4 chapters: Global Navigation Satellite Systems …geta.aalto.fi/en/courses/simona_lohan.pdfGlobal...
Transcript of 4 chapters: Global Navigation Satellite Systems …geta.aalto.fi/en/courses/simona_lohan.pdfGlobal...
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Graduate School in Electronics, Telecommunications and Automation
Global Navigation Satellite Systems (GNSS): present and future
Elena Simona Lohan, Academy Research Fellow., Dr. Techwww.cs.tut.fi/tlt/pos
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Outline
4 chapters:1. Overview of satellite navigation systems
(current and planned)2. Signals and frequencies in GNSS3. Receiver signal processing4. Dealing with wireless channels impairments
(multipaths, ionospheric delays, etc)
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OVERVIEW OF SATELLITE NAVIGATION SYSTEMS
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Chapter 1 outline
Motivation , applications and classification of GNSSs3 segment architecture of GNSSSystem-by-system overview:• GPS• Galileo• GLONASS• COMPASS
GNSS services and other satellite navigationsystems (SBAS)
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GNSS – some definitions
GNSS stands for Global Navigation Satellite SystemCurrently, there are 4 global navigation systems (on sky or under standardization):• Navstar Global Positioning System, GPS: US, military control,
fully functional, 32 operational satellites• GLONASS: Russia, military control, 24 operational satellites,
fully functional since Dec 2011• Galileo: Europe, civilian control, in standardization phase; first 2
satellites belonging to the final constellation launched in Oct2011; more to come in summer 2012
• COMPASS: China, former BEIDOU system, currently 10 satellites on sky (10th one launched on 1st of Dec 2011) –currently operating on a trial basis (full coverage around China)
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GNSS satellites
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Sources: http://www.navcen.uscg.gov/ftp/gps/ggeninfo/gps-iif.tif, http://ilrs.gsfc.nasa.gov/satellite_missions/list_of_satellites/g115_general.html, http://www.esa.int/http://www.blog.gpscompared.co.uk/tag/sat-nav
GPS Glonass
Galileo
Compass
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With satellite-based positioning we can acquire: • global coverage (with some limitations, for example indoors) • good accuracy• Integrity, especially if several GNSS systems are used together.
Inexpensive satellite navigation receivers:
Mini-GPS handheld receiver + location finder at about 40 EUR; a Garmin NUVI215 GPS receiver with UK and Ireland maps at about 120 EURAccording to the available maps inside the GPS receiver, price can reach few hundred EUR
Motivation for GNSS
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transportation (air, land, maritime), surveying and mapping, agriculture, telecommunications, natural resources exploration, commercial, etc.
The current global market of applications and services of positioning systems is estimated to about few tens billion EUR (according to the EU statistics) and it is expected to grow about 7 times over next 5 years.
Applications for satellite-based positioning
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Classification of satellite navigation systems
Global coverage (GNSS):• GPS (US)• GALILEO (Europe)• GLONASS (Russia)• COMPASS (China)
Local/regional coverage (RNSS)• QZSS (Japan)• IRNSS (India)
GPS/GNSS augmentation : they offer support to GPS/GNSS; do not offer stand-alone navigationsolutions
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- GNSS systems are quite complex, involving many different components. The satellites are the most visible part, but they require a heavy ground infrastructure in order to deliver the right signals with the right parameters to the users.
- All GNSS systems are based on the same architecture (3-segment architecture):
- Space segment: satellites- Ground segment: monitoring, controlling and
uploading stations- User segment: user community/GNSS receivers
GNSS system architecture (I)
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- The number of satellites and monitor stations differ according to the GNSS system (GPS, Glonass, Galileo, ...)- The geographical placement and number of ground stations is important, especially with respect to the integrity of the positioning solution. (Integrity is the characteristic that allows a user to evaluate the confidence he can attribute to the positioning the receiver is providing)
GNSS system architecture (II)
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Space segment
User segmentGround segment
downlinkUplink/downlink
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Tasks of space segment
The space segment is formed by the satellites, also abbreviated by SV (Satellite Value). The functions of a satellite are:
It receives and stores data from the ground control segment.It maintains a very precise time. In order to achieve such a goal, each satellite usually carries several atomic clocks of two different technologies (e.g., cesium and rubidium), depending on the generation of the satellite.It transmits data to users through the use of several frequenciesIt controls both its altitude and position.It may enable a wireless link between satellites
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Where are the satellites situated?
Typically in MEO (Medium Earth Orbit) orbits
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LEO : Low Earth OrbitMEO: Medium Earth OrbitGEO: Geo-synchronous Earth Orbit,(orbital period that synchronizes with the Earth’s speed of rotation)
IGSO = Inclined Geo-SynchronousOrbit – belongs to GEO type (the satellite is placed in orbit directly above the Earth’s equator at a precise height, so that it maintains the same position relative to the Earth’s surface)
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Where are the satellites situated?
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Type LEO MEO GEO
Height (above Earth) Up to 1600 km From about 6000 km
to about 32000 kmAt about 35874 Km
Time in LOS 15 min 2-4 hrs 24 hrs
Cycle around Earth Up to 18 times/day Around twice/day Once/day
Advantages
Lower launch costs Very short round trip delays Small path loss
Moderate launch cost Small roundtrip delays
Covers 42.2% of the earth's surface Constant view No problems due to Doppler
Disadv. Very short life 1-3 month
Larger delays Greater path loss
Very large round trip delays Expensive rx due to weak signal
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Tasks of ground segment
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The main functions of the ground segment are to:Monitor the satellites; activate spare satellites (if available) to maintain system availability; check the SV healthEstimate the on-board clock state and define the corresponding parameters to be broadcast (with reference to the constellation’s master time)Define the orbits of each satellite in order to predict the ephemeris data, together with the almanac;Determine the altitude and location orders to be sent to the satellites to correct their orbits.
Ephemeris = precise orbit and clock corrections for the satellites. Each satellite broadcast only its ephemeris data. In GPS, ephemeris is broadcast every 30 s.Almanac= coarse orbital parameters of the satellites (valid for up to several months)
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Tasks of user segment
The main functions of a GPS receiver are:Receive the data from the satellites belonging to one or several constellations (e.g. GPS; Galileo) on one or several frequencies. If several constellation => multi-system receivers. If several frequencies => multi-frequency receivers (dual-frequency GPS-GLONASS receivers are rather common nowadays)Acquire the signal from each satellite on sky (acquisition= identification of satellite code and coarse estimation of time delays and Doppler shifts)Track the signal received from the satellites on sky (tracking =fine estimation of time delay and Doppler shifts);Estimate the PVT solution (position, velocity time estimation).
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User segment (cont.)
Block diagram of a GNSS receiver
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ADC= Analog-to-Digital converterASIC = Application Specific Integrated Circuit (Note: alternative software GNSS receivers are also possible)PVT = Position Velocity Time computation
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GNSS frequency bands
GNSS occupy the so-called L-band (wavelengths between15 and 30 cm, frequencies between 1 and 2 GHz)
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7.2.20
fc
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Next slides:
Examples of architectures (focus on space & ground segments) for:• GPS• GALILEO• GLONASS• COMPASS
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Controlled by US Department of Defense (DoD) Initially for military use only, later on/nowadays also for civilian applications
Its 3 segments are as follows:Satellite constellation: currently 32 satellites; they provide the ranging signals and navigation data messages to the user equipment. Originally, there were 24 satellites.Ground control network: 1 Master Control Station (MCS), 3 uploading stations, and 11 monitor (surveillance) stations; this segment tracks and maintains the satellite constellation by monitoring satellite health and signal integrity, and by maintaining satellite orbit configuration.User equipment: it receives signals from the satellite constellations and computes user Position, Velocity and Time (PVT).
(Navstar) GPS - Overview
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Space segment: GPS constellation
Currently, there are 32 GPS satellites on the sky.(http://tycho.usno.navy.mil/gpscurr.html)
Originally -> Block II GPS satellites only (24):- In 6 nearly circular orbital planes.-Min 4 satellites/plane.- Orbital plane inclination of 55 degrees.- altitudes of 20200km above the earth.- Period: 11 h 58 min
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Source: http://mgitecetech.files.wordpress.com/2010/12/figure-1.jpg
Period: 14 hr 22 min
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1 Master Control Station (MCS): located at Schriever Air Force Base, Colorado; here the data from the monitor stations are processed 24 h a day in real time
3 uploading stations: located at Ascension, Diego Garcia and Kwajalein; they operate in S-band (2 - 4 GHz).
11 monitor (surveillance) stations: every satellite can be seen from at least two monitor stations; the monitor stations track all satellites in their range and collect data of the satellite signals. The raw data are then sent to the mater control station where the data are processed.
GPS ground segment (I)
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GPS ground segment (II)
The monitor stations measure signals from the Satellite Values which are incorporated into orbital models for each satellites: precise orbital data (ephemeris) and SV clock corrections.At the Schriever Air Force base, Colorado, the back-up “master clock” of the United States Naval Observatory is located, which has a stability of less than 1 s in 20 million years.
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GPS Control Segment – after 2005Source:http://www.kowoma.de/en/gps/control_segment.htm, taken fromEarthmap:NASA
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The Galileo Programme (so named to honor the great European scientist Galileo Galilei) is a joint initiative of the European Commission (EC) and the European Space Agency (ESA) to provide Europe with its own independent global civilian controlled satellite navigation system.It is an autonomous system, interoperable with GPS and globally available.It is based on the same technology as GPS (i.e., DS-CDMA) and provides a similar - and possibly higher - degree of precision, thanks to the structure of the constellation of satellites and the ground-based control and management systems planned.
Galileo system: overview
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1998: EU decides to develop its own satellite navigation system ”Galileo” 2000: Definition phase of Galileo starts (it was completed in 2003).Mar 2002: statement on GPS-Galileo cooperation; establishment of Galileo Joint Undertaking (GJU) for management and concession of Galileo.Nov 2003: Joint statement between European Commission and US regarding GPS-Galileo1June 2004: EU and US signed GPS-Galileo agreement:
Common civil signal: BOC(1,1) modulation was selected as the baseline for both Galileo and GPS future OS signals
Galileo history (I)
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July 2004: An official European Union Regulatory Authority, the European GNSS Supervisory Authority (GSA) was established. GSA replaced GJU completely in 2006.2005: first Galileo test satellite launched on orbit (GIOVE-A)May 2006: First Galileo standardization documents (for OS signal only) were made available2007: MBOC modulation adopted for common GPS-Galileo signal for civilian use 2008: second Galileo test satellite (Giove-B) launched on orbit2011: first two IOV Galileo satellites launched (in Oct). IOV= In-Orbit Validation.
Galileo history (II)
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Galileo Space Segment
Galileo will be based on a constellation of 30 satellites (27 + 3 reserve) and ground stations
It uses the same principles as Navstar GPS for position location
Constellation of 30 satellites at 23222 Km altitude (17 orbits in 10 days). Orbital inclination 56 degrees. 10 satellites per plane, 3 planes.
– Only 9 satellites per plane active.
– One satellite per plane is in-orbit spare.
Period: 14 hr 22 min
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Galileo space segment – spacecraft
• Dimensions: 2.7 x 1.2 x 1.1 m3
• Overall Spacecraft: 680 Kg / 1.6 kW class
• Launcher Options:
Ariane, Proton, Soyuz• Two on-board atomic clocks:
The Rubidium Atomic Frequency standard Clock: frequency around 6 GHz, 3.5 Kg mass, 30 W powerThe Passive Hydrogen Maser Clock: frequency around 1.4 GHz, 15 kg mass, 70 W power (the most stable clock ever to fly in space)
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Sourse: ESA pages
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Galileo - Trivia
First 2 operational satellites launched on 21st Oct2011 from Europe's Space Port in Kourou, FrenchGuianaPress release: http://ec.europa.eu/enterprise/
policies/satnav/galileo/satellite-launches/index_en.htm
Galileo satellites will be named with namesof EU children (one child per country, winner drawn according to a drawingcompetition)
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2 redundant Galileo Control Centers (GCS) (Europe): control of the satellites and navigation mission management; in Oberpfaffenhofen(Germany, near Munich) and Fucino (Italy, near Rome)10 mission up-link stations (ULS) (worldwide) in C-band (5.925–6.425 GHz)29-30 Galileo Sensor/surveillance stations (GSS) (worldwide) forming the Galileo Mission control System (GMS) together with the up-link stations: they will follow the satellite signals in order to provide the definition of the data to be uploaded5 Tracking, Telemetry and Control (TT&C) stations (worldwide) in S-band (2 - 4 GHz): these TT&C stations form the Galileo Ground Control System (GCS): monitoring and control of the satellites.
The number of stations is not finalized; modifications are still possible.
Galileo Ground Segment
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Galileo architecture -details
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Galileo Control Center (GCC) – 2 centers
Galileo space segment
5 TTC 10 ULS 29-30 GCS
S-band C-band L-band
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Dual-use (civil/military) system provided by RussiaCivil signals provided to all, free of user fees; It started in 1983; now it’s updatedGLONASS modernization directive, as of January 2006:
Constellation of 18 SV by end of 2007Full operationalcapability by end of 2009-> done in Dec 2011Comparableperformance with GPS and Galileo by 2010
GLONASS system: overview
Glonass currently usesFDMA (different from allthe other CDMA-basedsatellite navigationsystems)
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24 active satellitesAltitude - 19100 kmInclination - 64.8 degreesPeriod - 11 h 15 min.8 satellites per plane; 3 orbital planes
GLONASS space segment
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1 system control center (SCC) located in Krasnoznamensk, Moscow region5 TT&C stations, all located in Rusia30-40 surveillance
stations, distributedaround the world
GLONASS ground segment
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Source: http://www.glonass.it/images/glonass_network.jpg
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System under development by China; starting point was BEIDOU, later renamed as Compass 30 MEO satellites + 5 GEO satellites (MEO= Medium Earth Orbit; GEO= Geostationary Earth Orbit)Claimed accuracy: positioning 10 meters, velocity - 0.2 meter per second timing accuracy - 50 nanoseconds.Could institute user chargesCurrently, they have already launched 10 satellites (GEO/MEO and IGSO); more are planned to be launched before end of 2012
COMPASS system overview
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COMPASS space segment
Maximum 30 MEO satellites and 5 GEO satellites; Orbit height: 21500 km (MEO) and about 36000 km (GEO)Orbit inclination: 55 degrees
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COMPASS ground segment
1 master control station2 upload stations30 monitor stations
First and only Interface Control Document (ICD) for Compass published on 27th of Dec 2011 (13 pagesonly); however important information still missing fromthere (source: http://www.insidegnss.com/node/2879)
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System comparison
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GPS GALILEO GLONASS COMPASS
First launch 1978 2011 1982 2007
Full OperationalCapability(FOC)
1995 2017 (?) 2011 2015(?)
Number of SV 32 30 24 35 (?)
Orbital planes 6 3 3 3
Inclination(degrees)
55 56 64.8 55
Multiple access CDMA CDMA FDMA/CDMA CDMA
Orbital period 11h58m 14h05m 11h15m 12h50m
Total of121 SV possiblein the future
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Type of services offered by GNSS
Open services: free for everyone, typically no quarantee of serviceCommercial and/or authorized services: improved performance with limited accessibility
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GPS services
2 types of services specified in the US Federal RadionavigationPlan (1999):
Precise Positioning Systems (PPS) andStandard Positioning Service (SPS)
PPS Predictable Accuracy is: 22 meters horizontal accuracy, 27 meters vertical accuracy, and 200 nanosecond time (Universal Time Clock/UTC) accuracy.SPS Predictable Accuracy (for civil users; no military restriction) is: 100 meters horizontal accuracy, 156 meters vertical accuracy, and 340 nanosecond time (Universal Time Clock/UTC) accuracy.
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Open Service (OS): free for everyone; mass market applications, simple positioningSafety of Life (SoL): for professional applications; integrity; authentication of signalCommercial Service (CS): for maritime, aviation and train applications; encrypted; high accuracy; guaranteed servicePublic Regulated Service (PRS): encrypted; government-regulated; integrity; continuous availabilitySupport to Search and Rescue service (SAR):humanitarian purpose; near real time; precise; return link feasible
Galileo services
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GLONASS services
Civil services: open, free for everyone, standardprecision navigation signalsMilitary/Authorized service: high precisionnavigation signalsSearch and rescue service
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Two kinds of global services:
• Open Service free and open to users
Positioning Accuracy: 10 m
Timing Accuracy: 20 ns
Velocity Accuracy: 0.2 m/s
• Authorized Service: ensures highly reliable use even in complex situation.
COMPASS services
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About Regional Satellite Navigation Systems
QZSS: Quasi-Zenith Satellite System (Japan):Civil system for Asia Pacific regionSignals on the same frequency bands as GPS developped in collaboration with USInitial objective of 3 satellites, with possibility of more extensiveconstellation afterwardsAltitude 42164 km, 45 degree orbital inclination
IRNSS: Indian Regional Navigational Satellite System (India):
Constellation of 7 GEO satellites, due for completion in next 1-3 years; no satellite yet on skyGround segment: 1 master control sation + 4 monitor TT&C stations
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About GPS/GNSS augmentation
SBAS=Satellite based augmentation systems:• EGNOS (Europe)• WAAS (US)• CWAAS (Canada)• GAGAN (India)• MSAS (Japan)
Not used in a stand-alone modeOffer additional support to GPS
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Discussion: EGNOS (I)
Project was launched in 1998.Target accuracy is below 5 meters.It consists of 3 Geostationary satellites (Inmarsat AOR-E with PRN 120, Inmarsat IOR-W with PRN126 and Artemis with PRN 124) and a network of ground stations:
34 Ranging and Integrity Monitoring Stations (RIMS) deployed in 19 countries; 4 MCC (Mission Control Centres) deployed in Spain, Italy, UK and Germany; 6 Navigation Land Earth Stations (NLESs) deployed in Italy, France, Spain and the UK some support facilities in Spain and France.
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Discussion: EGNOS (II)
What are EGNOS satellites transmitting?• GPS-like signals in L1 band (carrier 1575.42 MHz)• 5 times faster data rates than GPS data rate => faster corrections than
with GPS• Forward error correction code
EGNOS is providing differential corrections (for pseudorange, orbit and clock computations) and ionospheric correctionsCannot be used alone for position computation(need GPS satellites)
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SIGNALS AND FREQUENCIES IN GNSS
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Chapter 2 outline
Multiple access techniques in GNSSSpreading codesused in GNSSModulations used in GNSS (main emphasis on BOC family)Spectral charcateristics of modulated waveformsSignals and spectra used in the 4 GNSS systems
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Signals’ tasks in GNSS
Can make the separationbetween satellites (multipleaccess)Enable the receiver to compute the pseudorange. Pseudoranges are estimatesof the true range (=distancefrom satellite to receiver). Pseudoranges differ from the true range due to variousrandom errors.Also carry the informationneeded by the receiver to compute the final position
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Rx: ’reads’ satellitesclock and location;computes Position, Velocity, Time (PVT)
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Recall: multiple access definition
Sharing (by different transmitters/ satellites) of the same transmission mediumTransmission medium = wireless channelGNSS use multiple signals:• Similar signal designs from different satellites
(e.g., C/A GPS signal sent from all GPS satellites)
• Different signals providing different services, from the same satellite (e.g., Galileo E1 and E5a signals)
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Multiple access techniques in GNSS
FDMA = FrequencyDivision Multiple Access (GLONASS)
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SV= Satellite Value
CDMA = Code Division Multiple Access (Galileo,GPS, Compass, some of the future GLONASS signals)
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How is the FDMA realized?
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FDMA
Signal fromone satellite
f f
power power
BW1 BW2
satellite1 satellite2……
Local oscillator with variable center frequencySimple transmitter implementationSeparation between signals at the receiver is done via filtering => need of tight filtering to reduce adjacent channel interference
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How is the CDMA realized?
Implemented via direct sequence spread spectrum (DS-SS) technology = spreading the narrowband signal into a wideband signal using a special (spreading) code
Spreading factor = BW2/BW1
Additional benefit of spread spectrum: inherent robustness to narrowband interference
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spreading
spread signal
signal
f f
power power
BW1 BW2
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Transmitter (satellite) simplified model
Mod. = modulation;MUX= multiplexing,LO =LocalOscillator,PA= Power Amplifier;*Navigationdata can beabsent (e.g, pilotchannels)
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Navigation data (I)
Navigation data message contains essential information for positioning computation:• Time• Information regarding satellite positions (almanac,
ephemeris)• Clock corrections• Ionospheric model• Time offsets among different frequencies and among
different systems, and with respect to Universal Time (UTC)
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Spreadingmod.
Channel mod.
Navigationdata
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Data message channel coding
Channel coding is used to protect (to a certain extent) the navigation data againstthe wireless channel errorsForward Error Correction (FEC) is a channelcoding method based on insertingredundancy in the transmitted data. Thisredundancy allows the receiver to correctsome of the transmission errorsError checking bits (e.g., parity bits) can alsobe used to detect errors
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Pilot channels
Some GNSS channels are transmitting PRN codes without any navigation data (withoutdata modulation)These are the so-called ’pilot channels’ => useful in the acquisition and trackingprocesses• Absence of data bit transitions allows for longer integration times
=> better performance in noisy environments• Code sequences are known at the receiver (except the delay),
but navigation data (when present) is not known. Without data modulation => less parameters to be estimated
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Spreading modulation
A pseudorandom noise (PRN) code at a rate fc (chip rate) is multiplied with a data sequence, at a much lower rate, fb (bitrate or code epoch rate)
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X
‘User’ data, bit rate fb
chipSequence(’PRN code’)at fc
spreadspectrumsignal, at fc
Example:fc = 1.023 MHzfb = 1 kHzfc /fb = 1023 = ’bandwidthexpansion’ factor or’spreading factor’
Note: navigation data rate is not the same as the bit rate fb. The current terminology comes from the communication world. In navigationworld, fb is called the code epoch rate.
Spreadingmod.
Channel mod.
Navigationdata
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Example of spread sequence (baseband)
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data sequence, at fb
chip sequence, at fc
Spread spectrumsignal, at fc
Spreading factor cF
b
fS
f
0 2 4 6 8 10 12-1
0
1NAV data
0 2 4 6 8 10 12-1
0
1PRN code
0 2 4 6 8 10 12-1
0
1Spread signal
Here, SF=5 chips per code epoch and data bit has 3 code epochs duration. Time axis is in code epochs.
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Some mathematics (I)
Data sequence, bn=data bits, T= bit interval =1/fb
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(t) Dirac pulse
t
0
( ) 1t dt
( ) , 0( ) 0, 0t tt t
( ) ( ) ( ), ( )t p t p t p t
( ) ( )nn
d t b t nT
=Convolution operator
1nb
nb
1nb 2nb
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Some mathematics (II)
Chip sequence (spreading code), as sequence of +1,-1 rectangular pulses:
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, ,1 1
( ) ( ) ( ) ( )F F
c c
S S
n k n T c T k n ck k
c t c p t kT p t c t kT
cT = chip interval =1/fc c bF
b c
f TSf T
,k nc = chip value (+1 or -1) corresponding to the k-thchip of the n-th code epoch
code epoch n code epoch n+1
chip k
( )cTp t = rectangular pulse of support
cT
cT
t
1
0
( )cTp t
cT
cT
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Some mathematics (III)
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,1
( ) ( ) ( )F
c
S
T n k n cn k
s t p t b c t n T k T
The spread signal, at the output of the spreading operation can be modeled as:
One important aspect when choosing a spreading code c(t) relates to its auto-correlation (correlation with itself) and cross-correlation (correlation with other signals) properties
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How to choose the spreading codes? (I)1. Good code auto-correlation properties: the code sequence for a
certain code epoch, without the rectangular pulse shaping part , is
Its auto-correlation equals to
A ’good’ auto-correlation function is the one which ressembles to a Diracpulse, that is
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,1
( )FS
k n ck
c t kT
, ,1 1
( )F FS S
k n p n c ck p
c c t kT pT
, ,1 1
2,
1
0,
1
F F
F
S S
k n p nk p
S
k nk
c c if k p
c
Meaning:-Correlations with delayedversions of the signal aresmall-Correlation with an alignedversion of the signal is high- Such properties help in the acquisition/tracking process
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How to choose the spreading codes? (II)2. Good code cross-correlation propertiesThe cross-correlation between 2 codes (without the pulse shaping part)
equals to
, are the chip sequences for 2 codes (1) and (2)A ’good’ cross-correlation function is the one having all-zero values (or
values much lower than the maximum of the code auto-correlation)
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(1) (2), ,
1 1( )
F FS S
k n p n c ck p
c c t kT pT
(1),k nc (2)
,p nc
(1) (2), ,
1 10
F FS S
k n p nk p
c cMeaning:
- Correlations with the codes of other satellites are small => help in detecting correctlywhich satellites are on the sky
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Other considerations about spreading codes
Number of different codes available -> to be enough for allsatellites and all signalsLength: longer codes have typically better correlationproperties, but receiver processing is easier with shortercodes. Rate of the spreading code (chip rate): determines the accuracy with which the position determination can be made. For example, with a chip rate of 1.023 MHz, each chipcorresponds to a light travel time of about 300 m.Good balance between number of ’zeros’ and ’ones’ (or +1/-1) in a code
Trivia: The code length of 1023 chips was chosen in GPS at the recommendation of J. Spilker
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Spreading codes used in GNSS
1. Maximal length or m-sequences (e.g., GLONASS)
2. Gold codes (e.g., GPS current signals)3. Memory codes (e.g., Galileo Open Service)4. Weil codes (e.g., GPS future L1C civil
signal)
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M-sequences
Generation based on an N-tap linear feedback shift register (accordingto on an underlying generator polynomial)
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Delay 1 Delay 2 Delay n………….
+ +
output• N= 2n-1 length sequences• Only 2 possible values of the normalized autocorrelation function, namely 1 and -1/N => good autocorrelation properties
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Gold codes
Combination (XOR) of two m-sequences (not any m-sequenceallowed; only a sub-set of them)N= 2n-1 code length (in GPS, n even, n=10)
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4 possible valuesof the normalizedautocorrelationfunction:
(e.g., 1, -1/1023, -65/1023, and 63/1023
2 22 21 2 1 2 11, , ,
n n
N N N
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Memory codes (’random’ codes)M-sequences and Gold codes do not have very good cross-correlation properties, especially when navigation data bittransitions are also taken into accountTherefore, an optimization-based code selection was proposedfor Galileo; optimization criteria:• Good balance of ’zeros’ and ’ones’• Small auto-correlation and cross-correlation properties with both
even and odd navigation data bit patterns (e.g., 1 followed by a 1, and 1 followed by a -1)
The complete sequences are saved in the memory (of tx & rx) and read from there=> larger memory tables than for m-sequences and Gold codes
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Weil codes
Based on Legendre sequences and XOR additionsCan have any prime length (not limited to 2n-1 length)Motivated by the need of finding codes of length N=10230 chips with good auto- and cross-correlation properties (e.g., for GPS L1C signal, Weil codes of prime length 10223 are used and padded with 7 chips in order to reach the 10230 chip length)Reported to have better cross-correlation properties than Gold codesNot as flexible as memory codes, e.g., not possible to drivethem to Autocorrelation Sizelobe Zero (ASZ) property (ASZ= zero auto-correlation value when the code is correlated with a delayed version of itself of 1 chip)
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Channel modulation
Modulation task: some characteristics (amplitude, phase or frequency) of a carrier wave are varied in accordance with an information bearing signal
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digitalmodulation
digitaldata analog
modulation
radiocarrier
basebandsignal
1-111-11-1-11
Channel Modulator
Spreadingmod.
Channel mod.
Navigationdata
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Binary Phase Shift Keying (BPSK)If p(t) denotes the basic pulse used in the construction of the binary data stream, then the BPSK-modulated PRN sequencecan be written as:
No pulse shaping currently used in GNSS => (rectangular pulse)Therefore, the modulated signal can be seen as the convolution between a code part c(t) (including navigationdata) and a modulation pulse
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,1
1 for binary symbol "1"( ) ( ),
1 for binary symbol "0"
FS
n k n c nn k
s t b c p t nT kT b
( ) ( )cTp t p t
,1
( ) ( ) ( ) ( ) ( )F
c
S
T n k n c BPSKn k
s t p t b c t nT kT s t c t
( ) ( )cB P SK Ts t p t
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BPSK (II)
The expression given in the previous slide is the expression for the baseband signal (in continuous-time form), which will bethe basis of our models in what follows
The analog passband signal (at carrier frequency) becomes:
Notation: BPSK(n) means a chip rate of n*1.023 MHz
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( ) ( ) cos(2 )c carrierm t A s t f t
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(Power) Spectral Density (PSD)
PSD is the Fourier transform of the auto-correlation function of a signalSince a BPSK-modulated signal has both discrete-time and continuous components, the PSD has two parts :
= the Fourier transform of the pulse waveform
= the PSD of the transmitted discrete-time symbol train
For infinite-length ideal codes (i.e., Dirac-shaped auto-correlation), we have = > the modulated-signal PSD is given by the square of the pulse shape frequency response:
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2 21( ) ( ) ( )c
c
j fTs T b
c
G f P f G eT
2( ) ( )c c
j ftT TP f p t e dt
2( )cj fTbG e
2( ) 1cj fTbG e
21( ) ( )
cs Tc
G f P fT
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Notes on terminology
Strictly speaking, we deal with finite-time signals => finiteenergy signalsThat is why, sometimes the preferred term is ’energyspectral density’ (or simply ’spectral density’) instead of PSD
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Equivalent baseband representation of modulated signals
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Baseband spectrum
Spectrum at carrierfrequency (passband)
0f
0 ffcarrier-fcarrier
( )sG f
( )s carrierG f f* ( )s carrierG f f
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PSD of BPSK signals (I)
Sinc-shaped PSD, maximum energy at 0 frequency (baseband representation)
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cTt
1
0
( )cTp t
2 21 sin( )( ) ( ) sin , sin ( )cs T c c
c
xG f P f T c fT c xT x
f
( )sG f
cT
1
cT01
cT2
cT2
cT
=
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PSD of BPSK signals (II)
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Power within main frequency lobe (2fc bandwidth) is about 90% of the whole signal power
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Binary Offset Carrier (BOC) modulation
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Sine BOC with NB=2fc/fsc•Square sub-carrier modulation, where the PRN code (of chip rate fc) is multiplied by a rectangular sub-carrier of frequency fsc, which splits the spectrum of the signal. •Typical notations:
•BOC(fsc; fc) or •BOC(m; n), m = fsc/1.023 MHz, n = fc/1.023 MHz.
•BOC modulation order
•Sine-BOC time waveform given by:
2 scB
c
fNf
( ) sin BSinBOC
c
N ts t signT
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Notes on Sine BOC
From the point of view of baseband characterization, BOC-modulated signal is fully defined by two parameters, namely NB and chip frequency fc
From the point of view of passband signal, also the carrierfrequency should be specified.The sine-BOC modulated signal can be written in a similar formas BPSK-modulated signal:
Equivalent representation of sine-BOC waveform [LLR06b] as an alternating sequence of +1 and -1
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,1
( ) ( ) ( ) ( ) ( )FS
SinBOC n k n c SinBOCn k
s t s t b c t nT kT s t c t
1
0( ) ( ) ( 1) ,
B
B
Ni c
SinBOC T B Bi B
Ts t p t t iT TN
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Cosine BOC
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Cosine BOC with NB=2fc/fsc
( ) cos BCosBOC
c
N ts t signT
• Cosine-BOC time waveform given by:
•Cosine BOC can be modeled as a double sine BOC modulation: first stagewith modulation order NB, and secondstage with modulation order 2 [LLR06b]
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0 02
( ) ( ) ( 1) ,2
B
B
Ni k B
CosBOC T Bk i
cB
B
Ts t p t t iT k
TTN
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Modeling BPSK, sine BOC and cosine BOC
Generic modulated-signal model
Generic modulation waveform:
Modulation factors:BPSK case
Sine BOC(m,n) case
Cosine BOC(m,n) case
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mod , mod1
( ) ( ) ( ) ( ) ( ),mod ,FS
n k n cn k
s t s t b c t nT kT s t c t BPSK SinBOC orCosBOC
2 1
1 2 1 221 1 2
1 1
mod0 0
( ) ( ) ( 1) , ,B B
B
N Ni k c c
T B B B Bk i B B B
T Ts t p t t iT kT T TN N N
1 21, 1B BN N
1 22 , 1B B
mN Nn
1 22 , 2B B
mN Nn
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PSD of Sine BOC-modulated signalsObtained by squared Fourier transform ofRandom part of the modulated signal ignored (e.g., assumptionthat we have ideal codes).
The above expressions are normalized to unit energy overinfinite bandwidth
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mod ( )s t
2
sin sin1
( )cos
cc
Bs
c c
B
Tf fTN
G fT Tf f
N
For SinBOC(m,n) with even NB
2BmNn2
sin cos1
( )cos
cc
Bs
c c
B
Tf fTN
G fT Tf f
N
For SinBOC(m,n) with odd NB
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PSD of Cosine BOC-modulated signals
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2
sin sin sin21
( )cos cos
2
c cc
B Bs
c c c
B B
T Tf f fTN N
G fT T Tf f f
N N
For CosBOC(m,n) with even NB
2BmNn
For CosBOC(m,n) with odd NB
2
sin sin cos21
( )cos cos
2
c cc
B Bs
c c c
B B
T Tf f fTN N
G fT T Tf f f
N N
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Examples of BOC spectra (I)
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Examples of BOC spectra (II)
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Effect of non-idealities of the code
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Power containment
Power within a certain (double-sided) bandwidth (e.g., filled area below)
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Power containment
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Examples: about 85% within 4 MHz double-sidedbandwidth for sineBOC(1,1)About 80% within 20 MHz for cosineBOC(15,2.5)
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Ideal ACF shaped by the modulation waveform
Auto-correlation function (ACF) is given by
Examples (over infinite bandwidth)• BPSK
• Sine BOC
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mod mod( ) ( ) ( ),mod ,R t s t s t BPSK SinBOC or CosBOC
( ) ( ) ( ) ( )B B BT T TR t p t p t t
1 1
0 0( ) ( 1) ,
B B
B
N Ni k c
T B B Bk i B
TR t t iT kT TN
BT BT
( )BT t
t
0
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Examples of ideal ACFs
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ACF role in receiver processing(I) Signal from the satellite is acquiredbased on the correlation betweenthe incoming signaland a reference PRN code, with varioustentative delays and tentative Dopplershifts
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ACF role in receiver processing (II) Correlationshape (given bythe ACF of the employedmodulation) influences alsothe trackingproperties
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Bandwidth impact on ACF (I)
Bandwidth-limiting filter impulse response p(t) should be taken into account:
Bandwidth limitation occurs due to the front-endfiltering stagesSampling frequency is determined by the front-end bandwidth (Nyquist condition): higherbandwidth => higher sampling rate => highercomplexity
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( ) ( )R t p t
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Bandwidth impact on ACF (II)
Correlationlosses’Rounding’ of peaksPossiblewidening of the correlation main lobeBW=double-sidedbandwidth
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Multiplexed BOC (MBOC)
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(1,1) (6,1)10 1( ) ( ) ( )11 11MBOC SinBOC SinBOCG f G f G f
Proposed (in 2004) for Galileo E1 signals and for modernized GPS L1C signalPower spectral density of the MBOC signal has to satisfy:
Several implementations possible
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Time-Multiplexed BOC (TMBOC)TMBOC: time-multiplexed sine BOC(1,1) symbols with sine BOC(6,1) symbols; 2-level waveform. Example: 10 PRN chips; chips 2 and 6 are SinBOC(6,1)-modulated
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Composite BOC (CBOC)
Weighted combination of SinBOC(1,1) and SinBOC(6,1) code symbolsCBOC(+)CBOC(-)CBOC(+/-): odd chips use CBOC(+) and even chips use CBOC(-) (or viceversa)
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( ) 1 (1,1) 2 (6,1)( ) ( ) ( )CBOC SinBOC SinBOCs t w s t w s t
( ) 1 (1,1) 2 (6,1)( ) ( ) ( )CBOC SinBOC SinBOCs t w s t w s t
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CBOC
Example: typical values
Note that
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1 210 1,11 11
w w
2 21 2 1w w
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Ideal ACF with MBOC
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PSD of MBOC
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Notes on MBOC PSD
Typically, the MBOC PSD is achievedwith a certain combination of data and pilot channelsFor example, in Galileo E1 Open Signal, data channel uses CBOC(+) modulationand pilot channel uses CBOC(-) modulation
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Advantages of MBOC over SinBOC(1,1)
Reported bettertrackingcapability (ifsufficiently highbandwidth)Reported bettermultipathmitigation[HRV06]
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Complexity issues in MBOC
Higher bandwidth consumption (due to extra SinBOC(6,1) component) => highersampling rates if full processingPossibility to process MBOC signals withSinBOC(1,1) receiver => mass-marketimplementations
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Alternate BOC (AltBOC)
Four signals modulated onto the two phases of orthogonal sub-carriers [ALI08]Sub-carrier waveforms are chosen so as to obtain a constant envelope at the transmitterMotivated by the need to transmit 2 complex signals (data and pilot, each with I and Q components) into 2 frequency bandsin Galileo
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AltBOC briefly
1. Form two Single Side-Band (SSB) carriers from SinBOC and CosBOCmodulations (via their sum and difference)
2. Modulate the 4 signals via the 2 SSB carriers
3. Use a 8-PSK mapping (look-up table) for the resulting symbols, in order to get a constant envelope signal
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Example: AltBOC(15,10)
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Main lobes separation of 30 MHz (=distance between E5a and E5b center frequencies in Galileo)
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Spectral properties (I)
Spectral Separation Coefficient (SSC) between 2 signals s1(t) and s2(t) [Bet00,Bet01]: should be as low as possible
Maximum value of the spectrum: shouldbe as small as possible => lessinterference
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1 2( ) ( )
W
SSC s sB
G f G f df
1( )max
W
MVS sf B
m G f
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Spectral properties (II)
RMS Bandwidth of the signal: the smaller, the better
Power containment factor (discussed before): the higher, the better demodulation process
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2 ( )W
BW sB
RMS f G f df
2
2
( )
W
W
B
sB
G f df
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SSC illustration
SSC between 2 BPSK signals (left) and betweenBPSK and sine BOC(1,1) signal, BT=8 MHz (right)
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Numerical example
Source: Lohan&al[LLR05]
BT=double-sidedbandwidth BW
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Notes on the modulation
Modulation ’shapes’ the spectrum of the transmitted signal => defines the level of spectral interference with other GNSS signalsModulation ’shapes’ the ACF => influences the acquisition and tracking capabilities of a signal
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GPS, Galileo, Compass frequencies
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Compass1561.098
RNSS=radionavigation satellite service;ARNS=aeronautical radionavigation service (radar, tactical air navigation, trafficcollision avoidance system, etc
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GLONASS frequencies
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Source: http://www.oosa.unvienna.org/pdf/icg/2007/icg2/presentations/05.pdf
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Frequencies and signal separation
Some overlapping between the frequency bandsof the 4 GNSS systemsSignal separation between different systemsdone via:• Different PRN codes (GLONASS also uses a
CDMA spreading code, same for all satellites)• Modulation type (spectral separation between
split-spectrum modulations and modulationswith peak energy at carrier frequency)
Inter-system interference still remaining
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GPS signals and modulations
Civil signals• C/A (Coarse/Acquisition) code on L1 band (since the
beginning; 1980s): BPSK(1) (it means a chip rate 1.023 MHz)
• L2C on L2 band (since 2005): BPSK(1)• L5 on L5 band (since Apr 2010): BPSK(10)• L1C on L1 band (to come): TMBOC
Restricted/military/encrypted signals:• P(Y) (Precise) code on L1 and L2 bands: BPSK(10)• M-code on L1 and L2 bands : SinBOC(10,5)
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Example: GPS L1 Spectra
Basebandrepresentation(offset 1575.42 MHz from 0 center frequency)Signals:
• C/A: BPSK(1)• P(Y):BPSK(10)• M: SinBOC(10,5)• L1C:
TMBOC(6,1,29/33)
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GPS frequency bands
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Band Edge frequencies[MHz]
Carrier frequency[MHz]
L1 1563-1587 1575.42 = 154 x 10.23L2 1215-1237 1227.60 = 120 x 10.23L5 1164-1191.795 1176.45 = 115 x 10.23
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GPS code lengths
1023 chips for L1 C/A10230 chip length on L1C2 codes: one with 10230 chip length and another one with 767250 chip length for L2C2 codes of 10230 chip length on L5
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Galileo signals
Open Service (OS) signals (E1, E5a, E5b)Safety of Life Service (SoL) signals (E1, E5b)Commercial Service (CS) signals (E1, E6)Public Regulated Service (PRS) signals (E1 E6)Search and Rescue (SAR) signals: separate frequency band
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Explanations on OS signals
Defined for mass-market applicationsFree of direct user chargeIntended for interoperability with GPSNo integrity information and no serviceguarantee
Note: all details subject to change. These are in accordancewith current Galileo SIS-ICD, published in 2011
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Explanations on SoL signals
Defined for transport applications where lifescan be endangered without the real-time noticeof system degradationHigh-integrity levelGalileo Operating Company or Concessionaire(GOC) will guarantee SoL
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Explanations on CS signals
For applications that need higher performancethan OSAccess to signal limited by encryption; fee-based value-added servicesService quarantees, precise timing services
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Explanations on PRS signals
For government-authorized use (police, customs, coast-guard, …)Protection against spoofing and jammingAccess limited by encryption
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Galileo modulations
CBOC(+) modulation for E1-B (data channel)CBOC(-) modulation for E1-C (pilot channel)AltBOC(15,10) modulation for E5BPSK(5) for E6 (Commercial Service CS)CosBOC(10,5) for E6 (Public regulated Service PRS)
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Example: Galileo E1 spectra
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Basebandrepresentation(offset 1575.42 MHz from 0 center frequency)Signals:• E1-C/E1-B
(OS/SoL): MBOC• PRS:
CosBOC(15,2.5)
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Galileo frequency bands
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Band Edge frequencies[MHz]
Carrier frequency[MHz]
E1 1587-1591 1575.42 = 154 x 10.23E6 1260-1278.75 1278.75= 125 x 10.23E5 1164-1214 1191.795 = 116.5 x
10.23E5a 1164-1191.795 1176.45 = 115 x 10.23E5b 1191.795-1214 1207.14 = 118 x 10.23
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Galileo code lengths
4092 chip length for E1 signals (Note: the spreading factor is still 1023)10230 chip length on E55115 chip length on E6
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GLONASS signals
Standard accuracy signals:• L1 open FDMA• L2 open FDMAHigh-accuracy signals:• L1 authorized FDMA (encrypted codes)• L2 authorized FDMAL3 signal (details not yet defined)
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GLONASS modulations
BPSK(0.5) on L1 and L2 (i.e., 0.511 MHz chip rate. Note: spreadingmodulation is still used in Glonass, although the multiple access schemeis mainly FDMA)Not yet public for L3 and L5 (probably, higher chipping rates)
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GLONASS frequency bands
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Band Edge frequencies [MHz] Carrier frequencies [MHz]
L1 1591-1610 1602 + 0.5625n , n=-7,-6, …6L2 1237-1260 1246+0.4375n, n=-7,-6,…,6L3 (TBD) 1191.795-1214 (same as
E5b)1208 *
L5 (TBD) 1164-1191.795 1176.45 *= 115 x 10.23
TBD =To Be Defined* On L3 and L5 we will have GLONASS CDMA signals
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Example: GLONASS spectrum, L1
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Basebandrepresentation(offset 1602MHz from 0 center frequency)Signal:• BPSK(0.5) and
FDMA
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Compass/BEIDOU signals
B1 Open signalB1 Authorized signalB2 Open signalB2 Authorized signalB3 Authorized signal
Note: scarce public information regarding Compass. May be subjected to changes.
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Compass modulations
MBOC for B1 open signalSine BOC(14,2) for B1 authorized signalAltBOC(15,10) for B2 open signalCosine BOC(15,2.5) and QPSK(10) for B3 authorized signal
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COMPASS frequency bands
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Band Edge frequencies[MHz]
Carrier frequency[MHz]
B1 1559.052-1591.788 1575.42 = 154 x 10.23B2 1166.22-1217.37 1191.795 =116.5 x 10.23B3 1250.618-1286.423 1268.52 = 124 x 10.23
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Example: Compass spectra in B1
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Basebandrepresentation(offset 1574.42MHz from 0 center frequency)Signal:• B1 open: MBOC• B1 authorized
SinBOC(14,2)
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GNSS CDMA signals together
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GPS
Galileo
Compass
Glonass
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GNSS navigation data rates
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Type GPS Galileo Glonass CompassBit rates [kbps] 50/200 50/125/200 50 25/50/100/
500
Bit durations [ms] 20/5 20/4/5 20 40/20/10/2
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Pilot presence in GNSS
Type GPS Galileo Glonass CompassNo pilot C/A - all N/ATime-multiplexedpilots
L2C E1 - N/A
Quadrature-phasemultiplexed pilots
L5 E5 - N/A
Power/codemultiplexed pilots
L1C E6 - B1, B2
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GNSS comparison
GPS Galileo GLONASS CompassMultipleaccess
CDMA CDMA FDMA/CDMA* CDMA
Chip rates 1.023/5.115/10.23 1.023/2.5575/5.115/10.23
0.5115 1.023/2.046/2.5575/10.23
Channel coding
None/FEC FEC Parity bits N/F
Pilot channels Only in modernizedGPS
yes no yes
Modulationtypes
BPSK; TMBOC; SinBOC
BPSK; CBOC; SinBOC; CosBOC;AltBOC
BPSK BPSK; QPSK;MBOC; SinBOC; CosBOC;AltBOC
PRN codes Gold and Weil codes Memory codes M-sequences N/F
Frequencybands
L1,L2, L5 E1, E6, E5, E5a, E5b
L1, L2, L3*,L5* B1,B2,B3
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* =planned; N/F=not found
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RECEIVER SIGNALPROCESSING
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Chapter 3 outline
Baseband processing:• Acquisition:
- Search Stage- Detection Stage
• Tracking:- Code tracking- Carrier Tracking
• Challenges dueto BOC modulation
Navigation processing:• Pseudoranges• Forming the location estimation• Satellite geometry
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GNSS receiver processing
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Basic operations are shown in the following block diagram
Navigation unit(computation of position, velocity and time: PVT
solution)
Sat 1Sat 2Sat 3Sat 4
Front-end and ADC
Baseband processing (acquisition,
tracking, data extraction
Coordinatesconversion ->map
position
01011...
(x,y,z; t)
fD, ...
Sat =SatelliteRuka skiSlope 10
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Code shift and Doppler frequency estimation are needed for reliable performance of any CDMA systemThe code synchronization task is typically split into:• coarse synchronization (or acquisition stage) and• fine synchronization (or code tracking stage).
Acquisition is used to get a rough timing estimate, say within +/- 1 chipTracking means finding and maintaining fine synchronizationCode tracking is much easier given the initial acquisitionCode acquisition, however, is usually considered as one of the most challenging tasks in a DS-SS systems
Acquisition and tracking problems
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Timing uncertainty: determined by the transmission time ofthe transmitter and the propagation delay (and clock uncertainties)• usually much longer than a chip duration.• due to a search through all possible delays, a larger timing
uncertainty means a larger search areaFrequency uncertainty: determined by the Doppler shift and mismatch between the transmitter and receiver oscillators.Angular uncertainty: determined by the direction of arrival of the signal. Separation in angular domain applies only for antenna array receivers (not applicable for current GNSS).
Uncertainty regions
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One correlation output forms a time-frequency bin. Several bins form a time-frequency window. The whole search space = time-frequency unertainty window.
Time-frequency uncertainty
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Typically performed in 2 stages:• Search stage: build the time-frequency window with various
delay and frequency candidates (via correlations).• Detection stage - form a decision variable and compare it with a
threshold in order to detect whether the signal is present or absent. Threshold choice is an important step in designing a good acquisition stage. Either constant or variable (e.g., according to SNR) thresholds can be used, as it will be discussed later on.
The larger the time or frequency uncertainty is the greater time will take to achieve acquisition, or the greater receiver complexity is required for a given acquisition time requirement.
Code acquisition
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The search strategy can be:• serial: there is only one bin per window low complexity (only
one complex correlator needed), high acquisition time (many bins to be searched; acquisition time is proportional with the code epoch length, i.e. 1023 chips for standard GPS, up to 10230 for Galileo and modernized GPS).
• hybrid: there are several bins per window and there are several windows in the whole search space tradeoff between complexity and acquisition time; general case.
• parallel: there are more than one bin per window and there is only one window in the whole search space high complexity (need many correlators), low acquisition time.
Acquisition: Search stage
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Basic principle
The basic principle of code acquisition is: try and match each possible phase of the reference spreading sequence to the received data=> correlator
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BPF= Band-pass filterED= Envelope DetectorSS= Spread Spectrum
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Examples
Left: signal present; right: signal absent (note: x-yaxes are different in these examples)
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05
1015
20
0
100
200
3000
0.2
0.4
0.6
0.8
1
x 10-3
Time indexFrequency index
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Correlation is done between the received signal and a reference (local) code at the receiver (e.g., C/A code)In time domain:
Time vs Frequency correlation
Discrete (I&D= Integrate and Dump)
Analog
In frequency domain:
FFT X
FFT
IFFT*
Rx signal
Ref. signal
Rx signal Rx signal
Ref. signal
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Example of FFT vs time correlation
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Acquisition: detection stage
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Acquisition problem is in fact a detection problem: detect signal in noise, or, equivalently, separate between hypothesis H1 (signal plus noise arepresent) and hypothesis H0 (noise only is present).
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Acquisition: threshold choice
Threshold can be chosen as a tradeoff between a good detection probabilityand a sufficiently low false alarm (detection probability increases when false alarm probability increases). Below: PDF= Probability Density Function
The Probability Distribution Functions (PDFs) under each hypothesis arederived according to the decision statistic (see previous slide), which can be, for example, the maximum in a certain correlation window
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Detection probability and false alarm probability: ’borrowed’ from classical detection problem of signal in noise
Acquisition: performance measures (I)
• A false alarm occurs when the decision statistic exceeds the threshold for an incorrect hypothesized phase•A miss occurs when the decision statistic falls below the threshold for a correct hypothesized phase.
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Mean Acquisition Time (MAT)Example:
Assume that the time uncertainty corresponds to N pseudorandom chips (or NTc = T seconds, where Tc = chip duration. Assume that there is no carrier frequency uncertainty (e.g., assisted acquisition)Assume also that detection probability at the correct hypotheses is Pd= 1 and the false alarm probability at incorrect hypotheses is Pfa = 0 (ideal case).What is the MAT time for a dwell time D if the timing search update is in half-chip increments (0.5Tc)?Answer: there are Q = 2N timing positions (hypotheses, bins) to be searched and the time to search one time bin is D Tacq = 2N D
If all hypotheses are equally probable the mean acquisition time can be approximated by half of Tacq => MAT N D
Acquisition: performance measures (II)
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Time to First Fix (TTFF):• The time from receiver turn on until the first navigation solution is
obtained.• The complete navigation solution (min 4 satellites in view) is needed to
compute TTFF• Typical values of TTFF: 30-40s without assistance; 1s with network
assistance (e.g., A-GPS)The TTFF is commonly broken down into three more specific scenarios:
• Cold (or factory): The receiver is missing, or has inaccurate estimates of, its position, velocity, the time, or the visibility of any of the GNSS satellites.
• Warm or normal: The receiver has estimates of the current time within 20 seconds, the current position within 100 kilometers, and its velocity within 25 m/s, and it has valid almanac data (i.e., coarse orbital information of satellites).
• Hot or standby: The receiver has valid time, position, almanac, and ephemerisdata (i.e., accurate orbital data of satellites), enabling a rapid acquisition of satellite signals.
Acquisition: performance measures (III)
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Once the coarse estimates of code delay and Doppler frequency are available, we move to the tracking stage, in charge with fine estimation of code delays and maintaining the lock:• Code tracking: fine delay estimation• Carrier tracking (needed for the carrier replica at the receiver)
Tracking
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The purpose of a tracking loop is to reduce the estimation error of the delay between the received signal and the replica code at the receiver.A coarse delay estimate is obtained from the acquisition stage; the tracking loop is further refining/improving this estimate and trying to keep track of delay changes (e.g., due to the relative receiver-transmitter movement).In practice, we need both carrier tracking (e.g., achieved with a PLL) and code phase tracking; here we focus only on the code tracking part. A short discussion on carrier tracking can be found towards the end of this lecture.
Code tracking
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The basic code tracking loop is the Delay Locked Loop or Early-Minus Late (EML) correlator with 1 chip early-late spacing (also called wideband early-minus-late correlator). Both coherent and non-coherent (see below) DLLs exist.
Code tracking: DLL
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Looking for maximum correlation is equivalent with searching for the zero-crossing of the derivative of the correlation functionThe derivative can be approximated via early-minus-late correlation difference
Principle of DLL
E<L => delay the signal E=L => signal ’in tune’; stay there!
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The S-curve or discriminator curve translates the correlation values into a delay error index. For example:
S-Curve of Discriminator curve
The zero-crossings (from above) of the S-curve signal the presence of a channel path they signal the delay error. Note: if late-minus-early (instead of early-minus-late) curve need to consider the zero crossings from below
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S-curve example
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According to the early-late correlator spacing, the early-minus-late correlator can be divided into:• Wide correlator (classical): =1 chip• Narrow correlator: Introduced by Dierendonck and Fenton in
1992, for GPS in order to reduce the code tracking error in the presence of noise and multipaths: < 1 chip
Narrow versus wide correlator
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DLL basic discriminator types
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Tracking noise variance: closed-form formulas are typically available for single-path static channelsMultipath Error Envelopes (MEEs): performance in multipathsMean Time to Lose Lock (MTLL, or MTTLL)
Tracking: performance measures
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Problem: in single-path situation and in the presence of background noise (modelled as white Gaussian), which is the variance of the code delay tracking error?
Answer:• It depends on the discriminator type.
• Case studies:- Non-coherent early minus-latecorrelator
- Dot-product discriminator
Tracking: Noise variance
Early-late correlator spacing Code loop bandwidth
Signal-To-Noise or Carrier-To-Noise ratio Coherent integration interval
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When early-late spacing decreases tracking loop error variance decreases => benefit of narrow correlator.
Example of tracking noise variances
Early-minus-late power Dot product
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’Lock’ condition: delay error smaller than a certain threshold (in absolute value); e.g., 0.5 chips for GPS C/A code and classical early-minus-late correlatorDue to noise, delay error might become too high and we go out the convergence region of the S-curve=> ’loss of lock’MTLL is a statistical measure showing the ability of a discriminator (or code tracker) to maintain the lock. The higher, the better.
Mean Time To Lose Lock (MTLL)
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Needed to obtain carrier information (i.e., to build an exact carrier replica at the receiver)Phase Locked Loops (PLL) are used to obtain carrier phase informationFrequency Locked Loops (FLL) are used to obtain carrier frequency information
Frequency and phase tracking (FLL/PLL)
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Similar principle with DLL. Different discriminator equations (e.g., atan(Q/I), ...)
Carrier tracking loops
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Source: Kaplan’s book.
Block-diagram of carrier-code tracking
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Challenges due to BOC modulation
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Most of the Galileo signals are split-spectrum signals, that is with power spectral density content away from the middle of the band.
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Galileo – specific processing: ambiguities
- Due to the split-spectrum modulations (BOC, MBOC) => ambiguities (notches) in the envelope of the correlation function and additional side lobes
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Ambiguities effects
- Acquisition stage:- Time-bin step in the searching process needs to be smaller (in
chips) than in BPSK modulation => longer time to spend in acquisition stage or need to remove the ambiguities
- Tracking stage:- False lock peaks- More difficult to cope with multipaths (how to make the
distinction between a ’side peak’ and a multipath)
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- Left: small bin step. Right: large bin step . - The number of states in the acquisition process is inversely
proportional to the time-bin step => a smaller step meanshigher time spent in the acquisition (or higher complexity)
Time-bin step in acquisition
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Unambiguous acquisition (I)
- Unambiguous aquisition methods: try to recover a ’BPSK-like’ correlation shape, such that a higher time-bin step can be used in the acquisition process
- As a rule of thumb, a time-bin step of ¼ of the width of the main lobe in the ACF envelope is used (e.g., 0.5 chips in GPS BPSK-modulated signals, about 0.35 chips in Galileo MBOC/SinBOC(1,1)-modulated signals)
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Example of unambiguous acquisition
Betz&Fishman unambiguous acquisition:
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Example of performance: unambiguous acq.
Mean Acquisition Time MAT
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In the tracking stage, the main problem related to Galileo signals is how to deal with the additional side lobes (lock to a false peak), while preserving the narrow width of the main correlation lobeDelay accuracy is directly proportional to the width of the main correlation lobe (its envelope)The unambiguous acquisition methods are not suitable in the tracking stage, because the width of the main correlation peak is increased in unambiguous acquisition => poorer tracking performance
Unambiguous tracking (I)
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Unambiguous tracking (II)
Sidelobe cancellation/mitigation approaches (SCM)
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Recall: GNSS receiver processing
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Navigation unit(computation of position, velocity and time: PVT
solution)
Sat 1Sat 2Sat 3Sat 4
Front-end and ADC
Baseband processing (acquisition,
tracking, data extraction
Coordinatesconversion ->map
position
01011...
(x,y,z; t)
fD, ...
Sat =SatelliteRuka skiSlope 10
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Underlying principle: trilateration
1 Satellite 2 Satellites => intersection is the red circle
3 Satellites=> 2 points of intersection; one point is outside Earth
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Pseudoranges
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7.2.20
Velocity x Time = Distance
Radio waves travel at the speed of light, roughly299 792 458 m/s (i.e., around 3*108 m/s).E.g., the time needed by a radio signal sent from a GPSsatellite to reach the Earth surface is about20000km/(3*108) m/s = 66.7 msIn the above equation, time = tR (Receiver time) – tT(Transmit time).
Pseudorange= estimate of the true sv-tx range (distance)
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Pseudorange concept
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Pseudorange = true range + errors3,2.1, iiiii d
Errors:- Clock errors (always present)- ionospheric and troposheric errors (satellite transmitters
only)- Multipath errors, etcErrors can be common to all transmitters (e.g., clock errors with stable transmitter clocks, such as in satellite case) or transmitter-dependent (e.g., multipaths)
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Navigation equations based on pseudoranges
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Receiver clock may have an (unknown) bias compared with the transmitterclock
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Satellite positions: ephemeris
Navigation data carries information about almanac(coarse orbit information) and the ephemeris (pl. ephemerides) or the accurate information about the satellites orbits and movements
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Examples of ephemeris data:a: Semi-major axis, e : Eccentricity (deviation) of orbit,i: Inclination angle,l : Right ascension of ascending node, …
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Navigation data decoding
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The output from the tracking loop is the value of the in-phase arm of the tracking block truncated to the values 1 and 1. Theoretically we could obtain a bit value every ms. However, we deal with noisy and weak signals =>a mean value for is computed and truncated to 1 or 1.
In GPS, one navigation bit has a duration of 20 ms => mean over 20 ms (see an example in the figure)
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Satellite geometry
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When the satellites are all in the same part of the sky, measurements will be less accurate.
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Satellite geometry: GDOP
A measure of the ’goodness’ of satellite geometry is the Geometrical Dilution of Precision (GDOP)GDOP has several components (e.g., Vertical DOP, Horizontal DOP)An intuitive physical measure of DOP is the inverse of the volume of the tetrahedron that is formed by the satellites and the receiver: 1/V
Lower DOP => better geometry
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Carrier-phase enhancements (I)
With code phase measurements, at the speed of light a microsecond (i.e., about 1 chip in GPS) is almost 300 meters of error. Carrier frequency has a cycle rate of over a GHz (which is 1000 times faster!)E.g., the wavelength of L1/E1 signals is
If we can measure the carrier cycles between the transmitter and the receiver (instead of the code delays) => centimeter level accuracy
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cmm 05.1910*575.1
10*39
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Carrier-phase enhancements (II)
Sine carrier:
We can express the phase cycles as:
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))(sin()2sin()( 0 tAftAts
2*)( 0tft cycle
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Carrier-phase enhancements (III)
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. ..
Finding N= ambiguity resolution problem -> N unknownbecause the receiver merely begins counting carrier cycles from the time a satellite is placed in activetracking mode
Source: Kaplan book
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Solving carrier-phase ambiguity
Reception of signal of two frequencies or via 2 antennas=> same N factor on both => the error can be corrected
Integer ambiguity remains the same, as long as nocycle slips occur
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2,1,, ifN tropoionoiclockbiasii
Phase observation
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High precision GNSS positioning
Combinations of carrier-phase and code-phasemeasurements are possibleIn addition to carrier-phase and code-phasemeasurements, we can also have the Precise Pointpositioning (PPP):- Uses a single receiver + reads correction data from some
databases in order to model and cancel errors: Satellite orbiterrors, Satellite and/or receiver clock errors, Fractional cyclebiases, Ionosphere errors, Troposphere errors, Antenna-relatederrors, Relativistic effects
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WIRELESS CHANNELS: MULTIPATHS AND OTHER CHANNEL IMPAIRMENTS
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Chapter 4 outline
Wireless channel impairments:• Multipaths• Ionospheric and troposheric delays• Other interference sources
Mitigation approaches:• Advanced dekay tracking structures
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What is multipath?
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-splitting of signal into 2 or more components due to reflections, scattering, refractions, dispersion, etc.
- replicas of the same tx signalarrive at the rxwith different attenuations (amplitudes), phases and delays
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Multipath terminology
LOS = Line Of Sight (directgeometrical non-obstructed pathbetween transmitter and receiver)NLOS = Non Line Of Sight (anymultipath component which is notLOS)TOA = Time Of Arrival
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GNSS Signal Transmission: Line Of Sight
Line of sight is the ability to draw a straight line between two objects without any other objects getting in the way.
GNSS receivers assume Line Of Sight (LOS) transmissions.
Obstructions such as trees, buildings, or natural formations may prevent clear line of sight.
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Multipath effect on position
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Triangulation principle for PVT computation is based on LOS TOAIf incorrect LOS estimate or NLOS case only => link-level errors will affect the final PVTExact amount depends on how many links are affected and what is the final algorithm for PVT computation
A rule of thumb at link-level:
e rr delay error => e r rc distance error.
c=3*108 m/s (speed of light)
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Example 1: multipath effect
2 channelpaths, shown in red dotsWithoutmultipathmitigation=> trackingerrors
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Example 2: multipath effect
The paths canadd togetherconstructively ordestructively(according to their phases)The multipatherrors are notnecessarilyincreasing withthe number of paths
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Challenges in GNSS
Falsepeaks dueboth to multipathsand BOC modulation(whenpresent)
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Criteria to evaluate multipath effects
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Link-level criteria:• Most used criterion is the Multipath Error Envelope (MEE),
see next slide• Multipath delay error mean/variance/root mean square
error (RMSE)• Probability Distribution Functions (PDF) of the delay
errors• Carrier to Noise Ratios (CNR) needed to achieve a
certain performance levelSystem-level criterion• Ultimately, the error on the estimated PVT (mean,
variance, RMSE,…) would be the most meaningful (also the hardest to evaluate during the algorithm design, since the whole chain including the navigation algorithms should be simulated)
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With multipath => zero-crossing point in S-curve is displaced, causing errors in the estimation. The horizontal error shown below is called MEE and it gives a measure of the discriminator ability to deal with multipaths
Multipath Error Envelopes (MEEs) (I)
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Multipath Error Envelope (MEE) (II)
2 static pathseither in-phase (0 degrees phaseshift) or out-of-phase (180 degrees phaseshift)Area in betweenthe curves definesthe error region
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Example
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How to cope with multipaths?
Stand-alone GNSS:• At baseband link-level: try to reduce/remove
the multipath effect for each satellite.• At navigation layer: system-level (multi-
satellite)• Combined link-level/system-level solutionsWith some external aid: • sensors, WLAN, inertial navigation systems
(INS), etc.
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High Resolution Correlator or Double-Delta correlators (also called Pulse Aperture Correlator, Strobe Correlator or Very Early-Very Late Correlator)Multiple Gate Delay structures (MGD): generalization of the multi-correlator structuresMultipath Estimator Delay Locked Loop (MEDLL)Deconvolution-based mitigationNon-linear operator based (e.g., Teager-Kaiser) Peak tracking (PT)
Advanced code tracking structures
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It adds 2 extra (complex) correlators: very early (VE) and very late (VL) (or, equivalently, 4 extra real correlators)It forms the discriminator output via:
The factor a above is typically set to 0.5It offers more resolution in multipaths
High Resolution Correlator (HRC)
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0.05 chips early-late spacing. BW=front-end bandwidth
MEE performance of narrow correlator vs HRC
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Variable number of correlators and variable spacings; possible to optimize those according to channelGeneral case; it covers the early-minus-late (3 correlators) and HRC (5 correlators) structures
Multiple Gate Delay structures (MGD)
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Maximum Likelihood (ML)-based approachReceived signal:After correlation with the reference code
Multipath Estimator Delay Locked Loop (MEDLL)
Amplitude of the l-th path of the channel Phase of the l-th path of the channel
Delay of the l-th path of the channel
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Number of paths is fixed to a certain value beforehand (e.g., max 2 paths) or the algorithm is repeated until a certain threshold is metAmplitudes, phases and delays are estimated for all paths, via maximum likelihood principle:
MEDLL
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Example: MEDLL estimation in good CNR
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The received signal is the result of the convolution between the (satellite) transmitted signal s(t) and the channel impulse response h(t):
Deconvolution methods
Deconvolution attempts to estimate the channel response h(t), invert it and then convolve it with the incoming signal, to estimate the transmitted signal. Usually, solved iteratively.Also constrained deconvolution methods possible, e.g., POCS (Projection Onto Convex Sets)
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z(n)= correlation functionThe following non-linear transform is applied on z(n); see below an example of the correlation after the non-linear transform in 1-path and 4-path cases
Teager Kaiser estimator
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Taken from [BLR08]. Some of the algorithms in the plot have not been metioned here. Among those mentioned in the course, nEML=narrow early-minus-late correlator; HRC= High Resolution Correlator; MEDLL= Multipath Estimator Delay Locked Loop and TK= Teager Kaiser
Performance Example
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Examples of advanced code tracking algorithms used by some GPS manufacturers
Company Multipath mitigation algorithm*
Ashtech Strobe CorrelatorCedar Rapids HRCMagellan Strobe CorrelatorNovatel MEDLL ,Pulse Aperture
Correlator, ...Sokkia Pulse Aperture Correlator
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Other channel impairments in GNSS
FadingAtmospheric delays:• Ionospheric delays• Tropospheric delays
Doppler shifts/spreadsNarrowband and wideband interferences
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Fading
Due to mobility, the channel
characteristics change over time• signal paths change• different delay variations of different
signal parts• different phases of signal partsquick changes in the instantaneous received power (short term fading)slow changes in the average receivedpower (long term fading)
t
223dB= Fading random component
s2
s1
s1+s2
s2
s1
s1+s2
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Atmospheric layers
Ionosphere: 50-1000 km above the Earth – introduces large, randomly fluctuating delays, frequency dependent
Troposphere: 0-50 km above the Earth – introduces small, randomlyfluctuating delay, frequencyindependent
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Random, frequency dependent delayIt depends on latitude of the receiver, season, time of day, solar
activity, etc.
Ionospheric delays
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2
3.40fTEC
iono
TEC= Total electron content, randomly fluctuatingf = carrier frequency
If a transmitter transmit on 2 or more frequencies, the TEC term is the same on all frequencies => we can use differential combining to reduce/remove the ionospheric delay
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Example: Ionospheric delays in Galileo
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Tropospheric delays
Caused by the signal refraction in the electrically non-ionized atmospheric layerTropospheric delay is a function of the satellite elevation angle and the altitude of the receiverDepends on atmospheric pressure, temperature, and water vapor pressureUnlike ionospheric effects, tropospheric ones do not depend on the signal’s frequency
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Chanel impairements: Doppler shifts/Doppler spreads
If the receiver or transmitter are moving, => Doppler shifts/spreads
If frequency f is transmitted, the received frequency = f +/- fD+ if mobile is moving towards the transmitter- if mobile is moving away fromthe transmitter
The Doppler shift equals
Also moving objects in the environment may introduce fast fading effects, even if the receiver and transmitter are stationary.
cosvfD
angle between the direction of motion and the direction of the wave wavelength
speed of the receiver
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Narrowband and wideband interferences
Wideband interference:• Inter-system (e.g., GPS-Galileo), sharing
same frequency bans• Intra-system (e.g., OS and PRS signals in
E1 band in Galileo)Narrowband interference:• Unintentional (LightSquared)• Intentional (jamming, spoofing)
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Summary and conclusions (I)
More than 110 navigation satellites forecast for the next5+ years4 main GNSS systems3 frequency bands per GNSS systemCDMA technique common for all (in GLONASS, onlyused for spreading; in GPS/Galileo/Compass used bothfor spreading and multiple access)Several signals transmitted in each band (more to come in the future)Several modulation types, with BOC family as the main candidate (generic models available)
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Summary and conclusions (II)
Main baseband tasks:• Acquisition• Tracking
GNSS affected by several sources of errors, also specific to other wireless systems (e.g., multipath, fading, Doppler shifts, interferences)Multipath and ionospheric delays are two of the most difficult phenomenon to cope with in GNSS receivers.
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Trivia: Galileo open-source software
Simulink Galileo E1 and E5a baseband transmitter-receiver chains, built within the GRAMMAR (Galileo Ready Advanced Mass Market Receiver, funded from the European Community's Seventh Framework Programme FP7/2007-2013 under grant agreement n°227890.) project- available as open-source (see http://www.cs.tut.fi/tlt/pos/Software.htm)
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Some references (I)
[LLR06a] E. S. Lohan, A. Lakhzouri, and M. Renfors, "Feedforward delay estimators in adverse multipath propagation for Galileo and modernized GPS signals", EURASIP Journal of Applied Signal Processing, vol 2006, Article ID 50971, 19 pages[LLR06b] E. S. Lohan, A. Lakhzouri, M. Renfors, "Binary-offset-carrier modulation techniques with applications in satellite navigation systems", Wireless Communications and Mobile Computing, Volume 7, Issue 6 (p 767-779), 2006.[LLR06c] E. S. Lohan, A. Lakhzouri, M. Renfors, ``Complex Double-Binary-Offset-Carrier modulation for a unitary characterization of Galileo and GPS signals'', IEE Proceedings on Radar, Sonar, and Navigation, vol. 153(5), pp. 403-408, Oct 2006.[Win06] J.O. Winkel, ”SPREADING CODES FOR A SATELLITE NAVIGATION SYSTEM”, ESA Patent application WO/2006/063613, http://www.wipo.int/pctdb/en/wo.jsp?WO=2006063613&IA=EP2004014488&DISPLAY=STATUS
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Some references (II)
[WRH07] Wallner, S., Avila-Rodriguez, J.A., Hein, G.W.: Galileo E1 OS and GPS L1C Pseudo Random Noise Codes - Requirements, Generation, Optimization and Comparison -, Proceedings of ION GNSS 2007, Fort Worth, Texas, USA, 25-28 September 2007[PP2010] B.W. Parkinson and S.T. Powers, ”Fighting to survive: fivechallenges, one key technology, the political battlefield – and GPS mafia”, GPS World, Jun 2010, pp.8-18. [Bet00] J. W. Betz, “Effect of Narrow Interference on GPS Code TrackingAccurancy,” in Proc. ION 2000, Institute of Navigation, Anaheim, CA, January26-28. 2000, pp. 16–27.[Bet01] J. W. Betz, “Effect of Partial-Band Interference on Receiver Estimationof C/N0: Theory ,” in Proc. ION 2001,Institute of Navigation, Long Beach, CA, January 22-24. 2001, pp. 16–27.[LLR05] E. S. Lohan, A. Lakhzouri, and M. Renfors ,”Benefits of using lower chip rates for Galileo OS and PRS signals”, ENC-GNSS 2005, Munich.
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Some references (III)
[HRV06] M. Fantino, P. Mulassano, F. Dovis, and L. L. Presti, “Performance of the Proposed Galileo CBOC Modulation in Heavy MultipathEnvironment,” Wireless Personal Communications, vol. 44, pp. 323– 339, Feb 2008. [ALI08] G. Artaud, L. Lestarquit, and J.-L. Issler, ”AltBOC for dummies oreverything you always wanted to know about AltBOC”, in Proceedings of the ION GNSS 2008, Savannah, GA, Sep 2008.[Cho09] C. Chong, Status of COMPASS/BeiDou Development , Standfordpresentation,http://scpnt.stanford.edu/pnt/PNT09/presentation_slides/3_Cao_Beidou_Status.pdf[BLR08] M.Z.H. Bhuiyan, E.S. Lohan, and M. Renfors, ``Code Tracking Algorithms for Mitigating Multipath Effects in Fading Channels for Satellite-based Positioning'', EURASIP Journal on Advances in Signal Processing , vol. 2008, article ID 863269, published on-line
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