1. Spatial Databases: Spatio-Temporal Databases Spring, 2015 Ki-Joune Li

2. STEMPNU 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. STEMPNU 3 Discrete Change of Spatio-Temporal Objects No assumption on movements  Example: Change of administrative boundary p3 p1 p2 p4 p5 p6 p11 p18 p13 p14 p15 [(2004,05,05), (2005,12,31) ) [(2006,01,01), present ) p16 p17 [(2000,04,01), (2001,12,31) ) [(2002,01,01), (2004,03,31) ) [(2005,04,01), present )

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

5. STEMPNU 5 Query Example p3 p1 p2 p4 p5 p6 p11 p18 p13 p14 p15 [(2004,05,05), (2005,12,31) ) [(2006,01,01), present ) p16 p17 [(2000,04,01), (2001,12,31) ) [(2002,01,01), (2004,03,31) ) [(2005,04,01), present ) Find the name of the district pointed by Q at (2000,10,1) How to process this query ?  By full scan of the database ? Q

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

7. STEMPNU 7 Versioning Object AObject A’ (t1,1)(t1,1) Object A’’ (t2,2)(t2,2) Object A (t 1,  A1 )(t 2,  A2 ) Object B (t 1,  B1 )(t 2,  B2 )  Less duplication  Need a Version Management Function

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

9. STEMPNU 9 Representation in 3-D (x, y, t ): Trajectory Representation in 3-D where t i is a sampling time and f x (o,t ), f y (o,t ) are interpolation method. Trajectory TR={ (p, t ) } y x t (x 2,y 2,t 2 ) (x 1,y 1,t 1 ) (x 3,y 3,t 3 ) t0t0

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

11. STEMPNU 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. STEMPNU 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. STEMPNU 13 Representation by Speed Model Speed Pattern of Vehicles  Parametric Model of Speed  Representation of Trajectories by Speed Model

14. STEMPNU 14 Speed Model on Road Network Speed Time t1t1 t2t2 t3t3 t4t4 v1v1 v2v2 v3v3  ( (t 1,v 1 ), (t 2,v 2,t 3 ), (t 4,v 3 ) )*

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

17. STEMPNU 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

18. STEMPNU 18 mTrack Basic Assumption  Moving Objects on Road Network  Tracking Moving Objects with Prediction Prediction-Based Tracking  Client : Moving Object Real position p real from GPS Estimated position p estimated from prediction algorithm If | p real - p estimated | > 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. STEMPNU 19 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

20. STEMPNU 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. STEMPNU 21 Point-Based Update Policy

22. STEMPNU 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. STEMPNU 23 Vector-Based Policy

24. STEMPNU 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. STEMPNU 25 Segment-Based Policy

26. STEMPNU 26 Tracking Algorithm Moble Client Server predict position compare with new GPS data send update receive settings (route) store settings (route) receive update update DB send threshold and new route [old connection] [finish] get GPS [within threshold] [out of threshold] [continue] [start] Query predict position Location DB

27. STEMPNU 27 Comparison of Update Policies

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

29. STEMPNU 29 Continuous Change of Shape How to represent it ?