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Estimation of uncalibrated hardware delays for single-
difference ambiguity resolution Javier Tegedor, Ola Øvstedal
Department of Mathematical Sciences and Technology
Norwegian University of Life Sciences (UMB)
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Contents
Implementation of Wide-Lane and Narrow-Lane Uncalibrated Hardware Delays (UHD)
Validation of WideLane UHDs with CNES products
Impact of Differential Code Biases (P1-C1) in the UHD estimation
Potential Extension for GLONASS
Format proposal for exchange of biases
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Introduction
Double difference (DD) ambiguity estimation has been traditionally used in network solutions
– Identification of DD integer ambiguities
– Hardware biases cancel out
Recent developments (CNES, GFZ, NrCan) propose the estimation of the hardware biases
– Ambiguity resolution for standalone receivers
• Single differences (SD) between satellites
• Zero-difference (ZD) when the station biases are also estimated
+ + - -
+ -
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IFik =
1f12 − f2
2 f12L1 − f2
2L2( )= ρ + c(Δti −Δt
k )−κNw −λn (N1 +ηi −ηk )
λn =c
f1 + f2≈10.7cm
Wide-lane ambiguity extracted from Melbourne-Wübbena phase and code combination:
Narrow-lane ambiguity are extracted from ionosphere-free phase
combination:
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Mathematical model
MWik =
1f1 − f2
f1L1 − f2L2( )− 1f1 + f2
f1P1 + f2P2( ) =
= λw (Nw +ωi −ωk )→ Nw = N1 − N2
λw =c
f1 − f2≈ 86.2cm
Wide-lane Uncalibrated Hardware Delays (W-UHD)
Narrow-lane Uncalibrated Hardware Delays (N-UHD)
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Estimation of UHD in a network solution
The estimation process uses undifferenced observations
Double differencing is used in the ambiguity fixing for adding integer constraints to the normal equations
As a by product, satellites and stations UHDs are generated
Full consistency is ensured between UHDs and clocks
1 constant W/N-UHD parameter per station/satellite over 24 hours
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Ambiguity Residuals from Network solution
Zero-difference ambiguity fractional parts after estimation of satellite and
stations UHDs:
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PPP with ambiguity fixing
The satellite UHD are used to recover integer ambiguities SD, added as a constraints to the normal equations
The use of SD is beneficial as the station UHDs do not need to be estimated additionally
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Ambiguity Residuals from PPP solution
Single-difference ambiguity residuals after correction with satellite UHDs:
80.2% 92.9 %
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Impact of P1-C1 bias on ambiguity resolution
Typical IGS-like process uses P1/P2/L1/L2
– Receivers providing P1: Ashtech, Septentrio, Javad, Topcon…
When only C1 observations are present (Trimble, Leica):
1. Estimate UHDs using C1/P2/L1/L2
• A different set of UHDs (and clocks) is generated:
2. Convert C1 to P1 applying DCBs to the observations
• Any error in the DCB will translate into the estimated UHDs
• Is the solution equivalent when using P1 or C1+DCB?
ωC1k =ωP1
k −f1
f1 + f2DCBP1−C1
k
ΔtC1k = ΔtP1
k +f12
c( f12 − f2
2 )DCBP1−C1
k
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Impact of P1-C1 bias on ambiguity resolution
Estimation of W/N-UHD, orbit and clocks, in 3 network configurations:
1. P1/P2
2. C1/P2, correcting C1 with Differential Code bias P1-C1:
• p1c1bias.hist and cc2noncc_v6.3
3. C1/P2 with no DCB correction
• Different set of biases and clocks
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Impact of P1-C1 bias on ambiguity resolution
-0.2
-0.15
-0.1
-0.05
0
0.05
0.1
0.15
0.2
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31
Wid
eLan
e U
HD
diff
eren
ce (
ccyl
es)
GPS PRN Number
Differences with CNES values
UMB:P1/P2
UMB:C1+DCB/P2
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31
Wid
eLan
e U
HD
(cc
yles
)
GPS PRN Number
Estimation of WideLane biases for DOY 150/2011
CNES
UMB : P1/P2
UMB : C1+DCB/P2
UMB : C1/P2
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Impact of P1-C1 bias on ambiguity resolution
Is it possible to resolve integer ambiguities with C1/P2 or C1+DCB/P2?
The PPP ambiguity residuals at SD level are very similar, but the estimated UHDs are different
PPP user needs to process the same signals for achieving successful ambiguity resolution
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Impact of P1-C1 bias on ambiguity resolution
Estimation of W-UHD with P1/P2 or C1+DCB/P2
– Process daily estimates for full year 2011
– Analyse impact of the DCBs in the estimated WideLane biases
– CNES values are taken as reference
– A common offset is removed to allow for comparison
– RMS for all satellites around 0.02 cycles
PRN30 anomaly
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PRN30 W-UHD estimation
PRN30/SVN30 decommissioned
Correct DCB value for
PRN30/SVN35
PRN30/SVN35 commissioned
2 3 1
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Ambiguity residuals for G30
Inaccuracies in the DCBs are directly absorbed in the W-UHDs
Fewer ratio of ambiguities fixed if DCB has an error
– Even ambiguities fixed to the wrong integer!
1.7%
21.7% 75.5% 1 2 3
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Would it work for GLONASS?
For GLONASS the inter-frequency biases do not cancel out completely in the differentiation process
How stable are the biases within the same frequency?
– Analyze wide-lane biases consistency between consecutive passes of the same satellite
– 48 h Rinex_v3 data from UNB3 (NETR5)
0
0.05
0.1
0.15
0.2
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
Wid
eLan
e cy
cles
GPS PRN Number
C1C/C2W
C1C/C2X
0
0.05
0.1
0.15
0.2
1 2 4 5 6 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
Wid
eLan
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cles
GLONASS orbit slot number
C1C/C2P
C1C/C2C
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Conclusions and format proposal
Uncalibrated hardware delays can be generated in a network using different code signals
– Accurate DCBs are needed to estimate reliable W-UHDs
For the PPP user, it is fundamental to keep consistency with the satellite biases in order to achieve ambiguity fixing
The proposed Bias Sinex format can be extended for accommodating these biases:
– Add new bias identifiers: WHD & NHD
– Example:
*-------------------------------------------------------------------------------!* Solution INdependent EXchange Format (SINEX) !*-------------------------------------------------------------------------------!+FILE/REFERENCE! REFERENCE FRAME IGS08!-FILE/REFERENCE!! DESCRIPTION Bias Sinex with Uncalibrated Hardware Delays ! CONTACT [email protected]!*-------------------------------------------------------------------------------!*-------------------------------------------------------------------------------!*-------------------------------------------------------------------------------!+BIAS/SOLUTION!*BIAS SVN_ PRN SITE DOMES____ OBS1 OBS2 BIAS_START__ BIAS_END____ UNIT __ESTIMATED_VALUE____ _STD_DEV___! WHD G048 G07 L1P L2P 11:200:00000 11:201:00000 m -.423123098473891E+00 .389234E-02! NHD G048 G07 L1P L2P 11:200:00000 11:201:00000 m .342346908876489E-02 .984758E-03!!
