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Intro Data GNSS Apps&SW Resources Acknowledgements Global Navigation and Satellite System A basic introduction to concepts and applications Suddhasheel Ghosh Department of Civil Engineering Indian Institute of Technology Kanpur, Kanpur - 208016 Expert Lecture on March 21, 2012 at UIET, Kanpur1 / 52 shudh@IITK Introduction to GNSS
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Intro Data GNSS Apps&SW Resources Acknowledgements Outline 1 Basic Concepts Motivation Mathematical concepts 2 Collecting Geospatial Data 3 Introducing GNSS GPS Basics GPS based Math Models 4 Applications and Software Applications Software and Hardware 5 Resources 6 Acknowledgements2 / 52 shudh@IITK Introduction to GNSS
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Intro Data GNSS Apps&SW Resources Acknowledgements Motivation MathCon Outline 1 Basic Concepts Motivation Mathematical concepts 2 Collecting Geospatial Data 3 Introducing GNSS 4 Applications and Software 5 Resources 6 Acknowledgements3 / 52 shudh@IITK Introduction to GNSS
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Intro Data GNSS Apps&SW Resources Acknowledgements Motivation MathCon Where am I? Locate and navigate One of the most favourite questions of mankind Stone age Using markers like stone, trees and mountains to ﬁnd their way back Star age Pole star was a constant reminder of the direction Most world cultures refer to the Pole star in their literature Radio age Radio signals for navigation purposes Satellite age: Modern technology Use of satellites To understand GPS we need to revise some mathematical concepts.4 / 52 shudh@IITK Introduction to GNSS
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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 is given as (x − a)2 f (x) = f (a) + f (a)(x − a) + f (a) + ... 2!5 / 52 shudh@IITK Introduction to GNSS
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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 n independent variables, then the Jacobian matrix is given by: ∂f1 ∂f1 ∂f1 ∂x 1 ∂x2 ... ∂xn ∂f2 ∂f2 ∂f2 ∂x1 ∂x2 ... ∂xn J = . . . . . ... . . . . ∂fm ∂fm ∂fm ∂x1 ∂x2 ... ∂xn If F denotes the set of functions, and X denotes the set of variables, the Jacobian can be denoted by ∂F ∂X6 / 52 shudh@IITK Introduction to GNSS
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Intro Data GNSS Apps&SW Resources Acknowledgements Motivation MathCon Least squares adjustment Fundamental example Given Problem Suppose (x1 , y1 ), (x2 , y2 ), . . . , (xn , yn ) be n given points. It is required 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 form δ1 x1 1 y1 δ2 x2 1 y2 m . = . . · − . . . . . c . . .. δn xn 1 yn7 / 52 shudh@IITK Introduction to GNSS
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Intro Data GNSS Apps&SW Resources Acknowledgements Motivation MathCon Least squares adjustment Fundamental example continued To determine m and c we use the formula: T −1 T x1 1 x1 1 x1 1 y1 x2 1 x2 1 x2 1 y2 m = . . . . . . . . . . . c . . . . . . . . .. xn 1 xn 1 xn 1 yn8 / 52 shudh@IITK Introduction to GNSS
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Intro Data GNSS Apps&SW Resources Acknowledgements Motivation MathCon Least squares adjustment For a general equation The set of equations is represented by Lb : set of observations, La = F(Xa ) X : set of parameters. Using Taylor’s series expansion, X0 : initial ∂F estimate of the Lb + V = F(X0 )|Xa =X0 + (Xa − X0 ) + . . . ∂Xa Xa =X0 parameters L0 : initial This can be represented as estimate of the observations. V = A∆X − ∆L V : correction which can be solved by applied to Lb La : adjusted ∆X = (AT A)−1 AT L observations. If case of weighted observations (P is the weight matrix), ∆X = (AT PA)−1 AT PL9 / 52 shudh@IITK Introduction to GNSS
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Intro Data GNSS Apps&SW Resources Acknowledgements Motivation MathCon Euclidean distance Formula for ﬁnding distance between two points If p1 (x1 , y1 , z1 ) and p2 (x2 , y2 , z2 ) be two different points in 3D space, then the distance between the two is given by: d(p1 , p2 ) = (x1 − x2 )2 + (y1 − y2 )2 + (z1 − z2 )210 / 52 shudh@IITK Introduction to GNSS
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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 Acknowledgements11 / 52 shudh@IITK Introduction to GNSS
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Intro Data GNSS Apps&SW Resources Acknowledgements Collecting Geospatial Data Early: Chains, tapes and sextants Mid: Theodolites, auto levels Modern: EDM, GNSS12 / 52 shudh@IITK Introduction to GNSS
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Intro Data GNSS Apps&SW Resources Acknowledgements Older methods of collecting geospatial data Pictures of some instruments13 / 52 shudh@IITK Introduction to GNSS
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Intro Data GNSS Apps&SW Resources Acknowledgements Coordinates of a point How to ﬁnd them? Figure: A typical resection problem in surveying. Given coordinates of the known points Ci , ﬁnd the coordinates of the unknown point P14 / 52 shudh@IITK Introduction to GNSS
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Intro Data GNSS Apps&SW Resources Acknowledgements The resection problem Issues of accuracy and geometry Resection problem requires the measurement of angles and distances All measurements made through theodolites, auto levels, EDMs etc contain errors Requirement for minimizing errors: The control points should be well distributed spatially.15 / 52 shudh@IITK Introduction to GNSS
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Intro Data GNSS Apps&SW Resources Acknowledgements Distance between objects How to ﬁnd it? What is the distance between the chalk and the blackboard? How to ﬁnd the distance between a ball and a chair? How to ﬁnd the distance between an aeroplane and the ground?16 / 52 shudh@IITK Introduction to GNSS
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Intro Data GNSS Apps&SW Resources Acknowledgements Distance between objects How to ﬁnd it? What is the distance between the chalk and the blackboard? How to ﬁnd the distance between a ball and a chair? How to ﬁnd the distance between an aeroplane and the ground? 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 therefore approximated by a mathematical surface.16 / 52 shudh@IITK Introduction to GNSS
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Intro Data GNSS Apps&SW Resources Acknowledgements The mathematical surface Datum and sphereoids Kalyanpur: Meaning of 127m above MSL?17 / 52 shudh@IITK Introduction to GNSS
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Intro Data GNSS Apps&SW Resources Acknowledgements The mathematical surface Datum and sphereoids Kalyanpur: Meaning of 127m above MSL? There is no sea in sight? What is mean sea level?17 / 52 shudh@IITK Introduction to GNSS
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Intro Data GNSS Apps&SW Resources Acknowledgements The mathematical surface Datum and sphereoids Kalyanpur: Meaning of 127m above MSL? There is no sea in sight? What is mean sea level? Geoid: The equipotential surface of gravity near the surface of the earth MSL - Mean sea level (an approximation to the Geoid Figure: Src: Ellipsoid / spheroid: http://www.dqts.net/wgs84.htm approximation to the MSL Mathematical surface: DATUM17 / 52 shudh@IITK Introduction to GNSS
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Intro Data GNSS Apps&SW Resources Acknowledgements World Geodetic System One 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 1 Inverse ﬂattening: f = 298.257223563 Complete description given in the WGS84 Manual http://www.dqts.net/files/wgsman24.pdf18 / 52 shudh@IITK Introduction to GNSS
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Intro Data GNSS Apps&SW Resources Acknowledgements Parallels and Meridians Figure: Latitudes and longitudes Figure: Measurement of angles19 / 52 shudh@IITK Introduction to GNSS
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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 Paper20 / 52 shudh@IITK Introduction to GNSS
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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 Conical Area preserving Cylindrical Angle preserving - Azimuthal conformal There are guidelines on how to chose a map projection for your map20 / 52 shudh@IITK Introduction to GNSS
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Intro Data GNSS Apps&SW Resources Acknowledgements Universal transverse mercator A cylindrical and conformal projection The world divided into 60 zones - longitudewise Each zone of 6 degrees The developer surface is a cylinder placed tranverse The central meridian of the zone forms the central meridian of the projection UTM Zone for Kanpur: Figure: The UTM zone division 44N (Src: Wikipedia) Combination of projection and datum: UTM/WGS84 and Zone 44N21 / 52 shudh@IITK Introduction to GNSS
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Intro Data GNSS Apps&SW Resources Acknowledgements Basics GPSmodel Outline 1 Basic Concepts 2 Collecting Geospatial Data 3 Introducing GNSS GPS Basics GPS based Math Models 4 Applications and Software 5 Resources 6 Acknowledgements22 / 52 shudh@IITK Introduction to GNSS
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Intro Data GNSS Apps&SW Resources Acknowledgements Basics GPSmodel NAVSTAR The US-based initiative Landmarks 1978: GPS satellite launched 1983: Ronald Raegan: GPS for TRANSIT: The Naval public Navigation System 1990-91: Gulf war: GPS used for NAVSTAR: ﬁrst time Navigation 1993: Initial operational Principally designed capability: 24 satellites for military action 1995: Full operational capability 2000: Switching off selective availability23 / 52 shudh@IITK Introduction to GNSS
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Intro Data GNSS Apps&SW Resources Acknowledgements Basics GPSmodel GLONASS The Russian initiative Global Navigation Satellite System First satellite launched: 1982 Orbital period: 11 hrs 15 minutes Number of satellites: 24 Distance of satellite from earth: 19100 km Civilian availability: 200724 / 52 shudh@IITK Introduction to GNSS
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Intro Data GNSS Apps&SW Resources Acknowledgements Basics GPSmodel GALILEO The 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 equator Src: http://download.esa.int/docs/Galileo_IOV_ Launch/Galileo_factsheet_20111003.pdf25 / 52 shudh@IITK Introduction to GNSS
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Intro Data GNSS Apps&SW Resources Acknowledgements Basics GPSmodel GAGAN The Indian initiative GPS And Geo-Augmented Navigation system Regional satellite based navigation Indian Regional Navigational Satellite System Improves the accuracy of the GNSS receivers by providing reference Figure: Some setbacks in the signals GAGAN programme Work likely to be completed by 2014 www.oosa.unvienna.org/pdf/icg/2008/expert/2-3.pdf26 / 52 shudh@IITK Introduction to GNSS
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Intro Data GNSS Apps&SW Resources Acknowledgements Basics GPSmodel How does a GPS look like?27 / 52 shudh@IITK Introduction to GNSS
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Intro Data GNSS Apps&SW Resources Acknowledgements Basics GPSmodel How does a GPS look like? Three segments Control segment Space segment User segment Figure: Src: http://infohost.nmt.edu/27 / 52 shudh@IITK Introduction to GNSS
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Intro Data GNSS Apps&SW Resources Acknowledgements Basics GPSmodel The Space Segment Concerns with satellites Satellite constellation 24 satellites (30 on date) Downlinks coded ranging signals position information atmospheric information almanac Maintains accurate time using on-board Cesium and Rubidium clocks Figure: Src: www.kowoma.de Runs small processes on the on-board computer28 / 52 shudh@IITK Introduction to GNSS
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Intro Data GNSS Apps&SW Resources Acknowledgements Basics GPSmodel The Control Segment Satellite control and information uplink GPS Master control Control Stations station at Colorado Colorado Springs (MCS) Springs, Colorado Ascension Master control station is Diego Garcia helped by different Hawaii monitoring stations Kwajalein distributed across the world What they do? These stations track the satellites and keep on Satellite orbit and clock regularly updating the performance parameters information on the Heath status satellites. Several updates Requirement of per day. repositioning29 / 52 shudh@IITK Introduction to GNSS
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Intro Data GNSS Apps&SW Resources Acknowledgements Basics GPSmodel User segment Real time positioning with receiving units Hand-held receivers or antenna based receivers Calculation of position using “Resection”30 / 52 shudh@IITK Introduction to GNSS
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Intro Data GNSS Apps&SW Resources Acknowledgements Basics GPSmodel GPS Signals Choices and contents Signals Basic frequency (f0 ): 10.23 MHz Atmosphere - refraction L1 frequency (154f0 ): Ionosphere: biggest 1575.42 MHz source of disturbance L2 frequency (120f0 ): GPS Signals need 1227.60 MHz minimum disturbance f0 C/A code ( 10 ): 1.023 MHz and minimum refraction P(Y) code (f0 ): 10.23 MHz Another civilian code L5 is going 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.31 / 52 shudh@IITK Introduction to GNSS
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Intro Data GNSS Apps&SW Resources Acknowledgements Basics GPSmodel GPS Signals Receivers and Policies Basic receiver: L1 carrier and C/A code (for general public) 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 at international levels32 / 52 shudh@IITK Introduction to GNSS
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Intro Data GNSS Apps&SW Resources Acknowledgements Basics GPSmodel GPS Signals Information available to the reciever Pseudoranges (?) C/A code available to the civilian user P1 and P2 codes available to the military user Carrier phases L1, L2 mainly used for geodesy and surveying Range-rate: Doppler Information is available in receiver dependent and receiver independent ﬁles (RINEX). Advanced receivers come with additional software to download information from them to the computer in proprietary and RINEX (Reciever INdependent EXchange) formats. ftp://ftp.unibe.ch/aiub/rinex/rinex300.pdf33 / 52 shudh@IITK Introduction to GNSS
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Intro Data GNSS Apps&SW Resources Acknowledgements Basics GPSmodel Range information Code Pseudorange True Range (ρ): Geometric distance between the satellite and the receiver Time taken to travel = Receiver time at the time of reception - Satellite time at time of emission of the signal ∆t = tr − t s tr = trGPS + δr , t s = t sGPS + δ s Pseudorange (P): ρ distorted by atmospheric disturbances, clock biases and delays Thus, true range is given by, ρ = P − c · (δr − δ s ) = P − c · δr s34 / 52 shudh@IITK Introduction to GNSS
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Intro Data GNSS Apps&SW Resources Acknowledgements Basics GPSmodel Mathematical model - code based Receiver watching multiple satellites Receiver coordinate: (X , Y , Z ) and satellite coordinates for m satellites: (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 ) ∂f j (X0 , Y0 , Z0 ) f j (X0 , Y0 , Z0 )+ ∆X + ∆Y + ∆Z ∂X0 ∂Y0 ∂Z035 / 52 shudh@IITK Introduction to GNSS
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Put, P 1 (t) − f 1 (X0 , Y0 , Z0 ) + cδ 1 (t) ∆X P 2 (t) − f 2 (X0 , Y0 , Z0 ) + cδ 2 (t) , ∆X = ∆Y L= ... ∆Z P m (t) − f m (X0 , Y0 , Z0 ) + cδ m (t) cδr (t) ∂f 1 (X0 ,Y0 ,Z0 ) ∂f 1 (X0 ,Y0 ,Z0 ) ∂f 1 (X0 ,Y0 ,Z0 ) 1 ∂X0 ∂f 2 (X ,Y ,Z ) ∂Y0 ∂Z0 v1 ∂f 2 (X0 ,Y0 ,Z0 ) ∂f 2 (X0 ,Y0 ,Z0 ) 0 0 0 1 v2 ∂X0 ∂Y0 ∂Z0A= ,V = . . . . . . ... . . . . . . ∂f m (X0 ,Y0 ,Z0 ) ∂f m (X0 ,Y0 ,Z0 ) ∂f m (X0 ,Y0 ,Z0 ) vm ∂X0 ∂Y0 ∂Z0 1Use the arrangement: V = A · ∆X − ∆LTo obtain, ∆X = (A T A)−1 A T ∆L
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Intro Data GNSS Apps&SW Resources Acknowledgements Basics GPSmodel Mathematical model - code based Generalized model Adapted from Leick (2004), j j j j PL1,CA (t) = ρj (t) + c∆δr (t) + IL1,CA + r j + T j + dL1,CA + εL1,CA j j j j PL1 (t) = ρj (t) + c∆δr (t) + IL1 + r j + T j + dL1 + εL1 j j j j PL2 (t) = ρj (t) + c∆δr (t) + IL2 + r j + T j + dL2 + εL2 I j : Ionospheric error d j : Hardware delay - r j : Relativistic error receiver, satellite, multipath (combination) T j : Tropospheric error ε: Receiver noise38 / 52 shudh@IITK Introduction to GNSS
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Intro Data GNSS Apps&SW Resources Acknowledgements Basics GPSmodel Mathematical model - carrier phase based Single receiver watching multiple satellites The basic ranging equation is given as: λφj (t) = ρj (t) + c(δr (t) − δ j (t)) + λN j Using Taylor’s series, we have ∂f j λφj (t) = f j (X0 ) + ∆X + c(δr (t) − δ j (t)) + λN j ∂X X=X0 All unknowns to one side, ∂f j λφj (t) − f j (X0 ) + cδ j (t) = ∆X + cδr (t) + λN j ∂X X=X0 Number of unknowns: (a) X: 3, (b) δr (t): 1 and (c) N j : Differs for each satellite. For a single instant and 4 satellites, the number of unknowns is: 839 / 52 shudh@IITK Introduction to GNSS
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Intro Data GNSS Apps&SW Resources Acknowledgements Basics GPSmodel Mathematical model - carrier phase based Single receiver watching multiple satellites Epoch-ID ∆X Bias Int.Amb. No.Var. No.Eqns 1 3 +1 4 8 4 2 3 +1 4 9 8 3 3 +1 4 10 12 4 3 +1 4 11 16 5 3 +1 4 12 20 Table: Table showing the number of unknowns and equations as the epochs progress Home Work: Compute the matrix notation for the phase-based model for at least 3-epochs and 4 satellites.40 / 52 shudh@IITK Introduction to GNSS
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Intro Data GNSS Apps&SW Resources Acknowledgements Basics GPSmodel Mathematical model - Advanced carrier phase based Single receiver watching multiple satellites Suppose that f1 and λ1 denote the frequency and wavelength of L1 carrier and f2 and λ2 denote the frequency of L2 carrrier. The carrier phase model is given by j f1 j c j j f1 j j φL1 (t) = ρ (t)+ ∆δr (t)−IL1 (t)+ T j (t)+R j +dr,L1 (t)+NL1 +wL1 +εr,L1 c λ1 c j f2 j c j j f2 j j φL2 (t) = ρ (t)+ ∆δr (t)−IL2 (t)+ T j (t)+R j +dL2 (t)+NL2 +wL2 +εr,L2 c λ2 c T j : Tropospheric error NL1/L2 : Integer ambiguity j wL1/L2 : Phase winding error dr,L1 : Hardware error j εr : Receiver noise IL1/L2 : Ionospheric error R j : Relativity error41 / 52 shudh@IITK Introduction to GNSS
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Intro Data GNSS Apps&SW Resources Acknowledgements Basics GPSmodel 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 the defence restrictions.42 / 52 shudh@IITK Introduction to GNSS
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Intro Data GNSS Apps&SW Resources Acknowledgements Basics GPSmodel Sources of errors Receiver clock bias Hardware error Receiver Noise Phase - wind up Multipath error Ionospheric error Troposheric error Antenna shift Satellite drift43 / 52 shudh@IITK Introduction to GNSS
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Intro Data GNSS Apps&SW Resources Acknowledgements Basics GPSmodel Status of GPS Surveying 10-12 yrs earlier Today For specialists Demand for higher accuracies National and and better models continental networks Speed, ease-of-use, advanced Importance of features are key requirements accuracy Surveying to centimeter Absence of good accuracy GUI Automated and user friendly 5 yrs ago software Only post processing Code measurements to cm level, Better and smaller phase measurements to mm receivers level Improvement in Better atmospheric models positioning methods Better software On its way to becoming a standard surveying tool44 / 52 shudh@IITK Introduction to GNSS
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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 Software Applications Software and Hardware 5 Resources 6 Acknowledgements45 / 52 shudh@IITK Introduction to GNSS
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Intro Data GNSS Apps&SW Resources Acknowledgements Applications SW Applications of GPS Civil Applications Military Applications Aviation Soldier guidance for Agriculture unfamiliar terrains Disaster Mitigation Guided missiles Location based services Mobile Rail Road Navigation Shipment tracking Surveying and Mapping Time based systems46 / 52 shudh@IITK Introduction to GNSS
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Intro Data GNSS Apps&SW Resources Acknowledgements Applications SW GPS Partial list of GPS makes GARMIN Leica LOWRANCE TomTom Trimble Mio Navigon47 / 52 shudh@IITK Introduction to GNSS
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Intro Data GNSS Apps&SW Resources Acknowledgements Applications SW Software for GPS Commercial University Based Leica Geoofﬁce GAMIT Leica GNSS Spider BERNESE Trimble EZ Ofﬁce Garmin Communicator Plugin48 / 52 shudh@IITK Introduction to GNSS
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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 Acknowledgements49 / 52 shudh@IITK Introduction to GNSS
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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 Positioning System: Theory and Practice Book: Joel McNamara – GPS For Dummies50 / 52 shudh@IITK Introduction to GNSS
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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 Acknowledgements51 / 52 shudh@IITK Introduction to GNSS
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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 license See www.creativecommons.org52 / 52 shudh@IITK Introduction to GNSS
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