lecture 22: Global Positioning System (GPS)
humans have always been interested in where things are…
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 falls…or 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
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
orbit ~ 12 hours
27 satellites: 24 operational and 3 spare
ground tracks
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
examples of applications
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
GSP satellite vehicles (SVs):
two generations: block I and block II
GPS block I
GPS block II
weigh ~1900 lbs.
built by Rockwell
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
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…
only place in universe is at
either of two points where
three spheres intersect
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
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
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 Einstein’s ideas about gravity and time
• previous clocks relied on pendulums
• early atomic clocks looked at vibrations of quartz crystal
…keep time to < 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
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
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, three…at 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…
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 millisecond…each 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.
GPS receiver produces replicas of C/A and/or P (Y) code
receiver produces C/A code sequence for specific SV
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
receiver slides replica of code in time until
finds correlation with SV signal
(codes are series of digital numbers)
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
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
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
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
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
position determined from multiple pseudo-range measurements
4 satellites…3 (X, Y, Z) dimensions and time
when clock offsets are determined, the receiver position is known
this leads us to why 4 GPS satellites are necessary and to…
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 > $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
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 weren’t correct?
what if receiver wasn’t perfect?
…receiver is off by 1 second
“real” time
X
XX
XX position is wrong;
caused by wrong time
measurements
wrong time
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…
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)
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”
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
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)
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…)
effects of noise, bias, and blunder
geometric dilution of precision (GDOP)
SVs occupy a small volume in the sky
SVs occupy a large volume in the sky
when measuring must have good GDOP and good visibility
…may not always be possible
user community…
primary application is GPS navigation
X, Y, Z (position) and time from 4 satellites to calculate position
GPS determines locations in Earth centered, Earth fixed (ECEF)
need to convert to latitude, longitude, and height above ellipsoid
need to use datum…descriptions of Earth’s 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
other reference ellipsoids exist
can convert from one datum to another (standard equations)
note position shifts…important to be consistent
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
can also use carrier phase (L1; L2)
two receivers must be < 30 kms from one another
(ionospheric delay must be less than one wavelength);
requires special software
…real-time kinematic (RTK) processing
old slide (1994): currently, dual-phase geodetic receivers ~$10K