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Effects of ionospheric small-scale structures on GNSS
G. WAUTELET
Royal Meteorological Institute of Belgium
Ionospheric Radio Systems & Techniques (IRST) Edinburgh, 28 – 30 April 2009
2
OUTLINE
Introduction
1. “One-station” method
2. Small-scale structures and double differences (DD)
3. Small-scale structures and relative positioning
Conclusions – future work
3
INTRODUCTION
Ionosphere = main error source of GNSS
Models exist (Klobuchar, NeQuick) BUT… occurrence of small-scale structures (local scale) which induce positioning error in the case of high accuracy applications (e.g. Real-Time Kinematics or RTK)
GOAL = detect and assess the influence of iono small-scale structures on GNSS precise applications
4
INTRODUCTION
3 steps 3 sections :
1. Detection of structures at 1 GPS station
2. Assess the influence of those structures on double differences (relative positioning basic observables)
in terms of L1 (or L2) cycles
3. Assess the influence of those structures on precise relative positioning like RTK
in terms of meters (user units)
1. “One-station” method
6
1.1. Methodology
Objective: isolate the high frequency changes in the TEC (Total Electron Content) observed at a given GPS station
HOW? Using the Geometric-Free (GF) combination of GPS phase measurements (GPS system uses 2 frequencies)
5 steps
7
1.1. Methodology
1. Computation of the TEC at each observation epoch
11 2
2
160,552.10 TEC
LGF L L
L
GF
f
f
N
[TECU/min]
2. Computation of the verticalized temporal gradients of TEC (ΔVTEC) at each observation epoch
1
1
( ) ( )ΔVTEC( ) 1,812 . cos( )
( )GF k GF k
k PIk k
t tt z
t t
8
1.1. Methodology
If σ > 0,08 TECU/min, ionospheric event detected
6 6.2 6.4 6.6 6.8 7
G P S tim e [ h ]
-0 .15
-0.1
-0 .05
0
0.05
0.1
RoT
EC
[ T
EC
U/m
in ]
15 min
3. Polynomial fitting of temporal series of ΔVTEC
4. Residuals computation: « ΔVTEC – polynomial » called Rate of TEC (RoTEC)
5. Every 15 min, computation of Std. Dev. σ of RoTEC
536000 540000 544000 548000 552000 556000
G PS tim e [ s ]
-0 .4
-0 .3
-0 .2
-0 .1
0
0.1
RoT
EC
[ T
EC
U/m
in ]
536000 540000 544000 548000 552000 556000
G PS tim e [ s ]
-0 .4
-0 .3
-0 .2
-0 .1
0
0.1
RoT
EC
[ T
EC
U/m
in ]
536000 540000 544000 548000 552000 556000
G PS tim e [ s ]
-0 .15
-0 .1
-0 .05
0
0.05
0.1
RoT
EC
[ T
EC
U/m
in ]
9
Travelling ionospheric disturbances (TID’s)
1.2. Two main types of structures
- Cause: interaction between gravity waves and ionosphere- Observation: wave-like fluctuation of the electronic density
- Different classes: SSTID's, MSTID's, LSTID's- Origin: non geomagnetic for SSTID's and MSTID's
geomagnetic for LSTID's
10
“Noise-like” structures (NLS)
1.2. Two main types of structures
- Cause : geomagnetic phenomena (CIR, storms)- Observation : RoTEC fluctuates randomly (« noise ») - Order of magnitude NLS > order of magnitude TID's
11
1.3. Climatological study
Time interval = 1994 – 2008 (i.e. more than a solar cycle)
Reference station = BRUS (Brussels)
Goal of the study = counting of the number of ionospheric events detected in function of time.
Different temporal dependencies (time scales) of the occurrence of such structures will be analyzed:
Solar cycle dependence
Seasonal dependence
Local time dependence
12
1.3. Climatological study
Solar cycle dependence
On average, number of events is higher during solar maximum (2001, 2003) than during solar minimum (1996, 2007)...
BUT seems to show a strong monthly dependence
13
1.3. Climatological study
Seasonal dependence
More small-scale structures during autumn/winter months
Stuctures more numerous during solar max
Computation of the monthly mean of the number of events: solar max (2001) and solar min (2006) are the most representative.
14
1.3. Climatological study
Local time dependence
Computation of the total number of events for each 15 min time interval : solar max (2001) and solar min (2006) are the most representative.
Maximum around 10 h
Secondary max during nighttime
15
1.3. Climatological study
Type of structure detected
Computation of the total number of events for each 15 min time interval for year 2001. We consider (red) or not (green) the days for which Kp
max > 5 (stormy
days).
Offset between the 2 graphs : phenomena due to geomagnetic storms occur all the time : Noise-like structures
Most of structures are not connected to geomagnetic activity : Travelling Ionospheric Disturbances (TID's)
16
Conclusions
1.3. Climatological study
2 main types of small-scale ionospheric structures have been detected :
Noise-like structures : very few and occur all the time TID's : numerous and are season and time-dependent
(more during autumn/winter than during spring/summer).
2 main types :Daytime TID's : around 10 h, very numerous
Nighttime TID's : between 22 h and 2 h, less numerous than daytime ones
2. Small-scale structures and double differences (DD)
18
2.1. Methodology
Relative positioning = determination of a baseline between 2 receivers with an accuracy of a few cm
Basic observable = double differences of phase measurements (DD) Advantages : cancellation of all error sources common to the two stations
no clocks/orbit errors usualy, atmospheric residual errors are negligible BUT…
Equation (neglecting multipath and noise):
REFERENCE STATION with a known position
USER with an unknown position
10-20 kmAABB
Residual ionosphere can however be a threat for such high-accuracy applications
ij ij ij ij ijAB AB AB AB AB
fD I T N
c
19
2.1. Methodology
, , ,
16, , ,0.552 10 TEC
ij ij ij1AB GF AB L1 AB L2
2
ij ij ij ijAB AB GF AB GF AB GF
f
f
N M
Objective = compute the ionospheric residual term for a given baseline
Use of the GF combination of double-differenced (DD) phase measurements:
a) Neglecting multipath and noise, we compute the ambiguity term and we obtain :
N AB ,GFij
I AB , GFij
= ionospheric residual term in DD (every 30 s)
b) We express this term into cycles of L1 carrier
16, , 0.552 10ij ij ij
AB GF AB GF ABN TEC
20
2.2. Nominal conditions
11.3 km
8.9 km
4.1 km
21
2.2. Nominal conditions
Statistics of (in L1 cycles), 1ijAB LI
GILL – LEEU
(11.3 km)
BRUS – GILL
(4.1 km)
LEEU – BRUS
(8.9 km)
P2.5 -0.135 -0.116 -0.105
P97.5 0.138 0.108 0.110
over 11 days during winter 2008 (DOY 300-310) solar min
For quiet days and in 95% of cases, residual ionosphere in DD represents less than 0.15 L1 cycle
22
2.3. Results on case study
Baseline of 11 km (GILL – LEEU) near Brussels (typical RTK baseline) 3 different (typical) ionospheric conditions :
– quiet (DOY 310/08)– occurrence of medium amplitude TID (DOY 359/04)– occurrence of geomagnetic storm (DOY 324/03)
RoTEC max [ TECU/min]
# events at BRUS
Kp max
310/08 0.309 2 0.3
359/04 0.837 44 2
324/03 8.933 230 9
23
2.3. Results on case study
Quiet day : DOY 310/08
95% of values (nominal conditions)
MAX < 0.4 L1 cycle
24
2.3. Results on case study
Medium-amplitude TID : DOY 359/04
MAX ~ 1 L1 cycle
25
2.3. Results on case study
Geomagn. storm : DOY 324/03
MAX ~ 2.5 L1 cycles
26
During TID's or geomagnetic storms, the residual delay due to the ionosphere is significantly larger than the nominal value (0.15 cycle), and even larger than 0.5 cycle
→ risk to fix the ambiguity to a wrong integer value
→ large positioning error
2.3. Results: summary
3. Small-scale structures and relative positioning
28
(b) Computation of the user position every 30 s using a least square adjustment corrected for the ionospheric effect computed in section 2 : residual error is mainly troposphere
(a) Computation of the user position every 30 s using a least square adjustment : residual errors are mainly troposphere and ionosphere
3.1. Methodology
,ijAB kI
ijABT
, , , , ,ij ij ij ij ij ij ijk kAB k AB k AB AB k AB AB k AB k
f fN D I T M
c c
Objective = assess the part due to the ionosphere in the positioning error
(c) Positioning error due to ionosphere obtained by substraction (a) - (b)
, , , , ,ij ij ij ij ij ij ijk kAB k AB k AB AB k AB AB k AB k
f fN D I T M
c c
,ijAB kI
(ΔX1, ΔY1, ΔZ1)
(ΔX2, ΔY2, ΔZ2)
(ΔX1 – ΔX2), (ΔY1 – ΔY2), (ΔZ1 – ΔZ2)
29
3.2. Nominal conditions
Statistics of (in meters)ionoD
GILL – LEEU
(11.3 km)
BRUS – GILL
(4.1 km)
LEEU – BRUS
(8.9 km)
P95 0.033 0.029 0.030
over 11 days during winter 2008 (DOY 300 - 310) solar min
For quiet days and in 95% of cases, residual ionosphere in DD is responsible for about 3 cm can be approximated to the ambient noise and multipath
Express the error in terms of distance:2 2 2
iono iono iono ionoD X Y Z
30
3.3. Results on case study
Quiet day : DOY 310/08
MAX < 5 cm
95% of values (nominal conditions)
outli
er
31
3.3. Results on case study
Medium-amplitude TID : DOY 359/04
MAX ~ 15 cm
32
3.3. Results on case study
Geomagn. storm : DOY 324/03
MAX ~ 65 cm
33
3.3. Results: summary
During TID's or geomagnetic storms, the positioning error due to the ionosphere is significantly larger than the nominal value (3 cm).
→ medium ampl. TID: ~ 15cm
→ geomagn. storm: ~ 65 cm
34
CONCLUSIONS
Three levels of observation of the ionosphere:
One-station: detects iono irregularities in time (temporal gradients) and allows to perform a climatological analysis of the iono irregularities for a mid-latitude station
Double differences: detect spatial gradients in ionosphere and allow to see the contribution of the ionosphere in the DD, which is especially important for ambiguity resolution
Relative positioning: assess the influence of spatial gradients in the ionosphere on positioning error (quantitative assessment)
These three levels allow us to determine the phenomena observed and their effects on relative positioning integrated tool for a service which warns users when degraded positioning errors occur or are expected
Thank you for your attention!
Effects of ionospheric small-scale structures on GNSS
G. WAUTELET
Royal Meteorological Institute of Belgium
Ionospheric Radio Systems & Techniques (IRST) Edinburgh, 28 – 30 April 2009
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