Ad Hoc Networks xxx (2014) xxx–xxx

Contents lists available at ScienceDirect

Ad Hoc Networks

journal homepage: www.elsevier .com/locate /adhoc

Real-time collaborative tracking for underwater networkedsystems

http://dx.doi.org/10.1016/j.adhoc.2014.10.0081570-8705/� 2014 Elsevier B.V. All rights reserved.

⇑ Corresponding author.E-mail addresses: dimirza@eng.ucsd.edu (D. Mirza), pnaughto@eng.

ucsd.edu (P. Naughton), cschurgers@ucsd.edu (C. Schurgers), kastner@cs.ucsd.edu (R. Kastner).

Please cite this article in press as: D. Mirza et al., Real-time collaborative tracking for underwater networked systems, Ad Hoc Netw.http://dx.doi.org/10.1016/j.adhoc.2014.10.008

D. Mirza a,⇑, P. Naughton a, C. Schurgers b, R. Kastner a

a Department of Computer Science and Engineering, University of California, San Diego, 9500 Gilman Drive, La Jolla, CA 92093, United Statesb Qualcomm Institute, Calit2, University of California, San Diego, United States

a r t i c l e i n f o a b s t r a c t

Article history:Received 3 March 2014Received in revised form 12 October 2014Accepted 13 October 2014Available online xxxx

Keywords:Underwater networksReal-time trackingAcoustic networks

Localization is a crucial requirement for mobile underwater systems. Real-time positioninformation is needed for control and navigation of underwater vehicles, in early warningsystems and for certain routing protocols. Past research has shown that the localizationaccuracy of networked underwater systems can be significantly improved using inter-vehicle collaboration. More specifically the Maximum Likelihood (ML) position estimatesof a mobile collective can be computed from measurements of relative positions andmotion, albeit in a non-real-time fashion. In this work we extend this solution to computethe position estimates of a network in real-time and in a distributed fashion. We firstdescribe a centralized approach to identify key factors that fundamentally limit the perfor-mance of a real-time solution. Using the centralized approach as a benchmark, we arrive ata real-time distributed solution that additionally computes the location of vehicles usinginformation obtained locally by them. We address practical considerations in the imple-mentation of our algorithm and propose solutions to mitigate computational errors. Withthis proposed implementation, we provide insight on how to appropriately plan a deploy-ment of nodes when collaborative tracking is to be utilized. Lastly, we shed light onsituations where implementing collaborative tracking can hinder the localization perfor-mance of the network so that these can be avoided.

� 2014 Elsevier B.V. All rights reserved.

1. Introduction

There has been a growing interest in operating groupsof autonomous underwater vehicles in a networked fash-ion, using short to medium range acoustic modems [1].Location information is critical to such networked mobileunderwater systems for correctly annotating data samples,control and navigation and in certain data routing proto-cols. However, since GPS is not available underwater, theposition of vehicles has to be estimated over time.

Most existing solutions based on Kalman or particle fil-ters are designed for tracking vehicles individually [2,3].This is achieved by combining measurements of relativeposition with respect to known landmarks or beaconstogether with estimates of the vehicle’s motion obtainedfrom on board sensors. These non-collaborative trackingmethods perform poorly in underwater networks wherevehicles have short to medium acoustic communicationrange. This is due to the fact that a vehicle may not bewithin the communication range of a sufficient numberof beacons or it may move out of range of beacons fromtime to time. A solution to this problem involves usingadditional measurements for localization, which can beobtained from communication between vehicles. Such acollaborative approach has been employed by a number

(2014),

2 D. Mirza et al. / Ad Hoc Networks xxx (2014) xxx–xxx

of localization techniques such as multi-dimensionalscaling and iterative multi-lateration. However, these tech-niques have been proposed for stationary networks. Theytypically use relative position information (distance, prox-imity or direction) as geometric constraints on theunknown location of devices. Since devices are stationary,the constraints can be considered concurrently to solve forthe unknown locations. In principle these algorithms canbe extended to mobile underwater networks by localizingtime snapshots of the network as suggested in [4–6].However this requires measurements of relative positionto be obtained concurrently. Further, position estimatesfor each snapshot must be computed before there is signif-icant displacement in the vehicle positions. In reality, dueto practical communication constraints, the use of suchtechniques for underwater networks would be severelylimited when deployments are sparse and vehicles aremoving.

Our prior work has shown that in sparse mobile under-water networks, localization accuracy can be significantlyimproved when vehicles collaborate [7], compared to bothindividual tracking and collaborative static localization.We proposed a collaborative solution that tracks a groupof vehicles as a collective by jointly computing thetrajectories of all vehicles using non-concurrent estimatesof inter-node distances together with measurements ofmotion from on-board navigational sensors. While thereexist a few collaborative tracking methods that also looselyfollow the same idea, our solution is optimal as it jointlycomputes the Maximum Likelihood (ML) positions of allvehicles over time.

The drawback of this optimal ML solution is that it iscentralized and can only be applied offline, after allmeasurements are available at a single location. It servesapplications where position information is only neededpost-facto, but cannot solve the problem of real-time local-ization. Creating a real-time tracking solution for mobileunderwater networks is a difficult task due to the powerrequired for inter-node communication and the bandlimited acoustic channel of the ocean. Despite these chal-lenges, our work in [8] modified our existing ML solutionto compute positions in real-time. In this work we firstpropose a centralized real-time algorithm which computesall position estimates at a central location albeit in real-time. We use this solution to highlight the inherent lossin localization performance when we go from a non-real-time to a real-time solution. More practically, wepropose a localized distributed solution for our real-timetracking that minimizes the communication overhead bystrategically sharing information between vehicles, yetachieves localization accuracies close to the best case.The essential problem that we address to this end is todetermine what information to share between vehiclesand when, as well as how to encode information tominimize the communication overhead.

While the work of [8,7] only considered one set oftrajectories in their analysis, in this work we provide addi-tional analysis of these techniques by applying them todifferent motion models. We find that there are caseswhere the collaborative framework for localization doesnot perform best, but often it can alleviate many different

Please cite this article in press as: D. Mirza et al., Real-time collaborativehttp://dx.doi.org/10.1016/j.adhoc.2014.10.008

sources of error in an underwater network and provideresults that are superior to the non-collaborative case.Ultimately, we propose that careful consideration of themotion models of the vehicles as well as the positioningof the beacons must be taken into account when planninga deployment of vehicles who are collaborating to deter-mine their position. We provide insight on how theseparameters affect the location accuracy of each vehicle sothat an informed decision can be made on whether ornot to collaboratively localize as well as how to set up anetwork to reduce localization error when collaborating.Before we can delve into this analysis, we will describeour prior work on non-real-time centralized tracking aswell as centralized and distributed real-time tracking. Thisknowledge forms the basis of later analysis on deploymentconsiderations.

2. Related work

A detailed discussion of how our factor-graph frame-work relates to other estimation techniques that are tradi-tionally used for underwater navigation, in robotics as wellin terrestrial sensor networks can be found in our priorwork [7]. A number of real-time and distributed localiza-tion techniques have been proposed for underwaternetworks [4,9,5,6]. Among these DNRL [4] and LSL [6] usemulti-lateration while USP [5] applies iterative bilatera-tion. To improve the localization accuracy, DNRL proposesthe use of mobile beacons. In LSL a hierarchical (infrastruc-tured) approach is proposed for localization [6]. Thesetechniques essentially estimate positions for time snap-shots of the network using only spatial constraints(estimates of inter-vehicle distances) and do not accountfor vehicle motion. The main drawback compared to oursolution is that they would not work well in sparse net-works and need more frequent signaling. A more in depthsurvey is available in [10]. A comparative performanceevaluation of some of these schemes has been done in [11].

AUV navigation using a single mobile beacon is pro-posed in [2,3]. Here measurements of vehicle motion arecombined with non-concurrent distance estimates to thebeacon. In addition path planning is done to improve thetracking performance [3]. A collaborative solution has beenproposed for under-ice AUV tracking where inter-vehicleestimates of distance and relative velocities (from mea-surements of Doppler shifts) are used for localization[12]. Vehicle positions are estimated using a least squaresapproach. To minimize the position uncertainty, a subset ofneighbor vehicles are selected as position references via anexhaustive search method.

3. Non-real-time centralized solution

Our centralized ML solution estimates the position ofvehicles by simultaneously capturing a number of spatialand temporal constraints. These constraints are the resultof the measurements that the vehicles collect to help themdetermine their positions. A first set of measurements,yielding the ‘spatial’ constraints, are inter-vehicle distanceestimates with neighbors within communication range,

tracking for underwater networked systems, Ad Hoc Netw. (2014),

D. Mirza et al. / Ad Hoc Networks xxx (2014) xxx–xxx 3

collected at different times by sending an acoustic ping andmeasuring the time-of-flight, as described by Eq. (1). Theso-called ‘temporal’ constraints are estimates of vehiclevelocity measurements as gathered by the navigationalsensors on-board each vehicle. The temporal constraintsare mathematically shown in Eq. (2). Calculating thecollection of vehicle positions over time within the set ofspatial and temporal constraints is a complex multi-dimensional estimation problem. To solve it optimally,we have proposed the framework of factor-graphs. Our fac-tor-graph solution efficiently computes the individual pdfsof the position of vehicles at discrete times from the jointpdf of all the unknown positions given measurements (ofinter-vehicle distances and motion). The factor-graph itselfis a graphical representation of this joint pdf. A detaileddiscussion of the complete solution and how these con-straints are represented is available in our prior work [7].The theoretical foundations of this technique have beenlaid out by Kschischang et. al.[13]. Here we only highlightthe key ideas behind our centralized and offline algorithm.To do this we use a simplified notation and describe thefactor-graph in terms of a dependency graph. The completefactor-graph can be reconstructed from the dependency-graph by replacing each vertex in the dependency graphby its internal representation as discussed in Section 3.1.

Fig. 1(a) shows the dependency graph for a network offour vehicles. We have shown the graph for only four vehi-cles to not overload the figure. The structure of the graphcan be viewed in terms of four chains stacked vertically.Each chain captures the evolution of the unknown positionof a vehicle over time. Correspondingly, each vertex in achain (shown as a hexagon) represents the unknown states

Fig. 1. Centralized non-real-time solution. (a) Dependency graph. (b) Iterative mthe dependency graph for any vehicle i at time tk .

Please cite this article in press as: D. Mirza et al., Real-time collaborativehttp://dx.doi.org/10.1016/j.adhoc.2014.10.008

(position and velocity) of the vehicle at a particular timeinstance. A link between any two vertices exists if thereis a measurement (or a set of measurements) thatrelates/constrains those states. Vertices within a chainare linked by measurements of motion, i.e. the temporalconstraints. Vertices across chains are linked by measure-ments of inter-node distance, i.e. the spatial constraints.The triangles represent the position of beacon nodes atany particular time instance. A link with a triangular vertexexists if a measurement of distance was made with thebeacon at that time. Note that measurements (of distanceand motion) are obtained in real-time and stored on thememory banks of the vehicles. However, the depen-dency-graph described above is constructed in non-real-time, after all the measurements are available at acentral location.

The links in the dependency graph shown in Fig. 1(a)establish pathways of information flow across vehicles inthe network as well as back and forth along the temporaldimension of each chain in the graph. Initially, positioninformation is only available at the triangular beacon-vertices (we assume beacons are, for example, buoys onthe surface equipped with a GPS receiver). The sum-product algorithm that runs on the above described graphgenerates this information. When we run the sum-productalgorithm on the graph, information from the beaconvertices eventually percolates to all the unknown states(vertices) of the factor-graph along the graph edges asdepicted in Fig. 1(a).

The dependency graph shown above is a simplifiednotation used for the actual factor-graph. Next, we describehow the factor-graph is obtained from the dependency

essage passing for position estimation. (c) Internal structure of a vertex in

tracking for underwater networked systems, Ad Hoc Netw. (2014),

4 D. Mirza et al. / Ad Hoc Networks xxx (2014) xxx–xxx

graph and present the operation of the sum-product algo-rithm to estimate vehicle positions.

3.1. Constructing the factor-graph from the dependency graph

The unknown positions are computed by running thesum-product (SP) algorithm (in non-real-time) on the fac-tor graph. The factor-graph representation is obtainedfrom the dependency graph shown in Fig. 1(a) by replacingeach hexagonal vertex by its corresponding internal struc-ture shown in Fig. 1(c).

To describe the internal structure of each vertex wedenote the unknown position of any vehicle i at time tk

as PiðtkÞ. A vertex in the dependency graph is a simplifiednotation for a state-variable, PiðtkÞ and a set of transforma-tion functions (f 1; f 2and f 3), as shown in Fig. 1(c). Byreplacing each vertex in the dependency graph with theseelements, the equivalent factor graph is obtained.

The transformation functions f 1; f 2and f 3 are computedfrom the statistical characterization of distance andvelocity measurements. We derive these functions fromequations relating the unknown positions of vehicles tomeasurements of distance and velocity. A distance mea-surement obtained at time tk as a result of communicationbetween two vehicles with positions PiðtkÞ and PjðtkÞ atthat time relates the unknown positions as follows:

zdðtkÞ ¼ PiðtkÞ � PjðtkÞ�� ��

2 þ eRk ð1Þ

where zdðtkÞ is the distance measurement, e is the error indistance estimates with any known pdf.

Next, a velocity measurement, zv ðtkÞ is related to theunknown position from first principles:

zvðtkÞ ¼1

jtkþ1 � tkjP tkþ1ð Þ � P tkð Þð Þ þ eV

k ð2Þ

where eVk ¼ evx

k ; evy

k

� �Tis the error in the velocity measure-

ment with known statistics.The transformation functions f 1; f 2and f 3 are defined as

follows:

f 1 ¼ pðPiðtkÞjPiðtk�1Þ; zvðtkÞÞ ð3Þf 2 ¼ pðPiðtkÞjPiðtkþ1Þ; zvðtkÞÞ ð4Þf 3 ¼ pðPiðtkÞjPjðtkÞ; zdðtkÞÞ ð5Þ

The exact definitions of the above conditional distribu-tions are obtained from Eqs. (1) and (2) and a statisticalcharacterization of the error terms in these equations.We have characterized the errors in our simulations to beuniformly distributed, however any other distributionscan be used to define the above conditionals. For complete-ness we describe the error in distance estimates are Gauss-ian: eR

k � U �rRmax;rRmaxð Þ. Further, the error in velocitymeasurements are also Gaussian evx

j � U �rVmax;rVmaxð Þ;evy

j � U �rVmax;rVmaxð Þ.In Fig. 1(c), the incoming and outgoing messages are

shown by dotted and solid arrows respectively. When thesum-product algorithm runs on the FG constructed usingthe above notation, the functions, f 1; f 2and f 3, operate onthe incoming messages l½Piðtk�1Þ�;l½Piðtkþ1Þ� and l½PjðtkÞ�,respectively, to compute independent estimates of the

Please cite this article in press as: D. Mirza et al., Real-time collaborativehttp://dx.doi.org/10.1016/j.adhoc.2014.10.008

pdf of PiðtkÞ, as per Eq. (6). The outgoing message l½PiðtkÞ�is computed as per Eq. (7).

3.2. Operation of the sum-product algorithm

The sum-product algorithm is essentially an iterativemessage passing algorithm. At each iteration, every vertexin the graph estimates the pdf of its own states based onincoming messages. (A vertex encapsulates the unknownstates and a set of transformation functions that operateon incoming messages to compute these estimates asdescribed in Section 3.1). The pdfs computed for each ver-tex are then passed on as messages to all neighbor vertices.

At each time instance the SP algorithm does two things.First, the state-variables are estimated by intersecting theindividual estimates from its function node neighbors,Eq. (7). Next the SP estimates the function nodes by mar-ginalizing the local likelihood function of each state-variable, Eq. (6). This is repeated until convergence. Notethat there are two very distinct notions of time here: thetime represented by states in the graph (which is the timeevolution of the network we are trying to estimate) and thetime post-facto during which we run our algorithm on acentral location (the running time).

lf�xðxÞ ¼X�fxg

f ðXÞY

y2ðf Þnfxgly�f ðyÞ

0@

1A ð6Þ

where the summary operation is defined as:X�x1

f ðx1; x2; x3Þ ¼X

x22A2

Xx32A3

f ðx1; x2; x3Þ

lx�f ðxÞ ¼Y

h2nðxÞnflh�xðxÞ ð7Þ

where X is the set of arguments of function nodef ; nðwÞ n fxg denotes the set of neighbors of a given nodew on the graph excluding the node x.

The key point in the above described factor-graphsolution is that to effectively fuse position information,messages have to be passed a number of times across eachof the links of the graph as depicted for a small section ofthe graph in Fig. 1(b). The solution above runs offline andcentrally after the actual sensing mission is over. Next,we will explore if and how we can modify this solutionto tackle the problem of real-time tracking in underwaternetworks.

4. Real-time tracking

4.1. Centralized real-time tracking

In this first subsection, we try to answer the ques-tion:what is the fundamental difference between a non-real-time and a real-time estimation of vehicle positions?Here we still assume that computation can run in a centrallocation. While in our offline non-real-time solution(discussed in Section 3) the factor-graph was constructedin one shot using all measurements made when vehicleswere underwater, here we propose a dynamic factor-graphsolution that evolves in time to (a) incorporate new

tracking for underwater networked systems, Ad Hoc Netw. (2014),

Table 1Simulation parameters.

Tracking granularity, d 2 minLocalization period, TLOC 8 minSimulation duration, Tsim 8 hNumber of vehicles, NU 8Number of beacons, NB 1Area of deployment, A 2 km � 2 kmMaximum depth of deployment, D 100 mMaximum transmission range, R 500 mAverage speed of vehicles, v 0.5 m/sBytes used to represent pdfs internally, Ninternal 512Bytes used to communicate pdfs, Ncomm 18

0 50 100 1500

0.2

0.4

0.6

0.8

1

RMS Error in position estimates

Frac

tion

of P

ositi

on E

stim

ates

Smoothing delay, τ = 0

Smoothing Delay, τ = 10 min

Smoothing Delay, τ = 20 min

Smoothing delay, τ = 75 min

Non−real−time, τ = ∞

Fig. 3. Cumulative Distribution Function (CDF) of the RMS error as afunction of the smoothing parameter, s. Each curve in the plot shows thefraction of position estimates (indicated by the y-axis), computed for allvehicles for the entire simulation duration, with RMS error less than agiven threshold (indicated by the x-axis).

D. Mirza et al. / Ad Hoc Networks xxx (2014) xxx–xxx 5

states (position and velocity), (b) incorporate estimatesof motion and distance with neighbor vehicles as theybecome available, and (c) limits the use of future informa-tion in estimating positions.

We are interested in knowing the positions of vehiclesat discrete times d apart. At any time t, the FG consists ofN chains of vertices representing the unknown states ofall vehicles until that time. A new vertex is added to the tailof each chain every d(s) as depicted in Fig. 2. In addition,when a measurement of distance becomes availablebetween two vehicles i and j, due to a communicationevent at time t, a new vertex is inserted to the ith and jth

chain in the graph corresponding to time t and a link is cre-ated between them. Each new state is also appropriatelylinked to previous states in a chain using measurementsof motion. Whenever the FG is updated with a new stateor measurement, the SP algorithm is run on the graph tocompute updated estimates of all states. To obtain positionestimates in real-time, the pdf of any state in the FG corre-sponding to time t is recorded at that time, before futuremeasurements become available. In principle we can esti-mate the vehicle positions semi real-time, by limiting theextent of future information to a time window s. Essen-tially, estimates corresponding to any time t are obtainedfrom the FG at t þ s. This is generally referred to as smooth-ing. Such a solution would be suitable for applications thatcan tolerate some delay in obtaining position estimates.

We implemented our centralized real-time trackingsolution in the NS2 simulator [14]. The simulation set upis described later in Section 4.3 with parameters given inTable 1. In this section we evaluate the localization perfor-mance as a function of the smoothing delay, s. Fig. 3 showsthe cdf of the RMS error in position estimates for differentvalues of s. In the figure, the performance of the offlinesolution corresponds to s ¼ 1 and that of the real-timetracking corresponds to s ¼ 0. Notice the loss in perfor-mance as we go from a non-real-time solution to a real-time one. This is due to the fact that the real-time solutiondoes not use any future measurements for estimating theunknown states. However, as time elapses informationflows backward (along the horizontal links of the graph)to refine past position estimates. Fig. 3 also shows the gainin localization performance as the smoothing parameter, sis increased. We observe that the performance of thesemi-real-time tracking coincides with that of the non-real-time solution for s ¼ 75 min which is a fraction ofthe total simulation time of 8 h.

While the simulation results suggest that we can getbetter localization accuracy by using estimates slightly inthe past, in reality we would still need to take into accountthe fact that the vehicle has moved during the intervals. Therefore, past (refined) estimates have to be interpo-lated to the present time. However, this is what our

Fig. 2. Evolution of dynamic FG. (a) FG

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tracking algorithm does in an optimal way using naviga-tional measurements. Therefore, applications that areinterested in knowing where a vehicle is ‘now’ in orderto make location-based decisions cannot leverage fromthe parameter s. This is true for most applications suchas navigation and control, routing and so on. However,refining past estimates would be useful for annotating datasamples with position information and batch processingthem in semi-real time. The smoothing delay is one ofthe parameters that inherently limits the performance ofa real-time and distributed solution. In Section 4.2 we willdiscuss other such factors.

As shown in Fig. 3, the improvement in the accuracy asa function of the smoothing delay diminishes for large

at time t. (b) FG at time t þ d.

tracking for underwater networked systems, Ad Hoc Netw. (2014),

6 D. Mirza et al. / Ad Hoc Networks xxx (2014) xxx–xxx

enough delays. This is because current updates do notaffect past estimates if we go far back enough in time.We therefore limit the number of past states in thedynamic FG to be within a time window T. As new statesare added to the FG, states older than t � T are removedfrom it to limit the computation.

4.2. Distributed real-time tracking

In this section we address the problem of performingthe tracking in a distributed fashion, i.e. How can we splitthe computation on different vehicles in order to jointlyestimate the vehicle positions?

Our factor-graph solution actually lends itself quitenaturally to a distributed solution. For a network with Nvehicles, we can view the centralized graph (shown inFig. 1(a) for N ¼ 4) as N communicating subgraphs. Thisdecomposed view of the centralized factor-graph is pre-sented in Fig. 4. Since each vehicle is primarily interestedin its own position, it would naturally implement thesubgraph corresponding to its own states as highlightedin the figure. A vehicle also maintains copies of the positionstates of other vehicles corresponding to times when a dis-tance measurement was obtained with them as depicted inFig. 2. If at a later time, more accurate estimates of thesestates are communicated to the vehicle, it incorporates thisinformation into its FG.

A direct consequence of implementing the subgraphson different vehicles is that the message-passing algorithmhas to now operate over the actual underwater acousticnetwork and information needs to be transferred betweenvehicles. This poses a number of challenges on the opera-tion of the sum-product algorithm compared to the cen-tralized case. To achieve the best case performance in adistributed setting, a vehicle has to share updates about

Fig. 4. Decomposed view of centralized dependency graph.

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all its states (past and current) with those vehicles thathad obtained a distance measurement to it. This is equiva-lent to passing messages over all links of the centralizedFG. However, in a distributed setting, messages can onlybe passed over the active communication links of the phys-ical acoustic network. The problem is that since vehiclesare moving, past states cannot be shared with those vehi-cles that have gone out of communication range.1 We havedepicted the problem that arises in the distributed case inFig. 5(a). The figure shows the network topology for threevehicles A;B and C at times t1 and t2. At time t1;B communi-cates with A and shares its current position state, PBðt1Þ.Vehicle A also estimates its distance to B at the same timeand incorporates this information in its factor-graph asshown in Fig. 5(c). Later at time t2;B gets new position infor-mation from vehicle C, which improves its past estimate att1. Now in a centralized solution, this updated informationwould have been passed to the subgraph of vehicle A, overthe link created at t1 as shown in Fig. 5(b). However, inthe distributed scenario this is not possible because A andB are no longer in communication range.

To achieve the best localization performance in the dis-tributed case, we propose that vehicles share their stateswith those that are multiple hops away. To do so they peri-odically broadcast their current and past position states aswell as forward the states of other vehicles. This addressesthe problem described in Fig. 5 because when B improvesits past estimate, PBðt1Þ at a later time t2, it routes thisimproved estimate to A. The limitation of this scheme com-pared to the centralized solution is that updates cannot beshared with vehicles that are not reachable via multihop.Nevertheless it gives the best possible real-time distrib-uted localization performance (by construction) and servesas a performance baseline. In the remainder of the paperwe will propose ways to minimize the energy overheadof the distributed tracking.

4.3. Distributed tracking with local information sharing

In the previous section, we presented the best distrib-uted real-time solution. However, since underwater acous-tic communication is resource intensive and the vehiclesare energy-constrained, we now consider ways to makeour distributed solution more practical. To limit thecommunication, we propose schemes that only use localinformation obtained from communication with immedi-ate neighbors. In the first scheme, each vehicle periodicallyshares its current and all past position states with itsimmediate neighbors. In the second scheme we furtherreduce the amount of information transmitted by vehiclesby having them periodically communicate only their currentposition state to their immediate neighbors. We next com-pare the performance of the tracking solutions presentedso far using the simulation setup described in [8].

1 Note that a similar problem exists in the centralized formulationbecause all measurements have to be routed to a single location, whilethere may be times when no route is available. However, in our simulationswe assume that measurements are always available at a single location forcentralized tracking. This was done to carry out a logical study of the factorsthat affect the performance of the distributed solution.

tracking for underwater networked systems, Ad Hoc Netw. (2014),

Fig. 5. (a) Network topology at times t1 and t2. FG at time t2. (b) Centralized tracking. (c) Distributed tracking.

0 20 40 60 80 100 120 140 160 180 2000

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1

RMS Error in Position Estimates (m)

Fra

ctio

n of

Pos

ition

Est

imat

es

Offline Centralized

Real−time Centralized

Real−time Distributed (best case)

Real−time Local (share all states with 1−hop neighbors)

Real−time Local (share current state with 1−hop neighbors)

NB

= 1, NU

= 8

Fig. 6. CDF of RMS error for proposed information schemes.

D. Mirza et al. / Ad Hoc Networks xxx (2014) xxx–xxx 7

Simulation setup: We implemented all the elements ofour real-time, centralized and distributed FG tracking inNS2 using the NSMiracle extensions for simulating under-water network protocols [14]. We simulated a networkwith 8 mobile vehicles and 1 beacon. The vehicles wereplaced in a 2 km � 2 km area. The beacons resided on thesurface, while the vehicles were at different depths. Weused the mobility model proposed in [7] where vehiclesfollow smooth curves. Vehicles transmitted localizationupdates every TLOC(s). While our proposed informationsharing schemes can be used with any MAC protocol,we chose a TDMA MAC. The simulation parameters aresummarized in Table 1.

Using the above described simulation set up we com-pared the performance of our offline solution (see Section3), real-time centralized (see Section 4.1), real-timedistributed (best case) (see Section 4.2) and the real-timedistributed tracking solutions with local informationsharing (described earlier in this section). The CDF ofRMS error in position estimates for the different trackingsolutions is shown in Fig. 6. As the results show themaximum loss in performance occurs when we go froman offline solution to a real-time one.

While there is some benefit in forwarding updates overmultiple hops, the energy overhead of doing so is substan-tial. However, we can come very close to the best casedistributed performance by sharing past estimates withimmediate neighbors. For these simulations, the resultssuggest that if performance is the key requirement withnominal constraints on energy a good compromise solu-tion may be to share current and past states with immedi-ate neighbors. However, if energy is of primary concern,then periodically sharing only the current state withimmediate neighbors is sufficient.

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To get a better understanding of the relative benefit ofthe different schemes, we evaluated their performancewhen the number of beacons, NB and number of vehiclesNU were varied. Later in Section 6, we provide a morein-depth discussion of how this affects the localizationperformance.

Fig. 7 shows the CDF of the RMS error in positionestimates for the different tracking solutions as well forthe non-collaborative case where vehicles only use mea-surements with beacons for position estimation. Theseresults show that there is significant gain in localizationaccuracy from inter-vehicle collaboration. Further, thisgain increases with the number of vehicles because of

tracking for underwater networked systems, Ad Hoc Netw. (2014),

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RMS Error in Position Estimates (m)

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ositi

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stim

ates

Real−time Centralized

Distributed (best case)

Local (share all states with 1−hop neighbors)

Local (share current state with 1−hop neighbors)

Non−collaborative

NB

= 1, NU

= 6(a)

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Fig. 7. Performance of real-time centralized, real-time distributed (best case) and real-time distributed tracking solutions with local information sharing fornetwors with (a) one beacon and 6 unknown nodes, (b) one beacon and 10 unknown nodes, (c) two beacons and 6 unknown nodes, (d) two beacons and 10unknown nodes.

8 D. Mirza et al. / Ad Hoc Networks xxx (2014) xxx–xxx

the additional constraints obtained from inter-vehicle dis-tance estimates. Among the collaborative schemes, sharingpast (refined) position states with other vehicles improveslocalization performance when there is only one beacon inthe network. For the networks with one beacon, when thenetwork connectivity is very low (NU ¼ 6), sharing paststates with only immediate neighbors almost achievesthe best case performance. However, when the connectiv-ity improves (NU ¼ 10), past states have to be shared overmultiple hops for the best case performance. This isbecause under conditions of low network connectivityvehicles that would benefit from past position updatesare not reachable via multihop. This also explains the per-formance difference between the real-time centralized andthe best case distributed solutions for NB ¼ 1 and NU ¼ 6.However, we observed that when the number of beaconsis increased (NB ¼ 2), the performance of the differentinformation sharing schemes almost overlap, showinglittle gain in sharing past estimates over single or multiplehops. Nevertheless we still observe a significant gain overthe non-collaborative case.

There may be times when the best performance isneeded, which requires vehicles to share updates aboutpast position estimates over single and multiple hops.However, we observed that in most cases, it is sufficient

Please cite this article in press as: D. Mirza et al., Real-time collaborativehttp://dx.doi.org/10.1016/j.adhoc.2014.10.008

to periodically share only the current position estimatewith neighbors.

5. Implementation details

5.1. Message representation

The sum-product algorithm operates efficiently on thepdf of discrete random variables while both position andvelocity are most naturally defined over continuous space.To address this problem, we approximate the true pdfof states by piece-wise constant distributions that are uni-formly weighted over 2D grids [7]. We have shown in ourprior work that if these distributions are binary weighted,the entire sum-product algorithm can be implemented inbinary logic which significantly reduces the computationoverhead [7].

To enable vehicles to control their energy consumptionwithout significantly deteriorating their localization accu-racy we propose to decouple the representation used whencommunicating pdfs over the wireless channel from thatused internally by vehicles. A more in depth descriptionof the proposed solution and how pdfs of different granu-larities can be compared can be found in our prior work

tracking for underwater networked systems, Ad Hoc Netw. (2014),

D. Mirza et al. / Ad Hoc Networks xxx (2014) xxx–xxx 9

[8]. The key point is that we can adapt the number of bytesused to communicate pdfs over the wireless channel,without significantly deteriorating the performance ofthe algorithm. This is summarized in Fig. 8 where we com-pare the localization performance for various values ofNcomm, the number of bytes used to represent communi-cated pdfs and Ninternal, the number of bytes used to repre-sent pdfs local to the nodes. The conclusion we can drawfrom this figure is that we maintain sufficient accuracywhen only transmitting 18 bytes of data for each pdf andmaintaining an internal pdf of 512 bytes. This low commu-nication overhead is key for a practical implementation ofthis system. There is a trade off between the number ofgrid points used to represent pdfs internally, Ninternal, andthe computation overhead of the algorithm. The numberof grid points is inversely related to the size of each grid.In the next section we will discuss why and how the gridsize adversely affects the accuracy of the algorithm andpropose an implementation to counter this effect as muchas possible under practical constraints.

5.2. Implementation of the factor graph for effectiveinformation fusion

While uniformly weighted piecewise constant distribu-tions minimize the computation and energy overhead ofthe sum-product algorithm, they deteriorate the accuracyof position estimates by introducing rounding errors. Inthis section we present why these errors are introducedand provide an approach that minimizes their effect.

The local factor graph of each vehicle essentially fusesdistance estimates to neighbor vehicles, obtained at differ-ent times, to compute the pdf of all the states specified bythe vertices of the graph. Each distance measurement (incombination with an estimate of the position of the neigh-bor vehicle) provides an independent estimate of the posi-tion of the vehicle at the time that it was obtained. Inprinciple the measurements of the vehicle’s motion allow

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Fig. 8. CDF of RMS error in position estimates as a function of the numberof bytes used to communicate each message, Ncomm and the number ofbytes used to represent the message internally, Ninternal .

Please cite this article in press as: D. Mirza et al., Real-time collaborativehttp://dx.doi.org/10.1016/j.adhoc.2014.10.008

these estimates to be translated to any past or futuretime, t where they are fused. The translation in time ismathematically given by

PðtjziÞ ¼ PðtijziÞ þ vðti; tÞjti � tj þ ev jti � tj ð8Þ

where zi denotes the distance estimate obtained at timeti; PðtijziÞ denotes the estimate of the position of the vehicleat time ti due to the distance measurement obtained at ti

alone, vðti; tÞis the estimate of the vehicle’s average veloc-ity in the interval ðti; tÞ and ev is the error in velocitymeasurements.

As the error term in the above equation shows there isadditional uncertainty in the translated position estimatePðtjziÞ since measurements of the vehicle’s motion arenot exact.

In practice, the translation step given by Eq. (8) is per-formed numerically by the SP algorithm. This introducesa rounding error every time a translation is performedbecause the true pdf is approximated by the binaryweighted piecewise constant pdfs (that were described inthe previous section). In effect the true pdf of any state issmeared every time information is passed from one statein the graph to an adjacent state. The extent of smearingat each stage depends on the grid size of the representa-tion. Further, the rounding errors introduced due to gridsize have a cumulative effect when information availablein one state has to pass through many intermediate states(that do not provide additional information) in order to bemerged with information available in a different state inthe graph.

To further elucidate the effect of intermediate statesand grid size on rounding errors, consider the examplefactor-graph shown in Fig. 9 where distance estimatesare obtained at two time instances t1 and t6. Each of thesemeasurements provides an independent estimate of theposition of the vehicle at the time that it was obtaineddenoted as Pðt1jz1Þ, and Pðt6jz6Þ respectively. Now to obtainthe final estimates of the positions at times t1 and t6 posi-tion information obtained at time t1 has to be translated tot6 and vice versa. In essence we need to compute Pðt6jz1Þand Pðt1jz6Þ. These estimates can be obtained as perEq. 8. However, the factor-graph in Fig. 9 shows that thereare 4 intermediate states between t1 and t6. These states donot have any measurements of distance associated withthem and are solely present because the applicationrequires an estimate of the vehicle’s position at thesetimes. Since the SP algorithm computes the pdf of any stateusing only that of its neighbor states, rounding errors areadded at every intermediate state when Pðt1jz1Þ is trans-lated to t6. Therefore, these errors have a cumulative effect.

To minimize the cumulative effect of rounding errorsthe size of the grids used to represent pdfs must be verysmall and far more grid points are required which increasesthe computation overhead. This problem becomes spe-cially pronounced when distance measurements becomeavailable very intermittently compared to the trackinggranularity, d. To address this issue we propose an alter-nate implementation of the factor-graph that was earlierpresented in Section 4. Note that logically our solution stillfollows the one presented in Section 4 to estimate posi-tions in real time.

tracking for underwater networked systems, Ad Hoc Netw. (2014),

Fig. 9. Factor graph with 4 intermediate states between t1 and t6.

10 D. Mirza et al. / Ad Hoc Networks xxx (2014) xxx–xxx

We refer to states corresponding to times when at leastone distance measurement is available as informativestates. All other states are referred to as empty states. Inour proposed implementation the pdfs of the unknownstates are computed in two steps as shown in Fig. 10. Wefirst define the factor-graph over all informative states.The implementation of this step for the original factorgraph shown in Fig. 2(b) is presented in Fig. 10(a). Notethat in this step aggregating the motion measurementsover the intervals between the informative states elimi-nates the empty states. The sum-product algorithm is thenexecuted on this factor-graph to estimate the pdf of allinformative states. By eliminating the intermediate emptystates, the effect of rounding errors are minimized whencombining distance estimates obtained at different times.

Next we interpolate between the informative states(using motion measurements) to compute the pdf of allother states. The factor-graph corresponding to this step(for the original FG, Fig. 2(b)) is shown in Fig. 10(b). Asshown in the figure, the pdf of each state in the intervalðt1; t2Þ is computed using the estimates at t1 and t2 andthe appropriate aggregated motion measurements. Simi-larly, states in the interval ðt2; t3Þ are computed from theposition estimates at t2 and t3 and those later than t3 arecomputed using the estimate at t3 alone.

We now evaluate the performance of our proposed FGimplementation versus the one where all the unknownstates are estimated in one shot. In order to isolate theeffect of intermediate empty states on the localizationaccuracy from all other parameters that affect performance,we simulated a scenario where only one vehicle wastracked using distance estimates from beacons. A measure-ment of distance was made with a beacon every 36s. Threebeacons were used for tracking. The vehicle position wasestimated every 3s. Keeping the maximum number of gridpoints used to represent the pdf of position estimates thesame, we compared the RMS error in position estimatesobtained over 20 min of simulation time using the FGimplementation shown in Fig. 2 and the proposed imple-mentation shown in Fig. 10. The cumulative distributionfunction (cdf) of the RMS error in estimates for the twoimplementations is shown in Fig. 11(a) and the RMS errorversus time is shown in Fig. 11(b). From these results we

Fig. 10. Proposed implementation. (a) FG for estimating informative st

Please cite this article in press as: D. Mirza et al., Real-time collaborativehttp://dx.doi.org/10.1016/j.adhoc.2014.10.008

observe that the localization accuracy improves signifi-cantly using our proposed implementation.

In summary, for real-time tracking the FG implementedby each vehicle will conceptually evolve as described inSection 4 however we implement it as explained in thissection. In addition, the grid size used to represent pdfsinternally is kept small by using signifcantly larger numberof bytes to represent these pdfs internally compared to thenumber of bytes used to communicate these pdfs betweenvehicles. This essentially translates to choosing a muchlarger value for the parameter Ninternal compared to theparameter Ncomm.

6. Deployment considerations

For the simulations in this section we compare non-collaborative localization to sharing the current state witha 1-hop neighbor (shortened to ‘‘Collaborative’’ for theremainder of this section) because it was shown in ourprevious work [8] that the localization accuracy obtainedby this scheme was the same as sharing all information withall reachable nodes. We specifically investigate how key fac-tors, namely, direct communication with beacons, networkconnectivity, and inaccuracies in the position estimateslimit the scenarios where the proposed collaborative algo-rithm outperforms a non-collaborative approach.

6.1. Dependence on proximity to beacon

Since position information always percolates into thenetwork starting at a beacon, one of the factors thatnaturally determines the error in position estimates isthe proximity of nodes to beacons. In this section we quan-tify the impact of direct communication with beacons onthe localization (relative to other factors). To do this wesimulated a scenario with 6 unknown nodes and onebeacon. The trajectory of one of the unknowns is shownin Fig. 12(a). The trajectory of other nodes followed asimilar pattern, however each track was generated inde-pendent of the others. The trajectory shown in Fig. 12(a)is color coded into three segments to indicate the level ofconnectivity of the node to the beacon and to other nodes

ates. (b) FG for estimating empty states from informative states.

tracking for underwater networked systems, Ad Hoc Netw. (2014),

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D. Mirza et al. / Ad Hoc Networks xxx (2014) xxx–xxx 11

in the network. The segments of the trajectory in redcorrespond to times when the node was within thecommunication range of the beacon, the segments in greencorrespond to times when it was within the communica-tion range of at least another node and the segments inblack correspond to times when it was not within thecommunication range of any node.

For the above described scenario we tracked the loca-tion of all unknowns in real-time using both collaborativeand non-collaborative localization. To quantify the impactof direct communication with a beacon on the localizationaccuracy, we separated the position estimates obtainedduring an entire simulation into two sets. The first setcorresponded to estimates obtained at times when a nodecommunicated directly with a beacon (the red segments ofthe trajectory in Fig. 12(a)) and the second set consisted oftimes when the node could not receive any beacon signal(the green and black segments of the trajectory inFig. 12(a)). The cdf of the RMS error in estimates for bothsets are shown in Fig. 12(b).

Fig. 12(b) shows the relative benefit of collaborativetracking to non-collaborative tracking based on directproximity to beacons. We observe that there is a muchgreater disparity in the localization performance between

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Fig. 12. (a) Trajectory of one of the nodes under evaluation with regions icommunication with only other unknown nodes (green) and regions of no commthe error when nodes are in range of the beacon versus when they are out of ranglegend, the reader is referred to the web version of this article.)

Please cite this article in press as: D. Mirza et al., Real-time collaborativehttp://dx.doi.org/10.1016/j.adhoc.2014.10.008

the non-collaborative and collaborative frameworks whennodes are not in the range of the beacon compared to whenthey are. If a node is in the range of beacons, there is notmuch gain from using collaboration. However, if it is outof range of beacons significant gains can be obtained byleveraging the localization information of other nodes.Notice that this gain can only occur when collaborationprovides the nodes good information, i.e. the collabora-tion nodes are in communication with a beacon. Whilethe specific trajectory is not important, what is importantis whether or not a node can receive good informationfrom other nodes when they are collaborating. We willsee examples later where sharing bad information canactually hurt the localization performance of a specificnode.

The results support what we intuitively expect: theerror in position estimates is least when a node is in thedirect communication range of a beacon. Additionally,we observe that both in the case of collaborative and non-collaborative localization, there is significant disparity inthe error when nodes are within the range of the beaconcompared to when they are not. This indicates that a keyfactor in determining the position accuracy of a node iswhether or not it is within the communication range of a

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ndicating direct communication with beacon (red), regions indicatingunication (black). (b) CDF of RMS error comparing the difference between

e of the beacon. (For interpretation of the references to colour in this figure

tracking for underwater networked systems, Ad Hoc Netw. (2014),

12 D. Mirza et al. / Ad Hoc Networks xxx (2014) xxx–xxx

beacon and the benefit of direct communication with abeacon outweighs the gains from inter-node collaboration.

Based on the above findings we would like to developthe importance of a node periodically receiving localizationinformation from a beacon. Addressing this questionrelates to strategizing the placement of beacons in a net-work, as the number of available beacons is increased.

6.2. First hand versus second hand information

In this section we consider the following question: If thenumber of beacons available for tracking is increased, would itbe better to distribute them uniformly or non-uniformly overthe area of deployment?

We consider the above question because when the spa-tial distribution of beacons is not uniform we expect theerror of a subset of the nodes to be minimized. In principlethese nodes can then localize other nodes in the networkthat have less frequent (or no access) to beacons. On theother hand when the beacons are uniformly distributedin the network we expect all nodes to achieve approxi-mately the same level of accuracy. Since most nodes donot have an information advantage over others, we wouldalso expect little gains from collaboration in such ascenario.

To investigate the above conjectures we considered twosimulation scenarios shown in Fig. 13(a) consisting of sixstationary beacons and two unknowns that are alwayswithin the communication range of each other. In one ofthe scenarios all six beacons were arranged linearly in anon-staggered fashion such that the bottom node (whosetrajectory is shown in blue) is always within the range ofa beacon and the top node never hears a beacon. In thesecond scenario the beacons were placed in a staggeredfashion, such that the bottom (blue) track intersects thecommunication range of three of the beacons and the top(green) track intersects the communication range of theother three beacons. We considered the localization errorof the top (green) track to compare the benefit of receiving

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Fig. 13. Experiments describing hearing a beacon versus receiving location infbeacon range) the top node cannot communicate with the beacons Staggered: (blbeacons (b) CDF of error in position estimates for collaborative and non collaborathis figure legend, the reader is referred to the web version of this article.)

Please cite this article in press as: D. Mirza et al., Real-time collaborativehttp://dx.doi.org/10.1016/j.adhoc.2014.10.008

information from a beacon and a neighboring node (thestaggered beacon arrangement) to the case where we onlyreceive information from a neighboring node who receivesinformation from twice as many beacons (the non-staggered beacon arrangement). The cdf of the RMS errorin the position estimate of the top track is shown inFig. 13(b). The results show that the staggered beaconarrangement provides much better localization accuracyfor the top node compared to the non-staggered arrange-ment. We also observe that there is little gain from collab-oration in the staggered case. This is because in this casethe errors in the position estimates of both nodes are com-parable. Consequently, there is little gain from sharingthese estimates. However, in the non-staggered arrange-ment where the top node never hears a beacon there isnoticeable gain from communicating with the bottomnode.

Additionally, we considered the case shown in Fig. 14(a)where the beacon range is extended so that the bottomnode intermittently receives updates from two beaconsat a time to further reduce its error. In this case there isan additional improvement in the accuracy of the top trackwhen the tracking is done collaboratively as shown inFig. 14(b). This indicates that we can increase the locationaccuracy of both nodes by increasing the number ofbeacons used to localize one of them. However, this gainis clearly inferior to allowing the top node to receivelocation information from a beacon directly.

6.3. Redundant information

In this section we would like to understand how muchcollaboration is really useful and when. We evaluatewhether a node can improve its estimate when communi-cating with nodes traveling in similar trajectories. To dothis we consider the networks of Fig. 15, where one nodeis never in communication range of a beacon while the restof the nodes are in range of the beacon at some pointduring the simulation. In the first case, Fig. 15(a), there

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ormation from another unknown (a) Non-Staggered: (red dotted line forack .- line for beacon ranges) the top node periodically communicates withtive localization schemes. (For interpretation of the references to colour in

tracking for underwater networked systems, Ad Hoc Netw. (2014),

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Fig. 14. (a) Non-Staggered beacon arrangement with increased beacon transmission range (blue .- line for beacon ranges) and (b) results plotted for the top(green) trajectory. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

D. Mirza et al. / Ad Hoc Networks xxx (2014) xxx–xxx 13

are 2 nodes following similar trajectories. The bottom node is inrange of the beacon for a portion of the simulation while thetop node can only receive localization information by commu-nicating with the bottom node. The other case presented inFig. 15(b) is different from Fig. 15(a) in that there are now fivenodes that receive a signal from the beacon and can communi-cate with the node that never hears a beacon.

The results of these simulations are shown in Fig. 15(c),plotted only for the node that can never communicate

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Fig. 15. Trajectories quantifying the results of sharing redundant information (beand (c) results-CDF of RMS error in position estimates: note that the perf(For interpretation of the references to colour in this figure legend, the reader is

Please cite this article in press as: D. Mirza et al., Real-time collaborativehttp://dx.doi.org/10.1016/j.adhoc.2014.10.008

with the beacon. These results show that the collaborativecase with only a two-node network provides the bestlocalization accuracy. In fact, the collaborative resultperforms worse than the non-collaborative case in thesix-node network. This brings up an interesting consider-ation about the proposed collaborative localization frame-work. When nodes have poor estimates of their positionsthe collaborative localization will actually decrease thelocalization accuracy of each node. In other words, sharing

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acon range shown in blue ellipse): (a) 2 node network, (b) 6 node networkormance of the non-collaborative tracking is the same for all cases.referred to the web version of this article.)

tracking for underwater networked systems, Ad Hoc Netw. (2014),

14 D. Mirza et al. / Ad Hoc Networks xxx (2014) xxx–xxx

bad information produces worse results than sharing no(or less) information. This effect is due to practical limita-tions on the implementation of the algorithm rather thanan inherent property of the algorithm.

The fact that the six node network performed worsethan the two node network can be explained by revisitingthe discussion of Section 5.2. In the above consideredsimulation scenarios, the five bottom nodes’ localizationaccuracy decreases when they leave the proximity of thebeacon, yet they are still receiving ranging informationfrom each other. Each time new range information isreceived by a node from a neighboring node, an additionalstate is inserted into the factor graph. As such the addi-tional states introduced in the graph are not informativesince all nodes have similar errors and these errors aregrowing monotonically. This causes us to go from ourdesired case of Fig. 10 to the case we were trying to getaway from in Fig. 9. The introduction of these uninforma-tive intermediate states causes our solution to suffer therounding errors discussed in Section 5.2. As explainedearlier in that section, these rounding errors are a resultof representing the estimated pdfs using only a finite andnominal number of grid points. As such this effect wouldnot come into play if the pdfs could be represented withinfinite accuracy. The above simulation scenario wasspecifically chosen to show that when all nodes in the net-work have poor estimates of their positions, sharing redun-dant information does not provide any benefit, but rathercan hurt the localization accuracy of the nodes due to prac-tical limitations in the implementation of the algorithm.

Our simulation results show that direct communicationwith beacons, network connectivity and inaccuracies in theposition estimates limit the scenarios where the proposedcollaborative algorithm outperforms a non-collaborativeapproach. To summarize our conclusions:

1. The localization accuracy of any node is primarilydetermined by the extent of time it is in direct commu-nication with beacons. If multiple beacons are availableit is more beneficial to distribute them in such a waythat all vehicles have an equal opportunity to periodi-cally hear at least one beacon

2. If a node is in the range of beacons, there is not muchgain from using collaboration. However, if it is out ofrange of beacons significant gains can be obtained byleveraging the position estimates of other nodes.

3. Collaboration is beneficial when nodes do not havedirect communication with beacons, however, due topractical limitations of the factor-graph algorithm,nodes with large and growing position errors shouldrefrain from sharing their estimates with others.

7. Conclusion

In this paper we reviewed a low overhead collaborativetracking solution for underwater mobile networks thatestimates the location of vehicles in real-time and in a dis-tributed fashion. We identified key factors that fundamen-tally limit the performance of real-time (centralized anddistributed) solutions, quantifying their effects via simula-tions. We also showed that in certain scenarios, vehicles

Please cite this article in press as: D. Mirza et al., Real-time collaborativehttp://dx.doi.org/10.1016/j.adhoc.2014.10.008

need to share information over multiple hops for best caseperformance. However, in our proposed scheme they onlyuse information that is obtained locally. We further testedthe collaborative localization framework against differentmotion models and concluded that in a network wherenodes follow more predictable trajectories, the localizationperformance can be most significantly enhanced by strate-gically placing beacons so that all vehicles have the oppor-tunity to periodically hear a beacon. The collaborativescheme is less suited to such networks, where there is littledisparity in the localization accuracy of vehicles due tosufficiently frequent communication with beacons. How-ever, networks where the vehicles move in an unpredict-able fashion are less amenable to a strategic placement ofbeacons. For such networks significant gains are possibleby using our proposed collaborative solution. Even still,the collaborative approach does have its limitations. Inpoorly designed networks, where nodes experienceextended outages in beacon communication as a group,the collaborative localization framework can do moreharm than good. By avoiding inter-node communicationduring these times, the collaborative localization can effec-tively expand the network, allowing good position esti-mates to nodes who temporarily or even permanentlyare not in range of a beacon.

Acknowledgements

This work is part of the project ‘‘Networked SensorSwarm of Underwater Drifters’’ supported by the NSFunder Award Number 1035828, ‘‘INSPIRE Track I: Distrib-uted Sensing Collective to Capture 3D Soundscapes’’ andby the National Science Foundation under IGERT AwardNumber DGE-0966375, ‘‘Training, Research and Educationin Engineering for Cultural Heritage Diagnostics.’’ Addi-tional support was provided by the Qualcomm Instituteat UC San Diego, the Friends of CISA3 and the World Cul-tural Heritage Society. Opinions, findings, and conclusionsfrom this study are those of the authors and do not neces-sarily reflect the opinions of the research sponsors.

Appendix A

This paper is an extension of our previous work oncollaborative tracking [8], published in the InternationalConference on Underwater Networks and Systems (WUW-Net’12). In this paper we have made two key additionscompared to the conference version:

1. An in depth discussion of the implementation of theFactor-Graph Algorithm, presented in Section 5.2

2. Deployment considerations that can significantly im-pact the localization accuracy of the network, presentedin Section 6. In this section we have identified and ana-lyzed scenarios where our collaborative approach showssignificant gains, as well as those that highlight thelimitations of our approach

The materials presented in both Sections 5.2 and 6 havenot appeared in any previous publication.

tracking for underwater networked systems, Ad Hoc Netw. (2014),

D. Mirza et al. / Ad Hoc Netwo

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Please cite this article in press as: D. Mirza et al., Real-time collaborativehttp://dx.doi.org/10.1016/j.adhoc.2014.10.008

Diba Mirza is currectly a Lecturer in theDepartment of Computer Science and Engi-neering at the University of California, SanDiego. She received a M.S. and Ph.D. in Elec-trical Engineering from UCSD in 2010 and aB.E. in Electrical Engineering from Birla Insti-tute of Technology and Science, Pilani, India in2002. She was a postdoc at the Department ofComputer Science and Engineering at UCSDfrom 2010 to 2013. Her research interestsinclude underwater acoustic navigation andnetworked systems.

rks xxx (2014) xxx–xxx 15

Perry Naughton is currently a Ph.D. studentin the Electrical Engineering department atthe University of California, San Diego. He isinterested in remote imaging tools for culturalheritage diagnostics, especially in underwaterenvironments. He received his B.S. in Electri-cal Engineering from the University of Cali-fornia, San Diego in 2012.

Curt Schurgers received his Ph.D. from UCLAin Integrated Circuits and Systems, and hisEngineering degree from the KatholiekeUniversiteit Leuven (Belgium). He was a Lec-turer at UCLA in VLSI System Design, and heldresearch assistantships at UCLA Networked &Embedded Sysytems Lab and the Interuniver-sity Microelectronics Center in Belgium. Hejoined UCSD in 2003 as a Professor in ECE, andcurrently works at the UCSD Qualcomm Insti-tute as a Research Engineer, Project Leader,Area Manager and Development Engineer.

Ryan Kastner is currently a Professor in theDepartment of Computer Science and Engi-neering at the University of California, SanDiego. He received a Ph.D. in Computer Sci-ence at UCLA, a masters degree (MS) in Engi-neering and bachelor degrees (BS) in bothElectrical Engineering and Computer Engi-neering, all from Northwestern University. Heis the co-director of the Wireless EmbeddedSystems Master of Advanced Studies Program.He also co-directs the Engineers for Explora-tion Program. His current research interests

reside in the realm of embedded system design, in particular, the use ofrecon gurable computing devices for digital signal processing.

tracking for underwater networked systems, Ad Hoc Netw. (2014),