gps-based navigation in static and dynamic environments
DESCRIPTION
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. The big question .. What are we doing here ? Das Problemo. - PowerPoint PPT PresentationTRANSCRIPT
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.
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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
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What is GPS ?
A collection of 24 geo-stationary satellites. Gives the position of an object in terms of its
longitude, latitude, and height.
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Data Collection
What about the cost of collecting the data ?
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Data Collection
What about the cost of collecting the data ?
We say ….
You only need some Bananas.
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Data Collection
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Data format
<longitude>, <latitude>, <date>, <time>
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
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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.
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Geometric Rounding Douglas-Peucker’s algorithm results
using Hersberger and Snoeyink variant
#points
Θ=10-7 10-6 10-5 10-4 10-3
1,277 766 558 243 77 22
1,706 1,540 1,162 433 117 25
2,365 2,083 1,394 376 28 7
50,000 48,432 42,218 17,853 4,385 1,185
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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
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# GPS Points
# Nodes in Graph
Time to sweep
1,277 1,473 0.42
1,706 1,777 0.27
2,365 2,481 0.37
50,000 54,267 11.13
Graph Construction Results of Line sweep
we are very much dependent on k
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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 ?
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Where am I ?
Voronoi Diagram to the rescue!!!
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Node localizationResults
# points
# queries
Construc-tion Time
Searching
Time
Naive Searchi
ng Time
1,277 1,277 0.10 0.30 12.60
1,706 1,706 0.24 0.54 24.29
2,365 2,365 0.33 1.14 43.3
50,000 50,000 13.73 14.26 >10,000
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My floppy is too small … how can I carry this file ?
Graph Compression
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My floppy is too small … how can I carry this file ?
Graph Compression
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My floppy is too small … how can I carry this file ?
Graph Compression (contd…)
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My floppy is too small … how can I carry this file ?
Graph Compression (contd…)Results of Graph Compression
# Nodes#
Compressed Nodes
Time
1,473 199 0.01
1,777 74 0.02
2,481 130 0.03
54,267 4,391 0.59
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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
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Accelerating SearchBounding-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
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Accelerating SearchBounding-Box pruning
In Dijkstra u DeleteMin(PQ) forall v \in adjacent_edges(u)
if t \in BB(u,v).....
.....
endif endfor
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Search Models
Basic model Shortest path
Time model Shortest + fastest path
Absolute-time model Timed queries
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Accelerating SearchBounding-Box pruningResults of 200 queries
#NodesTime
+Expansions
+Time
–Expansion
s –
199 0.34 6,596 0.60 19,595
4,391 8.11 65,726 12.88 217,430
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Schade MeldungDynamics
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.
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Types of Disturbances
Affected Edge
Area affected bya disturbance
Individual Edge ModelDisturbances as Geometrical
Objects Model
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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.
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Affect of disturbances on pre-computed information
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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
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Graph update – off-line approachin Disturbances as Geometrical Objects model
Rectangle Intersection Problem or more precisely
Red – Blue Rectangle Intersection Problem
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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.
2. 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.
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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.
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Exploration time checking – on-line approach
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Disturbances
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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.
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Thesis download
http://www.informatik.uni-freiburg.de/~jabbar/thesis.pdf