Presentation on theme: "Global Positioning System: what it is and how we use it for measuring the earth’s movement. April 21, 2011."— Presentation transcript:
1 Global Positioning System: what it is and how we use it for measuring the earth’s movement. April 21, 2011
2 ReferencesLectures from K. Larson’s “Introduction to GNSS”Strang, G. and K. Borre “Linear Algebra, Geodesy, and GPS”, Wellesley-Cambridge Press, 1997Blewitt, G., “Basics of the GPS Technique: Observation Equations”, in “Geodetic Applications of GPS”Lecture notes from G. Mattioli’ (comp.uark.edu/~mattioli/geol_4733/GPS_signals.ppt)
3 Basics of how it works Trilateration GPS positioning requires distance to 4 satellitesx,y,z,tEarth centered, Earth FixedWhy t?What are some of reasons why measuring distance is difficult?How do we know x, y, z, t of satellites?
4 GPS: Space segmentSeveral different types of GPS satellites (Block I, II, II A, IIR)All have atomic clocksStability of at least sec1 sec every ~300,000 yrsDynamics of orbit?Reference point?
5 Orbital Perturbations – (central force is 0.5 m/s2) SourceAccelerationm/s2Perturbation3 hrsTypeEarth oblateness (J2 )5 x 10-52 3 hrssecular + 6 hrSun & moon5 x 10-6hrssecular + 12hrHigher Harmonics3 x 10-7hrsVariousSolar radiation pressure1 x 10-7daysSecular + 3 hrOcean & earth tides1 x 10-9daysEarth albedo pressuredaysFrom K. Larson
6 GPS: Space Segment 24+ satellites in orbit Can see 4 at any time, any point on earthSatellites never directly over the polesFor most mid-latitude locations, satellites track mainly north-south
8 GPS Signal Satellite transmits on two carrier frequencies: L1 (wavelength=19 cm)L2 (wavelength=24.4 cm)Transmits 3 different codes/signalsP (precise) codeChip length=29.3 mC/A (course acquisition) codeChip length=293 mNavigation messageBroadcast ephemeris (satellite orbital parameters), SV clock corrections, iono info, SV healthSay something about PRN numbers?
9 GPS Signal Signal phase modulated: vs Amplitude modulation (AM) Frequency modulation (FM)
10 C/A and P code: PRN Codes PRN = Pseudo Random NoiseCodes have random noise characteristics but are precisely defined.A sequence of zeros and ones, each zero or one referred to as a “chip”.Called a chip because they carry no data.Selected from a set of Gold Codes.Gold codes use 2 generator polynomials.Three types are used by GPSC/A, P and Y
12 PRN Code propertiesHigh Autocorrelation value only at a phase shift of zero.Minimal Cross Correlation to other PRN codes, noise and interferers.Allows all satellites to transmit at the same frequency.PRN Codes carry the navigation message and are used for acquisition, tracking and ranging.
15 Schematic of C/A-code acquisition Since C/A-code is 1023 chips long and repeats every 1/1000 s, it is inherently ambiguous by 1 msec or ~300 km.
16 BASIC GPS MEASUREMENT: PSEUDORANGE Receiver measures difference between time of transmission and time of reception based on correlation of received signal with a local replicaThe measured pseudorange is not the true range between the satellite and receiver. That is what we clarify with the observable equation.
19 COMPARE PSEUDORANGE and CARRIER PHASE bias term N does not appear in pseudorangeionospheric delay is equal magnitude but opposite signtroposphere, geometric range, clock, and troposphere errors are the same in bothmultipath errors are different (phase multipath error much smaller than pseudorange)noise terms are different (factor of 100 smaller in phase data)
20 Atmospheric Effects Ionosphere (50-1000 km) Delay is proportional to number of electronsTroposphere (~16 km at equator, where thickest)Delay is proportional to temp, pressure, humidity.
22 Tropospheric effectsLowest region of the atmosphere – index of refraction = ~ at sea levelNeutral gases and water vapor – causes a delay which is not a function of frequency for GPS signalDry component contributes 90-97%Wet component contributes 3-10%Total is about 2.5 m forzenith to 25 m for 5 deg
23 Tropospheric effectsAt lower elevation angles, the GPS signal travels through more troposphere.
24 Dry Troposphere Delay Saastamoinen model: P0 is the surface pressure (millibars)f is the latitudeh is the receiver height (m)Hopfield model:hd is 43kmT0 is temperature (K)Mapping function:E – satellite elevation~2.5 m at sea level1 (zenith) – 10 (5 deg)
25 Wet Troposphere Correction Less predictable than dry part, modeled by:Saastamoinen model:Hopfield model:hw is 12kme0 is partial pressure of water vapor in mbarMapping function:0 – 80 cm
30 Ionosphere-free Pseudorange Ionosphere-free pseudoranges are more noisy than individual pseudoranges.
31 Multipath Reflected signals Can be mitigated by antenna design Multipath signal repeats with satellite orbits and so can be removed by “sidereal filtering”
32 Standard Positioning Error Budget Single FrequencyDouble FrequencyEphemeris Data2 mSatellite ClockIonosphere4 m0.5 – 1 mTroposphereMultipath0-2 mUERE5 m2-4 mUERE = User Equivalent Range Error
33 Intentional Errors in GPS S/A: Selective availabilityErrors in the satellite orbit or clockTurned off May 2, 2000With SA – 95% of points within 45 m radius. SA off, 95% of points within 6.3 m• Didn’t effect the precise measurements used for tectonics that much. Why not?
34 Intentional Errors in GPS A/S: Anti-spoofingEncryption of the P code (Y code)Different techniques for dealing with A/SRecover L1, L2 phaseCan recover pseudorange (range estimated using P-code)Generally worsens signal to noise ratio
45 Dilution of Precision (VDOP) Casey station, Antarctica, 66.3 latitudeWuhan, China, 30 lat
46 Positioning• Most basic: solve system of range equations for 4 unknowns, receiver x,y,z,tP1 = ( (x1 - x)2 + (y1 - y)2 + (z1 - z)2 )1/2 + ct - ct1…P4 = ( (x4 - x)2 + (y4 - y)2 + (z4 - z)2 )1/2 + ct - ct4Linearize problem by using a reference, or a priori, position for the receiverEven in advanced software, need a good a priori position to get solution.
47 Positioning vs. Differential GPS By differencing observations at two stations to get relative distance, many common errors sources drop out.The closer the stations, the better this worksBrings precision up to mm, instead of m.
48 Single Differencing • Removes satellite clock errors • Reduces troposphere and ionosphere delays to differential between two sites• Gives you relative distance between sites, not absolute position
49 Double Differencing • Receiver clock error is gone • Random errors are increased (e.g., multipath, measurement noise)• Double difference phase ambiguity is an integer
50 High precision GPS for Geodesy Use precise orbit products (e.g., IGS or JPL)Use specialized modeling softwareGAMIT/GLOBKGIPSY-OASISBERNESEThese software packages willEstimate integer ambiguitiesReduces rms of East component significantlyModel physical processes that effect precise positioning, such as those discussed so far plusSolid Earth TidesPolar Motion, Length of DayOcean loadingRelativistic effectsAntenna phase center variations
51 High precision GPS for Geodesy Produce daily station positions with 2-3 mm horizontal repeatability, 10 mm vertical.Can improve these stats by removing common mode error.