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In wireless sensor networks (WSNs), the location information of sensor nodes are important for implementing other network applications. In this paper, we propose a range-free Localization algorithm based on Neural Network Ensembles (LNNE). The location of a sensor node is estimated by LNNE solely based on the connectivity information of the WSN. Through simulation study, the performance of LNNE is compared with that of two well-known range-free localization algorithms, Centroid and DV-Hop, and a single neural network based localization algorithm, LSNN. The experimental results demonstrate that LNNE consistently outperforms other three algorithms in localization accuracy. An enhanced mass spring optimization (EMSO) algorithm is also proposed to further improve the performance of LNNE by utilizing the location information of neighboring beacon and unknown nodes.

Wireless sensor networks (WSNs) are the collections of spatially distributed autonomous inexpensive sensors with limited resources that are deployed in two or three dimensional geographic domains and cooperatively monitor physical or environmental conditions [

The localization algorithms proposed for WSNs can be divided into range-based and range-free categories according to the type of input data. The range-based algorithms compute the positions of unknown nodes based on the assumption that the absolute distance between an unknown node and a beacon node can be estimated from ranging measurements such as Received Signal Strength Indication (RSSI) [

Recently, a number of machine learning based localization techniques have been proposed [

In this study, we propose to use the ensemble of neural networks to build the sensor position prediction model based on the hop-count information. An ensemble of multiple predictors has been shown, which has better performance than a single predictor in average [

The rest of this paper is organized as follows.

In this section, we briefly review some related works on range-free and machine learning based localization algorithms.

Bulusu

Another well-known range-free localization algorithm is DV-Hop proposed by Niculescu and Nath [

Nguyen

Tran and Nguyen [

A neural network based localization algorithm was proposed in [

Chatterjee [

In this paper, we aim to improve the performance of single neural network based localizer of [

In this section, we present the proposed localization algorithm based on NNEs. The algorithm adopts similar modest assumptions as [

We consider a large scale WSN with _{1}_{2}_{N }

In the LNNE system, two NNEs with the same architectures

The architecture of _{h}_{i}_{i}_{j}_{i},S_{j}_{o}

Two combination rules are considered in this study:

(1) _{est}_{−}_{S}_{i}_{est}_{−}_{S}_{i,k}

(2) _{est}_{−}_{S}_{i}_{est}_{−}_{S}_{i,k}

The component neural network used in the localization system is a three layer Fletcher–Reeves update-based conjugate gradient FFNN with _{h}_{h}

A component neuralnetwork of

The input vector of each component neural network is _{S}_{i}_{i}, S_{1})_{i}, S_{2})_{i}, S_{M}_{i}, S_{m}_{i}_{m}_{mn}_{h}_{n}_{h}_{h}_{o}

The connection weights of each component neural network have to be adjusted through a learning algorithm based on the training data. The training data set for _{S}_{1}_{S}_{1 }_{,k}_{S}_{2}_{S}_{2 }_{,k}_{S}_{M}_{S}_{M}_{,k}_{S}_{m}_{,k}

During the training process, the weights of the network are updated as follows:

The performance of the BP algorithm can be improved by allowing the learning rate change during the training process. The conjugate gradient algorithm is such a method to accelerate the convergence speed [

The algorithm performs a linear search to determine the optimal distance to move along the current search direction

The next search is then performed in the conjugate direction of the previous directions. The algorithm determines the new search direction by combining the new steepest descent direction with the previoussearch direction:
_{k}_{k}

The protocol used in the LNNE system consists of four phases: info phase, training phase, advertisement phase, and localization phase.

In [

The refinement of unknown node’s position of MMSO algorithm is done with the help of the neighboring beacon nodes. To further improve the performance, we propose an enhanced mass-spring optimization (EMSO) algorithm that utilizes the location information of both the neighboring beacon and unknown nodes.

We denote _{i}_{j}_{i}, S_{j}_{est}_{i}, S_{j}_{j}_{i}_{i}_{i}_{i}_{est}_{i}, S_{j}_{i}_{j}_{i}_{j}_{i}, S_{j}_{est}_{i}, S_{j}_{j}_{i}_{i}_{i}_{i}_{i}_{i}_{i}_{i}_{i}_{i}_{i}_{i}_{i}

To improve localization accuracy, we need to minimize the total energy of the system, _{i}

In the mass-spring system, the force on the sensor node _{i}_{j}_{i}_{j}_{i}_{i}_{b}_{u}_{i}_{X}_{,S}_{i}_{Y}_{,S}_{i}

The EMSO algorithm for improving the location estimation of all unknown nodes is illustrated in Algorithm 1. The algorithm minimizes the total energy _{t}

The performance of the proposed LNNE system is evaluated through a simulation study. The simulations are carried out in MATLAB. In the simulation, the sensor nodes are placed in a 50

The performance metric used to evaluate the performance of different localization schemes is the average localization error for all unknown sensor nodes, _{i}

Simulation Parameters.

Parameter | Value |
---|---|

Number of Sensor Nodes, |
150/200/250/300/350/400 |

Beacon Ratio | 0.1–0.3 |

Sensor Field Size | 50 |

Transmission Range of a Sensor Node, r | 10 |

Number of Component NN, |
7 |

The performance of the proposed LNNE system is compared with two well-known range-free localization algorithms, Centroid and DV-Hop, as well as the localization algorithm based on signal neural network, LSNN.

Sample network with 400 sensor nodes and a beacon ratio of 0.2.

In the first two studies, the sensor nodes are uniformly placed in the field without coverage hole.

Next, the effect of network density on the performance of the localization algorithms is studied. The network density is changed by varying the number of sensor nodes in the field. In the simulation, the number of sensor nodes,

Performance comparison among different beacon ratios (

Performance improvement of LNNE

Performance comparison among different network densities (

Performance improvement of LNNE

Due to the obstacles in the sensor field, there are normally coverage holes in the sensor network. Similar to [

Sample networks with coverage holes (250 sensor nodes and 50 beacon nodes):(

Performance comparison under different beacon ratios (0.1-0.3) and 1 coverage hole.

Performance comparison under different beacon ratios (0.1-0.3) and 5 coverage holes.

Effect of coverage holes on LNNE (

Performance of refinement algorithms under different beacon ratios (

The performance of the refinement algorithms is also investigated. We study the effect of MMSO and EMSO on the performance of LSNN and LNNE. Only median rule is considered for LNNE since the mean rule produces comparable result as shown in

Performance of refinement algorithms with different network densities (

In this paper, neural network ensembles are used to improve the localization accuracy for WSNs by utilizing the diversity of the component neural networks. The localization system, LNNE, only utilize the connectivity information of the network to estimate the location of sensor nodes. Simulation studies are carried out to compare the performance of LNNE with two well-known range-free localization algorithms, Centroid and DV-Hop, and a single neural network-based localization algorithm, LSNN. The effects of beacon ratio, network density, and coverage holes on the performance of LNNE are investigated. The experimental results demonstrate that LNNE outperforms other three algorithms in all simulation cases. The EMSO algorithm is also proposed, which can significantly improve the performance of LNNE with the help of location information of the neighboring beacon and unknown nodes.

The work of Ashgar Dehghani was supported by Petroleum Recovery Research Center (PRRC) of New Mexico Institute of Mining and Technology.