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 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) – ?Bascs: 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 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 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 04/01/02 12.540 Lec 14 9 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 12.540 Lec 14 10 Clock errors -200 0 200 400 600 800 0 4 8 12162024 PRN 03 (June 14) Clock SA (ns) 1999 Clock NoSA (ns) 2000 Clock error (ns) Time (hrs) 04/01/02 12.540 Lec 14 11 Detrended -50 -25 0 25 50 0 4 8 12162024 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 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 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.