lecture 22: Global Positioning System GPS

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lecture 22 Global Positioning System (GPS)
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humans have always been interested in where
things are
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one of the basic questions has always
been where am I?.which leads to where am I
going and how do I get there?
early solutions marking trails with piles of
stones (problems when snow fallsor on
ocean) navigating by stars (requires clear
nights and careful measurements) most
widely used for centuries location within a
mile or so
modern ideas LORAN radio-based good for
coastal waters limited outside of coastal
areas Sat-Nav low orbit satellites use low
frequency Doppler problems with small
movements of receivers
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Department of Defense finally said we
need something better all-day and all-night
all terrain
end-product is Global Positioning System (GPS)
system (constellation) of 24 satellites in high
altitude orbits (cost 12 billion) coded
satellite signals that can be processed in a GPS
receiver to compute position, velocity, and
time parts of system include space
(GPS satellite vehciles, or SVs) control
(tracking stations) users
first one launched in 1978 .June 26, 1993
Air Force launched 24th SV
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orbit 12 hours
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27 satellites 24 operational and 3 spare
ground tracks
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basic concept is that the GPS constellation
replaces stars and gives us reference points
for navigation
examples of some applications (users)
navigation (very important for ocean travel)
zero-visibility landing for aircraft collision
avoidance surveying precision
agriculture delivery vehicles emergency
vehicles electronic maps Earth sciences
(volcano monitoring seismic hazard)
tropospheric water vapor
anything that involves location, motion, or
navigation
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examples of applications
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we will break system into five conceptual pieces
step 1 using satellite ranging step 2 measuring
distance from satellite step 3 getting perfect
timing step 4 knowing where a satellite is in
space step 5 identifying errors
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GSP satellite vehicles (SVs) two generations
block I and block II
GPS block II
weigh 1900 lbs.
built by Rockwell
GPS block I
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step 1 using satellite ranging
GPS is based on satellite ranging, i.e. distance
from satellites satellites are precise
reference points we determine our distance
from them
we will assume for now that we know exactly where
satellite is and how far away from it we are
if we are lost and we know that we are 11,000
miles from satellite A we are somewhere on a
sphere whose middle is satellite A and diameter
is 11,000 miles
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if we also know that we are 12,000 miles from
satellite B we can narrow down where we must
be only place in universe is on circle where two
spheres intersect
if we also know that we are 13,000 miles from
satellite C our situation improves immensely onl
y place in universe is at either of two points
where three spheres intersect
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three can be enough to determine position
one of the two points generally is not possible
(far off in space)
two can be enough if you know your elevation
why? one of the spheres can be replaced with
Earth center of Earth is satellite
position
generally four are best and necessary.why this
is a little later
this is basic principle behind GPS using
satellites for triangulation
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step 2 measuring distance from satellite
because GPS based on knowing distance from
satellite we need to have a method for
determing how far away the satellites are
use velocity x time distance
GPS system works by timing how long it takes a
radio signal to reach the receiver from a
satellite distance is calculated from that
time radio waves travel at speed of light
180,000 miles per second
problem need to know when GPS satellite
started sending its
radio message
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requires very good clocks that measure short
times electromagnetic waves move very quickly
use atomic clocks
came into being during World War II nothing to
do with GPS -physicists wanted to test
Einsteins ideas about gravity and time
previous clocks relied on pendulums early
atomic clocks looked at vibrations of quartz
crystal keep time to lt 1/1000th second per
day ..not accurate enough to assess
affect of gravity on time Einstein
predicted that clock on Mt. Everest would run
30 millionths of a second faster than
clock at sea level needed to look at
oscillations of atoms
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principle behind atomic clocks
atoms absorb or emit electomagnetic energy in
discrete amounts that correspond to
differences in energy between different
configurations of the atoms when atom goes from
one energy state to lower one, it emits an
electromagnetic wave of characteristic frequency
known as resonant frequency
these resonant frequencies are identical for
every atom of a given type cesium 133
atoms 9,192,631,770 cycles/second
cesium can be used to create extraordinarily
precise clock
(advances also led to using hydrogen and rubidium)
GPS clocks are cesium clocks
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now that we have precise clocks how do we know
when the signals left the satellite?
this is where the designers of GPS were
clever synchronize satellite and receiver
so they are generating same code at same time
analogy 2 people separated by some distance
both start yelling one, two, threeat same
time person 2 hears one shouted by person
1 when person 2 says three if
you both said one at same time, the distance
away person 2 is from person 1
is time difference between one and
three times the velocity of the sound
let us examine GPS satellite signals more closely
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SVs transmit two microwave carrier (carry
information) signals L1 (1575.42 MHz) carries
navigation message SPS code (SPS
standard positioning servic) L2 (1227.60 MHz)
measures ionospheric delay
3 binary codes shift L1 and/or L2 carrier phases
C/A code (coarse acquisition) modulates L1
carrier phase repeating 1 MHz pseudo random
noise (PRN) code pseudo-random because repeats
every 1023 bits or every
millisecondeach SV has its own C/A code
basis for civilian SPS P-code (precise)
modulates both L1 and L2 long (7 days)
pseudo random 10 MHz noise code basis for
PPS (precise positioning service) AS
(anti-spoofing) encrypts P-code into Y-code
(need classified module for receiver) navigation
message modulates L1-C/A 50 Mhz signal
.describes satellite orbits, clock corrections,
etc.
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GPS receiver produces replicas of C/A and/or P
(Y) code receiver produces C/A code sequence
for specific SV
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C/A code generator repeats same 1023 chip
PRN code sequence every millisecond PRN codes
defined for 32 satellite ID
numbers
modern receivers usually store complete set
of precomputed C/A code chips in memory
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receiver slides replica of code in time until
finds correlation with SV signal
(codes are series of digital numbers)
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if receiver applies different PRN code to SV
signal no correlation
when receiver uses same code as SV and codes
begin to align some signal power detected
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when receiver and SV codes align completely
full signal power detected
usually a late version of code is compared with
early version to insure that correlation peak
is tracked
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receiver PRN code start position at time of full
correlation is time of arrival of the SV PRN
at receiver the time of arrival is a measure of
range to SV offset by amount to which
receiver clock is offset from GPS time the time
of arrival is pseudo-range
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position of receiver is where pseudo-ranges from
set of SVs intersect
position determined from multiple pseudo-range
measurements from a single measurement epoch
(i.e. time) psuedo-range measurements used
together with SV position estimates based on
precise orbital elements (ephemeris data) sent
by each SV
GPS navigation data from navigation message
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each SV sends amount to which GPS time is offset
from UTC (universal time)
time correction used by receiver to set UTC to
within 100 nanoseconds
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position determined from multiple pseudo-range
measurements 4 satellites3 (X, Y, Z) dimensions
and time when clock offsets are determined,
the receiver position is known
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this leads us to why 4 GPS satellites are
necessary and to
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step 3 getting perfect timing
electromagnetic energy travels at 186,000 miles
per second an error of 1/100th second
leads to error of 1,860 miles
how do we know that receiver and satellite are on
same time?
satellites have atomic clocks (4 of them for
redundancy) at 100,000 apiece, they are not in
receivers! receivers have ordinary
clocks (otherwise receivers would cost gt
100K) can get around this by having an extra
measurement hence 4 satellites are necessary
three perfect measurements will lead to unique,
correct solution .four imperfect ones also
will lead to appropriate solution
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illustrate this in 2D
instead of referring to satellite pseudo-range in
distance, we will use time units
two satellites first at distance of 4
seconds second at distance of 6 seconds
this is if clocks were correct
X
location of receiver is X
what if they werent correct?
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what if receiver wasnt perfect? receiver is
off by 1 second
real time
X
XX
XX position is wrong caused by wrong time
measurements
wrong time
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how do we know that it is wrong? measurement
from third satellite (fourth in 3D)
3rd satellite at 3 seconds
all 3 intersect at X if time is correct
X
if time is not correct
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add our one second error to the third receiver
circle from 3rd SV cannot intersect where other
2 do
purple dots are intersections of 2 SVs
XX
define area of solutions
receivers calculate best solution (add or
subtract time from each SV)
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finally step 4 knowing where a satellite is
in space
Air Force injected satellites into known
orbits orbits known in advance and programmed
into receivers satellites constantly monitored
by DoD identify errors (ephemeris
errors) in orbits usually
minor corrections relayed back to
satellite data message about their
health
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sites have co-located VLBI (very long
baseline interferometry) lunar
laser-ranging (from instrument left by Apollo
astronauts) primarily for length of day
considerations satellite laser-ranging
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step 5 identifying errors
ionosphere electrically charged particles
80-120 miles up affects speed of
electromagnetic energy amount of affect
depends on frequency look at differences
in L1 and L2 (need dual-frequency receivers
to correct)
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tropospheric water vapor affects all
frequencies difficult to correct multipath
reflected signals from surfaces near
receiver noise combined effect of PRN noise and
receiver noise bias SV clock errors ephemeris
errors selective availability SA error
introduced by DoD turned off May,
2000 blunders human error in control segment
user mistakes (e.g. incorrect geodetic
datum) more on this in a minute
receiver errors geometric dilution of precision
(GDOP) errors from range vector
differences between receiver and SVs (pictures
coming)
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effects of noise, bias, and blunder
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geometric dilution of precision (GDOP)
SVs occupy a small volume in the sky
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SVs occupy a large volume in the sky
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when measuring must have good GDOP and good
visibility may not always be possible
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user community primary application is GPS
navigation
X, Y, Z (position) and time from 4 satellites to
calculate position
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GPS determines locations in Earth centered, Earth
fixed (ECEF)
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need to convert to latitude, longitude, and
height above ellipsoid
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need to use datumdescriptions of Earths
surface depends on projections flat Earth for
short distances ellipsoidal models for whole
Earth
GPS uses WGS-84 (ellipsoid) geoid surface
resulted from gravity alone
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other reference ellipsoids exist
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can convert from one datum to another (standard
equations)
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note position shiftsimportant to be consistent
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differential GPS improves accuracy
correct bias errors at one location
using measured bias errors at known position
(base station) requires software in reference
receiver that can track all SVs in view and
form individual pseudo-range corrections for
each
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can also use carrier phase (L1 L2) two
receivers must be lt 30 kms from one another
(ionospheric delay must be less than one
wavelength) requires special software
real-time kinematic (RTK) processing
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old slide (1994) currently, dual-phase geodetic
receivers 10K