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Node localization is a fundamental issue in wireless sensor network (WSN), as many applications depend on the precise location of the sensor nodes (SNs). Among all localization algorithms, DV_Hop is a typical range-free localization algorithm characterized by such advantages as simple realization and low energy cost. From detailed analysis of localization error for the basic DV_Hop algorithm, we propose a connectivity weighting DV_Hop localization algorithm using modified artificial bee colony optimization. Firstly, the proposed algorithm calculates the average hop distance (AHD) of anchor nodes in terms of the minimum mean squared distance error between the estimated distances of anchor nodes and the corresponding actual distances from them. After that, a connectivity weighting method, considering the influence from both local network properties of anchor nodes and the distances from anchor nodes to unknown nodes, is designed to obtain the AHD of unknown nodes. In addition, we set up the weighting calculation proportion of anchor nodes at the same time. Finally, a modified artificial bee colony algorithm which enlarges searching space is used to optimize the execution of multilateral localization. The experimental results demonstrate that the connectivity weighting approach has better localization effect, and the AHD of unknown nodes close to true value can be obtained at a relatively large probability. Moreover, the modified artificial bee colony algorithm can reduce the probability of premature convergence, and thus the localization accuracy is further improved.

WSN, bred by low-power embedded technology, wireless communication technology, microelectromechanical systems, and other related technologies, is a technological revolution on information sensing technology [

Generally, the position information of SNs is indispensable, and monitoring without position information may not be useful. Hence, node localization is one of the most critical issues for WSN [

Recently, many localization algorithms can be broadly categorized as range-based and range-free localization [

DV_Hop, firstly proposed by Niculescu, is a distributed localization method using distance vector routing principle and is the most popular among range-free algorithm because of its facility and feasibility. Nevertheless, a major drawback of DV_Hop algorithm is that the estimated distances between ANs and UNs are to be erroneous, which is the main cause of poor localization accuracy, and thus some various improvements in DV_Hop algorithm have been put forward. Considering the close relationship between the localization accuracy and the deployment of ANs, Poggi [

In this paper, a connectivity weighting DV_Hop localization algorithm using modified artificial bee colony optimization is proposed to improve localization accuracy. Our main contributions are delineated as follows:

We comprehensively take into account the influence from several ANs near to the UN. Besides that, some experimental analysis and demonstrations for the different proportion of ANs participating in the calculation have been carried out so as to compute the AHD of UNs more accurately.

A method for calculating the weight of ANs based on connectivity is designed. In this method, not only the distances from UNs to ANs are useful, but also the connectivity of ANs is employed to measure their local network attributes, and the AHD of UNs can be finally obtained after weighting normalization.

A modified artificial bee colony algorithm is used to further improve the localization accuracy. The core evolution equation for the modified artificial bee colony algorithm takes a random individual as the search center, which can enlarge the searching space and reduce the probability of premature convergence at the same time.

The remaining paper is structured as follows. The related works are introduced in Section

On the premise of maintaining the original advantage of basic DV_Hop algorithm, various improvements are mainly involved in three aspects; they are, respectively, the calculation for the AHD of ANs, the weighting calculation for the AHD of UNs, and the optimization for multilateral localization.

Because of the randomness deployment of SNs, the AHD of the whole network is proposed by Peng [

From the above review, we can conclude that in DV_Hop algorithm the calculation for the AHD of UNs and the optimization for multilateral localization are two important factors to improve the performance of localization. Up to now, reported literature provides several weighting methods to compute the AHD of UNs; however, there is no analysis in experiments that how many ANs participated in the weighting calculation can get better localization accuracy. Furthermore, most weighting methods depend on the hop number and distance error of ANs; the connectivity of ANs reflecting the attributes of local network has not been regarded which can also cause more errors. In the literature, localization of UNs is formulated as optimization problem; although many optimization techniques have been applied to optimize the localization error, we are encouraged to propose a modified artificial bee colony optimization algorithm, which can enlarge the searching space and reduce the probability of premature convergence.

In this section, we first describe the localization principle of the basic DV_Hop algorithm. On its basis, the reasons causing localization error are analyzed and some corresponding typical improvement methods are briefly introduced.

The core theoretical basis of DV_Hop is to estimate the distance from UNs to ANs by the product of the AHD and the corresponding hop number, rather than by using ranging methods, and the implementation of this algorithm consists of three steps as follows.

During the first step, all the ANs broadcast their message packets to neighbor SNs by the method of flooding. Figure

Structure of message packet.

When the AN _{i}, can be calculated using the following equation: _{i},_{i}) and (_{j},_{j}), respectively, indicate the coordinates of the AN_{ij} represents the minimum hop number from the AN

The AHD of all ANs should also be broadcasted in the network by flooding, and then all the UNs only save the AHD firstly received; the remaining AHD subsequently received are chosen to be discarded. By using this method, the UNs can receive the AHD from their nearest AN.

The estimated distances from UNs to ANs are equivalent to the product of the minimum hop number and the AHD obtained in second step, and subsequently the multilateral localization can be carried out to get the coordinates of UNs.

Let (_{u},_{u}) represent the coordinate of the UN_{ui} shows the estimated distance from the UN_{ui} is the minimum hop number from the UN_{u} indicates the saved AHD of the UN

Up to now, the system of equations can be formed by considering the coordinates of all ANs and their estimated distances to the UN

Then, equation (

By calculating this matrix equation with the least square method (LS), the estimated location of the UN

From the execution process of DV_Hop algorithm, it is known that the error mainly comes from the following three aspects.

To solve this problem, information from more ANs should be used, and the estimation for the AHD of UNs can be more accurate. Reference [

Liu [_{ui} is the minimum hop number from the UN

The distance error for ANs is inconsistent, and the distance error with a smaller value shows that the AHD of the AN may be more accurate. Therefore, an error weighting (EW) method is proposed by Zhao [_{ij} and_{ij} are, respectively, the estimated distance and the actual distance from the AN

_{uN}; if the deviation of_{uN} is large, the error for

Lin [_{i}(

So the first-order Taylor series expansion_{i}(_{0},_{0}) is as follows:

Therefore,

We can introduce equation (_{t} is the threshold of step size.

If the above condition is satisfied, the iterative calculation stops; otherwise, the initial position should be updated as follows:

(_{0},_{0}) should be replaced by the updated position until the termination condition is met. Finally, the position of the last iteration is regarded as the coordinate of the UN.

After analyzing the reason of localization error for the basic DV_Hop algorithm, this paper improves the algorithm from various aspects to promote the localization accuracy. The main contents are as follows: the calculation for the AHD of ANs based on the minimum mean square distance error, calculation for the AHD of UNs using connectivity weighting, and optimization of multilateral localization using modified artificial bee colony algorithm.

The unbiased estimation criterion is employed in the basic DV_Hop algorithm; that is to say, the average distance error for the AHD of ANs, calculated using equation (

Assuming that_{ij} indicates the distance error between the estimated distance from the AN

Let

We can deduce the equation for calculating the AHD of ANs as follows:

In the basic DV_Hop, all the UNs take the AHD from the nearest AN as their AHD. However, owing to the random distribution of SNs in WSN, the distance error for each AN is inconsistent, and the AHD of a single AN cannot be sufficient to reflect the properties of the whole network, which will bring about the error of estimated distance. In order to obtain the AHD of UNs more accurately, we comprehensively take into account the influence from several ANs near to the UN. When a UN has gotten some AHDs, different weight value should be assigned, and normalization for the weight value will be carried out to compute the final AHD of UNs. In summary, the design of weight value is mainly based on the following two aspects:

(1) For a UN, the influence from ANs having different distance to the UN is inconsistent, the AHD of the AN closer to the UN may be similar to the actual AHD of the UN at a larger probability.

(2) The local network properties of each AN is inconsistent, and the number of UNs which actually participate in the calculation for the AHD of ANs is not the same; that is, the total number of UNs on the shortest path from one AN to the remaining ANs is different. If an AN has more number of UNs on the shortest path, it will have stronger connectivity, and thus its impact on the AHD of UNs should also be greater.

We now introduce the connectivity weighting calculation method for the AHD of UNs in detail. Based on both the local network properties of ANs and the distance from ANs to UNs, the weight value is defined as follows: _{ui} indicates the minimum hop number from the UN_{ij} represents the minimum hop number from the AN

Before calculating the AHD of UNs, a unified criterion should be employed, and the weight value for different ANs must be normalized to make sure that the sum of all weight value is 1. Therefore, the normalized weight value is as follows:

The estimated distance in basic DV_Hop also depends on the minimum hop number between SNs, and the error of estimated distance may be greater when the minimum hop number is larger. Therefore, good solution cannot be obtained at the situation that ANs far from the UN participate in the above calculation for the AHD of UNs. In contrast, the small number of ANs participated in the calculation is not a good choice as well. When_{r} as follows:

An appropriate proportion should be set so that the calculation for the AHD of UNs can take into account information from more ANs, and then the AHD of UNs may be closer to its true value.

In the step of multilateral localization, the performance of LS in the basic DV_Hop algorithm heavily relies on the accuracy of distance estimation [

The basic artificial bee colony algorithm (ABC) is developed to find the optimal solution through the cooperation of individuals in the population, and it is a global convergence algorithm demonstrated in [

(

(

(

In basic ABC algorithm, each employed bee and onlooker bee generates a new food source in the neighborhood of its present position by using the following search equation:

During the search process, an looker bee chooses a food source based on the scheme of roulette wheel selection, after employed bees share information about food sources. The probability value associated with food source is _{i} is the fitness value of the food source_{i} is the value of the objective function corresponding to the food source

If a food source is not updated after_{j} and_{j} are the upper and lower bounds for dimension

When ABC algorithm is employed to execute the node localization, the objective function can be defined using equation (

ABC algorithm is an iterative algorithm to search for the optimal solution in the solution space, and it can get rid of the dependence on the initial value when optimizing the problem of node localization. However, similar to other evolutionary algorithms, ABC also faces up some challenging problems, like slow convergence and prematurity, and it is difficult to get the global optimal solution. We can see from (

The difference of searching area between (

Searching space analysis.

The flow chart of optimization of multilateral localization using RABC is shown in Figure

Flow chart of optimization of multilateral localization using RABC.

In this section, we describe the results of some experimental test to evaluate the performance of our proposed algorithm compared with some variants discussed in Section

The simulation experiments are carried out using the software Matlab R2013 on the computer platform in which the memory is 8G, CPU is the Inter Core i7 processor, and the operating system is Windows 7. The simulation area is set as

Let

Similarly,

Table

Parameter settings of RABC.

Parameters | Value |
---|---|

The maximum number of iterations | 100 |

The total number of individuals in the population | 50 |

The dimension of node localization | 2 |

The predetermined number of cycles for RABC | 0.1 × |

The threshold for the step size of the optimal solution | 0.5 m |

The calculation for the AHD of UNs is one of the important factors that affect the localization accuracy. When the number of ANs involved in the calculation is only one, the algorithm is the same as the basic DV_Hop algorithm, and a single AN is not sufficient to reflect the local network properties of UNs. On the contrary, if all ANs take part in the calculation, an AN far from the UN will make the estimated distance error greater. Therefore, when the weighting calculation proportion of ANs_{r} is fixed, we will compare the influence of AW, HW, EW, and our proposed connectivity weighting (CW) method on the localization accuracy.

In the simulation area, the total number of SNs is 150, the maximum communication radius is 30m; besides that, the AHD of ANs is computed using (_{r}, and the ordinate is the mean value of _{r} is 0.05 or 0.1, and the localization error will increase when_{r} gradually increases. This part of experimental results can provide guidance for the setting of_{r}.

The curve of localization error with different_{r}.

Based on the above experimental results in Figure _{r} as 0.1, the total number of SNs is still 150, and the maximum communication radius is set as 30m. In the simulation experiment, we also calculate the actual AHD of UNs using (

Accuracy analysis diagram of the estimated AHD of UNs.

Compared with LS, INLS, and ABC algorithm, this part of experiments is used to test the performance of RABC algorithm for multilateral localization. For INLS algorithm, initial value of iteration must be given at first, so we can take the solution of LS as its initial value, which is denoted as “INLS1.” Similarly, the centroids of polygons composed by several ANs around the UN can also be treated as initial value, and we define this situation as “INLS2.” At last, “INLS3” indicates the case that a random position in the monitoring area is regarded as the initial value. Besides that, the AHD of UNs should be calculated using the method of CW according to the experiment conclusion in above subsection; furthermore, the weighting calculation proportion_{r} is still set as 0.1. After that, we compare and analyze the performance from the three aspects including the total number of SNs, the total number of ANs, and the maximum communication radius. The values for variation parameters are shown in Table

The value of variation parameters.

Variable | Value |
---|---|

The total number of SNs | 100, 120, 140, 160, 180, 200 |

The total number of ANs | 20, 25, 30, 35, 40, 45, 50 |

The maximum communication radius/m | 20, 25, 30, 35, 40, 45, 50 |

Figures

The curve of the mean value of

The curve of the mean value of

The curve of the mean value of

From the results of Figures

The results in Figures

Cumulative distribution function of the normalized localization error.

A connectivity weighting DV_Hop localization algorithm using modified artificial bee colony optimization is proposed in this paper. In this algorithm, the AHD of ANs is calculated based on the minimum mean square distance error. On this basis, the AHD of UNS is computed using connectivity weighting method considering not only the distance from ANs to UNs but also the local network properties of each AN. In addition, a weighting calculation proportion is defined, and the appropriate value is obtained according to the experimental method. In the final step, a modified artificial bee colony algorithm with random location updating is used to optimize the multilateral localization, and searching space is expanded to reduce the probability of premature convergence. The experimental results demonstrate that the performance of connectivity weighting approach is better than that of the other weighting methods, and it can get the real average hop distance of unknown nodes at a larger probability. Besides that, the modified artificial bee colony algorithm can also improve the location accuracy. As a future work, we will analyze the impact of localization algorithms described in this article on a real environment and extend the localization of nodes in WSN applications.

The data used to support the findings of this study are available from the corresponding author upon request.

The authors declare that there are no conflicts of interest regarding the publication of this paper.

This research was funded partly by the National Natural Science Foundation of China grant number