雨自文大電园地 Principles of the Global Positioning System Lecture 05 YUAN Linguo Email:Igyuan@home.switu.edu.cn Dept of Surveying Engineering, Southwest Jiaotong University Outline Review u Examined basics of GPS signal structure and how gnal is tracked a Looked at methods used to acquire satellites and start g Today we look at o Basic gps observables Biases and nois o Examine rinex format and look at some raw"' data wv Principles of the Global Positioning System
1 Principles of the Global Positioning System Lecture 05 YUAN Linguo Email: lgyuan@home.swjtu.edu.cn Dept. of Surveying Engineering, Southwest Jiaotong University Principles of the Global Positioning System 2005-3-25 2 Outline Review: Examined basics of GPS signal structure and how signal is tracked Looked at methods used to acquire satellites and start tracking Today we look at: Basic GPS observables Biases and noise Examine RINEX format and look at some “raw” data
Review GPS Signal Summary Table odone Frequency Ratio of fundamental Wavelength [cm] 10.23 29326 LI Carrier 1, 575.42 154f6 19.04 L 2 Carrier 1.227.60 120f0 2445 L5 Carrier.176.45 l15f6 5 P-code 10.23 29326 C/A code 29326 W-code.5115 f/20 58651 Navigation 50-10 f。204,600 N/A Principles of the Global Positioning System 2005325(3 Basic GPs observables Code pseudoranges a precise/protected Pl, P2 codes available only to the military users a clear/acquisition C/A code available to the civilian users Phase pseuodranges a Ll, L2 phases, used mainly in geodesy and surveying Doppler data Gv Principles of the Global Positioning System 2005325(4
2 Principles of the Global Positioning System 2005-3-25 3 Review ：GPS Signal Summary Table GPS Signal Summary Table Component Frequency [MHz] Ratio of fundamental frequency fo Wavelength [cm] Fundamental frequency fo 10.23 1 2932.6 L1 Carrier 1,575.42 154⋅fo 19.04 L2 Carrier 1,227.60 120⋅fo 24.45 L5 Carrier 1,176.45 115⋅fo 25.5 P-code 10.23 1 2932.6 C/A code 1.023 fo/10 29326 W-code 0.5115 fo/20 58651 Navigation message 50⋅10-6 fo/204,600 N/A Principles of the Global Positioning System 2005-3-25 4 Basic GPS Observables GPS Code pseudoranges pseudoranges precise/protected P1, P2 codes - available only to the military users clear/acquisition C/A code - available to the civilian users Phase pseuodranges pseuodranges L1, L2 phases, used mainly in geodesy and surveying Doppler data Doppler data
Code pseudoranges e 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 pseudornage wy Principles of the Global Positioning System 2005-325(5) Code pseudoranges Pseudorange R=(t C Where R is the pseudorange between receiver R and satellite S; tR is the receiver clock time. t is the satellite transmit time and c is the This expression can be related to the true range by introducing t=rR+△tt=r3+△ t Rand r are true times; Atg and 4N are clock corrections wEI Principles of the Global Positioning System 20053-25(6
3 Principles of the Global Positioning System 2005-3-25 5 Code pseudoranges 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 “pseudornage” Principles of the Global Positioning System 2005-3-25 6 Code pseudoranges Pseudorange: R t t c S R = ( − )⋅ Where R is the pseudorange between receiver R and satellite S; tR is the receiver clock time, t S 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 S S S R R R t =τ + ∆t t =τ + ∆t τR and τS are true times; ΔtR and Δt S are clock corrections
Code pseudoranges Substituting into the equation of the pseudorange ields R=(x2-x)+(△M-△)e R=p2+(△2-△r3)c+IA+A lonspheric Atmospheric PR IS true range, and the ionospheric and atmospheric terms are introduced because the propagation velocity is not c wy Principles of the Global Positioning System Millisecond problem in C/A code The C/A-code repeats every millisecond which corresponds to 300km in range. Since the satellites are distance of about 20,000km from the earth, C/A-code pseudoranges are ambiguous How to resolve this problem? .Introduce approximate(within some few hundred kilometers) position coordinates of the receiver in initial satellite acquisition p=p(r3,tn)=p(,、(3+△)=p(3)+p(r3)△ The maximum radial velocity for GPS satellites in the case of a stationary receiver is p 0.9km/s, and the travel time of the satellite signal is about 0.07s. The correction term in Eq, thus amounts to some 60m NEE Principles of the Global Positioning System 8
4 Principles of the Global Positioning System 2005-3-25 7 Code pseudoranges Substituting into the equation of the pseudorange yields ρR S is true range, and the ionospheric and atmospheric terms are introduced because the propagation velocity is not c. [ ] N N delay Atmospheric delay Ionspheric ( ) ( ) ( ) S R S R S R S R S R S R R t t c I A R t t c = + ∆ − ∆ ⋅ + + = − + ∆ − ∆ ⋅ ρ τ τ Principles of the Global Positioning System 2005-3-25 8 Millisecond problem in C/Acode The C/A-code repeats every millisecond which corresponds to 300km in range. Since the satellites are distance of about 20,000km from the earth, C/A-code pseudoranges are ambiguous. How to resolve this problem? Introduce approximate (within some few hundred kilometers) position coordinates of the receiver in initial satellite acquisition. The maximum radial velocity for GPS satellites in the case of a stationary receiver is ≈0.9km/s, and the travel time of the satellite signal is about 0.07s. The correction term in Eq., thus, amounts to some 60m. ρ t t t t t t t t S S S S R S ρ = ρ( , ) = ρ( ,( + ∆ )) = ρ( ) + ρ( )∆
Notes of code pseudoranges corrections ap plied for propagation delays becauange and The equation for the pseudorange uses the true se the propagation velocity is not the in-vacuum value, c, 299792458x108m/s e 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 e Also need to account for noise in measurements p-code pseudoranges can be as good as 20 cm or less, while the LI C/A code range noise level reaches even a meter or more Principles of the Global Positioning System 2005-3-25(9) hase pseudoranges Carrier phase- a difference between the phases of a carrier signal received from a spacecraft and a reference signal generated by the receivers internal oscillator e contains the unknown integer ambiguity N. i.e. the number of phase cycles at the starting epoch that remains constant as long as the tracking is continuous phase cycle slip or loss of lock introduces a new ambiguity unknown typical noise of phase measurements is generally of the order of a few millimeters or less EX Principles of the Global Positioning System 5
5 Principles of the Global Positioning System 2005-3-25 9 Notes of code pseudoranges 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. P-code pseudoranges can be as good as 20 cm good as 20 cm or less, while the L1 C/A code range noise level reaches even a meter or more meter or more . Principles of the Global Positioning System 2005-3-25 10 Phase pseudoranges Carrier phase - a difference between the phases of a carrier signal received from a spacecraft and a reference signal generated by the receiver’s internal oscillator contains the unknown integer ambiguity, N unknown integer ambiguity, N, i.e., the number of phase cycles at the starting epoch that remains constant as long as the tracking is continuous phase cycle slip cycle slip or loss of lock loss of lock introduces a new ambiguity unknown. typical noise of phase measurements is generally of the order of a few millimeters or less