Assessment and Mitigation of Ionospheric Effects on GNSS

Accuracy and Integrity

Wu Chen, Duojie Weng, Shengyue Ji, Zhizhao Liu

Department of Land Surveying and Geoinformatics Hong Kong Polytechnic University

Background • GPS revolutionize the concepts of

positioning/navigation/timing (PNT) • GPS has become an important infrastructure to support

economic development – Military – Transportation – Telecommunication – Space Industry – Finance – Location Based Services – Surveying – Weather forecasting – Scientific researches

Background

• Major Concerns on GPS

– Military Design • not built or operated for safety of life requirements

– Military Control • No guarantee on performance and continuity of

services

– Single State Ownership • Clear economical benefits for US

Background • International Developments

– Augmentation systems • To improve performance of GPS

– Accuracy, Integrity, Coverage • Satellite Based Augmentation Systems (SBAS)

– WAAS, EGNOS, MSAS, QZSS, GAGAN, …. • Ground Based Augmentation systems (GBAS)

– Other Independent GNSS systems • GLONASS (Russian) • Compass (Beidou, China) • Galileo (Europe) • IRNSS (India)

Background

• GNSS Based Services – Global Services

• GPS, GLONASS, Beidou (III) – Regional Services

• Beidou (II), IRNSS • Satellite Based Augmentation Systems (SBAS)

– WAAS, EGNOS, MSAS, QZSS, GAGAN, …. – Local Services

• DGPS Services – i.e. DGPS station

• GNSS RTK Network – i.e. GNSS CORS network

• Ground Based Augmentation systems (GBAS)

GNSS Infrastructures in Hong Kong

• DGPS Service – Marine Department (DGPS Beacon for marine

navigation in Hong Kong Water) • Hong Kong GNSS active Network

– RTK for engineering surveying – Established in 2001 – 12 stations, – GPS/GLONASS since last year

• Airport Authority – Feasibility study for implementation of GBAS for Hong Kong

Airport

Hong Kong GNSS Active Network

Global Ionosphere activities

Example of ionosphere distribution in HK

01 02 03 04 05 06 07 08 09 10 11 12 -0.1

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7 Statistical Character of Temporal Differential VTEC (ROTI)

Month

RM

S (U

nit:

TEC

U)

Distribution of Ionospheric Scintillation in 2001

How to Model Ionospheric Delay in Low Latitude?

Analysis of Receiver Bias estimation

• How accurate is the ionosphere estimation? – The receiver bias estimation give a clue

• To test variations of bias estimation

– Global data – Different models – Different Regions

P=P1-P2=m(α)Iv(x,y,h)+DCB+n

Used dataset – 60 stations

DCB in America area

Range of daily variation and RMS increase while the latitude decreases.

The global vs the station-specific

Maximum difference can reach 14.3 TECU. Bigger ones at the low latitude stations.

Taylor series vs Spherical Harmonic model

Station Name

Taylor (TECU)

Regional SH (TECU)

Difference (TECU)

Geographic longitude

Geographic latitude

gold -12.6 -15.5 2.9 243.11 35.42 jplm 22.5 18.9 3.6 241.82 34.20 pin1 -12.1 -14.6 2.5 243.54 33.61 hers -30.8 -35.9 5.1 0.33 50.86 brus -6.3 -11.1 4.9 4.35 50.79 kosg 34.2 30.8 3.4 5.80 52.17

Daily variations vs distance between stations

similar latitude

Station name

Latitude longitude Distance To tcms(km)

Correlation coefficient of DCB daily variation

tcms 24.8 120.9 0 --- tnml 24.8 120.9 5 0.977 wuhn 30.5 114.3 910 0.843 kunm 25.0 102.7 1830 0.514 lhaz 29.5 91.1 2973 0.238

Station Latitude longitude Distance To tcms(km)

Correlation coefficient DCB daily variation

tcms 24.8 120.9 0 --- shao 31.1 121.2 698 0.894 pimo 14.5 121.1 1123 0.541 daej 36.3 127.37 1420 0.484

similar longitude

Summary

• Receiver Bias estimation accuracy is dependent on ionospheric model accuracy

• Spherical harmonics or Taylor series are commonly used – Large number of coefficients – Difficult for prediction

• Can we have a good model to model ionospheric TEC distribution?

five mathematical functions

cosine normal distribution parabola

cubics witch of Agnesi

• No.1 function:

• No.2 function:

• No.3 function:

• No.4 function:

• No.5 function:

Function performance

• Result-RMS (DCBs are estimated with Bernese)

Comparison of No. 1 and 3 • DCBs as unknown parameters

Predictability of model

• Model derived from former day to fit next day

Use 2 hours data to predict the next 2 hours

• The improved constraint condition

0

2

4

6

8

10

12

2to4 4to6 6to8 8to10 10to12 12to14 14to16 16to18 18to20 20to22 22to24

RMS without constraint

RMS with constraint

RMS with improved constraint

RMS(TecU)

Period(hours)

Prediction Results • Klobuchar

• Residual error of Prediction model without constraint

• Residual error of Prediction model with constraint

Prediction Results

Models unit: TECU

Klobuchar (STDEV) 9.14 Without constraint (RMS) 5.71 With constraint (RMS) 4.67

MEASURES OF PRECISION AND

ACCURACY • Sigma (σ)

– Standard deviation in one, two and three dimensions

– Associated probability levels (in %)

1-d

1 σ 68.0

2 σ 95.0

3 σ 99.7

Probability Density

0.1 0.2 0.3 0.4

-3σ

-2σ

-1σ

0

1σ

2σ

3σ

y

x

High Accuracy Positioning Service in Hong Kong

• DGNSS + • Data quality improvement

–Smoothing • Spatial Error correction

–Localized models • Reduce effects of scintillation

–Data statistical models

Data Smoothing

• Data smoothing

Standard Kalman Filter

Smoothed P1, P2

GPS observablesParameter setting

Code smoothing

• Results – original and smoothed

Differential Positioning

Modeling Ionospheric delay along Satellite tracks

Satellite one

Satellite two

Ionosphere gradients

Positioning Results

Results: the std of noise under different ionosphere conditions

Group Number Intervals / meter (RMS of DVTEC)

(Overbounding)

(Overbounding

) Quiet 1,243,192 <0.02 0.372 0.602 0.201

Medium I 7,686, 0.02--0.04 0.412 0.966 0.322

Medium II 3,437 0.04--0.06 0.506 1.396 0.465

Severe 3,607 >0.06 0.743 1.531 0.510

IFσ ,noise IFσ noiseσ

STD of noise under different ionosphere conditions in March, 2001

Groups of the observations

Class

RoTI /TECU

Quiet

0-0.09

Moderate I

0.09-0.18

Moderate II

0.18-0.27

Severe

> 0.27

41

/0 1

cnoise a a e θ θσ −= +

Noise level under different ionosphere conditions in 2001

42

Positioning Results

Summary

• We have developed a local ionospheric model suitable for low latitude region, with the accuracy of 5 TECU

• To achieve high accuracy positioning in low latitudes: – Gradient of Ionosphere – Statistical models for ionosphere scintillation