Spatial Databases: SpatioTemporal Databases

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Spatial DatabasesSpatio-Temporal Databases

• Spring, 2007
• Ki-Joune Li

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Spatio-Temporal Databases

• Everything is changing!
• Spatio-Temporal Objects
• Change the position or shape according to time
• Discrete Change vs. Continuous Change
• Discrete change
• Example Change of administrative boundary
• Continuous change
• Example Moving Objects, Meteorological Lines,
  Pollution Areas

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Discrete Change of Spatio-Temporal Objects

• No assumption on movements
• Example Change of administrative boundary

(2006,01,01), present )
p1
p5
p11
p6
(2000,04,01), (2001,12,31) )
p15
p4
p2
p3
p18
p13
(2004,05,05), (2005,12,31) )
p14
p17
(2005,04,01), present )
p16
(2002,01,01), (2004,03,31) )
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Discrete Change of Spatio-Temporal Objects

• Representation A naïve approach

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Query Example

• Find the name of the district pointed by Q at
  (2000,10,1)
• How to process this query ?
• By full scan of the database ?

(2006,01,01), present )
p1
p5
p11
p6
(2000,04,01), (2001,12,31) )
p15
p4
p2
Q
p3
p18
p13
(2004,05,05), (2005,12,31) )
p14
p17
(2005,04,01), present )
p16
(2002,01,01), (2004,03,31) )
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Problems

• Large amount of duplication
• Duplication of similar values

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Versioning
Object A
Object A
Object A
(t1,?1)
(t2,?2)
Object A
(t1, ?A1)
(t2, ?A2)
Object B
(t1, ?B1)
(t2, ?B2)

• Less duplication
• Need a Version Management Function

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Continuous Change of Location

• Representation of continuous movement
• Function e.g. Newtonian Mechanics or
• Needs a infinite set of values
• Impossible
• Sampling ltS, Fest gt
• Assumption on continuous movements
• Set of snapshots
• Interpolation method e.g. Linear Interpolation

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Representation in 3-D (x, y, t ) Trajectory

• Representation in 3-D
• where ti is a sampling time and fx(o,t ), fy(o,t
  ) are interpolation method.
• Trajectory TR (p, t )

y
(x1,y1,t1)
(x2,y2,t2)
x
(x3,y3,t3)
t0
t
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Interpolation (or Prediction)

• Interpolation
• From past data e.g. Estimate p at t where ti lt t
  lt ti 1
• Mostly linear interpolation is used
• Prediction (Extrapolation or Tracking)
• From the current data
• Estimate p at t where ti lt t and ti is the most
  recent snapshot
• Linear prediction ?

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Representation in Euclidean Space

• Trajectory of Moving Objects in Euclidean Space
• Sequence of Points in (x,y,t) Space
• (x,y,t) with Interpolation Method such as Linear
  Interpolation
• Inappropriate for objects in Road Network Space
• Euclidean distance is meaningless for vehicles
• Queries are given on road network space rather
  than Euclidean space
• Linear Interpolation is not correct

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Representation in Road Network Space

• Trajectory of Moving Objects in RN Space
• Sequence of Tuple (SegID, offset, t)
• (SegID, offset, t) with Speed Interpolation
  Method
• SegID ID of Road Segment
• Offset Distance from the starting point of the
  segment
• Advantages
• Smaller size of data for SegID and offset than x,
  y coordinates
• Distance in RN Space is meaningful
• No more incorrect interpolation error
• Elimination of repeating SegID
• (SegID, n, (offset,t) )

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Representation by Speed Model

• Speed Pattern of Vehicles
• Parametric Model of Speed
• Representation of Trajectories by Speed Model

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Speed Model on Road Network
? ( (t1,v1), (t2,v2,t3), (t4,v3) )
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Technical Details

• How to Separate Three Phases
• Constant Speed Phase
• Acceleration Phase
• Deceleration Phase
• A simple Heuristic k-Consecutive Points
• If k consecutive points of a same phase are
  encountered, then separate it.
• How to define k ?
• How to define acceleration ?
• Least Mean Square vs. Simple Straight Line
• Wavelet

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Analysis of Speed Model Representation

• Accuracy
• Data Size More than 60 of reduction

NormalizedSpeed
Estimated Speed
Real Speed
Time
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Tracking on Road Network m-Track

• Collaboration with
• ETRI,
• Prof. Christian Jensen at Aalborg Univ. in
  Denmark
• Tracking
• Maintaining the current location of moving
  objects at server
• Goal
• Development of a tracking method for vehicles on
  road network
• To reduce the number of updates from vehicles

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mTrack

• Basic Assumption
• Moving Objects on Road Network
• Tracking Moving Objects with Prediction
• Prediction-Based Tracking
• Client Moving Object
• Real position preal from GPS
• Estimated position pestimated from prediction
  algorithm
• If preal - pestimated gt threshold, then
  report update to the server
• Server DB for moving objects
• If there is a update request from client, then
  update position.
• Otherwise, positional data in DB is considered as
  correct.
• Prediction
• Road-Based Prediction

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Tracking Algorithm
Server
MobleClient
predict position
compare with new GPS data
Query
predict position
within threshold
old connection
out of threshold
Location DB
send update
receive update
get GPS
start
update DB
continue
receive settings (route)
storesettings (route)
send threshold and new route
finish
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Prediction Policies

• Previous Prediction Methods
• In Euclidean Space
• Linear Movement e.g. C. Jensen in ACM-GIS 2003
• Arbitrary Movement e.g. U. Tao in SIGMOD 2004
• Point-Based Prediction
• Vector-Based Prediction
• Road-Based Prediction
• In Road Network Space
• Constant Speed on a Road Segment
• Parametric Speed Model

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Point-Based Update Policy

• Only the position of a moving object is taken
  into account.
• The database makes constant position prediction
  of the position.
• The client sends a new position after the given
  threshold is crossed

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Point-Based Update Policy
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Vector Policy

• Object position, speed, and direction of movement
  are taken into account.
• It is assumed that the object moves linearly, at
  a constant speed.

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Vector-Based Policy
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Segment-Based Policy

• The moving object is sending its position and
  velocity vector.
• The road on which the object is moving is known.
• The moving object moves along the shape of the
  road

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Segment-Based Policy
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Comparison of Update Policies
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Improvement of mTrack

• Merging Segments
• Avoid Irrelevant Segmentation
• Routing Information
• Avoid Unnecessary Updates due to Segment Changes

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Continuous Change of Shape

• How to represent it ?