1. GPS-based Navigation 1 GPS-based Navigation in Static and Dynamic Environments Master’s Thesis Presentation Shahid Jabbar Institut für Informatik Universität Freiburg Supervisor: PD Dr. Stefan Edelkamp Co-supervisor: Prof. Dr. Th. Ottmann

2. GPS-based Navigation Shahid Jabbar 2 The big question.. What are we doing here ? Das Problemo  Digital maps available in the market are very expensive.  Most of those maps do not allow updates.  Not possible to have timed queries. The travel time can change drastically during different kinds of days like, workdays and holidays … Can even change during different times of a day like, from 8 to 9 AM as compared to 10 to 11 PM.

3. GPS-based Navigation Shahid Jabbar 3  Why not let people make their own maps that they can query and update ?  But how ? How to collect the data ? How to process that data ? Global Positioning System (GPS) Receiver + Computational Geometry The big question.. What are we doing here ? The Solution

4. GPS-based Navigation Shahid Jabbar 4 What is GPS ?  A collection of 24 geo-stationary satellites.  Gives the position of an object in terms of its longitude, latitude, and height.

5. GPS-based Navigation Shahid Jabbar 5 Data Collection What about the cost of collecting the data ?

6. GPS-based Navigation Shahid Jabbar 6 Data Collection What about the cost of collecting the data ? We say …. You only need some Bananas.

7. GPS-based Navigation Shahid Jabbar 7 Data Collection

8. GPS-based Navigation Shahid Jabbar 8 Data format,,, 48.0070783, 7.8189867, 20030409, 100156 48.0071067, 7.8190150, 20030409, 100158 48.0071850, 7.8191400, 20030409, 100200 48.0071650, 7.8191817, 20030409, 100202 48.0071433, 7.8191867, 20030409, 100204 48.0071383, 7.8191883, 20030409, 100206 48.0071333, 7.8191917, 20030409, 100208 48.0071317, 7.8191917, 20030409, 100212

9. GPS-based Navigation Shahid Jabbar 9 Not everything that glitters is Gold. Filtering + Rounding  Kalman Filter GPS Information + Speed-o-meter reading as the inertial information => removes the outliers  Douglas-Peuker Line Simplification Algorithm Simplifies a polyline by removing the waving affect.

10. GPS-based Navigation Shahid Jabbar 10 Geometric Rounding Douglas-Peucker’s algorithm results using Hersberger and Snoeyink variant #pointsΘ=10 -7 10 -6 10 -5 10 -4 10 -3 1,2777665582437722 1,7061,5401,16243311725 2,3652,0831,394376287 50,00048,43242,21817,8534,3851,185

11. GPS-based Navigation Shahid Jabbar 11 Lets sweeeeep … Graph Construction Bentley - Ottmann Line Segment Intersection Algorithm. We have multiple traces. Some of them might be intersecting  Road crossings!!! We need to convert them into a graph to be able to apply different graph algorithms e.g. shortest path searching Seems very simple, just convert: Point  Vertex Segment  Edge

12. GPS-based Navigation Shahid Jabbar 12 # GPS Points # Nodes in Graph Time to sweep 1,2771,4730.42 1,7061,7770.27 2,3652,4810.37 50,00054,26711.13 Graph Construction Results of Line sweep we are very much dependent on k

13. GPS-based Navigation Shahid Jabbar 13 Where am I ?  I am at building 101 and I want to go to CinemaxX.  Schade!!! I have no existing trace that pass through building 101.  What to do ? Hmmmm …interesting problem  How about going to the nearest place that is in my existing traces ?

14. GPS-based Navigation Shahid Jabbar 14 Where am I ?  Voronoi Diagram to the rescue!!!

15. GPS-based Navigation Shahid Jabbar 15 Node localization Results # points# queries Construc- tion Time Searching Time Naive Searching Time 1,277 0.100.3012.60 1,706 0.240.5424.29 2,365 0.331.1443.3 50,000 13.7314.26>10,000

16. GPS-based Navigation Shahid Jabbar 16 My floppy is too small … how can I carry this file ? Graph Compression

17. GPS-based Navigation Shahid Jabbar 17 My floppy is too small … how can I carry this file ? Graph Compression

18. GPS-based Navigation Shahid Jabbar 18 My floppy is too small … how can I carry this file ? Graph Compression (contd…)

19. GPS-based Navigation Shahid Jabbar 19 My floppy is too small … how can I carry this file ? Graph Compression (contd…) Results of Graph Compression # Nodes # Compressed Nodes Time 1,4731990.01 1,777740.02 2,4811300.03 54,2674,3910.59

20. GPS-based Navigation Shahid Jabbar 20 I have to reach CinemaxX ASAP.. What to do ? Search  Dijkstra – Single-Source shortest path.  A* - Goal directed Dijkstra  Number of queries is much more than the updates.  How about pre-computing some information ?  How about running All-pairs shortest path algorithm and saving all the paths: Nope … O(n²) space

21. GPS-based Navigation Shahid Jabbar 21 Accelerating Search Bounding-Box pruning (Wagner, Willhalm)  With every edge, save a bounding box that contains at least all the nodes that can be reached on a shortest path originating from that particular edge. 9,24

22. GPS-based Navigation Shahid Jabbar 22 Accelerating Search Bounding-Box pruning  In Dijkstra u  DeleteMin(PQ) forall v \in adjacent_edges(u) if t \in BB(u,v)..... endif endfor

23. GPS-based Navigation Shahid Jabbar 23 Search Models  Basic model Shortest path  Time model Shortest + fastest path  Absolute-time model Timed queries

24. GPS-based Navigation Shahid Jabbar 24 Accelerating Search Bounding-Box pruning Results of 200 queries #Nodes Time + Expansions + Time – Expansions – 1990.346,5960.6019,595 4,3918.1165,72612.88217,430

25. GPS-based Navigation Shahid Jabbar 25 Schade Meldung Dynamics  Disturbances on road: A road accident or a traffic jam  A road not usable at all  Edge weight = +inf  Probably one lane of the road is still opened  Edge weight increases by some delta  Consequence: The pre-computed information becomes invalid and useless. Re-computing bounding boxes is very expensive. This disturbance is temporary.

26. GPS-based Navigation Shahid Jabbar 26 Types of Disturbances Individual Edge Model Disturbances as Geometrical Objects Model

27. GPS-based Navigation Shahid Jabbar 27 Affect of disturbances on pre-computed information  Which information has become invalid ? Everything ? Nope, only those bounding boxes that have intersections with affected edges are potentially affected.

28. GPS-based Navigation Shahid Jabbar 28 Affect of disturbances on pre-computed information

29. GPS-based Navigation Shahid Jabbar 29 Graph update – off-line approach Introduce the affect of disturbances on the graph Simple for Individual Edge model – just increase the edge weight of the affected edge. A bit complex for Disturbances as Geometrical Object model. Problem: We need all the edges that are covered by a rectangle. Solution: WindowQuery using Segment trees Perform search on the updated graph Use pruning information only if it is not affected

30. GPS-based Navigation Shahid Jabbar 30 Graph update – off-line approach in Disturbances as Geometrical Objects model Rectangle Intersection Problem or more precisely Red – Blue Rectangle Intersection Problem

31. GPS-based Navigation Shahid Jabbar 31 Exploration time checking – on-line approach Observations: 1.Since the weights are always increased, if the shortest path is not affected, it remains to be the shortest path.  It is possible that some of the constraints have terminated and no longer be there by the time the mobile object will reach that area.

32. GPS-based Navigation Shahid Jabbar 32 Exploration time checking – on-line approach General Strategy: Before exploring an edge e, check if e is affected or not  if e is affected then check whether the constraints would be valid by the time e would be traversed. if constraints are valid then declare the search procedure as invalid and use standard Dijkstra or A*. else continue.  else continue.

33. GPS-based Navigation Shahid Jabbar 33 Exploration time checking – on-line approach

34. GPS-based Navigation Shahid Jabbar 34 Future Issues Handling of large data sets The compressed edges should not be considered straight => Curved Edges Visualization of route on a topographic map. Bridges => 3D navigation.

35. GPS-based Navigation Shahid Jabbar 35 Thesis download  http://www.informatik.uni-freiburg.de/~jabbar/thesis.pdf