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Introduction to GPS • “… it isn’t hard to operate a GPS receiver – matter of fact, most of them are so user-friendly you don’t need to know the first thing about GPS to make them work; that is, until they don’t. Getting coordinates from a GPS receiver is usually a matter of pushing buttons, but knowing what those coordinates are, and more importantly, what they aren’t, is more difficult.” Jan Van Sickle
Use of Satellites in Surveying • Started as early as Sputnik (1957) • Continued with other satellites • Measuring positions of satellites against background stars on photographs • Laser ranging • Used Doppler effect to determine velocity vector
TRANSIT Satellite • Navy Navigation Satellite System (NNSS) started in 1960s • Used the Doppler shift of the signal to determine velocity vector • Six satellites in low (1100 km) circular, polar orbits • One satellite every 90 minutes, need 2 passes • Susceptible to atmospheric drag and gravitational perturbations • Poor quality orbital parameters • Produces poor positions (by modern standards)
Brief History of GPS • Initial work in 1970s • Counselman, Shapiro, etc. (MIT) • First used for practical purposes in 1980s • Civilian use ahead of military use • Initial operational capability (IOC) July ‘93 • Full operational capability (FOC) 17 July 1995
GPS Overview • Consists of ~24 satellites • 4 satellites in 6 orbital planes • Planes inclined 55° • 20,000 km orbits • Periods of 11h 58m • Each satellite carries multiple atomic clocks
GPS Segments • User Segment • Military and civilian users • Space Segment • 24 satellite constellation • Control Segment • Worldwide network of stations
Space Segment • Block I • Block II • Block IIA (A – advanced) • Block IIR (R – replenishment) • Block IIF (F – Follow on) • Block III • See http://www.spaceandtech.com/spacedata/constellations/navstar-gps-block1_conspecs.shtml
Control Segment • Worldwide network of stations • Master Control Station – Colorado Springs, CO • Monitoring Stations – Ascension Island, Colorado Springs, Diego Garcia, Hawaii, Kwajalein • Other stations run by National Imagery and Mapping Agency (NIMA) • Ground Control Stations – Ascension, Diego Garcia, Kwajalein
USNO USNO AMC Data Flow Satellite Signal Timing data Control Timing Links Satellite Signal Master Control Station Data Monitor Station Time
Basic Idea • Broadcast signal has time embedded in it • Need to determine distance from satellite to receiver • One way uses distance = velocity * time • If time between when the signal is sent and when it is received is known, then distance from satellite is known • Using multiple distances, location can be determined (similar to trilateration)
GPS Signal Frequency • Fundamental Frequency 10.23MHz (f0) • 2 Carrier Frequencies • L1 (1575.42 MHz) (154 f0) • L2 (1227.60 MHz) (120 f0) • 3 Codes • Coarse Acquisition (C/A) 1.023 MHz • Precise (P) 10.23 MHz • Encrypted (Y) • Spread Spectrum • Harder to jam
Codes • Stream of binary digits known as bits or chips • Sometimes called pseudorandom noise (PRN) codes • Code state +1 and –1 • C/A code on L1 • P code on L1 and L2 • Phase modulated
C/A Code • 1023 binary digits • Repeats every millisecond • Each satellite assigned a unique C/A-code • Enables identification of satellite • Available to all users • Sometimes referred to as Standard Positioning Service (SPS) • Used to be degraded by Selective Availability (SA)
P Code • 10 times faster than C/A code • Split into 38 segments • 32 are assigned to GPS satellites • Satellites often identified by which part of the message they are broadcasting • PRN number • Sometimes referred to as Precise Positioning Service (PPS) • When encrypted, called Y code • Known as antispoofing (AS)
Future Signal • C/A code on L2 • 2 additional military codes on L1 and L2 • 3rd civil signal on L5 (1176.45 MHz) • Better accuracy under noisy and multipath conditions • Should improve real-time kinematic (RTK) surveys
Time Systems • Each satellite has multiple atomic clocks • Used for time and frequency on satellite • GPS uses GPS Time • Atomic time started 6 January 1980 • Not adjusted for leap seconds • Used for time tagging GPS signals • Coordinated Universal Time (UTC) • Atomic time adjusted for leap seconds to be within ±0.9 s of UT1 (Earth rotation time)
Pseudorange Measurements • Can use either C/A- or P-code • Determine time from transmission of signal to when the signal is received • Distance = time*speed of light • Since the position of the satellite is assumed to be known, a new position on the ground can be determined from multiple measurements
Carrier-phase Measurements • The range is the sum of the number of full cycles (measured in wavelengths) plus a fractional cycle • ρ = N*λ + n* λ • The fraction of a cycle can be measured very accurately • Determining the total number of full cycles (N) is not trivial • Initial cycle ambiguity • Once determined, can be tracked unless …
Cycle Slips • Discontinuity or jump in phase measurements • Changes by an integer number • Caused by signal loss • Obstructions • Radio interference • Ionospheric disturbance • Receiver dynamics • Receiver malfunction
How to Fix Cycle Slips? • Slips need to be detected and fixed • Triple differences can aid in cycle slips • Will only affect one of the series • Should stand out • Once detected, it can be fixed
GPS Errors and Biases • Satellite Errors • Potentially different for each satellite • Transmission Errors • Depends on path of signal • Receiver Errors • Potentially different for each receiver
Linear Combination • Errors and biases, which cannot be modeled, degrade the data • Receivers that are ‘close enough’ have very similar errors and biases • Data can be combined in ways to mitigate the effects of errors and biases
Linear Combination • Combine data from two receivers to one satellite • Should have same satellite and atmospheric errors • Differences should cancel these effects out
Linear Combination • Combine data from one receiver to two satellites • Should have same receiver and atmospheric errors • Differences should cancel these effects out
Linear Combination • Combine data from two receivers to two satellites • Should have same receiver, satellite and atmospheric errors • Differences should cancel out
Linear Combination • Can also combine the L1 and L2 data to eliminate the effects of the ionosphere • Ionosphere-free combination • L1 and L2 phases can also be combined to form the wide-lane observable • Long wavelength • Useful in resolving integer ambiguity
Two Reference Frames • Satellites operate in an inertial reference frame • Best way to handle the laws of physics • Receivers operate in a terrestrial reference frame • Sometimes called an Earth-centered, Earth-fixed (ECEF) frame • Best way to determine positions
Inertial Frame (Historically) • X axis through the vernal equinox • Y axis is 90° to the ‘east’ • Z axis through the Earth’s angular momentum axis • X-Y plane is the celestial equator • Z axis is through the celestial North Pole
Inertial Frame From http://celestrak.com/columns/v02n01/
Inertial Frame • Defined by the positions of distant radio sources called quasars • Realization from observations provided by Very Long Baseline Interferometry (VLBI) • e.g. International Celestial Reference Frame • Right-handed, Cartesian coordinate system
Terrestrial Frame (Historically) • X axis through the Greenwich meridian • Y axis is 90° to the east • Z axis through the Earth’s angular momentum axis • X-Y plane is the equator • Z axis is through the North Pole
Terrestrial Frame From http://www.nottingham.ac.uk/iessg/coord1.htm
Terrestrial Frame • Defined by the positions of reference points • Realization from observations provided by VLBI, SLR, and GPS • e.g. International Terrestrial Reference Frame • e.g. World Geodetic System (WGS)-84 • Right-handed, Cartesian coordinate system
Terrestrial Frame • Can transform from non-Cartesian (geodetic) coordinates to Cartesian coordinates • X = (N+h) cosφ cosλ • Y = (N+h) cosφ sinλ • Z = [ N(1-e2)+h] sin φ • Where N = a/sqrt(1-e2sin2 φ) • h = ellipsoid height • φ = latitude • λ = longitude
Transformation between Frames • Transformation is accomplished through rotation by Earth orientation parameters (EOPs) • Polar Motion (W) • Earth rotation (T) • Precession/nutation (P)(N) • xcts = (W)(T)(N)(P)xcis
Datums • Based on a reference ellipsoid • Semimajor axis (a) and semiminor axis (b) or semimajor axis (a) and flattening (f) • Needs to have a well defined center (origin) • Needs to have a well defined direction or axes (orientation)
Datums • Can be done with 8 parameters • 2 define the ellipsoid • 3 define the origin of the ellipsoid • 3 define the orientation of the ellipsoid
Datums • North American Datum 1927 (NAD27) • Clarke ellipsoid of 1866 • North American Vertical Datum 1929 (NAVD29) • North American Datum 1983 (NAD83) • GRS 1980 ellipsoid • North American Vertical Datum 1988 (NAVD88) • Even the last two have minimal input from GPS
Vertical Measurements • Vertical measurements from GPS are relative to the ellipsoid (ellipsoid height) • Not from the geoid or topography • To translate to other surfaces (either reference or real) requires additional information • Orthometric or geoid heights
Vertical Surfaces From http://www.butterworth.uk.com/geodesy.html
HARN • High Accuracy Reference Network (HARN) • Created by states, with federal assistance (NGS) • Predominantly based on GPS observations • Very accurate
Plane Coordinate Systems • Used over ‘local’ areas • State Plane Coordinate (SPC) systems • Results of projection onto surface • Lambert conic projection • Mercator (cylindrical) projection
Time Systems • Earth rotation time • Solar/sidereal • Dynamical • Barycenter/terrestrial • Atomic (off by integer seconds) • Coordinated Universal Time (UTC) • International Atomic Time (TAI) • GPS Time