112.215 Modern NavigationThomas Herring ([email protected]),MW 11:00-12:30 Room 54-820Ahttp://geoweb.mit.edu/~tah/12.21511/25/2009 12.215 Modern Naviation L18 2Review of last Class• GPS measurements– Tracking methods used in GPS (“codeless”tracking)– Basic geometry of orbits (discuss more later)– Specific details of the GPS signal structure211/25/2009 12.215 Modern Naviation L18 3Todayʼs class• GPS measurements– Basics of pseudorange measurements– Phase measurements (allow millimeter levelposition with GPS and cm in real-time)– Examine some GPS data.• Positioning modes• Dilution of precision numbers11/25/2009 12.215 Modern Naviation L18 4Basic measurement types• Substituting into the equation of the pseudorangeyields• ρkp is true range, and the ionospheric andatmospheric terms are introduced because thepropagation velocity is not c. € Pkp= (τk−τp) + (Δtk− Δtp)[ ]⋅ cPkp=ρkp+ (Δtk− Δtp) ⋅ c + IkpIonsphericdelay{+ AkpAtmosphericdelay{311/25/2009 12.215 Modern Naviation L18 5Basic measurement types• The equation for the pseudorange uses the true rangeand corrections applied for propagation delaysbecause the propagation velocity is not the in-vacuumvalue, c, 2.99792458x108 m/s• To convert times to distance c is used and thencorrections applied for the actual velocity not equalingc. (Discussed in later lectures)• The true range is related to the positions of the groundreceiver and satellite.• We also need to account for noise in measurements11/25/2009 12.215 Modern Naviation L18 6Pseudorange noise• Pseudorange noise (random and not so random errors inmeasurements) contributions:– Correlation function width:The width of the correlation isinversely proportional to the bandwidth of the signal.Therefore the 1MHz bandwidth of C/A produces a peak 1µsec wide (300m) compared to the P(Y) code 10MHzbandwidth which produces 0.1 µsec peak (30 m)Rough rule is that peak of correlation function can bedetermined to 1% of width (with care). Therefore 3 m for C/Acode and 0.3 m for P(Y) code.411/25/2009 12.215 Modern Naviation L18 7Pseudorange noise• More noise sources– Thermal noise: Effects of other random radio noise in theGPS bandsBlack body radiation: I=2kT/λ2 where I is the specific intensityin, for example, watts/(m2Hz ster), k is Boltzmanʼsconstant,1.380 x 10-23 watts/Hz/K and λ is wavelength.Depends on area of antenna, area of sky seen (ster=ster-radians), temperaure T (Kelvin) and frequency. Since P(Y)code has narrower bandwidth, tracking it in theory has 10times less thermal noise power (cut by factor of 2 becauseless transmission power)Thermal noise is general smallest effect– Multipath: Reflected signals (discussed later)11/25/2009 12.215 Modern Naviation L18 8Pseudorange noise• The main noise sources are related to reflectedsignals and tracking approximations.• High quality receiver: noise about 10 cm• Low cost receiver ($200): noise is a few meters(depends on surroundings and antenna)• In general: C/A code pseudoranges are of similarquality to P(Y) code ranges. C/A can use narrowbandtracking which reduces amount of thermal noise• Precise positioning (P-) code is not really the case.511/25/2009 12.215 Modern Naviation L18 9Phase measurements• Carrier phase measurements are similar topseudorange in that they are the difference in phasebetween the transmitting and receiving oscillators.Integration of the oscillator frequency gives the clocktime.• Basic notion in carrier phase: φ=fΔt where φ is phaseand f is frequency• “Big” problem is know the number of cycles in thephase measurements11/25/2009 12.215 Modern Naviation L18 10Phase measurements• The carrier phase is the difference between phase ofreceiver oscillator and signal received plus thenumber of cycles at the initial start of tracking• The received phase is related to the transmitted phaseand propagation time by€ φkp(tr) =φk(tr) −φrp(tr) + Nkp(1)€ φrp(tr) =φtp(tt) =φtp(tr−ρkp/c) =φtp(tr) −˙ φ p(tr) ⋅ρkp/c611/25/2009 12.215 Modern Naviation L18 11Phase measurements• The rate of change of phase is frequency. Notice thatthe phase difference changes as ρ/c changes. Ifclocks perfect and nothing moving then would beconstant.• Subtle effects in phase equation– Phase received at time t = phase transmitted at t-τ(riding the wave)– Transmitter phase referred to ground time (usedlater). Also possible to formulate as transmit time.11/25/2009 12.215 Modern Naviation L18 12Phase measurements• When phase is used it is converted to distance usingthe standard L1 and L2 frequencies and vacuumspeed of light.• Clock terms are introduced to account for differencebetween true frequencies and nominal frequencies.As with range ionospheric and atmospheric delaysaccount for propagation velocity711/25/2009 12.215 Modern Naviation L18 13Precision of phase measurements• Nominally phase can be measured to 1% ofwavelength (~2mm L1 and ~2.4 mm L2)• Again effected by multipath, ionospheric delays(~30m), atmospheric delays (3-30m).• Since phase is more precise than range, more effectsneed to be carefully accounted for with phase.• Precise and consistent definition of time of events isone the most critical areas• In general, phase can be treated like rangemeasurement with unknown offset due to cycles andoffsets of oscillator phases.11/25/2009 12.215 Modern Naviation L18 14GPS data• Next set of plots will look at the GPS data• Examples for one satellite over about 1 hour interval:– Raw range data– Raw phase data– Differences between data811/25/2009 12.215 Modern Naviation L18 15Raw range data232000002340000023600000238000002400000024200000244000002460000018.8 19.0 19.2 19.4 19.6 19.8C1_range P2_rangeC1_range (m)HrsDrop outBad measurement11/25/2009 12.215 Modern Naviation L18 16Raw phase data (Note: sign)-20000000200000040000006000000800000018.8 19.0 19.2 19.4 19.6 19.8L1_phase L2_phasePhase (cycles)HrsCycle slip at L2911/25/2009 12.215 Modern Naviation L18 17L2-L1 range differences5101520253018.8 19.0 19.2 19.4 19.6 19.8ΔP2-C1 (m)ΔP2-C1 (m)Hrs11/25/2009 12.215 Modern Naviation L18 18L2-L1 phase differences-50000500010000150002000018.8 19.0 19.2 19.4 19.6 19.8ΔL2*λ2-L1*λ1 (m)ΔL2*λ2-L1*λ1 (m)HrsCycle slip repaired approximatelyNotice time to re-lock1011/25/2009 12.215 Modern Naviation L18 19Zoomed L2-L1 phase-20-15-10-50518.8 19.0 19.2 19.4 19.6 19.8ΔL2*λ2-L1*λ1 (m)ΔL2*λ2-L1*λ1 (m)Hrs11/25/2009 12.215