12.540 Principles of the Global Positioning System ecture 14 Prof. Thomas Herring 04/01/02 12.540Lec14 Propagation Medium · Summary Paper topics from those not yet submitted Review homework #1 Homework #2. Due April 17, 2002 Propagation Signal propagation from satellite to receiver Light-time iteration Basic atmospheric and ionospheric delays Propagation near receiving antenna 04/01/02 2.540Lec14
04/01/02 12.540 Lec 14 1 12.540 Principles of the Global Positioning System Lecture 14 Prof. Thomas Herring 04/01/02 12.540 Lec 14 2 Propagation Medium – – – . Due April 17, 2002 – – – – • Summary Paper topics from those not yet submitted Review homework #1 Homework #2 • Propagation: Signal propagation from satellite to receiver Light-time iteration Basic atmospheric and ionospheric delays Propagation near receiving antenna
Propagation · Basics Signal, tagged with time from satellite clock transmitte About 66 msec(20,000 km) later the signal arrives at gPs receiver satellite has moved about 66 m during the time it takes signal to propagate to recelver Time the signal is received is given by clock in recelver ference between transmit time and receive time is pseudorange During the propagation, signal passes through the ionosphere (10-100 m of delay phase advance and neutral atmosphere(2 o m depending on elevation angle) 04/01/02 12.540Lec14 Propagation To determine an accurate position from range data. we need to account for all these propagation effects and time offsets In later lectures examine ionospheric and atmospheric delays, and effects near antenna Basic clock treatment in GPs True time of reception of signal needed True time of transmission needed (afo af1 from broadcast ephemeris initially OK Position of satellite when signal transmitted 04/01/02 2.540Lec14
04/01/02 12.540 Lec 14 3 Propagation i – transmitted. – at GPS receiver. Satellite has moved about 66 m during the time it takes signal to propagate to receiver. – receiver. Difference between transmit time and receive time is pseudorange. – and neutral atmosphere (2.3-30 m depending on elevation angle). 04/01/02 12.540 Lec 14 4 Propagation data, we need to account for all these propagation effects and time offsets. atmospheric delays, and effects near antenna. – – broadcast ephemeris initially OK) – • Bas cs: Signal, tagged with time from satellite clock, About 66 msec (20,000 km) later the signal arrives Time the signal is received is given by clock in During the propagation, signal passes through the ionosphere (10-100 m of delay, phase advance), • To determine an accurate position from range • In later lectures, examine ionospheric and • Basic clock treatment in GPS True time of reception of signal needed True time of transmission needed (af0, af1 from Position of satellite when signal transmitted
Times RINEX data files tag measurements by reception time as given by the receiver clock The error in the receiver time must be determined iteratively For linearized least squares or kalman filter need to establish non-linear model and then estimator determines adjustments to parameters of model (e.g. receiver site coordinates) and initial clock error estimates that "best" match the data 04/01/02 12.540Lec14 Non-linear model Basics of non -linear model Rinex data file time tags give approximate time measurement was made Using this time initially, position of satellite can be computed Range computed from receiver and satellite position Difference between observed pseudorange and computed ranges, gives effects of satellite and receiver clock errors. In oint positioning satellite clock error is assumed known and When removed from difference error in receiver clock determined With new estimate of receiver clock, process can be iterated If receiver position poorly known, then whole system can be iterated with updated receiver coordinates 04/01/02 2.540Lec14
04/01/02 12.540 Lec 14 5 Times reception time as given by the receiver clock. The error in the receiver time must be determined iteratively least squares or Kalman filter need to establish non-linear model and then estimator determines adjustments to parameters of model (e.g. receiver site coordinates) and initial clock error estimates that “best” match the data. 04/01/02 12.540 Lec 14 6 Non-linear model • was made. In point positioning, satellite clock error is assumed known and when removed from difference, error in receiver clock determined. iterated with updated receiver coordinates. • RINEX data files, tag measurements by • For linearized Basics of non-linear model: – Rinex data file time tags give approximate time measurement – Using this time initially, position of satellite can be computed – Range computed from receiver and satellite position – Difference between observed pseudorange and computed ranges, gives effects of satellite and receiver clock errors. – With new estimate of receiver clock, process can be iterated. – If receiver position poorly known, then whole system can be
Sensitivities Satellites move at about 1 km/sec. therefore an error of 1 msec in time results in 1 m satellite position(and therefore in range estimate and receiver position) For pseudo-range positioning, 1 msec errors OK. For phase positioning(1 mm), times needed to 1 usec (1 usec is about 300 m of range Pseudorange accuracy of a few meters in fine 04/01/02 12.540Lec14 Light-time-iteration To compute theoretical range two basic methods used (a" Doppler shift corrections" ie Account for rate o change of range during propagation time used ght-time-iteration "Method most commonly Light time iteration Basic process is to compute range using simple Cartesian geometry but with position of receiver at receive time and position of transmitter at transmit time 04/01/02 2.540Lec14
04/01/02 12.540 Lec 14 7 Sensitivities position (and therefore in range estimate and receiver position). OK. For phase positioning (1 mm), times needed to 1 µsec. µsec is about 300 m of range. Pseudorange accuracy of a few meters in fine). 04/01/02 12.540 Lec 14 8 “Light-time-iteration” methods used – (a) “Doppler shift corrections” ie. Account for rate of change of range during propagation time – (b) “Light-time-iteration” Method most commonly used. compute range using simple Cartesian geometry but with position of receiver at receive time and position of transmitter at transmit time. • Satellites move at about 1km/sec, therefore an error of 1 msec in time results in 1 m satellite • For pseudo-range positioning, 1 msec errors • (1 • To compute theoretical range; two basic • Light time iteration: Basic process is to
Light-time-iteration Light time iteration must be computed in a non rotating frame Reason: Consider earth-fixed frame: one would simply compute earth fixed coordinates at earlier time In non-rotating frame, rotation to inertial coordinates would be done at two different time (receiver when signal received; transmitted when signal transmitted Difference is rotation of earth on 60 msec. Rotation rate +460 m/sec: therefore difference is about 30 meters 04/01/02 12.540Lec14 Clock errors PRN 03 June 14) 800 Clock SA( Clock nosa (ns) 2000 400 200 162024 Time(hrs) 12.540Lec14
04/01/02 12.540 Lec 14 9 Light-time-iteration • Light time iteration must be computed in a nonrotating frame • Reason: Consider earth-fixed frame: one would simply compute Earth fixed coordinates at earlier time. In non-rotating frame, rotation to inertial coordinates would be done at two different time (receiver when signal received; transmitted when signal transmitted). • Difference is rotation of Earth on ~60 msec. Rotation rate ~460 m/sec; therefore difference is about 30 meters. 04/01/02 12.540 Lec 14 10 Clock errors -200 0 200 400 600 800 0 4 8 12 16 20 24 PRN 03 (June 14) Clock SA (ns) 1999 Clock NoSA (ns) 2000 Clock error (ns) Time (hrs)
Detrended Prn 03 Detrended: e=0. 02 Clock· trend(ns) GR Effect (ns) 8 16 Time(hrs) 12.540Lec14 Receiver clocks: ASC 1 0 15.5 04/01/02 2.540Lec14
04/01/02 12.540 Lec 14 11 Detrended -50 -25 0 25 50 0 4 8 12 16 20 24 PRN 03 Detrended; e=0.02 Clock - trend (ns) GR Effect (ns) Clock error (ns) Time (hrs) 04/01/02 12.540 Lec 14 12 Receiver clocks: ASC1 -150 -100 -50 0 50 100 150 14.0 14.5 15.0 15.5 ASC1_Clk_(m) ASC1_Clk_(m) Day
Receiver Clock: HOB2 Hydrogen Maser 2000 HOB2 clk( 2200 04/0102 12.540Lec14 ASC/HOB2 Detrended ASC1 detrended (m 5 漂家 20L,A,⊥,A⊥⊥41 14.0 14.5 0 15.5 12.540Lec14
04/01/02 12.540 Lec 14 13 Receiver Clock: HOB2 Hydrogen Maser -2250 -2200 -2150 -2100 -2050 -2000 -1950 14.0 14.5 15.0 15.5 HOB2_clk_(m) HOB2_clk_(m) Day 04/01/02 12.540 Lec 14 14 ASC/HOB2 Detrended -20 -15 -10 -5 0 5 10 15 20 14.0 14.5 15.0 15.5 ASC1 detrended (m) HOB2 detrended (m) Detrended (m) Day
HOB2 only 1.0产千千千千千千千千千千千千 HOB2 detrended (m) E5 15.5 Day 04/0102 12.540Lec14 Summary of clocks In some cases; clock are well enough behaved that linear polynomials can be used Most commonly: receiver clocks are estimated at every measurement epoch(white noise clocks) Errors in receiver clocks are often thousands of km of equivalent time. Homework #2 will show a bad"clock in receiver 04/01/02 2.540Lec14
04/01/02 12.540 Lec 14 15 HOB2 only -1.0 -0.5 0.0 0.5 1.0 14.0 14.5 15.0 15.5 HOB2 detrended (m) Detrended (m) Day 04/01/02 12.540 Lec 14 16 Summary of clocks • In some cases; clock are well enough behaved that linear polynomials can be used. • Most commonly: receiver clocks are estimated at every measurement epoch (white noise clocks) • Errors in receiver clocks are often thousands of km of equivalent time. Homework #2 will show a “bad” clock in receiver
