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