14.propagation medium - propagation
TRANSCRIPT
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12.540 Principles of the GlobalPositioning System
Lecture 14
Prof. Thomas Herring
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Propagation Medium
Propagation: Signal propagation from satellite to receiver Light-time iteration Basic atmospheric and ionospheric delays Propagation near receiving antenna
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Propagation Basics:
Signal, tagged with time from satellite clock,
transmitted. About 60 msec (20,000 km) later the signal arrives
at GPS receiver. Satellite has moved about 66 mduring the time it takes signal to propagate to
receiver. Time the signal is received is given by clock inreceiver. Difference between transmit time andreceive time is pseudorange.
During the propagation, signal passes through theionosphere (10-100 m of delay, phase advance),and neutral atmosphere (2.3-30 m depending onelevation angle).
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Propagation
To determine an accurate position from rangedata, we need to account for all thesepropagation effects and time offsets.
In later lectures, examine ionospheric andatmospheric delays, and effects near antenna.
Basic clock treatment in GPS
True time of reception of signal needed True time of transmission needed (af0, af1 frombroadcast ephemeris initially OK)
Position of satellite when signal transmitted
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Times
RINEX data files, tag measurements byreception time as given by the receiver clock.The error in the receiver time must bedetermined iteratively
For linearized least squares or Kalman filterneed to establish non-linear model and thenestimator determines adjustments toparameters of model (e.g. receiver sitecoordinates) and initial clock error estimatesthat best match the data.
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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 computedranges, gives effects of satellite and receiver clock errors. Inpoint positioning, satellite clock error is assumed known andwhen 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.
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Sensitivities
Satellites move at about 1km/sec, therefore anerror of 1 msec in time results in 1 m satelliteposition (and therefore in range estimate andreceiver position).
For pseudo-range positioning, 1 msec errorsOK. For phase positioning (1 mm), timesneeded to 1 sec.
(1 sec is about 300 m of range.Pseudorange accuracy of a few meters in
fine).
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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 coordinateswould be done at two different time (receiver whensignal received; transmitted when signal transmitted).
Difference is rotation of Earth on ~60 msec. Rotationrate ~460 m/sec; therefore difference is about 30meters.
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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
Clockerror(ns)
Time (hrs)
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Relativistic effects
General relativity affects GPS in three ways Equations of motions of satellite Rates at which clock run Signal propagation
In our GPS analysis we account for the second twoitems
Orbits only integrated for 1-3 days and equation of
motion term is considered small
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Clock effects
GPS is controlled by 10.23 MHz oscillators
On the Earths surface these oscillators are set to10.23x(1-4.4647x10-10) MHz (39,000 ns/day ratedifference)
This offset accounts for the change in potential andaverage velocity once the satellite is launched.
The first GPS satellites had a switch to turn this effect
on. They were launched with Newtonian clocks
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Propagation and clock effects
Our theoretical delay calculations are made inan Earth centered, non-rotating frame using alight-time iteration i.e., the satellite position at
transmit time is differenced from groundstation position at receive time.
Two corrections are then applied to this
calculation
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Corrections terms
Propagation path curvature due to Earths potential (a
few centimeters)
Clock effects due to changing potential
For e=0.02 effect is 47 ns (14 m)
=2GM
c3
lnR
r+ R
s+
Rr+ R
s
= GM
c2e a sinE
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Effects of General Relativity
-50
-25
0
25
50
0 4 8 12 16 20 24
PRN 03 Detrended; e=0.02
Clock - trend (ns)GR Effect (ns)
Clockerror(ns)
Time (hrs)
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Tests of General Relativity In the parameterized post-Newtonian formulation, the
time delay expression becomes:
In PPN, is the gravitational term. In generalrelativity = 1
The clock estimates from each GPS satellite allowdaily estimates of . Interesting project for someone.
= GM
c2
(1+)2
e a sinE
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Using GPS to determine Each day we can fit a linear trend and once-per-
revolution sin and cos terms to the each of the 27-28GPS satellites.
Comparison between the amplitude and phase(relative to sin(E)) allows and estimate of gamma tobe obtained
Quadrature estimates allows error bound to beassessed (cos(E) term)
Problem: Once-per-orbit perturbations are common.However should not be proportional to eccentricity.
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Examples of receiver clock behavior
Examples of satellite and station clock behaviors can
be found at:
http://geoweb.mit.edu/~tah/MITClk
IGS Time Standards are given at:https://goby.nrl.navy.mil/IGStime/index.php
Directories are by GPS week number and directoriesending in W are total clock estimates; folders endingin D are differences between IGS analysis centers
Now examine some examples
http://geoweb.mit.edu/~tah/MITClkhttps://goby.nrl.navy.mil/IGStime/index.phphttps://goby.nrl.navy.mil/IGStime/index.phphttp://geoweb.mit.edu/~tah/MITClk -
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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
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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
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ASC/HOB2 Linear trends removed
-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
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HOB2 only
-1.0
-0.5
0.0
0.5
1.0
14.0 14.5 15.0 15.5
HOB2 detrended (m)
Detren
ded(m)
Day
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Summary of clocks
In some cases; clock are well enoughbehaved that linear polynomials can be used.
Most commonly: receiver clocks are estimated
at every measurement epoch (white noiseclocks) or GPS data is differenced to removeclock (as in question 2 of HW 2).
Errors in receiver clocks are often thousandsof km of equivalent time. Homework #3 willshow a bad clock in receiver.