differential ad hoc positioning systems presented by: ramesh tumati feb 18, 2004

Differential Ad Hoc Positioning Systems

Presented By:Ramesh TumatiFeb 18, 2004

Sensor Networks - Introduction

Def: An ad hoc sensor network is a collection of small,cheap and low powered sensor nodes which can dynamically form a network without any infrastructure support.

Sensor nodes properties Gather data from its environment, process the data and

communicate it to the other nodes. Self organizing and self aware . Dynamically adapt to the changes in the network

conditions and other environmental factors. Limited networking and communication capabilities. Different kinds of sensors – temperature, light, seismic,

etc.

Support large number of applications

Applications

They are emerging as a key tool for many applications because of their reliability, accuracy,cost effectiveness and ease of deployment.

Possible applications of sensor networks: Environmental control and monitoring(to study air, water and soil

chemistry) Tracking and monitoring in hostile environments. Reporting hazardous conditions or events of interest like

earthquakes , floods, fire, etc. Condition based monitoring(to monitor the functioning of a

machine and report when there is a potential failure)

Location information needed along with data.

Localization Definition

It is important but challenging because of the following properties of the sensor networks:

Lack of infrastructure Low bandwidth and high error rate wireless communication Energy constrained nodes.

It is required to support: Location aware applications Location based routing Collaborative signal processing Ad hoc routing to conserve energy by load balancing and control

network utilization.

GPS

GPS, a world wide used radio-navigation system, which uses a constellation of 24 satellites as reference nodes along with ground stations to provide positioning services for the ground nodes.

Cannot be used for node localization for several reasons: Inaccessibility Cost Energy Consumption Form factor

Design Issues and Goals

Dynamic (Low response time) Distributed

Robust to central node failure Load Balancing Less traffic and power consumption Fast position updates.

Infrastructure less Energy efficient Scalable Accurate and consistent

Depends on the application for which the system is being used Must be comparable to node’s communication range

Background and Related Work Many GPS free localization algorithms for the sensor networks

have been proposed in the recent years which depend on recursive trilateration/multilateration techniques.

Beacon node : Unknown node:

A fraction of the nodes in the network are assumed to know their position by some means and they are referred to as Beacon Nodes.

Unknown nodes use the information from the beacon nodes to estimate their own position.

Fundamentals

In most of the existing position estimation approaches , the node estimates its position in two phases:

Phase 1:Estimates distances to at least three beacon nodes to estimate its position in 2-dimensional space or to at least four beacon nodes to estimate its position in 3-dimensional space.

Phase 2:Estimates the position from the ranges obtained using lateration techniques.

Phase 1 Signal Strength Method

The distance is estimated from the path loss good propagation model is required. Unpredictable- suffers from multipath, fading and

shadowing effects Can be used only with radio signals

Time based Methods(ToA, TDoA) Records time of arrival or time difference of arrival of the

signal. Translated into distance based on the known signal

propagation speed Can be used with radio, acoustic, infrared and ultrasound

signals More robust and precise than signal strength method

Phase 2 - Trilateration Most basic method Used when a node has distances to atleast three beacon

nodes . Position of a node is obtained by calculating the intersection of

three circles formed by the three beacon nodes.

23

22

21

23

23

22

22

21

21

)()(

)()(

)()(

d

d

d

yyxx

yyxx

yyxx

Phase 2 - Multilateration Used when there are more than three beacons.

The maximum likelihood estimate is obtained by taking minimum mean square estimate of a system of equations which represent the differences between the estimated and the actual distances from the node to the beacon nodes.

Related Work(1)

The most related work to our algorithms is Ad Hoc Positioning System(APS)

In APS two propagation methods are proposed: DV-Hop DV-Distance

The two methods differ in the information stored and propagated by the nodes to the neighboring nodes(hop Count or hop distance).

Beacons periodically broadcast their position information .

DV-Hop Each node maintains and propagates number of hops to beacon

nodes. Beacon node calculates the average hop distance and broadcasts

it to the nearby nodes.

Nodes compute the distances to the beacons using the average hop size and hop distances it has to the beacon nodes.

Finally computes the position using trilateration.

2

1

321

Related Work(2)

Average Hop Size = (d1 + d2)/(3+2)

d1

d2

BN-1 BN-3

BN-2

Related Work(3)

DV-Distance Beacon nodes periodically broadcasts its position information. Nodes maintain and propagate cumulative hop distances to

beacon nodes. Nodes use the cumulative distances obtained to estimate their

positions using lateration technique.

222

3

BN-1

BN-2

BN-3

UN-k2

5

4

,3

,2

,1

kest

kest

kest

d

d

d

DAPS We proposed two simple and efficient localization algorithms for ad

hoc sensor networks which uses the hop by hop propagation feature of the APS.

Hop Count Method Hop Distance Method

The fundamental idea behind our algorithms is motivated by DGPS.

Similar idea is used in our proposed algorithms to reduce errors. Unknown node uses the error correction factors from the nearest

beacon node to estimate the effective distances to at least three beacon nodes and thereby reduce the errors in the position estimate.

Overview of Algorithms(1)

Applicable to both two dimensional and three dimensional space.

Requires at least four beacon nodes.

Proposed algorithms operate in two phases: Error Calculations and propagation of error to the nearby nodes Effective Distance Estimation Position Estimation

Phase 1: Each beacon node broadcasts a HELLO packet to the network

announcing its position.

Distance metric(hop count or cumulative hop distance) to the beacon node is updated, maintained and propagated by all the nodes.

Algorithms differ in the distance metric used and in how the the distance between two nodes is determined.

Beacon node upon receiving a HELLO message from other beacon nodes computes the correction for the other beacon nodes(difference between the estimated and actual distances).

Each beacon node after computing the corrections broadcast them to the nearby nodes using DISTANCE-INFO message.

Overview of Algorithms(2)

Overview of Algorithms(3)

Phase 2 Unknown nodes use the corrections obtained from the

nearest beacon node and the distance metrics it has to the other beacon nodes to estimate the effective distances to the other beacon nodes.

Phase 3 An unknown node now has the locations and effective

distances to at least three beacon nodes. Now it can obtain its position using trilateration.

Hop Count Method Number of hops is used as the distance metric. Each node is assumed to have the same transmission range Phase 1(Estimating Corrections)

Hop Count is initially set to 1 by the beacon node which sends it through the network.

Each node in the network maintains a table which contains a entry for each beacon.Each entry in the table contains the beacon node id, coordinates and its distance in hops.

When a beacon node receives a HELLO message from other beacon node, it computes the estimated distance using the number of hops and hop size(initially it is equal to the node’s transmission range)

From the estimated distance it computes the correction as:

jixji

est nTd ,,

ji

jiact

jiest

ji n

ddC

,

,,

,

Phase 2(Effective Distance Estimation) During this phase each beacon node broadcasts the corrections for

the other beacon nodes to the nearby unknown nodes using DISTANCE-INFO message.

An unknown node computes the effective distances to at least three beacon nodes using the corrections obtained from the nearest beacon node as follows:

Phase 3(Position Estimation) The unknown node estimates its position from coordinates and the

effective distances of at least three beacon nodes using trilateration.

Let

Contd..

)( ,,,

jixikik

eff CTnd

2xT

Hop Count Method(3)

1 2 3

2

11

2

BN-1

BN-4

BN-3BN-2

UN-k

3

3

3

4,3

4,2

4,1

n

n

n

3

3

3

4,3

4,2

4,1

act

act

act

d

d

d

23

23

23

4,3

4,2

4,1

act

act

est

d

d

d

3/)36(

3/)36(

3/)36(

4,3

4,2

4,1

C

C

C

3)12(3)(3

3)12(3)(3

2)12(2)(2

4,3,3

4,2,2

4,1,1

CTd

CTd

CTd

xk

eff

xk

eff

xk

eff

Hop Count Method(4)

Merits Beacons need not have network wide transmission range Takes advantage of multihop routing and forwarding

techniques present in ad hoc networks Simple, robust, distributed and scalable Position accuracy is greatly improved with the use of

corrections. Position Accuracy increases with increase in the number of

beacon nodes

De-Merits Applicable only to isotropic networks All hops should have the same size All nodes should have the same transmission range

Hop Distance Method(1)

Position estimation requires three phases. Phase 1(Estimating Corrections)

Nodes store cumulative hop distances to the beacon nodes rather than number of hops on receiving HELLO messages.

Beacon node i computes the correction for each other beacon node j as follows:

After computing the corrections for all the other beacon nodes it broadcasts them to the nearby nodes.

jiact

jiestji ddC ,,

,

Hop Distance Method(2)

Phase 2(Effective Distance Estimation) Node , say k, uses the corrections received from the nearest

beacon node to compute the effective distances to at least three beacon nodes.

Phase 3(Position Estimation) The node estimates its position from the effective distances

obtained in the previous phase using trilateration or multilateration.

jijk

estjk

eff Cdd ,,,

Hop Distance Method(3)

1 2 3

2

11

2

BN-1

BN-4

BN-3BN-2

UN-k

3

3

3

4,3

4,2

4,1

est

est

est

d

d

d

2

7.2

5.2

4,3

4,2

4,1

act

act

act

d

d

d

23

7.23

5.23

4,3

4,2

4,1

C

C

C

213

7.23.03

5.15.02

,3

,2

,1

keff

keff

keff

d

d

d

Hop Distance Method(4)

Merits All hops need not have the same hop size. Simple , distributed and scalable. More robust than the previous method. Position accuracy is greatly improved by the use of corrections. Position accuracy increases with increase in the number of beacon

nodes.

Demerits Requires accurate timing/synchronization mechanisms to use time

of flight techniques to compute the distances between nodes.

Simulation Model,Assumptions and Performance Metric The network model used for the simulating and evaluating the

proposed algorithms is based on the following assumptions: Contains at least four beacon nodes Wireless links between nodes are symmetrical All nodes have the same transmission range Free space propagation model is being considered

Implemented the proposed algorithms using GLOMOSIM library and PARSEC simulation language.

Protocols used IEEE 802.11 MAC protocol(RTS/CTS handshake is enabled) AODV routing protocol is used

For the performance evaluation , we used the following equation to compute the position estimation accuracy

22 )()( iact

iest

iact

iest yyxxerror

Simulation Results Initially simulations are performed to study the performance of our

algorithms over non-differential based algorithms.

Results(2)

Results(3)

Im pact of Transm ission Range on Position Accuracy

0

20

40

60

80

100

120

0-10%

11-20%

21-30%

31-40%

41-50%

51-60%

61-70%

71-80%

81-90%

91-100%

>100%

Position Error

Nu

mb

er o

f N

od

es

HopCount(100m)

HopCount(200m)

HopCount(300m)

Results(4)

Im pact of Transm ission Range on Position Accuracy

0

20

40

60

80

100

1200-10%

11-20%

21-30%

31-40%

41-50%

51-60%

61-70%

71-80%

81-90%

91-100%

Position Error

Nu

mb

er o

f N

od

es

HopDistance(100m)

HopDistance(200m)

HopDistance(300m)

Conclusions

We proposed two algorithms which use the idea similar to the one in DGPS to reduce the position errors.

In our algorithms beacon nodes function in a similar way as a reference station.

Using our algorithms nodes over multiple hops from the beacon nodes can compute their positions.

Unknown nodes improve their position estimates using the corrections obtained from the nearest beacon node.

Distributed and scalable Key contribution of this work is the illustration of how the error

correction can be used to reduce the position estimation errors and improve the position accuracy significantly.