Spatial Databases: Spatio-Temporal Databases Spring, 2017 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 Example: Change of administrative boundary Continuous change Example: Moving Objects, Meteorological Lines, Pollution Areas

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) )

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)

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) )

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)

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

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

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

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 ?

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

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)* )*

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

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

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

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

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

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

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

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

Point-Based Update Policy

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.

Vector-Based Policy

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

Segment-Based Policy

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]

Comparison of Update Policies

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

Continuous Change of Shape How to represent it ?