A range ratio is used to adjust the accumulated hop-count and this effectively reduces distance overestimation. Comparing .... In N-hop Multilateration [9], cumulative ranges are used to gauge ... DHL does not require network-wide uniformity.
Density-Aware Hop-Count Localization (DHL) in Wireless Sensor Networks with Variable Density Sau Yee Wong1,2,
Joo Ghee Lim1, SV Rao1,
Winston KG Seah1
1
Communications and Devices Division, Institute for Infocomm Research (Member of A*STAR), 21, Heng Mui Keng Terrace, Singapore 119613, Tel: +65 6874 7588. 2 Department of Electrical and Computer Engineering, National University of Singapore. {stuwsy,limjg,raosv,winston }@i2r.a-star.edu.sg
Abstract— Localization schemes using hop-counts to reference nodes of known positions have been proposed to localize nodes in a sensor network. However, these schemes usually work well only when the networks have uniform and dense node distribution. In view of this, a novel Density-aware Hop-count Localization (DHL) algorithm is described here to improve the accuracy of location estimation when the node distribution is non-uniform. When the density is low, each hop traversed is not necessarily equivalent to the maximum range distance. A range ratio is used to adjust the accumulated hop-count and this effectively reduces distance overestimation. Comparing to the algorithms without density consideration, simulations show that our algorithm improves the localization accuracy. In addition, the overhead incurred by DHL is found to be lower than that incurred by conventional schemes. Keywords - Density-awareness; Localization; Sensor Networks.
I.
INTRODUCTION
Wireless sensor networks are task-based networks. Usually, sensors form a network to monitor habitat, moving targets or environmental phenomenon. The collected data is then transported back to the sink node. In some cases, in order for the sink node to extract meaningful information, location information needs to be attached along with the data. However, the inherent characteristics of wireless sensor networks make acquiring this position information a challenging issue. Hop-count is a suitable and simple localization metric in sensor networks. This is because sensor networks are multi-hop in nature and majority of the sensors usually have low mobility. Since hop-count and average distance per hop-count are the only essential information needed in the distance estimation, the packet size is small and constant. Besides, each node only needs to communicate with its local neighbors. However, the drawback is that conventional hop-count localization algorithms only provide good location estimation if the node distribution in the network is dense and uniform. The accuracy of the estimation is greatly affected by the network density. The impacts of network density and node distribution are significant, and yet these issues have not received much research attention. In view of this, we propose a novel Densityaware Hop-count Localization (DHL) algorithm that provides more accurate distance estimation when the node distribution is sparse or non-uniform.
The structure of the paper is organized as follows. Section II reviews background and related works. Section III presents Density-aware Hop-count Localization (DHL) algorithm. Section IV reports and interprets the simulation results, and finally, Section V presents a conclusion. II.
BACKGROUND AND RELATED WORKS
The node distribution in a sensor network is not always uniform throughout the network lifetime, but can be affected by factors such as terrain contour (e.g. more sensors accumulate at the bottom of a slope), hostile environment (e.g. sensors are moved away by enemies), network dynamism (e.g. sensors enter sleep mode), and others. In a 2D (or 3D) sensor network, it is assumed that there are at least three (or four) nodes that contain a priori location information, henceforth known as Reference Nodes (RNs), from which other nodes can determine their locations. In a highly dense and uniformly distributed network, a direct and short multi-hop path is likely to exist between a RN and any other nodes (Fig. 1a). Thus, distance between a RN and any node can be estimated by the product of hop-count and transmission range, i.e. D = HC x R, where D is the distance from the RN, HC is the hop-count from the RN and R is the transmission range. This is because by advancing one hop away from a RN, distance is likely to be incremented accordingly by one transmission range. In Fig. 1a, the estimated distance between the “Reference Node” and “node P” is “2 x R”, which is a close approximation to the actual distance.
Figure 1. (a) Direct path (b) Forwarding nodes not close to boundary (c) Propagation path not straight (d) Hybrid case of b and c.
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can help to improve the accuracy of hop-count localization. A small group of mobile nodes is intentionally introduced to do averaging and correction. In comparison to the abovementioned algorithms, our algorithm introduces density-awareness to dynamically estimate distances in non-uniformly distributed networks. The aim is to reduce distance-overestimation and improve localization accuracy. Figure 2. Estimated distance from RN1 by DV-Hop in (a) uniform and high density; (b) uniform and low density; and (c) non-uniform networks.
However, if nodes are sparse, the product of hop-count and transmission range is likely to overestimate the distance from RN. As the number of nodes is less, it is more difficult to have sufficient nodes to constitute straight and short paths in hopcount propagation. If the next forwarding node is not located sufficiently close to the transmission boundary, the distance traversed for each hop does not equate to the propagation range (Fig. 1b). Thus, more hops are taken to propagate the packet. If the end-to-end path taken is not straight (Fig. 1c), the winding and twisted path taken accumulates more hop-counts. The hybrid case of the previous two cases (Fig. 1d) usually causes greater distance over-estimation compared to Case 1 and Case 2. Thus, we can summarize that the effective progress for each hop is less than the transmission range in a sparse network since the probability of finding a point close to the boundary in the direction of traveling diminishes. A. Related Work DV-Hop [5,6] uses average distance per hop-count, Davg to account for this overestimation. Thus, the estimated distance from RN is Di = HCi × Davg. instead of Di = HCi × R. If the node distribution is uniform and highly dense, Davg is computed as a larger value, since for each hop, the distance advanced is further (Fig. 2a). If the node distribution is maintained as uniform but the node density is lower (i.e. nodes have lower connectivity), Davg will be computed as a smaller value to account for the decreased distance per hop-count (Fig. 2b). However, when a network has a combination of dense and sparse regions, the use of Davg actually shows degraded performance (Fig. 2c). This is because the distance traversed for each hop is no longer consistent. The distance per hop is greater in dense regions and smaller in sparse regions. In fact, Langendoen and Reijers [2] who conducted comparisons of distributed localization algorithms stated that “a drawback of DV-Hop is that it fails for highly irregular network topologies, where the variance in actual hop-distance is very large”. In Robust Positioning [8], a Refinement stage is introduced where each node repeats triangulation iteratively by using their neighbors’ estimated positions and ranges. However, error can be propagated fast and it is a priori unknown when the iteration stops. In N-hop Multilateration [9], cumulative ranges are used to gauge the distance. However, this method is subjected to range error. Nagpal et al. [4] propose local averaging where each sensor collects its neighboring hop-count values and computes an average of its own and its neighbors’ values, a method that is only suitable for evenly spaced sensors. In a study conducted by Lim and Rao [3], they show that mobility
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III.
DENSITY -AWARE HOP-COUNT LOCALIZATION (DHL)
In this paper, sensor network is assumed to be connected and sensors have low mobility. Due to the broadcast nature of wireless channel, each node is assumed to know its number of neighbors after the network is deployed. An omni-directional radio propagation model and a 2D network model which is extendable to 3D are assumed. The radio range of the sensors is denoted by R. Unlike conventional hop-count localization algorithms, DHL does not require network-wide uniformity. Within a network, some regions may have higher or lower density. This type of non-uniform node distribution is more often encountered in actual applications. The neighbors of a node are distributed randomly surrounding the node. Local density is defined as the number of neighboring nodes per unit transmission area. For simplicity, the number of neighboring nodes, Nngbr, is used to represent local density. We also define the incremented distance by traveling a hop as hopdistance. Depending on Nngbr, we classify the node density into a few categories and each category has a corresponding range ratio. Range ratio, µ, represents the ratio of expected hopdistance to the transmission range for a particular local density. The selection of number of density categories is a tradeoff between accuracy and overhead. Increasing the number of categories can increase the accuracy of estimated hop-distance, but at the expense of higher number of exchanged messages. In our study, we divide the node density into three categories, viz. low, medium and high (Table 1). A wireless network requires at least a certain p number of neighbors to maintain connectivity [1]. Thus, if a node has less than p neighbors, it is classified as located in a low density region. When connectivity reaches a certain high number of neighbors, q, hop-distance tends to be a constant. Thus, a node with q neighbors and above is regarded as being in a high density region. Similarly, a node with p
