Download The Global Positioning System (GPS)

The Global Positioning System
(GPS)
Brief History of Navigation
PreHistory - Present: Celestial Navigation
– Ok for latitude, poor for longitude until accurate clock
invented ~1760
13th Century: Magnetic Compass
1907: Gyrocompass
1912: Radio Direction Finding
1930’s: Radar and Inertial Nav
1940’s: Loran-A
1960’s: Omega and Navy Transit (SatNav)
1970’s: Loran-C
1980’s: GPS
Brief History of GPS
Original concept developed around 1960
– In the wake of Sputnik & Explorer
Preliminary system, Transit, operational in 1964
– Developed for nuke submarines
– 5 polar-orbiting satellites, Doppler measurements only
Timation satellites, 1967-69, used the first onboard
precise clock for passive ranging
Fullscale GPS development begun in 1973
– Renamed Navstar, but name never caught on
First 4 SV’s launched in 1978
GPS IOC in December 1993 (FOC in April 1995)
GPS Tidbits
Development costs estimate ~$12 billion
Annual operating cost ~$400 million
3 Segments:
– Space: Satellites
– User: Receivers
– Control: Monitor & Control stations
Prime Space Segment contractor: Rockwell International
Coordinate Reference: WGS-84 ECEF
Operated by US Air Force Space Command (AFSC)
– Mission control center operations at Schriever (formerly
Falcon) AFB, Colorado Springs
Who Uses It?
Everone!
Merchant, Navy, Coast Guard vessels
– Forget about the sextant, Loran, etc.
Commercial Airliners, Civil Pilots
Surveyors
– Has completely revolutionized surveying
Commercial Truckers
Hikers, Mountain Climbers, Backpackers
Cars now being equipped
Communications and Imaging Satellites
– Space-to-Space Navigation
Any system requiring accurate timing
How It Works (In 5 Easy Steps)
GPS is a ranging system (triangulation)
–
The “reference stations” are satellites moving at 4 km/s
1. A GPS receiver (“the user”) detects 1-way ranging
signals from several satellites
– Each transmission is time-tagged
– Each transmission contains the satellite’s position
2. The time-of-arrival is compared to time-of-transmission
3. The delta-T is multiplied by the speed of light to obtain
the range
4. Each range puts the user on a sphere about the satellite
5. Intersecting several of these yields a user position
Multi-Satellite Ranging
1 range puts user
on the spherical
face of the cone.
Intersecting with
a 2nd range
restricts user to
the circular arcs.
Pictures courtesy http://giswww.pok.ibm.com/gps
A 3rd range
constrains user
to 1 of the 2
points.
Which point is determined
by “sanity” – 1 point
obviously wrong.
The GPS Constellation
24 operational space vehicles (“SV’s”)
– 6 orbit planes, 4 SV’s/Plane
– Plus at least 3 in-orbit spares
Orbit characteristics:
–
–
–
–
Altitude: 20,180 km (SMA = 26558 km)
Inclination: 550
Eccentriciy: < 0.02 (nominally circular)
Nodal Regression: -0.0040/day (westward)
The altitude results in an orbital period of 12 sidereal
hours, thus SV’s perform full revs 2/day.
Period and regression lead to repeating ground tracks,
i.e. each SV covers same “swath” on earth ~ 1/day.
Simulation: GPS and GLONASS Simulation
GPS Visibility
GPS constellation is such that between 5 and 8 SV’s are
visible from any point on earth
Each SV tracked by a receiver is assigned a channel
Good receivers are > 4-channel (track more than 4 SV’s)
– Often as many as 12-channels in good receivers
– Extra SV’s enable smooth handoffs & better solutions
Which SV’s are used for a solution is a function of
geometry
– GDOP: Geometric Dilution of Precision
 Magnification of errors due to poor user/SV geometry
– Good receivers compute GDOP and choose “best” SV’s
Timing
Accuracy of position is only as good as your clock
– To know where you are, you must know when you are
– Receiver clock must match SV clock to compute delta-T
SVs carry atomic oscillators (2 rubidium, 2 cesium each)
– Not practical for hand-held receiver
Accumulated drift of receiver clock is called clock bias
The erroneously measured range is called a pseudorange
To eliminate the bias, a 4th SV is tracked
– 4 equations, 4 unknowns
– Solution now generates X,Y,Z and b
If Doppler also tracked, Velocity can be computed
Position Equations
P1 
( X  X 1 ) 2  (Y  Y1 ) 2  ( Z  Z 1 ) 2  b
P2 
( X  X 2 ) 2  (Y  Y2 ) 2  ( Z  Z 2 ) 2  b
P3 
( X  X 3 ) 2  (Y  Y3 ) 2  ( Z  Z 3 ) 2  b
P4 
( X  X 4 ) 2  (Y  Y4 ) 2  ( Z  Z 4 ) 2  b
Where:
Pi = Measured PseudoRange to the ith SV
Xi , Yi , Zi = Position of the ith SV, Cartesian Coordinates
X , Y , Z = User position, Cartesian Coordinates, to be solved-for
b = User clock bias (in distance units), to be solved-for
The above nonlinear equations are solved iteratively using an
initial estimate of the user position, XYZ, and b
GPS Time
GPS time is referenced to 6 January 1980, 00:00:00
– GPS uses a week/time-into-week format
– Jan 6 = First Sunday in 1980
GPS satellite clocks are essentially synched to
International Atomic Time (TAI) (and therefore to UTC)
– Ensemble of atomic clocks which provide international
timing standards.
– TAI is the basis for Coordinated Universal Time (UTC),
used for most civil timekeeping
– GPS time = TAI + 19s

Since 19 leapseconds existed on 1/6/1980
GPS time drifts ahead of UTC as the latter is “held”
(leapseconds) to accommodate earth’s slowing
More About Time
GPS system time referenced to Master USNO Clock, but
now implements its own “composite clock”
SV clocks good to about 1 part in 1013
Delta between GPS SV time & UTC is included in
nav/timing message
Correction terms permit user to determine UTC to better
than 90 nanoseconds (~10-7 sec)
– The most effective time transfer mechanism anywhere
Satellite velocity induces relativistic time dilation of
about 7200 nanosec/day
The 10-bit GPS-week field in the data “rolled-over” on
August 21/22 1999 – some receivers probably failed!
GPS Signals
GPS signals are broadcast on 2 L-band carriers
– L1: 1575.42 MHz
 Modulated by C/A-code & P-code
– L2: 1227.6 MHz
 Modulated by P-code only
– (3rd carrier, L3, used for nuclear explosion detection)
Most unsophisticated receivers only track L1
If L2 tracked, then the phase difference (L1-L2) can be
used to filter out ionospheric delay.
– This is true even if the receiver cannot decrypt the P-code
(more later)
– L1-only receivers use a simplified correction model
For Signal-Heads Only
Antenna Polarization: RHCP
L1
– Center Frequency: 1.57542 GHz
– Signal Strength: -160 dBW
– Main Lobe Bandwidth: 2.046 MHz
– C/A & P-Codes in Phase Quadrature
L2
– Center Frequency: 1.22760 GHZ
– Signal Strength: -166 dBW
Code modulation is Bipolar Phase Shift Key (BPSK)
Total SV Transmitted RF Power ~45 W
PRN Codes
GPS signals implement PseudoRandom Noise Codes
– Enables very low power (below background noise)
– A form of direct-sequence spread-spectrum
– Specifically a form of Code Division Multiple Access
(CDMA), which permits frequency sharing
Codes are known “noise-like” sequences
– Each bit (0/1) in the sequence is called a chip
– Each GPS SV has an assigned code
Receiver generates equivalent sequences internally and
matches signal to identify each SV
There are currently 32 reserved PRN’s
PRN Code Matching
Receiver slews internally-generated code sequence until
full “match” is achieved with received code
Time data in the nav message tells receiver when the
transmitted code went out
Slew time = time delay incurred by SV-to-receiver range
– Minus clock bias and whole cycle ambiguities
Receiver/Signal Code Comparison
Coarse Acquisition (C/A) Code
1023-bit Gold Code
Originally intended as simply an acquisition code for Pcode receivers
Modulates the L1 only
Chipping rate = 1.023 MHz (290 meter “wavelength”)
Sequence Length = 1023 bits, thus Period = 1 millisec
– ~300 km range ambiguity: receiver must know range to
better than this for position solution
Provides the data for Standard Positioning Service (SPS)
– The usual position generated for most civilian receivers
Modulated by the Navigation/Timing Message code
Precise (P) Code
Generally encrypted into the Y-code
– Requires special chip to decode
Modulates both L1 & L2
– Also modulated by Nav/Time data message
Chipping rate = 10.23 MHz
Sequence Length = BIG (Period = 267 days)
– Actually the sum of 2 sequences, X1 & X2, with sub-
period of 1 week
P-code rate is the fundamental frequency (provides the
basis for all others)
– P-Code (10.23 MHz) /10 = 1.023 MHz (C/A code)
– P-Code (10.23 MHz) X 154 = 1575.42 MHz (L1).
– P-Code (10.23 MHz) X 120 = 1227.60 MHz (L2).
Code Modulation
Image courtesy: Peter Dana, http://www.colorado.Edu/geography/gcraft/notes/gps/gps_f.html
Navigation Message
In order to solve the user position equations, one must
know where the SV is.
The navigation and time code provides this
– 50 Hz signal modulated on L1 and L2
The SV’s own position information is transmitted in a
1500-bit data frame
– Pseudo-Keplerian orbital elements, fit to 2-hour spans
 Determined by control center via ground tracking
– Receiver implements orbit-to-position algorithm
Also includes clock data and satellite status
And ionospheric/tropospheric corrections
The Almanac
In addition to its own nav data, each SV also broadcasts
info about ALL the other SV’s
– In a reduced-accuracy format
Known as the Almanac
Permits receiver to predict, from a cold start, “where to
look” for SV’s when powered up
GPS orbits are so predictable, an almanac may be valid
for months
Almanac data is large
– Takes 25 subcommutations of subframes 4,5
– 12.5 minutes to tranfer in entirety
Selective Availability (SA)
To deny high-accuracy realtime positioning to potential enemies,
DoD reserves the right to deliberately degrade GPS performance
– Only on the C/A code
By far the largest GPS error source
Accomplished by:
– “Dithering” the clock data
 Results in erroneous pseudoranges
– Truncating the nav message data
 Erroneous SV positions used to compute user position
Degrades SPS solution by a factor of 4 or more
– Long-term averaging is the only effective SA compensator
FAA and Coast Guard needs are pressuring DoD to eliminate
ON 1 MAY 2000: SA WAS DISABLED BY DIRECTIVE
How Accurate Is It?
Remember the 3 types of Lies:
– Lies, Damn Lies, and Statistics…
Loosely Defined “2-Sigma” Repeatable Accuracies:
– All depend on receiver quality
SPS (C/A Code Only)
– S/A On:



Horizontal: 100 meters radial
Vertical: 156 meters
Time: 340 nanoseconds
– S/A Off:



Horizontal: 22 meters radial
Vertical: 28 meters
Time: 200 nanoseconds
PPS (P-Code)
– Slightly better than C/A Code w/o S/A (?)
Differential GPS
A reference station at a known location compares
predicted pseudoranges to actual & broadcasts
corrections: “Local Area” DGPS
– Broadcast usually done on FM channel
– Corrections only valid within a finite range of base
 User receiver must see same SV’s as reference
– USCG has a number of DGPS stations operating
Base stations worldwide collect pseudorange and SV
ephemeris data and “solve-for” time and nav errors
– “Wide Area” DGPS
– Not yet (?) available in realtime
DGPS can reduce errors to < 10 meters
Carrier Phase Tracking
Used in high-precision survey work
– Can generate sub-centimeter accuracy
The ~20 cm carrier is tracked by a reference receiver
and a remote (user) receiver
The carrier is not subject to S/A and is a much more
precise measurement than pseudoranges.
Requires bookeeping of cycles: subject to “slips”
– Ionospheric delay differences must be small enough to
prevent full slips

Requires remote receiver be within ~30km of base
Usually used in post-processed mode, but RealTime
Kinematic (RTK) method is developing
Available Receivers
Garmin, Magellan, Lowrance, DeLorme, Trimble, etc.
Basic 6-12 channel receivers ~$100
– Usually includes track & waypoint entry
With built-in maps ~$150
Combination GPS receiver/cell phone ~$350
Survey-quality: $1000 and up
– Carrier tracking
– FM receiver for differential corrections
– RS232 port to PC for realtime or post-processing
Military Standard: $10000+ ??