GPS 101
HOW GPS WORKS
University of Idaho GIS Day
November 19, 2014
Dr. Lawrence R. Weill
lweill@cs.com
PRE-SATELLITE RADIONAVIGATION SYSTEMS
LF Radio Direction Finding (~1900 to present): Angle-based
position fixing and homing.
Radar (1934-1939 to present): Angle- and range-based positioning relative
to surrounding objects.
Omega (1971 to 1997): Hyperbolic phase-difference positioning on a
global scale.
DECCA (1944-2001): European hyperbolic phase difference positioning.
Loran A (1942 to 1980), Loran C (1974 to present): Hyperbolic TOA
difference positioning.
VOR/DME (1946 to present): Aviation angle- and range-based position
fixing and homing using VHF and UHF frequencies.
TACAN (~1960 to present): Military version of VOR/DME.
LF RADIO DIRECTION FINDING
RADIOBEACON
F
RD
RADIOBEACON
LL
NU
NE
LI
POSITION
FIX
E
LIN
L
L
NU
F
RD
NORTH
NORTH
COMPASS
AZIMUTHS
LO
P
#1
LORAN & DECCA POSITIONING (HYPERBOLIC)
LO
P
#2
SLAVE
MASTER
SLAVE
POSITION FIX
MASTER
ACCURACY OF PRE-SATELLITE
RADIONAVIGATION SYSTEMS
OMEGA
GLOBAL
VOR/DME
LOCAL
TACAN
DECCA, LORAN C
180 M
400 M
900 M
2200 M
1957: SPUTNIK, WORLD’S FIRST SATELLITE
DOPPLER-BASED SATELLITE NAVIGATION
Sputnik gave rise to satellite radionavigation using Doppler.
1957: Scientists at MIT noted frequency variation of Sputnik’s signal due
to Doppler, and realized this can be used to track the satellite’s location.
In reverse, the received Doppler frequency variation can be used to find
the position of the receiver.
1959: The Doppler principle for finding location was used in TRANSIT,
the first operational satellite-based navigation system. It was developed
by Johns Hopkins Applied Physics Laboratory (APL) to support the U.S.
Navy submarine fleet, and eventually used 10 low-earth orbit satellites.
Transit positioning accuracy was roughly 400 meters. Ships had to wait
for satellite passes and resolve a cross-track ambiguity. Ship movement
complicated the process of establishing a position.
TRANSIT POSITIONING (DOPPLER CURVE)
DOPPLER SHIFT AT POINT A
DOPPLER SHIFT AT POINT B
0
TIME
B
A
SATELLITE GROUND TRACK
EVOLUTION OF GPS (1)
1960: Raytheon Corporation suggests the first 3-D TDOA satellite
navigation system (MOSAIC) for the Mobile Minuteman ICBM system.
MOSAIC was dropped in 1961 when the Mobile Minuteman program
was cancelled.
1963: Aerospace Corporation develops its concept of a 3-D satellite
navigation system. The Air Force supports this effort and designates it
System 621B, which later demonstrated a new pseudorandom noise
(PRN) ranging signal.
1964: The Naval Research Laboratory (NRL) develops the Navy
Timation satellite system for advancing the development of highstability clocks in space, an important foundation for GPS. The first
Timation satellite is launched in 1967.
1964-1973: Various groups, including the Army, Navy, and Air
Force, are engaged in satellite navigation concept debates.
EVOLUTION OF GPS (2)
December 17, 1973: The NAVSTAR GPS concept is solidified.
1973 to 1979: GPS concept validation takes place.
July 14, 1974: The very first NAVSTAR satellite is launched,
carrying an atomic clock.
1978 to 1985: 10 Block I GPS satellites, used for full-scale
development and testing of the GPS system, are launched.
1989 to 1994: 24 Block II operational satellites are launched.
December 1990: GPS system becomes operational.
April 1995: GPS reaches full operational capability.
GPS
Constellation
6 Orbits
55o
Inclination
20,200 km
Altitude
~ 32 Sats
11 hr 56 min
Orbital Period
(X1,Y1,Z1)
2D POSITIONING
EARTH
E
NC
A
T
DIS 0 Km
50
24,
POSITION FIX
TYPICAL ACCURACY
10 - 30 METERS
DIS
23,
TA
N
500
CE
Km
(X2,Y2,Z2)
(X,Y,Z)
Satellite
"Next pulse xmitted at time T1
and satellite position (X,Y, Z)"
Pulse
Receiver
Message
T1
Signal speed = c
Atomic
satellite
clock
Receiver
clock
T1
Message
T2
Atomic
satellite
clock
Receiver
clock
T2
Distance = c x (T 2 - T 1)
COPs WITH FAST
RCVR CLOCK
SAT #
2
SA
COP
COPs WITH
SYNCHRONIZED
SAT & RCVR
CLOCKS
C
T #1
OP
SATELLITE
RA
NG
E
PS
EU
RECEIVER
DO
RA
N
GE
RC
CL VR
O
ER CK
RO
R
RCVR CLOCK ERROR
CAUSES NON-CONCURRENT
INTERSECTIONS
SA
SAT #
2
COP
#
OP
C
3
T
SA
C
T #1
OP
2D POSITIONING EQUATIONS
 X ,Y , Z  
receiver position
GPS also provides
very accurate time!
Ce  receiver clock error (m)
 xk , yk , zk  
position of k th satellite
 k  pseudorange to k th satellite
1 
 x1  X    y1  Y    z1  Z   Ce
2 
 x2  X    y2  Y    z2  Z 
3 
 x3  X    y3  Y    z3  Z 
2
2
2
2
2
2
2
2
 Ce
2
 Ce
X 2  Y 2  Z 2  R  radius of earth  6.37 106 m
NOISE
Each pulse
replaced by
One period of pseudorandom code
TRANSMISSION OF REPEATING CODE PERIODS
INSTEAD OF TRANSMITTING A SEQUENCE OF PULSES,
TIME
GPS SATELLITES TRANSMIT A STREAM OF REPEATING CODE PERIODS:
CODE EPOCHS
(BEGINNING OF PERIODS)
N
N+1
PERIODS
N+2
N+6
1023
CHIPS
1 MSEC
PERIOD
ONE PERIOD OF C/A CODE
EPOCH
1 CHIP (0.9775 m icros e c or 293 m )
1
-1
1023 CHIPS = 1 C/A CODE PERIOD = 1 M ILLISECOND
1.023 M HZ CHIPPING RATE
Each satellite has its own unique C/A code
WHY USE A PSEUDORANDOM CODE?
● A pseudorandom code can have much greater energy than a short
pulse while still providing high-resolution measurement of range.
● The high resolution is accomplished by a correlation process.
● Correlation also provides protection from any interfering signal
that does not match the pseudorandom code being used.
● By using a unique pseudorandom code for each satellite, all
satellites can transmit on the same frequency without mutual
interference.
CORRELATION
RECEIVED CODE
1
MULTIPLY
ACCUMULATE
-1
1
-1
RECEIVER-GENERATED
CODE REPLICA
CORRELATION
OUTPUT
RECEIVED CODE
1
-3 chip misalignment
-1
Sum of chip products = -4
1
-1
REPLICA GENERATED BY RECEIVER
1
Alignment
-1
1
Sum of chip products = 35
-1
1
1
-1
+3 chip misalignment
Sum of chip products = -4
-1
CORRELATION FUNCTION
RECEIVED CODE
4 CHIPS EARLY
CODES
ALIGNED
RECEIVED CODE
4 CHIPS LATE
DELAY, CHIPS
-4
-3
-2
-1
0
1
2
3
4
CORRELATOR REJECTION CAPABILITY
MULTIPLY
ACCUMULATE
SMALL OUTPUT
ACCUMULATE
SMALL OUTPUT
ACCUMULATE
SMALL OUTPUT
(ALL SATS CAN
TRANSMIT ON
SAME FREQUENCY!)
NOISE
MULTIPLY
INTERFERENCE
MULTIPLY
CODE FROM ANOTHER SAT
RECEIVED CODE
TOO EARLY
EARLY-LATE
CODE TRACKING
DELAY
RECEIVED CODE
ALIGNED
EARLY
CORRELATION
PUNCTUAL
CORRELATION
LATE
CORRELATION
DELAY
RECEIVED CODE
TOO LATE
DELAY
GPS CODE TRACKING LOOP
LP FILTER
LP FILTER
FE
FP
DESPREAD
SIGNAL
RECEIVED
SIGNAL
LP FILTER
IN NOISE
FL
(LP FILTERS
ACT AS
ACCUMULATORS)
CODE
EARLY
FL2 - F E
CODE
CODE
PUNCTUAL
2
"CLEAN" CODE ALIGNED
WITH RECEIVED CODE
LATE
ERROR
SIGNAL
3-BIT SHIFT REGISTER
CODE
GENERATOR
CODE
CONTROL
C/A Code Period
Most Recent
Tracking
Code Epoch
X1 = time into code period
Rcvr Clock
Sat #1
Time
T1 = xmit time of epoch
C/A Code Epoch
X2
Sat #2
T2
X3
Sat #3
T3
X4
Sat #4
T4
TRCVE
th
Pseudorange to k satellite = c[TRCVE - (Tk + Xk)] meters
50 BPS DATA BIT STRUCTURE
1
2
3
19
20
NORMAL C/A CODE FOR DATA BIT = 1
INVERTED C/A CODE FOR DATA BIT = 0
1
2
3
ONE DATA BIT
LENGTH = 20 MSEC
20 C/A CODE PERIODS
19
20
L1 CARRIER
C/A CODE
50 BPS
DATA
TRANSMITTED
SIGNAL
GPS DATA FRAME
Subframe #
0
30
60
TIME
1
300
330
600
630
360
900
930
1200
1230
TIME
6
600
12
900
660
EPHEMERIS OF TRANSMITTING SATELLITE
18
1200
960
TIME
4
300
EPHEMERIS OF TRANSMITTING SATELLITE
TIME
3
Bit Numbers
CLOCK CORRECTION
TIME
2
5
Preamble (1 0 0 0 1 0 1 1) at Beginning of Each Subframe
Elapsed Time
(Seconds)
ALMANAC (PAGES 1-25)
24
1500
1260
ALMANAC (PAGES 1-25)
30
GPS RECEIVER OPERATIONS AT TURNON
● Determine visible satellites and approximate Dopplers: Uses
approximate receiver position (if known) and stored almanac data.
● Signal acquisition: Search for each visible satellite, both in frequency
and code shift.
● Signal tracking: Track the code and carrier of each satellite.
● Bit synchronization: Determine start times of bits in the 50 bps
navigation data message.
● Read navigation data message: Get timing and ephemeris data
to put transmit time tags on received code epochs and establish
positions of satellites. Ephemeris data may take up to 30 seconds.
● Make code and/or carrier pseudorange measurements.
● Solve positioning equations.
PSEUDORANGE ERROR SOURCES
Ionospheric Error: Up to 20-30 meters. Reduced by dual-frequency
operation, reference station corrections, and differential GPS (DGPS).
Tropospheric Error: Up to 20 meters. Reduced by tropospheric
model corrections, using higher-elevation satellites, and DGPS.
Multipath: Up to 30-40 meters. Reduced by avoiding nearby
reflectors, using receiver multipath mitigation technology, and using
higher bandwidth signals. Not reducible by DGPS.
Satellite Clock and Ephemeris Errors: Generally below 1 meter.
Almost completely eliminated by DGPS.
Receiver Errors (Thermal Noise, Processing): Generally below 13 meters. Reduced by improved signal processing in HW or SW.
POSITION DILUTION OF PRECISION (PDOP)
PDOP is a number indicating the ratio of position accuracy to
pseudorange accuracy. It depends on satellite position geometry.
Poor Geometry
(PDOP = ~18)
SAT #3
SAT #1
SAT #2
SAT
#1
SAT #3
Good Geometry
(PDOP = ~3)
SAT #2
CODE-BASED DIFFERENTIAL GPS
(Sub-meter Positioning Accuracy)
ROVER GPS
POSITION
R
CTO
E
V
NT
BASE STATION
GPS POSITION
POSITION
ERROR
E
CEM
A
L
P
IS
ED D
T
A
IM
EST
E
TRU
R
CTO
E
V
T
M EN
E
C
LA
DISP
POSITION
ERROR
ROVER
TRUE POSITION
BASE STATION
TRUE POSITION
POSITION ERRORS EQUAL
DISPLACEMENT VECTORS EQUAL
CODE-BASED DIFFERENTIAL GPS METHODS
METHOD 1
BASE STATION
SEND BASE STATION POSITION ERROR VECTOR
ROVER
ROVER SUBTRACTS ERROR VECTOR
FROM ROVER GPS POSITION
METHOD 2
BASE STATION
SEND PSEUDORANGES & XMIT TIMES OF OBSERVED SATS,
ROVER
AND BASE STATION TRUE LOCATION
BASE OBSERVED SATS:
ROVER OBSERVED SATS:
3 4 7 11 16
2 4 6 7 11 13 16 22
METHOD 2 ROVER OPERATIONS:
1. Use only data from sats observed in common.
2. Compute rover GPS position.
3. Use pseudoranges and xmit times
received from base station to compute
base station GPS position.
4. Compute base station position error vector
and subtract it from rover GPS position.
GPS RECEIVER CARRIER TRACKING
FREQUENCY
COMPARATOR
CARRIER
+ NOISE
FREQ.
ERROR
LOWPASS
FILTER
FREQUENCY
CONTROL
cos(t + )
OSCILLATOR
cos( t + 0)
+ n(t)
PHASE
COMPARATOR
PHASE
ERROR
LOWPASS
FILTER
PHASE
CONTROL
"CLEAN" COPY OF CARRIER
WITH  =  0 and  = 0
DIFFERENTIAL CARRIER PHASE
CARRIER AT BASE STATION
CARRIER AT ROVER
1 CYCLE
TIME
1/3 CYCLE
PHASE DELAY
DELAYS OF 1-1/3 CYCLES, 2-1/3 CYCLES, ETC.
LOOK THE SAME AS A DELAY OF 1/3 CYCLE
DIFFERENTIAL CARRIER PHASE PRINCIPLE
SATELLITE AT
KNOWN POSITION
CRESTS OF
CARRIER WAVE
0<
Ca
M
<1
MEASURED BASE-TO-ROVER
PHASE DIFFERENCE IS
(y - x) + (M - N) CYCLES
s
r Cycle
Carrie
0 <= x
+y
cm
N+x
rrie
= y r Cy
< 1 cle
s
9
=1
M - N IS AN INTEGER
AMBIGUITY
ROVER
BASE STATION
AT KNOWN POSITION
SECOND-DIFFERENCE CARRIER PHASE PRINCIPLE
SAT #1
SAT #2
SATELLITES AT
KNOWN POSITIONS
 = 19
RECEIVED
SAT 1 - SAT 2
CARRIER PHASE
DIFFERENCE:
M + y Cycles
ROVER
SECOND DIFFERENCE:
ROVER SAT 1-2 DIF
MINUS
BASE SAT 1-2 DIF
cm
RECEIVED
SAT 1 - SAT 2
CARRIER PHASE
DIFFERENCE:
N + x Cycles
BASE STATION
AT KNOWN POSITION
DIFFERENTIAL CARRIER PHASE POSITIONING
(Centimeter-level Accuracy)
SATS
1&
SA
TS
1&5
3
SATS 1 & 2
SA
TS
1
&
4
ROVER TRUE RELATIVE POSITION
DISTANT AMBIGUITIES
REMOVED BY CODE
DIFFERENTIAL POSITIONING
GPS MODERNIZATION: NEW CIVILIAN SIGNALS
L1 C/A: The legacy civil signal, which will continue to be
broadcast on L1 frequency 1575.42 MHz.
L2C: ● Signal on L2 frequency 1227.60 MHz, currently broadcast
by seven satellites.
● Enables L1/L2 ionospheric error corrections.
● Higher transmitted power level for faster signal acquisition
and better positioning accuracy.
L5:
● Signal on L5 frequency 1176.45 MHz.
● Technically advanced signal with higher power and greater
bandwidth
L1C: ● Signal at L1 frequency designed to enable interoperability
betweeen GPS and international GNSS systems.
MAGELLAN SYSTEMS
● Ad in Los Angeles Times, 1986
● Technical Founders of Magellan Systems: Don Rea
(hardware), Norm Hunt (software), Larry Weill (algorithms)
● Seed money from Ed Tuck
● Design challenges with steep learning curve
● Difficulty finding investors willing to commit
● Don’s breadboard
Magellan NAV 1000: World’s
first handheld GPS receiver, first
sold in 1989.
Single-channel slow sequencing
design.
Approximately the size of a brick.
Weight approximately 1 ½ lbs.
Rotatable quadrifilar antenna.
Dot-matrix LCD display.
Powered by 6 AA alkaline cells.
Battery life approximately 4 hrs.
TTFF from cold start 1 to 3 min.
MEMORABLE EVENTS
● Discovery of map error
● Communicating with aliens
● Saving lives
● NAV 1000 in the Gulf War—Iraq invades Kuwait in 1990
● Two new products designed under the radar
● BTG vs. Magellan
● Magellan in the Time and Navigation exhibit at the
Smithsonian National Air and Space Museum