12.540 Principles of the global Positioning System Lecture 08 Prof. Thomas Herring 12540Lec08 Summary R Examined methods for measuring distances Examined GPS codes that allow a type of distance measurement and phase to be measured Examine how the range measurements are defined Use of carrier phase measurements Examine rinEx format and look at some "raw data
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
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 12540Lec08 Basic measurement types Pseudorange PP=(,-t)'c Where PPk is the pseudorange between receiver k and satellite p: tk is the receiver clock time, te 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 tk=Tk+△tkt=t T, and T are true times, At, and At are clock corrections 12540Lec08
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 Pk p = (tk - t p )⋅ c p k is the pseudorange between receiver k and satellite p; tk p is the satellite transmit time; and c is the speed of light This expression can be related to the true range by introducing tk = t k tk t p = t p t p tk and tp are true times; Dtk and Dt p are clock corrections Where P is the receiver clock time, t corrections to the clock times +D +D
Basic measurement types Substituting into the equation of the pseudorange yields P"-[(r4-)+(△4-△小c P=p+(△-△")c+1+A lonspheric Atmospheric Pk is true range, and the ionospheric and atmospheric terms are introduced because the propagation velocity is not c 12540Lec08 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 vaue,c,2.99792458X108m/s To convert times to distance c is used and then corrections applied for the actual velocity not equali C. In RINEX data files, pseudorange is given in ng distance units The true range is related to the positions of the ground receiver and satellite Also need to account for noise in measurements
03/05/03 12.540 Lec 08 5 Basic measurement types • rk p Pk p = (t k - t p ) + (Dtk t p [ ]) ⋅ c Pk p = rk p + (Dtk t p )⋅ c + Ik p Ionspheric delay { + Ak 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, 2.99792458x108 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
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 1 MHz bandwidth of C/a produces a peak usec wide(300m) compared to the P(Y)code 10MHz bandwidth which produces 0. 1 usec peak (30 m) Rough rule is that peak of correlation function can be determined to 1% of width(with care). Therefore 3 m for CIA code and 0.3 m for P(Y)code 12540Lec08 Pseudorange noise More noise sources Thermal noise: Effects of other random radio noise in the GPS bands Black body radiation: /=2kT/2 where / is the specific intensity in, for example, watts/(m2Hz ster), k is Boltzman's constant, 1. 380 x 10-23 watts/Hz/K and n is wavelength Depends on area of antenna, area of sky seen(ster=ster adians), temperature t( Kelvin) and frequency. Since P( code has narrower bandwidth, tracking it in theory has 10 less thermal noise power(cut by factor of 2 because transmission power) Thermal noise is general smallest effect Multipath: Reflected signals(discussed later)
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/l2 where I is the specific intensity in, for example, watts/(m2 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=sterradians), temperature T (Kelvin) and frequency. Multipath: 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 Precise positioning(P-)code is not really the case 12540Lec08 hase 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:φ-f△ t whereφis phase and f is frequency
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=fD f 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