Range and Phase Data - Principles of the Global Positioning System

Summary • Review: – 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 2 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 3 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 4 Melbourne-Wubena Wide Lane (MW-WL) ( f1 − f 2 ) mw − wl = φ1 − φ 2 − [R1 f1 /c + R2 f 2 /c ] ( f1 + f 2 ) • 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 ∆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) 5 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? 6 Direct comparison 25000000 Range (m) 24000000 23000000 22000000 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) 21000000 20000000 16.0 17.0 18.0 19.0 20.0 Time_Hrs 21.0 22.0 23.0 24.0 7 Zoom of “jump” section 24000000 23500000 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) 23000000 22500000 22000000 21500000 21000000 20500000 20000000 19.7 19.8 19.8 19.9 19.9 Time_Hrs 20.0 20.0 20.1 8 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). 9 Observed - Theory, Clock values from broadcast ephemeris 300000 200000 Range (m) 100000 0 -100000 -200000 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 -300000 -400000 -500000 16.0 17.0 18.0 19.0 20.0 Time_Hrs 21.0 22.0 23.0 24.0 Notice that omc is opposite to clock, Next plot satellite clock corrections added 10 Observed - theory + satellite clock 200000 Range Residual (m) 100000 0 C1_07-Theory+SV clock C1_02-Theory+SV clock C1_11-Theory+SV clock -100000 C1_26-Theory+SV clock C1_28-Theory+SV clock -200000 -300000 16.0 17.0 18.0 19.0 20.0 Time_Hrs 21.0 22.0 23.0 24.0 11 Zoom of last plot 34500 C1_07-Theory+SV clock C1_02-Theory+SV clock 34000 Range Residual (m) C1_11-Theory+SV clock C1_26-Theory+SV clock C1_28-Theory+SV clock 33500 33000 32500 32000 19.5 19.5 19.5 19.6 Time_Hrs 19.6 19.6 19.6 12 Residuals • After correcting for the satellites, the large fluctuations can be removed with the receiver clock. Once this is done the remaining residuals are 10-100 meters. • What needs to be corrected at this point? 13 Main model parts missing • We already saw that L1-L2 range values change by up to 5m for the short span we looked at Monday (next page shows longer segment). • Errors in station coordinates could add 5-10 m of error depending on quality • Atmospheric delays (and 3-10 m, especially for low elevation satellites) • Time the satellite position is calculated: We assumed the time tag on the rinex file but clearly in error by 0.1 msec due to receiver clock. A bigger error is the light propagation time (~7 msec). • Satellites move in radial direction at ~1km/sec, therefore 7 ms translates to about 7 meters of range change. Later in course you will need to do this calculation 14 L1-L2 range for PRN 07 -4 L1-L2 range (m) -6 L1-L2 range (m) -8 -10 -12 -14 Missing data, should not be a jump in L1-L2 -16 -18 18.0 19.0 20.0 21.0 Time_Hrs 22.0 23.0 24.0 15 MW-WL (used for detecting cycle slips and resolving phase ambiquities) -23500000 MW_WL_07_cycles -24000000 MW_WL_07_cycles -24500000 -25000000 Cycle slip -25500000 18.0 19.0 20.0 21.0 Time_Hrs 22.0 23.0 24.0 16 MW-WL Last part of data (plus PRN 28) MW_WL_07_cycles MW_WL_28_cycles -23578697 -24380364 -23578698 -24380365 -23578699 -24380366 -23578700 -24380367 -23578701 -24380368 -23578702 -24380369 -23578703 -24380370 -23578704 -24380371 -23578705 19.0 20.0 21.0 22.0 23.0 MW_WL_28_cycles MW_WL_07_cycles etab.07 -24380372 24.0 Time_Hrs 17 MW-WL Characteristics • In one-way form as shown the MW-WL does not need to be an integer or constant • Slope in one-way is common, but notice that both satellites show the same slope. • If same satellite-pair difference from another station (especially when same brand receiver and antenna) are subtracted from these results then would be an integer (even at this one station, difference is close to integer) • The MW-WL tells you the difference between the L1 and L2 cycles. To get the individal cycles at L1 and L2 we need another techique. • There is a formula that gives L1+L2 cycles but it has 10 times the noise of the range data (Σf/∆f) and generally is not used. • Discuss more in the processing methods of the course 18