A Space Odyssey: Mathematical journeys across

uncharted territory

Professor Marek ZiebartDirector, Space Geodesy and Navigation Laboratory

Department of Civil, Environmental and Geomatic Engineering

University College London

Inaugural Lecture of

Prof Ziebart

Professing….. Space Geodesy

Space Geodesy Science and Engineering: the underlying

mathematics and models for satellite navigation (GPS)

Space Geodesy Science and Engineering:

GPS derived global velocity vectors

Jason-1 satellite sea level model from one 10 day pass

Red = higher than normal sea level (~20cm)

Space Geodesy science and engineering:

Sea level variations from Space

Space Geodesy and Society:

El Nino, the Dust Bowl and the Great Depression

Project: Low Earth Orbiter (LEO) attitude determination

Publications: •Ziebart,M. and Cross,P., (2003) LEO GPS Attitude Determination Algorithm For A Micro-satellite Using Boom-arm Deployed Antennas, GPS Solutions, Vol.6, No.4

•Cross,P., and Ziebart,M., (2002), LEO GPS Attitude Determination Algorithm Designed for Real-time On-board Execution, Proceedings of ION GPS-2002, Portland, Oregon, USA (Winner of best paper award, attitude session)

Low Earth Orbiter (LEO) attitude determination: the maths

j

B

j

A

i

B

i

A

BFS

B

BFS

B

BFS

B

LLS

j

BFS

B

BFS

B

BFS

B

LLS

j

BFS

B

BFS

B

BFS

B

LLS

j

BFS

A

BFS

A

BFS

A

LLS

j

BFS

A

BFS

A

BFS

A

LLS

j

BFS

A

BFS

A

BFS

A

LLS

j

BFS

B

BFS

B

BFS

B

LLS

i

BFS

B

BFS

B

BFS

B

LLS

i

BFS

B

BFS

B

BFS

B

LLS

i

BFS

A

BFS

A

BFS

A

LLS

i

BFS

A

BFS

A

BFS

A

LLS

i

BFS

A

BFS

A

BFS

A

LLS

i

zmymxmz

zmymxmyzmymxmx

zmymxmz

zmymxmyzmymxmx

zmymxmz

zmymxmyzmymxmx

zmymxmz

zmymxmyzmymxmx

ij

AB

2

333231

2

232221

2

131211

2

333231

2

232221

2

131211

2

333231

2

232221

2

131211

2

333231

2

232221

2

131211

N

21

21

21

21

• Mathematical, gravity-based

model used as the Ordnance

Survey’s national height datum

• Derived from multiple forms of

satellite-derived data products

• Incorporated into tens of

thousands of computers, data

loggers, science-grade GPS

receivers

• On-going developments with OS

to release new generation of

models

Publications:

•Ziebart, M. K., J. C. Iliffe, R. Forsberg, and G. Strykowski (2008), Convergence of the UK OSGM05 GRACE-based

geoid and the UK fundamental benchmark network, J. Geophys. Res., 113, B12401

•Ziebart,M., J. C. Iliffe, P. A. Cross, R. Forsberg, G. Strykowski, and C. C. Tscherning., (2004) Great Britain's GPS Height

Corrector Surface, Proceedings of ION GNSS 2004, Long Beach, California, USA, 203-210.

(winner of best paper award, Land Applications session)

Project: OSGM05 - the UK gravity field model

Project: Vertical Offshore

Reference Frame (VORF)

• Commissioned by

UK Hydrographic Office

• Developed mathematical models of

sea surfaces

• Operational sea surface models now

used routinely in offshore work

• Approach from the Royal Navy to

develop a global model

Publications:

•Iliffe, J. C., Ziebart, M. K. and Turner, J. F. (2007)

'A New Methodology for Incorporating Tide Gauge Data in Sea

Surface Topography Models', Marine Geodesy, 30:4, 271 - 296

•Ziebart, M., J.Iliffe, J.Turner, J.Oliveira and R.Adams (2007),

VORF The UK Vertical Offshore Reference Frame: Enabling

Real-time Hydrographic Surveying, proceedings of ION GNSS2007,

Fort Worth, Texas, USA, September, 2007, pp 1943-1949.

(winner of best paper award, Marine Applications session)

Sule Skerry

Orkney Isles

Shetland

Isles

Foula

Orbit determination

Orbit prediction

accuracy: cm to mm

accuracy: m to cm

Projects:

Forces acting on a GPS spacecraft

PRP

(planetary radiation

pressure)

Thermal forcing

(TRR)

Antenna thrust

(AT)

Solar radiation pressure

Resultant force from

solar photons

Thermal Re-radiation forces

Resultant force from

Thermal emissions

How big are these forces?

What effect do they have?

Computer model

of spacecraft

Pixel array simulating

photon flux

Photon force modelling

radiation flux

Secondary intersections

regions of shadow

computed automatically

Pixel array rotated around spacecraft,

solar panels adjusted

Publications:Ziebart,M.,(2004) Generalised Analytical Solar Radiation Pressure Modelling Algorithm for Spacecraft of Complex Shape,

Journal of Spacecraft and Rockets, Vol.41, No.5, pp 840-848(9)

Ziebart,M., Adhya, S., Sibthorpe, A., and Cross, P., (2003) GPS Block IIR Non-conservative Force Modelling: Computation

and Implications, Proceedings of ION GPS/GNSS 2003, Portland, Oregon, US (winner of best paper award, Science/timing

application session)

NASA Jet Propulsion Laboratory, Pasadena, California

Earth radiation flux incident on a GPS satellite

Force modelling on GPS satellites

• Computer codes adapted to run on supercomputers

• Contract research for US Air Force/JPL

• Won several international awards

• Orbit determination accuracy of 2cm achieved

• Earth radiation pressure modelling adopted as

international standard (IGS)

• Commercial contract to develop orbit prediction and

orbit determination code for one of the world’s

largest providers of GPS positioning services

-2

0

2

4

6

8

10

0 1 2 3 4 5 6 7 8 9 10 11 12

Time (hours)

Orb

it P

red

icti

on

Err

or

(m)

Solar radiation pressure (SRP) only

SRP + Thermal force (TRR)

SRP + TRR + Antenna Thrust (AT)

SRP + TRR + AT + Planetary Radiation Pressure

Along-track orbit prediction errors over 12 hours for one GPS satellite with

different photon-based force models

8 metre

orbit error

Jason-1 modelling (SRP and TRR)

• Extensive tests carried out at JPL

• Dynamic orbit improvements in cross overs,

SLR residuals, orbit overlaps and scale factors

• Model subsequently tested by Goddard Space

Flight Centre

• North hemisphere – South hemisphere mass

transfer anomaly resolved

• Anomalous 60 day period signature removed

• Model adopted by NASA as operational

standard

Summary of orbit modelling research

Publications:•N. P. Zelensky, F. G. Lemoine, M. Ziebart, A. Sibthorpe, D. S. Chinn, D. D. Rowlands, S.B. Luthcke, B. D. Beckley, D. Pavlis,

S.M. Klosko, P. Willis, and V. Luceri, (2010) DORIS/SLR POD Modelling Improvements for Jason-1 and Jason-2, Advances in

Space Research, In press

•Ziebart, M., S. Adhya, A. Sibthorpe, S. Edwards and P. Cross, (2005) Combined Radiation Pressure and Thermal Modelling of

Complex Satellites: Algorithms and On-orbit tests, Advances in Space Research, Volume 36, Issue 3, 2005, Pages 424-430

Designing a navigation system

for manned and robotic

missions to Mars

European Space Agency project

• Why build a navigation system?

• Design the space segment

(spacecraft instruments, orbit configuration)

• Design the surface-based system components

• Simulate and test system performance

at three landing sites

Space segment design Satellite ground track

5° mask angle zone

Beacon location

Inclined orbit

Polar orbit

Equatorial orbit

• Missions using pressurised

rover vehicles with

two astronauts

• All missions are

‘over the horizon’

• Each traverse may take

several days

Base and

central time facility

Holden Crater Mission Traverses

Sample simulation results: four

beacons, one way ranging,

clock resets on orbiter pass

The geometry of Roman amphitheatres

Hume

Sarmizegatuza, Romania Guildhall amphitheatre, London

Publications:

Ziebart, M., J. Arthur, N. Bateman, P. Rauxloh, D. Lees and J. Brown, (2006), Determination of the Parameters of the

Guildhall Amphitheatre Ellipse in London, J. Archaeol. Sci., Volume 34, Issue 9, pages 1505-1514

Reported in „The Times‟, September 18th, 2007: “Design of London‟s amphitheatre revealed”

National Centre for Earth Observation:

Dynamic Earth and Hazards

• New instrument design

• Seismometry/high rate

multi-constellation GNSS

• Sidereal filter

• Real-time tsunami and earthquake

warning system

• Aim: order of magnitude more

sensitive than current instruments

• Funding: ~62 PhDs

• Value: ~£11M

• Inspired by: Flooding;

Foot and Mouth

outbreak; Jared

Diamond’s ‘Collapse’

• Funding from EPSRC

and industry

What is the future of

Space Geodesy?

Has it even arrived

yet?

Why is there a

picture of

Dr Who on the

screen?

Looking forward:

Vice Dean for Research FACULTY OF ENGINEERING SCIENCES

Looking forward:

• Biochemical Engineering

• Chemical Engineering

• Civil, Environmental and Geomatic Engineering

• Computer Science

• Electrical and Electronic Engineering

• Jill Dando Institute for Crime Science

• Management Science and Innovation

• Mechanical Engineering

• Medical Physics and Bioengineering

• School of Energy and Resources, Australia

Governing Board Member

International GNSS Service (IGS)Working Group Leader:

Orbit Dynamics and Space Vehicle Attitude

Looking forward:

Space Geodesy and Navigation Laboratory

Looking forward:

Looking forward:

Space Geodesy: challenges and opportunities

• Developing effective early warning systems for natural hazards

• Understanding the exchange mechanisms between the cryosphere,

atmosphere, ocean and solid earth

• Modelling and predicting how sea level and the ice caps will respond

to climate change

• 120 ‘science grade’ navigation satellites on orbit

• Ultra stable spatial and time reference frames

• Public understanding of the value of space-based measurement

platforms

• A generation of scientists who have grown up with space technology

Personal Research Themes (technical)

Looking forward:

• Develop understanding and application of orbit dynamics modelling at higher

altitudes (GEO to interplanetary)

• Extend orbit dynamics techniques at LEO altitudes (ram profiling, surface

charge coupling with terrestrial magnetic field, rigorous earth radiation effects)

• Extend modelling techniques to space debris constellation prediction

• Build on understanding of atomic clocks/timescale realisation (with National

Physical Laboratories), linking to orbit dynamics

• Roll out our research in orbit dynamics/clocks to UK industry (chip

manufacturers)

• Maintain world lead in orbit dynamics

• Develop training for PhD/Post-Doctoral Researchers

• Build on the group’s expertise and collaborations with UK and international

partners

Partners and clients to date…

Thanks to:

Prof Paul Cross

UCL

Prof Nick Tyler

UCL

Prof Bernard Buxton

Dean of Faculty, UCL

Prof Duncan Wingham

UCL

Prof Barry Parsons

Earth Sciences, Oxford

Prof Philip England

Earth Sciences, Oxford

Prof James Jackson

Cambridge

Dr Yoaz Bar-Sever

NASA Jet Propulsion Lab

Dr Frank Lemoine

Goddard Space Flight Centre

NASA

Dr Geoff Blewitt

University of Nevada

Thanks to:

Dr Moriba Jah

Air Force Research

Laboratory, USAF

SGNL Group

Members

Karen Rafferty

Toby Godfrey, Katy Haile

and Dan Black,

Opus Design Consultants

Thanks to:

My Family

Thanks to:

Conclusions Conclusions

Thanks for listening

Please stay tuned

….and watch this space