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Multihop Localization with Density and Path Length Awareness in Non-Uniform Wireless Sensor Networks Sau Yee Wong1,2, 1

Joo Ghee Lim1, SV Rao1,

Winston KG Seah1,2

Institute for Infocomm Research (Member of A*STAR), 21, Heng Mui Keng Terrace, Singapore 119613 2 National University of Singapore {stuwsy,limjg,raosv,winston }@i2r.a-star.edu.sg

Abstract— Localization of wireless micro-sensors which are non-uniformly scattered over a region is a challenging problem. Solutions relying on simple inter-node ranging and then summing up ranges between a node and reference nodes do not necessarily provide reliable position estimation. Besides, in multihop localization, error in distance estimation tends to accumulate with the increase of path length. This is because by increasing hop-counts, the disparity between the actual progressed distance and estimated progressed distance is accumulated. In view of this, a novel multi-hop localization scheme that incorporates density and path-length awareness is proposed for non-uniformly distributed wireless sensor networks. Also, we seek to reduce errors in position estimation introduced by long propagation path.

I. INTRODUCTION Spatial localization is of paramount importance to ad hoc wireless sensor networks since location information is vital for target detection, data aggregation, sensor query, position-based routing, etc. However, sensor networks, which are often deployed outdoors, are subjected to uneven node distribution arising from various factors, such as methods of sensor deployment and terrain contour (e.g. air-dropped sensors tend to accumulate at the bottom of a slope, thus, node density is higher at the bottom than the peak of a slope), hostile environment (e.g. sensors can be swept away by currents, corroded by chemical solution, or moved away by animals) and network dynamism (e.g. the power of a sensor may have depleted and it is no longer functioning, a node may move out of the transmission range of its neighbors or switch between active and sleep modes). The uneven node distribution poses a challenging problem to position estimation in sensor networks. Besides, in designing a localization algorithm, some network constraints such as lack of infrastructure, cost, form factor, limited computation and communication capabilities, and finite energy supply should be taken into consideration. In addition, some influencing factors need to be taken into account. A localization algorithm should be (a) distributed (i.e. does not rely on some powerful nodes to do centralized computation) (b) self-organizing (i.e. does not rely on preinstalled infrastructure or set up) (c) robust (i.e. tolerant to network dynamisms like node failure) (d) energy-efficient (i.e. does not incur large computation and communication overheads) and (e) scalable (i.e. practical for large number of nodes).

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In view of this, we propose a Density-aware Hop-count Localization (DHL) scheme for these network scenarios. The main contribution of our work is to identify two potential issues that have not received substantial research attention but have great impacts on non-uniform ad hoc wireless sensor networks. The issues are: (i) Density issue: Localization accuracy is not guaranteed for non-uniform and sparse networks; (ii) Path length issue: Cumulative error in distance estimation becomes significant for long hop-count propagation path (especially common in large networks with small number of reference nodes, i.e. nodes with a priori knowledge of position information). II. RELATED WORK There are many works done for localization in wireless and mobile networks. Tseng et al.[16] review the importance and applications of location awareness in ad hoc wireless mobile networks. In another study, Hightower and Borriello[6] survey the existing research in location systems for mobile computing applications. Niculescu and Nath[12][13] propose a distance-vector based ad hoc localization algorithm, Ad Hoc Positioning System (APS). This algorithm uses the hop-by-hop propagation capability of the network to forward distances to the reference nodes. There are four methods in measuring the distance to the reference nodes, i.e. DV-Hop, DV-Distance, Euclidean, and DV-Coordinate. DV-Hop is the only method that uses hop-count information without requiring range or angle measurements. However, DV-Hop does not provide good performance when the variance of hop-distance (i.e. the mean distance per hop) is high[8]. The Robust Positioning algorithm[14] enhances DV-Hop by proposing an additional Refinement phase. After a node has computed a coarse estimated position of its own location using DV-Hop, the node obtains the estimated positions from all of its immediate neighbors. The node also measures the ranges from each of these neighbors. Then, making use of this information and assuming that these neighboring nodes are some reference nodes, the node re-computes triangulation to refine its estimated position. The process is iteratively computed until certain stopping criterion is met. However, the complexity of Robust

Positioning is difficult to measure since it is a priori unknown how many iterations it takes to reach equilibrium[8]. In N-hop Multilateration[15], cumulative ranges are used to gauge the distance. However, this method is subjected to range error. Nagpal et al.[11] 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[10], they show that mobility can help to improve the accuracy of hop-count localization. A small group of mobile nodes is intentionally introduced to do averaging and correction. According to Cho and Chandrakasan[4], sensor density can range from a few to a few hundred in a region that is less than 10m in diameter. Cerpa et al.[3] point out that in habitat monitoring, the number of sensors can range from 25 to 100 per region. This implies that node density is not uniform throughout a network. A region can have many times more sensors than the other regions in a sensor network. Therefore, the impact of non-uniform node density should be taken into consideration in hop-count localization. Node density also affects power management, network connectivity management, and data aggregation. Intanagonwiwat, et al.[7] state that in a high density network, the greedy-tree aggregation approach achieves more significant energy savings (up to 45%) than the opportunistic aggregation. Ganesan, et al.[5] discover that at high node density, the maintenance overhead of localized two-disjoint paths is nearly an order of magnitude higher than localized braided path. On the other hand, at low node density, they find that localized path construction sometimes fails to find an alternate path. The Geographical Adaptive Fidelity (GAF) algorithm[17] suggests that network lifetime increases proportionally with node density, where a four-fold increase in node density can lead to network lifetime increases by 3 to 6 times. Bulusu, et al.[1] improve localization quality by placement of new reference nodes at low node density and rotating functionality among redundant reference nodes at high node density. Thus, node density is an interesting issue not only in localization, but also other areas in sensor networks. III. ALGORITHM DESCRIPTION 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. In our network model, there exists a total of N sensors, of which only K sensors (where 0