Integer Ambiguity Resolution For Precise Point Positioning

VI Hotine-MarussiVI Hotine-Marussi Symposiumof Theoretical and Computational Geodesy:Challenge and Role of Modern GeodesyMay 29 - June 2, 2006, Wuhan, ChinaInteger Ambiguity Resolution For PrecisePoint PositioningApplied To Fast Integrated Estimation of Very Huge GNSS NetworksM. Ge. G. Gendt, and M. RothacherGeoForschungsZentrum PotsdamPotsdam, May 2006

OutlineVI Hotine-Marussi‣ Motivation‣ New Strategy For Very Huge Networks‣ Reference Network‣ Precise Point Positioning‣ Ambiguity Fixing Approach For PPP‣ Solution With Fixed Ambiguities‣ Preliminary Results‣ Summary And Further Work

Motivation (1)VI Hotine-Marussi‣ Procedure For Processing Of Daily Data Iteratively Real-valued Solution For Data Cleaning Integer Ambiguity Fixing Fixed SolutionBut Only Fixed Solution Is Required‣ Software Capability Number Of Stations < 100 For Most Of The Acs GFZ Extended Up To 400, Best < 250Major Reason: Huge Num. Of Amb. Parameters‣ Integrated Estimation GNSS Networks (More Stations, Multi-systems) Low Earth Orbiting SatellitesMore Amb. Parameters

Motivation (2)VI Hotine-Marussi‣ Any Other Approach For Data Cleaning ?If Ambiguities Are Fixed‣ Can We Fix Ambiguities Before Network Solution? PPP For Data Cleaning And Ambiguity Fixing+ LSQ For Fixed Solution

Strategy For Very Huge NetworkVI Hotine-Marussi‣ Reference Network ERP, ORBITS, CLOCKS‣ Precise Point Positioning For New Stations‣ Clean Data And Fix Ambiguity Based OnPPP Results‣ Ambiguity Mapping‣ Integrated Solution With Known Ambiguities

VI Hotine-MarussiPrecise Point Positioning⎥⎥⎥⎦⎤⎢⎢⎢⎣⎡+⎥⎥⎥⎥⎥⎥⎦⎤⎢⎢⎢⎢⎢⎢⎣⎡⎥⎥⎥⎥⎤⎢⎢⎢⎢⎡=⎥⎥⎥⎦⎤⎢⎢⎢⎣⎡3213213,3.332,2,221,1,11321000000lllxxxxxaaaaaaaaavvverpsaterpsaterpsaterpsat( )( )( )00000003,3,3332,2,2221,1,111321332211=⎥⎥⎥⎦⎤⎢⎢⎢⎣⎡+++++++⎥⎥⎥⎦⎤⎢⎢⎢⎣⎡⎥⎥⎥⎦⎤⎢⎢⎢⎣⎡erperpsatsatTerperpsatsatTerperpsatsatTxaxalaxaxalaxaxalaxxxNNN‣ PPP == Network + Fixed ORB CLK ERP( ) 0,, =+++ erperpisatsatiiTiiiiixaxalaxN

Precise Point PositioningVI Hotine-Marussi‣ AccuraciesDepends On “Products Used” Model Consistence‣ Advantages : Simple, Fast and Run Parallel‣ Disadvantages : No Full Covariance, No FixedSolutionIF Ref. Net Is Dense Enough, Additional StationsWill Not Change Network Solution Very Much.Data Cleaning Using PPP ResidualsAmbiguity Fixing Based On PPP Results

Uncalibrated Phase Delay in Sat&Rec.VI Hotine-Marussi‣ Basic Observation Model (Freq. i)Li=ρ −κ/fi2+ λ biiPi=ρ + κ /fi2b + +i= δpδprec, i sat,iNi‣ Uncalibrated Phase Delay Originating In TheSatellite And Receiver‣ Can Only Form SD Between Satellites

Ambiguity Fixing For LC Solution‣ LC Ambiguity (Estimated)Lc= α L −αL =1 1 2 2ρ+bcVI Hotine-Marussibcw=βLfwbwff+Lβ‣ Wide-Lane (Range&Phase Combination)L=f−−‣ Narrow-Lane111222−nfb1nPf11++ff22P2= λ b + εwwwbn=( b − β b ) λc w w n

WL--Estimation Of Uncalibrated DelayVI Hotine-Marussi1. Difference Of Wide-lane Between Satellites i, jΔbw( i,j,l)=bw( i,l)over _ epoch−bw(j,l)over _ epoch=( Δδp+ ΔNwsat , i , j i,j,l)

WL--Estimation Of Uncalibrated DelayVI Hotine-Marussi2. Constant ? Yes Data Piece > 30 Minutes Stable In Time And Space (Gaps, Days)

WL--Estimation Of Uncalibrated DelayVI Hotine-Marussi3. Estimated Fractional Part Fractional Part: From -1.40 0.70 To -0.40 -0.30 ? RMS=0.1, STD=0.014 CyclesΔδpw= Δb( i,j,l)− Δsat : i , j wNi,j,lover _ all _ stations150Fractional Part of WL Bias[Cycle]0,750,2510050Number of WL Pairs-0,253231302928272625242322212019181716151413121110987654321Satellite PRN0

WL– Uncalibrated Delay For Fixing‣ Fixing Based on Estimated Uncalibrated DelayVI Hotine-MarussiΔbw( i,j,l)+ Δδpsat,i,j−nint( )Δb( i,j,l)+ Δδpwsat,i,j

WL– Uncalibrated Delay For FixingVI Hotine-Marussi‣ Results (Receivers Used: AOAD/ASH/TRM=5/3/1)Fixing Rate For All 93%, For Independent 99%Lower Fixing Rate 75% For CrossCorrel. ReceiversTRIM29659.00+ASHREC (100%) AOA/M_T+TRIMREC (76%)

Uncalibrated Delay --- Narrow-Lane(1)‣ Difference Of Narrow-Lane Between SatellitesnΔb( i,j,l)= b ( i)− b ( j)= Δδp+ Δnn( )nnlsat , i , ji , j , lVI Hotine-MarussiΔδpnsat , i , j=Δbn( i,j,l)− Δni , j , l‣ Constant ? NOTime/Position Dependent Bias, Up To 5cmGood Agreement Within A Time Interval

Uncalibrated Delay --- Narrow-Lane(2)‣ CorrectionΔδpn= Δbi j lsat , i , j n, , )( − Δni , j , lUsing Average Of All SD NL ( 79%)Using Only SD NL With > 10 Min Common Data (> 94%)Fixing Rate Of Independent Should Be HigherVI Hotine-Marussi

Integer Ambiguity Substitution‣ DD-Ambiguities To UDVI Hotine-Marussi⎡b1⎤⎢b⎥⎢2⎥⎢⎣d ⎥⎦⎡ I=⎢⎢0⎢D10ID2‣ Integrated Fixed Solution00D3⎤⎡b⎥⎢⎥⎢b⎥⎢⎣b123⎤⎥⎥⎥⎦→b3=D b b 1 reference ambiguities, selected freely d fixed DD-ambiguities, known values22+( D d + D b ) b 2 represent unfixable DD-ambiguities, to form afull rank transformation Only very small number of b 3 link with b 2 , most ofthem are constants311

Procedure Of The StrategyVI Hotine-Marussi‣ Reference Network‣ Estimate Phase Delay For SD WL, And Fix SD WL‣ Generate SD NL Ambiguities Using fixed SD WL‣ PPP For Additional Stations‣ Fixing WL Using WL PD, Calculate SD NL‣ Fixing NL Using NL PD From Nearby Station(s)‣ Ambiguity Transformation‣ Integrated Estimation (With Known Ambiguities)

Validation (1)VI Hotine-Marussi‣ EPOS Software At GFZ‣ Reference Network 95 IGS Stations‣ 96 Additional IGS Stations‣ New Strategy (95 + 96 PPP) VS‣ Current Strategy (191 Stations)

Validation (2)VI Hotine-MarussiFor The New Stations‣ 98% WL Ambiguities Fixable (Independent)‣ 91% Of ~25000 NL, 96% of Independent‣ Fixing Rate Of Independent ~94%

Validation (3)VI Hotine-MarussiFixed Solution‣ Fixable Ambiguities Are IntroducedInto NEQ As Constraints‣ Coordinate RMS 0.2,0.2,0.5mmCompared with Current Strategy

Summary And Further WorkVI Hotine-Marussi‣ With GPS data we demonstrated the uncalibratedphase delay is very stable. can be estimated preciselyand applied to ambiguity-fixing for PPP (94%).‣ By using PPP+Amb.Fix, a new strategy is developedfor very huge GNSS networks in order to savememory and computation time‣ Applicable to users with own PPP software forregional Network, where NL might be also a constant‣ It will improve PPP results, especially for Short TimeData and Moving Object, as well as ZTD/Slant Delay.‣ With increasing range accuracy and better IGSproducts, it might be able to challenge the currentVRS system.