Underwater Localization with Time-Synchronization and Propagation Speed Uncertainties

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1 Underwater Localization with Time-Synchronization and Propagation Speed Uncertainties Roee Diamant and Lutz Lampe University of British Columbia, Vancouver, BC, Canada Abstract Underwater localization is a key element in most underwater communication applications. Since GPS signals highly attenuate in water, accurate ranging based techniques for localization need to be developed. In this paper we describe a sequential algorithm for time-synchronization and localization in the underwater acoustic channel. We consider the realistic case where nodes are not time-synchronized and the sound speed in water is unknown, and formalize the localization problem as a sequence of two linear estimation problems. Simulation results demonstrate that our algorithm compensates for timesynchronization and signal propagation speed uncertainties, and achieves good localization accuracy using only two anchor nodes. Index Terms Underwater acoustic localization (UWAL), propagation speed uncertainties, time synchronization and localization I. INTRODUCTION Underwater acoustic localization (UWAL) has recently attracted much attention due to advances of technology enabling reliable and efficient acoustic communication underwater [1]. Applications such as environmental monitoring, navigation or command and control systems, typically include several autonomous sensor nodes with acoustic communication capabilities and require accurate localization of these nodes. Localization also improves routing capabilities and scheduling decisions in underwater acoustic communications networks. Since GPS signals are highly attenuated underwater, UWAL is a difficult task with similarities to indoor localization []. There exist several industrial underwater navigation systems for self-localization based on speed and direction estimation, e.g., [3], [4]. While some of these systems showed good navigation capabilities for short duration in experimental settings (with an accuracy of about 1 meter for 10 minutes of circular motion [3]), for longer periods of time these systems often suffer from low accuracy due to accumulated errors [5]. Therefore, network localization techniques are often based on ranging using underwater acoustic communications [5]. Since node depth can be self-estimated, e.g., using pressure probes, we are interested in two-dimensional (-D) UWAL. Such localization requires ranging to at least three reference nodes at known locations, also called anchor nodes. However, since acoustic signals are highly attenuated by the channel and since network topology may be sparse, a sensor or network This work was supported by the National Sciences and Engineering Research Council (NSERC) of Canada through a Vanier Scholarship and a Strategic Project Grant. node that wishes to learn its location may not be in the communication range of at least three anchor nodes. Moreover, due to self motion or ocean current, nodes permanently move in the underwater environment [6]. Thus, scenarios where a node at a fixed location obtains range measurements to at least three anchor nodes are rare. Ranging in wireless networks is usually performed by measuring the time of arrival (ToA), time difference of arrival (TDoA), received signal strength indicator (RSSI), or angle of arrival (AoA) of received signals. Since accurate attenuation models for the underwater acoustic channel are difficult to find [7], and AoA methods require multiple transducers which might not be available, most approaches for UWAL rely on ToA and TDoA for distance estimation [8]. ToA or TDoA measurements tend to be noisy due to synchronization errors (caused by node clock skew and offset), unpredictable delays in the scheduling mechanism, and node self-movements. As a result, several least squares (LS) estimators have been suggested to mitigate such noise, assuming the availability of multiple ToA or TDoA measurements from anchor nodes at a static unlocalized node (cf., [9]). Unfortunately, this makes the system even more sensitive to node movements. While existing UWAL protocols assume the sound speed to be a-priori known [9], in practice its value varies and should be considered as an unknown propagation-channel parameter. [10] suggested measuring water temperature and salinity to estimate the sound speed in water based on the sound speed model in [7]. Alternatively, [11] suggested to jointly estimate the node location and the propagation speed in the channel by constructing a matrix of TDoA measurements and applying an LS solution. However, they make the assumptions that all nodes in the network are static, at least four anchor nodes are available and that all nodes are time synchronized, which do not hold true in most UWAL applications. While it is usually assumed that clock offset is the main cause of time-synchronization errors [11], UWAL poses an additional challenge as clock skew cannot be neglected due to the long propagation delay in the channel [1]. Furthermore, since anchor nodes are usually submerged we cannot assume these nodes to be time synchronized. Regarding this problem, [1] suggested to estimate both skew and offset based on packet exchange with an already synchronized node. For terrestrial networks, Zheng et al. [13] suggested to jointly synchronize and localize nodes by exchanging packets with

2 anchor nodes to measure ToA in the channel, and applying a sequence of LS and weighted LS (WLS) estimators. However, since they assume that channel propagation speed is given and that anchor nodes are synchronized, this work cannot be directly applied in UWAL. In this paper, we consider the problem of UWAL in a practical setting where the sound speed is unknown, and nodes are not time-synchronized and move permanently. Relying on the assumption that nodes are equipped with self-navigation systems (e.g., [3], [4]) and that these systems are accurate for use in short periods of time, we offer a heuristic solution for this problem, which we refer to as the sequential time-synchronization and localization () algorithm. We demonstrate the advantages of our algorithm by comparing simulation results for the algorithm and two benchmark localization methods and showing that for the latter significant localization errors occur if nodes are not synchronized or the speed of sound is not estimated. The remainder of this paper is organized as follows. In Section II we describe the system model and assumptions. In Section III, we formalize the UWAL problem and present our algorithm for time synchronization and localization. Simulation results are presented in Section IV, and conclusions are drawn in Section V. II. SYSTEM MODEL We are interested in a UWAL algorithm which is performed as part of an underwater acoustic communications network, where nodes transmit at the beginning of globally established time slots. We consider an unlocalized node (UN) directly connected to L anchor nodes, which have means to accurately measure their time-varying -D location. We assume that nodes are not time-synchronized. Suppose the global time t 0 corresponds to the time t l according to the lth node s local clock, then t 0 corresponds to the time t UN = t l S l +O l in the UN local clock, where S l and O l are the time-invariant clock skew and offset of the UN relative to l, respectively, and can be different for each l. However, we assume that S l and O l are relatively small and that the duration of each time slot is large enough such that a node can match a received packet with the time slot it was transmitted in. Thus, since nodes always transmit at the beginning of the time slot, the transmission time of a received packet according to the transmitter clock is known and a time stamp (which considerably increases communication overhead, considering the low bit rate in underwater acoustic communication) is not required. This is a valid assumption in UWAL, due to the low signal-propagation speed (about 1500 m/sec). We consider a dynamic scenario in which all nodes permanently move either by own means or by ocean current. Our objective is to estimate the location of the UN after a pre-defined delay of W seconds, referred to as the localization window. During the localization window, we rely on a periodic packet exchange between the L anchor nodes and the UN as part of the communications network, to obtain ToA measurements at the different locations of the UN and the L anchor nodes. We assume that the UN is equipped with a directional navigation (DR) system (e.g., [3], [4]), which during the localization window provides N position estimations j n = [ j x n, j y n] T for the true location j n, n = 1...,N, in terms of the -D universal transverse mercator (UTM) coordinates j x n and j y n. These locations are translated into a series of motion vectors, ω(n,n ) = [ d n,n, ψ n,n ] T, n,n = 1,...N, where d n,n and ψ n,n are the distance and angle between two self-estimated locations j n and j n, respectively. More specifically, assuming depth differences to be small (extensions are straightforward but not included here for brevity), the elements of a single motion vector ω(n,n ) are d n,n = j n j n tan( ψ n,n ) = j y n j y n j x n j x n. (1) While we do not directly use the self-estimated locations j n, we rely on the accuracy of the motion vectors for all locations n and n visited by the UN during the localization window. We note that this assumption sets limits on the value of W which is determined by the specifications of the DR system in use. We next introduce our algorithm for UWAL. III. THE ALGORITHM The algorithm uses a sequential approach in which first nodes are time-synchronized and then location is estimated. We start with quantizing the spatial domain by representing the continuous motion of nodes as a series of discrete locations. That is, we define the sets of quantized locations K = {k 1,...,k I }, k ρ = [k x ρ,k y ρ] T, and U = {u 1,...,u Q }, u ν = [u x ν,u y ν] T, for the UN and l, respectively, and are interested in the estimation of location j N at the end of the localization window. This representation allows us to associate multiple exchanged packets with discrete node locations to obtain two-way ToA measurements. Consider, for example, the time-varying one-dimensional coordinates of the UN and an anchor node l in Figure 1, and a scenario where nodel transmits two packets,a 1 anda, when it is located at - D positionsp 1 andp, respectively. These packets are received by the UN when it is located at the self-estimated locations j 1 and j 3, respectively. By mapping the self-estimated locations j 1, j and j 3 of the UN onto one quantized locationk 1, and by mapping locations p 1 and p onto one quantized location u 1, we associate packets a 1 and a with the quantized locations k 1 and u 1. Thus, despite the continuous motion of nodes in the channel, we associate several packets with the same node locations. This allows us to obtain two-way ToA estimation as we further discuss below. For each received packet, the receiving node estimates the ToA of the direct path. During the localization window, twoway ToA measurements for the link (UN,l) are obtained by piggybacking the ToA information estimated by node l on packets transmitted from node l to the UN, along with node l s time-varying location, p i. These measurements are used

3 1 D UTM coordinate p 1 node m node l j 1 j p u 1 j 3 k time [sec] Fig. 1: Illustration of the quantized location representation. to estimate the clock skew and offset of the UN relative to node l s internal clock and to estimate the propagation delay in the channel. Following this step, the time-varying location information of the anchor nodes and the motion vectors measured by the UN are used to estimate location j N. In the following we describe the details of our algorithm starting from the quantization procedure of the spatial domain and followed by the time-synchronization and the localization steps. A. Quantized Representation of Node Movements In this section we describe the quantization procedure in which ToA measurements are matched with the locations of the anchor nodes and the UN to obtain two-way ToA measurements. Consider two packets arriving to the UN from anchor node l at local times t UN (i) and t UN (i ) which include the location of node l during their transmissions, p i and p i, respectively. The UN regards locations p i and p i as two different locations if the distance between the two exceeds a threshold, T h. More specifically, if p i p i > Th, then p i and p i are considered as separate quantized locations, u ν and u ν, respectively. Otherwise, they are mapped onto the single quantized location, u ν. Similarly, if d n,n [see (1)] is larger than T h, the UN considers positions j n and j n estimated by its DR system at local times t UN (n) and t UN (n ) as two separate quantized locations, k ρ and k ρ, respectively. Otherwise, they are mapped to a single location k ρ. The recording times of the quantized locations u ν and k ρ are determined as an average between the recording times of packets arriving at the beginning and ending of the quantized location. For the latter case in the above example, the recording time of the joint quantized location k ρ is ˆt UN (ρ) = tun(n)+tun(n ). Since we are using a sequential approach to first timesynchronize nodes and then localize the UN, there is a tradeoff for choosing T h in the above quantization procedure. If T h is too large, the accuracy of the time-synchronization process decreases, while if it is too small there might not be enough twoway ToA measurements for each pair of quantized locations u ν and k ρ, and again accuracy of the time-synchronization process decreases, as we further discuss below. Using the above quantization procedure we can readily match ToA measurement of a packet received at the UN s with the locations of its transmitter and receiver. Consider, for example, three different quantized locations of node l, u ν, u ν+1 and u ν+, recorded by the UN at local times t UN (ν), t UN (ν+1) and t UN (ν+). Also consider three different quantized locations of the UN, k ρ, k ρ+1 and k ρ+, recorded at local times ˆt UN (ρ), ˆt UN (ρ +1) and ˆt UN (ρ +), respectively. We match the ToA measurement of the packet to the transmitter quantized location u ν+1 if ˆt UN(ν)+ˆt UN(ν+1) local timet Rx UN t Rx UN ˆt UN(ν+1)+ˆt UN(ν+). Similarly, we match the ToA measurement of the packet to the receiver quantized location k ρ+1 if ˆt UN(ρ)+ˆt UN(ρ+1) t Rx UN ˆt UN(ρ+1)+ˆt UN(ρ+). Next, we use the matched ToA measurements to timesynchronize the network nodes. B. Step 1: Time-Synchronization The objective of the time-synchronization step of the algorithm is to estimate the propagation delay,t pd, for signals transmitted between locations p i and j n of anchor node l and the UN, respectively. Since nodes are not time-synchronized, to this end we first estimate the clock skew and offset of the UN relative to anchor node l and then estimate the T pd. Denote T a (v) and R a (v) as the transmission and reception local times of the vth packet transmitted from node l at location p i and received by the UN at location j n, and T b (q) and R b (q) as the transmission and reception local times of the qth packet transmitted from nodel at locationp i and received by the UN at location j n, respectively. That is, for the signal propagation delays T pd (i,n) and T pd (i,n ), we can write equations of the form R a (v) = S l (T a (v)+t pd (i,n)+γ a (v))+o l T b (q) = S l (R b (q) T pd (i,n ) γ b (q))+o l, (a) (b) respectively, whereγ a (v) andγ b (q) are the ToA measurementnoise samples at locations j n and p i, respectively, assumed to be zero mean i.i.d. random variables. Recall that since packets are transmitted at the beginning of a time slot, the UN is aware of T a (v) by matching the received packet with its corresponding time slot. Thus, by measuring R a (v) and recording T b (q), and by obtaining R b (q) via communications with anchor nodel, for each anchor nodel and for each pair of packets v and q, the UN is able to construct equations of the form of (a) and (b). Although our main objective in this step is to estimate the single propagation delay, we first estimate S l and O l. This is because T pd (i,n) is different for each pair of locations p i and j n, and thus the number of equations of the form of (a) is small resulting in low accuracy when directly estimating T pd (i,n). For locations p i and p i mapped onto the same quantized location u ν, and for locations j n and j n mapped onto the same quantized location k ρ, we neglect the differences between the propagation delays T pd (i,n) and T pd (i,n ) in

4 (a) and (b). We assume that this mapping results into M pairs of equations (), wherem increases witht h. Then, since S l and O l are assumed to be time invariant, (a) and (b) can be turned into M equations of the form R a (v) O l T a (v) γ a (v) = O l T b (q) +R b (q) γ b (q). S l S l (3) Introducing the variable vector θ l = [ 1 S l, O l S l ] T, we express (3) as the linear equation B l θ l = b l +ǫ l (4) for each anchor node l, where B l is an [M ] matrix with rows [R a (v)+t b (q), ], and b l and ǫ l are column vectors of appropriate length with elements R b (q)+t a (v) and γ a (v) γ b (q), respectively. Next, the UN applies the LS estimator ( 1B ˆθ l = B T l l) B T l b l (5) for each anchor node l to obtain the estimates Ôl and Ŝl. Using Ôl and Ŝl from (5), the UN estimates the signal propagation delay for each pair of locations p i and j n a ˆT pd (i,n) = 1 M C. Step : Localization M R a (v) v=1 Ŝ l Ôl Ŝ l T a (v). (6) The objective of the localization step of the algorithm is to estimate coordinates jn x and jy N visited by the UN at the end of the localization window W. Consider a location j n, n N, and corresponding motion vector ω(n,n) [see (1)]. Let R N and R n be the sets of cardinality R N and R n which include locations p i and p i for which ˆT pd (i,n) and ˆT pd (i,n) were estimated using (6), respectively (note that these locations are not restricted to be locations of the same anchor node l). Then, for a given constant sound speed in water, c, we get T pd (i,n) = 1 c j N p i T pd (i,n) = 1 c j n p i d N,n = j N j n tan(ψ N,n ) = jy N jy n j x N jx n (7a) (7b) (7c). (7d) To estimate j N we first estimate the variable vector ζ N = [ T (jn x ) +(j y N ),jn N] x,jy d. Denote αn,n = N,n 1+tan( ψ N,n) and β N,n = α N,n tan( ψ N,n ) and assume d N,n = d N,n and ψ N,n = ψ N,n (recall that we rely on the accuracy of the motion vectors during the localization window). Also denote v(i,n) = ( T pd (i,n)+η(i,n) ) and v(i,n) = ( T pd (i,n)+η(i,n) ), where η(i,n) and η(i,n) are the noise components of the propagation delay estimations ˆT pd (i,n) and ˆT pd (i,n), respectively, assumed to be zero mean i.i.d. random variables with unknown variance σ. Since c is unknown, for each index n and locations p i and p i, we divide (7a) by (7b) to obtain R = N 1 of the form n=1 R N R n equations µ ζ N = v(i,n) ( (p x i α N,n ) +(p y i β N,n) ) ( v(i,n) (p x i ) +(p y i )), (8) where µ = [µ 1,µ,µ 3 ] with µ 1 = v(i,n) v(i,n), µ = v(i,n)(p x i α N,n) v(i,n)p x i and µ 3 = v(i,n)(p y i β N,n) v(i,n)p y i. Settingv(i,N) = ˆT pd (i,n) and v(i,n) = ˆT pd (i,n), we construct an [R 3] matrix A N with rows [µ 1,µ,µ 3 ] and vector b N with elements of the form of the right hand side of (8). Thus, defining an error vector e N including the remaining noise components, the R equations (8) can be arranged in the matrix form A N ζ N = b N +e N. (9) We observe that the elements of the error vector e N are a function of the system variables ζ N. Thus, direct estimation of ζ N from (9) will result in low accuracy. Hence, we follow [13] and offer a two-step heuristic approach in which first we get a rough estimate of ζ N, and then we perform a refinement step. The rough estimate is given by ˆζ LS N = ( A T NA N ) 1AN b N. (10) We note that the covariance matrix σ Q N of e N is a diagonal matrix whose ith diagonal element is equal to the square of the ith element of e N. Thus, using ˆζ LS N from (10) to estimate e N, we construct the estimated covariance matrix, ˆQ N. Using ˆQ N, the refined estimate of ζ N follows as ( ) ˆζ WLS N = A T 1 1AN N ˆQ N A N ˆQ 1 N b N, (11) with the error covariance matrix [14] ( ˆQ N = A T 1 1 N ˆQ N N) A. (1) Finally, we use the inner connection of the elements of ζ N to estimate the location vector j N. Defining G N = ˆζ N WLS () ˆζWLS N (3) WLS 1 0, where ˆζ N (i) is the ith element of 0 1 ˆζ WLS N, we obtain G N jn = ˆζ WLS N +ǫ N, (13) where ǫ N is a [3 1] estimation noise vector of ˆζ WLS N (13), ˆQ N from (1) and of j N is ĵ N = ˆζ WLS N. Using from (11), the WLS estimator ( ) G T 1 1GN N ˆQ N G N ˆQ 1 WLS N ˆζ N, (14) whose elements ĵ N (1) = ĵn x and ĵ N () = ĵ y N are the desired location coordinates.

5 IV. RESULTS To evaluate the performance of our algorithm, we conducted 10, 000 Monte-Carlo simulations. The simulations included two anchor nodes and one unlocalized node for a fixed localization window of W = 60 time slots, where the time-slot duration was 5 seconds considering the long propagation delay in the channel (e.g., 4 sec for 6 Km). The three nodes were placed at random positions in a square area of meters and moved at random speed, not exceeding 5 knots, and in random direction from their previous location. We used a threshold value of T h = 38 meters to quantize locations (see Section III-A). To simulate errors we added a zero mean i.i.d. Gaussian noise with variance σ to each of the ToA estimations. Considering the results in [3] we added a zero mean i.i.d. Gaussian noise with variance 1 m to each of the distance elements of the motion vectors [see (1)] while regarding their angle components to be accurate. Furthermore, to simulate time-synchronization errors the clock of each of the three nodes had a Gaussian distributed random skew and offset relative to a common clock with mean values 1 and 0 sec and variances and 0.5 sec, respectively. We compare the localization accuracy of the algorithm with that of the multilateration method [15] and that of the method proposed in [13], which we refer to as the joint protocol. Both benchmark methods require a given propagation speed c. Furthermore, while the joint protocol performs joint time-synchronization and localization (assuming anchor nodes are time-synchronized), the multilateration method assumes all nodes to be time-synchronized. Since both benchmark methods do not regard movements in the channel, we used a different simulation environment for the two benchmark methods such that a fair comparison with the algorithm is possible. The simulation environment for the benchmark methods considers fixed nodes and adds virtual anchor nodes according to nodes movements in the original simulation scenario (i.e., the one used to test the performance of the algorithm). Consider, for example, an anchor node l moving between locations p 1 and p while communicating with the unlocalized the UN, located in j n. To test the benchmark methods, such a scenario would change into a scenario where two static anchor nodes, l 1 and l, are located in p 1 and p, respectively. Allowing a fair comparison between the three tested localization methods, the added (virtual) anchor nodes, l 1 and l, have the same local clock as that of the real anchor node l. The three methods are compared in terms of the localization error of the unlocalized the UN, j N ĵn. Recall that the quantization procedure is used only for the estimation of Ôl andŝl and not for the estimation of ˆT pd (i,n) which is later used in the localization step. Thus, localization accuracy of the algorithm is not limited to T h. First, we consider a scenario where the sound speed is fixed at a nominal value of c = 1500 m/sec, given to the two benchmark methods but not to the algorithm. Figure shows the average estimation error as a function of 1/σ when nodes are perfectly time-synchronized. As expected, / σ [db] Fig. : Average estimation error vs. 1/σ. Sound speed is constant and all nodes are time-synchronized S(l)W + O(l) [sec] Fig. 3: Average estimation error vs. S l W +O l (l = 1). Constant sound speed, non-synchronized nodes, 1/σ = 35 db. the results show that both multilateration and joint protocol methods achieve better performance than our algorithm. This is mainly due to the fact that both benchmark methods have more information than the algorithm (i.e., c is known), and also because of estimation errors in the timesynchronization step performed by the algorithm (even though such synchronization is not required in the considered scenario). The latter is also the reason why the multilateration method achieves slightly better performance than the joint protocol method. In Figure 3 we compare the performance of the three methods when all nodes are not time-synchronized for 1/σ = 35 db as a function of S l W + O l for l = 1. Here, we observe that while the performance of the algorithm is almost unaffected by the synchronization error (compared with the results in Figure ), the joint protocol method, designed for time-synchronized anchor nodes, and the multilateration method suffer from significant estimation errors even for small synchronization errors. We now compare the performance of the three methods when the sound speed, c, varies. For this scenario, the sound speed was sampled from a uniform distribution between 140

6 Sound speed in water [m/sec] Fig. 4: Average estimation error vs. sound speed. Timesynchronized node, and 1/σ = 35 db / σ Fig. 5: Average estimation error vs. 1/σ for timesynchronization and sound speed uncertainties. and 1560 m/sec, while the two benchmark methods were still given the nominal value of c = 1500 m/sec. To understand the effect of the varying sound speed on localization accuracy, we first compare the results when all nodes are time-synchronized. The results are shown in Figure 4 as a function of c, again for 1/σ = 35 db. We observe that the estimation errors of the multilateration and the joint protocol methods are becoming significant even for a small difference of 10 m/sec between the nominal and actual sound speed, which motivates the need to estimate the sound speed in water. However, the performance of the algorithm is hardly affected by the varying sound speed. Finally, in Figure 5 we show the estimation errors of the three methods as a function of 1/σ for the practical case where all nodes are not time-synchronized and the sound speed is unknown, averaged over time-synchronization offset and skew and over random sound speed. From the results we observe that while both multilateration and joint protocol methods suffer from significant localization error floor, the performance of the algorithm is similar to that in Figure. Hence, it fully compensates both synchronization and propagation speed uncertainties. V. CONCLUSIONS In this paper we considered UWAL in the practical scenario where nodes are not time-synchronized and are permanently moving, and where the sound speed in water is unknown. We introduced a sequential time-synchronization and localization algorithm which relies on the existence of a navigation system that self-estimates the motion vector of nodes in short periods of time. The algorithm utilizes the constant movements of nodes in the channel and relies on packet exchange to acquire multiple ToA measurements at different locations. Our simulation results showed that our algorithm compensates both time-synchronization and propagation speed uncertainties, and achieves a reasonable localization accuracy even for small number of anchor nodes. Further work would include a real sea trial to verify our assumptions. REFERENCES [1] M.Chitre, S.Shahabodeen, and M.Stojanovic, Underwater acoustic communications and networking: Recent advances and future challenges, in Marine Technology Society Journal, vol. 4, no. 1, Garmish- Partenkirchen, Germany, Apr. 008, pp [] J. Weber and C. Lanzl, Desigining a positioning system for finding things and people indoors, in IEEE Spectrum, vol. 35, no. 9, Sep. 1998, pp [3] C. Lee, P. Lee, S. Hong, and S. Kim, Underwater navigation system based on inertial sensor and doppler velocity log using indirect feedback kalman filter, in Journal of Offshore and Polar Engineering, vol. 15, no., jun 005, pp [4] R. Hartman, W. Hawkinson, and K. Sweeney, Tactical underwater navigation system (TUNS), in IEEE/ION Position, Location and Navigation Symposium, Fairfax, Virginia, USA, May 008, pp [5] V. Chandrasekhar, W. K. Seah, Y. S. Choo, and H. V. Ee, Localization in underwater sensor networks - survey and challenges, in Proc. of ACM International Conference on Mobile Computing and Networking (MobiCom), New York, NY, USA, Sep. 006, pp [6] J. Partan, J. Kurose, and B. Levine, A Survey of Practical Issues in Underwater Networks, in International Conference on Mobile Computing and Networking (MobiCom), Los Angeles, CA, USA, Sep [7] W. Burdic, Underwater Acoustic System Analysis. Los Altos, CA, USA: Peninsula Publishing, 00. [8] M. Erol, H. Mouftah, and S. Oktug, Localization techniques for underwater acoustic sensor networks, in IEEE Commun. Mag., vol. 48, no. 1, 010, pp [9] H. Tan, R. Diamant, W. Seah, and M. Waldmeyer, A survey of techniques and challenges in underwater localization, Accepted for Publication in the ACM Journal of Ocean Engineering [Online: [10] J. Garcia, Adapted distributed localization of sensors in underwater acoustic networks, in MTS/IEEE international Oceans conference, Singapore, May 006. [11] J. Zheng, K. Lui, and H. So, Accurate three-step algorithm for joint source position and propagation speed estimation, in Journal of Signal Processing, vol. 87, Dec. 007, pp [1] A. Syed and J. Heidemann, Time synchronization for high latency acoustic networks, in Proc. of IEEE Conference on Computer Communications (Infocom), Barcelona, Spain, Apr [13] J. Zheng and Y. Wu, Joint time synchronization and localization of an unknown node in wireless sensor networks, in IEEE Transactions on Signal Processing, vol. 58, no. 3, Mar. 010, pp [14] S. Kay, Fundamentals of Statistical Signal Processing: Estimation Theory. Englewood Cliffs, NJ: Prentice-Hall, [15] J. Zheng and Y. Wu, Localization and time synchronization in wireless sensor networks: A unified approach, in IEEE Asia Pacific Conf. on Circuits and Sys., Macao, China, Nov. 008.