Single-Station Ionosphere Modelling Single-Station Ionosphere Modelling for Precise Point Positioningfor Precise Point Positioning

Paul CollinsPaul Collins, Reza Ghoddousi-Fard, Simon Banville , Reza Ghoddousi-Fard, Simon Banville FranFranççois Lahayeois Lahaye

Geodetic Survey Division, Natural Resources Canada, Geodetic Survey Division, Natural Resources Canada, Ottawa, Ontario, Canada Ottawa, Ontario, Canada

PPP Workshop: Reaching Full PotentialJune 12-14, 2013, Ottawa, Canada

2

IntroductionIntroduction

A clearer understanding of the role of the ionosphere in high-precision GNSS permits: rapid PPP-AR (under some circumstances), those ‘circumstances’ look suspiciously like RTK…

One goal of this presentation is to retain: a distinction between PPP & RTK techniques.

Motivation: What was the point of GPS in the first place? Why the desire for dense reference networks?

3

PPP/RTK ReviewPPP/RTK Review

Two kinds of RTK: Observation Space Representation (OSR-RTK) State Space Representation (SSR-RTK)

Preferably not PPP-RTK, because…

Differentiator between RTK and PPP: Network Size:

RTK: local/regional. PPP: (wide-area)/global.

Network Dependence: RTK User: No network, no solution. PPP User: What network?

4

-1

-0.5

0

0.5

1

-1 -0.5 0 0.5 1

Ionosphere/Ambiguity RelationshipIonosphere/Ambiguity Relationship

-1

-0.5

0

0.5

1

-1 -0.5 0 0.5 1

Ionosphere-free model

Ionosphere-fixed model

code = 10cm; phase = 1mm

L1 iono bias = 2cm/0.12TECU

5

Four-observable PPP modelFour-observable PPP model

Original three-observable decoupled clock model:

44444464

3413333

3333

)6017()(

)(

AsA

rA

LsL

rL

PsP

rP

NbbAPL

NNdtdtcTL

dtdtcTP

Split widelane-phase/narrowlane-code observable:

)]()[(

)(

)(

34434*

4

4*

444334

6*

444336

sL

sLL

rL

rLL

LLsL

rL

PLsA

rA

sL

rL

bbIbbI

INdtdtcTL

IbbdtdtcTP

Result: phase ionosphere. Biased by datum ambiguities and hardware delays.

6

Slant ionosphere estimatesSlant ionosphere estimates

fixed sigmafloat sigma

7

Applying the ConstraintsApplying the Constraints

Ionospheric Slant delays contain: Integer-biased satellite phase equipment delay.

Common to all stations. Integer-biased station phase equipment delay.

Unique to all stations, can change on solution reset. Use single-differences to eliminate station bias:

Add as pseudo-observations:

i~ iCC ~ 0A

ii~~

Tii CC ~~

,

8

PPP-ICAR MethodologyPPP-ICAR Methodology

LAMBDA

float solution

fixed solutionsAR AR ARAR AR AR

LAMBDA

float/fixed solutions

constrained solutionsion ion ion ion

AV

ARAR AR AR

ion ion

9

PPP-ICAR TestingPPP-ICAR Testing

Local stations around Ottawa. JO2P (30sec); NRC1 (1sec).

Two receivers driven on the Rideau Canal (frozen). 0015, 0019 (1sec). frozen surface should be ‘level’.

S1

S2aS2c

S2b

JO2PNRC1

00150019

8.5km

10

Solution 1 JO2P Solution 1 JO2P → NRC1 (2D-Horiz.)→ NRC1 (2D-Horiz.)

67% ~1cm 95% ~2cm

11

Solution 1 JO2P Solution 1 JO2P → NRC1 (3D)→ NRC1 (3D)

67% ~3cm

95% ~7cm

12

Solution 2: Height EstimatesSolution 2: Height Estimates

PPP(SMD) HGT = 30.34 ± 0.10 PPP(ICAR) HGT = 30.26 ± 0.05 RTK(NRC1) HGT = 30.25 ± 0.02

29.75

30.00

30.25

30.50

30.75

18 18.5 19 19.5 20Local Time (Hours)

Geo

m. H

gt. (

m)

0.0

2.5

5.0

7.5

10.0

Velocity (km

/hr)

VEL(km/hr)

PPP(STD)

PPP(ICAR)

RTK(NRC1)

13

0019 (JO2P ION)

-0.30

-0.20

-0.10

0.00

0.10

0.20

0.30

18 18.5 19 19.5 20

Local Time (Hours)

Sol

uti

on D

iffe

ren

ce (

m)

DLAT 0.9cm rms

DLON 1.3cm rms

DHGT 3.9cm rms

Solution 2: JO2PSolution 2: JO2P→→00190019→→NRC1NRC1→→00150015

NRC1 (0019 ION)

-0.30

-0.20

-0.10

0.00

0.10

0.20

0.30

18 18.5 19 19.5 20

Local Time (Hours)

Sol

uti

on D

iffe

ren

ce (

m)

DLAT 0.8cm rms

DLON 0.5cm rms

DHGT 2.4cm rms

0019 (kinematic)

NRC1 (stationary)

Ion

Ion

JO2P NRC1

00150019

0015 (NRC1 ION)

-0.30

-0.20

-0.10

0.00

0.10

0.20

0.30

18 18.5 19 19.5 20

Local Time (Hours)

Sol

uti

on D

iffe

ren

ce (

m)

DLAT 1.0cm rms

DLON 1.1cm rms

DHGT 4.8cm rms

0015 (kinematic)

14

RTK NetworkRTK Network

Master

User

Ref.

15

PPP Local ‘Network’PPP Local ‘Network’

User

“Ref.”

16

PPP Local AugmentationPPP Local Augmentation

17

Point Positioning ScalabilityPoint Positioning Scalability

STD

PPP

PPP−AR

PPP−ICAR

Broadcast Orbits & Clockspseudoranges

Precise Orbits & Clockscarrier phases

Decoupled Clock Modelequipment delays

Ionosphere Constraintsambiguity constraints

18

ConclusionsConclusions

Key Points: Know the Ionosphere, Know the Ambiguities. Constrain ambiguity resolution, not the observation model.

Using external ionosphere constraints for AR pushes PPP as close to RTK as possible, without being RTK. An RTK solution is still (a little) better!

In principle, Permits a generalised local augmentation concept: Peer-to-Peer in nature,

no centralised solution or coordination required; state space representation of information.

Regular PPP-AR solution possible at all times and all locations.

19

Future WorkFuture Work

Analyse Ionosphere Spatial Gradients

20

AcknowledgementsAcknowledgements

Pierre Héroux and Christian Prévost Rideau Canal dataset

Thank You