12. 540 Principles of the Global Positioning System Lecture 09 Prof. Thomas Herring 03/06/02 12.540Lec09
03/06/02 12.540 Lec 09 1 12.540 Principles of the Global Positioning System Lecture 09 Prof. Thomas Herring
Summary · Review Examined definitions of pseudorange and carrier pnase Looked at some actual raw measurements from a RINEX file · Today we look at: Combinations of range and phase measurements Simple differences between observed and rough calculation of expected range and phase measurements Sources of gPs data 03/06/02 12.540Lec09
03/06/02 12.540 Lec 09 2 Summary • R e vie w: – Examined definitions of pseudorange and carrier phase – Looked at some actual raw measurements from a RINEX file • Today we look at: – Combinations of range and phase measurements – Simple differences between observed and rough calculation of expected range and phase measurements – Sources of GPS data
Range and phase data As we have seen with real data there are drops out of data missing data and often associated with this cycle slips in the phase data The difference between the L1 and L2 range measurements reflects noise and the ionospheric delay ( grew by 5 meters in the hour of data we looked at) Difference between L1 and L2 phase, when converted to distance using standard frequencies and speed of light, also reflects noise(much smaller than range) and ionospheric delay but with opposite sign to range ionospheric delay This difference can be used to check for cycles slips independent of ionosphere and movement of receivers. called the Melbourne -Wubena wide lane 03/06/02 12.540Lec09
03/06/02 12.540 Lec 09 3 Range and phase data • As we have seen, with real data there are drops out of data (missing data) and often associated with this cycle slips in the phase data. • The difference between the L1 and L2 range measurements reflects nois e and the ionospheric delay (grew by 5 meters in the hour of data we looked at) • Difference between L1 and L2 phase, when converted to distance using standard frequencies and speed of light, also reflects nois e (much smaller than range) and ionospheric delay but with opposite sign to range ionospheric delay. • This diffe rence can be used to check for cycles slips independent of ionosphere and movement of receivers. Called the Melbourne-Wubena Wide Lane
Melbourne-Wubena wide lane The difference between L1 and l2 phase with the l2 phase scaled to the L1 wavelenth is often called simply the widelane and used to detect cycle slips However it is effected fluctuations in the ionospheric delay which in delay is inversely proportional to frequency squared The lower frequency L2 has a larger contribution than the higher frequency L1 The mw-w removes both the effects on the ionspheric delay and changes in range by using the range measurements to estimate the difference in phase between L1 and L2 03/06/02 12.540Lec09
03/06/02 12.540 Lec 09 4 Melbourne-Wubena Wide Lane • The difference between L1 and L2 phase with the L2 phase scaled to the L1 wavelenth is often called simply the widelane and used to detect cycle slips. However it is effected fluctuations in the ionospheric delay which in delay is inversely proportional to frequency squared. • The lower frequency L2 has a larger contribution than the higher frequency L1 • The MW-WL removes both the effects on the ionspheric delay and changes in range by using the range measurements to estimate the difference in phase between L1 and L2
Melbourne-Wubena Wide Lane(Mw-WL mw-wI [Rf/c+R,/2/c] (f+f2) Equation for the Mw-WL. The term Rf/ c are the range in cycles(notice the sum due to change of sign ionospheric delay) The Af/Ef term for GPS is -0 124 which means range noise is reduced by a about a factor of ten Because of phase and biases range biases, the ML WL should be integer(within noise)when data from differerent sites and satellites double differences )are used. (EXample shown later) 03/06/02 12.540Lec09
03/06/02 12.540 Lec 09 5 Melbourne-Wubena Wide Lane (MW-WL) • Equation for the MW-WL. The term Rf/c are the range in cycles (notice the sum due to change of sign ionospheric delay) • T h e ∆f/ Σf term for GPS is ~0.124 which means range noise is reduced by a about a factor of ten. • Because of phase and biases range biases, the MLWL should be integer (within noise) when data from differerent sites and satellites (double differences) are used. (Example shown later) mw − wl = φ1 − φ2 − ( f1 − f2 ) ( f1 + f2 ) R1 f1 / c + R 2 f2 [ ] / c
Simple mathematical model We know examine as series of results based on the results you are generating for homework #f1 and the rinex data collected at the time How closely can the observed ranges and phases be matched with a simple calculation? Simplest calculation: At the time given in the rinex data files, compute the position of satellite and based on rinex header position compute the range. How accurate is this? 03/06/02 12.540Lec09
03/06/02 12.540 Lec 09 6 Simple mathematical model • We know examine as series of results based on the results you are generating for homework #1 and the rinex data collected at the time. • How closely can the observed ranges and phases be matched with a simple calculation? • Simplest calculation: At the time given in the rinex data files, compute the position of satellite and based on rinex header position compute the range. How accurate is this?
Direct comparison 25000000 Theory(m) 24000000 C128_(m) Theory(m) C126_(m) ≈23000000 Theory(m) C111(m) …… Theory(m) C102(m) 22000000 Theory(m) 21000000 20000000 16017.018.019.020.021.022023.024.0 Time hrs 03/06/02 12.540Lec09
03/06/02 12.540 Lec 09 7 Direct comparison 20000000 21000000 22000000 23000000 24000000 25000000 16.0 17.0 18.0 19.0 20.0 21.0 22.0 23.0 24.0 C1_07_(m) Theory_(m) C1_28_(m) Theory_(m) C1_26_(m) Theory_(m) C1_11_(m) Theory_(m) C1_02_(m) Range (m) Theory_(m) Time_Hrs
Zoom of“ ump section 24000000 E 23500000 C107m) Theory(m) 23000000 C128(m) Theory_(m) 22500000 0-C126(m) … heory(m) 22000000 C111(m) Theory(m) C1_02(m) 21500000 Theory(m) 21000000 20500000 ▲▲▲▲▲ 20000000 19.7 198 198 199 199 20.0 20.0 20.1 Time hrs 03/06/02 12.540Lec09
03/06/02 12.540 Lec 09 8 Zoom of “jump” section 20000000 20500000 21000000 21500000 22000000 22500000 23000000 23500000 24000000 19.7 19.8 19.8 19.9 19.9 20.0 20.0 20.1 C1_07_(m) Theory_(m) C1_28_(m) Theory_(m) C1_26_(m) Theory_(m) C1_11_(m) Theory_(m) C1_02_(m) Theory_(m) Range (m) Time_Hrs
C1 range to theory comparison Clearly the theoretical range and observed ranges are sort-of tracking each other but there are large differences The jump"with missing data seems to show the same jump for all satellites(difficult to tell at this scale) Class notes have data files, so you can check) Pseudorange is difference of clock times, but we have not taken into account the clocks Examine the difference between observed and theoretical range(omc) 03/06/02 12.540Lec09
03/06/02 12.540 Lec 09 9 C1 range to theory comparison • Clearly the theoretical range and observed ranges are “sort-of” tracking each other but there are large differences. • The “jump” with missing data seems to show the same jump for all satellites (difficult to tell at this scale) (Class notes have data files, so you can check). • Pseudorange is difference of clock times, but we have not taken into account the clocks. • Examine the difference between observed and theoretical range (omc)
Observed -Theory, Clock values from broadcast ephemeris 300000 200000 Clock 07(m) C1 07-Theory 100000 Clock 28(m C1 28-Theory Clock 26(m) C1 26-Theory 100000 Clock 11(m) C1 11-Theory 200000 Clock 02(m) C1 02-Theory 300000 -400000 500000 16017018.019.020.021.022.023.024.0 Time Hrs Notice that omc is opposite to clock, Next plot satellite clock corrections added 03/0602 12.540Lec09
03/06/02 12.540 Lec 09 10 Observed - Theory, Clock values from broadcast ephemeris -500000 -400000 -300000 -200000 -100000 0 100000 200000 300000 16.0 17.0 18.0 19.0 20.0 21.0 22.0 23.0 24.0 Clock_07_(m) C1_07-Theory Clock_28_(m) C1_28-Theory Clock_26_(m) C1_26-Theory Clock_11_(m) C1_11-Theory Clock_02_(m) C1_02-Theory Range (m) Time_Hrs Notice that omc is opposite to clock, Next plot satellite clock corrections added