expert lecture on gps at uiet, csjm, kanpur

Intro Data GNSS Apps&SW Resources Acknowledgements

Global Navigation and Satellite SystemA basic introduction to concepts and applications

Suddhasheel Ghosh

Department of Civil EngineeringIndian Institute of Technology Kanpur,

Kanpur - 208016

Expert Lecture on March 21, 2012 at UIET, Kanpur

1 / 52 shudh@IITK Introduction to GNSS


Outline

1 Basic ConceptsMotivationMathematical concepts

2 Collecting Geospatial Data

3 Introducing GNSSGPS BasicsGPS based Math Models

4 Applications and SoftwareApplicationsSoftware and Hardware

5 Resources

6 Acknowledgements


Intro Data GNSS Apps&SW Resources Acknowledgements Motivation MathCon

Outline

1 Basic ConceptsMotivationMathematical concepts


3 Introducing GNSS

4 Applications and Software

5 Resources

6 Acknowledgements



Where am I?Locate and navigate

One of the most favourite questions of mankind

Stone ageUsing markers like stone, trees and mountains to find theirway back

Star agePole star was a constant reminder of the directionMost world cultures refer to the Pole star in their literature

Radio ageRadio signals for navigation purposes

Satellite age:Modern technologyUse of satellites

To understand GPS we need to revise some mathematical concepts.



Taylor’s series expansion

If f (x) is a given function, then its Taylor’s series expansion isgiven as

f (x) = f (a) + f ′(a)(x − a) + f ′′(a)(x − a)2

2!+ . . .



Jacobian

If f1, f2, . . . , fm be m different functions, and x1, x2, . . . , xn be nindependent variables, then the Jacobian matrix is given by:

J =

∂f1∂x1

∂f1∂x2

. . . ∂f1∂xn

∂f2∂x1

∂f2∂x2

. . . ∂f2∂xn

. . . . . ....

...∂fm∂x1

∂fm∂x2

. . . ∂fm∂xn

If F denotes the set of functions, and X denotes the set ofvariables, the Jacobian can be denoted by

∂F∂X



Least squares adjustmentFundamental example

Given Problem

Suppose (x1, y1), (x2, y2), . . . , (xn, yn) be n given points. It isrequired to fit a straight line through these points.

Let the equation of “fitted” straight line be Y = mX + c.

y1 + δ1 = m · x1 + c, y2 + δ2 = m · x2 + c, and so on . . .

Arrange into matrix formδ1

δ2...δn

=

x1 1x2 1...

...xn 1

·[

mc

]−

y1

y2...

yn



Least squares adjustmentFundamental example continued

To determine m and c we use the formula:

[mc

]=

x1 1x2 1...

...xn 1

T

x1 1x2 1...

...xn 1

−1

x1 1x2 1...

...xn 1

T

y1

y2...

yn



Least squares adjustmentFor a general equation

Lb : set ofobservations,

X : set ofparameters.

X0 : initialestimate of theparameters

L0 : initialestimate of theobservations.

V : correctionapplied to Lb

La: adjustedobservations.

The set of equations is represented by

La = F(Xa)

Using Taylor’s series expansion,

Lb + V = F(X0)|Xa=X0+

∂F∂Xa

∣∣∣∣Xa=X0

(Xa − X0) + . . .

This can be represented as

V = A∆X−∆L

which can be solved by

∆X = (AT A)−1AT L

If case of weighted observations (P is the weightmatrix),

∆X = (AT PA)−1AT PL



Euclidean distanceFormula for finding distance between two points

If p1(x1, y1, z1) and p2(x2, y2, z2) be two different points in 3Dspace, then the distance between the two is given by:

d(p1,p2) =√

(x1 − x2)2 + (y1 − y2)2 + (z1 − z2)2



Outline

1 Basic Concepts


3 Introducing GNSS


5 Resources

6 Acknowledgements



Collecting Geospatial Data

Early: Chains, tapes and sextants

Mid: Theodolites, auto levels

Modern: EDM, GNSS



Older methods of collecting geospatial dataPictures of some instruments



Coordinates of a pointHow to find them?

Figure: A typical resection problem in surveying. Given coordinatesof the known points Ci , find the coordinates of the unknown point P



The resection problemIssues of accuracy and geometry

Resection problem requires the measurement of anglesand distances

All measurements made through theodolites, auto levels,EDMs etc contain errors

Requirement for minimizing errors: The control pointsshould be well distributed spatially.



Distance between objectsHow to find it?

What is the distance between the chalk and theblackboard?

How to find the distance between a ball and a chair?

How to find the distance between an aeroplane and theground?

If there is a mathematical surface (e.g. plane, sphere etc.)then it is easier to find the distance.

The Earth has a rough surface, and it has to be thereforeapproximated by a mathematical surface.



The mathematical surfaceDatum and sphereoids

Kalyanpur: Meaning of 127mabove MSL?

There is no sea in sight? What ismean sea level?

Geoid: The equipotential surfaceof gravity near the surface of theearth

MSL - Mean sea level (anapproximation to the Geoid

Ellipsoid / spheroid:approximation to the MSL

Mathematical surface: DATUM

Figure: Src:http://www.dqts.net/wgs84.htm



World Geodetic SystemOne of the most prevalent datums

It is an ellipsoid

Semi-major Axis: a = 63, 78, 137.0m

Semi-minor axis: b = 63, 56, 752.314245m

Inverse flattening: 1f = 298.257223563

Complete description given in the WGS84 Manualhttp://www.dqts.net/files/wgsman24.pdf


http://www.dqts.net/files/wgsman24.pdf


Parallels and Meridians

Figure: Latitudes and longitudes Figure: Measurement of angles



Map Projections... and their needs

It is a three dimensional world ...

But the mapping paper is two-dimensional

A mathematical function: Project 3D world to 2D Paper

Distance preserving

Area preserving

Angle preserving -conformal

Conical

Cylindrical

Azimuthal

There are guidelines on how to chose a map projection foryour map



Universal transverse mercatorA cylindrical and conformal projection

The world divided into 60zones - longitudewise

Each zone of 6 degrees

The developer surface is acylinder placed tranverse

The central meridian ofthe zone forms the centralmeridian of the projection

UTM Zone for Kanpur:44N

Combination of projectionand datum: UTM/WGS84and Zone 44N

Figure: The UTM zone division(Src: Wikipedia)


Intro Data GNSS Apps&SW Resources Acknowledgements Basics GPSmodel

Outline

1 Basic Concepts


3 Introducing GNSSGPS BasicsGPS based Math Models


5 Resources

6 Acknowledgements



NAVSTARThe US-based initiative

TRANSIT: The NavalNavigation System

NAVSTAR:Navigation

Principally designedfor military action

Landmarks

1978: GPS satellite launched

1983: Ronald Raegan: GPS forpublic

1990-91: Gulf war: GPS used forfirst time

1993: Initial operationalcapability: 24 satellites

1995: Full operational capability

2000: Switching off selectiveavailability



GLONASSThe Russian initiative

Global Navigation SatelliteSystem

First satellite launched:1982

Orbital period: 11 hrs 15minutes

Number of satellites: 24

Distance of satellite fromearth: 19100 km

Civilian availability: 2007



GALILEOThe European initiative

30 satellites

14 hours orbit time

23,222 km away from the earth

At least 4 satellites visible from anywhere in the world

First two satellites have been already launched

3 orbital planes at an angle of 56 degrees to the equatorSrc: http://download.esa.int/docs/Galileo_IOV_Launch/Galileo_factsheet_20111003.pdf


http://download.esa.int/docs/Galileo_IOV_Launch/Galileo_factsheet_20111003.pdf

http://download.esa.int/docs/Galileo_IOV_Launch/Galileo_factsheet_20111003.pdf


GAGANThe Indian initiative

GPS And Geo-AugmentedNavigation systemRegional satellite basednavigationIndian RegionalNavigational SatelliteSystemImproves the accuracy ofthe GNSS receivers byproviding referencesignalsWork likely to becompleted by 2014

Figure: Some setbacks in theGAGAN programme

www.oosa.unvienna.org/pdf/icg/2008/expert/2-3.pdf


www.oosa.unvienna.org/pdf/icg/2008/expert/2-3.pdf


How does a GPS look like?

Three segments

Control segment

Space segment

User segment

Figure: Src: http://infohost.nmt.edu/



The Space SegmentConcerns with satellites

Satellite constellation

24 satellites (30 on date)Downlinks

coded ranging signalsposition informationatmosphericinformationalmanac

Maintains accurate timeusing on-board Cesiumand Rubidium clocks

Runs small processes onthe on-board computer

Figure: Src: www.kowoma.de



The Control SegmentSatellite control and information uplink

GPS Master controlstation at ColoradoSprings, Colorado

Master control station ishelped by differentmonitoring stationsdistributed across theworld

These stations track thesatellites and keep onregularly updating theinformation on thesatellites. Several updatesper day.

Control Stations

Colorado Springs (MCS)

Ascension

Diego Garcia

Hawaii

Kwajalein

What they do?

Satellite orbit and clockperformance parameters

Heath status

Requirement ofrepositioning



User segment

Real time positioning withreceiving units

Hand-held receivers orantenna based receivers

Calculation of positionusing “Resection”



GPS SignalsChoices and contents

Atmosphere - refractionIonosphere: biggestsource of disturbanceGPS Signals needminimum disturbanceand minimum refraction

Signals

Basic frequency (f0): 10.23MHz

L1 frequency (154f0):1575.42 MHz

L2 frequency (120f0):1227.60 MHz

C/A code ( f0

10 ): 1.023 MHz

P(Y) code (f0): 10.23 MHz

Another civilian code L5 isgoing to be there soon

L1 and L2 frequencies are known as carriers. The C/A and P(Y) carry the navigation message from the satellite to

the reciever. The codes are modulated onto the carriers. In advanced receivers, L1 and L2 frequencies can be used

to eliminate the iospheric errors from the data.



GPS SignalsReceivers and Policies

Basic receiver: L1 carrier and C/A code (for generalpublic)

Dual frequency receiver: L1 and L2 carriers and C/A code(for advanced researchers)

Military receivers: L1 + L2 carriers and C/A + P(Y) codes(for military purposes)

GPS and other GNSS policies are based on various scenarios atinternational levels



GPS SignalsInformation available to the reciever

Pseudoranges (?)C/A code available to the civilian userP1 and P2 codes available to the military user

Carrier phasesL1, L2 mainly used for geodesy and surveying

Range-rate: Doppler

Information is available in receiver dependent and receiverindependent files (RINEX). Advanced receivers come withadditional software to download information from them tothe computer in proprietary and RINEX (RecieverINdependent EXchange) formats.ftp://ftp.unibe.ch/aiub/rinex/rinex300.pdf


ftp://ftp.unibe.ch/aiub/rinex/rinex300.pdf


Range informationCode Pseudorange

True Range (ρ): Geometric distance between the satelliteand the receiver

Time taken to travel = Receiver time at the time ofreception - Satellite time at time of emission of the signal

∆t = tr − t s

tr = trGPS + δr , t s = t sGPS + δs

Pseudorange (P): ρ distorted by atmosphericdisturbances, clock biases and delays

Thus, true range is given by,

ρ = P − c · (δr − δs) = P − c · δsr



Mathematical model - code basedReceiver watching multiple satellites

Receiver coordinate: (X ,Y ,Z) and satellite coordinates for msatellites: (X i,Y i,Z i)

Initial estimate of receiver position: (X0,Y0,Z0)

True range

ρj(t) =√

(X j(t)− X )2 + (Y j(t)− Y )2 + (Z j(t)− Z)2 = f j(X ,Y ,Z)

The “adjusted coordinates”: X = X0 + ∆X , Y = Y0 + ∆Y ,Z = Z0 + ∆Z

Thus f j(X ,Y ,Z) =

f j(X0,Y0,Z0)+∂f j(X0,Y0,Z0)

∂X0∆X +

∂f j(X0,Y0,Z0)

∂Y0∆Y +

∂f j(X0,Y0,Z0)

∂Z0∆Z


The pseudo-range equations for the m satellites

Pj(t) = ρj(t) + c[δr(t)− δj(t)]

Therefore we have:

Pj(t) = f j

(X0, Y0, Z0)+∂f j(X0, Y0, Z0)

∂X0∆X +

∂f j(X0, Y0, Z0)

∂Y0∆Y +

∂f j(X0, Y0, Z0)

∂Z0∆Z + c[δr (t)− δj

(t)]

Take all unknowns to one side

Pj(t)− f j

(X0, Y0, Z0)+cδj(t) =

∂f j(X0, Y0, Z0)

∂X0∆X +

∂f j(X0, Y0, Z0)

∂Y0∆Y +

∂f j(X0, Y0, Z0)

∂Z0∆Z +c ·δr (t)

Put,

L =

P1(t)− f 1(X0,Y0,Z0) + cδ1(t)P2(t)− f 2(X0,Y0,Z0) + cδ2(t)

. . .Pm(t)− f m(X0,Y0,Z0) + cδm(t)

,∆X =

∆X∆Y∆Z

cδr(t)

A =

∂f 1(X0,Y0,Z0)

∂X0

∂f 1(X0,Y0,Z0)∂Y0

∂f 1(X0,Y0,Z0)∂Z0

1∂f 2(X0,Y0,Z0)

∂X0

∂f 2(X0,Y0,Z0)∂Y0

∂f 2(X0,Y0,Z0)∂Z0

1

. . ....

... . . .∂f m(X0,Y0,Z0)

∂X0

∂f m(X0,Y0,Z0)∂Y0

∂f m(X0,Y0,Z0)∂Z0

1

,V =

v1

v2...

vm

Use the arrangement:

V = A ·∆X −∆L

To obtain,∆X = (AT A)−1AT ∆L


Mathematical model - code basedGeneralized model

Adapted from Leick (2004),

PjL1,CA(t) = ρj(t) + c∆δ

jr(t) + I j

L1,CA + r j + T j + djL1,CA + εL1,CA

PjL1(t) = ρj(t) + c∆δ

jr(t) + I j

L1 + r j + T j + djL1 + εL1

PjL2(t) = ρj(t) + c∆δ

jr(t) + I j

L2 + r j + T j + djL2 + εL2

I j : Ionospheric error

r j : Relativistic error

T j : Tropospheric error

dj : Hardware delay -receiver, satellite,multipath (combination)

ε: Receiver noise



Mathematical model - carrier phase basedSingle receiver watching multiple satellites

The basic ranging equation is given as:

λφj(t) = ρj(t) + c(δr(t)− δj(t)) + λN j

Using Taylor’s series, we have

λφj(t) = f j(X0) +∂f j

∂X

∣∣∣∣X=X0

∆X + c(δr(t)− δj(t)) + λN j

All unknowns to one side,

λφj(t)− f j(X0) + cδj(t) =∂f j

∂X

∣∣∣∣X=X0

∆X + cδr(t) + λN j

Number of unknowns: (a) X: 3, (b) δr(t): 1 and (c) N j : Differsfor each satellite. For a single instant and 4 satellites, thenumber of unknowns is: 8



Mathematical model - carrier phase basedSingle receiver watching multiple satellites

Epoch-ID ∆X Bias Int.Amb. No.Var. No.Eqns

1 3 +1 4 8 42 3 +1 4 9 83 3 +1 4 10 124 3 +1 4 11 165 3 +1 4 12 20

Table: Table showing the number of unknowns and equations as theepochs progress

Home Work: Compute the matrix notation for thephase-based model for at least 3-epochs and 4 satellites.



Mathematical model - Advanced carrier phase basedSingle receiver watching multiple satellites

Suppose that f1 and λ1 denote the frequency and wavelengthof L1 carrier and f2 and λ2 denote the frequency of L2 carrrier.The carrier phase model is given by

φjL1(t) =

f1

cρj(t)+

cλ1

∆δjr(t)−I j

L1(t)+f1

cT j(t)+Rj+dj

r,L1(t)+N jL1+wL1+εr,L1

φjL2(t) =

f2

cρj(t)+

cλ2

∆δjr(t)−I j

L2(t)+f2

cT j(t)+Rj+dj

L2(t)+N jL2+wL2+εr,L2

T j : Tropospheric error

djr,L1: Hardware error

I jL1/L2: Ionospheric error

Rj : Relativity error

NL1/L2: Integer ambiguity

wL1/L2: Phase winding error

εr : Receiver noise



Advanced methods of positioning

Differential and Relative Positioning

Rapid static

Stop and Go

Real time kinematic (RTK)

RTK is difficult to implement in India for civilians owing to thedefence restrictions.



Sources of errors

Receiver clock bias

Hardware error

Receiver Noise

Phase - wind up

Multipath error

Ionospheric error

Troposheric error

Antenna shift

Satellite drift



Status of GPS Surveying

10-12 yrs earlierFor specialistsNational andcontinentalnetworksImportance ofaccuracyAbsence of goodGUI

5 yrs agoOnly post processingBetter and smallerreceiversImprovement inpositioning methodsBetter software

Today

Demand for higher accuraciesand better models

Speed, ease-of-use, advancedfeatures are key requirements

Surveying to centimeteraccuracy

Automated and user friendlysoftware

Code measurements to cm level,phase measurements to mmlevel

Better atmospheric models

On its way to becoming astandard surveying tool


Intro Data GNSS Apps&SW Resources Acknowledgements Applications SW

Outline

1 Basic Concepts


3 Introducing GNSS

4 Applications and SoftwareApplicationsSoftware and Hardware

5 Resources

6 Acknowledgements



Applications of GPS

Civil Applications

Aviation

Agriculture

Disaster Mitigation

Location based services

Mobile

Rail

Road Navigation

Shipment tracking

Surveying and Mapping

Time based systems

Military Applications

Soldier guidance forunfamiliar terrains

Guided missiles



GPSPartial list of GPS makes

GARMIN

Leica

LOWRANCE

TomTom

Trimble

Mio

Navigon



Software for GPS

Commercial

Leica Geooffice

Leica GNSS Spider

Trimble EZ Office

Garmin CommunicatorPlugin

University Based

GAMIT

BERNESE



Outline

1 Basic Concepts


3 Introducing GNSS


5 Resources

6 Acknowledgements



Resources

www.gps.gov

www.kowoma.de

www.gmat.unsw.edu.au/snap/gps/about_gps.htm

Book: Alfred Leick – GPS Satellite Surveying

Book: Jan Van Sickle – GPS for Land Surveyors

Book: Hofmann-Wellehof et al – Global PositioningSystem: Theory and Practice

Book: Joel McNamara – GPS For Dummies


www.gps.gov

www.kowoma.de

www.gmat.unsw.edu.au/snap/gps/about_gps.htm


Outline

1 Basic Concepts


3 Introducing GNSS


5 Resources

6 Acknowledgements



Acknowledgements

Prof. Onkar Dikshit, Prof., IIT-K

P. K. Kelkar Library, IIT-K

Thank you

For the hearing and the bearing!

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expert lecture on gps at uiet, csjm, kanpur

Technology

gnss gps basics gps

geospatial data early

geospatial data pictures

xn f2 f2 f2 x1 x2

x1 1x1 1y1 x2

x a2f x

given function

software applications