evaluation and calibration of receiver inter-channel ... gnss 20… · these biases are known as an...

Evaluation and Calibration of

Receiver Inter-channel Biases for

RTK-GPS/GLONASSHideki 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 PositioningInstantaneous RTK (Real Time Kinematic) is precise positioning

with epoch by epoch carrier-phase ambiguity resolution (AR).

Results of Mobile RTK Positioning

Fix solution : 43 %

Float solution : 57 %

NovAtel - NovAtel

Fix solution : 1 %

Float solution : 99 %

NovAtel - JAVAD

We aim to improve GLONASS positioning performance

in RTK-GPS/GLONASS between different types of receivers.

GPS + GLONASS L1 + L2

0 1 2 3 4 5 6 7 8 x 104-0.2-0.15-0.1-0.0500.050.10.150.2

Time (sec)Position Error (m)

RTK POSITION ERROR (FIX) : BASELINE=0.3km RATIO=29.5% RMSE : E: 0.0032m N: 0.0057m U: 0.0157m East (m)North (m)Up (m)Results of Static RTK Positioning

GPS + GLONASS L1 + L2 instantaneous AR

Base length = 300 m

0 1 2 3 4 5 6 7x 104-0.2-0.15-0.1-0.0500.050.10.150.2

Time (sec)Position Error (m)

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)P

osi

tio

nin

g E

rro

rs (

m)

Fix solution : 99.0 %

Float solution : 1.0 %

NovAtel -NovAtel

Time (s)P

osi

tio

nin

g E

rro

rs (

m)

NovAtel - JAVAD

Fix solution : 29.5 %

Float solution : 70.5 %

Time (s)

Background and Objective

Inter-channel bias

- The RF hardware design of a receiver will introduce frequency-

dependent 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.

What is main source of observation errors to prevent

GLONASS ambiguity from being fixed ?

Background and Objective

• 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.

Inter-channel Bias Calibration

Antenna

Splitter

TopconNovAtel

GPS/GLONASS Antenna

TrimbleJAVAD

Zero baseline test

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.

Inter-channel Bias Calibration

Roof of our university (Open sky)Site

2009/12/23

24 hours/30 s24 hours/30 s20 hours/30 s24 hours/30 s

Date

Total/interval

Trimble (Zephyr 2 )Antenna

R7GNSSNET-G3OEMVLegacyReceiver type

TrimbleTopconNovAtelJAVAD

Experimental Environment

Calibrated L1 Inter-channel Code Biases

Tables of bias with slot 21

-6 -4 -2 0 2 4 6-3

-2

-1

0

1

2

3

GLONASS frequency number

NovAtel-NovAtel

Javad-Javad

DD

of L

1 in

ter-chan

nel co

de b

iases (m)

1 mD

D o

f L1

inter-ch

ann

el cod

e biases (m

)

-6 -4 -2 0 2 4 6-3

-2

-1

0

1

2

3


NovAtel-Trimble

NovAtel-Topcon

NovAtel-Javad1 m

Calibrated L2 Inter-channel Code Biases

Tables of bias with slot 21

-6 -4 -2 0 2 4 6-1

-0.5

0

0.5

1


NovAtel-NovAtel

Javad-Javad

DD

of L

2 in

ter-chan

nel co

de b

iases (m)

50 cm

-6 -4 -2 0 2 4 6-1

-0.5

0

0.5

1


NovAtel-Trimble

NovAtel-Topcon

NovAtel-JavadD

D o

f L2

inter-ch

ann

el cod

e biases (m

)50 cm

RTK-GPS/GLONASS with Calibrated Biases

( ) ( )

( ) ( )ij

rb

ij

rb

ij

rb

ij

rb

j

b

j

r

i

b

i

r

ij

rb

ij

rb

ij

rb

ij

rb

ij

rb

ij

rb

j

b

j

rj

i

b

i

ri

ij

rb

PPmpPd

ppppP

mpdN

)()()(

)()()(

ερ

φεφφρ

φφλφφλ

+++=

−−−≡

++++=

−−−≡Φ

1.GLONASS double difference equation

2.Compensation by tables of biases

sj

rb

si

rb

ij

rb ddd +−=

d(P) : inter-channel code bias, dφ: inter-channel carrier bias

Assumption on d(P) = d(φ)

RTK Positioning

RTK Processing Options

We evaluate positioning accuracy and fix rate of RTK-GPS/GLONASS

in order to improve the GLONASS positioning performance by tables of bias.

- 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

0 2 4 6 8

x 104

-0.2

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

0.2RTK POSITION ERROR (FIX) : BASELINE=0.3km RATIO=9.0% RMSE : E: 0.0037m N: 0.0032m U: 0.0145m

East (m)

North (m)

Up (m)

0 2 4 6 8

x 104

-0.2

-0.15

-0.1

-0.05

0

0.05

0.1

0.15


East (m)

North (m)

Up (m)

Positioning Results of RTK with

GLONASS ambiguity fix solution RTK-GPS/GLONASS L1 + L2

Baseline : NovAtel - Trimble

Fix rate 25.1 % Fix rate 9.0 %

No improvement

No correction

Po

siti

on

ing

Err

or

(m)

Time (s)

Correction with tables of biases

Po

siti

on

ing

Err

or

(m)

Time (s)

5 cm 5 cm

Considerations

( ) ( )

( ) ( )ij

rb

ij

rb

ij

rb

ij

rb

j

b

j

r

i

b

i

r

ij

rb

ij

rb

ij

rb

ij

rb

ij

rb

ij

rb

j

b

j

rj

i

b

i

ri

ij

rb

PPmpPd

ppppP

mpPdN

)()()(

)()()(

ερ

φεφρ

φφλφφλ

+++=

−−−≡

++++=

−−−≡Φ

From the next slide, we try to evaluate the positioning performance of RTK-GPS/GLONASS

with GLONASS ambiguity float solution.

1.Estimation of d(ρ) has poor accuracy.

Why can not we fix GLONASS ambiguity by tables of inter-channel code bias ?

2. Assumption on d(ρ) = d(φ) might not be true.

Inter-channel carrier bias can be obtained by subtracting the

GLONASS integer ambiguity fixed in static mode from

DD of carrier-phase measurement.

→ Estimation of dρ is producted by code

measurements.

The variation of inter-channel code and carrier biases

(slot 23 - slot 7)

7500 8000 8500 9000 9500 10000 105000.74

0.75

0.76

0.77

0.78

0.79

0.8

0.81

0.82

Time (s)In

ter-c

han

nel

bia

ses

(m)

Code

Carrier

0 2 4 6 8

x 104

-5

-4

-3

-2

-1

0

1

2

3

4

5RTK POSITION ERROR (FLOAT) : BASELINE=0.3km RATIO=100.0% RMSE : E: 0.2500m N: 0.2927m U: 0.6581m

East (m)

North (m)

Up (m)

0 2 4 6 8

x 104

-5

-4

-3

-2

-1

0

1

2

3

4

5RTK POSITION ERROR (FLOAT) : BASELINE=0.3km RATIO=100.0% RMSE : E: 0.2677m N: 0.4188m U: 1.0192m

East (m)

North (m)

Up (m)

Use of GLONASS Float Ambiguity

We use GLONASS float ambiguity as the aid of GPS ambiguity resolution.

Accuracy of float solution has an effect on the performance of ambiguity fixing.

Float Solution

E/N/U (m) 0. 27/0.42/1.02

Only GPS

Po

siti

on

ing

Err

or

(m)

Time (s)

E/N/U (m) 0.25/0.29/0.65

GPS + GLONASS

Po

siti

on

ing

Err

or

(m)

Time (s)

1 m 1 m

0 2 4 6 8

x 104

-0.2

-0.15

-0.1

-0.05

0

0.05

0.1

0.15


East (m)

North (m)

Up (m)

0 2 4 6 8

x 104

-0.2

-0.15

-0.1

-0.05

0

0.05

0.1

0.15


East (m)

North (m)

Up (m)

Positioning Results of RTK with GLONASS ambiguity float solution

RTK-GPS/GLONASS L1

Improved by 20 %

No correction

Fix rate : 31.9 %

E/N/U (m) : 0.12 /0.19/0.32

Time (s)

Po

siti

on

ing

Err

or

(m)

Correction with tables of bias

Fix rate : 52.1 %

E/N/U (m) : 0.05/0.07/0.11

Time (s)

Po

siti

on

ing

Err

or

(m)


5 cm 5 cm

0 2 4 6 8

x 104

-0.2

-0.15

-0.1

-0.05

0

0.05

0.1

0.15


East (m)

North (m)

Up (m)

0 2 4 6 8

x 104

-0.2

-0.15

-0.1

-0.05

0

0.05

0.1

0.15


East (m)

North (m)

Up (m)

Positioning Results of RTK with GLONASS ambiguity float solution

No correction

Fix rate : 96.7 %

E/N/U (m) : 0.01 /0.01/0.02

Correction with tables of bias

Fix rate : 99.0 %

E/N/U (m) : 0.01/0.01/0.02

RTK-GPS/GLONASS L1 + L2

Po

siti

on

ing

Err

or

(m)

Po

siti

on

ing

Err

or

(m)

Time (s) Time (s)


5 cm 5 cm

Accuracy of RTK positioning with L1 measurements

0.04/0.06/0.140.04/0.06/0.140.09/0.11/0.32

68.8 %68.7 %41.0 %JAVAD - Topcon

0.10/0.11/0.300.17/0.23/0.530.12/0.14/0.32

36.5 %21.9 %35.8 %JAVAD - Trimble

0.11/0.18/0.350.12/0.17/0.400.13/0.21/0.54

33.8 %31.9 %29.9 %NovAtel - JAVAD

0.07/0.09/0.150.10/0.16/0.270.09/0.17/0.39

47.0 %41.5 %45.5 %NovAtel - Topcon

0.05/0.07/0.110.11/0.17/0.310.07/0.09/0.25

52.1 %31.9 %49.5 %NovAtel -Trimble

E/N/U (m)E/N/U (m)E/N/U (m)

Fix rateFix rate Fix rate

GPS + GLONASS

(GLONASS float + bias)

GPS + GLONASS

(GLONASS float)Only GPS

Baseline

300 m

Accuracy of RTK positioning with L1 + L2 measurements

0.01/0.01/0.020.01/0.01/0.020.01/0.01/0.02

98.0%98.0%98.2%JAVAD -Topcon

0.01/0.01/0.020.01/0.01/0.020.01/0.01/0.02

97.0%95.3%98.1%JAVAD -Trimble

0.01/0.01/0.020.01/0.01/0.020.01/0.01/0.02

98.5%98.0%98.2%NovAtel - JAVAD

0.01/0.01/0.020.01/0.01/0.020.01/0.01/0.02

98.9%96.4%98.9%NovAtel - Topcon

0.01/0.01/0.020.01/0.01/0.020.01/0.01/0.02

99.0%96.7%98.9%NovAtel - Trimble

E/N/U (m)E/N/U (m)E/N/U (m)

Fix rateFix rateFix rate

GPS + GLONASS

(GLONASS float + bias)

GPS + GLONASS

(GLONASS float)Only GPS

Baseline

300 m

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

7500 8000 8500 9000 9500 10000 105000.74

0.75

0.76

0.77

0.78

0.79

0.8

0.81

0.82

0.83

0.84

Time (s)

Inte

r-chann

el b

iase

s (m

)

Code

Carrier

evaluation and calibration of receiver inter-channel ... gnss 20… · these biases are known as an...

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