probabilistic continuous update scheme in location dependent continuous queries

1Department of Computer ScienceCity University of Hong Kong

Department of Computer Science

City University of Hong Kong

Probabilistic Continuous Update Scheme in Location

Dependent Continuous Queries

Song Han and Edward Chan

Department of Computer Science, City University of Hong Kong83 Tat Chee Avenue, Kowloon, HONG KONG

2



Probabilistic Continuous Update Scheme in LDCQ

Agenda

Introduction Objective System Model Methodology Performance Analysis Conclusion

3




IntroductionModeling of Moving Object

Moving Object Spatio -Temporal (MOST) Model For location management and location prediction To reduce the update cost (frequency of Update)

Predictive Approach If next update time is t1, at time t’ during [t0 ,t1], the position of A

<x’,y’> is predicted as:

x’ = x0 + v0 * cosα0 * (t’ – t0); y’ = y0 + v0 * sinα0 * (t’ – t0)

Mobile Object Update Time Position Speed Direction

A t0 <x0 ,y0> v0 α0

4




IntroductionWhat is a LDCQ?

Example: A user walking along a road wants to know whether there exists a taxi inside the range of 1km around him from now to 10 min later.

Special Features: 1. Location Dependent

Different time, Different Position, Different Query Result

2. Continuous Query The active period of the query is from now to 10 min later

5




IntroductionBasic Location Update Methods

Time-based Location Update (TB) A periodic update scheme Generate an update every fixed time threshold T How to define T?

Distance-based Location Update (DB) If the difference between current location and last

update location is larger than the distance threshold D, an update is generated How to define D?

6




Introduction

Time-based Update Distance-based Update

7




IntroductionBasic Location Update Methods

Hybrid (time-based + distance-based) Either condition from Time-based Location Update or

Distance-based Location Update is satisfied, an update is generated.

Speed-dead-reckoning (SDR) An update is generated if the deviation of its current

location is greater than the predicted location by a pre-defined distance threshold

8




Introduction

Hybrid Method Speed-dead-reckoning

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Objective

To formulate an update strategy to meet user fidelity requirement.

To related the update frequency to the overall accuracy of the query.

10




System Model

The system architecture of a mobile computing system

Location Database Server

Query Processor

Moving Objects

Database

Location Updates

Moving Objects

Continuous Queries

Wireless Network

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Uncertainty Model

Definition 1 : Uncertainty Region

An Uncertainty Region of mobile object M at time t, U (p, t), is a closed region such that M can be found inside this region with a probability p.

Definition 2 : Uncertainty PDF

Uncertainty Probability Density Function of a mobile object M at time t, f (x, y, t), is the probability density function of M ’s location at time t and

( , )

( , , )U p t

f x y t dxdy p

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Methodology

Probabilistic Continuous Update Scheme Object Location Update (OLU):

Issued by both Query Object and Moving Object To guarantee at time t, the mobile object ’s position will

not be outside its uncertainty region U (p, t). Query Accuracy Update (QAU):

Issued only by Moving Object When the change of the moving object’s uncertainty

region will affect the answer set for a certain Q with a probability p which is specified by the user.

13




Example of OLU

14




Example of QAU

15




Generation of OLU

Calculation is independent and same for moving objects and query objects

The uncertainty PDF for the position of MO satisfy normal distribution X ~ N (xP, σX), Y ~ N (yP, σY)

An update will be issued if its actual position at time t exceeds the predicted position’s confidence interval c (xP - u (1-c)/2 * σX, xP - u (1-c)/2 * σX)

(yP - u (1-c)/2 * σy, yP - u (1-c)/2 * σy)

16




Generation of OLU

Improvement in Generation of Object Location Update

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Generation of OLU

02 sin( )R R

L t H LB B D B B B

0

min

0 min

min

0 0 min

20 min

1 (log ( 1))( )

{ , 1 (log ( 1)) }

x tH t H L

x t tH H t H L

B B B t t t tf t

MIN B B B B t t t

Condition :

Update Threshold :

Where

0

min

cos( )R Rt

R

Dt

v

18




Generation of QAU

In a range query, all moving objects are independent. We consider the calculation between OM and OQ.

XM ~ N (xMP, σx

2),YM ~ N (yMP, σy

2),

XQ ~ N (xQP, σx

’2), YQ ~ N (yQP, σy

’2)

xMP = xM + vM * (t - tM) * cos(α)

yMP = yM + vM * (t - tM) * sin(α)

xQP = xQ + vQ * (t - tQ) * cos(β)

yQP = yQ + vQ * (t - tQ) * sin(β)

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Generation of QAU

The relative movement of OM and OQ. <X’, Y’> X’ = XM -XQ => X’ ~ N (xM

P-xQP, σx

2+σx’2)

Y’ = YM -YQ => Y’ ~ N (yMP- yQ

P, σy2 +σy

’2)

The probability that the OM will cross the query boundary at time t.μ1 = xM

P - xQP, μ2 = yM

P - yQP σ1

2 = σx2 +σx

’2, σ22 = σy

2 +σy’2

'')()(

2

1

21

2

2

2'

2

1

1'

2

1dYdXeP

YX

QB

20




Generation of QAU

Integration Area Ω is different depending on M’s moving Direction

21




Prediction of the next QAU time2 2 2

2 2 2

2 2 2

2 2 2

' 2 2 2

'

cos 0 (cos 0 ( ) sin ) (1)( cos ( ) sin ) /

( cos ( ) sin ) /cos 0 ( ) sin

( cos ( ) sin ) /

( co

begin

Rend

begin

Rend

Rbegin

end

t nowor and R b a

t a b R a v

t nowR b a b R

t a R b a vand R b a

t a R b a v

t a

2 2 2

2 2 2

2 2 2

2 2 2

2 2

2 2 2

(2 * )

s ( ) sin ) /

cos 0 (cos 0 ( ) sin ) (3)

( cos ( ) sin ) /( ) sin

( cos ( ) scos 0 ( ) sin

R

begin

end

Rbegin

end

b R a v

tor and b R a

t

t a b R a vR b aa b R

t a R b aand b R a

2

2 2 2

2 2 2

2 2 2

2 2 2

2 2 2

(4)in ) /

( cos ( ) sin ) /( ) sin (5)

( cos ( ) sin ) /

( cos ( ) sin ) /(6

( cos ( ) sin ) /

R

Rbegin

Rend

Rbegin

Rend

v

t a b R a vR b a

t a b R a v

t a R b a va R b

t a b R a v

)

22




Simulation Model

Random Waypoint Mobility Model Continuous query length: 1000 sec Query Boundary: 200 m Number of Moving Object: 100 Size of the area: 1000 m * 1000 m Fidelity Requirement: 95% Confidence Level: 95% Speed of the moving object: U [12km/h, 60km/h]

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Performance Analysis

Fidelity vs. Object Location Variance Number of updates vs. OLV

24




Performance Analysis

Total number of updates vs. OLV Fidelity vs. Number of Updates

25




Conclusion

Probabilistic Continuous Update Scheme is proposed to meet user fidelity requirement

Goes beyond traditional location update schemes Related the update frequency to the overall

accuracy of the query.

26




Future Work

Adaptive OLU generation How to calculate the predicted update time

directly How to reduce to calculation complexity in

calculating the predicted update time Extend Entity Query to Count Query Extend RQ to NNQ and kNNQ

27




References [1] M. H. Dunham and V. Kumar, Location Dependent Data and its

Management in Mobile Database, Database and Expert Systems Applications, 1998, Proc. 9h International Workshop on Database and Expert Systems Applications, 1998.

[2] A. P. Sistla, O. Wolfson, S. Chamberlain, and S. Dao, Querying the Uncertain Position of Moving Objects, Temporal Database – Research and Practice Lecture Notes in Computer Science 1399, 1998.

[3] O. Wolfson, S. Chamberlain, S. Dao, L. Jiang and G. Mendez, Cost and Imprecision in Modeling the Position of Moving Objects, Proc. 14th International Conference on Data Engineering, 1998.

[4] Reynold Cheng, Dmitri V. Kalashnikov, and Sunil Prabhakar, Querying imprecise data in moving object environments, IEEE Trans. on Knowledge and Data Engineering, Vol. 16(7), July 2004.

[5] Jinfeng Ni and C. V. Ravishankar, Probabilistic Spatial Database Operations, Proc. 8th Intl. Symposium on Spatial and Temporal Databases (SSTD), 2003.

28




Thank you!

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Simulation Metrics

Fidelity of the Probabilistic Range Query It measures the deviation of the results in the database from

the correct results for a range query Q. Based on the concepts of false positives and false negatives Sdbase (Q, t) is the result set of Q at time t from database

Sideal (Q, t) is the result set of Q at time t from actual location

f+ (Q, t) measures the fraction of objects wrongly included into the answer of Q and f - (Q, t) measures the portion of objects that are missing in the correct answer of Q.

|),(|

|),(),(|),(

tQS

tQStQStQf

dbase

idealdbase

|),(|

|),(),(|),(

tQS

tQStQStQf

ideal

dbaseideal

30




Simulation Metrics

Fidelity of Continuous Range Query

E (t) = f+ (Q, t) + f - (Q, t) < ε where E (t) is the error ratio of Q at time t and ε, the fidelity requirement, is a real-valued system parameter for Q.

( )_ ( )

end

begin

t

t

end begin

F t dtoverall fidelity Q

t t

otherwise

tEtF

1

)(0)(

probabilistic continuous update scheme in location dependent continuous queries

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