基于时间序列分解的GPS卫星钟差预报

145005272946255000ARMA(AutoregressiveMovingAverage)IGS(InternationalGPSServiceforGeodynamic)ARMA;ARMAP228.4GPSsatelliteclockerrorpredictingbasedonARMAanalysisAbstract:AccordingtothebenefitsofquadraticpolynomialsandtheGraymodelinpredictionofsatelliteclockerror,thispaperproposedtoimproveitwithARMA(AutoregressiveMovingAverage)model.TodecomposethepreciseGPSclockerrorprovidedbytheIGS(InternationalGPSServiceforGeodynamic),thetrenditemwasfitinaccordancewithquadraticpolynomialmodelandtheGraymodelwhosedifferenceliesonlyinthelengthoftime,andtherandomitemwassimulatedbyARMAmodel.Atlast,intheshort-termandlong-termGPSclockerrorforecastswithARMA,goodresultswereachieved.Keywords:preciseclockerror;timeseriesanalysis;ARMACHENZheng-sheng①,LVZhi-ping①,ZHANGQing-hua①,WANGPeng①②(①InstituteofSurveyingandMapping,InformationEngineeringUniversity,Zhengzhou450052,China;②72946Troops,Zibo255000,China)GPS[12]IGS0.1ns13d[3]IGS3,2,1,=++=tRSTXtttt1}{tT}{tS}{tR}{tX}{tTt}{tS}{tRARMADOICNKI:11-4415/P.20101111.0938.0102010-11-119:38)()(ttattaatT−+−+=−20a1a2a0ttnttt,,,213iv202010)()(ttattaavxiiii−+−+=+30ˆa1ˆa2ˆa0a1a2a202010)(ˆ)(ˆˆˆttattaaxiii−+−+=4⎥⎥⎥⎦⎤⎢⎢⎢⎣⎡=210ˆˆˆˆaaaa⎥⎥⎥⎥⎥⎦⎤⎢⎢⎢⎢⎢⎣⎡−−−−−−=20120120100201)()()(111ttttttttttttAn444⎥⎥⎥⎥⎦⎤⎢⎢⎢⎢⎣⎡=nxxxL4105LAAAaTT1)(ˆ−=6}n,...，21,=i(i),{X＝X(0)(0)}n,…，2，1＝k，(k){X＝X(1)(1)∑==kikX1(0))1((i)X)(uXdtdX=+)1()1(aueauka+=−−)1((0)(1))－(1)(X(k)Xˆ)1()()()1()1()0(−−=kXkXkX(0)(1)(1)(X(1)aakueea−−⎡⎤=−−⎢⎥⎣⎦kaˆaˆaˆaˆB3(1)(1)(1)(1)(1)(1)1(1)(2)121(2)(3)1211(1)()2XXXXBXnXn⎡⎤⎡⎤−+⎣⎦⎢⎥⎢⎥⎢⎥⎡⎤−+⎣⎦⎢⎥=⎢⎥⎢⎥⎢⎥⎡⎤−−+⎢⎥⎣⎦⎣⎦44(0)(0)(0)(2)(3)()⎡⎤⎢⎥⎢⎥=⎢⎥⎢⎥⎣⎦4NXXYXn}{tT}{tRARMA}{tRARMAARARMAMA}{tRkγkϕAICNjkjkInjkAIC)(2)),(ˆ(),(2++=σ13),(jkARMA(pq)),(ˆ2jkσNjk,AR(p)1,0ptjtjtjXaXtε−==+≥∑,2~WN(0,)tεσ14Yule-Walker12{,,,}Nxxx312(,,,)Tpaaa=a32σ.pa{}kγ0111121022120ppppppaaaγγγγγγγγγγγγ−−−−⎡⎤⎡⎤⎡⎤⎢⎥⎢⎥⎢⎥⎢⎥=⎢⎥⎢⎥⎢⎥⎢⎥⎢⎥⎢⎥⎢⎥⎢⎥⎣⎦⎣⎦⎣⎦334444643152σ20Tppσγ=−γa12{,,,}Nxxx3,Np,,1~ttNyxxtN=−=;11ˆ,0,1,,NkkjjkjyykpNγ−+===∑3;12,,,Nxxx3,ˆpΓ,1ˆˆˆppp−=aΓγ,2100ˆˆˆˆˆˆˆˆTTpppppσγγ−=−=−γaγΓγ.16,Levinson(,):42001,1102221,1,11,21,1,101,12,2,1,,1,1,1ˆˆˆˆˆˆˆˆ(1)(1)ˆˆˆˆˆˆˆ...ˆˆˆˆˆˆˆˆ...ˆˆˆˆ,1,kkkkkkkkkkkkkkkkkkkjkjkkkkjaaaaaaaaaaaaajkkpσγγγσσγγγγγγγγ−+−++++++−⎧=⎪=⎪⎪=−⎪⎨−−−−⎪=⎪−−−−⎪=−≤≤≤⎪⎩1712,1,2,ˆˆˆˆˆˆ(2)(,,,)(,,,)pppppaaaaaa=33,22ˆˆpσσ=.18Yule-Walker:1ˆˆ()10,when||1pjjjAzazz==−≠≤∑19ARMAYule-WalkerMA(p)Ζ∈+=∑=−tbXqjjtjtt,1εε20}{tε),0(2σNTqbbbb),,,(213Χ=∑=≠+=qjjjzbzB101)(1≤z21qbΧ2σ10=bbΧ)(1102qkqkkkbbbbbb−++++=3σγqk≤≤022bΧbΧ2σkγˆ.2,1,0qk3=bΧ2σ)0(,]),0(,),0(),0([)0(2211σTqbbbb3Χ=23)(,]),(,),(),([)(2211jjbjbjbjbTqσ3Χ=24j⎪⎪⎪⎩⎪⎪⎪⎨⎧=−−++−−−=−++−+=−+)(ˆ)()]1()1()1()1([)(ˆ)()1()1(1ˆ)(211222102jjbjbjbjbjbjjbjbjbjqqqkqkkkqσγσγγσ3311−≤≤qk3IGSigs****.clk_30s140846h6h56hIGS1-4IGS40500100015002000250030005.1045.1065.1085.115.1125.1145.1165.1185.12x10-5历元钟差(秒)卫星PRN:G09050010001500200025003000-2.5377-2.5376-2.5376-2.5375x10-4历元钟差(秒)卫星PRN:G18050010001500200025003000-2.1884-2.1883-2.1882-2.1881-2.188-2.1879-2.1878-2.1877-2.1876-2.1875x10-5历元钟差(秒)卫星PRN:G200500100015002000250030002.112.1112.1122.1132.1142.1152.1162.1172.1182.1192.12x10-5历元钟差(秒)卫星PRN:G305-80500100015005.1045.1055.1065.1075.1085.1095.115.1115.1125.1135.114x10-5历元钟差(秒)卫星PRN:G09校正钟差二次多项式灰色模型时间序列分解050010001500-2.5377-2.5376-2.5376-2.5376-2.5376-2.5376-2.5376-2.5376-2.5376-2.5376x10-4历元钟差(秒)卫星PRN:G18校正钟差二次多项式灰色模型时间序列分解6050010001500-2.1883-2.1882-2.1881-2.188-2.1879-2.1878-2.1877-2.1876x10-5历元钟差(秒)卫星PRN:G20校正钟差二次多项式灰色模型时间序列分解0500100015002.112.1112.1122.1132.1142.1152.116x10-5历元钟差(秒)卫星PRN:G30校正钟差二次多项式灰色模型时间序列分解9-1200.511.522.5x1044.94.9555.055.15.155.25.25x10-5历元钟差(秒)卫星PRN:G09校正钟差二次多项式灰色模型时间序列分解00.511.522.5x104-2.539-2.538-2.537-2.536-2.535-2.534-2.533-2.532-2.531-2.53x10-4历元钟差(秒)卫星PRN:G18校正钟差二次多项式灰色模型时间序列分解00.511.522.5x104-2.32-2.3-2.28-2.26-2.24-2.22-2.2-2.18-2.16x10-5历元钟差(秒)卫星PRN:G20校正钟差二次多项式灰色模型时间序列分解00.511.522.5x1042.112.122.132.142.152.162.172.182.19x10-5历元钟差(秒)卫星PRN:G30校正钟差二次多项式灰色模型时间序列分解PRN(ns)(ns)(ns)G090.11000.18090.0715G180.01430.11480.0093G200.01990.01320.0129G300.02310.02120.0149PRN(ns)(ns)(ns)7IGS[1]GPS[M]199799-103[2]GuochangXuGPSTheory,AlgorithmsandApplications[M]Springer,2007:76-77[3][J]2005(5)447-450[4]GPS[J]200631(12)1075-1077[5]MATLAB7.0[M]2005361-369[6]BockH.EfficientMethodsforDeterminingPreciseOrbitsofLowEarthOrbitsUsingtheGlobalPositioningSyetem[D]AstronomicalInstituteUniversityofBerneBerne200336-38[7][D]2006[8]GPS[M][e-mail]2009-10-108632009AA12Z30540874008