The Comparison of WGS-84 and ITRF 2.2 Transformation of Coordinate System General remarks bservations from the tranSi transformation between the celestial Reference while itrf is based on nd VlBI me(CRF)and the Terrestrial Reference Frame (TRF) by accuracy of th reference stations is XERRRRx estimated to be in of 1 to 2 meters while Where the accuracy of the erence stations is at the RM rotation matrix for polar motion RS rotation matrix for sidereal time Why do we need RN rotation matrix for nutation learn the The comparison of parameters of wGS-84 and ITRF RP rotation matrix for precession transformation of reveals remarkable differences. WHY? coordinate systems? 1. Precession T represents the time-span expressed in Julian centuries of 365.25 mean solar days between the standard epoch The position of the mean vernal equinox at the standard J2000.0 and the epoch of observation. epoch to is denoted by Eo and the position at the observation epoch t is denoted by E. The precession matrix x(to R3{-=R2{-)R;{ related to time? mean equator(t) The precession parameters are computed from this time mean equator(to) series 5=23062181T+0.3018872+001799873 z=23062181T+1”.0946872+0″01820373 Xi(to) =2004.3109T-04266572-0”41833T3 The definition of Precession 2. Nutation The mean obliquity of the ecliptic e has been determined denoted by E and the true equinox by Er. The nutation E=23°2621:"448-46″81501-0.″0005912+0.″001813T matrix" is composed of three successive rotation matrice where T is the same time factor RN=R-(e+△e)R3-△o)}Rle} The nutation parameters△rand△4 are computed from the harmonic series. nutation△in longitude△e P35,Eq.3.15 mean equator and the nutation be treated differential true equator 方=12 quantities3 The Comparison of WGS-84 and ITRF 1. The WGS-84 was established through Doppler observations from the TRANSIT satellite system while ITRF is based on SLR and VLBI observations. 2. The accuracy of the WGS-84 reference stations is estimated to be in the range of 1 to 2 meters while the accuracy of the ITRF reference stations is at the centimeter level. The comparison of parameters of WGS-84 and ITRF reveals remarkable differences. WHY? 2.2 Transformation of Coordinate System General remarks The transformation between the Celestial Reference Frame (CRF) and the Terrestrial Reference Frame (TRF) by Where: RM rotation matrix for polar motion RS rotation matrix for sidereal time RN rotation matrix for nutation RP rotation matrix for precession CRF M S N P TRF x = R R R R x Why do we need learn the transformation of coordinate systems? 1. Precession The position of the mean vernal equinox at the standard epoch t0 is denoted by E0 and the position at the observation epoch t is denoted by E. The precession matrix R = R3{−z}R2{−ϑ}R3{−ς} P The precession parameters are computed from this time series 2 3 ς = 2306′′.2181T + 0′′.30188T + 0′′.017998T 2 3 ϑ = 2004′′.3109T − 0′′.42665T − 0′′.41833T 2 3 z = 2306′′.2181T +1′′.09468T + 0′′.018203T The definition of Precession T represents the time-span expressed in Julian centuries of 365.25 mean solar days between the standard epoch J2000.0 and the epoch of observation. Why does the precession is related to time? 2. Nutation The mean vernal equinox at the observation epoch is denoted by E and the true equinox by Et . The nutation matrix is composed of three successive rotation matrices N R R R1{ (ε ε )}R3{ φ)}R1{ε} N = − + ∆ −∆ where both the nutation in longitude ; and the nutation in obliquity can be treated as differential quantities. ∆ε ∆φ The mean obliquity of the ecliptic has been determined as ε ∆ε ∆φ ε P35., Eq. 3.15 where T is the same time factor. = 23°26'21.″448 - 46.″8150T – 0.″00059T2 + 0.″001813T3 The nutation parameters and are computed from the harmonic series: