Lecture 4.
Global Navigation Satellite
Systems
Contents
• Navigation
• History of GPS
• GPS Satellite Concept
• GPS System Segments
• Principle of Positioning
• GPS codes and the determination of travel time
• Accuracies / Error sources
History of Navigation
• Navigation on the Ocean (must be independent from the
continents)
Latitude and Longitude
j – Latitude
l – Longitude
History of Navigation
Navigation on the Ocean
• Speed and Bearing measurements to keep the
course.
• Sextant and Chronometer to determine the
Latitude and Longitude and update the position
History of Navigation
How do we determine the latitude?
90
j = 90 – a - b
a
j
b
a
History of Navigation
How to determine the Longitude?
• 24h = 360o
• We set the Chronometer on the Greenwich Meridian at noon to
0h.
• We read the time at the local noon on the sea.
l = DZeit x 15o
Contents
• Navigation
• History of GPS
• GPS Satellite Concept
• GPS System Segments
• Principle of Positioning
• GPS codes and the determination of travel time
• Accuracies / Error sources
History of GPS
• After the 2nd World War it became important to
create the global Navigation solution.
• In the Space era the satellites could be used as
„control points”.
• Surveyors used various satellites equiped with
reflectors as signals to link control networks (e.g.
islands)
• After 1960 the „US Navy Navigation Satellite System“
(NNSS) was created, after renamed to TRANSIT
History of GPS
• TRANSIT contained 6 satellites in polar orbits with the
elevation of ca. 1100 km (period ca 107 Min).
• The satellites were tracked from ground stations in US, and
the orbital parameters were updated twice a day.
• The satellites broadcasted the orbital parameters. The
position could be computed from the observation of Doppler
shifts with the accuracy of 1m.
Disadvantages
• Good satellite constellation in every two hours only
• Accurate position could be measured by long observations
only.
History of GPS
GPS (Global Positioning System) was developed to
• determine 3D positions in real time.
• determine accurate time
Speed
Bearing
NAVSTAR GPS (Navigation Satellite Time And Range) from
1973 as prototype
• First GPS satellite was started on June 27, 1977. Orbit
elevation ca. 20000 km.
Today the term GNSS (Global Navigation Satellite
System) is also used. Under this term, the NAVSTAR
GPS, GLONASS and GALILEO is also meant.
Contents
• Navigation
• History of GPS
• GPS Satellite Concept
• GPS System Segments
• Principle of Positioning
• GPS codes and the determination of travel time
• Accuracies / Error sources
GPS satellite concept
A minimum of 4 satellites must be tracked at the same
time to determine position.
Basically 3 satellite could be enough, but we
have to face some errors.
1 Satellite
2 Satellites
GPS satellite concept
Error-free
solution
Error-free
solution
Error-free
solution
3 Satellites
GPS satellite concept
• 24 Satellites planned
• 12-hour circular orbit in the elevation of 20200
km
• 55o inclination
• 4 satellites on each orbital plane (6 Orbital
planes – rect ascebsion difference 60°)
• At least 3 (now 8) reserve satellites
GPS satellite concept
GPS satellite concept
GPS Carrier phases
• L1 = 1575,42 Mhz (C/A Code, P-Code)
• L2 = 1227,6 Mhz (P-Code)
C/A Kode – „coarse acquisiton code“ (low accuracy)
P Kode – „precision code“ (high accuracy)
Contents
• Navigation
• History of GPS
• GPS Satellite Concept
• GPS System Segments
• Principle of Positioning
• GPS codes and the determination of travel time
• Accuracies / Error sources
GPS System Segments
Three segments:
• space segment
• control segment
• user segment
GPS System segments
Space segment:
• 24+8 GPS Satellites
• Orbits (20183 km, Inclination 55o and 60o between
the orbital planes)
• At least 4 Satellites on each orbital plane, where
the angular difference is 120o
• Period 12 hours
• Each satellite has its own ID, which is
boradcasted to the user.
• The satellites are equiped with atomic clocks.
GPS System segments
Ground segment
GPS System segments
Tasks of the ground segment:
• Controlling and managing the telemetry and
control stations.
• Computation of ephemerids (orbit
parameters) for each satellite.
• Ordering satellite maneuvres.
• Computing the data for the almanach
• Determine the GPS time (Atomuhr)
• Communication link to the satellites
GPS System segments
User segment:
GPS receivers
• track L1 and/or L2 frequencies
• track C/A code for at least 4 satellites, and
demodulation
• Time synchronization (Quartz clocks in the receivers)
• Decrypt satellite data from the code observations
(orbit, etc.)
• receive P(Y) code (US Army)
• Compute the pseudo-range to each satellite
• Compute the time offset (receiver clock error)
• Compute the position.
Contents
• Navigation
• History of GPS
• GPS Satellite Concept
• GPS System Segments
• Principle of Positioning
• GPS codes and the determination of travel
time
• Accuracies / Error sources
Principle of Positioning
Coordinate system (WGS-84)
The coordinates of satellites are given in this system.
Principle of Positioning
Equal time circles
2 Satellites
3 Satellites
p = cT
Principle of Positioning
Accuracies
• Depends on the accuracy of distance measurements
• Distance measurements – Travel time measurement
• 1ms (=) 300m (only atomic clocks could measure with
this accuracy)
• clock offset – a fourth satellite is also necessary for
the determination of positions. (Receiver clock error)
Principle of Positioning
Observation equations:
p1 
x
p
- x1   y p - y1   z p - z1   Dp  ei
p2 
x
p
- x2   y p - y2   z p - z2   Dp  ei
p3 
x
p
- x3   y p - y3   z p - z3   Dp  ei
p4 
x
p
- x4   y p - y4   z p - z4   Dp  ei
2
2
2
2
2
2
2
2
2
2
2
2
Dp  cDT
p1..p4
Pseudoranges
xp, yp, zp
Coordinates of the receiver
xi, yi, zi
Coordinates of the satellite i, i=1..4
Dp
Offset due to the clock error
DT
Receiver clock correction
ei
additional error
Principle of Positioning
The navigation solution provides us a worlwide
accurate time system.
By determining the receiver clock error, one can
restore the GPS time using cheap quartz clocks.
Since the GPS time is an atomic time, we can
substitute an atomic clock using a GPS receiver.
Contents
• Navigation
• History of GPS
• GPS Satellite Concept
• GPS System Segments
• Principle of Positioning
• GPS codes and the determination of travel time
• Accuracies / Error sources
• Differential GPS (DGPS)
• Applications in Surveying
GPS codes and their travel time
Two frequencies: L1=1575,42 Mhz and L2=1227,60 Mhz
Both of them are a multiple of the ground freqency: L0=10,23
Mhz
The carrier phases are with PRN-codes („pseudo random
noise“) modulated (L1 – C/A u. P, L2 – P).
All codes are
biploar codes:
Positive
Amplitude=0
Neg. Alplitude=1
GPS codes and their travel time
What is a PRN code?
• It is a statistical distribution of impulses, which are similar
to noise.
• In reality the sequence of the impulses follow a
complicated rule, which is necessary for the decryption.
The receiver knows this algorithm.
If one can determine the time delay with the accuracy of 1%:
C/A Code
accuracy of 3 m
chiprate 1ms=300m
P Code
accuracy of 0,3 m
chiprate 0,1ms = 30m
GPS codes and their travel time
GPS Signal modulation:
• The C/A code contains 1023 positive and negative
Impulses (bits) with the span of 1 ms each. The whole
sequence has the length of 300km (corresponds to
1ms).
• A navigation message is also modulated to the carrier
freqency with the frequency of 50bit/sec. The length of
the message is 1500 bits (30 sec)
• These 1500 Bits are split into 5 sub-frames with 10
words of 30 bits in each subframe. Each subframe is
started with two special words:
•„Telemetry Word“ (TLM) = Orbit corrections
• „Hand Over Word“ (HOW) = GPS time
GPS codes and their travel time
Clock corrections are present in the first subframe.
In the second and third the orbit parameters and iono
corrections are broadcasted.
Contents
• Navigation
• History of GPS
• GPS Satellite Concept
• GPS System Segments
• Principle of Positioning
• GPS codes and the determination of travel time
• Phase observations
• Accuracies / Error sources
Phase observations
It could be seen that the code observation is too inaccurate for
the applications in surveying;
A more accurate method is needed for the determination of the
satellite-receiver distance.
Instead of using the codes, the carrier phases are measured;
Since the wavelength of the L1 carrier signal is approx. 19cm,
a more accurate distance observation can be achieved (in the
order of a few mm)
Phase observations
Contents
• Navigation
• History of GPS
• GPS Satellite Concept
• GPS System Segments
• Principle of Positioning
• GPS codes and the determination of travel time
• Phase observations
• Accuracies / Error sources
Error sources
Accuracy and error sources
Error sources – signal propagation
• The atmosphere has an impact on the signal
propagation path.
• Troposphere and Ionosphere
Ionosphere
• The Ionosphere (70-1000 km elevation) contain
electrons and ions, which have an effect on the
propagation of electromagnetic signals.
• the delays depend on the frequency, intensity of the
radiation of the sun (day-night variation, seasonal
variation, effect of the solar activity - sunspots);
Accuracy and error sources
Troposphere
• Up to 40-70 km (tropospheric refraction)
• Meteorological factors (weather, air pressure,
temperature, etc.)
• Empirical models
• overall effect is ca. 2.3m in the vertical direction
Multipath
• GPS signals are reflected,
and direct and indirect signals
are also received.
Indirect
Direct
Accuracy and error sources
Cycle slips
• The continuous signal reception is broken;
• Thus the counting of the number of full cycles is
erroneous (nl)
• Solution: avoid nearby objects that could obscure the
satellites
Dj
S t
R t
0
Accuracy and error sources
Error sources – receiver error
• Thermal noise
• receiver clock corrections
• antenna phase center offsets and variations
Accuracy and error sources
Error sources – satellite geometry
• Not all of the satellite constellation enables the
optimal positioning.
• DOP – „Dilution of Precision“
 POS DOP  r
r
accuracy of the pseudorange observation
POS
accuracy of the positioning
PDOP is the reciprocal value of the volume V of a
tetraeder of 4 satellites + 1 ground station.
Accuracy and error sources
Good
Bad