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

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.

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

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.

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

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

GPS-based Navigation Shahid Jabbar 7 Data Collection

GPS-based Navigation Shahid Jabbar 8 Data format,,, , , , , , , , , , , , , , , , , , , , , , , , ,

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.

GPS-based Navigation Shahid Jabbar 10 Geometric Rounding Douglas-Peucker’s algorithm results using Hersberger and Snoeyink variant #pointsΘ= , ,7061,5401, ,3652,0831, ,00048,43242,21817,8534,3851,185

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

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

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 ?

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

GPS-based Navigation Shahid Jabbar 15 Node localization Results # points# queries Construc- tion Time Searching Time Naive Searching Time 1, , , , >10,000

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

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

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

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, , , ,2674,

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

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

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

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

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

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.

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

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.

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

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

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

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.

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.

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

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.

GPS-based Navigation Shahid Jabbar 35 Thesis download 