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12.540 Principles of the Global
Positioning System
Lecture 14
Prof. Thomas Herring
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Propagation Medium
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– . Due April 17, 2002
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? 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
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Propagation
i
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transmitted.
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at GPS receiver. Satellite has moved about 66 m
during the time it takes signal to propagate to
receiver.
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receiver. Difference between transmit time and
receive time is pseudorange.
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and neutral atmosphere (2.3-30 m depending on
elevation angle).
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Propagation
data, we need to account for all these
propagation effects and time offsets.
atmospheric delays, and effects near antenna.
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broadcast ephemeris initially OK)
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?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
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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.
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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
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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).
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“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
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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 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.
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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)
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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)
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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 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
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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)
Detrended (m)
Day
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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.