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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
Intro Data GNSS Apps&SW Resources Acknowledgements
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
2 / 52 shudh@IITK Introduction to GNSS
Intro Data GNSS Apps&SW Resources Acknowledgements Motivation MathCon
Outline
1 Basic ConceptsMotivationMathematical concepts
2 Collecting Geospatial Data
3 Introducing GNSS
4 Applications and Software
5 Resources
6 Acknowledgements
3 / 52 shudh@IITK Introduction to GNSS
Intro Data GNSS Apps&SW Resources Acknowledgements Motivation MathCon
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.
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Intro Data GNSS Apps&SW Resources Acknowledgements Motivation MathCon
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!+ . . .
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Intro Data GNSS Apps&SW Resources Acknowledgements Motivation MathCon
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
6 / 52 shudh@IITK Introduction to GNSS
Intro Data GNSS Apps&SW Resources Acknowledgements Motivation MathCon
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
7 / 52 shudh@IITK Introduction to GNSS
Intro Data GNSS Apps&SW Resources Acknowledgements Motivation MathCon
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
8 / 52 shudh@IITK Introduction to GNSS
Intro Data GNSS Apps&SW Resources Acknowledgements Motivation MathCon
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
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Intro Data GNSS Apps&SW Resources Acknowledgements Motivation MathCon
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
10 / 52 shudh@IITK Introduction to GNSS
Intro Data GNSS Apps&SW Resources Acknowledgements
Outline
1 Basic Concepts
2 Collecting Geospatial Data
3 Introducing GNSS
4 Applications and Software
5 Resources
6 Acknowledgements
11 / 52 shudh@IITK Introduction to GNSS
Intro Data GNSS Apps&SW Resources Acknowledgements
Collecting Geospatial Data
Early: Chains, tapes and sextants
Mid: Theodolites, auto levels
Modern: EDM, GNSS
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Intro Data GNSS Apps&SW Resources Acknowledgements
Older methods of collecting geospatial dataPictures of some instruments
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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
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Intro Data GNSS Apps&SW Resources Acknowledgements
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.
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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.
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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.
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Intro Data GNSS Apps&SW Resources Acknowledgements
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
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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
17 / 52 shudh@IITK Introduction to GNSS
Intro Data GNSS Apps&SW Resources Acknowledgements
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
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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
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Parallels and Meridians
Figure: Latitudes and longitudes Figure: Measurement of angles
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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
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Intro Data GNSS Apps&SW Resources Acknowledgements
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
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Intro Data GNSS Apps&SW Resources Acknowledgements
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)
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Intro Data GNSS Apps&SW Resources Acknowledgements Basics GPSmodel
Outline
1 Basic Concepts
2 Collecting Geospatial Data
3 Introducing GNSSGPS BasicsGPS based Math Models
4 Applications and Software
5 Resources
6 Acknowledgements
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Intro Data GNSS Apps&SW Resources Acknowledgements Basics GPSmodel
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
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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
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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
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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
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How does a GPS look like?
Three segments
Control segment
Space segment
User segment
Figure: Src: http://infohost.nmt.edu/
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How does a GPS look like?
Three segments
Control segment
Space segment
User segment
Figure: Src: http://infohost.nmt.edu/
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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
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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
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User segment
Real time positioning withreceiving units
Hand-held receivers orantenna based receivers
Calculation of positionusing “Resection”
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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.
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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
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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
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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
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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
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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
Intro Data GNSS Apps&SW Resources Acknowledgements Basics GPSmodel
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
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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
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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.
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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
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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.
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Sources of errors
Receiver clock bias
Hardware error
Receiver Noise
Phase - wind up
Multipath error
Ionospheric error
Troposheric error
Antenna shift
Satellite drift
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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
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Intro Data GNSS Apps&SW Resources Acknowledgements Applications SW
Outline
1 Basic Concepts
2 Collecting Geospatial Data
3 Introducing GNSS
4 Applications and SoftwareApplicationsSoftware and Hardware
5 Resources
6 Acknowledgements
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Intro Data GNSS Apps&SW Resources Acknowledgements Applications SW
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
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Intro Data GNSS Apps&SW Resources Acknowledgements Applications SW
GPSPartial list of GPS makes
GARMIN
Leica
LOWRANCE
TomTom
Trimble
Mio
Navigon
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Intro Data GNSS Apps&SW Resources Acknowledgements Applications SW
Software for GPS
Commercial
Leica Geooffice
Leica GNSS Spider
Trimble EZ Office
Garmin CommunicatorPlugin
University Based
GAMIT
BERNESE
48 / 52 shudh@IITK Introduction to GNSS
Intro Data GNSS Apps&SW Resources Acknowledgements
Outline
1 Basic Concepts
2 Collecting Geospatial Data
3 Introducing GNSS
4 Applications and Software
5 Resources
6 Acknowledgements
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Intro Data GNSS Apps&SW Resources 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
50 / 52 shudh@IITK Introduction to GNSS
Intro Data GNSS Apps&SW Resources Acknowledgements
Outline
1 Basic Concepts
2 Collecting Geospatial Data
3 Introducing GNSS
4 Applications and Software
5 Resources
6 Acknowledgements
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Intro Data GNSS Apps&SW Resources Acknowledgements
Acknowledgements
Prof. Onkar Dikshit, Prof., IIT-K
P. K. Kelkar Library, IIT-K
Thank you
For the hearing and the bearing!
Download, Share, Attribute, Non-Commercial, Non-Modifiable licenseSee www.creativecommons.org
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