Introduction

A network of small,

low cost sensor nodes with basic functionality, spread out in an area for

sensing specific parameters of the environment and with wireless links is

generally termed as a Wireless sensor network (WSN). Each node in a WSN usually

consists of an independent power source, a sensor unit, a transceiver unit and

a processing unit making each wireless sensor node autonomous. This enables

large scale distribution of these nodes over larger areas for better and faster

data gathering. Recent technological advances have made manufacture of small,

low cost sensors nodes technologically and economically feasible 1.

Characteristics of WSN, like mobility of nodes, ease of addition

or removal nodes to the network, heterogeneity of the nodes and ability to cope

with node failure, ensure a wide range of application of wireless sensor

networks. Precision Agriculture,

Environmental Monitoring, Vehicle Tracking, Health care Monitoring, Smart

Buildings, Military Applications, Animal Tracking are few applications of WSNs

2. The information gathered by the wireless sensor nodes, in certain

applications, becomes useful only when locations from where the data has been

collected is known. Hence, Localisation of wireless sensor nodes is essential,

especially for applications like tracking intruders in battlefield, locating

objects in building, determining their number, positions, and movements,

emergency response applications, industrial and environmental monitoring 3.

Several

algorithms have been developed for localization of nodes in a WSN. Global

Positioning System (GPS) is currently the most commonly used positioning

systems in the world 4. However, GPS cannot be used in applications where the

wireless sensor nodes are small and it is not feasible to configure each node

with GPS and in applications where the nodes are spread out in indoors and are

heavily dense. Hence many other algorithms are used for such situations. These

algorithms can be broadly classified into Range based and Range free algorithms.

Time of Signal Arrival (TOA), Time Difference of Signal Arrival (TDOA), Angle

of Arrival and Received Signal Strength Indicator (RSSI) are few range based

localization algorithms. RSSI based localisation is more popular because it is

simple and does not require any sophisticated hardware 5.

Unlike in outdoor,

localization parameters would not remain constant in complex indoor

environments. The wireless signal is more severely affected by multipath error,

diffraction, obstacles, the direction of antennas and other factors 6.

Because of these, a huge amount of noise would be added to RSSI and would result

in error in localization. To reduce the error, feedback error control using

multiplicative distance-correction factor, Time Window Statistics, UWB Ranging and other techniques are used

789. However, all these techniques increase the computational time

required for localization.

In this paper, we discuss how the error in localization of nodes can be

reduced with help of neural networks. We first train the neural network in our

environment and then use this trained neural network for error correction. We

also compare the performance of localization with different parameters.

RSSI

Estimating distance from RSSI

RSSI based localization

algorithms estimate the distance of a node from a given node, which transmits a

signal, by measuring the power of the signal received by the receiving node.

The node which transmits the signal are static and are aware of their location.

These nodes are called anchor nodes or beacon nodes. If the power received by a

node which is at a given distance from an anchor node is known, then the power

at a distance d is given as follows

3:

Where Pr is the power received at a

distance d from the anchor node, A is the power received at a unit

distance from the anchor node and np

is the transmission factor whose value describes the environment and

is different from place to place. The parameters A and np are

constant over a given area for outdoor environment, but they vary considerably

over short distances in an indoor environment. Hence, for indoor localization,

the environment has to divided into smaller areas over which the parameters A and np can be considered constant. Each area would have a

different value for the parameters and can be estimated experimentally 4.

Once the parameters A and np are known, the distance of

a node from the anchor node by the following equation:

Predicting the location with the measured distances.

To predict the

location of a node, in a two-dimensional area, distances has to be measures

from at least three anchor nodes which do not fall in the same line. With the

locations of these anchor nodes, location of the node is the point of

intersection of the three circles, drawn with the anchor nodes as centre and

radius equal to the distances of the node from the anchor nodes. If (xa, ya), (xb,

yb) and (xc, yc) are the coordinates of three anchor nodes and da, db, dc

are the distances of a node from these anchor nodes respectively, then the

coordinates of the node (x, y) is estimated by solving the equations:

In case of a

three-dimensional localization, distances of the node from 4 anchor nodes,

which do not fall on the same plane has to be measured. Location can be

estimated by finding the intersection of the four spheres formed from the

anchor nodes

Considering effects of noise.

Due to the presence

of noise in the signals, randomness in the indoor environment and other factors

introduce error in the distances measured by the nodes and the location data

sent by the anchor nodes. Due to these errors, the constant distance circle

from the anchor nodes a, b and c may not meet at a common point as shown in

fig1. Which means the equations may not have a single point solution. Hence, we

estimate the location to the point of intersection of lines l, m

and n, which are lines obtained by

connecting the points of intersection of a pair of circles. Equations of l, m

and n can be obtained by taking the

difference of equations 4 3, 5 4 and 3 5 respectively. Solving the so obtained

equations would give the estimated location of the node 10.

Error correction using neural networks