[PPT] - Towards traffic Towards traffic-aware routing using o a ds t a o a PowerPoint Presentation

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Towards traffic Towards traffic-aware routing using aware routing using

a ds t a

c

a ds t a

c a a e out g us g a a e out g us g GPS vehicle trajectories GPS vehicle trajectories

Carola Wenk Carola Wenk University of Texas at San Antonio University of Texas at San Antonio carola@cs utsa edu carola@cs utsa edu carola@cs.utsa.edu carola@cs.utsa.edu

Collaboration with:

Dieter Pfoser, Computer Technology Institute, Athens, Greece
Peter Wagner, German Aerospace Center, Berlin, Germany

SLIDE 2

Outline Outline

1 Problem Description Problem Description

1. 1.

Problem Description Problem Description

Enable in Enable in-

car navigation systems to find the best routes using

car navigation systems to find the best routes using current traffic situation current traffic situation

2. 2.

Travel Times and GPS curves Travel Times and GPS curves

3. 3.

Map Map-

Matching

Matching

I t l I t l t hi t hi

1. 1.

Incremental map Incremental map-

matching

matching

2. 2.

Global map Global map-

matching: Fr

matching: Fréchet distance échet distance

3. 3.

Global map Global map-

matching: Weak Fréchet distance

matching: Weak Fréchet distance

4. 4.

Routing System Setup and Future Work Routing System Setup and Future Work

2

SLIDE 3

In In-

Car Navigation Systems

Car Navigation Systems

Navigation systems perform the

Navigation systems perform the routing task routing task: Find a shortest route from A to B Find a shortest route from A to B Find a shortest route from A to B Find a shortest route from A to B

What does “shortest” mean?

– Shortest length? No.

Shortest length? No.

– Shortest travel time !

Shortest travel time !

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SLIDE 4

Model for Routing Task Model for Routing Task

Model the street network as a graph:

Vertices: Intersections of roads Vertices: Intersections of roads

– Vertices: Intersections of roads

Vertices: Intersections of roads

– Edge: A road segment between two intersections

Edge: A road segment between two intersections

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Model for Routing Task Model for Routing Task

Routing Task: Find shortest path in the graph from

Routing Task: Find shortest path in the graph from A to to B

A B

5

SLIDE 6

How to Compute Shortest Paths? How to Compute Shortest Paths?

Dijkstra’s shortest path algorithm:

Given A B and a graph with non-negative edge weights

– Given A, B, and a graph with non-negative edge weights – Among all paths from A to B in the graph, compute such a

path whose total weight (= sum of edge weights) is minimized minimized

What are our edge weights?

– Travel times – The travel time on a (directed) edge from c to d is the time it

takes to travel from c to d

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Outline Outline

1 Problem Description Problem Description

1. 1.

Problem Description Problem Description

Enable in Enable in-

car navigation systems to find the best routes using

car navigation systems to find the best routes using current traffic situation current traffic situation

2. 2.

Travel Times and GPS curves Travel Times and GPS curves

3. 3.

Map Map-

Matching

Matching

I t l I t l t hi t hi

1. 1.

Incremental map Incremental map-

matching

matching

2. 2.

Global map Global map-

matching: Fr

matching: Fréchet distance échet distance

3. 3.

Global map Global map-

matching: Weak Fréchet distance

matching: Weak Fréchet distance

4. 4.

Routing System Setup and Future Work Routing System Setup and Future Work

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Travel Time of an Edge Travel Time of an Edge

How do we know the travel time on an edge / road

How do we know the travel time on an edge / road segment? segment? segment? segment?

– Usually, navigation systems derive travel times from speed

limits. A very smart system might take a small number of congestion

– A very smart system might take a small number of congestion

points into account

– Usually variation of travel times during rush hour is not taken

into account into account

New approach: Maintain a database of current travel times

– Use GPS trajectory data from vehicle fleets (delivery trucks,

Use GPS trajectory data from vehicle fleets (delivery trucks, i ) i ) taxis, etc.) taxis, etc.)

Challenge: How do we build this database?

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GPS Floating Car Data GPS Floating Car Data

Floating car data (FCD)

A sequence (trajectory) of data points each consisting of: A sequence (trajectory) of data points each consisting of: A sequence (trajectory) of data points, each consisting of: A sequence (trajectory) of data points, each consisting of:

– Basic vehicle telemetry, e.g., speed, direction, ABS use

Basic vehicle telemetry, e.g., speed, direction, ABS use

– The

The position of the vehicle position of the vehicle ( tracking data) obtained by GPS tracking data) obtained by GPS tracking tracking tracking tracking

– A time stamp

A time stamp

Traffic assessment

– Data from one vehicle as a sample to assess the overall

Data from one vehicle as a sample to assess the overall traffic condition traffic condition – – cork swimming in the river cork swimming in the river

– Large amounts of tracking data

Large amounts of tracking data (e.g., taxis, public transport, (e.g., taxis, public transport, g g g g ( g , , p p , ( g , , p p , utility vehicles, private vehicles) utility vehicles, private vehicles) Accurate picture of the traffic condition Accurate picture of the traffic condition

– Tracking data needs to be related to the road network

Tracking data needs to be related to the road network

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g Map matching Map matching

– Time stamps

Time stamps from FCD yield from FCD yield travel times travel times for road segments for road segments

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GPS Vehicle Tracking Data GPS Vehicle Tracking Data

Problems: Problems:

1) Measurement error: 1) Measurement error:

GPS points do not exactly lie on the roadmap roadmap

2) Sampling error:

GPS curve is a by- d t d ll

Map matching: Find a curve in the graph that corresponds

product, and usually sampled every 30s

g p p to the GPS curve

⇒ The GPS curve does not lie on the roadmap

10 Roadmap of Athens, Greece GPS curve Corresponding path in the roadmap

roadmap

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Outline Outline

1 Problem Description Problem Description

1. 1.

Problem Description Problem Description

Enable in Enable in-

car navigation systems to find the best routes using

car navigation systems to find the best routes using current traffic situation current traffic situation

2. 2.

Travel Times and GPS curves Travel Times and GPS curves

3. 3.

Map Map-

Matching

Matching

I t l I t l t hi t hi

1. 1.

Incremental map Incremental map-

matching

matching

2. 2.

Global map Global map-

matching: Fr

matching: Fréchet distance échet distance

3. 3.

Global map Global map-

matching: Weak Fréchet distance

matching: Weak Fréchet distance

4. 4.

Routing System Setup and Future Work Routing System Setup and Future Work

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Available Map Available Map-

Matching Algorithms

Matching Algorithms

Incremental map

Incremental map-

matching

matching

Follo greed strateg of incrementall e tending sol tion Follo greed strateg of incrementall e tending sol tion

– Follow greedy strategy of incrementally extending solution

Follow greedy strategy of incrementally extending solution from an already matched edge, e.g., [BPSW05] from an already matched edge, e.g., [BPSW05]

– No quality guarantee

No quality guarantee

– Classical approach

Classical approach

Global map

Global map-

matching

matching

– Find among all possible trajectories in the road network the

Find among all possible trajectories in the road network the g p j g p j

ne that is most similar to the vehicle trajectory
ne that is most similar to the vehicle trajectory

– Distance measure assesses similarity

Distance measure assesses similarity = quality guarantee = quality guarantee

– Fr

Fréchet distance (strong weak) [BPSW05 WSP06] chet distance (strong weak) [BPSW05 WSP06] Fr Fréchet distance (strong, weak) [BPSW05, WSP06] chet distance (strong, weak) [BPSW05, WSP06]

BPSW05: ``On Map-Matching Vehicle Tracking Data'' (S. Brakatsoulas, D. Pfoser, R. Salas, and C. Wenk), Proc. 31st Conference on Very Large Data Bases (VLDB): 853-864, 2005, Trondheim, Norway. WSP06: ``Addressing the Need for Map Matching Speed: Localizing Global Curve Matching Algorithms''(C Wenk

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WSP06: Addressing the Need for Map-Matching Speed: Localizing Global Curve-Matching Algorithms (C. Wenk and R. Salas and D. Pfoser), Proc. 18th International Conference on Scientific and Statistical Database Management (SSDBM): 379-388, 2006, Vienna, Austria.

SLIDE 13

Outline Outline

1 Problem Description Problem Description

1. 1.

Problem Description Problem Description

Enable in Enable in-

car navigation systems to find the best routes using

car navigation systems to find the best routes using current traffic situation current traffic situation

2. 2.

Travel Times and GPS curves Travel Times and GPS curves

3. 3.

Map Map-

Matching

Matching

I t l I t l t hi t hi

1. 1.

Incremental map Incremental map-

matching

matching

2. 2.

Global map Global map-

matching: Fr

matching: Fréchet distance échet distance

3. 3.

Global map Global map-

matching: Weak Fréchet distance

matching: Weak Fréchet distance

4. 4.

Routing System Setup and Future Work Routing System Setup and Future Work

13

SLIDE 14

Incremental Map Incremental Map-

Matching

Matching

Position

Position-

by

by-

position, edge

position, edge-

by

by-

edge strategy for map

edge strategy for map-

matching

matching

αi 1

g

c1 c3 d1 d3 αi,3

i,1

pi

c2 li d2 pi-1

– Initialization: Find first correspondence

Initialization: Find first correspondence using a spatial range query. Assume the using a spatial range query. Assume the graph has been preprocessed for spatial range queries graph has been preprocessed for spatial range queries

αi,2

graph has been preprocessed for spatial range queries. graph has been preprocessed for spatial range queries.

– Evaluate for each trajectory edge (or GPS point) all road

Evaluate for each trajectory edge (or GPS point) all road network graph edges incident to the last vertex. network graph edges incident to the last vertex.

– Runtime O(

Runtime O(nd + log m nd + log m), with ), with n being the number of GPS being the number of GPS

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( g ) g points in the trajectory, m the size of the graph, and points in the trajectory, m the size of the graph, and d the the maximum degree of any vertex in the graph. In practice maximum degree of any vertex in the graph. In practice d is is a constant and O( a constant and O(nd) nd) dominates the runtime. dominates the runtime.

SLIDE 15

Outline Outline

1 Problem Description Problem Description

1. 1.

Problem Description Problem Description

Enable in Enable in-

car navigation systems to find the best routes using

car navigation systems to find the best routes using current traffic situation current traffic situation

2. 2.

Travel Times and GPS curves Travel Times and GPS curves

3. 3.

Map Map-

Matching

Matching

I t l I t l t hi t hi

1. 1.

Incremental map Incremental map-

matching

matching

2. 2.

Global map Global map-

matching: Fr

matching: Fréchet distance échet distance

3. 3.

Global map Global map-

matching: Weak Fréchet distance

matching: Weak Fréchet distance

4. 4.

Routing System Setup and Future Work Routing System Setup and Future Work

15

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Global Map Global Map-

Matching

Matching

Find a

Find a curve in the road network curve in the road network that is as that is as close as close as possible to the vehicle trajectory possible to the vehicle trajectory possible to the vehicle trajectory possible to the vehicle trajectory

Curves are compared using

– Fréchet distance and

Fréchet distance and Fréchet distance and Fréchet distance and

– Weak Fréchet distance

Weak Fréchet distance

Minimize over all possible curves in the road

Minimize over all possible curves in the road network network

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Fréchet Distance Fréchet Distance

Dog walking example

– Person is walking his dog (person on one curve and the dog

Person is walking his dog (person on one curve and the dog

n other)
n other)

– Allowed to control their speeds but not allowed to go

Allowed to control their speeds but not allowed to go backwards backwards

– Fréchet distance of the curves:

Fréchet distance of the curves: minimal minimal leash leash length length necessary for both to walk the curves from beginning to end necessary for both to walk the curves from beginning to end

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Fréchet Distance Fréchet Distance

Fréchet Distance

– – where

where α and and β range over continuous non range over continuous non-

decreasing

decreasing

α β

δ α β

→ ∈

= −

, :[0,1] [0,1] [0,1]

( , ) : inf max ( ( )) ( ( ))

F t

f g f t g t

reparametrizations only reparametrizations only

Weak Fréchet Distance

–

~

( , )

F f g

δ

– drop the non

drop the non-

decreasing requirement for

decreasing requirement for α and and β

–

( , )

F

g δ

~

( , ) ( , )

F F

f g f g δ δ ≤

Well

Well-

suited for the comparison of trajectories since they

suited for the comparison of trajectories since they take the continuity of the curves into account take the continuity of the curves into account

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Free Space Diagram Free Space Diagram

Decision variant

Decision variant of the global map

f the global map-
matching problem

matching problem

– For a fixed

For a fixed ε > 0 decide > 0 decide whether there exists a whether there exists a path path in the road in the road

– For a fixed

For a fixed ε > 0 decide > 0 decide whether there exists a whether there exists a path path in the road in the road network with network with distance at most distance at most ε ε to the vehicle trajectory to the vehicle trajectory α

For each (straight

For each (straight-

line) edge

line) edge ( (i i,j j) in in a graph a graph G let its let its corresponding Freespace Diagram FD corresponding Freespace Diagram FD = FD( = FD(α (i j i j)) )) corresponding Freespace Diagram FD corresponding Freespace Diagram FDi,j

i,j = FD(

= FD(α, ( , (i,j i,j)) ))

i (i,j) i

α

1 (i,j)

ε

j 1 2 3 4 5 6

α

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Free Space Surface Free Space Surface

Glue free space diagrams

Glue free space diagrams FD FDi,j

i,j together according

together according to adjacency information in the graph to adjacency information in the graph G to adjacency information in the graph to adjacency information in the graph G

Free space surface of trajectory

Free space surface of trajectory α and the and the graph graph G graph graph G

G

h α shown shown implicitly by implicitly by the free space the free space

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the free space the free space surface surface

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Free Space Surface Free Space Surface

TASK

TASK: Find Find monotone path monotone path in free space surface in free space surface

– starting in some lower left corner, and

starting in some lower left corner, and

– ending in some upper right corner

ending in some upper right corner

G

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Map Map-

Matching Using the Fr

Matching Using the Fréchet Distance échet Distance

Find monotone path in free space surface using dynamic

Find monotone path in free space surface using dynamic programming programming programming programming

– O

O(mn (mn log log mn mn) time for fixed ) time for fixed ε ε, where , where m is the size of the is the size of the graph and graph and n the size of the trajectory the size of the trajectory

S l S l i i i ti bl i i i ti bl f i bi h i bi h

Solve

Solve minimization problem minimization problem for for ε ε using binary search using binary search

– O(

O(mn mn log log mn mn log log b) time, where ) time, where b is the desired bit precision is the desired bit precision

Conclusion

– Finds a curve in the graph together with a given quality

Finds a curve in the graph together with a given quality guarantee (= Fr guarantee (= Fré échet distance to the GPS curve) chet distance to the GPS curve)

– The algorithm needs O(

The algorithm needs O(mn mn) space which for large graphs will ) space which for large graphs will

– The algorithm needs O(

The algorithm needs O(mn mn) space which for large graphs will ) space which for large graphs will cause a large overhead cause a large overhead

Accurate map

Accurate map-

matching results

matching results

Slow algorithm

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Slow algorithm

SLIDE 23

Outline Outline

1 Problem Description Problem Description

1. 1.

Problem Description Problem Description

Enable in Enable in-

car navigation systems to find the best routes using

car navigation systems to find the best routes using current traffic situation current traffic situation

2. 2.

Travel Times and GPS curves Travel Times and GPS curves

3. 3.

Map Map-

Matching

Matching

I t l I t l t hi t hi

1. 1.

Incremental map Incremental map-

matching

matching

2. 2.

Global map Global map-

matching: Fr

matching: Fréchet distance échet distance

3. 3.

Global map Global map-

matching: Weak Fréchet distance

matching: Weak Fréchet distance

4. 4.

Routing System Setup and Future Work Routing System Setup and Future Work

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Adaptive Clipping Map Adaptive Clipping Map-

Matching Algorithm

Matching Algorithm

Uses the weak Fr

Uses the weak Fréchet distance échet distance

Output sensitive Map

Output sensitive Map-Matching (algorithmic improvement) Matching (algorithmic improvement)

Output sensitive Map

Output sensitive Map Matching (algorithmic improvement) Matching (algorithmic improvement)

– Construct and traverse free space graph (which has

Construct and traverse free space graph (which has quadratic complexity) on the fly quadratic complexity) on the fly

– Improved runtime: O(K log K), where K is the size of the

Improved runtime: O(K log K), where K is the size of the Improved runtime: O(K log K), where K is the size of the Improved runtime: O(K log K), where K is the size of the traversed free space which in our experiments is much traversed free space which in our experiments is much smaller than smaller than mn mn

Error

Error-Aware Map Aware Map-Matching (metadata information) Matching (metadata information) p g ( ) g ( )

– Use known GPS error sources to define those trajectories in

Use known GPS error sources to define those trajectories in the roadmap that could have led to the observed vehicle the roadmap that could have led to the observed vehicle trajectory trajectory

Adaptive Clipping algorithm

Adaptive Clipping algorithm:

– Solves this error

Solves this error-

aware map

aware map-

matching task

matching task

– Corresponds to pruning/clipping Fréchet

Corresponds to pruning/clipping Fréchet-

based algorithms

based algorithms

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Output Output-

Sensitive Map Matching

Sensitive Map Matching

The

The weak weak Fr Fréchet distance requires finding échet distance requires finding any any (possibly non (possibly non-

monotone) path in the free space surface

monotone) path in the free space surface ) p p ) p p

Express the problem as finding a shortest path in the

Express the problem as finding a shortest path in the Free Free Space Graph Space Graph

–

Allows running Dijkstra’s shortest path algorithm, which also finds Allows running Dijkstra’s shortest path algorithm, which also finds ε (no binary search needed) (no binary search needed)

–

Allows constructing only the Allows constructing only the traversed traversed portion of the free space portion of the free space surface / graph on the fly surface / graph on the fly → (Pseudo) output → (Pseudo) output-

sensitive

sensitive ( ) p ( ) p

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Free Space Cell Free Space Cell

ε3 ε4 ε2 ε1 < < < ε3 ε4 ε3 ε1 ε2

26

Store Store ε2 as the as the weight weight of the

f the

vertical free space boundary vertical free space boundary

SLIDE 27

Free Space Graph Free Space Graph

Encodes connectivity information of the free space

For each cell boundary store optimal

For each cell boundary store optimal ε as its weight as its weight

Weak Fr

Weak Fréchet distance = maximum of all échet distance = maximum of all ε’s along an ’s along an

ptimal path in the free space graph
ptimal path in the free space graph
ptimal path in the free space graph
ptimal path in the free space graph

Need to find a

Need to find a shortest path (with minimum total shortest path (with minimum total ε)

Run Dijkstra’s algorithm on the free space graph

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Free space graph can be constructed

Free space graph can be constructed on the fly

n the fly

SLIDE 28

Algorithm Algorithm

Running Time

– O(

O(K K log log K), with ), with K being the size of the being the size of the traversed traversed free space free space graph graph

– K = O(

K = O(mn mn) in the worst case for traversing all the graph ) in the worst case for traversing all the graph BUT t h h t t th t d t i f d BUT t h h t t th t d t i f d

Need to find a

Need to find a shortest path (with minimum total shortest path (with minimum total ε)

Run Dijkstra’s algorithm on the free space graph

– BUT, stops when shortest path to end vertex is found

BUT, stops when shortest path to end vertex is found

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Free space graph can be constructed

Free space graph can be constructed on the fly

n the fly

SLIDE 29

Error Error-

Aware Map Matching

Aware Map Matching

Considering data acquisition errors

– measurement error

measurement error

– sampling error

sampling error

Active Regions

– areas delimiting

areas delimiting possible positions possible positions

Sequence of all

Sequence of all active regions active regions error error aware aware error error-aware aware representation representation of the

f the

vehicle trajectory vehicle trajectory

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j y j y

SLIDE 30

Error Error-

Aware Map Matching

Aware Map Matching

Find curve that fulfills the

Find curve that fulfills the following properties following properties following properties following properties

– Starts at the origin

Starts at the origin

– Stops at the destination

Stops at the destination

– Intersects measurement

Intersects measurement error disks around all error disks around all position samples position samples

– Is within active regions

Is within active regions

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Adaptive Clipping Algorithm Adaptive Clipping Algorithm

Incremental algorithm

For For each acti e region each acti e region of an edge

f an edge

For For each active region each active region of an edge

f an edge

– Run output

Run output-

sensitive weak

sensitive weak-

Frechet/Dijkstra algorithm

Frechet/Dijkstra algorithm

– Stitch Dijkstra graphs together

Stitch Dijkstra graphs together at active regions of at active regions of vertices vertices

– Construct overall result by tracing back stitched

Construct overall result by tracing back stitched-

together

together Dijkstra graphs Dijkstra graphs

Solves error

Solves error-

aware map

aware map-

matching task

matching task

The clipping immensely reduces K. In practice K is almost

The clipping immensely reduces K. In practice K is almost constant constant constant. constant.

The algorithm is very fast, almost O(n log n) runtime

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Empirical Evaluation Empirical Evaluation

GPS vehicle tracking data

27 t j t i 27 t j t i

– 27 trajectories

27 trajectories (~16k GPS points) (~16k GPS points)

– sampling rate 30 seconds

sampling rate 30 seconds

– max speed 80km/h

max speed 80km/h

Road network data

– vector map of Athens Greece

vector map of Athens Greece vector map of Athens, Greece vector map of Athens, Greece (40 x 40km) (40 x 40km)

Evaluating matching quality

lt f lt f i t l i t l l b l l b l th d th d

– results from

results from incremental incremental vs.

vs. global

global method method

– Averaged

Averaged Fr Fréchet distance (uses sampled integral / échet distance (uses sampled integral / sum instead of maximum) sum instead of maximum)

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SLIDE 33

Empirical Evaluation Empirical Evaluation

Matching quality

(Use a erage Fréchet distance (Use a erage Fréchet distance

Matching speed

– Adaptive Clipping runs as fast

Adaptive Clipping runs as fast (Use average Fréchet distance (Use average Fréchet distance as a quality measure) as a quality measure)

140 Adaptive Clipping Incremental 90 100 Adaptive Clipping

– Adaptive Clipping runs as fast

Adaptive Clipping runs as fast as the Incremental Algorithm as the Incremental Algorithm

80 100 120 ters Incremental 60 70 80 90 nds Incremental

é

20 40 60 meters 20 30 40 50 seconds 5 10 15 20 25 30 20 5 10 15 20 25 30 10 20

33

Adaptive Clipping is

Adaptive Clipping is fast fast and yields and yields good matching good matching quality quality

SLIDE 34

Outline Outline

1 Problem Description Problem Description

1. 1.

Problem Description Problem Description

Enable in Enable in-

car navigation systems to find the best routes using

car navigation systems to find the best routes using current traffic situation current traffic situation

2. 2.

Travel Times and GPS curves Travel Times and GPS curves

3. 3.

Map Map-

Matching

Matching

I t l I t l t hi t hi

1. 1.

Incremental map Incremental map-

matching

matching

2. 2.

Global map Global map-

matching: Fr

matching: Fréchet distance échet distance

3. 3.

Global map Global map-

matching: Weak Fréchet distance

matching: Weak Fréchet distance

4. 4.

Routing System Setup and Future Work Routing System Setup and Future Work

34

SLIDE 35

Routing System Setup (work in progress) Routing System Setup (work in progress)

Maintain a database of current travel times

– Update database with

Update database with current feed of GPS current feed of GPS data data

– Test system in Athens gets new data every 5

Test system in Athens gets new data every 5

central

y g y y g y minutes minutes

– Data provided by vehicle fleet systems which

Data provided by vehicle fleet systems which already have an uplink for GPS data transfer already have an uplink for GPS data transfer

server

already have an uplink for GPS data transfer already have an uplink for GPS data transfer between the vehicle and a central server between the vehicle and a central server

Communication with in

Communication with in-

car navigation

car navigation system system

– Through GPRS (cell phone)

Through GPRS (cell phone) – – not yet not yet implemented implemented

in-car client

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implemented implemented

SLIDE 36

Client Access to Travel Time Database Client Access to Travel Time Database (work in progress) [KW07] (work in progress) [KW07] (work in progress) [KW07] (work in progress) [KW07]

Local computation model:

– Client computes routes itself

Client computes routes itself

– Updated travel times (in neighborhood of initial

Updated travel times (in neighborhood of initial route) are transferred when they differ too route) are transferred when they differ too ) y ) y much from original travel time much from original travel time

Central computation model:

– Central server computes routes

Central server computes routes

KW07: ``Dynamic Routing'' (N. Kalinowski and C. Wenk), Technical Report CS-TR-2007-005, Department of C S f S

36

Computer Science, University of Texas at San Antonio, 2007.

SLIDE 37

Real Real-

World Applications

World Applications

This is an extremely hot research area

Almost every car manufacturer and GPS receiver

Almost every car manufacturer and GPS receiver manufacturer is building a manufacturer is building a similar similar prototype prototype system system system system

– Different models for GPS data collection and client

Different models for GPS data collection and client-

server setup / communication

server setup / communication

– GPS manufacturers download “old” GPS data offline

GPS manufacturers download “old” GPS data offline from GPS receivers from GPS receivers → Not current travel times → Not current travel times

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Other Types of Tracking Data Other Types of Tracking Data

GPS drawbacks

GPS i d li f i ht t t llit GPS i d li f i ht t t llit

– GPS receiver needs line of sight to satellites.

GPS receiver needs line of sight to satellites. → Does not work inside buildings, and has problems in → Does not work inside buildings, and has problems in cities with very tall buildings cities with very tall buildings

Oth t f t ki d t Oth t f t ki d t

Other types of tracking data

– Other positioning technology (wireless networks, GSM)

Other positioning technology (wireless networks, GSM) → Measurement error is much higher → Measurement error is much higher → Pilot project in Athens to collect GSM signal → Pilot project in Athens to collect GSM signal strength data strength data

– Type of moving objects (planes, people)

Type of moving objects (planes, people)

38

SLIDE 39

Thank You Thank You

Thank you for your attention Thank you for your attention

39

SLIDE 40

Quality of Matching Result Quality of Matching Result

Comparing Fr

Comparing Fréchet distance of original and matched échet distance of original and matched trajectory trajectory trajectory trajectory

Fr

Fréchet distances strongly affected by outliers, since it échet distances strongly affected by outliers, since it takes the takes the maximum maximum over a set of distances.

ver a set of distances.

Average

Average Fr Fréchet distance échet distance – replace the maximum with a eplace the maximum with a

α β

δ α β

→ ∈

= −

, :[0,1] [0,1] [0,1]

( , ) : inf max ( ( )) ( ( ))

F t

f g f t g t

Average

Average Fr Fréchet distance échet distance – replace the maximum with a eplace the maximum with a path integral over the reparametrization curve ( path integral over the reparametrization curve (α(t), (t),β(t)): (t)):

( , ) : inf ( ( )) ( ( ))

F f g

f t g t δ α β = −

∫

–

Remark: Dividing by the arclength of the reparametrization curve Remark: Dividing by the arclength of the reparametrization curve i ld li ti d h “ f ll di t i ld li ti d h “ f ll di t

, :[0,1] [0,1] ( , )

( , ) ( ( )) ( ( ))

F

g g

α β α β

β

→

∫

40