Abstract— An accurate localization scheme is essential to many underwater sensor applications. However, due to the persistent existence of uncertainties and measurement errors, an accurate localization is very difficult to achieve. The communication cost is much higher in underwater networks compared to terrestrial networks and this calls for more accurate localization schemes even if they involve more computational burden. In the paper, a scheme based on minimum mean absolute error (MMAE) is introduced and extensive simulation results are presented to compare this and the commonly used minimum mean squared error (MMSE) method. Both uniform error distribution and normal error distribution are considered. Our results indicate that MMAE clearly result in better localization accuracy when compared to MMSE. Index Terms — localization, minimum mean absolute error (MMAE), minimum mean squared error (MMSE) I. INTRODUCTION UNDERWATER tetherless sensor networks have attracted significant research interest in recent years due to their potential applications in environmental monitoring, assisted navigation, disaster warning, offshore oil and gas exploration [1][2][3][4]. An accurate localization scheme is essential to many of these applications. It is very challenging to achieve accurate localization in underwater applications. Most of the existing localization schemes rely on the measured distance between nodes for localization calculation [5]. However, obtaining an accurate distance in underwater environment is not easy. The widely used GPS system will not function due to the large path loss for underwater radio transmission. The accuracy of distance measurement can be greatly affected by underwater acoustic channel properties, time synchronization jitters, time-varying sound speed, and possible drifting/swings of the anchor nodes, whose positions are supposed to be known and steady. In order to improve the localization precision, least squares estimate is often adopted [6][7][8][9]. Least squares estimation can be also used in probabilistic localization schemes [9][10][11], where the probability distribution of the measured error are considered to further improve the localization accuracy. MMSE scheme (minimum mean squared error), is often used for position estimation that minimizes the average of squared errors. In the paper, we consider utilizing minimum mean absolute error (MMAE) to improve localization accuracy. The performance of the two schemes is elaborately compared in term of (a) exhaustive localization error distribution over a smaller region, where the localization error is the distance between estimated location and the real location; (b) localization error distribution for two dimensional (2D) Monte Carlo simulations (a grid of 40 by 40), where the localization error is the root mean square distance (RMSD) value based on 1000 simulation trials at each point; (c) uniform distribution and normal distribution in distance measurement uncertainties; (d) rectangle pre-deployed anchors and randomly located anchors. Extensive simulations are used to study the performance. Our results indicate that MMAE can lead to better localization accuracy, especially when the event is located near the border or outside the area enclosed by the anchors. II. RELATED WORK In general, a localization process includes distance measurement followed by a procedure to compute the position [6]. The error in the distance measurement will lead to imprecise results, hence, further localization process is necessary. The straightforward and most common localization approach is MMSE. The MMSE method can achieve a good localization precision if the measurement error is small or if the number of measurements to determine the location is very large. However, in underwater tetherless sensor networks, communication cost is high and exchange of large amounts of measurement data among the anchor nodes cannot be usually afforded; therefore, it is imperative to explore other schemes, such as minimum mean absolute error (MMAE), Cramer-Rao lower bound (CRLB) based algorithm, and residual weighting algorithm (RWGN), to improve localization accuracy. For underwater distance measurement, a number of approaches can be considered, such as Received Signal Strength Indicator (RSSI), Time Difference of Arrival (TDoA), Time of Arrival (ToA) [4]. Besides distance measurement, angle measurement also helps in some applications [4]. There are a few factors which contribute to the estimation errors. For example, flexible reflection from water surface, dynamic geometric spreading of sound energy under flowing water, and various noise (tides, current, storm, wind and rain) lead to Tao Bian, R.Venkatesan, and Cheng Li Faculty of Engineering and Applied Science, Memorial University of Newfoundland St. John’s, NL, A1B 3X5, Canada Email: {tao.bian, venky, licheng}@mun.ca A Refined Localization Method for Underwater Tetherless Sensor Networks This work is supported in part by the Natural Sciences and Engineering Research Council (NSERC) of Canada, Atlantic Innovation Fund (AIF), Wireless Communications and Mobile Computing Research Center (WCMCRC), and Atlantic Canada Opportunities Agency (ACOA) This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the WCNC 2010 proceedings. 978-1-4244-6398-5/10/$26.00 ©2010 IEEE