Part VI

Precise Point Positioning Supported by

Local Ionospheric Modeling

GS894G

Presentation Outline

Research objectives

The Benefits of PPP

MPGPS™ Software

Methodology

Experiments and test results

Summary and Conclusions

Research Objectives

Develop precise point positioning (PPP) methodology and algorithms for surveying and navigation applications

Take advantage of the existing IGS products (precise orbits and clock corrections)

Provide local ionospheric maps (LIM) and tropospheric total zenith delays (TZD) from permanent GPS stations to support single-frequency PPP

Evaluate the quality of single and dual-frequency static and kinematic PPP in post processing

MPGPS™ - Multi Purpose GPS software

Developed at The Ohio State University (OSU)

Positioning Modules Long-range instantaneous (single epoch) RTK GPS Rapid-static Static Multi-station DGPS Precise point positioning (PPP)

Atmospheric Modules Ionosphere modeling and mapping Troposphere modeling

Positioning Solutions Single-baseline Multi-baseline (network) Stand-alone

The Benefits of PPP

Single receiver operation (low-cost)

Can be applied anywhere and anytime under

different dynamics (remote areas, space

applications, etc)

Not limited by baseline length as relative

techniques

Independence on GPS reference stations

Can be applied for static and kinematic platforms

MethodologyError Sources in PPP

Errors affecting the GPS observations Satellite orbit and clock corrections, (provided by IGS)

• accuracy < 5 cm and <0.1 ns (3 cm) Relativistic effects (included in the IGS orbits, except for the

periodic

relativity, which is modeled in MPGPS™)• periodic relativity - up to 30 ns (~9 m)

Receiver and satellite antenna phase center offsets (provided by IGSor NGS)• satellites - up to 1.023 m, receiver up to - 0.2 m

Satellite P1P2 and P1-C1 differential code biases (DCBs) (provided by IGS)• up to 2 ns (0.6 m), accuracy 0.1 ns (3 cm)

Receiver DCB (GPS receiver calibration in MPGPS™ or IGS)• up to 20 ns (6 m), accuracy 0.1 ns (3 cm)

Phase wind-up• up to 1 cycle (~0.2 m) of carrier phase data

MethodologyError Sources in PPP

Errors affecting the GPS observations (cont.) Ionospheric refraction

• Ranges from <1 m to >100 m Tropospheric refraction

• TZD = ~ 2.3 m (for standard atmosphere)

Errors affecting the station coordinates Atmospheric loading

• correction: vertical < 1 cm Ocean loading

• corrections : horizontal < 2 cm, vertical < 5 cm Solid Earth tides

• correction: horizontal < 5 cm, vertical < 30 cm Earth Rotation Parameters, i.e., pole position and UT1-

UTC (included in the IGS orbits)

MethodologyAdjustment Model

bXL

All parameters in the mathematical model are considered

pseudo-observations with a priori information (σ = 0 ÷ )

GLS – Generalized Least Squares adjustment

( , ) 0b bF XF L L 0F F X X FB V B V W

bFL - instantaneous parameters (e.g., ionospheric

delays)- accumulated parameters (e.g., ambiguities)

Two groups of parameters (pseudo-observations) of interest:

Flexibility, easy implementation of:

stochastic constraints fixed constraints weighted parameters filters

MethodologyPPP Functional Model

( ) 0

( ) ( ) 0

k k k k k ki i i i i i i

k k k k k ki i i i i i i

L c t t T I B

P c t t T I c b b

- undifferenced carrier phase and code observations (in

meters)

- geometric distance (satellite-receiver)

- constant bias, where

- integer carrier phase ambiguity and non-zero initial fractional

phase

- receiver and satellite clock offsets

- tropospheric total zenith delay (TZD)

- troposphere mapping function

- slant ionospheric delay

- receiver and satellite code and phase hardware delays

- corresponding carrier wavelength

- speed of light

- random error or residual

( ) ( )k k k ki i i iB N N c d d

,k ki iN N

,k ki iL P

, kit t

iTkikiI

, ; ,k ki ib b d d

c

kiB

ki

MethodologyPPP - Functional Model Unknowns

Permanent GPS station solution for local ionosphere maps (LIM)

receiver clock tropospheric TZD slant ionospheric delays bias parameters (non-integer ambiguities and hardware

delays) Single-frequency positioning solution

rover coordinates receiver clock bias parameters

Dual-frequency (ionosphere-free) positioning solution

rover coordinates receiver clock tropospheric TZD bias parameters

Methodology Local Ionospheric Model (LIM)

Supports PPP in case of single-frequency receiver

Single layer model (SLM) ionosphere approximation

Slant ionospheric delays estimation from dual-frequency GPS data at the neighboring permanent stations

Slant ionospheric delays conversion to vertical total electron content (VTEC) at ionosphere pierce points (IPPs)

Kriging interpolation to produce LIM in a form of a grid using the calculated vertical TEC values at IPPs

SLM assumes that all free electrons are contained

in a shell of infinitesimal thickness at altitude H

z - zenith angle

H - SLM height

R - Earth radius

SLM – Single Layer Model

Methodology Local Ionospheric Model (LIM)

1 TECU = 1016 ellectron/m2

= 0.162 m delay/advance

Methodology PPP Models

Three PPP MPGPS™ models were tested in post processing mode Static PPP – dual-frequency (ionosphere-free)

Static PPP – single-frequency supported by LIM

Kinematic PPP – single-frequency supported by LIM

Adaptive filter for kinematic solution Follows the dynamic variations of the system

estimates and stochastic models

Propagates the coordinate and ionosphere residuals together with their stochastic characteristics

Forward and backward filters

Experiments and test resultsData Source

Four stations, IGS/EPN (EUREF permanent network)

Three stations were used to derive LIM and TZD (BOR1, GOPE, KRAW)

One station was selected as a rover (WROC)

Two three-hour sessions

01 - 04 UTC (nighttime - lowest TEC level)

13 - 17 UTC (daytime - highest TEC level)

30-second sampling rate (i.e., 360 epochs per session)

Phase-smoothed pseudoranges

Distances between permanent stations ~330 km (average)

Distances to the rover ~130–230 km

Experiments and test results

Test Area Map

Czech Republic

Poland

- LIM/TZD

- PPP (rover)

N

____________________________________________________

Rover

Experiments and test resultsSatellite Geometry - Station WROC

01-04 UTC nighttime

4-7 satellites

13-17 UTC daytime

4-5 satellites

Poor satellite geometry, high GDOP - usually over 5

A short period with very poor geometry occurred in both sessions

50 100 150 200 250 300 3503

4

5

6

7

8

No.

of s

at.

50 100 150 200 250 300 3500

5

10

15

20

Epochs

GD

OP

50 100 150 200 250 300 3503

4

5

6

7

8

No.

of s

at.

50 100 150 200 250 300 3500

5

10

15

20

Epochs

GD

OP

____________________________________________________

GDOP = ~80

GDOP =~1000

Experiments and test resultsExample LIM-derived ionospheric delays

0 50 100 150 200 250 300 3500

1

2

3

4

5

6

7

Epochs

[m]

PRN 15PRN 16PRN 18PRN 23PRN 31PRN 14PRN 11PRN 3

0 50 100 150 200 250 300 3500

1

2

3

4

5

6

7

Epochs

[m]

PRN 8PRN 27PRN 28PRN 29PRN 26PRN 9

Station WROC (rover)

01-04 UTC nighttime

lowest TEC

13-17 UTC daytime

highest TEC

_______________________________________________________

Experiments and test resultsStatic PPP Analysis – Station WROC

50 100 150 200 250 300 350-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

Epochs

[m]

neu

50 100 150 200 250 300 350-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1Static ion-free

neu

Epochs

[m]

50 100 150 200 250 300 350-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

Epochs

[m]

neu

50 100 150 200 250 300 350-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1neu

[m]

Epochs

Nighttime, dual-frequency(ionosphere-free LC)

Daytime, dual-frequency(ionosphere-free LC)

Nighttime, single-frequencysupported by LIM

Daytime, single-frequencysupported by LIM

____________________________________________________

Experiments and test resultsStatic PPP Analysis – Station WROC

Ionosphere-free solution Horizontal - sub-decimeter-level position accuracy Vertical - decimeter-level Nighttime - convergence after 40 minutes Daytime - convergence after 25 minutes

Single-frequency solution supported by

LIM Good agreement with its ionosphere-free counterpart Similar accuracies and convergence times LIM proved to be efficient in removing the ionospheric

delays

Experiments and test resultsKinematic PPP Analysis – Station WROC

01-04 UTC (nighttime) 13-17 UTC (daytime)

Unfiltered single-

frequencysupported by

LIM

Filteredsingle-

frequencysupported by

LIM

50 100 150 200 250 300 350-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

Epochs

[m]

neu

50 100 150 200 250 300 350-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1neu

[m]

Epochs

50 100 150 200 250 300 350-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

Epochs

[m]

nee

50 100 150 200 250 300 350-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1neu

[m]

Epochs

____________________________________________________

The unfiltered solutions are very noisy in both sessions

In the filtered solution the large residuals were smoothed out after a few iterations (3-4)

The filtered kinematic solutions show similar accuracies as obtained in the static case

Sub-decimeter horizontal and decimeter-level vertical position accuracy was achieved

Experiments and test resultsKinematic PPP Analysis – Station WROC

Summary and Conclusions

The sequential GLS adjustment was successfully applied in

the PPP algorithm

Single-frequency static and kinematic PPP solutions,

supported by LIM, are comparable to the ionosphere-free

solutions

The results prove a good quality of the obtained LIM

The effectiveness of the adaptive filter was presented in the

kinematic mode, even under unfavorable satellite geometry

This algorithm may be applied in geodetic applications,

where sub-decimeter level accuracy is required