Some map matching algorithm for personal navigation assistants

1
Some map matching algorithm for personal
navigation assistants

• Paper by Christopher White,
• David Bernstein, Alain Kornhauser
• Slides and Presentation by
• Alireza Vahdatpour

2
Outline

• Background
• Problem statement
• Literature review
• Four solutions
• Evaluation
• Results

3
Background

• Personal Navigation Assistants
• Reconcile the users location with the underlying
  map
• Users location coming from GPS (inacurate)
• Underlying map
• Could be inaccurate in some cases
• Accurate map may not be available
• Limited device memory
• Security issue

4
Problem Statement

• Map matching algorithm to reconcile inaccurate
  locational data with an inaccurate map
• A person/vehicle is moving along a finite set of
  streets
• We are provided by an estimate of his location in
  times T0, , Tt (denoted by Pt)
• Goal is to determine the set of streets that
  contain Pt

5
Problem Statement

• Street system is usually represented by a network
• Network consists of a set of curves (arc)
• Arcs are piece-wise linear
• Arcs can completely represented by a sequence of
  nodes A (A1, A2, ., An-1)
• The goal is to match the estimated points Pt with
  and arc A

6
Problem Statement

• Example

7
Literature review

• Map matching as a search problem
• Match Pt to the closest arc
• Algorithms to find the closest match are called
  range query
• Pros
• Fast, easy to implement
• Cons
• Inaccurate

8
Literature review

• Example

9
Literature review

• Map matching as statistical estimation
• Attempt to fit a curve to the sequence of
  estimated locations
• The curve is considered to lie on the network
• Perfect if the model of the motion is simple
  (straight lines)
• Not easy to model motions dictated by networks
  (streets)

10
Literature review

• Example

11
Algorithm 1

1. Find nodes that are close to the GPS estimated
   locations
2. Find the set of arcs that are incident to these
   nodes
3. Find the closest of these arcs and project the
   point onto that arc

12
Algorithm 1

• Two cases

13
Algorithm 1

• Cons
• Do not use historical data
• Unstable

14
Algorithm 2

• Algorithm 1 Heading information
• Example benefit
• Will not match a point to an arc that is
  perpendicular to the current direction of travel

15
Algorithm 3

• Algorithm 2 topological information
• Uses connectivity information to locate candidate
  arcs for matching (in addition to range query)
• Cons
• One bad match can lead to a sequence of bad
  matches

16
Algorithm 4

• Algorithm 3 Curve to curve matching
• Locates candidate nodes the same way as algorithm
  3
• Constructs piece-wise linear curves from the set
  of paths originating from that node
• Construct piece-wise linear curve from GPS points
• Calculate distance between this curve ad network
  curves
• Return the closest match

17
Algorithm 4

• Example

18
Evaluation

• Driving a vehicle ,utilized with GPS receiver, in
  Mercer county, New Jersey
• Limited to 4 routes

19
Results

• Accuracy of each algorithm vs. route

20
Results

• Comparison of Algorithm 1 and Algorithm 2

21
Results

• All algorithms work better on longer routes
• All algorithms work better with better GPS
  points
• Higher speed is better