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Spatial Databases: Spatio-Temporal Databases

Spatial Databases: Spatio-Temporal Databases. Spring, 2007 Ki-Joune Li. Spatio-Temporal Databases. Everything is changing! Spatio-Temporal Objects Change the position or shape according to time Discrete Change vs. Continuous Change Discrete change

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Spatial Databases: Spatio-Temporal Databases

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  1. Spatial Databases:Spatio-Temporal Databases Spring, 2007 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

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

  7. 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

  8. 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 Continuous Change of Location

  9. 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) (x3,y3,t3) x t0 t

  10. Interpolation (or Prediction) • Interpolation • 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. 10:10 10:05 10:00 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

  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 v2 v3 v1 Time t2 t1 t3 t4 Speed Model on Road Network  ( (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 NormalizedSpeed 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

  18. 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 | > 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. Tracking Algorithm Server MobleClient 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] update DB [continue] storesettings (route) receivesettings (route) send threshold and new route [finish]

  20. 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

  21. 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

  22. Point-Based Update Policy

  23. 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.

  24. Vector-Based Policy

  25. 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

  26. Segment-Based Policy

  27. Comparison of Update Policies

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

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

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