Principles of the Global Positioning System - Pseudorange Measurements

Principles of the Global Positioning System 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 1 Pseudorange measurements • When a GPS receiver measures the time offset it needs to apply to its replica of the code to reach maximum correlation with received signal, what is it 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 “pseudorange” Basic measurement types • Pseudorange: Pkp = (t k - t p ) ⋅ c Where Ppk is the pseudorange between receiver k and satellite p; tk is the receiver clock time, tp is the satellite transmit time; and c is the speed of light This expression can be related to the true range by introducing corrections to the clock times t k = t k + Dt k t p = t p + Dt p tk and tp are true times; Dtk and Dtp are clock corrections 2 Basic measurement types • Substituting into the equation of the pseudorange yields Pkp = [(t k - t p ) + (Dt k - Dt p )] ⋅ c Pkp = rkp + (Dt k - Dt p ) ⋅ c + I{kp Ionspheric delay + Akp { Atmospheric delay • rkp is true range, and the ionospheric and atmospheric terms are introduced because the propagation velocity is not c. Basic measurement types • The equation for the pseudorange uses the true range and corrections applied for propagation delays because the propagation velocity is not the in-vacuum value, c, 2.99792458x108 m/s • To convert times to distance c is used and then corrections applied for the actual velocity not equaling 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 3 Pseudorange noise • Pseudorange noise (random and not so random errors in measurements) contributions: – 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 msec peak (30 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 • More noise sources – Thermal noise: Effects of other random radio noise in the GPS bands Black body radiation: I=2kT/l2 where I is the specific intensity in, for example, watts/(m2Hz ster), k is Boltzman’s constant,1.380 x 10-23 watts/Hz/K and l is wavelength. Depends on area of antenna, area of sky seen (ster=sterradians), temperature T (Kelvin) and frequency. 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 – Multipath: Reflected signals (discussed later) 4 Pseudorange noise • The main noise sources are related to reflected signals 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 similar quality to P(Y) code ranges. C/A can use narrowband tracking which reduces amount of thermal noise • Precise positioning (P-) code is not really the case. Phase measurements • Carrier phase measurements are similar to pseudorange in that they are the difference in phase between the transmitting and receiving oscillators. Integration of the oscillator frequency gives the clock time. • Basic notion in carrier phase: f=fDt where f is phase and f is frequency 5 Phase measurements f kp (t r ) = f k (t r ) - f rp (t r ) + N kp (1) • 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 f rp (t r ) = f tp (t t ) = f tp (t r - r kp /c) = f tp (t r ) - ḟ p (t r ) ⋅ r kp /c Phase measurements • The rate of change of phase is frequency. Notice that the phase difference changes as r/c changes. If clocks perfect and nothing moving then would be constant. • Subtle effects in phase equation – Phase received at time t = phase transmitted at t-t (riding the wave) – Transmitter phase referred to ground time (used later). Also possible to formulate as transmit time. 6 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 • Nominally phase can be measured to 1% of wavelength (~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 effects 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 measurement with unknown offset due to cycles and offsets of oscillator phases. 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) Rinex header 2.00 OBSERVATION DATA G (GPS) RINEX VERSION / TYPE teqc 1998Jul1 20020117 06:28:28UTCPGM / RUN BY / DATE Thomas Herring COMMENT Linux 2.0.30|PentPro|gcc|Linux|486/DX+ COMMENT BIT 2 OF LLI FLAGS DATA COLLECTED UNDER A/S CONDITION ETAB MARKER NAME tah MIT OBSERVER / AGENCY 7910 NP 7.19; SP 3.04 REC # / TYPE / VERS TRIMBLE 4000SSE 7910 TRM22020.00+GP ANT # / TYPE -2225431.6719 -4676995.2141 3711599.9580 APPROX POSITION XYZ 1.0000 0.0000 0.0000 ANTENNA: DELTA H/E/N 1 1 WAVELENGTH FACT L1/2 7 L1 L2 C1 P2 P1 D1 D2 # / TYPES OF OBSERV 15.0000 INTERVAL COMMENT SNR is mapped to RINEX snr flag value [1-9] COMMENT L1: 3 -> 1; 8 -> 5; 40 -> 9 COMMENT L2: 1 -> 1; 5 -> 5; 60 -> 9 2002 1 16 18 49 15.000000 TIME OF FIRST OBS END OF HEADER 8 RINEX Data block 2 1 16 18 49 15.0000000 0 6G 2G 7G11G26G27G28 787986.44256 602246.12855 23296205.6024 23296215.6954 -1344.9694 -1048.0284 -2277471.81757 -1740781.13556 21398430.3444 21398436.5904 2700.6094 2104.3714 23502300.4844 -1100283.16556 -822375.51955 23502290.7894 1062.9224 828.2514 -1925082.16955 -1445658.56955 23293616.9844 23293626.4574 2176.8284 1696.2304 21979561.0984 1016475.79056 786021.95356 21979554.0634 -1782.8124 -1389.2054 -572573.66057 -446158.58357 20873925.7664 20873929.7624 446.3594 347.8134 2 1 16 18 49 30.0000000 0 6G 2G 7G11G26G27G28 • Phase in cycles, range in meters 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 interval: – Raw range data – Raw phase data – Differences between data 9 Raw range data 24600000 24400000 C1_range P2_range C1_range (m) 24200000 24000000 Drop out 23800000 23600000 23400000 Bad measurement 23200000 18.8 19.0 19.2 19.4 19.6 19.8 Hrs Raw phase data (Note: sign) 8000000 L1_phase Phase (cycles) 6000000 L2_phase 4000000 2000000 Cycle slip at L2 0 -2000000 18.8 19.0 19.2 Hrs 19.4 19.6 19.8 10 L2-L1 range differences 30 DP2-C1 (m) DP2-C1 (m) 25 20 15 10 5 18.8 19.0 19.2 Hrs 19.4 19.6 19.8 L2-L1 phase differences DL2*l 2-L1*l 1 (m) 15000 DL2*l 2-L1*l 1 (m) Cycle slip repaired approximately 20000 10000 5000 0 -5000 18.8 19.0 19.2 Hrs 19.4 Notice time to re-lock 19.6 19.8 11 Zoomed L2-L1 phase 5 DL2*l 2-L1*l 1 (m) 0 -5 DL2*l 2-L1*l 1 (m) -10 -15 -20 18.8 19.0 19.2 Hrs 19.4 19.6 19.8 Plot characteristics • 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 12 Summary • Looked at definitions of data types • Looked at data and its characteristics. • Next class, we finish observables and will examine: – Combination of range and phase that tell us more things – How well with a simple model can we match the data shown. – Where do you get GPS data? 13