Ionosphere-free Single Frequency Multi-Constellation GNSS PPP model for Low Cost

Applications

Mahmoud Abd Rabbou and Adel El-Shazly

Department of Civil Engineering,

Cairo University

Presented by;Dr. Mahmoud Abd Rabbou

Outlines

• Introduction

• Problem statement

• Mathematical models

• Results and analysis

• Conclusion

Introduction

• The ionosphere is part of the Earth’s atmosphere, extendingfrom about 50 km up to about 1,000 km or more above theEarth depending on the sun activities.

• The ionosphere layer is a shell of electrons and electricallyatoms.

• The number electrons affects the GPS signal path through thelayer, is affected by the sun activities .

• The effect of the ionosphere is proportional to the total numberof the electrons along the path of the signals called the totalelectron content TEC and the signal frequecy.

• For GPS signals which have high frequencies, it causes a delayof GPS signal - code modulation and carrier phases.

• It causes a delay in code pseudorange measurement andadvances the phase measurement by the same amount .

http://www.wirelessdictionary.com/Wireless-Dictionary-Ionospheric-Delay-

Definition.html

Introduction• GPS dual frequency observations can eliminate the effect of

the ionosphere by using a linear combination of L1,L2 (L3).

• In Signal frequency observation the effect of ionosphereshould be modeled and add to the equation to get highaccuracy.

• The IGS global ionospheric maps (GIMs) are typically used tocorrect for the ionospheric error for single frequency PPP dueto its superior accuracy compared with the empirical methods.

• IGS is The main organization responsible for the production ofprecise satellite ephemerides, clock corrections andionospheric maps,------

Introduction

• The products generated from the IGS are based on thecombined effort from all, or most of the IGS centers.

• Each of the centers uses data collected from all IGS stationsaround the world. Presently IGS manages a network of 384stations

• For ionospheric maps, four IGS Ionosphere Associate AnalysisCentres (IAACs) are contributing their ionospheric products tothe IGS.

• Include the CODE, ESOC, JPL, and Technical University ofCatalonia (UPC).

• The four centers produce 2-dimensional ionosphere TEC mapsthat refer to a 450km shell height.

Acquired from IGS website

Problem statement

• The accuracy of these maps is affected by the IGS stations

distribution and network resolution.

• Up to date, unfortunately, there are no IGS stations in Egypt

which in role affected the IGS product accuracy for PPP

accuracy.

• In PPP where only one GNSS receiver is used, there is nooption to reduce the effect of poor quality ionosphericmodelling as there is no base station.

• Based on the ionospheric effect characteristic, in singlefrequency the average of code and phase can eliminate theeffect of the first order ionosphere delay.

• The average observation is called the quasi phase or singlefrequency ionosphere free.

• However, the new observation suffers from the unresolvedambiguity parameters.

• In this research, we overcome this problem by introducing anew observation constrain for the single frequency quasiphase obaservation

Problem statement

Mathematical Model• The mathematical equations of the single frequency ionosphere-free

observation can be written as

• To overcome the rank deficiency problem, additional observationsshould be added to constrain the ambiguity parameters working as apriori observations.

•

2 2

s sGs sG G G G G G

G G r G G G G G

Φ P [ N +c( -d )-c( -d )]Φ = =ρ +c(dt +d )-cd t -c(B )+T + +

2 2

s sJs sJ J J J J J

J J r J J J J J J

Φ P [ N +c( -d )-c( -d )]Φ = =ρ +c(dt +d )-cd t -c(B )+T +c[ISB ]+ +

Mathematical Model

2 2

s sGG G G G G G

G G G

Φ -P [ N +c( -d )-c( -d )]ˆ ˆΦ = = -I +

2 2

s sJJ J J J J J

J J J

Φ -P [ N +c( -d )-c( -d )]ˆ ˆΦ = = -I +

(10)

• In current research, the a priori observation is selected as the half of code and phase difference as follows

• However, as can be seen, the ionospheric parameters areaffecting the constrained equations. This can be overcome bycorrecting these observations using the existing ionosphericmodels such as the GIM model or can totally ignoring theionospheric range delay with assuming higher observationuncertainty. In this research, the second option is employed.

Mathematical Model• The extended Kalman filter (EKF) is employed to estimate the unknown

parameters.

1[ ]w r R E C nx , , h,T , cdt , cISB , cISB , cISB , A , .. A

0

0

Φ -Φ

Φ -Φ

Φ̂

Φ̂

G G

J J

IF

G

J

Y

1 0 0 0 1 0 0 0

1 1 0 0 0 0 0 0

1 0 1 0 0 1 0 0

1 0 0 1 0 0 0

0 1

0 0 0 0 0 0 1 0 0 0

0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 1 0 0

0 0 0 0 0 0 0 0 0

0 1

G G

R R

E E

C C

IF

A m

A m

A m

A m

H

Mathematical Model• The quasi-phase observables are assumed linearly correlated with the

ambiguity-constrained observables and the precision of both observables

are taken as ½ of the code precision

2 21 1

ˆΦ,Φ

2 21 1

1 1

4 2

1 1

2 4

P P

P P

R

Results and Analysis• Estimated ionospheric delay using leveling geometry-free linear combination

compared with GIM delay products

Comparable vertical ionospheric delay is extracted from GIM for Station CRO1.

Results and Analysis• Estimated ionospheric delay using leveling geometry-free

linear combination compared with GIM delay products in Egypt.

GPS data at Alexandria GPS data at Helwan

In contrast, the GIM ionospheric delay products variation is far from the leveling geometry-free ionospheric delay estimated trend.

Results and Analysis

Results and Analysis

Conclusions• The vertical ionospheric effect is estimated using geometry-

free leveling technique.

• The Geometry free based ionospheric trend shows poor quality of the GIM ionospheric product in Egypt due to the low resolution of GIM stations distribution.

• As a result, this research develop the ionosphere-free single frequency PPP model to remove the ionospheric effect.

• The result shows the positioning accuracy enhanced by an average of 50 % in both latitude and longitude while 60 % in altitude.

• The using of the new constellation GNSS such as Galileo and BeiDou has a marginal effect on the positioning accuracy.