Consistency-Based On-line Localization in Sensor Networks Jessica Feng, Lewis Girod, and Miodrag Potkonjak 4821 Boelter Hall, Los Angeles, California 90034, USA {jessicaf, miodrag}@cs.ucla.edu,
[email protected]
Abstract. We have developed a new on-line error modeling and optimizationbased localization approach for sensor networks in the presence of distance measurement noise. The approach is solely based on the concept of consistency, and is developed specifically for the case of on-line localization, which refers to the situation when references are not available a priori. The localization problem is formulated as the task of maximizing the consistency between measurements and calculated distances. In addition, we also present a localized localization algorithm where a specified communication cost or the location accuracy is guaranteed while optimizing the other. We evaluated the approach in (i) both GPS-based and GPS-less scenarios; (ii) 1-D, 2-D and 3-D spaces, on sets of acoustic ranging-based distance measurements recorded by deployed sensor networks. The experimental evaluation indicates that localization of only a few centimeters is consistently achieved when the average and median distance measurement errors are more than a meter, even when the nodes have only a few distance measurements. The relative performance in terms of location accuracy compares favorably with respect to several state-of-the-art localization approaches. Finally, several insightful observations about the required conditions for accurate location discovery are deduced by analyzing the experimental results. Keywords: Consistency, Location Discovery, Statistical Modeling.
1 Introduction Sensor networks and pervasive computing systems form one of the fastest growing computer and networking research frontiers. Once the nodes that form a network or an infrastructure are deployed, invariably there is a need that each node discovers its position. Global position system (GPS) can greatly facilitates this task. However, due to obstacles such as trees and walls, the GPS system often does not lock to satellite signals. At the same time, GPS systems are relatively expensive and consume a significant amount of energy. Therefore, usually only a limited subset of nodes is equipped with GPS; other nodes deduce their locations by measuring distances between themselves. For this purpose, a variety of distance measurement technologies have been employed, including signal strength attenuation techniques, ultra wide band approaches, Doppler-assisted methods, carrier-phase-based measurements and acoustic signal-based techniques. The technologies differ significantly in terms of P. Gibbons et al. (Eds.): DCOSS 2006, LNCS 4026, pp. 529 – 545, 2006. © Springer-Verlag Berlin Heidelberg 2006
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Fig. 1. Motivational example topology Table 1. The distance measurements information ID N1 N2 N3 N4 N5 N6 N7 N8 N9
LOCATION (75, 195) (60, 135) (79, 110) (122.5, 180) (150, 85) (75, 159.4) (125, 187.5) (57.5, 165.4) (70, 85)
REAL 45.893 42.5 48.654 35.355 87.5 22.926 42.573 41.337 75.208
GAUSSIAN 45.791 43.432 78.066 35.294 86.362 53.285 42.938 42.831 71.427
STAT 1 56.697 42.895 49.008 34.355 56.988 23.001 43.837 41.111 87.449
STAT 2 44.193 42.043 39.964 42.139 87.479 27.077 41.992 49.604 74.574
Table 2. Solutions resulted using different error models (columns) based on different sets of measurements (rows)
GAUSSIAN STAT 1 STAT 2
GAUSSIAN 0.0208 8.179 7.658
STAT 1 7.993 0.0117 6.042
STAT 2 4.258 5.275 0.0303
CONSISTENCY 0.0424 0.0315 0.0396
maximum and minimum measuring range, resilience toward obstacles, power consumption, cost of deployment and power budget. Nevertheless they share a common denominator: distance measurements are prone to both small fluctuation and occasional large errors [1]. The localization (location discovery) problem can be defined in the following way. A total of N nodes, K of which (K
