1. Spatial Databases: Spatio-Temporal Databases
Spring, 2017
Ki-Joune Li

2. 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

3. 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
[(2004,05,05), (2005,12,31) )
p13
p14
p17
[(2005,04,01), present )
p16
[(2002,01,01), (2004,03,31) )

4. Discrete Change of Spatio-Temporal Objects
Representation – A naïve approach
Object
Valid Time Interval
Geometry A1
[(2004,05,05), (2005,12,31) )
(p1,p2,p3,p4,p5)
[(2006,01,01), present )
(p1,p2,p6,p4,p5) A3
[(2000,04,01), (2001,12,31) )
(p11,p12,p13,p14,p15)
[(2002,01,01), (2004,03,31) )
(p11,p12, p16,p17,p15)
[(2005,04,01),present) )
(p11,p18,p16,p17,p15)

5. 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
[(2004,05,05), (2005,12,31) )
p13
p14
p17
[(2005,04,01), present )
p16
[(2002,01,01), (2004,03,31) )

6. Problems Large amount of duplication Duplication of similar values
Object
Valid Time Interval
Geometry A1
[(2004,05,05), (2005,12,31) )
(p1,p2,p3,p4,p5)
[(2006,01,01), (present) )
(p1,p2, p6,p4,p5) A3
[(2007,04,01), present) )
(p11,p12,p13,p14,p15)
[(2002,01,01), (2004,03,31) )
(p11,p12, p16,p17,p15)
[2005,04,01),present )
(p11,p18,p16,p17,p15)

7. Versioning Object A Object A’ Object A’’ (t1,1) (t2,2) Object A
Object B
(t1, B1)
(t2, B2)
Less duplication
Need a Version Management Function

8. Continuous Change of Location
Representation of continuous movement
Function e.g. Newtonian Mechanics or
Needs a infinite set of values
Impossible
Sampling <S, Fest >
Assumption on continuous movements
Set of snapshots
Interpolation method: e.g. Linear Interpolation

9. Representation in 3-D (x, y, t ): Trajectory
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)
(x3,y3,t3) x t0 t

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

11. 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
10:00
10:10
10:05

12. 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)* )*

13. Representation by Speed Model
Speed Pattern of Vehicles
Parametric Model of Speed
Representation of Trajectories by Speed Model

14. Speed Model on Road Network
Time t1 t2 t3 t4 v1 v2 v3
 ( (t1,v1), (t2,v2,t3), (t4,v3) )*

15. 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

16. Analysis of Speed Model Representation
Accuracy
Data Size : More than 60% of reduction
Normalized Speed
Estimated Speed
Real Speed
Time

17. 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
The second topic I’d like to give is about tracking method to reduce the number of update reports from mobile clients.
This work has been done by the collaboration between our team and Prof. Jensen in Denmark.
The basic goal of this method is to track the location of mobile objects with reduced number of update reports.
Our tracking method is based on prediction-based tracking. It means that
Based on this assumption, we have de

18. mTrack Basic Assumption Prediction-Based Tracking
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 | > 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

19. Prediction Policies Previous Prediction Methods Point-Based Prediction
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

20. 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

21. Point-Based Update Policy

22. 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.

23. Vector-Based Policy

24. 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

25. Segment-Based Policy

26. Tracking Algorithm Moble Client Server predict position compare
with new GPS data
Query
predict position
[within threshold]
[old connection]
[out of threshold]
Location DB
get GPS
send
update
receive
update
[start]
As shown by this slide, the server receives update reports from mobile clients store them on a DB. When a query is submitted, the server answer to this query by checking the DB. That is, if there is the exact record for this time, ok, it sends this location to the user. But if there is not the exact location at the time, it returns a predicted location by some kinds of prediction algorithms.
And at the same time, mobile client has the same prediction algorithm of the server, it knows whether the prediction done by the server is correct, i.e. within a given threshold or not. That is, since mobile client is equiped with GPS for gathering location data, it has on one hand the real data or correct data and the predicted data. And it compares these two data, and if the difference exceeds a given threshold, it decides to report GPS data to the server. By doing so, we can reduce the number of unncessary update reports.
Here the point is how to predict the location data. We have invented 3 strategies, point-based method, vector-based method, and road segment based method. I’ll show some examples for these method.
update DB
[continue]
store settings (route)
receive settings (route)
send threshold
and new route
[finish]

27. Comparison of Update Policies

28. Improvement of mTrack Merging Segments Routing Information
Avoid Irrelevant Segmentation
Routing Information
Avoid Unnecessary Updates due to Segment Changes

29. Continuous Change of Shape
How to represent it ?