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Evaluation and Calibration of
Receiver Inter-channel Biases for
RTK-GPS/GLONASS
Hideki Yamada,
Tomoji Takasu, Nobuaki Kubo and Akio Yasuda
Tokyo University of Marine Science and Technology
Outline
•
•
•
•
•
Background and Objective
Inter-channel Bias Calibration
RTK-GPS/GLONASS with Calibrated Biases
Use of GLONASS Float Ambiguity
Summary and Conclusions
Mobile RTK Positioning
Instantaneous RTK (Real Time Kinematic) is precise positioning
with epoch by epoch carrier-phase ambiguity resolution (AR).
Results of Mobile RTK Positioning
NovAtel - NovAtel
Fix solution : 43 %
Float solution : 57 %
NovAtel - JAVAD
Fix solution : 1 %
Float solution : 99 %
GPS + GLONASS L1 + L2
We aim to improve GLONASS positioning performance
in RTK-GPS/GLONASS between different types of receivers.
Results of Static RTK Positioning
NovAtel -NovAtel
RTK POSITION ERROR (FIX) : BASELINE=0.3km RATIO=99.0%
RMSE : E: 0.0025m N: 0.0044m U: 0.0157m
East (m)
North (m)
Up (m)
0.15
0.1
) 0.05
m
(
ro
rr
E 0
no
iti
so
P -0.05
-0.15
-0.2
0
1
2
3
4
Time (sec)
Time (s)
5
6
RMSE : E: 0.0032m N: 0.0057m U: 0.0157m
0.1
Fix solution : 29.5 %
Float solution : 70.5 %
-0.1
-0.15
-0.2
7
4
x 10
East (m)
North (m)
Up (m)
0.15
) 0.05
m
(
ro
rr
E 0
no
iti
so
P -0.05
Fix solution : 99.0 %
Float solution : 1.0 %
-0.1
0.2
Positioning Errors (m)
0.2
Positioning Errors (m)
NovAtel - JAVAD
0
1
2
3
4
5
Time (sec)
Time (s)
GPS + GLONASS L1 + L2 instantaneous AR
Base length = 300 m
6
7
8
x 10
4
What is main source of observation errors to prevent
GLONASS ambiguity from being fixed ?
Inter-channel bias
- The RF hardware design of a receiver will introduce frequencydependent biases. These biases are known as an inter-channel bias.
- These biases can not be canceled out with double differencing
between different types of receivers in GLONASS, except for GPS.
• Estimates of GLONASS inter-channel bias for several
receivers are obtained in short baseline [Wanninger, L., et al,
ION GNSS 2007].
• Narrow band loop filter smoothes SD residual to get on line
code bias [Kozlov, D., et al, ION GNSS 2000].
• In this study, we try to improve the positioning performance
of instantaneous RTK with off line tables of GLONASS
inter-channel bias at various receivers calibrated in only
zero baseline measurements.
Zero baseline test
GPS/GLONASS Antenna
Antenna
Splitter
JAVAD
NovAtel
Trimble
Topcon
In the zero baseline, double-difference (DD) of code measurements can cancel
out terms of orbital errors, clock errors, atmospheric delays and multipath,
and remain DD of receiver noises and inter-channel biases.
Experimental Environment
Receiver type
JAVAD
NovAtel
Topcon
Trimble
Legacy
OEMV
NET-G3
R7GNSS
Antenna
Trimble (Zephyr 2 )
Site
Roof of our university (Open sky)
Date
Total/interval
2009/12/23
24 hours/30 s
20 hours/30 s
24 hours/30 s
24 hours/30 s
Calibrated L1 Inter-channel Code Biases
Tables of bias with slot 21
NovAtel-NovAtel
Javad-Javad
2
1
0
-1
-2
1m
-3
-6
-4
-2
0
2
4
GLONASS frequency number
6
DD of L1 inter-channel code biases (m)
3
3
2
1
0
-1
-2
1m
-3
-6
-4
NovAtel-Trimble
NovAtel-Topcon
NovAtel-Javad
-2
0
2
4
6
Calibrated L2 Inter-channel Code Biases
Tables of bias with slot 21
NovAtel-NovAtel
Javad-Javad
0.5
0
-0.5
50 cm
-1
-6
-4
-2
0
2
4
6
1
1
0.5
0
-0.5
50 cm
-1
-6
-4
NovAtel-Trimble
NovAtel-Topcon
NovAtel-Javad
-2
0
2
4
6
RTK-GPS/GLONASS with Calibrated Biases
1.GLONASS double difference equation
(
ij
rb
i
r
i
b
)
(
j
b
j
r
Φ ≡ λi φ − φ − λ j φ − φ
ij
rb
ij
rb
)
ij
rb
ij
rb
= ρ + N + d (φ ) + mp(φ ) + ε (φ )
ij
rb
P
(
i
r
i
b
) (
j
r
j
b
≡ p −p − p −p
ij
rb
ij
rb
)
ij
rb
= ρ + d ( P) + mp ( P) + ε ( P)
d(P) : inter-channel code bias, dφ: inter-channel carrier bias
Assumption on d(P) = d(φ)
2.Compensation by tables of biases
ij
rb
si
rb
d = −d + d
sj
rb
ij
rb
ij
rb
RTK Positioning
We evaluate positioning accuracy and fix rate of RTK-GPS/GLONASS
in order to improve the GLONASS positioning performance by tables of bias.
RTK Processing Options
- AR mode
: Instantaneous AR (epoch by epoch)
- AR method
: LAMBDA, ratio-test (threshold : 3)
- Base length :300 m
(Rover: NovAtel, Javad. Base: NovAtel, Javad, Trimble,Topcon )
- Date
: 2009/12/23 24 h (epoch intervals 30 s)
- Elevation mask angle : 15 deg
Positioning Results of RTK with
GLONASS ambiguity fix solution
RTK-GPS/GLONASS L1 + L2
Baseline : NovAtel - Trimble
No correction
Correction with tables of biases
RMSE : E: 0.0035m N: 0.0047m U: 0.0166m
East (m)
North (m)
Up (m)
0.15
0.1
Positioning Error (m)
0.2
5 cm
0.05
0
RMSE : E: 0.0037m N: 0.0032m U: 0.0145m
East (m)
North (m)
Up (m)
0.15
0.1
5 cm
0.05
0
-0.05
-0.05
-0.1
-0.1
-0.15
-0.15
-0.2
0
0.2
2
4
Time (s)
6
-0.2
0
8
4
x 10
Fix rate 25.1 %
2
4
6
Time (s)
Fix rate 9.0 %
No improvement
8
x 10
4
Considerations
Why can not we fix GLONASS ambiguity by tables of inter-channel code bias ?
1.Estimation of d(ρ) has poor accuracy. 2. Assumption on d(ρ) = d(φ) might not be true.
(
ij
rb
i
r
i
b
) (
j
r
j
b
Φ ≡ λi φ −φ − λj φ −φ
The variation of inter-channel code and carrier biases
(slot 23 - slot 7)
)
= ρrbij + Nrbij + d(P)ijrb + mp(φ)ijrb + ε (φ)ijrb
(
) (
Prbij ≡ pri − pbi − prj − pbj
)
= ρrbij + d(P)ijrb + mp(P)ijrb + ε (P)ijrb
0.82
Inter-channel biases (m)
→ Estimation of dρ is producted by code
measurements.
0.81
0.8
0.79
Code
Carrier
0.78
0.77
0.76
0.75
0.74
7500 8000 8500 9000 9500 10000 10500
Time (s)
Inter-channel carrier bias can be obtained by subtracting the
GLONASS integer ambiguity fixed in static mode from
DD of carrier-phase measurement.
From the next slide, we try to evaluate the positioning performance of RTK-GPS/GLONASS
with GLONASS ambiguity float solution.
Use of GLONASS Float Ambiguity
Accuracy of float solution has an effect on the performance of ambiguity fixing.
We use GLONASS float ambiguity as the aid of GPS ambiguity resolution.
Float Solution
Only GPS
GPS + GLONASS
5
4
3
RTK POSITION ERROR (FLOAT) : BASELINE=0.3km RATIO=100.0%
RMSE : E: 0.2677m N: 0.4188m U: 1.0192m
RTK POSITION ERROR (FLOAT) : BASELINE=0.3km RATIO=100.0%
1m
2
1
0
-1
-2
-3
-4
-5
0
East (m)
North (m)
Up (m)
2
4
Time (s)
6
RMSE : E: 0.2500m N: 0.2927m U: 0.6581m
1m
2
1
0
-1
-2
-3
-4
-5
0
8
x 10
5
4
3
East (m)
North (m)
Up (m)
2
4
4
E/N/U (m) 0. 27/0.42/1.02
Time (s)
6
8
x 10
4
E/N/U (m) 0.25/0.29/0.65
Positioning Results of RTK with GLONASS ambiguity float solution
RTK-GPS/GLONASS L1
Correction with tables of bias
No correction
0.2
RMSE : E: 0.1156m N: 0.1650m U: 0.3184m
0.2
0.15
0.1
5 cm
0.05
0
-0.05
East (m)
North (m)
Up (m)
-0.1
-0.15
-0.2
0
2
4
Time (s)
6
x 10
0.15
0.1
5 cm
0.05
0
-0.05
-0.1
-0.15
-0.2
0
8
RMSE : E: 0.0524m N: 0.0733m U: 0.1120m
East (m)
North (m)
Up (m)
2
4
4
Fix rate : 31.9 %
E/N/U (m) : 0.12 /0.19/0.32
Time (s)
6
8
x 10
Fix rate : 52.1 %
E/N/U (m) : 0.05/0.07/0.11
Improved by 20 %
4
Positioning Results of RTK with GLONASS ambiguity float solution
RTK-GPS/GLONASS L1 + L2
Correction with tables of bias
No correction
RMSE : E: 0.0026m N: 0.0051m U: 0.0168m
East (m)
North (m)
Up (m)
0.15
0.1
0.2
5 cm
0.2
0.05
0
-0.05
-0.1
-0.15
-0.2
0
2
4
Time (s)
6
x 10
0.1
5 cm
0.05
0
-0.05
-0.1
-0.15
2
4
4
Fix rate : 96.7 %
E/N/U (m) : 0.01 /0.01/0.02
East (m)
North (m)
Up (m)
0.15
-0.2
0
8
RMSE : E: 0.0026m N: 0.0052m U: 0.0169m
Time (s)
6
8
x 10
Fix rate : 99.0 %
E/N/U (m) : 0.01/0.01/0.02
4
Accuracy of RTK positioning with L1 measurements
Baseline
300 m
Only GPS
GPS + GLONASS
(GLONASS float)
GPS + GLONASS
(GLONASS float + bias)
Fix rate
Fix rate
Fix rate
E/N/U (m)
E/N/U (m)
E/N/U (m)
49.5 %
31.9 %
52.1 %
0.07/0.09/0.25
0.11/0.17/0.31
0.05/0.07/0.11
45.5 %
0.09/0.17/0.39
29.9 %
0.13/0.21/0.54
35.8 %
0.12/0.14/0.32
41.0 %
0.09/0.11/0.32
41.5 %
0.10/0.16/0.27
31.9 %
0.12/0.17/0.40
21.9 %
0.17/0.23/0.53
68.7 %
0.04/0.06/0.14
47.0 %
0.07/0.09/0.15
33.8 %
0.11/0.18/0.35
36.5 %
0.10/0.11/0.30
68.8 %
0.04/0.06/0.14
NovAtel -Trimble
NovAtel - Topcon
NovAtel - JAVAD
JAVAD - Trimble
JAVAD - Topcon
Accuracy of RTK positioning with L1 + L2 measurements
Baseline
300 m
NovAtel - Trimble
NovAtel - Topcon
NovAtel - JAVAD
JAVAD -Trimble
JAVAD -Topcon
Only GPS
GPS + GLONASS
(GLONASS float)
GPS + GLONASS
(GLONASS float + bias)
Fix rate
Fix rate
Fix rate
E/N/U (m)
E/N/U (m)
E/N/U (m)
98.9%
0.01/0.01/0.02
98.9%
0.01/0.01/0.02
98.2%
0.01/0.01/0.02
98.1%
0.01/0.01/0.02
98.2%
0.01/0.01/0.02
96.7%
0.01/0.01/0.02
96.4%
0.01/0.01/0.02
98.0%
0.01/0.01/0.02
95.3%
0.01/0.01/0.02
98.0%
0.01/0.01/0.02
99.0%
0.01/0.01/0.02
98.9%
0.01/0.01/0.02
98.5%
0.01/0.01/0.02
97.0%
0.01/0.01/0.02
98.0%
0.01/0.01/0.02
Summary and Conclusions
• We analysis and improve the performance
degradation on GLONASS AR epoch by epoch.
• We can obtain tables of inter-channel biases
with zero baseline test.
• Tables of inter-channel biases are effective in
GLONASS ambiguity float solution.
• More precise calibration method of the biases is
required for GLONASS Fixed ambiguity.
Future work
• Complete tables of inter-channel carrier bias as
well as more precise code bias calibration
• Evaluate the difference between carrier and
code bias
Inter-channel biases (m)
0.84
0.83
0.82
C ode
C arrier
0.81
0.8
0.79
0.78
0.77
0.76
0.75
0.74
7500 8000 8500 9000 9500 10000 10500
T ime (s)

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