(Polar Motion, PM) ERP Vol.29, No PROGRESS IN ASTRONOMY Jul., (2011) P183.3 ( )

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1 29 3 Vol29, No PROGRESS IN ASTRONOMY Jul, ( AR ( AR 3 X Y AR P1833 A 1 (Polar Motion, PM [1] X Y (LOD (ERP [2] ERP ( VLBI SLR GPS ERP ERP [3 5] ERP ERP [6] ERP [4 15] Zhu [9, 10] (AW (CW ( ( (2011ssxt054

2 (LS [4 8, 12, 13] Schuh [4] (LS+ANN Kosek [12, 13] (LS+AR LS AW CW [10] AW CW [16, 17] LS AW CW AR (WLS+AR t ( AW CW LS+AR WLS+AR 2 WLS+AR WLS AR 21 WLS X Y (1 (2 X(t=A x + B x t+ C 1 x cos ( 2πt +C 2 x sin ( 2πt + D 1 x cos ( 2πt +D 2 x sin ( 2πt +E 1 x cos ( 2πt + E 2 x sin ( 2πt, Y(t=A y + B y t+ C 1 y D 1 y 2πt cos ( +C 2 2πt y sin ( + cos (2πt +D 2 y sin (2πt +Ey 1 cos (2πt + Ey 2 sin (2πt, (1 (2 A x B x X C 1 x C 2 x D 1 x D 2 x E 1 x E 2 x X a t UTC

3 3 AR 345 a X(t t X [10] Y X P : X= A x B x C 1 x C 2 x D 1 x D 2 x E 1 x E 2 x A y B y Cy 1 Cy 2 D 1 y D 2 y Ey 1 Ey 2, (3 1 t 1 cos ( 2πt 1 sin ( 2πt 1 cos ( 2πt 1 sin ( 2πt 1 cos ( 2πt 1 sin ( 2πt 1 B= 1 t 2 cos ( 2πt 2 sin ( 2πt 2 cos ( 2πt 2 sin ( 2πt 2 cos ( 2πt 2 sin ( 2πt 2 1 t n cos ( 2πt n sin ( 2πt n cos ( 2πt n sin ( 2πt n cos ( 2πt n sin ( 2πt n, (4 L= ˆX(t 1 ˆX(t 2 ˆX(t n Ŷ(t 1 Ŷ(t 2 Ŷ(t n, (5 X B L X Y X X=(B T PB 1 B T PL, (6 P 22 WLS f= P t i P t j (t i < t j, (7 (7 t i t j i j P ti P t j i j (7 f ( f 1 f (

4 ( ( f ( 1 f f 3 t P i = 1 (i=1, 2, 3,, n, (8 t i P i = 1 t 2 i (i=1, 2, 3,, n, (9 P i = 1 t 3 i (i=1, 2, 3,, n, (10 f 1 f 2 f 3 f f 1 < f 2 < f AR WLS AR WLS AR AR z t = p ϕ j z t j + a t, (11 j=1 z t (t = 1, 2, 3,, n WLS ϕ 1,ϕ 2,,ϕ p a t p p AR(p [18] AR p AR 3 [2, 19] 3 AR FPE(M= N+M N M P M, (12

5 3 AR 347 P M = 1 N M N (z t t=m+1 M ϕ j z t j 2 (13 j=1 P M AR(M z t (t=1, 2, 3,, n M = 1, 2, 3,, N FPE(M M [2] (Le- Vinson AR [19] 24 (AE (MAE AE MAE (14 (15 AE AE j = P j O j, (14 P j j O j j AE j j MAE MAE i = 1 n P i j n Oi j, (15 j=1 P j j O j j i MAE i i 3 31 (IERS EOP 05 C04 WLS+AR LS+AR WLS+AR LS+AR 8 a 10 a 12 a LS+AR 1 X Y 1 30 d 10 a ( Y 10 a 12 a d 300 d 8 a 10 a 10 a 10 a LS+AR 3 WLS+AR 72 1, 6, 11, 16,, 356 ( 5 d d 2 860

6 LS+AR 32 WLS+AR LS+AR 2 3 X Y 2 X (AE

3 AR 349 3 Y (AE 3 f 2 3 X Y LS+AR 3 WLS+AR 2007 2010 2006 LS+AR f 3 2003 1 1 2010 10 31 4 4 3 WLS+AR (1 360 d (1 30 d

7 3 AR Y (AE 3 f 2 3 X Y LS+AR 3 WLS+AR LS+AR f WLS+AR (1 360 d (1 30 d MAE LS+AR WLS+AR LS+AR WLS+AR 3 X Y X 1 30 d d Y WLS+AR X 1 30 d d d d X WLS+AR Y WLS+AR f f f f

8 X Y (MAE Y 4 AR WLS AR WLS AR LS+AR WLS+AR 3 3 WLS+AR 3 X Y WLS LS LS WLS f 3

9 3 AR 351 f X Y 3 f [20, 21] (IERS IERS [1],, : [2], : 2000, 26: 466 [3], 2007, 25(4: 346 [4] Schuh H, Ulrich M, Egger D, et al J Geod, 2002, 76: 247 [5] Akyilmaz O, Kutterer H J Geod, 2004, 78: 82 [6] :, 2007: 1 [7],, 2010, 29(2: 70 [8],,, 2007, 52(15: 1728 [9] Zhu S Y Prediction of Earth Rotation and Polar Motion : 2 [10] Zhu S Y Bull Geod, 1982, 56: 258 [11] Chao B F Bull Geod, 1985, 59: 81 [12] Kosek W, McCarthy D D, Johnson T J, et al Astrometry, geodynamics and Solar system dynamics: from milliarcseconds to microarcseconds St Petersburg: Inst of Applied Astronomy of the Russian Acad of Sciences, 2004: 164 [13] Kosek W, Kalarus M, Niedzielski T The Celestial Reference Frame for the Future Paris: Observatoire de Paris Syst mes de R f rence Temps-Espace UMR8630/CNRS, 2008: 155 [14] Iz H B J Geod, 2008, 82: 871 [15] Kalarus M, Schch H, Kozek W, et al J Geod, 2010, 84: 587 [16] Kosek W, McCarthy D D, Luzum B J Studia geoph et geod, 2001, 45:347 [17] Schuh H, Nagel S, Seitz T J Geod, 2001, 74: 701 [18],,, :, 2000: 83 [19] :, 1998: 307 [20],, 1996, 11: 70 [21],,, 2000, 45: 2588

10 Joint Model of Weighted Least-squares and AR in Prediction of Polar Motion ZHANG Hao, WANG Qi-jie, ZHU Jian-jun, ZHANG Xiao-hong (School of Geosciences and Info-Physics, Central South University, Changsha , China Abstract: Earth rotation parameters (ERPs include length of day and polar motion Precise transformations between the international celestial and terrestrial reference frames are needed for many advanced geodetic and astronomical tasks including positioning and navigation on Earth and in space To perform this transformation, accurate ERPs are necessary However, the precise measurements of ERPs by space-geodetic techniques have to be pre-processed before the ERPs are available This causes a delay of 15 to 20 hours in case of GPS and of a few days in case of very-long-baseline interferometry (VLBI and satellite laser ranging (SLRThus it s necessary to predict the ERPs over at least a few days In addition, it might be interesting to look further into the future to estimate the Earth s rotation in the next few months Therefore, this paper deals with short-term predictions for next 30 days, long-term predictions for 360 days Various prediction methods have been developed, such as the joint model of least-squares and AR, joint model of least-squares and artificial neural networks(ann, and so on These methods most treat the Chandler Wobble(CW and Annual Wobble(AW of the polar motion as constants However, the CW and AW are of time variant characteristics as a matter of fact This paper puts forward a new joint model of weighted least-squares(wls and AR, according to the time variant characteristics of CW and AW One important issue in building the WLS+AR model is the right choice of the weight matrix ccording to the statistical properties of the polar motion series, the rule of weight choice is determined: the fitting value nearer to prediction value is given larger weight In accordance with the rule, three kinds of weight function are built and compared in order to assess the weight function of the weighted least-squares The more appropriate weight function for X series and Y series are suggested respectively Finally the WLS+AR model is compared with LS+AR model and shown that the new models are effective for improving the accuracy of the PM prediction The model is an interesting and new attempt in the PM prediction, and could be seen as an alternative prediction method However, in the paper, the theoretical basis of the model is not analyzed in depth, and which will be further studied in the later research Key words: Polar Motion Prediction; Weighted Least-squares; AR Model; Weight Function

Analysis of the Accuracy of Prediction of the Celestial Pole Motion

Analysis of the Accuracy of Prediction of the Celestial Pole Motion ISSN 163-7729, Astronomy Reports, 21, Vol. 54, No. 11, pp. 153 161. c Pleiades Publishing, Ltd., 21. Original Russian Text c Z.M. Malkin, 21, published in Astronomicheskiĭ Zhurnal, 21, Vol. 87, No. 11,