Transcript Novel Self-Configurable Positioning Technique for Multi

Novel Self-Configurable
Positioning Technique for
Multihop Wireless Networks
Authors：Hongyi Wu
Chong Wang
Nian-Feng Tzeng
IEEE/ACM TRANSACTIONS ON NETWORKING, VOL. 13, NO. 3, JUNE 2005
Outline


Overview
Proposed self-configurable positioning
technique





Euclidean Distance Estimation
Coordinates System Establishment
Selection of Landmarks
Simulation
Conclusion
Overview(1/2)

Establish a local positioning system with the
following features:




Self-configurable : need no assistance from other
infrastructure.
Independence : independent of other global
positioning systems.
Robustness : should tolerate possible
measurement inaccuracy.
High accuracy : provide location information that
is accurate enough to support target applications
Overview(2/2)


Estimate the Euclidean distance between two
nodes
Select a number of nodes serving as the
landmarks



Estimates its distance to other landmarks.
Exchange information and establish a coordinate
system by themselves without the support of
GNSS.
The other nodes (called regular nodes) can
accordingly contact the landmarks and
compute their own coordinates.
Proposed self-configurable
positioning technique



Euclidean Distance Estimation
Coordinates System Establishment
Selection of Landmarks
Euclidean Distance Estimation

What to do?


To have an accurate estimation of the distance
between two landmarks or between a regular
node and a landmark.
How to do?

If two nodes are adjacent (within the transmission
range of each other)：


RSS, ToA, or TDoA
When the two nodes are not adjacent：

Finding the length of the shortest path.
Euclidean Distance Estimation


Consisting of N nodes uniformly distributed in a 1 1 area.
The transmission range of a node in the network is r << 1.
(d,0)
(0,0)
Euclidean Distance Estimation


There are in average a set Φ of N  r2 nodes
within S’ s transmission range.
The distance between node D and a node i
(with coordinates (Xi ,Yi ) ) in Φ is given by
where Xi and Yi are random variables with a
uniform distribution
Euclidean Distance Estimation


We can derive the density function of Zi
We assume a node  Φ , and has the shortest
Euclidean distance to D, is selected as the next hop
along the shortest path.
Euclidean Distance Estimation

the density function of Z

its mean value
where
of Zi
is the cumulative probability distribution
Euclidean Distance Estimation

To derive the coordinates of node  , we draw an arc
ACB with node D as the center and
as the radius
Euclidean Distance Estimation

Assuming node is uniformly distributed along AC (or
BC), then the mean length of the first hop along the
shortest path from S to D
where
Euclidean Distance Estimation

Recursively applying the above method, we can
obtain the length of the remaining hops along the
shortest path.

The total length of a shortest path with m hops is
Euclidean Distance Estimation
Coordinates System
Establishment
1.
2.
Identify the landmarks and determine the
landmarks’ coordinates by exchanging
information between each other and
minimizing an error objective function.
Calculate the coordinates of regular nodes.
Determine The Landmarks’
Coordinates

Assuming the coordinates of a landmark i is (xi ,yi), then
the distance between two landmarks i and j is
and the error function is defined to be
where Lij can be learned through the Euclidean distance
estimation model,
is expressed by the coordinates
variables
The Simplex method is then used to determine the
coordinates variables such that is minimized.
Determine The Landmarks’
Coordinates
Calculate The Coordinates of
Regular Nodes

A regular node needs to know the
coordinates of landmarks and its distances to
the landmarks.
Calculate The Coordinates of
Regular Nodes

After obtaining these information, node P(xp,yp)
calculates its coordinates by minimizing an error
objective function similar to what mentioned before.
and the error function is defined to be
Again, the Simplex method can be used to minimize
the error function
,and determine the coordinates
(xp,yp)
Calculate The Coordinates of
Regular Nodes


After calculating its coordinates, node P may
label itself as a “semi-landmark” and respond
to the requests of other regular nodes
Other regular nodes may decide whether or
not to use the information obtained from the
semi-landmarks, according to their
requirements on delay, accuracy, and/or
computational complexity.
Selection of Landmarks
Two issues：

1.
2.
How many nodes should be selected to serve as
landmarks?
Which nodes shall be selected?
Number of Landmarks


The more the landmarks, the higher the
accuracy of the established coordinates
system.
It’s not practical to employ a large number of
landmarks since the computational
complexity increases exponentially with the
number of landmarks.
Number of Landmarks


After a regular node calculates its
coordinates, it may announce itself as a
“semi-landmark” if it is stable and
computationally powerful.
As a result, there are landmarks and semilandmarks, which are usually sufficient for
highly accurate coordinates calculation.
Locations of Landmarks


We consider four landmarks in a network with
N nodes uniformly distributed in a 11 area.
Assume that the four landmarks locate at the
vertices of a square which is centered at
( Xc,Yc) and has an edge of G.
Experimental results


We observe the maximum error when the
square with four landmarks as vertices is at
the center of the network.
The error decreases as the landmarks
deviate from the center.


the longer the average path length from the
regular nodes to the landmarks, thus decreasing
the path error.
The landmarks should be separated as far as
possible
Algorithm : Landmark Selection


We develop an algorithm to determine K
corner nodes of the network.
Initially any node is a candidate of landmark if
its stability and computing power are higher
than a predefined threshold.
Algorithm : Landmark Selection



：a set , which includes all landmark candidates.
Ci： Candidacy degree for node i.
where Si,j is the length of the shortest path from i to j,
if node j is in set ; or otherwise, Si,j=.
A node i with the highest value of Ci is most
probably located at the center of network, and thus
should be removed from  first.

The landmarks (∆) locate largely at the corners of the network, except
that node 83 seems a better choice than the one selected at the
lower-left corner.

The algorithm also works well in a sparse network
Simulation：Node Density

Fig. 9. Euclidean distance. (a) N = 50. (b) N = 100. (c) N = 400.
Simulation：Node Density

Fig. 10. No translation. (a) N = 50. (b) N = 100. (c) N = 400.
Simulation：Node Density

Fig. 11. Center match. (a) N = 50. (b) N = 100. (c) N = 400.
Simulation ：Node Density

Fig. 12. GPS tuning. (a) N = 50. (b) N = 100. (c) N = 400.
Simulation ：Node Density
Simulation：
One-Hop Measurement Error
Simulation：
One-Hop Measurement Error

Fig. 15. N = 100. (a) = 2%. (b) = 5%. (c) = 10%. (d) = 20%. (e) =
30%. (f) = 40%.
Simulation：
The Number of Landmarks
Simulation：Control Overhead



The overhead for initial landmark discovery is
relatively high because flooding is used to
locate the landmarks. However, it happens
only during system initialization .
We ignore the overhead in the initial stage
and focus on the overhead for coordinates
update only.
The total control overhead increases with the
number of nodes
Simulation：Control Overhead
Conclusion




Proposed a self-configurable positioning technique
for multihop wireless networks.
A number of nodes at the “corners” of the network
serve as landmarks for estimating the distances by a
Euclidean distance estimation model and
establishing the coordinates themselves by
minimizing an error objective function
Other nodes calculate their coordinates according to
the landmarks.
The proposed positioning technique is independent
of global position information.