03/05/03 12.540 Lec 08 1 12.540 Principles of the Global Positioning System Lecture 08 Prof. Thomas Herring Summary ? Review: – Examined methods for measuring distances – Examined GPS codes that allow a type of distance measurement and phase to be measured ? Today: – Examine how the range measurements are defined and used – Use of carrier phase measurements – Examine RINEX format and look at some “raw” data 03/05/03 12.540 Lec 08 2 1 03/05/03 12.540 Lec 08 3 Pseudorange measurements ? When a GPS receiver measures the time offset it needs to apply to its replica of the code to reach measuring? ? It is measuring the time difference between when a signal was transmitted (based on satellite clock) and when it was received (based on receiver clock). ? If the satellite and receiver clocks were synchronized, this would be a measure of range ? Since they are not synchronized, it is called Basic measurement types maximum correlation with received signal, what is it “pseudorange” ? Pseudorange: 2 03/05/03 12.540 Lec 08 4 P k p =(t k -t p )?c p k is the pseudorange between receiver k and satellite p; t k p is the satellite transmit time; and c is the speed of light This expression can be related to the true range by introducing t k =t k t k t p =t p t p t k and t p are true times; Dt k and Dt p are clock corrections Where P is the receiver clock time, t corrections to the clock times +D +D 03/05/03 12.540 Lec 08 5 Basic measurement types ? r k p P k p = (t k -t p )+(Dt k t p ) [] ?c P k p =r k p +(Dt k t p )?c+ I k p Ionspheric delay { + A k p Atmospheric delay { ? Substituting into the equation of the pseudorange yields is true range, and the ionospheric and atmospheric terms are introduced because the propagation velocity is not c. -D -D 03/05/03 12.540 Lec 08 6 Basic measurement types ? The equation for the pseudorange uses the true range because the propagation velocity is not the in-vacuum value, c, 2.99792458x10 8 m/s ? To convert times to distance c is used and then c. In RINEX data files, pseudorange is given in distance units. ? The true range is related to the positions of the ground receiver and satellite. ? Also need to account for noise in measurements and corrections applied for propagation delays corrections applied for the actual velocity not equaling 3 03/05/03 12.540 Lec 08 7 Pseudorange noise ? – Correlation function width:The width of the correlation is inversely proportional to the bandwidth of the signal. Therefore the 1MHz bandwidth of C/A produces a peak 1 msec wide (300m) compared to the P(Y) code 10MHz bandwidth which produces 0.1 m Rough rule is that peak of correlation function can be determined to 1% of width (with care). Therefore 3 m for C/A code and 0.3 m for P(Y) code. Pseudorange noise (random and not so random errors in measurements) contributions: sec peak (30 m) 03/05/03 12.540 Lec 08 8 Pseudorange noise ? More noise sources – Thermal noise: Effects of other random radio noise in the GPS bands Black body radiation: I=2kT/l 2 where I is the specific intensity in, for example, watts/(m 2 k constant,1.380 x 10 -23 watts/Hz/K and l is wavelength. Since P(Y) code has narrower bandwidth, tracking it in theory has 10 times less thermal noise power (cut by factor of 2 because less transmission power) Thermal noise is general smallest effect – Reflected signals (discussed later) Hz ster), is Boltzman’s Depends on area of antenna, area of sky seen (ster=ster- radians), temperature T (Kelvin) and frequency. Multipath: 4 03/05/03 12.540 Lec 08 9 Pseudorange noise ? The main noise sources are related to reflected ? High quality receiver: noise about 10 cm ? Low cost receiver ($200): noise is a few meters ? quality to P(Y) code ranges. C/A can use narrowband ? Precise positioning (P-) code is not really the case. 03/05/03 12.540 Lec 08 10 oscillators. f=fDf is signals and tracking approximations. (depends on surroundings and antenna) In general: C/A code pseudoranges are of similar tracking which reduces amount of thermal noise Phase measurements ? Carrier phase measurements are similar to pseudorange in that they are the difference in phase between the transmitting and receiving Integration of the oscillator frequency gives the clock time. ? Basic notion in carrier phase: t where phase and f is frequency 5 03/05/03 12.540 Lec 08 11 f k p (t r )=f k (t r )-f r p (t r )+N k p (1) f r p (t r )=f t p (t t )=f t p (t r -r k p /c)=f t p (t r )- ˙ f p (t r )?r k p /c Phase measurements ? The carrier phase is the difference between phase of receiver oscillator and signal received plus the number of cycles at the initial start of tracking ? The received phase is related to the transmitted phase and propagation time by 03/05/03 12.540 Lec 08 12 r – Phase received at time t = phase transmitted at t-t (riding the wave) – Transmitter phase referred to ground time (used later). Phase measurements ? The rate of change of phase is frequency. Notice that the phase difference changes as /c changes. If clocks perfect and nothing moving then would be constant. ? Subtle effects in phase equation Also possible to formulate as transmit time. 6 03/05/03 12.540 Lec 08 13 03/05/03 12.540 Lec 08 14 ? Nominally phase can be measured to 1% of wavelength (~2mm L1 and ~2.4 mm L2) ? (~30m), atmospheric delays (3-30m). ? need to be carefully accounted for with phase. ? Precise and consistent definition of time of events is one the most critical areas ? In general, phase can be treated like range offsets of oscillator phases. Phase measurements ? When phase is used it is converted to distance using the standard L1 and L2 frequencies and vacuum speed of light. ? Clock terms are introduced to account for difference between true frequencies and nominal frequencies. As with range ionospheric and atmospheric delays account for propagation velocity Precision of phase measurements Again effected by multipath, ionospheric delays Since phase is more precise than range, more effects measurement with unknown offset due to cycles and 7 GPS Data file formats ? Receivers use there own propriety (binary) formats but programs convert these to standard format called Receiver Independent Exchange Format (RINEX) ? teqc available at http://www.unavco.ucar.edu/data_support/software/teqc/teqc.html is one of the most common ? The link to the RINEX format is: ? ftp://igscb.jpl.nasa.gov/igscb/data/format/rinex2.txt 03/05/03 12.540 Lec 08 15 03/05/03 12.540 Lec 08 16 2.00 teqc 1998Jul1 COMMENT COMMENT ETAB tah MIT 7910 7910 TRM22020.00+GP 3711599.9580 1.0000 0.0000 0.0000 1 1 7 L1 L2 C1 P2 P1 D1 D2 15.0000 INTERVAL COMMENT COMMENT COMMENT 2002 1 16 18 49 15.000000 Rinex header OBSERVATION DATA G (GPS) RINEX VERSION / TYPE Thomas Herring 20020117 06:28:28UTCPGM / RUN BY / DATE Linux 2.0.30|PentPro|gcc|Linux|486/DX+ BIT 2 OF LLI FLAGS DATA COLLECTED UNDER A/S CONDITION MARKER NAME OBSERVER / AGENCY TRIMBLE 4000SSE NP 7.19; SP 3.04 REC # / TYPE / VERS ANT # / TYPE -2225431.6719 -4676995.2141 APPROX POSITION XYZ ANTENNA: DELTA H/E/N WAVELENGTH FACT L1/2 # / TYPES OF OBSERV SNR is mapped to RINEX snr flag value [1-9] L1: 3 -> 1; 8 -> 5; 40 -> 9 L2: 1 -> 1; 5 -> 5; 60 -> 9 TIME OF FIRST OBS END OF HEADER 8 03/05/03 12.540 Lec 08 17 RINEX Data block 20 787986.44256 602246.12855 23296205.6024 23296215.6954 -1344.9694 -1048.0284 -2277471.81757 -1740781.13556 21398430.3444 21398436.5904 2700.6094 2104.3714 -1100283.16556 -822375.51955 23502290.7894 23502300.4844 1062.9224 828.2514 -1925082.16955 -1445658.56955 23293616.9844 23293626.4574 2176.8284 1696.2304 1016475.79056 786021.95356 21979554.0634 21979561.0984 -1782.8124 -1389.2054 -572573.66057 -446158.58357 20873925.7664 20873929.7624 446.3594 347.8134 20 ? Phase in cycles, range in meters 1 16 18 49 15.0000000 6G 2G 7G11G26G27G28 1 16 18 49 30.0000000 6G 2G 7G11G26G27G28 03/05/03 12.540 Lec 08 18 interval: – Raw range data – Raw phase data – Differences between data Examine Rinex file data ? Next set of plots will look at the contents of a rinex file. ? Examples for one satellite over about 1 hour 9 10 03/05/03 12.540 Lec 08 19 Raw range data 23200000 23400000 23600000 23800000 24000000 24200000 24400000 24600000 18.8 19.0 19.2 19.4 19.6 19.8 C1_range P2_range C1_range (m) Hrs Drop out Bad measurement 03/05/03 12.540 Lec 08 20 Raw phase data (Note: sign) -2000000 0 2000000 4000000 6000000 8000000 18.8 19.0 19.2 19.4 19.6 19.8 L1_phase L2_phase Phase (cycles) Hrs Cycle slip at L2 11 03/05/03 12.540 Lec 08 21 L2-L1 range differences 5 10 15 20 25 30 18.8 19.0 19.2 19.4 19.6 19.8 DP2-C1 (m) D P2-C1 (m) Hrs 03/05/03 12.540 Lec 08 22 L2-L1 phase differences -5000 0 5000 10000 15000 20000 18.8 19.0 19.2 19.4 19.6 19.8 DL2*l 2 -L1*l 1 (m) D L2* l 2 -L1* l 1 (m) Hrs Cycle slip repaired approximately Notice time to re-lock 12 03/05/03 12.540 Lec 08 23 Zoomed L2-L1 phase -20 -15 -10 -5 0 5 18.8 19.0 19.2 19.4 19.6 19.8 DL2*l 2 -L1*l 1 (m) D L2* l 2 -L1* l 1 (m) Hrs 03/05/03 12.540 Lec 08 24 Plot characteristics ? Data set plotted etab.plt.dat ? Notice phase difference is opposite sign to range difference (discuss more in propagation lectures) ? More manipulation can me made of data: How about C1-L1*l 03/05/03 12.540 Lec 08 25 examine: – Combination of range and phase that tell us more things – data shown. – Summary ? Looked at definitions of data types ? Looked at data and its characteristics. ? Next class, we finish observables and will How well with a simple model can we match the Where do you get GPS data? 13