10.1 Positioning
10.2 Car Navigation 10.3 Map Matching 10.4 Privacy
10.5 Summary
10 Location Based Services
hBp://de.wikipedia.org/
• Location Based Services (LBS) are services,
– That are accessible with mobile devices through the mobile network
– Integrating a mobile’s device location with other
information so as to provide added value to the user
• Classification of LBS applications
– Person-oriented
• Person located can control the service
– Device-oriented
• Person or object located is not controlling the service
10 Location Based Services
www.m3-‐systems.com/en/projects.php
• Types of application design
– Pull Services
– Push Services
10 Location Based Services
Event Data transfer
Request Response
• Application examples
10 Location Based Services
Push Services Pull Services Person-‐
oriented Communica$on A message is pushed to you asking whether you allow a friend to locate you
You request from a friend finder applica$on who is near you
Informa$on You get an alert that a terror alarm has been issued by the city you are in
You look for the nearest cinema in your area and naviga$on
instruc$ons to get there M-‐Commerce
and Adver$sing A discount voucher is being sent to you from a restaurant in the area you are in
You look for events happening in the area you are in
Device-‐
oriented
An alert is sent to you from an asset-‐tracking applica$on that one of your shipments has just deviated from its foreseen route
You request informa$on on
where your truck fleet currently is located in the country
• Application areas
– Travel services
• Routing, city, hotel and restaurant guides
– Emergency
• Locating a person in need, warn persons in danger
– Fleet management – Phone tracker
• Child watch, anti-theft tracking
– Friend finder, blind dating – Mobile phone tariffs
10 Location Based Services
hBp://sourceforge.net/dbimage.php?id=132227
• Self-locating: User (his mobile device) locates himself
– Global Positioning System (GPS) – Manual position input (not smart)
• External locating: Operator locates the user’s mobile device
– Determining the current mobile network cell – Signal comparison between three adjacent cells
• Locating provided by third parties, mobile device involved
– Location transponder – Peer-to-Peer locating
10.1 Positioning
hBp://www.nundenn.de/a_standortbes$mmung2.gif
• Global Positioning System (GPS)
– Enables three dimensional positioning near the earth – Measuring the runtime of signals between the satellite
and the GPS-receiver, from which the distance and the position can be deduced (trilateration).
– The transmitted signal describes a circular sphere centered at the
satellite on which surface the
signal is received at the same
time → circular baseline of
equal receiving times
on earth
10.1 Positioning
hBp://www.uni-‐giessen.de/ilr/frede/
lehrveranstaltungen/MP_51/2.6-‐GPS.pdf
– From the intersection of baselines of (at least) three satellites the position on the earths surface is deduced – Prerequisite is the temporal coordination of the
satellites and the receiver,
otherwise the baseline of a
fourth satellite is needed
10.1 Positioning
hBp://www.uni-‐giessen.de/.../2.6-‐GPS.pdf
– Navigational Satellite Timing and Ranging - Global Positioning System (NAVSTAR-GPS)
• Currently the most important positioning and navigation system worldwide
• Operator: United States Air Force 50th Space Wing
• 1973: decision on development
• 1978-1985: launch of 11 block I-satellites
• March 1994: launch of the last block II-satellites
• July 1995: full operational capability
• 1.5.2000: enhanced accuracy for civilian users (from approx.
100m to 20m)
10.1 Positioning
– Three major segments: space, control and user segment
– Between 24 and 32 satellites – Six orbits
• 55o inclination each
• 20200 km altitude
• 11 h 55 min orbital period
– From every point at earth at least 5 satellites are always visible
– 5 different types of satellites:
Block I, Block II, Block IIA, Block IIR und Block IIF
10.1 Positioning
hBp://www.iww.forst.uni-‐goeangen.de/
– Block II satellites
• Weight: 1500 kg
• Span 5,1 m
• Durability 7,5 years
• 2 (IIR 3) rubidium and 2 cesium atomic clocks with a stability of at least 10 - 13 s
• Power source: solar panels 750 watt
• Radiated power 50 watt
10.1 Positioning
hBp://www.kowoma.de/
gps/Satelliten.htm
IIF
IIA IIR
– Control segment
• Passive ground stations to track the flight paths of the satellites
4 monitoring stations operated by the U.S. air force
Since end of 2005 6 more stations operated by the NGA (National Geospatial-Intelligence Agency)
One "Master Control Station" for evaluation
• Every satellite can
always be received
by at least two
ground stations
10.1 Positioning
hBp://www.kowoma.de/gps/Bodensta$onen.htm
– GPS-receiver
• Composed of an antenna, receiver-processors, and a highly- stable clock
• May also include a display for providing location and speed information
• Dedicated devices or
integrated into cars,
mobile phones,
watches, etc.
10.1 Positioning
hBp://www.connect.de/.../Bluetooth-‐
GPS-‐Empfaenger-‐im-‐Test_210778.html hBp://images.fuzing.com/.../
1231.300x300.jpg www.ecvv.com/product/1233023.html
– Message format
• Week and time within the week
• Health of the satellite
• Ephemeris
– In a spherical polar coordinate
system
– Updated every 2h
• Almanac
– Coarse orbit and status information for all satellites
– Data related to error correction – Updated every 24h
10.1 Positioning
hBp://www.uni-‐giessen.de/ilr/frede/
lehrveranstaltungen/MP_51/2.6-‐GPS.pdf
– Random errors: current local conditions at the location of the receiver
• Dense forests: signal damping
• Mountains, narrow valleys, street canyons: shadowing effects
• Large buildings: multipath effect
• Tall metal construction elements:
echo effect, signal distortion
• Strong transmitters and
high-voltage power lines
– Best receiving conditions in the open country with small relief
10.1 Positioning
hBp://www.kowoma.de/en/gps/errors.htm
– Clock errors
• Relativistic effects
– Time moves the faster the weaker the field of gravitation is – Time runs slower during very fast movements
• Inaccuracy of the time of the receiver clock
– Change of speed of propagation of radio waves in the atmosphere
• Ionosphere (70-1000 km): electromagnetic waves are slowed down inversely proportional to the square of their frequency
• Troposphere (40-70 km): refraction due to different concentrations of
water vapour
10.1 Positioning
hBp://www.kowoma.de/en/gps/errors.htm
• Differential GPS (DGPS)
10.1 Positioning
base or reference sta$on:
set up on a precisely known loca$on calculates its posi$on based on
satellite signals and compares this loca$on to the known loca$on
correc$on signal GPS receiver
calculates its posi$on based on satellite signals and applies the difference
underlying premise: any two receivers that are rela$vely close together will experience similar atmospheric errors
• Cell of Origin COO
– Every cell belongs to one base station
– Different frequencies are used in neighbouring cells
– Base stations know about mobile phones within their cell
– Accuracy of the position
depends on the size of the cell
10.1 Positioning
hBp://v.hdm-‐stuBgart.de/~riekert/vortraege/03lbs.pdf
• Signal comparison
– Cell phone is in contact with several base stations – Either base station calculates the position
• Angle of Arrival (AOA)
• Signal strength
• Time of Arrival (TOA)
– Or cell phone calculates its
position:
• Signal running time difference
– Accuracy: approx. 50-200m
10.1 Positioning
hBp://v.hdm-‐stuBgart.de/~riekert/vortraege/03lbs.pdf
• Location transponder
– Mobile device gets location information from transponders (e.g. infrared, bluetooth)
– Advantages
• Quite precise: 5-15m
• Able to show user’s orientation
• May send additional information
• Suitable for indoor applications
– Disadvantages
• Mobile device needs additional software
• Transponders have to cover the whole area
• Synchronization of transponders and applications is necessary
10.1 Positioning
• Example: “Balise”
– Data is transmitted while the train passes over the
“Balise” (transponder principle)
• Some “Balisen”send always the same information
• Others are controlled by so-called Lineside Equipment Units (LEU)
– Receiver in the train: Balise Transmission Module (BTM)
– Components of the European Train Control System (ETCS)
10.1 Positioning
hBp://de.wikipedia.org/
– Technical data
• Messages consists of 1023 bits or 341 bits, payload: 830 respectively 210 bits
• Data transfer rate: 564,48 kBit/s
• It is possible to transmit a complete message up to a speed of 500 km/h
• FSK-modulated magnetic field, 3,951 MHz equates to a logical '0' and 4,516 MHz to a logical '1'‚
• Power supply by the BTM’s vertical magnetic field with a frequency of
27,095 MHz
(electromagnetic induction)
10.1 Positioning
hBp://www.sicherungstechnik-‐bahn.de/
download/Augau_Workshop_2/Luz.pdf
– Transmitted data:
• Position
• Gradient
• Speed-limit
• Next stop of the
train
– Allows the on-board ETCS equipment to
• Control the compliance with speed limit and the correct direction
• Use emergency breaking in time
• Be independent of national defined signal distances and route geometries
10.1 Positioning
hBp://de.wikipedia.org/
• Peer-to-peer positioning
– Exchange of position information between mobile devices
– Advantages
• Decentralized position
information acquisition
• Position information
from specialized devices
– Disadvantages
• Quality of information unknown
• No standardized peer-to-peer system
10.1 Positioning
hBp://lion.disi.unitn.it/intelligent-‐op$miza$on/research.html
• Intelligent transportation systems (ITS)
– Automotive navigation systems are a part of ITS – Goals of ITS
• Preserve mobility in view of increased motorization, urbanization and population growth
• Increase road safety
• Minimize congestion and
environmental pollution
– Based on new information
technology for simulation,
real-time control, and
communications networks
10.2 Car Navigation
hBp://www.advantech.com.tw/.../Transporta$on_page2.htm
• Components of a navigation system
10.2 Car Navigation
traffic reports
map sec$on (current posi$on)
communi-‐
ca$on
sensor system mass storage
posi$oning map
matching
HMI rou$ng
route guidance
digital map
traffic reports
measurements
screen speech
input keyboard
speech output
map data (off board)
> route segments
< rerou$ng
> opera$ng instruc$ons
< status
> route segments, route list
< chosen route
map sec$on (start)
• GDF (Geographic Data Files)
– Standardized geometrical and topological model for road networks and other geographic data(ISO)
– Interchange file Format – Contains rules for
• Data capture
• Management
• Representation
– Nationwide GDF-data for Germany since 1995
– A GDF database (in the exchange format) will never be used as such
10.2 GDF
• Level 0: geometry and topology
– Nodes, edges and faces
• Level 1: features.
– “Simple features” e.g. road segments, rivers, borders and road signs
– Features may
have specific
attributes (e.g. one way
street, roadway width,
number of lanes) and relations
10.2 GDF
hBp://www.er$co.com/download/misc/GDF/gdf_intro.pdf
• Level 2: complex features.
– Aggregation of simple features
– Simplified representation (Generalization)
10.2 GDF
hBp://www.er$co.com/download/misc/GDF/gdf_intro.pdf
10.2 GDF
Junc$on
Road Element Level 1
Level 2
Inter-‐
sec$on
hBp://www.ikg.uni-‐bonn.de/vorlesungsarchiv/Gis_iv_SS_02/Vortraege/Becker.ppt
• Features are grouped into feature themes
10.2 GDF
hBp://www.er$co.com/download/misc/GDF/gdf_intro.pdf
• Feature Themes are divided into Feature Classes
– Example: Theme: Roads and ferries(Code 41)
Classes: 4110 RoadElement 4120 Junction
4130 FerryConnection
• Physical representation of GDF
– In ASCII files, ISO 8251-1
– A country consists of a collection of files
– A file contains several records, one for every GDF-element e.g.
a PointFeature is one (logical) record – Mediarecords of 80 signs each
– Data within one record is exactly defined by fields and length
10.2 GDF
10.2 GDF
52= Line Feature ID = 20001532 Feature Code = 4110=RoadElement Split = 0
#Edges = 1
20003220
#Faces = 0
#AFributes = 1 20002083 From 20001751 To 20001752 24 = Edge Feature
ID = 20003220 from 20002222 to 20002223 Face 20000611 RighMace 20003926 Status = 2
51 = Point Feature ID = 20001751 Feature Code = 4120 = juncPon
#Knots = 1
20002222
#AFributes = 0
51 = Point Feature ID = 20001752 Feature Code = 4120 = juncPon
#Knots = 1
20002223
#AFributes = 0 25 = New Node
ID = 20002222 XYZ-‐ID 20009835 Status = 2 (normal)
25 = New Node ID = 20002223 XYZ-‐ID 20009837 Status = 2 (normal)
44= Segm AFribute ID = 20002083
#AFributes = 6
ON Official Name 20001871 AN Alternate Name 20001872 FC FuncPonal Road Class
1 8B Net 1 Class FW Form of Way 3 4 Part of a roundabout DF DirecPon of Traffic 3 Closed in negaPve 41 = Name Record
ID = 20001871
GER//LANDWEHRKREISEL
41 = Name Record ID = 20001872
GERFRANKFURTER ALLEE
10.2 GDF
www.maps.google.de
• Attributes
– Simple Attributes: consists of one component
– Composite Attributes: consists of several components
→ so called Sub-Attributes
– Restrictive Sub-Attributes: restricts the validity of other attributes
→ may only be used within composite attributes
– Segmented Attributes: only valid for a part of a feature
→ position-from-, position-to-value
10.2 GDF
Feature:
Road Element
ABribut:
Speed Restric2on 50 km/h
Restr.Sub-‐ABribute:
Validity Period 8.00 – 18.00 Uhr
10.2 GDF
hBp://www.ikg.uni-‐bonn.de/.../Becker.ppt
• Relations
– Not topological e.g. the relation ´is capital of´ between Paris and France
– Usually relations between two features
– N-nary relations also possible, e.g. a bridge leads a road over a river
10.2 GDF
hBp://www.er$co.com/download/misc/GDF/data_model.pdf
• Automotive navigation
– Pilotage, recognition of “landmarks“
– Dead reckoning
• Previously determined position
• Recordings of the wheel rotation and steering direction
– Inertial navigation systems (INS)
• Initially provided with the car’s position, orientation, and speed
• Recordings of motion and rotation sensors
– Radiolocation
• Measuring phase and runtime of radiowaves
• Terrestrial (e.g. GSM) or satellite-based (GPS)
10.2 Car Navigation
• Sensor system
– Wheel speed sensors
• Provide the speed of the vehicle and the covered distance
• Electronic tacho-signal
– Odometer
• Measuring the covered distance
• Change of direction can be calculated using two odometers, one each for the wheels on an axle (differential odometer)
– Electronic compass – Gyroscope
• Measuring orientation
10.2 Car Navigation
www.ikg.uni-‐hannover.de
hBp://en.wikipedia.org
• Problems
– Dead reckoning and INS: the errors of the process are cumulative
– GPS: in urban areas often unavailable or degraded
• Goal
– Accuracy of odometer and gyroscope – Long-tern accuracy of GPS
• Solution: sensor fusion
– GPS + odometer: good but
perhaps problems with turns in
tunnels
– GPS + odometer + gyroscope
10.2 Car Navigation
hBp://www.al-‐nasir.com/.../
INS_Iner$al_Naviga$on_explained.shtml
• Sensor Fusion
10.2 Car Navigation
positioning
change of direction
number of wheel rotations
covered distance coordinates
electric compass gyroscope
wheel speed sensor odometer
dead reckoning
GPS / DGPS
coordinates corrected coordinates
road network
map matching digital map
data
position with respect to the road network
coordinates
• Routing
– Search the best way in a weighted graph – Cost
• Distance
• Effective velocity
– Algorithms (chapter 2.6)
• Dijkstra
• Bellman-Ford
• Floyd-Warshall
10.2 Car Navigation
hBp://commons.wikimedia.org
• Map matching
– Process of aligning a sequence of observed user positions with the road network on a digital map
– Influencing factors
• Accuracy of the positioning
• Systematic error behavior of the used sensors
• Quality of the map
10.3 Map Matching
hBp://www.unibw.de/bauv11/geoinforma$k/lehre/
skripten/skripte/skripten_ht_08/map_matching.pdf
10.3 Map Matching
hBp://www.uni-‐stuBgart.de/iagb/forschung/messtechnik/projekte/mapmatching-‐Dateien/Cz_Internet_Strasse.pdf
– Simplified matching algorithm
10.3 Map Matching
measure posi$on determine error
region determine possible
roads
chose “best“
matching does
calculated one?
region equals measured adjust posi$on
yes no
• Point-to-Point Matching
– Match the measured position to the “closest” point (node) on the map
– Difficulties
• The position is usually not represented as node on the map it is one point on a line (street) instead
• Streets with more shape points are chosen with higher probability
10.3 Map Matching
• Point-to-Curve Matching
– Identify the road segment which is “closest” to the measured point
– Distance measures might be
• Minimum distance, mean distance, Hausdorff distance
• Let A denote the segment between a=(a1,a2) and b=(b1,b2).
The minimum distance between some point c=(c1,c2) and A is the minimum of:
with
– Shortcoming: No use of “historical” information
10.3 Map Matching
• Curve-to-Curve Matching
– A better way to proceed is to consider m positions simultaneously
10.3 Map Matching
hBp://ebus.informa$k.uni-‐leipzig..../vt06-‐ve07-‐pdf.pdf
• Curve-to-Curve Matching
– A better way to proceed is to consider m positions simultaneously
10.3 Map Matching
hBp://ebus.informa$k.uni-‐leipzig..../vt06-‐ve07-‐pdf.pdf
– Further criteria to evaluate the quality of a matching
• Angle between segments and the direction of movement
• Connectivity of segments
– Additional Information that might help to improve the quality or reduce the computation costs
• Allowed driving directions (one way streets, ban on turns, separated lanes)
• Driving speed e.g. helps to decide whether a car drives on a highway or a street parallel to it
10.3 Map Matching
hBp://www.unibw.de/.../map_matching.pdf
• Threats to privacy
– Subsequent queries of a user’s location may be used to create a movement profile
– Tracking of persons
possible (stalking)
– Danger of a
"glassy citizen"
• Data privacy
protection necessary
10.4 Privacy
hBp://pixelbuy.com/Ebay/Import/GPS%20TK202/google+.jpg
• Legal aspects
– Directive on privacy and electronic communications of the European Parliament (2002/58/EC, 2009/136/EC)
10.4 Privacy
• Classification of system architectures
– Non-cooperative architecture
• Users depend only on their knowledge to preserve their location privacy
– Centralized trusted party architecture
• A centralized entity is responsible for gathering information and providing the required privacy for each user
– Peer-to-Peer cooperative architecture
• Users collaborate with each other without the interleaving of a centralized entity to provide customized privacy for each single user
10.4 Privacy
• Non-cooperative architecture
– Landmark objects
• Instead of reporting the exact location, report the location of a closest landmark
• The query answer will be based on the landmark
• Voronoi diagrams can be used to identify the closest landmark
– „False Dummies“
• A user sends m locations, only one of them is the true one while m-1 are false dummies
• The server replies with a service for each received location
• Only the user knows the true location, and hence the true answer
10.4 Privacy
hBp://mdm2007.uni-‐mannheim.de
• Centralized trusted party architecture
– Quadtree Spatial Cloaking
• Achieve k-anonymity, i.e., a user
is indistinguishable from other
k-1 users
• Recursively divide the space
into quadrants until a quadrant
has less than k users
• The previous quadrant, which
still meet the k-anonymity
constraint, is returned
10.4 Privacy
Goal: 5-‐Anonymity for
hBp://mdm2007.uni-‐mannheim.de/downloads/
Seminar_Mokbel_Aref_MDM_2007-‐05-‐09.ppt
– Clique Cloak Algorithm
• Each user requests
– A level of k anonymity – A maximum cloaked area
• Build an undirected
constraint graph
• Two nodes are neighbors,
if their maximum areas
contain each other
• The cloaked region is the MBR that includes the user and neighboring nodes. All users within an MBR use that MBR as their cloaked region
10.4 Privacy
A (k=3)
C (k=2) B (k=4)
D (k=4) F (k=5) H (k=4) E (k=3)
hBp://mdm2007.uni-‐mannheim.de/downloads/
Seminar_Mokbel_Aref_MDM_2007-‐05-‐09.ppt
– Clique Cloak Algorithm
• Each user requests
– A level of k anonymity – A maximum cloaked area
• Build an undirected
constraint graph
• Two nodes are neighbors,
if their maximum areas
contain each other
• The cloaked region is the MBR that includes the user and neighboring nodes. All users within an MBR use that MBR as their cloaked region
10.4 Privacy
A (k=3)
C (k=2) B (k=4)
D (k=4) F (k=5) H (k=4) E (k=3)
hBp://mdm2007.uni-‐mannheim.de/downloads/
Seminar_Mokbel_Aref_MDM_2007-‐05-‐09.ppt
– Clique Cloak Algorithm
• Each user requests
– A level of k anonymity – A maximum cloaked area
• Build an undirected
constraint graph
• Two nodes are neighbors,
if their maximum areas
contain each other
• The cloaked region is the MBR that includes the user and neighboring nodes. All users within an MBR use that MBR as their cloaked region
10.4 Privacy
A (k=3)
C (k=2) B (k=4)
D (k=4) F (k=5) H (k=4) E (k=3)
m (k=3)
hBp://mdm2007.uni-‐mannheim.de/downloads/
Seminar_Mokbel_Aref_MDM_2007-‐05-‐09.ppt
– Clique Cloak Algorithm
• Each user requests
– A level of k anonymity – A maximum cloaked area
• Build an undirected
constraint graph
• Two nodes are neighbors,
if their maximum areas
contain each other
• The cloaked region is the MBR that includes the user and neighboring nodes. All users within an MBR use that MBR as their cloaked region
10.4 Privacy
A (k=3)
C (k=2) B (k=4)
D (k=4) F (k=5) H (k=4) E (k=3)
m (k=3)
hBp://mdm2007.uni-‐mannheim.de/downloads/
Seminar_Mokbel_Aref_MDM_2007-‐05-‐09.ppt
– Clique Cloak Algorithm
• Each user requests
– A level of k anonymity – A maximum cloaked area
• Build an undirected
constraint graph
• Two nodes are neighbors,
if their maximum areas
contain each other
• The cloaked region is the MBR that includes the user and neighboring nodes. All users within an MBR use that MBR as their cloaked region
10.4 Privacy
A (k=3)
C (k=2) B (k=4)
D (k=4) F (k=5) H (k=4) E (k=3)
m (k=3)
hBp://mdm2007.uni-‐mannheim.de/downloads/
Seminar_Mokbel_Aref_MDM_2007-‐05-‐09.ppt
– Nearest-Neighbor k-Anonymizing
• Determine a set S containing u and k - 1 u’s nearest neighbors
• Randomly select an element v from S
• Determine a set S’ containing v
and v’s k - 1 nearest neighbors
• The MBR of all users in S’ and
u is taken as the u’s location
10.4 Privacy
S
hBp://mdm2007.uni-‐mannheim.de/downloads/
Seminar_Mokbel_Aref_MDM_2007-‐05-‐09.ppt
– Nearest-Neighbor k-Anonymizing
• Determine a set S containing u and k - 1 u’s nearest neighbors
• Randomly select an element v from S
• Determine a set S’ containing v
and v’s k - 1 nearest neighbors
• The MBR of all users in S’ and
u is taken as the u’s location
10.4 Privacy
S’
hBp://mdm2007.uni-‐mannheim.de/downloads/
Seminar_Mokbel_Aref_MDM_2007-‐05-‐09.ppt
– Nearest-Neighbor k-Anonymizing
• Determine a set S containing u and k - 1 u’s nearest neighbors
• Randomly select an element v from S
• Determine a set S’ containing v
and v’s k - 1 nearest neighbors
• The MBR of all users in S’ and
u is taken as the u’s location
10.4 Privacy
hBp://mdm2007.uni-‐mannheim.de/downloads/
Seminar_Mokbel_Aref_MDM_2007-‐05-‐09.ppt
– Basic Pyramid Structure
• The entire system area is represented
as a complete pyramid structure
divided into grids at different
levels of various resolution
• Each grid cell maintains the
number of users in that cell
• To anonymize a user request,
we traverse the pyramid
structure from the bottom
level to the top level
until a cell satisfying
the user privacy
profile is found
10.4 Privacy
hBp://mdm2007.uni-‐mannheim.de/.../Seminar_Mokbel_Aref_MDM_2007-‐05-‐09.ppt
• Peer-to-peer based systems
– Peer searching
• Broadcast a multi-hop request until at least k-1 peers are found
– Location adjustment – Spatial Cloaking
• Blur user location into
a region aligned to a
grid that cover the
k-1 nearest peers
10.4 Privacy
hBp://mdm2007.uni-‐mannheim.de/downloads/
Seminar_Mokbel_Aref_MDM_2007-‐05-‐09.ppt
• Positioning
– GPS
– Network-based locating – Location transponder
• Car Navigation
– Detour [GDF]
– Sensor system
– Navigation systems – Routing
10.5 Summary
• Map Matching
• Privacy
– System architectures – Algorithms
10.5 Summary
10.5 Summary
GIS collect
manage
analyse
display
opera$ons on
graphs
LBS
naviga$on systems
encryp$on of loca$ons
GDF
posi$on
map matching
rou$ng
