Post on 12-Jan-2016
description
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
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Department of Computer Science
City University of Hong Kong
Probabilistic Continuous Update Scheme in LDCQ
Agenda
Introduction Objective System Model Methodology Performance Analysis Conclusion
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Department of Computer Science
City University of Hong Kong
Probabilistic Continuous Update Scheme in LDCQ
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
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Department of Computer Science
City University of Hong Kong
Probabilistic Continuous Update Scheme in LDCQ
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
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Department of Computer Science
City University of Hong Kong
Probabilistic Continuous Update Scheme in LDCQ
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?
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Department of Computer Science
City University of Hong Kong
Probabilistic Continuous Update Scheme in LDCQ
Introduction
Time-based Update Distance-based Update
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Department of Computer Science
City University of Hong Kong
Probabilistic Continuous Update Scheme in LDCQ
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
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Department of Computer Science
City University of Hong Kong
Probabilistic Continuous Update Scheme in LDCQ
Introduction
Hybrid Method Speed-dead-reckoning
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Department of Computer Science
City University of Hong Kong
Probabilistic Continuous Update Scheme in LDCQ
Objective
To formulate an update strategy to meet user fidelity requirement.
To related the update frequency to the overall accuracy of the query.
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Department of Computer Science
City University of Hong Kong
Probabilistic Continuous Update Scheme in LDCQ
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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Department of Computer Science
City University of Hong Kong
Probabilistic Continuous Update Scheme in LDCQ
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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Department of Computer Science
City University of Hong Kong
Probabilistic Continuous Update Scheme in LDCQ
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.
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Department of Computer Science
City University of Hong Kong
Probabilistic Continuous Update Scheme in LDCQ
Example of OLU
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Department of Computer Science
City University of Hong Kong
Probabilistic Continuous Update Scheme in LDCQ
Example of QAU
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Department of Computer Science
City University of Hong Kong
Probabilistic Continuous Update Scheme in LDCQ
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)
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Department of Computer Science
City University of Hong Kong
Probabilistic Continuous Update Scheme in LDCQ
Generation of OLU
Improvement in Generation of Object Location Update
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Department of Computer Science
City University of Hong Kong
Probabilistic Continuous Update Scheme in LDCQ
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))( )
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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
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Department of Computer Science
City University of Hong Kong
Probabilistic Continuous Update Scheme in LDCQ
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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Department of Computer Science
City University of Hong Kong
Probabilistic Continuous Update Scheme in LDCQ
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
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2
1
21
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2
1
1'
2
1dYdXeP
YX
QB
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Department of Computer Science
City University of Hong Kong
Probabilistic Continuous Update Scheme in LDCQ
Generation of QAU
Integration Area Ω is different depending on M’s moving Direction
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Department of Computer Science
City University of Hong Kong
Probabilistic Continuous Update Scheme in LDCQ
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 ) /
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Rbegin
Rend
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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
)
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Department of Computer Science
City University of Hong Kong
Probabilistic Continuous Update Scheme in LDCQ
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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Department of Computer Science
City University of Hong Kong
Probabilistic Continuous Update Scheme in LDCQ
Performance Analysis
Fidelity vs. Object Location Variance Number of updates vs. OLV
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Department of Computer Science
City University of Hong Kong
Probabilistic Continuous Update Scheme in LDCQ
Performance Analysis
Total number of updates vs. OLV Fidelity vs. Number of Updates
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Department of Computer Science
City University of Hong Kong
Probabilistic Continuous Update Scheme in LDCQ
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.
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Department of Computer Science
City University of Hong Kong
Probabilistic Continuous Update Scheme in LDCQ
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
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Department of Computer Science
City University of Hong Kong
Probabilistic Continuous Update Scheme in LDCQ
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.
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Department of Computer Science
City University of Hong Kong
Probabilistic Continuous Update Scheme in LDCQ
Thank you!
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Department of Computer Science
City University of Hong Kong
Probabilistic Continuous Update Scheme in LDCQ
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.
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tQStQStQf
dbase
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tQS
tQStQStQf
ideal
dbaseideal
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Department of Computer Science
City University of Hong Kong
Probabilistic Continuous Update Scheme in LDCQ
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.
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F t dtoverall fidelity Q
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otherwise
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