The Tornado Model:Uncertainty Model for Continuously

Changing Data

Byunggu Yu1, Seon Ho Kim2, Shayma Alkobaisi2, Wan Bae2, Thomas Bailey3

Department of Computer ScienceNational University1

byu@nu.eduUniversity of Denver2

{seonkim, salkobai, wbae}@cs.du.eduUniversity of Wyoming3

tbailey@uwyo.edu

Outline

• Introduction• Motivation • Definition of CCDO• Uncertainty Models

– Cylinder Model (CM)

– Revised Ellipse Model (REM)

• Tornado Uncertainty Model (TUM)• Experiments• Conclusion

Introduction

• An increasing number of emerging applications deal with a large number of continuously changing data objects (CCDOs)

• Efficient support for CCDO applications will offer significant benefit in:– mobile databases – sensor networks – environmental control

• To support large-scale CCDO applications, a data management system needs to:– store CCDOs– update CCDOs– retrieve CCDOs

Introduction Cont.

• Each CCDOs has:– Non-spatiotemporal properties such as ID, name,

type– Spatiotemporal properties such as location,

velocity

• Each object reports its spatiotemporal data and a database stores them

Introduction Cont.

• Challenges for CCDOs data management systems:– CCDOs spatiotemporal properties continuously

change over time– Databases can only manage discrete records

• Missing states (in between records) form the uncertainty of the object’s history

Motivation

• As technology advances More sophisticated location reporting devices become able to report:– Locations– Higher derivatives (velocities, acceleration)

• Existing models utilize only some of these inputs• So, why not utilize higher derivatives inputs to devise

more efficient models?• Approach: a 2nd degree uncertainty model to reduce

the uncertainty improve efficiency (reduce false-drop rate)

Definition of CCDO

• CCDO: data object consisting of non-temporal properties and trajectories (temporal property)

• Trajectory segment: connects two consecutively reported states (positions) P1 and P2 of the object

• Uncertainty region: all possible states between two reported states

• Uncertainty model: computational approach to manage (quantify) in-between states

• Snapshot: all possible states at a specific time t

Snapshot Definition

dimension i

t2

t1

time (i.e., dimension d+1)

e e

e

e e

P1

P2P2

P1

e e e

Snapshot

t

Cylinder Model (CM)

• CM (Trajcevski et al.) models the uncertainty region as a cylindrical body:

– End points P1 and P2 of a trajectory segment are associated with a circle

– Radius of the circle r is called the uncertainty threshold;

– Using the maximum velocity Mv, CM calculates the maximum displacement )( 12 ttMMD v

MDer

CM Cont.

time (i.e., dimension d+1)

e e

e er

r

dimension i

r

r

t2

t1

P2

P1

Revised Ellipse Model (REM)

• REM models the uncertainty region as the intersections of two funnels:

– End points P1 and P2 of a trajectory segment are associated with a circle

– Radius of the circle r is the instrument and measurement error e

– Using the maximum velocity Mv, REM calculates the maximum displacement as a linear function of time

REM Cont.

time (i.e., dimension d+1)

e e

e e

P1

P2

dimension i

t2

t1

Snapshot of REM

• Given:– P1 reported at t1

– P2 reported at t2

– Measurement and instrument error e

– Maximum velocity Mv

• Snapshot of REM at time t is: 2222

1111

,

,

ttMvePttMeP

ttMePttMeP

v

vv

Tornado Uncertainty Model (TUM)

• TUM models the uncertainty region as the intersections of two funnels of degree 2:

– End points P1 and P2 of a trajectory segment are associated with a circle

– Radius of the circle r is the instrument and measurement error e

– Using the maximum velocity Mv, and maximum acceleration Ma, TUM calculates the maximum displacement as a non-linear function of time

Definitions for TUM

• Given a velocity v, acceleration a and time t, TUM defines a 1st degree and 2nd degree displacement as follows:

t

tatvdxxavtavdispl

tvtvdipsl

0

22

1

)2/()(),,(

),(

TUM Cont.

t2

t1

Snapshot of TUM

• Snapshot of TUM at time t is:

),,(

),(),,(),(

121

11211

otherwisetMVdisplP

ttifttMdispltMVdisplPtPE

mva

MvMvvMva

),,(

),(),,(),(

222

12222

otherwisetMVdisplP

ttifttMdispltMVdisplPtPE

mva

MvMvvMva

Domain of Acceleration

• All possible accelerations is defined by a hyper circle with a constant radius Ma

D(2): a region (set) of all possible actual accelerations

circular approximation

velocity vector

positive accelerations

negative accelerations

Macc Ma

Set of possible actual acceleration

Example

• A car moving in 2D space from P1 at time t1 to P2 at time t2 , calculate the uncertainty region (area) at a given time t = 6 between t1 and t2:

tim e

xyR S 0

R S 120

0

tE (R S 0,t)

E (R S 1,t)(0)

(0)

P1

P2

E(P1,6)

E(P2,6)

Experiments (settings and data set)

• Using a portable GPS device that records <location-time, velocity> every second

• A car with GPS drove from north of Denver to Loveland in Colorado, USA

• Collected (longitude, latitude, time) every second:– Straight movement on highway– Winding movement in a city area

• Settings:– Maximum velocity: Mv = 50 m/s– Maximum acceleration: Ma = 2.78 m/s2

Experiments Cont.

88

90

92

94

96

98

100

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33

Reported PointsPe

rcen

tage

Red

uctio

n

Percentage Reduction

Comparison of TUM and REM with 20 sec fixed interval (TI=20)

0

1000

2000

3000

4000

5000

6000

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33

Reported Points

Unc

erta

inty

Vol

ume

(100

0 cu

bic

met

er)

revised ellipse model

tornado model

Uncertainty Volume

Experiments Cont.

Percentage Reduction

Comparison of TUM and REM with random interval (5<TI<35)

0

20

40

60

80

100

120

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39

Reported PointsP

erc

en

tag

e R

ed

uc

tio

n

Uncertainty Volume

0

2000

4000

6000

8000

10000

12000

14000

16000

18000

20000

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39

Reported Points

Un

cert

ain

ty V

olu

me

(100

0 cu

bic

met

er)

revised ellipse model

tornado model

Experiments Cont.

TI Range inSeconds

Average% Reduction

5-10 99.25

11-15 98.41

16-20 96.40

21-25 93.94

26-30 88.22

30-35 87.71

Varying time interval (TI) Varying maximum acceleration Ma

The average percentage reduction of uncertainty volume

Max. Acceleration(Ma)

Average% Reduction

10 94.30

20 81.79

30 69.26

40 58.90

50 51.66

60 46.30

Conclusion

• Proposed a 2nd degree uncertainty model, The Tornado Uncertainty Model (TUM) that:– Used Maximum Velocity and Maximum Acceleration to

calculate the maximum displacement as a non-linear function of time

– Minimized the Uncertainty Region• Experimental results showed:

– TUM reduced the uncertainty volumes by more than an order of magnitude compared to REM

• Expected future results:– TUM model combined with an efficient MBR indexing will

reduce the rate of false drops in the filtering-refinement steps of query processing

Thank You!