This document presents a method for improving distance estimation in anisotropic wireless sensor networks. It aims to make estimated distances as close as possible to actual distances by constructing a "virtual ruler" to measure irregularities. It identifies "turning nodes" where paths are inflected, divides irregular paths into straight sub-paths, and calculates bending angles. It then establishes a relationship between bending angles and node properties to adjust distance estimations. Simulations show the method improves accuracy over conventional approaches. However, it may not be effective for very specialized hole shapes or holes far from beacon nodes.

1. Distance Estimation by
Constructing The Virtual Ruler in
Anisotropic Sensor Networks
Presented by –
Sikder Tahsin Al-Amin
ID- 1015052076

2. Outline
• Introduction
• Objectives
• Method
• Simulation
• Conclusion

3. Introduction
• In Wireless Sensor Networks (WSN)
applications, abundances of sensor nodes are
deployed randomly.
• Locations of these sensor nodes are important
for operations in WSNs.

4. Introduction
• Most studies relying on the condition that a
small proportion of sensor nodes, called
beacon nodes, know their exact positions
through GPS devices or manual configuration.
• Other sensor nodes estimate their distances
to beacon nodes and calculate positions

5. Introduction
• Performance heavily depends on the precision
of distance estimation.
Beacon node
Sensor node

6. Introduction
• In an anisotropic WSN, huge errors may be introduced into
distance estimation because of irregular deployment.
Beacon node
Sensor node

7. Objective
• Make the estimated distance ED(s,t) as close
to its corresponding D(s,t) as possible.
ED(s,t)
D(s,t)

8. Challenges
• Two challenging problems in distance
estimation-
I. Environmental noises fluctuate tremendously.
II. Shortest path is inflected when it bypasses
holes.

9. System Model & Assumptions
• Let G(N, E) - an undirected graph.
• N - vertices representing nodes.
- Beacon nodes- Know their accurate positions.
- Sensor nodes - Others.
• E - edges representing links among nodes.
• P(s, t) - shortest path between any two vertices
• Three types of distance values
i) Measured distances - M(s, t)
ii) Euclidean distances - D(s, t) and
iii) Estimated distances - ED(s, t)

10. System Model & Assumptions
• Large number of sensor nodes in a WSN
- so that pair of neighboring nodes can
communicate with each other.
• Not concerned with the issues of energy
consumption.

11. Overview
S to t1
S to t2

12. Overview
• Construct a virtual ruler to measure the irregularity of a wsn.
• Measure the degree of anisotropy from M(s,t) and D(s,t).
Small difference means path straight , otherwise curved.
Beacon node
Sensor node
Hole
),(
),(),(
=
ts
ts-tsM
Link_error
Ｄ
Ｄ
2.0=
10
1012-
1012

13. Overview
• If curved, turning nodes divide the path into
several nearly straight sub paths.
Beacon node
Sensor node
Hole
TN:Turning Node1012

14. Overview
• Then a distributed algorithm to calculate the
bending angles of paths.
Beacon node
Sensor node
Hole
TN:Turning Node1012

15. Dominating Degree
• Turning nodes are identified from dominating degree
• DD(n1, m, n2) - dominating degree of m.
• DN(n1, m, n2) - set of nodes correlated with n1, m & n2.
• AvgDegree(DN(n1, m, n2)) - average degree of all the
nodes in DN(n1, m, n2)
• NodeNum(DN(n1, m, n2)) - size of the DN(n1, m, n2)

16. Identifying Turning Nodes
2 round calculation –
I. A Threshold is set up from Avg. value – Std.
deviation of all nodes
II. Nodes compare their Dominating degrees
(DD) with Threshold.
- if DD< Threshold, then it’s a turning node.

17. Constructing the Virtual Ruler
I. Adjust distance estimation from each node
to corresponding beacon nodes.
II. Calculate bending angles at each turning
node.
III. Establish relationship between Bending
angles and Dominating degrees of the
turning nodes.

18. Constructing the Virtual Ruler
Method consists of two stages –
I. Initialization
II. Scale Setting

19. Initialization
• Measure true distance from each turning
node to end-point of the path.
• This distance is used to calculate the Bending
angle.

20. Initialization
• First step is coarse-grained calculation.
• Adjustment factor of P(s,t) is computed based
on M(s,t), E(s,t) and DD of turning nodes.

21. Initialization
Error Calculation
Mod (Measured Error)
Increases/Decreases
HopDist= Measured distance
of the Hop
Scale = enlarges according
to DD(m)

22. Initialization
Fine-grained step:
• Reverse of the first step.
• Calculate Measurement Error for each node
based on P(s,t)

23. Scale Setting Stage
• This stage establish the relationship between
the bending angle and the dominating degree
of each turning node, i.e., set the scale of the
VR.

24. Scale Setting Stage
can be obtained from ED(t1, TN1),
ED(TN1, TN2) & ED(TN2, t1)
Can be obtained from ED(t1, TN2),
ED(TN2, s) & ED(s, t1)
(TN1, TN2, s) = (TN1, TN2, t1) + (t1, TN2, s)

25. Scale Setting Stage
Triangle Created
Angle of the
Turning Node
Current & Last Angle
from law of cosine

26. Relationship Establishment
• After executing Algorithm 2, the bending
angles of all the turning nodes are obtained.
• For each turning node, relationship between
the bending angle and its dominating degree
is set up as follows –
Avg_DD_Value + DD_Scale ∗ Angle = DD_Value

27. Relationship Establishment
• For 𝑁 𝑇𝑁 Turning nodes -

28. Relationship Establishment
• Bending angle for each inflection among the
path-

29. Simulation
• 5548 nodes are randomly deployed
• Average node degree 6.2

30. Simulation
DV-DistanceOur method

31. Simulation

32. Simulation

33. Limitations
• This method isn’t effective when holes are in
very special shapes. Ex- circles
• Virtual ruler will be hard to construct if the
holes are far from all beacon nodes.

34. Thank you

35. Questions & Answers