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School of
Engineering
MSE, Rumc, GPS, 1
References
[1] Jean-Marie Zogg [HTW Chur], „GPS, Essentials of Satellite Navigation, Compendium“,
Document: GPS-X-02007-D, February 2009, http://www.u-blox.com/de/tutorials-links-gps.html.
Chapter 1.1: The principle of measuring signal transit time
Chapter 2.3.4: WGS-84
Chapter 4: GNSS technology: the GPS example
Chapter 7.2: Sources of GPS error
Chapter 8.2: Data interfaces
[2] GPS SPS Signal Specification, 2nd Edition (June 2, 1995),
http://www.navcen.uscg.gov/pubs/gps/sigspec/default.htm
[3] beautiful visualisation of the satellites‘ positions by HSR / ICOM
http://icom4u.hsr.ch/giove_a/index.htm
[4] Parkinson, Spilker, „Global Positioning System: Theory and Applications“, Volume I/II,
Progress in Astronautics and Aeronautics, Volume 163/164, 1996.
Terms
NAVSTAR GPS („Navigational Satellite Timing and Ranging - Global Positioning System)
is a GNSS (Global Navigation Satellite System), developed by the US-DoD in 197x and
fully operational since 1993.
Other GNSS under „development“: Glonass (Ru), Galileo (EU), Beidou/Compass (China)
GPS (Introduction)
School of
Engineering GPS-Principle
Assumptions
1. distance A between Tx is known.
2. Tx transmit synchronously,
Rx can only measure TDOA
(time difference of arrival).
Determination of positions via Time-of-Fly measurements
Conclusions
x-position (and time) with 2 Tx and
x,y,z-positions (and time) with 4 Tx
determinable!
Source: [1]
MSE, Rumc, GPS, 2
School of
Engineering
TDOA measurement by code correlation
Tx1 Tx2 Rx
D = (Δt∙c+A)/2
A
Code s1 with N chips
Tx1
Tx2
Rx
t
t
t
DSSS-modulation
(small peak-power
supports CDMA)
after correlation
with code s1
with code s2
∆τ
Tchip
Tchip
∆τ2
∆τ1
N chips
N chips
GPS-Principle MSE, Rumc, GPS, 3
Code s2 with N chips
School of
Engineering
Worldwide Reference Ellipsoid WGS-84
Ellipsoid approximates true (complex) shape of the earth
there are many different reference systems
GPS works with geocentric WGS-84 reference system
Source: [1]
cartesian coordinates
ellipsoidal coordinates (longitude, latitude, altitude) used for further processing
1° Grad = 60’ Bogenminuten.
1’ Bogenminute Breite = 1 Seemeile bzw. 1 nautischen Meile (NM) = 1.852 km.
1’ Bogenminute Länge = 1.852 km mal cos(Breitengrad).
conversion into CH-1903
coordinates required
[1]
GPS-Principle MSE, Rumc, GPS, 4
School of
Engineering
Basic equations
x,y,z,t coordinates and time of user
xi,yi,zi,ti coordinates and time of 4 satellites
(x1-x)2 + (y1-y)2 + (z1-z)2 = [c·(t1-t)]2
(x2-x)2 + (y2-y)2 + (z2-z)2 = [c·(t2-t)]2
(x3-x)2 + (y3-y)2 + (z3-z)2 = [c·(t3-t)]2
(x4-x)2 + (y4-y)2 + (z4-z)2 = [c·(t4-t)]2
4 equations (c: speed of light) and 4 unknowns
GPS-Principle
Source: [1]
MSE, Rumc, GPS, 5
School of
Engineering GPS-Subsystems
(orbital data)
1 Master Control Station (Colorado)
5 Monitor Stations world wide
3 Ground Control Stations
(with Satellite Uplink)
Source: [1]
MSE, Rumc, GPS, 6
School of
Engineering GPS-Space Segment
24 to 32 Satellites
55°
• at a height of 20‘180 km
• 6 different orbital planes
(4-5 satellites per plane)
• time of circulation ≈ 12 h
• always ≥ 4 satellites
visible everywhere on
earth
MSE, Rumc, GPS, 7
School of
Engineering
[1]
coverage area
GPS-Space Segment
Orbit and coverage area
MSE, Rumc, GPS, 8
School of
Engineering GPS-Space Segment
Link budget
25119 km (border of coverage area)
L1 (1575.42 MHz) Coarse/Acquisition (C/A-) Code for civil use
min. sensitivity
specified in [2]
[1]
MSE, Rumc, GPS, 9
School of
Engineering
Spectral power density of received signal and (thermal) noise floor
MSE, Rumc, GPS, 10
Link Budget
<= -130 dBm / MHz
-
source
bandwidth
1 MHz ≈ 1/Tchip
[1]
-174
signal before
despreading
-160
+ 14 dB
signal after
despreading
f – fL1
<= thermal noise + noise figure F
School of
Engineering Satellite-Signal
1575.42 MHz
Tchip ≈ 1 / Bandwidth
Source: [1]
MSE, Rumc, GPS, 11
t / ms 1 2 20
C/A-code C/A-code C/A-code
Tbit
1023 Tchip
School of
Engineering
32 Gold- / PRN-codes with N = 1023 chips
Generation with 2 LFSR, chip rate 1.023 Mchip/s
satellite identified by PRN-number
=> CDMA
GPS-Coarse/Acquisition-Codes MSE, Rumc, GPS, 12
School of
Engineering GPS User Segment
Correlation receiver Source [1]
(Doppler-Shift ± 5000 Hz)
Process-Gain 10·log10(1023) ≈ 30 dB
SNR = -16 dB before despreading => SNR = +14 dB after despreading
correlation time for data demodulation is 20 times longer
Gain
MSE, Rumc, GPS, 13
School of
Engineering GPS Navigation Message
Source: [1]
MSE, Rumc, GPS, 14
School of
Engineering
Navigation message contains 25 frames and lasts 12.5 minutes
a GPS-frame has 5 x 300 = 1500 bits and lasts 30 s
Subframes 1-3 are identical for all the 25 frames
subframe 1 contains clock data of transmitting satellite
subframes 2 and 3 contain ephemeris data of transmitting satellite
ephemeris data are highly accurate orbital data
a receiver has the complete clock values and ephemeris
data from the transmitting satellite every 30 seconds
Time-To-First-Fix (cold start autonomous) at least 18-36 s
=> slow start-up is a system-inherent limitation of GPS
Subframe 4-5 are different for all the 25 frames
subframe 5 contains almanac data of first 24 satellites plus health
almanac data are less accurate than ephemeris data
subframe 4 contains almanac data of satellites 25-32
and difference between GPS and UTC time
GPS Navigation Message MSE, Rumc, GPS, 15
School of
Engineering Accuracy without Selective Availability
Source: [1]
95%- or 2σ-accuracy: 100 m 95%- or 2σ-accuracy: 13 m
Deactivation of SA in the year 2000
68% or σ-accuracy: 6.5 m
MSE, Rumc, GPS, 16
School of
Engineering Improved GPS
Accuracy
90% < 10 m, artifical degradation switched off since 2000
Differential GPS
Main sources of GPS errors
effect of the ionosphere (counter measure: two frequency receiver)
multipath (mainly in urban areas)
effect of the satellite constellation (DOPs [Dilution of Precision])
transmission of
correction factors Source: [1]
MSE, Rumc, GPS, 17
School of
Engineering
EGNOS (European Geostationary Navigation Overlay System)
34 ground stations calculate correction signals (à la DGPS)
for GPS correction in a radius of about 200 km around the reference station
broadcast of correction signals via 3 geostationary satellites (C/A-Codes >32)
1-3 m accuracy
Improved GPS
Source: [1]
MSE, Rumc, GPS, 18
School of
Engineering Improved GPS
Achievable accuracy with DGPS and SBAS
SBAS: satellite based augmentation systems
[1]
MSE, Rumc, GPS, 19
School of
Engineering Improved GPS
Some Location Based Services are based on satellite navigation
GPS-Rx not always „on“, e.g. because of current consumption
time to first fix (cold start): 18-36 s (missing orbital data)
Assisted GPS (A-GPS)
delivery of missing orbital data via „fast“ channel, e.g. GSM/GPRS
[1]
MSE, Rumc, GPS, 20
School of
Engineering Data Interface to Peripherals
NMEA-0183 data interface
standardized by National Marine Electronics Association (NMEA)
data telegram for serial interface
Example: GGA data set (GPS fix data)
$GPGGA,130305.0,4717.115,N,00833.912,E,1,08,0.94,00499,M,047,M,,*58<CR><LF>
MSE, Rumc, GPS, 21
School of
Engineering Time Pulse
Most GPS-Rx generate 1- 4 time pulses per s
time puls is synchronized to UTC-time
Accuracy 5 - 60 ns
[1]
MSE, Rumc, GPS, 22
GPS-time-pulse is often used to synchronize devices
in a «large» area as e.g. base stations, gliders, …
School of
Engineering Performance Data of a GPS-Rx MSE, Rumc, GPS, 23
NEO-M8 series:
12.2 x 16.0 x 2.4 mm
School of
Engineering Modernization: BOC-Modulation
Advantages higher interference robustness and bandwidth efficiency
[1]
MSE, Rumc, GPS, 24
School of
Engineering Modernization: BOC-Modulation
BOC(1,1) and BPSK(1) have minimal impact on each other
Source: [1]
MSE, Rumc, GPS, 25
School of
Engineering GPS-Modernization
2. and 3. frequency for civil applications
compensation of ionosphere errors!
after 2013
integrity-signals, Search-and-Rescue-Functions
Source: [1]
MSE, Rumc, GPS, 26
School of
Engineering GPS-Simulator: An Example MSE, Rumc, GPS, 27
GPSG-1000 from Aeroflex / Cobham
• validation and test of GPS receivers
as well as navigation and tracking systems
• 3D position may be user entered
or 3D position may be dynamically simulated
• simultaneous GPS/Galileo simulations
antenna coupler
School of
Engineering
GNSS-Update: Frequency Bands see Navipedia http://www.navipedia.net/index.php/Main_Page
and some comments, https://www.zhaw.ch/~rumc/MSEwirecom.html
T. Kouwenhoven, "Gnss navigational frequency bands.png",, Jan 2011, also available at
http://www.navipedia.net/index.php/File:GNSS_navigational_frequency_bands.png
MSE, Rumc, GPS, 28
School of
Engineering Availability of GPS civil signals (Sep 2016) MSE, Rumc, GPS, 29
School of
Engineering Availability of Galileo civil signals (Sep 2016) MSE, Rumc, GPS, 30
School of
Engineering GNSS-Update: Signal-Spectra MSE, Rumc, GPS, 31
Source: Stefan Wallner, http://www.navipedia.net/index.php/GNSS_signal
School of
Engineering GNSS-Update: Signal-Spectra MSE, Rumc, GPS, 32
Source: Stefan Wallner
School of
Engineering Correlation Matrices of GPS-Satellite 9
PRN periode = 20 ms
∆f = 3100 Hz ∆f = 2400 Hz
doppler shift ∆f = 2300 Hz correlations show expected coherence
regarding the doppler shifts (∆f is
proportional to carrier frequency fc)
MSE, Rumc, GPS, 33
School of
Engineering
MSE, Rumc, GPS, 34
Real Time Kinematics (RTK)
• is a differential GNSS technique
• provides cm-level positioning performance in the vicinity of a base station
• carrier-based (rather than code-based) positioning
• see also: http://www.novatel.com/an-introduction-to-gnss/chapter-5-
resolving-errors/real-time-kinematic-rtk/
GNSS-Update: RTK
complicated process
“ambiguity resolution”
is needed to determine
the number of whole cycles.
School of
Engineering
u-blox, „u-blox bringt GNSS-Technologie mit zentimetergenauer Präzision
für den Massenmarkt“, https://www.u-blox.com/de/press-release/u-blox-
brings-centimeter-level-precision-gnss-technology-mass-market
Example: GNSS RTK module from uBlox
RTCM protocol
MSE, Rumc, GPS, 35
NEO-M8P (1-frequency Rx)
faster with multi-frequency GNSS-Rx
some m to 1-10 km
Recommended