Optimal Performance Evaluation of Localization of Sensor Nodes in Wireless Sensor Networks

Wireless Sensor Networks are a collection of nodes which contain tiny devices having low power and work with minimal cost. In such a network, the functioning of these nodes plays a very important role to sense data and also forward the sensed data to the target observer. For segregation of nodes in effective locations, there is a need to localize these nodes by combining location information with the sensed data for tracking and monitoring of malicious nodes, goods tracking etc. The various approaches towards localization may be classified as range-free or range-based, both having their own pros and cons. This paper presents a discussion on different localization approaches, followed by simulation results of localization using lognormal shadowing model for distance estimation and trilateration for location computation. The results depict the individual impacts of node density and area of sensed region on the localization error. It is observed that with a fixed node count, the errors in location estimates increase with the increase in node density. It is also depicted that the localization error increases towards the boundary of a network. Since the approach discussed in the paper uses loss in received power for distance computation, there is no cost overhead for additional hardware involved in the implementation. Thus the approach used is cost effective.


Introduction
Sensor networks rely on a coordinating group of self configuring devices that work in tandem by sensing their operational environment, and exchanging this information over a network. The application areas of such networks range from agriculture, military, industries, logistics, home automation etc. [1], catering to various requirements in these realms. Many a times, the sensed information mandates a requirement to stimulate a change in the sensed environment [2]. This indicates an implicit need for localizing the sub-area which reported an exceptional condition. Some of the problem areas that can be addressed by means of localization include, finding the agricultural regions in large fields with deficit irrigation, narrowing down areas with high seismic activity in an earth-quake prone geographical stretch, identifying location of malicious nodes in a secure network and so on. Localization results may also be used for solutions to problems related to network operations like route discovery, estimating network coverage etc.
The granularity of required localization accuracy is dependent on the application for which the network was deployed. Although environments controlled by automated actuators would require a high level of precision, applications dependent on manual intervention and control are tolerant to relatively larger localization error values.
The paper is organized as follows-Sect. 1 provides an introduction to the paper, Sect. 2 presents background information related to this work, Sect. 3 describes the details of the simulation parameters and results, and finally the concluding remarks for this paper are given in Sect. 4.

Related Work
Over the last decade, active research in the area of sensor networks has led to development of various approaches to localization. These approaches exploit different characteristics of received signals in order to estimate the location of transmitting device. The quality of localization results is highly dependent upon the nature of chosen characteristic, and the same also controls the fixed and the recurring costs incurred in the estimation process [3].
The approaches towards localization may broadly be classified as range based and range free. Range based approaches involve measurement of distance between the communicating devices which is followed by using techniques like trilateration and triangulation to compute the location coordinates. Range free approaches on the other hand work on the basis of connectivity between communicating devices. These approaches don't rely on additional hardware and hence are more suitable for WSN being cost effective solutions, but the results obtained are generally not as accurate as those obtained from range based approaches.
Signal characteristics that can be exploited for ranging include Received Signal Strength (RSS), Time of Arrival (ToA), and Angle of Arrival (AoA) [4]. Use of RSS is based on the fact that the signal undergoes attenuation as it travels through the communication medium, and apart from other parameters, the attenuation is a function of the distance traversed. This property is exploited in order to compute the distance between the two communicating devices. ToA requires perfect synchronization between the clocks of communicating devices and records the time taken by the signal to travel from the sender to the receiver and uses the same to compute the distance traversed. Time Difference of Arrival (TDoA) works by recording the time gap between arrival times of the two types of signals viz. radio and acoustic and uses this gap for distance computation. AoA involves measurement of the angle between arriving signal and a reference direction. The metric is recorded for multiple arrival points using an array on antennas in order to compute the required distance.
In [5], the authors have discussed about the latest advancement in the field of wireless positioning by considering cooperation, mobility, and advanced array processing concepts, which are important key enablers for the layout of novel localization solutions in sensor networks.
In [6], the authors proposed a novel technique, node segmentation with improved particle swarm optimization (NS-IPSO), that divides SNs into segments to improve the accuracy of the estimated distances between pairs of anchor nodes and unknown nodes. The proposed scheme achieved higher accuracy in comparison with the recent state-of-the-art methods.
In [7], Sekhar etal. have designed an effective metaheuristic-based Group Teaching Optimization Algorithm for Node Localization (GTOA-NL) technique for WSN where an extensive set of simulations were performed to highlight the supremacy of the GTOA-NL model. The obtained results have ensured the superior performance of the GTOA-NL model over the other compared methods under varying number of anchor nodes, ranging error, and transmission range.
For our analysis, we identify the following listed metrics required for identifying location of nodes, as shown in figure more precisely:

Quality Metrics
The quality of the approach used for measuring distance may be quantified using various attributes like accuracy and precision [8], power consumed, consistency, hardware overheads [9] etc.
(i) Precision: The precision of localization results gives an indication of the error margins in the computed coordinates of the unknown nodes. Precision requirements are governed by the nature of application for which the sensor network is deployed and generally the applications that are related to security or the ones that need automated actuation have higher precision requirements as compared to other counterparts ( Fig. 1). (ii) Power Consumed: WSNs are generally composed of energy constrained nodes, hence a large chunk of research efforts are directed towards reducing power consumption. Amongst the activities involved in operations of a sensor network, signal transmission poses the maximum energy requirements on sensor nodes. Hence the most effective approach would be the one that requires least number of signal exchanges without compromising on accuracy of distance measurements. (iii) Consistency: Ranging approaches that present consistent level of precision are more desirable since these make it possible to compute correction factors for computed coordinates. Inconsistency in reported errors, on the other hand make localization a more challenging task. (iv) Cost of additional hardware: AoA, ToA and TDoA pose additional cost requirements due to dependency on additional hardware for precise clocks, acoustic receivers, array of antenna etc. This dependency makes these choices less desirable options, especially for densely populated networks. Since anchor nodes might be required to be GPS enabled or non energy constrained, number of anchor nodes required would further impact the hardware cost.
Network characteristics are controlled by the nature and placement of nodes and the terrain of deployment region. Quality of localization results, as computed on the basis of the above stated metrics, is impacted by these characteristics that relate to the sensor network under consideration [10]. E.g. mobility of nodes poses additional requirement of repeated computation of node coordinates, hence leading to more energy consumption. Count of beacon nodes, i.e. the nodes with known locations that serve as reference points, and their average distances from the unknown nodes govern the accuracy of measurements. Node density i.e. number of nodes per unit area, impacts the interference levels in the communication signals, and the nature of terrain impacts the levels of diffusion and fading experienced by the signals. Hence, these factors need to be kept in mind while deciding the ranging approach. There is also a need to study the impact of these factors while analysing the results of the chosen algorithm.

Localization Approaches
Distance estimates are used in triangulation or trilateration algorithms in order to compute the location of unknown nodes. Triangulation uses angles between communication lines and a fixed baseline along with the position of anchor nodes in order to compute the location coordinates. Trilateration on the other hand uses intersection points of circles centred at anchor nodes and having radii equal to respective measured distances in order to compute the desired locations.
Localization techniques can also be categorized as either range based or range free. We shall now discuss the two in details.

Range Based Localization
The following section discusses different range based techniques that rely on estimating distance between a set of anchor nodes and the node with unknown position [11]. These estimates are then translated to location coordinates by using triangulation/trilateration algorithms.

Received Signal Strength (RSS)
As the radio signal propagates through the wireless communication medium, it experiences attenuation, theoretically, this reduction in RSS is a function of inverse of square of distance travelled by the signal and hence may be measured in order to compute the distance between communicating devices, which can further be used in order to deduce the relative position of the transmitting device with respect to the receiving device. This mechanism is often used by setting up beacon nodes at known locations, which serve as reference points for the nodes whose position needs to be discovered.
An inherent problem of using RSS for distance estimation is that ideal free space and line of sight communication is virtually non-existent in real scenarios. Hence, inverse quadratic relation between distance and RSS is impacted due to interference from stray signals, fading due to multipath propagation, diffusion etc.
In [12], the authors have proposed an equal-arc trilateral localization algorithm based on received signal strength indicator and noted that the RSSI becomes more and more unstable with the increase of distance.
An RSSI based implementation by Sugano et al. [13] presents results amount to a localization error of around 1.5 to 2 m when 27 nodes are deployed in an area of hundred sq. m. Another experimental setup in [14] compares results of RSSI based localization algorithms. The test setup in an area of 100 sq. m. with 48 deployed nodes, reported errors in the range of 2-4.5 meters.

Time of Arrival (ToA)
The transit period between the transmission and receipt of the radio signal can also be used in order to compute the distance between communicating entities. The distance is given by the formula dist ij = s r * (t r -t s ) [15]. Where s r is the speed of the radio signal and t r -t s represents the time gap between the sending and the receipt of the signal.
Though this mechanism doesn't require any additional hardware, but is dependent on perfect synchronization between the clocks of the two devices. Also, since multipath channels may cause receipt of multiple signals separated in time, the accuracy of computed distance would be dependent on the choice of peak signal used. Patwari et al. [16] suggest the usage of first local peak signal instead of the highest-peak because like indirect signals, LOS communication is also prone to noise and may not be the strongest signal received. Patwari et al. reported RMS error of 1 m in [17] using the ToA.

Time Difference of Arrival (TDoA)
TDoA works by recording the difference between arrival times of two different types of signals having different speeds of propagation, e.g. radio and acoustic. The basic idea behind the approach is to compute the difference between arrival times of the two signals and use the same to compute the distance between the communicating nodes using the formula d = S sound * (T sound − T radio ) [10]. Though this approach eliminates the need for synchronizing clocks of the anchor and the unknown nodes but it poses a requirement of additional hardware which in turn adds to the cost of the equipment, hence making it unsuitable for cost effective applications especially if the network is densely populated. [18] introduces the usage of acoustic and radio signals for the purpose of range estimation. In [19], a simulation of location estimation presents the variation in estimation errors with change in the number of measurement periods. It was observed that increase in measurement periods reduces the error while increasing the communication overhead. s = C r * C s ∕ C r − C s

Angle of Arrival (AoA)
AoA requires Line of Sight (LOS) communication and works by measuring the angle between the communication path and a reference direction. The technique requires anisotropic antennas and works by measuring either the amplitude or the phase of the received signal. While considering amplitude, the transmitter is considered to be in the direction corresponding to the maximum RSS. Phase based measurements need either a large receiver antenna to an array of multiple antennas.

Range free localization
Range Free algorithms rely on connectivity information rather than use of direct distance estimates. These mechanisms generally do not rely on expensive hardware and hence offer more cost effective solutions as compared to range based counterparts. Range free approaches on the other hand are not as accurate as Range based approaches, hence the applications that require automated and real-time changes in the environment based upon localization results, may not use these solutions. A discussion on various range free approaches like DV-Hop, Centroid and APIT follows.

Distance Vector Hop (DV Hop)
DV Hop approach utilizes communication with location-aware anchor nodes in order to compute the location of unknown nodes [20]. The algorithm works by estimating the distance from anchors in terms of hop-count. This information, along with estimated hopsize is used in order to compute distance from the anchors, which in turn is fed to trilateration algorithm for the purpose of location computation. The original simulation proposed by Niculescu et al. in [21] lead to a localization error of less than 6%. Intermittent data exchanges in DV-Hop include tabulated data of position of each anchor node along with the distance in terms of hop count of the node from the anchor. Once this information is propagated from one anchor to another via the network, the receiving anchor determines the Correction Factor which is basically the size of one hop. This Correction Factor or the hop size is again broadcast over the network, thus enabling all location unaware nodes to compute their distance from each anchor using the hop count based distance.

Centroid
The basic Centroid approach [22], proposed as an alternative to GPS for low cost devices, recorded correlation of 87% with reality. The approach uses multiple neighbouring reference nodes in order to compute the position of the unknown node. The simulation of the location of the unknown node is assumed to be coincident with the centroid of the polygon formed by the reference nodes with which the unknown node can establish connectivity. The approach, progressively, computes the locations of all nodes based upon the information derived in preceding phases using the formula: This simplistic approach is improved in weighted centroid approach [11], by giving higher weights to the coordinates of those reference nodes that offer better connectivity, thus changing the location formula to:

Approximate Position in Triangle (APIT)
It is based on PIT (Position in Triangulation) test which is conducted to check if a point is in the interior or exterior of a triangle [23]. According to this test, a point is considered to be in exterior of a triangle if there exists a point, around the point under test, which is either closer to or farther away from all the vertices of the triangle. Since this test would require the node to be moved to all possible directions, direct usage of the same is infeasible in WSNs. A variation of the test works by considering information shared from neighbouring nodes as an emulation of node movement. Thus, a node is considered to be within a triangle formed by reference nodes, if none of the neighbours is either farther from or closer to all the reference nodes. The process is repeated of all the reference nodes to form multiple intersecting triangles and the position of the node is narrowed down to centroid of the polygon of intersection of all the triangles in which the unknown node resides. The simulations made by the authors of APIT [23] demonstrated that and error of about half the radio range is reported when the number of anchor nodes heard by a location unaware node is increased to 12. This error reduces further as the number of anchors heard is increased beyond 12.

Propagation Models
Inherent irregularities in unguided wireless communication medium, subject the radio waves to propagation effects like refraction, fading, diffraction, scattering etc., thus leading to loss in signal strength. The strength of the received signal is best estimated using statistical models [24]. The following section presents a discussion on different propagation models.

Free Space Propagation Model
This model assumes unobstructed line of sight communication and uses Friss free space equation, given below, to predict the received power assuming that loss in signal strength is due to filter and antenna losses and not due to propagation.
where P t is the transmitted power, P r (d) is the power received at distance d, G t & G r represent the gains of transmitting and receiving antennas respectively and L is the system loss factor. An important point to be noted here is that the Friss equation is only applicable for distances more than d f given by: where D is the antenna dimension.

Two Ray Reflection Model
This model is used to represent the attenuation due to interference between the direct LOS wave and a wave reflected off the ground. The variation in received power, caused due to this interference is given by: Associated with this model is the concept of cross-over distance, which represents the change over in computation of received power from Friss Equation, where Pr varies as inverse of square of distance to the above mentioned situation where Pr varies as inverse of fourth power of distance. The cross-over distance is given by:

Log-normal Shadowing Model
The log-normal statistical model is used to represent the uncertainties in the received power based on characteristics of the real world. As per the model the attenuation in power is inversely proportional to d n , where n is a constant dependent on propagation environment, the value of which varies between 2 and 6, the minimum value of 2 represents free space. The equation for power loss in dB is given by: where PL(d) represents the loss in received power at distance d, measured in decibels; n is the path loss exponent and X σ is a normal random variable.

Simulation Parameters and Results
This paper presents a simulation on Omnet + + in order to perform localization on a varying set of nodes laid out in grid format in areas of different sizes. The approach uses loss in received power in order to compute the distance from the location aware nodes. The computed distances were then fed to trilateration algorithm and the received results were recorded for network areas ranging from 10 × 10 m 2 to 30 × 30 m 2 . The results received give an indication of the impact of network size and node density on the location estimation errors ( Table 1).
The following section presents the recorded results in form of graphs. The graph in Fig. 2, depicts the impact of network size on localization error, the results were recorded keeping the node count fixed, which resulted in increase in the distance between nodes since the network was laid out in the fashion of a uniform grid.
The graph in Fig. 3, on the other hand depicts the impact of increasing node count in a sensed are of size 7 × 7 m 2 . It was observed that as the node count, in the sensed area of a given size, increases; the recorded localization error also increases.
The scatter plots in Figs. 4 and 5, depict the actual and computed locations of nodes in 25 × 25 m 2 network with nodes laid out in a 5 × 5 and 7 × 7 grids respectively. It is observed that localization error increase towards the boundary of the network. This observation could be dependent on the fact for the nodes which are near the network boundary; there is a non uniformity in the distance from anchor nodes thus leading to increased contribution in distance estimation error from the farther anchors, which in turn has adverse impact on localization results.

Conclusion
This work presents a discussion on different localization approaches suitable for WSNs. The paper also presents results of simulation of path loss based distance estimation followed by trilateration for localization. The simulations were repeated for a fixed node count by varying the size of sensed region and thereafter, for a fixed region by varying the node count. The results of simulation based on log normal shadowing model depict that increase in the distance between nodes due to keeping the node count fixed, results in a decrease in the localization error. It was also observed that as the node count(in the sensed area of a given size) increases, the recorded localization error also increases. Hence, we conclude that with a fixed node count, the errors in location estimates increase with the increase in node density. It is also observed that localization error increases towards the boundary of the network due to non uniformity in the distance from the anchor nodes thus leading to increased contribution in distance estimation error from the farther anchors. Graphical representation of differences between actual and estimated coordinates is also presented in the paper. The information may be used in order to setup blocks, bounded by location aware anchor nodes, in a large sensed area so that location of all sensor nodes may be computed.  Publisher's Note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
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Akanksha Gupta is working as an assistant professor in the department of Computer Science, University of Delhi and currently pursuing Ph.D in the area of Internet of Things, from Shri Venkateshwara University. She completed B.Sc honors in Computer science from University of Delhi in 2009 and MCA from Bharatiya Vidyapeeth college, Indraprastha University, Delhi in 2012. She has also qualified UGC NET in computer science in 2013. She has a teaching experience of over 7 years and has earlier published 2 research papers in reputed international journals and 2 chapters in edited books and also participated in many conferences.
Umang Singh pursued her UG degree in Computer Applications(BCA). She followed it with MCA, Ph.D(CS). She has over 14 years of teaching experience. She actively guides Ph.D students. She has published over 50 research papers in international and national journals. Currently, she is associated with MCA department at ITS Mohan Nagar, Ghaziabad as an Associate Professor.