Distance Estimation by Constructing The Virtual Ruler in

Anisotropic Sensor Networks

Presented by – Sikder Tahsin Al-Amin

ID- 1015052076

Outline

• Introduction• Objectives• Method• Simulation• Conclusion

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.

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

Introduction• Performance heavily depends on the precision

of distance estimation.

Beacon node

Sensor node

Introduction• In an anisotropic WSN, huge errors may be introduced into

distance estimation because of irregular deployment.

Beacon node

Sensor node

Objective• Make the estimated distance ED(s,t) as close

to its corresponding D(s,t) as possible.

ED(s,t)

D(s,t)

Challenges

• Two challenging problems in distance estimation-

I. Environmental noises fluctuate tremendously.II. Shortest path is inflected when it bypasses

holes.

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)

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.

Overview

S to t1

S to t2

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 nodeHole

),(),(),(

=ts

ts-tsMLink_error

ＤＤ

2.0=101012 -

1012

Overview• If curved, turning nodes divide the path into

several nearly straight sub paths.

Beacon node

Sensor nodeHole

TN:Turning Node1012

Overview• Then a distributed algorithm to calculate the

bending angles of paths.

Beacon node

Sensor nodeHole

TN:Turning Node1012

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)

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.

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.

Constructing the Virtual Ruler

Method consists of two stages –

I. InitializationII. Scale Setting

Initialization

• Measure true distance from each turning node to end-point of the path.

• This distance is used to calculate the Bending angle.

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.

Initialization

Error Calculation

Mod (Measured Error)Increases/Decreases

HopDist= Measured distanceof the Hop

Scale = enlarges accordingto DD(m)

Initialization

Fine-grained step:

• Reverse of the first step.• Calculate Measurement Error for each node

based on P(s,t)

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.

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)

Scale Setting Stage

Triangle Created

Angle of theTurning Node

Current & Last Angle from law of cosine

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

Relationship Establishment

• For Turning nodes -

Relationship Establishment

• Bending angle for each inflection among the path-

Simulation

• 5548 nodes are randomly deployed• Average node degree 6.2

Simulation

DV-DistanceOur method

Simulation

Simulation

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.

Thank you

Questions & Answers