IntroductionA network of small,low cost sensor nodes with basic functionality, spread out in an area forsensing specific parameters of the environment and with wireless links isgenerally termed as a Wireless sensor network (WSN). Each node in a WSN usuallyconsists of an independent power source, a sensor unit, a transceiver unit anda processing unit making each wireless sensor node autonomous. This enableslarge scale distribution of these nodes over larger areas for better and fasterdata 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 additionor removal nodes to the network, heterogeneity of the nodes and ability to copewith node failure, ensure a wide range of application of wireless sensornetworks. Precision Agriculture,Environmental Monitoring, Vehicle Tracking, Health care Monitoring, SmartBuildings, Military Applications, Animal Tracking are few applications of WSNs2. The information gathered by the wireless sensor nodes, in certainapplications, becomes useful only when locations from where the data has beencollected is known. Hence, Localisation of wireless sensor nodes is essential,especially for applications like tracking intruders in battlefield, locatingobjects in building, determining their number, positions, and movements,emergency response applications, industrial and environmental monitoring 3.

 Severalalgorithms have been developed for localization of nodes in a WSN. GlobalPositioning System (GPS) is currently the most commonly used positioningsystems in the world 4. However, GPS cannot be used in applications where thewireless sensor nodes are small and it is not feasible to configure each nodewith GPS and in applications where the nodes are spread out in indoors and areheavily dense. Hence many other algorithms are used for such situations. Thesealgorithms can be broadly classified into Range based and Range free algorithms.Time of Signal Arrival (TOA), Time Difference of Signal Arrival (TDOA), Angleof Arrival and Received Signal Strength Indicator (RSSI) are few range basedlocalization algorithms.

RSSI based localisation is more popular because it issimple and does not require any sophisticated hardware 5.  Unlike in outdoor,localization parameters would not remain constant in complex indoorenvironments. 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 resultin error in localization. To reduce the error, feedback error control usingmultiplicative distance-correction factor, Time Window Statistics, UWB Ranging and other techniques are used789. However, all these techniques increase the computational timerequired for localization.

 In this paper, we discuss how the error in localization of nodes can bereduced with help of neural networks. We first train the neural network in ourenvironment and then use this trained neural network for error correction. Wealso compare the performance of localization with different parameters.           RSSI  Estimating distance from RSSI               RSSI based localizationalgorithms estimate the distance of a node from a given node, which transmits asignal, 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 anode which is at a given distance from an anchor node is known, then the powerat a distance d is given as follows3:              Where Pr is the power received at adistance d from the anchor node, A is the power received at a unitdistance from the anchor node and npis the transmission factor whose value describes the environment andis different from place to place. The parameters A and np areconstant over a given area for outdoor environment, but they vary considerablyover 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 adifferent value for the parameters and can be estimated experimentally 4.

Once the parameters A and np are known, the distance ofa node from the anchor node by the following equation:            Predicting the location with the measured distances.               To predict thelocation of a node, in a two-dimensional area, distances has to be measuresfrom at least three anchor nodes which do not fall in the same line. With thelocations of these anchor nodes, location of the node is the point ofintersection of the three circles, drawn with the anchor nodes as centre andradius 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, dcare the distances of a node from these anchor nodes respectively, then thecoordinates of the node (x, y) is estimated by solving the equations:                In case of athree-dimensional localization, distances of the node from 4 anchor nodes,which do not fall on the same plane has to be measured. Location can beestimated by finding the intersection of the four spheres formed from theanchor nodes Considering effects of noise.

                Due to the presenceof noise in the signals, randomness in the indoor environment and other factorsintroduce error in the distances measured by the nodes and the location datasent by the anchor nodes. Due to these errors, the constant distance circlefrom the anchor nodes a, b and c may not meet at a common point as shown infig1. Which means the equations may not have a single point solution. Hence, weestimate the location to the point of intersection of lines l, mand n, which are lines obtained byconnecting the points of intersection of a pair of circles.

Equations of l, mand n can be obtained by taking thedifference of equations 4 3, 5 4 and 3 5 respectively. Solving the so obtainedequations would give the estimated location of the node 10.                 Error correction using neural networks

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