(-ε0-ε)Rz(-ψ)Rx(ε0)]Txyzt=(NR)Txyzt

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    ε0=84381.448-46.815×t-0.00059×t2+0.001813×t3(1)

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    xyzECI=[Rz(-ZA)Ry(θA)Rz(-ξA)]TxyzM=(PR)TxyzM

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    ξA=2306.2181×t+0.30188×t2+0.017998×t3θA=2004.3109×t-0.42665×t2-0.041833×t3ZA=2306.2181×t+1.094687×t2+0.018203×t3

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    xyzECI=[Rz(-ZA)Ry(θA)Rz(-ξA)]T[Rx(-ε0-ε)Rz(-ψ)Rx(ε0)]T×[Rz(GAST)]T[Ry(-xp)Rx(-yp)]TXYZ0

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    xGPSyGPSzGPSECI-xstaystazstaECI=cos(α)cos(δ)sin(α)cos(δ)        sin(α)

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    XYZCC=Ry(-90)Rx(φc)Rz(-90+λc)XYZ0-XYZOC

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    Xcc=Rcos(A)cos(E)Ycc=Rsin(E)Zcc=Rsin(A)cos(E)

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    Chang-ming LU, Xin GAO, Xi-yu LI, Mei-lin XIE, Zhi-guo LI. A Method for Evaluating Medium and High-earth Orbit Object Telescope's Precision by Beidou's Precise Ephemeris[J]. Acta Photonica Sinica, 2020, 49(10): 1012001
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