An Introduction to GPS

Transcription

1 An Introduction to GPS You are here The GPS system: what is GPS Principles of GPS: how does it work Processing of GPS: getting precise results Yellowstone deformation: an example

2 What is GPS? System to provide location on Earth s surface Developed by Department of Defense Consists of three elements: Control segment Space segment User segment

3 Control Segment Global system of tracking stations Monitor GPS satellites Transmit corrections for: clock offsets satellite ephemerides

4 Space Segment Constellation of 24 satellites Orbital period: 12 hours Altitude: 20,200 km Orbital plane: 55º to equator Satellite components: radio transceiver atomic clocks computer ancillary equipment

5 User Segment GPS receivers use broadcast satellite signals Calculate position, velocity, time Applications: Navigation Surveying/Mapping Geodetic studies of ground deformation Earth rotation parameters Atmospheric studies of troposphere GIS

6 Precision Precision depends on equipment and computation strategy Handheld Receivers Handheld Receivers with Differential GPS Receivers with Differential GPS Receivers with Phase measurements Differential GPS Receivers with Phase measurements Differential GPS Double-Frequency m m 1-5 m.1-1 m m (1-10 mm)

7 How GPS Works Calculate distance from receiver to satellite Solve for position (x,y,x) and time t Basic equation: d = v t Distance = Rate time d

8 Satellite Broadcast Signals Two microwave carrier signals: L1 signal MHz 19 cm wavelength Navigation message C/A code P code L2 signal MHz 24 cm wavelength Navigation message P code (encrypted) Two codes modulate signals: C/A code 300 m wavelength Repeats every millisecond P code 30 m wavelength Repeats after 267 days

9 Distance Calculations Code tracking: Compare satellite and receiver codes Signal travel time is code offset Precision ~1% code periods 30 cm for P 3 m for C/A REC SAT Phase tracking: Measure phase of L1 and L2 signal Count integer number of wavelengths Precision ~1% of carrier wavelength 2 mm for L1 2.4 mm for L2

10 Electromagnetic Signal Propagation Propagation of wave described by: y(t) = Acos(ωt kx + φ) y(t) = amplitude at time t A = amplitude ω = radian frequency = 2πf k = wave number x = distance φ = phase = fraction of cycle λ = wavelength c = velocity For distance calculations, we need fλ = c

11 Code Ranging Range = distance from satellite to receiver Pseudo-range = Range with errors 1. ρ = cδt ρ = range c = speed of light Δt = travel time 2. R = cδt + c(dt r dt s + dt p ) R = code distance dt r = receiver clock error dt s = satellite clock error dt p = other errors

12 Phase Ranging φ = ft φ b =φ s (t s ) φ r (t r ) φ r (t r ) =φ s (t s ) + fδt φ b = fδt φ= phase (fraction of periodic wave) f = frequency t = time φ b = carrier beat phase φ s (t s ) = satellite signal phase φ r (t r ) = receiver signal phase Receiver phase is offset of satellite 7. φ b = f c ρ Substitute range from eqn 1 and add error term 8. φ b = f c ρ f (dt r dt s + dt p )

13 Phase Ranging Receiver measures fractional phase and integer count of cycles since signal was acquired φ tot = Fr(φ) + Int(φ) + N φ tot = φ meas + N N = integer cycles between receiver and satellite But φ tot = φ b, so combine with eqn f c ρ f (dt r dt s + dt p ) = φ meas + N Multiply eqn 11 by wavelength λ, recalling that fλ = c Then let phase distance Φ = -λφ meas : 12. Φ=ρ c(dt r dt s + dt p ) + λn

14 Error Sources Error Source Effects Correction Selective Availability Degraded broadcast signals Record and average data at GPS site over several hours Anti-Spoofing Encrypt P-code Use high-end receiver, phase data Ionospheric refraction Alters signal travel time Use both L1 and L2, differential GPS Tropospheric delay Alters signal travel time Troposphere models, differential GPS Ephemeris (satellite position) error Biases range calculations Use precise orbits, differential GPS Clock errors Biases range calculations Use differential GPS Multipath Reflect signals Better antenna, site locations

15 Satellite Geometry Receiver position requires 4 satellites Distribution of satellites will affect precision Satellite-receiver range defines a sphere Intersection of spheres defines position Good Geometry Bad Geometry

16 Differential GPS Requires at least two GPS stations Base station has fixed a priori position Distance between base station and 2nd station is baseline Short (<100 km) baselines will have common-mode errors

17 Single Differencing Recall equations for phase pseudo-range: 12. Φ=ρ c(dt r dt s + dt p ) + λn Taking difference of pseudo-range at one station at different times will eliminate cycle ambiguity term δφ=φ(t 1 ) Φ(t 2 ) = δρ c(δdt r δdt s + δdt p ) 13. Taking difference at two stations will give station baseline and eliminate satellite clock error ΔΦ = Φ 1 Φ 2 = Δρ c(δdt r + Δdt p ) + λδn 14. Taking difference at two satellites will give satellite baseline and eliminate receiver clock error Φ = ρ c( dt s + dt p ) + λ N 15.

18 Network Solutions Alternate equation for range in Earth-centered coordinates: ρ = R j i 16. s R R s = satellite radius vector r R r = radius receiver vector 17. R = x 2 + y 2 + z 2 So for i th station and j th satellite 18. ρ i j = [x j (t) x i ] 2 + [y j (t) y i ] 2 + [z j (t) z i ] 2 Station coordinates (x i, y i,z i ) are unknown,so use a priori coordinates 19. x i = x io +Δx i y i = y io +Δy i z i = z io +Δz i

19 Network Solutions Apply Taylor expansion to eqn 18: 20. ρ i j (t) = ρ io j (t) [x j (t) x i ] ρ io j (t) Δx i [y j (t) y i ] ρ io j (t) Δy i [z j (t) z i ] ρ io j (t) Δz i Substitute pseudo-range equations to obtain system of linear equations 21. L = Dx L = matrix with range expression D = design matrix with coordinates x = vector of unknowns For phase data, unknowns are: coordinate offsets (Δx i, Δy i, Δz i ) phase ambiguity N i receiver clock error Solve through least-squares methods

20 GPS Processing Automates computations of differential GPS Input: station data, orbit data Output: daily station positions

21 GPS Input Data GPS receivers record data in proprietary formats Data converted to RINEX (Receiver-Independent Exchange) format Types of RINEX files: OBS - observation file with time, range, phase data NAV - navigation file with satellite orbit data MET - meteorological data file

22 GPS Input Data Precise orbits downloaded from IGS ~2 week time delay before final orbits available

23 GPS Output Summary file of daily position solutions Binary file of solution data (used for additional computations)

24 GPS Station Velocities Velocities based on change in position over time Velocities assumed to be linear Solve for velocities in network with least-squares adjustment

25 GPS Application: Studying the Yellowstone Hotspot Yellowstone hotspot drives volcanism of YSRP Measure volcanic deformation at Yellowstone Plateau Measure regional tectonic deformation

26 Yellowstone GPS Network GPS campaigns Campaigns in 1987, 1989, 1991, 1993, 1995, 2000, sites Station velocity precision ~1 mm/yr Sites concentrated in YS Plateau Continuous GPS (CGPS) network Operation began in 1996 Presently has 36 stations + PBO Station velocity precision < 1 mm/yr Campaign network covers more area, but continuous solutions are more precise

27 Yellowstone Plateau Campaign GPS Velocities Plot horizontal and vertical velocities Track changes in deformation over time

28 Yellowstone Plateau CGPS Time Series Plot change in position over time Deformation not uniform over time

29 Northern Basin-Range and YSRP Velocity and Strain Fields Interpolated Velocity Field Interpolated Strain Rates Compile velocity data from multiple sources Characterize regional velocity field Identify concentrated deformation from strain field

30 GPS Velocities in Modeling Distribution of WUS GPS Sites WUS Interior Faults Combine GPS velocities and fault slip rates

31 GPS Velocities in Kinematic Modeling Regional GPS Velocity Field Log-Normalized Strain Field

32 GPS and Dynamic Modeling Geoid Calculate deviatoric stresses from lateral mass variations in lithosphere Mass variations in upper mantle from geoid Boundary stresses from outside model constrained by GPS data Deviatoric Stresses Boundary Stresses

33 GPS and Dynamic Modeling Total Deviatoric Stress Field from Variations in Geoid Effective Viscosity Geoid Model Estimate total deviatoric stress from geoid Combine stress and strain rates for effective lithosphere viscosity

34 Seismic Slip Contribution to Deformation Budget M>3 Earthquakes Seismic Moment Moment Ratios Earthquakes: ANSS Catalog Moment is measure of work done to produce deformation Seismic moment depends on fault slip and rupture area Total moment calculated from GPS strain rates Seismic slip on faults contributes <1% to total deformation Significant earthquakes make up seismic moment deficit