1

LAVAL UNIVERSITYDEPARTMENT OF GEOMATICS

Mohammed Boukhecha (Laval University)Marc Cocard (Laval University)René Landry (École technique supérieure Montréal)

Instantaneous ambiguity resolution for future GNSSa simulation study

2

Overview

1.Introduction2.Theoretical approach3.Results of the simulations4.Conclusions

3

In the near future there will be a modernization of GNSS• Additional 3rd frequency on GPS

• Galileo will become operational

• Hybrid solutions of GPS and Galileo

Situation nowadays with GPS only:

(Quasi-) Instantaneous ambiguity resolution works under certain conditions :

• Differential mode

• Dual frequency receivers

• Negligible ionospheric noise --» short baselines (up to 10 km)

Introduction

4

Introduction

Main question of our research :

What will be the impact of modernized GNSS

on instantaneous ambiguity resolution ?

In order to elucidate this question lets do some simulations

5

Theoretical approach

Review of basic search strategy in ambiguity resolution :

• Define the search space containing all possible candidates of integer sets

• Look for the best set (characterized by the smallest variance factor) and the second best set (characterized by the second smallest variance factor)

• Apply a statistical test in order to discard the second best set as highly improbable. If the test is successful, only one set remains (the best one) which is accepted as the correct one.

Discrimination factor :2221

2122

where,

: estimated variance factor for the best integer ambiguity set

: estimated variance factor for the 2nd best integer ambiguity set

6

Theoretical approach

In the absence of real observations this discrimination factor has to be adapted to the a priori case.

2 2 21 0{ } { }floatE E

1 12 2 22 1 0{ } { }

T Ta aa Q a a Q a

E E

a

where,

best solution

2nd best solution

20 : a priori variance factor

: cofactor matrix of the float ambiguities

: difference between 2nd best and best integer ambiguity set

aQ : degree of freedom

can be obtaineda priori

7

Theoretical approach

Satellite orbits simulated by a Keplerian representation

Normal Equation Matrix

A priori Discrimination

factor

Choice of several parameters

(will be presented in details later on)

Observation equations forcode and phase measurements

Simplified structure of the simulator

8

Theoretical approach

Observation equations and unkown parameters

P cl I

cl I k a

Coordinates (X Y Z) Clocks

Ionosphere biases Receiver phase bias

Integer ambiguityCode measurement

Phase measurement

9

Theoretical approach

Ionospheric modeling and constrains

Ionospheric layer

Short baseline Large baseline

Ionospheric layer

I > 0I = 0

Iz is regarded as a pseudo-observation having expectation value of 0 with a knowna priori variance I

The ionospheric delay I is related to the unknown vertical ionospheric delay Iz by the following relationship:

GroundStation

Ionosphere layer

z’II

z

1

cos ' zI Iz

10

Theoretical approach

Position de la station fixe P() Latitude 45o , longitude 0o

Elevation mask 15o

Combination of frequencies

Mono Double Triple

GPS L1 2 of 3 L1 L2 L5

GALILEO E1 2 of 3 E1 E5 E6

HYBRID L1 E1 All comb. L1 L2 L5 E1 E5 E6

Std. dev. of ionospheric delay I 0 cm , 1cm, 2cm …. 1m

Std. dev. of observationscode 30 cm

Phase 3 mm

Confidence level 1 – a 99%

Range of simulation parameters

11

Results Number of satellites and PDOP

0 12 24 36 48 60 7201

23

45

67

89

02

46

810

1214

1618

PD

OP

EPOCH (h)

Nu

mb

er

of

sa

tellit

es

GPS GALILEO HYBRID

12

The normalized discrimination factor

Results

99% ( , )F

Statistical validation of integer ambiguity resolution

: success: failure

: degree of freedom

: discrimination factor

99%F : Fisher distribution with 99% confidence level

13

ResultsNormalized discrimination factor

Ionospheric Noise : I I = = 0 cmcm

GNSS dual frequency

14

ResultsNormalized discrimination factor

Ionospheric Noise : I I = = 0 cmcm

GNSS mono frequency

15

ResultsNormalized discrimination factor

Ionospheric Noise : I I = = 0 cmcm

GNSS dual frequency

16

ResultsNormalized discrimination factor

Ionospheric Noise : I I = = 0 cmcm

GNSS triple frequency

17

ResultsNormalized discrimination factor

Ionospheric Noise : I I = = 0 cmcm

0 12 24 36 48 60 72

048

1216202428323640

048

1216202428323640

048

1216202428323640

Mo

no

EPOCH (h)

DO

UB

LE

T

RIP

LE

GPS GALILEO HYBRIDE

18

0 12 24 36 48 60 72

01234567

01234567

01234567

MO

NO

EPOCH (h)

DO

UB

LE

T

RIP

LE

GPS GALILEO HYBRIDE

ResultsNormalized discrimination factor

Ionospheric Noise : I I = = 10 cmcm

19

0 12 24 36 48 60 72

0

1

2

3

0

1

2

3

0

1

2

3

MO

NO

EPOCH (h)

DO

UB

LE

T

RIP

LE

GPS GALILEO HYBRIDE

ResultsNormalized discrimination factor

Ionospheric Noise : I I = = 20 cmcm

20

0 12 24 36 48 60 72

0

1

2

0

1

2

0

1

2

MO

NO

EPOCH (h)

DO

UB

LE

T

RIP

LE

GPS GALILEO HYBRIDE

ResultsNormalized discrimination factor

Ionospheric Noise : I I = = 30 cmcm

21

Submitting the instantaneous discrimination factor to a statistical test leads to a binary results :

Ambiguity resolution theoretically possible (YES) or not (NO)

Based on this test a success rate is calculated over a period of 3 days with a sampling rate of 1 minute.

Success rate (an other interesting indicator)

Results

22

GNSS mono frequency

ResultsImpact of ionospheric noise on the success rate

23

GPS only and GALILEO only dual frequency

ResultsImpact of ionospheric noise on the success rate

24

HYBRIDE dual frequency

ResultsImpact of ionospheric noise on the success rate

25

GNSS triple frequency

ResultsImpact of ionospheric noise on the success rate

26

Frequencies Systems

Max. ionospheric noise (cm)

SR=100

%

SR=95%

SR=90%

TRIPLE

HYBRIDE 43 55 60

GALILEO 21 24 25

GPS 17 21 22

DOUBLE

HYBRIDE 40 60 65

GALILEO 9 17 23

GPS 3 19 21

ResultsImpact of ionospheric noise on the success rate

Classifying GNSS solutions as a function of the maximum ionospheric noise allowed still leading to different success rate (SR) values

27

Conclusions

Approach Simulation is an appropriate tool for analyzing the performance of future GNSS in the absence of real observations.

Results Concerning instantaneous ambiguity resolution Galileo shows a similar or even slightly better performance compared to GPS. HYBRID RTK solutions will allow instantaneous ambiguity resolution even with mono-frequency receivers (in the absence of ionosphere). Especially the HYBRID dual and triple frequency will allow to absorb quite a high ionospheric noise still leading to an instantaneous ambiguity resolution.

Future work Integration of GLONASS in the simulations.

28

Questions ?Questions ?