- Research Article
- Open Access

# Distributed Range-Free Localization Algorithm Based on Self-Organizing Maps

- PhamDoan Tinh
^{1}Email author and - Makoto Kawai
^{1}

**2010**:692513

https://doi.org/10.1155/2010/692513

© P. D. Tinh and M. Kawai. 2010

**Received:**28 August 2009**Accepted:**21 September 2009**Published:**10 November 2009

## Abstract

In Mobile Ad Hoc Networks (MANETs), determining the physical location of nodes (localization) is very important for many network services and protocols. This paper proposes a new Distributed Range-Free Localization Algorithm Based on Self-Organizing Maps (SOMs) to deal with this issue. Our proposed algorithm utilizes only connectivity information to determine the location of nodes. By utilizing the intersection areas between radio coverage of neighboring nodes, the algorithm has maximized the correlation between neighboring nodes in distributed implementation of SOM and reduced the SOM learning time. An implementation of the algorithm on Network Simulator 2 (NS-2) was done with the mobility consideration to verify the performance of the proposed algorithm. From our intensive simulations, the results show that the proposed scheme achieves very good accuracy in most cases.

## Keywords

- Neighboring Node
- Anchor Node
- Arrival Packet
- Absolute Location
- Radio Coverage

## 1. Introduction

Recently, mobile ad-hoc network localization has received attention from many researchers [1]. Many algorithms and solutions have been presented so far. These algorithms are ranging from simple to complicated schemes, but they can be categorized as range-based and range-free algorithms. Range-free algorithms utilize only connectivity information and the number of hops between nodes. The others utilize the distance measured between nodes by either using the Time-Of-Arrival (TOA) [2], Time-Differential-Of-Arrival (TDOA) [3], Angle-Of-Arrival (AOA) [4], or Received-Signal-Strength-Indicator (RSSI) [5] technologies. However, they usually need extra hardware to achieve such measurement. When calculating the absolute location, most schemes need at least three anchors (nodes that are equipped with Global Positioning System or know their location in advance).

DV-HOP is a typical range-free algorithm. It was proposed by Niculescu and Nath [6] as an Ad-hoc Positioning System (APS). DV-HOP uses distance-vector forwarding technique to get the minimum hop count from a node to heard anchors. By using corrections calculated by anchors (average hop-distance between anchors), nodes estimate their location by using lateration (triangulation) method. Besides DV-HOP, some other algorithms seem to be more complicated, but have better accuracy. The Multidimensional Scaling Map (MDS-MAP) proposed by Shang et al. [7] is an example. MDS-MAP is originated from a data analytical technique by displaying distance-like data in geometrical visualization. It computes the shortest paths between all pairs of nodes to build a distance matrix and then applies the classical Multidimensional Scaling (MDS) to this matrix to retain the first two largest eigenvalue and eigenvector to a 2D relative map. After that, with three given anchors, it transforms the relative map into an absolute map based on anchors' absolute location. There are some variances of MDS-MAP such as centralized method: MDS-MAP(C), and distributed one: MDS-MAP(P). But, in the distributed method, to get the absolute location, nodes need global information about the subnetwork's map that contains at least three anchors. Tran and Nguyen [8] proposed a new localization scheme based on Support Vector Machine (SVM). The authors have contributed another machine learning method to the localization problem, and proved the upper bound error of this method.

Regarding the localization based on Self-Organizing Maps, some researchers have employed SOM directly or with some modification. The method presented by Giorgetti [9] employed the classical SOM to the localization. This method uses centralized implementation and requires thousands of learning steps in convergence of network topology. The authors also realize that this method is good for small and medium size networks of up to 100 nodes. S. Asakura et al. proposed a distributed localization scheme [10] based on SOM. Hu and Lee [11] also proposed another version of distributed localization based on SOM. In this work, the authors employed a deduced SOM version [12]. But, this method still needs too many iterations (at least 4000) to make the topology to be converged with a relatively low accuracy. In another work [13], the authors use SOM to track a mobile robot with the utilization of surrounding environments from readings of sensor data. In the work presented by Ertin and Priddy [14], another version of SOM was used to implement the localization in wireless sensor networks. This paper extends one of our previous work [15] to improve and adapt it with mobility scenarios. The main contribution of this paper is the utilization of intersection between radio coverage of neighboring nodes in our modified SOM, and the adaptation of the algorithm to the mobility scenarios. It is also noted that our method was verified in both MATLAB and NS-2 environments.

## 2. Motivation for Distributed SOM-Based Localization

### 2.1. Self-Organizing Maps

- (1)
- (2)Finding the BMU: determine the Best Matching Unit (BMU) or winning neuron at the iteration by using Euclidean minimum-distance criterion:
where represents the input pattern, is the total number of SOM neurons, and the input pattern has dimensions.

- (3)
where is the learning rate at time step and is the function for topological neighborhood of neuron at time step

Steps and are repeated until the convergent criterion is satisfied.

### 2.2. Motivation for Distributed SOM-Based Localization

Suppose that we have a mobile ad-hoc network of connected nodes, in which only a small number of nodes know their location in advance (anchor nodes). Now we have to determine the location of the remaining nodes that do not know their location, especially in distributed manner. In our proposed scheme, one can think that a mobile ad-hoc network itself is an SOM network, in which each neuron is a node in that network, and these neurons are connected to their 1-hop neighboring nodes (nodes have direct radio links). The topological position and the weight of each neuron are associated with its estimated location. The learning process takes place locally at each node, where the input pattern is estimated location of the node (this input is dynamically changed over time except that the anchors use their known location). The neighborhood neurons of a node are determined by its 1-hop neighboring nodes. It is obvious that each node becomes the Best-Matching Unit (BMU) at its local region. So when updating weights at the BMU, only its 1-hop neighbors' weights are updated. The BMU node also receives updates from other nodes when it becomes 1-hop neighbor of other nodes. Anchors do not update their known positions during the learning process, so if the network has some nodes know their location in advance (anchors), then each node will utilize the information from these anchors by adjusting its location towards the estimated absolute location based on the information from these heard anchors. At the end of the learning process, the weight at each node (SOM neuron) is its estimated location.

## 3. Proposed Distributed Localization Algorithm Based on SOM

In this section, we will introduce about our proposed Distributed Range-free Localization Algorithm (LS-SOM). The first two sections describe about initialization and learning stages of the main algorithm. The mobility consideration is presented in the third section.

### 3.1. Initialization Stage

- (1)
If the packet is already in the cache, the node then compares the hop count of the packet with that of the cached packet. If the hop count of the arrival packet is less than that of the cached packet, then the cached packet is replaced with a new arrival packet, and forwarded to its neighboring nodes with hop count modified to add one hop. If the hop count of the arrival packet is greater than or equal to that of cached packet, then it is dropped.

- (2)
If the packet is not in the cache, then it is added to the cache and forwarded to its neighboring nodes with hop count modified to add one hop.

Having information from some anchors, the nodes now initialize their location ready for SOM learning process. In our proposed method, the initial location of a node is calculated based on either randomized value (if node does not receive enough information from three anchors) or a value calculated using a trilateral method. In this initialization stage, nodes also exchange information (using short "HELLO" message broadcast) so that each node has information about its neighboring nodes (1-hop neighbors). Each node also exchanges information about 1-hop neighbors (just the IDs of 1-hop neighbors) with its neighboring nodes, so that all nodes in the network have information about both 1-hop and 2-hop neighboring nodes.

### 3.2. Learning Stage

Before going into our algorithm details, let us formulate the mathematical notations which will be used in this paper. We represent a wireless ad-hoc network as an undirected connected graph. The vertices are nodes' locations, and edges are the connectivity information (direct connection between neighboring nodes). The target wireless ad-hoc network is formed by anchors with known locations and N nodes with unknown locations. The unknown nodes have actual locations denoted as and estimated locations denoted as .

( ) Estimated location exchange: at this step, each node forwards its estimated location to all of its neighbors, so that it also knows the estimated location of its neighbors as with is the number of nodes within its communication range.

( ) Local update of relative location: we will now shape the topology at each region formed by the node with location together with all of its neighboring nodes. The node with location plays as the input vector and becomes the winning neuron for that region. Consequently, the neighboring nodes of the node with location will receive the updating vector from node with location . Suppose that the node with the estimated location has neighbors. The locations of these neighbors are denoted as . Based on classical SOM, neighboring nodes of the node with location will update their weight with the following formula:

in which is the learning rate exponential decay function at iteration defined in (5).

The update by (7) makes each node move toward the intersection area as showed in Figure 2. This update also maximizes the correlation between the neighboring nodes that is the key problem for the speed and accuracy of topological convergence using SOM. In (7), is a learning bias parameter calculated using

with is a learning threshold. This threshold determines the step to apply this modification. Basically, we can apply this modification after several steps of SOM learning when nodes are in relative order to ensure the convergence of the learning process. At the end of this step, the node with location transmits its neighbor location updates based on (7) to all of its neighbors. As a result, it also receives the similar updates from its neighboring nodes as . Node with location now calculates its newly estimated location by averaging its current location and the updates from the neighboring nodes using

### 3.3. Mobility Consideration

In MANETs, nodes may move in arbitrarily manner, so the movement of nodes will affect the performance of the algorithm. To adapt LS-SOM with MANETs, we proposed a repeated learning algorithm as follows.

( ) First Time Initialization. Anchors participate in localization will flood the network just one time, so that nodes can calculate the initial location for fast topology convergence.

( ) Repeated Learning. At specified interval, nodes perform neighboring detection by exchanging short "HELLO" messages. Having neighboring information, nodes now proceed with the learning process.

## 4. Simulation Evaluations

To evaluate the performance of our proposed method, we use the average error ratio in comparison with the radio range of the nodes presented in

### 4.1. Simulation Parameters

To ease the comparison, we call the method in the existing work [10] as SOM, and our proposed method as LS-SOM. We conducted the simulation for static and mobile scenarios by using MATLAB (we integrated SOM, DV-HOP, and LS-SOM into the program received from [7]) and NS-2, respectively. For static scenarios, each experiment is done on thousands of randomly generated topologies that are deployed by 100 nodes on an area of 10 by 10. For mobile scenarios, we simulated on networks with 25 randomly distributed nodes on an area of 300 by 300 square meters. The propagation model is TwoRayGround and transmission range of each node is 100 meters. The common parameters used in simulation are as follows. Number of SOM learning steps is 15, and Learning bias threshold is 1.

### 4.2. Static Networks

### 4.3. Mobile Networks

## 5. Conclusions

We have presented our proposed Distributed Range-free Localization Algorithm Based on Self-Organizing Maps (LS-SOMs) in this paper. By introducing the utilization of intersection areas between radio coverage of neighboring nodes, the algorithm maximizes the correlation between neighboring nodes in distributed SOM implementation. With this correlation maximization, our method increases the quality of the topology estimation and reduces the time of the topological convergence. With our proposed solution for mobility management, LS-SOM is capable of working with networks having high mobility. From intensive simulations, the results show that LS-SOM has achieved good accuracy over the original SOM and other algorithms. LS-SOM has reduced the SOM learning steps to just around 15 to 30 steps. Besides that, LS-SOM is capable of working not only with static networks, but also with mobile networks. Future work will investigate in a more precise distance measurement method to make LS-SOM to be more flexible.

## Authors’ Affiliations

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