Underwater Localization with Time-Synchronization and Propagation Speed Uncertainties

Transcription

1 Underwater Localization with Time-Synchronization and Propagation Speed Uncertainties 1 Roee Diamant and Lutz Lampe University of British Columbia, Vancouver, BC, Canada {roeed,lampe}@ece.ubc.ca Abstract Underwater acoustic localization (UWAL) is a key element in most underwater communication applications. The absence of GPS as well as the signal propagation environment make UWAL similar to indoor localization. However, UWAL poses additional challenges. The propagation speed varies with depth, temperature and salinity, anchor and unlocalized nodes cannot be assumed time-synchronized, and nodes are constantly moving due to ocean currents or self motion. Taking these specific features of UWAL into account, in this paper we describe a new sequential algorithm for joint time-synchronization and localization for underwater networks. The algorithm is based on packet exchanges between anchor and unlocalized nodes, makes use of directional navigation systems employed in nodes to obtain accurate short-term motion estimates, and exploits the permanent motion of nodes. Our solution also allows selfevaluation of the localization accuracy. Using simulations, we compare our algorithm to two benchmark localization methods as well as to the Cramér-Rao bound. The results demonstrate that our algorithm achieves accurate localization using only two anchor nodes and outperforms the benchmark schemes when node synchronization and knowledge of propagation speed are not available. Moreover, we report results of a sea trial where we validated our algorithm in open sea. Index Terms Underwater acoustic localization (UWAL), propagation speed uncertainties, time-synchronization.

2 2 I. INTRODUCTION Underwater acoustic localization (UWAL) has recently attracted much attention due to advances of technology enabling reliable and efficient underwater acoustic communication (UWAC) [1]. Applications such as environmental monitoring, navigation or command and control systems typically include several autonomous nodes with UWAC capabilities and require accurate localization of these nodes. Localization also improves routing capabilities and scheduling in UWAC networks. Since GPS signals are highly attenuated underwater, UWAL is a difficult task with similarities to indoor localization [2]. Our setting includes several reference nodes at known locations, also called anchor nodes, and one or more unlocalized (UL) node, whose location is estimated. We assume that UL nodes are equipped with means to self-evaluate their speed and direction such as accelarometer and compass. Since such inertial systems are relatively light weight and inexpensive, there is a large variety of applications that satisfy this assumption for UL nodes. These include unmanned underwater vehicles (AUV), remotely operated underwater vehicles (ROV), manned vehicles, and divers. While inertial systems could also be used for self-localization, e.g., [3], [4], these systems often suffer from low accuracy due to accumulated errors when used stand alone [5]. Therefore, UWAL is often based on ranging using packet exchange [5]. Since node depth can be self-estimated, e.g., using pressure probes, we are interested in twodimensional (2-D) UWAL. Such localization requires ranging to at least three anchor nodes. However, since transmission range is limited and since network topology may be sparse, a sensor or network 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 always-accurate attenuation models for the underwater acoustic channel are not available, and AoA methods require multiple hydrophones, most approaches for UWAL rely on ToA or TDoA for distance estimation [7]. Several works suggested obtaining TDoA measurements by sequentially generating packets from anchor nodes, where the anchor-

3 3 to-anchor distance is known, allowing the UL node to remain silent and not requiring either the UL node or the anchor nodes to be time-synchronized [8], [9], [10]. However, due to unpredictable multiple access control (MAC) delays, an anchor node might not be able to respond immediately upon detecting a localization packet, thus significantly decreasing the accuracy of TDoA measurements. In these cases, ToA-based localization seems more suitable. ToA measurements tend to be noisy due to synchronization errors (caused by node clock skew and offset) and multipath. Assuming the availability of multiple ToA measurements at a static UL node, [10] suggested using least squares (LS) estimators to mitigate such noise. Unfortunately, this makes the system even more sensitive to node movements. While several protocols have been suggested to compensate for node movements, either by regarding these movements as ToA noise or by applying mobility prediction [6], these approaches consider node movements as an undesired phenomenon and do not utilize the possibility of additional ToA measurements when coupled with self-localization. Another significant challenge of UWAL is the variability of the propagation speed in water as it depends on water temperature, depth and salinity [11]. Considering this problem, [12] suggested to first estimate the propagation speed using packet exchange between floating buoys on the seabed and the sea surface. Alternatively, several works suggested propagation speed estimation based on measuring the channel characteristics and a sound speed model, e.g., [13], [14]. Differently, [15] suggested to jointly estimate the node location and the propagation speed in the channel by considering the propagation speed as an additional variable. However, they made 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, also clock skew cannot be neglected for UWAL due to the long propagation delay in the underwater channel [16]. Furthermore, since anchor nodes are usually submerged we cannot assume these nodes to be time synchronized. Regarding this problem, [16] suggested to estimate both skew and offset based on packet exchange with an already synchronized node. For terrestrial networks, [17] suggested to jointly synchronize and localize nodes by exchanging packets with anchor nodes to measure ToA in the channel, and applying a sequence of LS and weighted LS (WLS) estimators. However, since they assume that the propagation speed is known and that

4 4 anchor nodes are time-synchronized, this work cannot be directly applied in UWAL. In this paper, we propose a new algorithm for UWAL that overcomes the shortcomings of the above-mentioned solutions. In particular, our algorithm takes into account anchor and UL node mobility as well as propagation speed uncertainties, can function with only one anchor node, and includes time-synchronization of nodes. These abilities are important to enable localization under varying conditions, such as static or mobile nodes, in shallow or deep water, and when nodes are submerged for short or long periods of time. Operating in tandem with self-localization systems, our algorithm makes use of the permanent movements of underwater nodes. It also performs a self-evaluation of localization accuracy, by estimating the propagation speed and checking its validity, relying on known model boundaries for it. According to the structure of the proposed algorithm we refer to it as sequential time-synchronization and localization (STSL) algorithm. We demonstrate the advantages of the STSL algorithm by simulative comparisons with two benchmark localization methods, which reveal significant localization errors for the latter if nodes are not time-synchronized or the propagation speed is not accurately estimated. Furthermore, we formalize the Cramér-Rao lower bound for UWAL and show that it is well approached by the STSL algorithm. Considering the problem of accurately modeling the underwater acoustic channel in a simulation environment, we also conducted a sea trial in August 2010 in Haifa, Israel, and present results that confirm the performance of the proposed algorithm under real conditions. The remainder of this paper is organized as follows. In Section II, we briefly summarize the general structure of our algorithm and the intuition behind it. In Section III, we introduce the system model, followed by a detailed description and discussion of our STSL algorithm in Section IV. Cramér-Rao lower bounds pertinent to our problem are derived in Section V. Simulation and sea trial results are presented and discussed in Sections VI and VII, respectively. Finally, conclusions are drawn in Section VIII. The notations used in this paper are summarized in Table I. II. STSL INTUITION The intuition behind our approach is the use of relative speed and direction information available at the mobile UL node to compensate for node mobility. In doing so, three or more range measurements obtained at different times and locations can be combined for 2-D localization.

5 5 TABLE I: List of major notations Notation L j i p i c W N S l O l T i T i R i Explanation Number of anchor nodes directly connected to the UL node 2-D UTM coordinates of the UL node at the time it transmits or receives the ith packet. 2-D UTM coordinates of the lth anchor node at the time it transmits or receives the ith packet. Sound speed in water [m/sec] Duration of the localization window Number of packets transmitted during the localization window Clock skew of the UL node relative to the lth anchor node Clock offset of the UL node relative to the lth anchor node [sec] Propagation delay of the ith packet [sec] Transmission local time of the ith packet [sec] Reception local time of the ith packet [sec] d i,i Self estimation of distance between locations j i and j i ψ i,i Self estimation of angle between locations j i and j i [rad] Threshold for location quantization [m] σ 2 variance of ToA measurement noise [sec 2 ] ς li Ratio between T i (according to anchor node l i -th local clock) and the actual propagation delay of packet i This approach allows us to readily include the localization procedure as part of the operation of a communication network. More specifically, instead of using designated localization packet exchange (which is necessary if node mobility is not compensated), we rely on periodic packet exchange between the network nodes. This characteristic renders our approach more flexible and easy to integrate into a UWAC system and also reduces communication overhead. The STSL algorithm uses a two-step approach, in which first nodes are time-synchronized and then location is estimated. In both steps, the measured time of flight of packets exchanged between anchor and UL nodes and self-localization data obtained at UL nodes are linked to the unknown location, synchronization (clock skew and offset), and propagation speed parameters through linearized matrix equations. Our algorithm is modular in the sense that both timesynchronization and localization steps can be readily replaced with alternative solutions (as we do in this paper to benchmark the STSL performance). Before describing the STSL algorithm in detail, we next present the system model and assumptions used in this work.

6 6 III. SYSTEM SETUP AND ASSUMPTIONS Our setting includes one or more UL nodes directly connected to L 1 anchor nodes, which have means to accurately measure their time-varying 2-D location and transmit it to the UL node. Both UL and anchor nodes operate in a time-slotted UWAC network, where nodes transmit at the beginning of globally established time slots as in, for example time division multiple access (TDMA) [18], slotted handshake [19] or slotted Aloha [20] transmission 1. Since UL nodes perform localization independently of each other, we consider localization of one UL node in the following. We are interested in estimating the 2-D location of the UL node in terms of the universal transverse mercator (UTM) coordinates j N = [jn x, jy N ]T (the subscript N becomes clear below) after a pre-defined localization window of duration W time-slots, which without loss of generality starts at the UL node local time t UL = 0. We assume that nodes are not time-synchronized. Suppose that the local time at the UL node t UL corresponds to the time t l according to the local clock of anchor node l, and let S l and O l denote the clock skew and offset of the UL node relative to node l, l = 1,..., L, which are constant within the localization window. Then, t UL = t l S l + O l. (1) We assume that the time-synchronization error is small relative to the globally established timeslot duration, such that a node can match a received packet with the time slot it was transmitted in. Thus, local transmission times of received packets are known and time stamps of packets are not required. We note that long time slots are common in UWAC [1] due to the low propagation speed underwater, which is modeled between 1420 m/sec and 1560 m/sec [11]. For localization we rely on a two-way packet exchange between the anchor nodes and the UL node. Let N be the total number of packets exchanged between the UL node and the L anchor nodes during the localization window W. For convenience, we define the sets N a and N b for enumerating the packets to and from the UL node, respectively, such that N a N b = N = {1,..., N}. Denote l i the index of the anchor node that transmits (i N a ) or receives (i N b ) the ith packet, and T i and R i the transmission and reception local times of this packet. Also 1 We note that a relaxation of this assumption is possible by having anchor nodes time-stamp their packets, thereby informing the UL node of the transmission time.

7 7 denote T i the propagation delay for packet i according to local clock of anchor node l i. (Note that the propagation delay according to the clock of the UL node is T i S li ). Consider packet i N a transmitted at local time T i and detected by the UL node at anchor node l i local time T i + T i + γ i, where γ i is a propagation-delay-measurement-noise sample. Also, consider packet i N b received by anchor node l i at local time R i + γ i and transmitted at anchor node l i local time R i + γ i T i. Then, following the relation in (1), the above time variables are related by R i = S li (T i + T i + γ i ) + O li, i N a (2a) T i = S li (R i + γ i T i ) + O li, i N b. (2b) Since for i N a the UL node measures R i and is aware of T i via packet association (recall we assume transmissions in globally established time slots), and since for i N b the UL node records T i and is informed of R i through communication with anchor node l i, the UL node is able to construct equations (2a) and (2b). For mathematical tractability and formulating a practicable algorithm, we assume that the noise γ i is a zero-mean i.i.d. Gaussian random variable with variance σ 2. Since more complicated models, such as mixture models with one component having non-zero mean, would likely be a more faithful noise representations, we study the effect of model mismatch in Section VI. Considering a dynamic scenario in which all nodes permanently move either by own means or by ocean current, we assume that the UL node uses an inertial system to self-estimate its speed and direction. During the localization window, the inertial system provides N position estimations j i = [ j x i, j y i ]T for the true locations j i of the UL node at the time of transmission (i N b ) or reception (i N a ) of the ith packet. These locations are translated into a series of motion vectors, ω i,i = [ d i,i, ψ i,i ] T, where d i,i and ψ i,i are the distance and angle between two self-estimated locations j i and j i, 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 i,i are d i,i = j i j i 2, tan( ψ i,i ) = j y i j y i j x i j x i. (3) While we do not directly use the self-estimated locations j i, whose errors accumulate with time, we rely on the accuracy of the motion vectors for all packet pairs i, i transmitted or received by the UL node during the localization window. That is, we assume that for i, i N the estimated

8 8 distance d i,i equals the true distance d i,i and that ψ i,i equals the true angle ψ i,i. We note that this assumption sets limits on the value of W, which is determined by the specifications of the inertial system in use. We are now ready to present the STSL algorithm for UWAL. IV. THE STSL ALGORITHM We are interested in accurately estimating the position j N of the UL node at the end of the localization window. In this section we first formalize the optimization problem for estimating j N, using ToA measurements obtained from received packets and taking into account inertial system information. Then, we derive a sub-optimal solution, namely the STSL algorithm, in which first nodes are time-synchronized and then localization is performed. According to the system description in the previous section, the location p i of anchor node l i when transmitting (i N a ) or receiving ( i N b) the ith packet, the transmission and reception local times T i and R i, respectively, and the motion vector ω i,i between locations j i and j i are available at the UL node. Hence, denoting the propagation speed c, the UWAL problem can be formulated as ĵ N = arg min j N i N ( ς li T i 1 c j i p i 2 ) 2 (4a) s.t. 1420m/sec c 1560m/sec (4b) where the factor ς li R i = S li (T i + T i ) + O li, i N a (4c) T i = S li (R i T i ) + O li, i N b (4d) d i,i = j i j i 2, i, i N (4e) tan( ψ i,i ) = jy i jy i j x i jx i, i, i N, (4f) in (4a) accounts for the difference between T i (according to anchor node l i local clock) and the actual propagation delay of packet i. Note that problem (4) is different from conventional localization problems due to the time-synchronization constraints (4c) and (4d), and due to the unknown sound speed c. Since (4) is a non-convex problem, we device our STSL algorithm as a pragmatic solution to the localization problem at hand, and we will compare its performance to the Cramér-Rao lower bound (CRLB) associated with estimating the desired location j N as well as the unknown parameters S l and O l, l = 1,..., L, and c.

9 9 In the following we describe the details of our STSL algorithm starting from the timesynchronization step and followed by the localization step. A. Step 1: Time-Synchronization The objective of the time-synchronization step is to provide estimates of the propagation delays T i, i N. This is accomplished by two-way packet exchange, obtaining equations of type (4c) and (4d). However, due to the permanent motion of nodes in the channel, propagation delays T i, i N a, and T j, j N b, might not be equal, and thus (4c) and (4d) cannot be readily compared. Common time-synchronization approaches for UWAC deal with this problem by letting the receiving node respond immediately to limit any possible movements (e.g., [16]). However, such a requirement limits the scheduling protocol. We choose a different approach and apply a quantization mechanism to allow for differences in the propagation delay of separate packets and to enable time-synchronization per anchor node making use of the ongoing network communications. 1) Quantized Representation of Node Movements: In the quantization step, the locations of the UL node and the anchor nodes are quantized so that multiple ToA measurements from two-way communication are associated with the same pair of quantized locations. More specifically, consider the two packets n, m, n N a, m N b. If the two sets of UL node locations j n, j m and anchor node locations p n, p m with l n = l m = l are associated with the same quantized location k ρ and u l,ν of the UL node and anchor node l, respectively, we assume that T n = T m and (2a) and (2b) can be combined as we show further below. The variables ν and ρ are used to enumerate quantized locations. To quantize the locations of anchor nodes, we introduce subsets U l,ν N including all packets associated with the same anchor node l such that for each pair of packets n, m U l,ν, p n p m 2 <, where is a fixed threshold. Next, we associate location p i, i U l,ν, with the quantized location u l,ν. Similarly, to quantize locations of the UL node we form subsets of packets K ρ N such that for each pair of packets n, m K ρ, d n,m <, and associate location j i, i K ρ, with the quantized location k ρ. We note that a single packet can be associated with multiple subsets U l,ν and K ρ.

10 10 There is a tradeoff for choosing. If is too large, the assumption of identical propagation delay is notably flawed and thus the accuracy of the time-synchronization process is low. If is too small, there might not be enough two-way ToA measurements associated with each pair of quantized locations u l,ν and k ρ, and again accuracy of the time-synchronization process is degraded, as we further discuss below. 2) Estimating the Clock Skews and Offsets: We now use the quantized locations to estimate clock skews S l and offsets O l, l = 1,..., L. Let us define subsets N a l N a and Nl b N b, with cardinality Nl a and Nl b, respectively, including all packets associated with anchor node l. Consider the pair of packets n, m, n N a l, m N b l, for which locations p n and p m are mapped onto the same quantized location u l,ν, and locations j n and j m are mapped onto the same quantized location k ρ. We assume that for each anchor node l, this mapping results into M l pairs of equations (2a) and (2b). Clearly, M l increases with the quantization threshold,. As stated above, we neglect the differences between the propagation delays T n and T m in (2a) and (2b) and thus obtain M l equations of the form R n + T m S l 2O l S l = T n + R m + γ n + γ m, n N a l, m N b l. (5) Note that equations of type (5) are introduced separately for each anchor node l. This is because the estimated clock skew and offset are different for each l. Introducing the variable vector θ l = [θ l (1), θ l (2)] T = [ 1 S l, O l S l ] T, we express (5) as the linear matrix equation B l θ l = b l + ϵ l (6) for each anchor node l, where B l is an [M l 2] matrix with rows [R n + T m, 2], and b l and ϵ l are column vectors of appropriate length with elements T n + R m and γ n + γ m, respectively, with n Nl a, m N l b. Next, we apply the LS estimator ˆθ l = ( B T l B l ) 1 B T l b l (7) for each anchor node l. By (7), the covariance matrix of ˆθ l is [21] Q θ = 2σ 2 ( B T l B l ) 1, (8)

11 11 whose main diagonal elements are proportional to 1 M l and 1, respectively. Hence, for large M Ml 2 l the estimates ˆθ l (1) and ˆθ l (2) are expected to have much smaller variance than σ 2. 3) Estimating Propagation Delays: After estimating θ l (1) and θ l (2), the quantized locations are no longer in use and we return to our initial objective, which is to estimate the propagation delay. Thus, localization accuracy of the STSL algorithm is not limited to. Considering (2), for packets n N a l the UL node estimates the propagation delay as ˆT n = R nˆθl (1) ˆθ l (2) T n, n Nl a and m N b l, ˆT m = ˆθ l (2) T mˆθl (1) + R m, m N b l. (9) We observe from (9) that the propagation delay estimation error is a function of both ToA measurement error, γ i, and clock skew and offset estimation errors. However, since during the localization window R n and T n are bounded by W, the variances of R nˆθl (1) ˆθ l (2), n N a l, and ˆθ l (2) T mˆθl (1), m Nl b, are expected to be much smaller than σ2. Thus, we use the approximation ˆT i = T i + γ i in the following. B. Step 2: Localization We now introduce the localization step of the STSL algorithm. This step is performed immediately after time-synchronization, using propagation delay estimations (9). The objective of the localization step of the STSL algorithm is to estimate the UL node UTM coordinates j x N and j y N at the end of the localization window W. For this purpose, we adopt the common approach to linearize the estimation problem [17], and first estimate the transformed variable [ T vector ζ N = (jn x )2 + (j y N )2, jn N] x, jy. Define α i,i = d i,i β i,i = α i,i tan( ψ i,i ), (10) 1 + tan( ψ i,i ) 2 and assume d i,i and ψ i,i in (3) to be equal to d i,i and ψ i,i from (4), respectively (recall that we rely on the accuracy of the motion vectors during the localization window). Thus, j x i = jx i α i,i, j y i = j y i β i,i, i, i N. (11)

12 12 Furthermore, we have from (4) that ˆT i = 1 ς li c j i p i 2 + γ i, i N. (12) Since c is unknown, and assuming small differences between ς l such that ς l ς l = 1, l, l = 1,..., L (a relaxation of this assumption is given further below), we reduce the set of N equations (12) to N 1 equations, which together with (11) can be written as with vector µ N,i = [µ N,i (1), µ N,i (2), µ N,i (3)], where ( ) 2 ( a N,i = ˆT i (p x N) 2 + (p y N )2) µ N,i (1) = µ N,i (2) = 2 µ N,i (3) = 2 ( ˆT N ( ˆT i ( ˆT i µ N,i ζ N = a N,i + ϵ N,i, i =..., N 1 (13) ) 2 ( ) 2 ˆT i, ) 2 p x ( ) 2 ˆT N (p x N 2 ) 2 ( p y N 2 ˆT N ( ˆT N ) 2 ( (p x i + α N,i ) 2 + (p y i + β N,i) 2), i + α N,i ), ) 2 (p y i + β N,i), (14) and ϵ N,i is the noise component originating from the noisy estimations (9). For the localization window W, we construct an [(N 1) 3] matrix A with rows µ N,i and vectors a and ϵ with elements a N,i and ϵ N,i, respectively. Then, the (N 1) equations (13) are arranged in Aζ N = a + ϵ. (15) The elements of the error vector ϵ depend on the elements of ζ N. Thus, direct estimation of ζ N from (15) will result in low accuracy. Hence, we follow [17] and offer a two-step heuristic approach in which first we get a coarse estimate of ζ N, and then we perform a refinement step. The coarse estimate is given by ˆζ LS N = ( A T A ) 1 Aa. (16) We note that ϵ N,i from (13) can be formalized as γ i f N,i, where f N,i is a function of the elements of ζ N, not given here for brevity. Thus, ϵ N,i are i.i.d random variables and the covariance matrix σ 2 Q N of ϵ is a diagonal matrix whose ith diagonal element equals σ 2 fn,i 2 LS. Using ˆζ N from (16) to estimate the elements of f N,i, i = 1,..., N 1, we estimate Q N as ˆQ N. The refined estimate of ζ N follows as ˆζ WLS N = ( A T ˆQ 1 N A ) 1 A ˆQ 1 N a, (17)

13 13 with the error covariance matrix [21] ˆQ N = ( A T ˆQ 1 N A) 1. (18) Finally, we use the inner connection of the elements of ζ N to estimate the location vector j N. ˆζ N WLS(2) LS ˆζW N (3) WLS WLS Defining G N = 1 0, where ˆζ N (i) is the ith element of ˆζ N, we obtain 0 1 where ϵ N is a [3 1] estimation noise vector of from (17), the WLS estimator of j N is ( ) ĵ N = G T 1 1 N ˆQ N G N GN ˆQ 1 N whose elements ĵ N (1) = ĵ x N and ĵ N (2) = ĵ y N We would like to mention that if assumption ς l ς l G N j N = ˆζ WLS N + ϵ N, (19) ˆζ WLS N. Using (19), ˆQ N from (18) and ˆζ WLS ˆζ WLS N N, (20) are the desired location coordinates. = 1 used to obtain (13) does not hold, the localization process can be performed on a per-anchor-node basis. To this end, packet index i in (13) is limited to packets transmitted or received by the same anchor node, and the number of equations (13) is reduced to N 1 L (assuming equal number of transmissions pre anchor node in the network). Since L is expected to be small (we use L = 2 in our simulations and sea trial described below), the accuracy of the localization process is not expected to deteriorate much. Then, the UL node location at the end of the localization window can be estimated by combining per-anchor-node based estimations ĵn per-anchor-node based estimations ĵn by mismatch of ς l between anchor nodes. from (20) using data fusion techniques, cf., [22]. Since are independent of ς l, such combination is not affected C. Extensions In this section we introduce two extensions for the above location estimation. The first is a refinement step in which we iteratively improve the location estimation (20). The second is a self-evaluation process to test the accuracy of the localization process.

14 14 1) Iterative Refinement: The accuracy of estimation (20) depends on the quality of the coarse estimate ˆζ LS from (16), used to construct the error covariance matrix, ˆQ N. We now follow [23] and propose an iterative refinement procedure in which the accuracy of ˆQ N is improved. In the kth step of our iteration, vector ĵ N,k is estimated using (20) from which the vector ˆζ N,k is constructed. Next, in the (k + 1)st step ˆζ N,k replaces ˆζ LS N in the construction of ˆQ N. As a stopping criterion, we use the covariance matrix of the kth estimation (20), ( ) ˆQ N,k = G T 1 1 N ˆQ N G N. (21) Since the determinant, ˆQ N,k, is directly proportional to the estimation accuracy [21], the iteration stops when the absolute value of ˆQ N,k ˆQ N,k 1 is below some empirically chosen threshold, iter, or if the number of iterations exceeds its maximum, N iter. While we could not prove the convergence of this process, we demonstrate it by means of numerical simulations in Section VI. 2) Self-Evaluation of Localization Performance: In this section, we describe a binary test for self-evaluating localization accuracy. It can be used to adjust STSL parameters, such as the localization window W, for refining the localization procedure, such as data fusion of peranchor-node based localization (see discussion after (20)), or to decide whether an UL node can be used as a new reference node. For the latter application localization should be extended to tracking though, to make sure that location estimates remain accurate when nodes move. Our self-evaluation test relies on a widely used model that bounds propagation speed underwater between 1420 m/sec and 1560 m/sec [11]. In particular, given an estimate of the propagation speed, c est, the binary test output ξ is computed as 1, if 1420 c est 1560 ξ = 0, otherwise, (22) and ξ = 1 and ξ = 0 indicate accurate and non-accurate localization, respectively. Using (12) and since ς l are expected to be close to 1, we obtain the propagation-speed estimate as c est = 1 N ĵ i p i 2, (23) N ˆT i i=1 where ĵi, i = 1,..., N 1, follow from ĵn in (20) using relation (11). Different from traditional self-evaluation techniques involving the broadcast of a confidence index obtained from comparing the measured propagation delay to the estimated one (e.g. [24], [25]), the advantage of the our

15 15 method lies in the comparison of c est to a given model of propagation speed, which is independent of the estimation. Our numerical results (see Section VI) show that when localization error is accurate (i.e., below 10 m), we obtain ξ = 1 in more than 99% of the cases, and when localization error is non-accurate (i.e., above 10 m), ξ = 0 results in 90% of the cases. If more reliable evaluation performance is needed, the proposed test could be combined with other self-evaluation tests. D. Scalability When more network nodes are added, often fewer packets are transmitted per node. Hence, performances of both time-synchronization and localization degrade with increasing number of UL nodes, N UL. Furthermore, since time-synchronization is performed per-anchor node, its performance degrades with increasing number of anchor nodes, L. However, since the number of propagation delay measurements, available for localization, increases with L, performance of the localization step by itself improves with L. However, since localization depends on the output of the synchronization step, the overall performance may improve or degrade with increasing number of anchor nodes. In summary, scalability of the STSL algorithm is closely related to the scalability of the underlying communications protocol. E. STSL Pseudo-Code The operation of the STSL algorithm is summarized in the pseudo-code in Algorithm 1. For simplicity, the quantization mechanism introduced in Section IV-A1 is not included, and we start when positions are already quantized into locations u l,ν and k ρ. First, equations (5) are formed, and an LS estimator is used to estimate clock skew and offset for each anchor node l (lines 2-9). Then, the time-synchronization step is concluded by estimating propagation delays for each transmitted or received packet (line 12). The localization step begins with forming equations (13) (line 13), followed by an initial LS estimator (line 15). Then, an iterative procedure begins where in each step the covariance matrix ˆQ N and location ĵ N,k are estimated (lines 18-19). The latter is then used to refine the initial estimation by iteratively forming matrix ˆQ N till convergence is reached (lines 19-23). The algorithm performs a series of LS and WLS estimations with complexity of O (N 3 + N) and is executed only once at the end of the localization window. A software implementation of the algorithm can be downloaded from [26].

16 16 Algorithm 1 Estimate j N 1: {Step 1: Time-synchronization} 2: for (l = 1,..., L) do 3: for (n N a l, m N b l ) do 4: if (p n, p m U l,ν ) ( j n, j m K ρ ) then 5: Form equations (5) using T n, R n, T m and R m 6: end if 7: end for 8: Estimate O l and S l using (7) 9: end for 10: {Step 2: Localization} 11: for (i = 1,..., N) do 12: set ˆT i using (9) 13: Form equations (13) 14: end for 15: Estimate ˆζ N,1 using (16) 16: for (k := 1 to N iter ) do 17: Estimate ˆQ N using ˆζ N,k 18: Estimate ĵ N,k using (20) 19: Construct matrix ˆQ N,k using (21) 20: if ( ˆQ N,k ˆQ N,k 1 iter ) then 21: Return 22: end if 23: Construct ˆζ N,k+1 using ĵ N,k 24: end for V. CRAMÉR-RAO LOWER BOUND (CRLB) For the purpose of gauging the performance of the STSL algorithm, in this section we develop analytical expressions to lower bound the performance of any unbiased UWAL estimator, assuming nodes not to be time-synchronized and propagation speed unknown. We start with

17 17 general expressions for the CRLB, and then apply it to our specific localization problem. A. General CRLB Consider a measurement vector y = h(π, ν) + n, where n is a noise vector, and h(π, ν) is some function of a vector of wanted variables, π, and a vector of nuisance variables, ν. For an unbiased estimator, the variance of the nth element of π, π n, can be bounded by the Cramér-Rao bound (CRB) [27] where CRB(π n ) = ( I 1) n,n element is E [ (ˆπ n π n ) 2] CRB(π n ), (24) and I is the Fischer information matrix (FIM), whose (n, m)th [ ] 2 ln P (y π) I n,m = E y π n π m, (25) and P (y π) is the probability density function of y given π. To calculate P (y π) one needs to average the nuisance variables, ν, i.e., P (y π) = E ν [P (y, ν π)], which makes it hard to calculate (25), since often P (y, ν π) cannot be expressed. Therefore, instead of CRB(π n ), the modified Cramér-Rao bound MCRB(π n ) = In [28] it was shown that (Ĩ 1 ) n,n [ ] 2 ln P (y π, ν) Ĩ n,m = E y,ν π n π m Hence, MCRB(π n ) may be too loose to compare with. is often used [28], where. (26) CRB(π n ) MCRB(π n ). (27) A different approach would be to consider the nuisance variables ν as part of the estimation problem. That is, we consider a new variable vector Φ = [π T, ν T ] T and formalize CRB(Φ n ) for [ ] 2 ln P (y Φ) I n,m = E y Φ n Φ m We note that CRB(Φ n ) does not bound E [ (ˆπ n π n ) 2] but E serve as a lower bound for estimators which estimate both π and ν.. (28) [ (ˆΦn Φ n ) 2 ]. Thus, it can only

18 18 B. Application to STSL Since the STSL algorithm includes a sequence of LS and WLS estimators, it is an unbiased estimator. Thus, we next apply the MCRB(π n ) and CRB(Φ n ) bounds for our STSL algorithm. We consider the measurement vector in (2) for which y = R i, π = [j x N, jy N ], ν = [S 1,..., S L, O 1,..., O L, c], and n is as γ i in (2). Then, we have [ ) 2 ) ] 2 E (ĵx N jn x + (ĵy N jy N CRB(π 1 ) + CRB(π 2 ). (29) We note that the variance of y depends on the clock skew, S li. Thus, although γ i is assumed Gaussian, the often used simplification for the CRB in the Gaussian case (cf. [27]) cannot be used to solve (26) and (28). Expressions of these equations can be found in [26]. Following our discussion in Section V-A, we consider the alternative CRLB formulations CRB = CRB(Φ 1 ) + CRB(Φ 2 ), MCRB = MCRB(π 1 ) + MCRB(π 2 ). (30) and compare MCRB and CRB to ρ err = E [ (ĵx N jx N ) 2 ) ] 2 + (ĵy N jy N. (31) VI. SIMULATION RESULTS In this section, we present and discuss simulation and sea trial results demonstrating the performance of the STSL algorithm in different environments. We conducted 10, 000 Monte- Carlo simulations of a scenario with two anchor nodes and one UL node, communicating in a simple TDMA fashion. The three nodes were placed uniformly in a square area of 1 1 km 2 and moved between two adjacent packet transmission times at uniformly distributed speed and angle between [ 5, 5] knots and [0, 360] degrees, respectively. We added a zero mean i.i.d. Gaussian noise with variance σ 2 to each of the ToA estimations [see (2)]. Furthermore, considering the results in [3] we added a zero mean i.i.d. Gaussian noise with variance 1 m 2 to each of the distance elements of the motion vectors [see (3)] while regarding their angle components to be accurate. 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 2, respectively. We used a quantization threshold = 38 meters and a localization window of W = 20 timeslots. The time-slot duration was selected T slot = 5 seconds, considering the long propagation

19 STSL STSL mix Multilateration JLS CRB MCRB ρerr [m] /σ 2 [db] Fig. 1: ρ err from (31) as a function of 1/σ 2. Sound speed is known and all nodes are timesynchronized. Vertical bars show 95% confidence intervals of the simulation results for STSL. delay in the UWAC channel (e.g., 4 sec for a range of 6 km). We compare the performance of the STSL algorithm with those of the multilateration method [14] and the method proposed in [17], which we refer to as the joint localization and synchronization (JLS) algorithm. Both benchmark methods use an assumed propagation speed c. Furthermore, while the JLS algorithm performs joint time-synchronization and localization (assuming anchor nodes are time-synchronized but the UL node is not), the multilateration method assumes all nodes to be time-synchronized. Since both benchmark methods assume static nodes, we used a different simulation environment for them such that a fair comparison with the STSL algorithm is possible. The simulation environment for the benchmark methods considers fixed nodes and adds virtual anchor nodes according to node movements in the original simulation scenario (i.e., the one used to test the performance of the STSL algorithm). Consider, for example, an anchor node l moving between locations p l1 and p l2 while communicating with a static UL node. To test the benchmark methods, such a scenario would change into a scenario where two static anchor nodes, l 1 and l 2, are located at p l1 and p l2, respectively. Allowing a fair comparison between the three tested localization methods, the virtual anchor nodes, l 1 and l 2, have the same local clock as that of the real anchor node l. The implementation code of the STSL algorithm can be downloaded from [26]. First, we consider a scenario where c = c = 1500 m/sec and all nodes are time-synchronized.

20 ρerr [m] STSL Multilateration JLS e sync [%] Fig. 2: ρ err from (31) as a function of e sync. Sound speed is known and 1 σ 2 bars show 95% confidence intervals of the simulation results for STSL. = 46 db. Vertical Figure 1 shows ρ err from (31) as a function of 1 σ 2 for the three methods and the CRB and MCRB from (30). For clarity, here and in the following we show 95% confidence intervals in error bars only for the STSL algorithm. The results show that both benchmark methods achieve better performances than the STSL algorithm. This is mainly because STSL redundantly estimates c as well as clock offsets and skews, which introduces errors. This is also why the multilateration method achieves slightly better performance than the JLS protocol method. We note that the MCRB is slightly lower than the CRB and both bounds are quite close to the STSL error, which implies that although STSL is a heuristic estimator it achieves good localization results. To show the effect of possible mismatch of our model for the measurement noise γ i (see (2)), Figure 1 also includes results for STSL-mix, in which γ i is modeled as a mixture of two distributions. The first distribution (with weight 0.9) is a zero mean Gaussian with variance σ 2 and the second (with weight 0.1) is a Rayleigh(σ) distribution, which accounts for multipath propagation [29]. From Figure 1, we observe that the performance of STSL-mix decreases compared to that in the Gaussian-noise case, which is mainly due to the non-zero mean of noise. However, this degradation is fairly moderate demonstrating some robustness of STSL to model mismatch. In Figure 2 we compare ρ err for the three methods when c = c = 1500 m/sec, but nodes are not time-synchronized and 1 σ 2 = 46 db, as a function of e sync = SW +Ō W, where S and Ō is the W

21 ρerr [m] STSL Multilateration JLS c - c [m/sec] Fig. 3: ρ err from (31) as a function of c c. All nodes are time-synchronized and 1 σ 2 Vertical bars show 95% confidence intervals of the simulation results for STSL. = 46 db. average of S l and O l, l = 1,..., L, respectively. While the performance of the STSL algorithm are hardly affected by the synchronization error (compared to the results in Figure 1), the JLS 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 performance when c is chosen with uniform distribution between the model boundaries, 1420 m/sec and 1560 m/sec, and the two benchmark methods were still given the nominal value c = 1500 m/sec. To understand the effect of mismatched propagation-speed information on localization accuracy, we compare ρ err from (31) when all nodes are timesynchronized. The results are shown in Figure 3 as a function of c c, again for 1 σ 2 = 46 db. We observe that for both benchmark methods, ρ err dramatically increases even for a small difference of c c = 10 m/sec, which motivates the need to accurately estimate c in UWAL. Furthermore, compared to the results of Figure 1 the STSL is almost unaffected by the variations of c. Next, we consider the practical case where all nodes are not time-synchronized (same scenario as for Figure 2) and c is unknown (same scenario as for Figure 3). We study two of the properties of the STSL algorithm, namely the convergence of the refinement iterative process discussed in Section IV-C1 and the self-evaluation process discussed in Section IV-C2. In Figure 4, we demonstrate the convergence of the refinement iterative process by showing ρ err from (31),

22 /σ 2 = 30 db 1/σ 2 = 40 db 1/σ 2 = 50 db ρerr [m] Number of iterations Fig. 4: ρ err from (31) for the STSL algorithm as a function of number of iteration steps ρ err < 10m ρ err >10m 0.7 PDF of ĉ ĉ Fig. 5: Empirical PDF of c est for c = 1500 m/sec. averaged over all clock offsets and skews and c instances, as a function of the number of iteration steps and several values of 1 σ 2. The results indicate that a significant performance improvement is achieved after only a few iteration steps. In Figure 5 we show the empirical probability density function (PDF) of the estimated propagation speed, c est, from (23) when c = 1500 m/sec. The results are shown for two cases: 1) when ρ err 10 m and 2) when ρ err 10 m. The results show that for small values of ρ err, in more than 99% of the cases, c est is inside the model boundaries

23 ρerr [m] STSL STSL,L=3 STSL,2UL Multilateration JLS CRB MCRB /σ 2 Fig. 6: ρ err from (31) for time-synchronization and sound speed uncertainties. (i.e., 1420 c est 1560), with a standard deviation of less than 10 m/sec. For large values of ρ err, c est seems to be almost uniformly distributed, with only 10% of the estimations being inside the model boundaries. However, for some applications (e.g., localization in sparse networks) this missed-detection probability may be too large. Thus, we conclude that c est can serve as a good indicator to confirm accurate localization, but may be used to complement other self-evaluation techniques to identify non-accurate localization. Finally, in Figure 6 we consider the same scenario as for Figure 4 and show ρ err from (31) as a function of 1 σ 2. For clarity, since results for STSL are similar to those shown in Figure 1, error bars are omitted. We observe that while both benchmark methods suffer from a significant error floor, the error for the STSL algorithm decreases with 1 σ 2 and is the same as in Figure 1. Hence, the algorithm compensates for both synchronization and propagation speed uncertainties. To demonstrate the relation between the number of anchor nodes, L, and the number of UL nodes, N UL (see discussion in Section IV-D), in Figure 6 we also include results for L = 3, N UL = 1 (STSL, L = 3) and L = 2, N UL to the case of L = 2, N UL = 2 (STSL, 2UL), which had similar standard deviation = 1. We note that since multilateration does not include timesynchronization, and since JLS performs joint time-synchronization and localization, clearly their performance improves with L and degrades with N UL. Results show that, as expected, also performance of the STSL algorithm slightly improves with L and decreases with N UL.

24 24 Minutes Node 1 Node 2 Node UTM Y (offset by ) UTM X (offset by ) Fig. 7: Time-varying location of nodes in the sea trial. VII. SEA TRIAL RESULTS In this work we assumed 1) node s clock skew and offset are time-invariant within the localization window, 2) propagation speed is time and space invariant for small depth differences, 3) propagation delay measurements are affected by a zero-mean Gaussian noise, and 4) node movements are relatively slow such that quantization of node locations is possible. While the first assumption depends on the system clock, the second and the third depend on the channel. To verify our assumptions and confirm our results we tested the STSL algorithm in a sea trial along the shores of Haifa, Israel in August The sea trial included three drifting vessels, representing three mobile nodes, and lasted for T exp = 300 minutes. In Figure 7, we show the UTM coordinates of the nodes during the sea trial. We note that node 3 needed to turn on its engines around time slot 150, which explains the sudden change in its direction and speed. Each node was equipped with a transceiver, deployed at 10 meters depth, allowing UWAC at 100 bps with a transmission range of 5 km. The nodes communicated in a TDMA network with a time-slot of T slot = 60 seconds, allowing significant node motion between transmission of each packet. Time-slot management was performed at each node using an internal clock. These internal clocks were manually time-synchronized at the beginning of the experiment with an expected clock offset of up to one second. We also note that pre-testing of these clocks showed a clock skew of one second per day. We used GPS receivers as reference for the location of each node as well as its inertial system

25 Link (1,2) Link (1,3) Link (2,3) T diff [sec] Average increase: 1.2msec / time slot Average increase: 13.5msec / time slot 0.5 Average increase: 14.3msec / time slot Time slot Fig. 8: ˆT diff for all communication links as a function of time slots. to obtain motion samples [see (3)]. The localization error of the GPS-based reference locations was reported to be uniformly distributed between 0 and 10 m. To test the effect of this uncertainty in the anchor-node location we conducted simulations similar to the scenario considered in Figure 1 with error-free ToA measurement but with anchor-node location uncertainties similar to those of the GPS receivers in use. The results showed that using our STSL algorithm such uncertainty results in an average estimation error of 15 m. Thus, in the sea trial any location error below 15 m is considered accurate. A. Channel and System Characteristics At the beginning and end of the sea trial we measured the propagation speed in water using a measuring probe. Both measurements showed that the propagation speed c was bounded in between 1552 m/sec (for depth of 40 m) and 1548 m/sec (for depth of 1 m) and was on average 1550 m/sec. The small variance of the measurements of c confirms our assumption that the propagation speed can be considered fixed throughout the localization window. In the following, for performance evaluation we consider c = 1550 m/sec, which is within the boundaries of our model (see Section III) but is different from the commonly used value of 1500 m/sec. In Figure 8 for each pair of nodes we show ˆT diff, which is the time difference between propagation delay estimations at both sides of the communication link in a single set of receiver-

26 26 transmitter quantized locations, measured directly from (2a) and (2b) neglecting the clock skew and offset. For example, for a two-way packet transmission between the quantized locations k ρ and u l,ν with propagation delay estimations ˆT 1 and nodes are time-synchronized, we would expect ˆT diff ˆT 2, ˆT diff = ˆT 1 ˆT 2. We note that if to be on the same order of the length of the impulse response, which was measured as 20 msec on average and did not exceed 30 msec. However, the results show that ˆT diff increases with time and is much greater than 30 msec. This implies that nodes suffered from considerable clock skew and offset. Furthermore, since the values of ˆT diff are different for each pair of nodes, the nodes skew and offset are different, which confirms with our system model (see Section III). B. Results In the following, we compare the performance of the STSL algorithm in the sea trial with that of a method aimed to solve a relaxed sequential time-synchronization and localization (R-STSL) problem, in which an a-priori propagation speed c is given. In the R-STSL, time-synchronization is performed similar to the process described in Section IV-A, but the localization process is modified as c is known. The results are shown for all three nodes, where each time a different node was considered as the UL node and the other two nodes were the anchor nodes. We measure the performance in terms of the Euclidean distance between the estimated location and the reference GPS location, averaged over a sliding localization window of W time-slots, i.e., ρ err = 1 T exp T slot W + 1 Texp T slot n=w ĵn j n 2, (32) where for each UL node location estimation ĵn we used ToA and inertial system measurements from time-slot n W + 1 till n. In Figure 9, we demonstrate the effect of mismatched propagation speed, i.e., c c, by showing ρ err from (32) for W = 30 time-slots as a function of c c, where c = 1550 m/sec. We note that although such choice of W seems large due to the long time slot duration, the number of transmissions for each node was only 10, which is in the same order as considered in our simulations. The results show that ρ err significantly increases with c c even for a relatively small difference of 10 m/sec. This result, as well as the results in Figure 3, validate the need to consider the propagation speed as an additional variable in UWAL. In the following we consider a matched version of

27 Node 1 Node 2 Node ρerr [m] c - c [m/sec] Fig. 9: ρ err from (32) as a function of c c for W = 30 time slots. R-STSL method P( ρerr x) W=10 (STSL) 0.4 W=20 (STSL) W=30 (STSL) W=30 (MR STSL) x [m] Fig. 10: Probability that ρ err x for STSL and MR-STSL. R-STSL (MR-STSL), i.e., when c = c, which in the absence of benchmark localization methods that take into account time-synchronization uncertainties and availability of inertial system to track short-term node movements, can serve as a lower bound for the STSL. Finally, in Figure 10 we show the empirical cumulative density function CDF of ρ err, averaged over the three nodes, for STSL and MR-STSL and W = 10, 20, 30 time-slots, i.e., in a single localization window an average number of packet transmissions of 3.3, 6.6, 10 for each node,

28 28 respectively. We observe that both mean and variance of ρ err improve with W, however, at a cost of delay. We observe that since STSL estimates an additional variable, its performance is worse than that of MR-STSL. However, the difference is not significant. We note that the average ρ err for STSL and W = 30 time-slots is 21.5 m, which is close to the expected localization accuracy due to the GPS location uncertainties. Therefore, STSL fully compensates the large clock skew and offset shown in Figure 8, node movements and propagation speed uncertainty. VIII. CONCLUSIONS In this paper we considered UWAL in the practical scenario where nodes are not timesynchronized and permanently moving, and where the propagation speed is unknown. We introduced a localization algorithm which uses existing self-estimations of motion vectors of nodes, assumed to be accurate for 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. We also presented a method to self-evaluate the localization accuracy of the node. In addition, we used the applicable Cramér-Rao lower bounds as references for the performance of STSL. Considering the problem of establishing a faithful simulation environment for the underwater acoustic channel, alongside simulations we tested our algorithm in a designated sea trial. Both simulations and sea trial results demonstrated that our algorithm can cope with time-synchronization and propagation speed uncertainties in a dynamic environment, and achieves a reasonable localization accuracy using no more than two anchor nodes. Further work will include extension to tracking to continuously localize nodes, which will also allow us to fully use our self-evaluation method in sparse networks, where already localized nodes often serve as anchor nodes. REFERENCES [1] M.Chitre, S.Shahabodeen, and M.Stojanovic, Underwater acoustic communications and networking: Recent advances and future challenges, Marine Technology Society, vol. 42, no. 1, pp , [2] J. Weber and C. Lanzl, Desigining a positioning system for finding things and people indoors, IEEE Spectrum, vol. 35, no. 9, pp , Sep [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, Offshore and Polar Engineering, vol. 15, no. 2, pp , Jun [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 2008, pp

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30 30 [26] R. Diamant, MATLAB implementation code for the STSL algorithm, 2011, roeed/downloads. [27] H. Trees, Detection, Estimation, and Modulation Theory. John Wiley and Sons, Inc., 2001, pp [28] A.N.D Andrea, U. Mengali, and R. Reggiannini, The modified Cramer-Rao bound and its applications to synchronization problems, IEEE Sensors J., vol. 42, no. 2, pp , Feb [29] M. A. Chitre, A high-frequency warm shallow water acoustic communications channel model and measurements, Acoustical Society of America, vol. 122, pp , Nov Roee Diamant (S 09) received the B.Sc. and the M.Sc. degrees from the Technion, Israel Institute of Technology, in 2002 and 2007, respectively. From 2001 to 2009, he was working in Rafael Advanced Defense Systems, Israel as a project manager and system engineer. He was awarded the Intel Research Excellent Prize in 2007 and the Excellent Research Work in Communication Technology Prize from the Tel-Aviv University in In 2009 he received the Israel Excellent Worker First Place Award from the Israeli Presidential Institute. Currently, he is working towards the Ph.D. degree in the Communications Group at the Department of Electrical and Computer Engineering, University of British Columbia, with support of an NSERC Vanier Canada Graduate Scholarship. His research interests are in underwater acoustic networks and underwater acoustic localization. Lutz Lampe (M 02, SM 08) received the Diplom (Univ.) and the Ph.D. degrees in electrical engineering from the University of Erlangen, Germany, in 1998 and 2002, respectively. Since 2003 he has been with the Department of Electrical and Computer Engineering at the University of British Columbia, where he is a Full Professor. He is (co-)recipient of a number of Best Paper Awards, including awards at the 2006 IEEE International Conference on Ultra-Wideband (ICUWB), 2010 IEEE International Conference on Communications (ICC), and 2011 IEEE International Conference on Power Line Communications (ISPLC). He was awarded the Friedrich Wilhelm Bessel Research Award by the Alexander von Humboldt Foundation in 2009 and the UBC Charles A. McDowell Award of Excellence in Research in He is an Associate Editor for the IEEE Wireless Communications Letters and the IEEE Communications Surveys and Tutorials, and he has served as Associate Editor for the IEEE Transactions on Wireless Communications from 2007 to 2011, the IEEE Transactions on Vehicular Technology from 2004 to 2008 and the International Journal on Electronics and Communications (AEUE) from 2007 to He was the General Chair of the 2005 International Symposium on Power Line Communications (ISPLC) and the 2009 IEEE International Conference on Ultra-Wideband (ICUWB). He is the Chair of the IEEE Communications Society Technical Committee on Power Line Communication.