Review Article A Survey of Sound Source Localization Methods in Wireless Acoustic Sensor Networks

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1 Hndaw Wreless Communcatons and Moble Computng Volume 7, Artcle ID 39568, 4 pages Revew Artcle A Survey of Sound Source Localzaton Methods n Wreless Acoustc Sensor Networks Maxmo Cobos, Fabo Antonacc, Anastasos Alexandrds, 3,4 Athanasos Mouchtars, 3,4 and Bowon Lee 5 Department of Computer Scence, Unverstat de Valènca, 46 Burjassot, Span Dpartmento d Elettronca, Informazone e Bongegnera, Poltecnco d Mlano, 33 Mlano, Italy 3 Insttute of Computer Scence (ICS), Foundaton for Research & Technology-Hellas (FORTH), Heraklon, 73 Crete, Greece 4 Department of Computer Scence, Unversty of Crete, Heraklon, 73 Crete, Greece 5 Department of Electronc Engneerng, Inha Unversty, Incheon, Republc of Korea Correspondence should be addressed to Maxmo Cobos; maxmo.cobos@uv.es Receved 8 May 7; Accepted 8 June 7; Publshed 7 August 7 Academc Edtor: Álvaro Marco Copyrght 7 Maxmo Cobos et al. Ths s an open access artcle dstrbuted under the Creatve Commons Attrbuton Lcense, whch permts unrestrcted use, dstrbuton, and reproducton n any medum, provded the orgnal work s properly cted. Wreless acoustc sensor networks (WASNs) are formed by a dstrbuted group of acoustc-sensng devces featurng audo playng and recordng capabltes. Current moble computng platforms offer great possbltes for the desgn of audo-related applcatons nvolvng acoustc-sensng nodes. In ths context, acoustc source localzaton s one of the applcaton domans that have attracted the most attenton of the research communty along the last decades. In general terms, the localzaton of acoustc sources can be acheved by studyng energy and temporal and/or drectonal features from the ncomng sound at dfferent mcrophones and usng a sutable model that relates those features wth the spatal locaton of the source (or sources) of nterest. Ths paper revews common approaches for source localzaton n WASNs that are focused on dfferent types of acoustc features, namely, the energy of the ncomng sgnals, ther tme of arrval (TOA) or tme dfference of arrval (TDOA), the drecton of arrval (DOA), and the steered response power (SRP) resultng from combnng multple mcrophone sgnals. Addtonally, we dscuss methods not only amed at localzng acoustc sources but also desgned to locate the nodes themselves n the network. Fnally, we dscuss current challenges and fronters n ths feld.. Introducton Wth the rapd development n felds lke crcut desgn and manufacturng, wreless nodes ncorporatng a varety of sensors, communcaton nterfaces and compact mcroprocessors have become economcal resources for the desgn of nnovatve montorng systems. Networks of such type of devces, referred to as wreless sensor networks (WSNs) [, ], have been wdely spread and used n many felds, wth applcatons rangng from survellance and mltary deployments to ndustral and health-care systems [3]. When the nodes ncorporate acoustc transducers and the processng nvolves the manpulaton of audo sgnals, the resultng network s usually referred to as a wreless acoustc sensor network (WASN). A WASN conssts of a set of sensor nodes nterconnected va a wreless medum [4]. Each node has one or several sensors (mcrophones), a processng unt, a wreless communcaton module, and, sometmes, also one or several actuators (loudspeakers) [5]. Durng the last decade, the use of locaton nformaton and ts potentalty n the development of ambent ntellgence applcatons has promoted the desgn of local postonng systems wth WSNs [6]. Usng WSNs to perform localzaton tasks has always been a desrable property snce, besdes beng consderably cheap, they are easly deployable. Localzaton and rangng n WSNs have been typcally addressed by measurng the receved sgnal strength (RSS) or tme of arrval (TOA) of rado sgnals [7]. However, the RSS approach, whle beng sgnfcantly nexpensve, ncurs sgnfcant errors due to channel fadng, long dstances,

2 Wreless Communcatons and Moble Computng and multpath. In the context of acoustc sgnal processng, WASNs also provde advantages wth respect to tradtonal (wred) mcrophone arrays [8]. For example, they enable ncreased spatal coverage by dstrbutng mcrophone nodes overalargervolume,ascalablestructure,andpossblybetter sgnal-to-nose rato (SNR) propertes. In fact, snce the rangng accuracy depends on both the sgnal propagaton speed and the precson of the TOA measurement, acoustc sgnals may be preferred wth respect to rado sgnals [9]. There are two typcal localzaton tasks n WASNs: the localzaton of one or more sound sources of nterest and the localzaton of the nodes that make up the network. The frst case may nvolve locatng the poston of unknown sound sources, for example, talkers nsde a room or unexpected acoustc events or sometmes other devces emttng known beacon sgnals. The second case s usually related to the selfcalbraton or automatc rangng of the nodes themselves. To estmate the locatons of the sound sources that are actve n an acoustc envronment montored by a WASN, dfferent methods exst n the lterature. Usually, a centralzed scheme s adopted where a dedcated node, known as the fuson center, s responsble for performng the localzaton task based on nformaton t receves from the rest of nodes. The sensor network tself poses many lmtatons and challenges that must be consdered when desgnng a localzaton approach n order to facltate ts use n practcal scenaros. Such challenges nclude the bandwdth usage whch lmts the amount of nformaton that can be transmtted n the network and the lmted processng power of the nodes whch prohbts them from carryng out very complex and computatonally expensve operatons. Moreover, each node has ts own clock for samplng the sgnals and snce the nodes operate ndvdually, the resultng audo n the network wll not be synchronzed. A taxonomy of sound source localzaton methods can be bult up upon the nature of nformaton from the sensors that t s utlzed n order to estmate the locatons. Hence, thewasncanestmatethelocatonsoftheacoustcsources based on () energy readngs, () tme-of-arrval (TOA) measurements, () tme-dfference-of-arrval (TDOA) measurements, and (v) drecton-of-arrval estmates or (v) by utlzng the steered response power (SRP) functon. In DOA-based approaches, each node estmates the DOA of the sources t can detect and transmts the DOA estmates to the fuson center. Although such approaches requre ncreased computatonal power and multple mcrophones n each node, they can attan very low-bandwdth usage, as only the DOA estmates need to be transmtted. Also, snce the DOA estmaton s carred out n each node ndvdually, the audo sgnals at dfferent nodes need not be synchronzed: DOA-based approaches can tolerate unsynchronzed nput as long as the sources move at a rather slow rate relatve to the analyss frame. The locaton estmators are generally based on estmatng the locaton of a sound source as the ntersecton of lnes emanatng from the nodes at the drecton of the estmated DOA. However, for multple sources several challenges arse: the number of detected sources (and thus thenumberofdoaestmates)neachtmenstantcanvary across the nodes due to mssed detectons (.e., a source s not detected by a node) or false-alarms (.e., overestmaton of the number of detected sources) and an assocaton procedure s needed to fnd the DOA combnatons that correspond to the same source. Ths s known as the data-assocaton problem and s crucal for the localzaton task. TheTDOAsrelatedtothedfferencenthetmeofflght (TOF) of the wavefront produced by the source at a par of mcrophones n the same node. TDOAs can be estmated at a moderate computatonal cost through the generalzed cross correlaton (GCC) [] of the sgnals acqured by mcrophonesnthepar.thesourcelocatonestmates accomplshed by combnng TDOA measurements comng from multple sensors. Notce that, as for the DOA, only the TDOA measurements must be transmtted over the wreless network, wth clear advantages n terms of transmsson power and requred bandwdth. Though sutable for WASNs, n practcal scenaros (reverberant envronments, presence of nose, and nterferers), TDOA measurements are prone to errors, whch n ther turn lead to wrong localzaton. In order to mtgate the mpact of these adverse phenomena, several technques have been presented wth the am of dentfyng and removng outlers n the TDOA set [ 3]. A TDOA measurement bounds the source to le on a branch of hyperbola whose vertces are n mcrophone postonsandwhoseaperturesdetermnedbythetdoa value. When two (three n 3D) measurements from dfferent pars are avalable, the source can be localzed through ntersecton of hyperbolas. The resultng cost functon, however, s strongly nonlnear, and therefore ts mnmzaton s dffcult and prone to errors. Lnearzed cost functons have been proposed to overcome ths dffculty [4 6]. It s mportant to notce, however, that the lnearzed cost functons requre the presence of a reference mcrophone, wth respect to whch the remanng mcrophones n all the sensors must be synchronzed. Ths poses technologcal constrants that, n some cases, hnder the use of such technques. More recently, methodologes that nclude the synchronzaton offset n the optmzaton of the cost functon have been proposed to overcome ths problem [, 7]. TOA measurements are obtaned by detectng the tme nstantatwhchthesourcesgnalarrvesatthemcrophones present n the network. Snce n passve source localzaton the source emsson tme s unknown, the TOA s not equvalent to the TOF of the sgnal, preventng a drect mappng from TOAs to source-to-node dstances. Whle some applcatons nvolve the use of sound-emttng nodes that allows performng localzaton by usng trlateraton technques, TDOA localzaton methods are usually chosen. In ths case, although the source emsson tme does not need to be known, the regstered TOAs need to be referenced to a common clock, requrng precse tmng hardware and synchronzaton mechansms. Energy-based localzaton reles on the averaged energy readngs computed over wndows of sgnal samples acqured by the mcrophones ncorporated by the nodes [8]. Compared to TDOA and DOA methods, energy-based approaches are attractve because they do not requre the use of multple mcrophones at the nodes and are free of synchronzaton ssues unlke those based on TOA.

3 Wreless Communcatons and Moble Computng 3 () () 3 x s 3 () r () y () m r 3 () m (3) 3 m 3 () q m () m () m 3 (w) y 3 q 3 m (3) y m 3 () m () Fgure: WASN wthm =3nodes and N=3mcrophones per node. q However, TDOA- and DOA-based methods, consdered as sgnal-based approaches, offer generally better performance than energy-based methods. Ths s due to the fact that the nformatonconveyedbyallthesamplesofthesgnals drectly exploted nstead of ther average, at the expense of more sophstcated capturng devces and transmsson resources [8, 9]. SRP approaches are beamformng-based technques that compute the output power of a flter-and-sum beamformer steered to a set of canddate source locatons defned by a predefned spatal grd. Snce the computaton of the SRP nvolves the accumulaton of GCCs from multple mcrophone pars, the synchronzaton requrements are usually thesameasthoseoftdoa-basedmethods.thesetofsrps obtaned at the dfferent ponts of the grd make up the SRP power map, where the pont accumulatng the hghest value corresponds to the estmated source locaton. When usng unsynchronzed nodes wth multple mcrophones, the SRP power maps computed at each node can be used to obtan ther correspondng DOAs. Alternatvely, the SRP power maps from the dfferent sensors can be accumulated at a central node to obtan a combned SRP power map, dentfyng the true source locaton by ts maxmum. Besdes the localzaton of acoustc sources, approaches for localzng the nodes n the network are also of hgh nterest wthn a WASN context. Based on the estmated TOAs and TDOAs, algorthms for self-localzaton of the sensor nodes usually assume known source postons playng known probe sgnals. In practcal scenaros, each sensor node does not have any nformaton regardng other nodes or synchronzaton between the sensor and the source. These assumptons allow all processng to take place on the node tself. Several ssues, for example, reverberaton, asynchrony betweenthesoundsourceandthesensor,poorestmaton of the speed of sound, and nose, need to be consdered for robust self-localzaton methods. In addton, the processng needs to be computatonally nexpensve n order to be run onthesensornodetself. Some state-of-the-art solutons for acoustc sensor localzaton detal the challenges facng these algorthms and methods to tackle such problems n a unfed context [, ]. Furthermore, recent methodologes have been proposed for probe sgnal desgn amed at mprovng TOF estmaton [], the jont localzaton of sensors and sources n an ad hocarraybyusnglow-rankapproxmatonmethods[3], and an teratve peak matchng algorthm for fast node autocalbraton [4]. Thepapersstructuredasfollows.Sectondscusses some general consderatons regardng a general WASN structure and the notaton used throughout ths paper. Secton 3 presents the fundamentals of energy-based source localzaton methods. Secton 4 dscusses TOA-based localzaton approaches. Methods for TDOA-based localzaton are presented n Secton 5. Secton 6 dscusses the use of DOA measurements to perform localzaton of one or several sound sources. In Secton 7, the fundamentals of the conventonal and modfed SRP methods are explaned. Secton 8 revews some recent methods for the self-localzaton of the nodes n the network. Some future drectons n the feld are dscussed n Secton 9. Fnally, the conclusons of ths revew are summarzed n Secton.. General Consderatons In order to clarfy the notaton used throughout ths paper and the type of locaton cues used to perform the localzaton task, Fgure shows a general WASN wth a set of wreless nodes and an emttng sound source. It s assumed that the network conssts of M nodes and that each node ncorporates N mcrophones. In the example shown n Fgure, M=3and N=3.Thenodesareassumedtobelocatedatpostonsq m = [q x,m,q y,m,q z,m ] T, m =,...,M, whle the mcrophone locatons are denoted as m (m) =[x (m),y (m),z (m) ] T, =,..., N, where the superscrpt(m) dentfes the node at whch themcrophoneslocated.thesourcepostonsdenoted

4 4 Wreless Communcatons and Moble Computng as x s = [x s,y s,z s ] T, whle a general pont n space s x = [x,y,z] T. Note that all these locaton vectors are referenced tothesameabsolutecoordnatesystem.thedstancefrom any mcrophone to the sound source s denoted as r (m),whle the tme t takes the sound wave to travel from the source to a mcrophone, that s, the tme of flght (TOF), s denoted by η (m).thetmenstantatwhchthesourcesgnalarrves to a gven mcrophone, that s, the TOA, s denoted as τ (m). TDOAs are denoted by τ (m) and correspond to the observed TOA dfferences between pars of mcrophones (). Itsa common practce to dentfy dfferent pars of mcrophones by usng an ndex p =,...,P,wherePs the total number of mcrophone pars nvolved n the localzaton task. The DOA corresponds to the angle that dentfes the drecton relatvetothenodemcrophonearraythatpontstothesound source and s denoted by θ m. Fnally, the energy values of the source sgnal measured at the nodes are denoted as y m. Theseareneglgbleformcrophoneslocatedatthesamenode (especally f the nodes are relatvely far from the source), so t s usually assumed that only one energy readng s obtaned for each node. 3. Energy-Based Source Localzaton Tradtonally, most localzaton methods for WASNs have been focused on sound energy measurements. Ths s motvated by the fact that the acoustc power emtted by targets usually vares slowly n tme. Thus, the acoustc energy tme seres does not requre as hgh a samplng rate as the raw sgnal tme seres, avodng the need for hgh transmsson rates and accurate synchronzaton. The energy-based model was frst presented n [5]. In ths model, the acoustc energy decreases approxmately as the nverse of the square of the source to sensor dstance. Wthout loss of generalty, t wll be assumed n ths secton that the node locatons determne the mcrophone postons and that nodes only ncorporate one mcrophone (M = N). Note that, as opposed to tme delay measurements, the dfferences n energy measurements obtaned from dfferent mcrophones at the same node are neglgble. 3.. Energy-Decay Model. Assumng that there s only one source actve, the acoustc ntensty sgnal receved by the th sensor at a tme nterval l s modeled as [5] y (l) =g I(l η ) r +ε (l) =s (l) +ε (l), () where s (l) sthesourcentenstyatthesensorlocaton,g s a sensor gan factor,i(l) denotes the ntensty of the source sgnal at a dstance of one meter from the source, η s the propagaton delay from the source to the sensor, r s the dstance between the sensor and the source, and ε (l) s an addtve nose component modeled as Gaussan nose. In practce, for each tme nterval l, asetoft samples s used to obtan an energy readng y (l) at the sensor: y (l) T l+t/ x l T/ (t), () where x (t) are the samples obtaned from the mcrophone of the th node. In the case when several mcrophones are avalable at each node, the fnal energy readng s obtaned by averagng the energes computed from each of the mcrophones. By assumng that the maxmum propagaton delay between any par of sensors s small compared to T and takng nto account the averagng effect, η can be neglected for the energy-decay functon, so that y (l) g I (l) r +ε (l). (3) 3.. Energy Ratos. Consderng the energy measurements obtaned by a group of N sensor nodes, the energy rato κ between the th and the jthsensorssdefnedas κ ( y / /y j ) = x s m g /g j x = r, (4) s m j r j where x s sthelocatonofthesourceandm and m j are the locatons of the two mcrophones. For <κ =,allthe possble source coordnates x that satsfy (4) must resde on a hypersphere (sphere f x R 3 or crcle f x R ) descrbed by x c =, (5) where the center c and the radus of ths hypersphere are c m κ m j κ, κ m m j κ. In the lmtng case, when κ, the soluton of (4) forms a hyperplane between m and m j : (6) w T x =ψ, (7) where w m m j and ψ (/)( m m j ). By usng the energy ratos regstered at a par of sensors, the potental target locaton can be restrcted to a hypersphere wth center and radus that are functons of the energy rato and the two sensor locatons. If more sensors are used, more hyperspheres can be determned. If all the sensors that receve the sgnal from the same target are used, the correspondng target locaton hyperspheres must ntersect at a partcular pontthatcorrespondstothesourcelocaton.thssthe basc dea underlyng energy-based source localzaton. In the

5 Wreless Communcatons and Moble Computng x c n = n, a hyperplane can be determned by elmnatng the common terms: 5 (c m c n ) T x = ( c m c n ) ( m n ). () y (m) The combnaton of (7) wth () leads to a least squares optmzaton problem wthout nconvenent nonlnear terms, known as the energy-rato least squares (ER-LS) method, wth cost functon: x (m) Fgure : Example of energy-based localzaton wth three nodes. The red crcle ndcates the true source locaton. Note that due to measurement nose crcles do not ntersect at the expected source locaton. The center of the contour plots ndcates estmated target locaton, accordng to the nonlnear cost functon of (9). absence of nose, t can be shown that for N measurements only N of the total N(N )/ ratos are ndependent, and all the correspondng hyperspheres ntersect at a sngle pont for four or more sensor readngs. For nosy measurements, however, more than N ratosmay be used for robustness, andtheunknownsourcelocatonx s s estmated by solvng a nonlnear least squares problem, as explaned n the next subsecton.asanexample,fgureshowsadsetupwth three sensors and the crcles resultng from nosy energy ratos Localzaton through Energy Ratos. Gven N sensor nodes provdng P = N(N )/energy ratos, the followng least squares optmzaton problem can be formulated: P P J (ER) NLS (x) = x c p p + wt p x ψ p, (8) p = p = x (ER-NLS) s = arg mn x J (ER) NLS (x), (9) where P s the number of hyperspheres and P s the number of hyperplanes (κ closeto),wthcorrespondngndcesp and p ndcatngtheassocatedsensorpars() (P =P +P ). Note that the above cost functon s nonlnear wth respect to x, resultng n the energy-rato nonlnear least squares (ER- NLS) problem. It can be shown that mnmzng ths cost functon leads to an approxmate soluton for the maxmum lkelhood (ML) estmate. A set of strateges were proposed n [6] to mnmze J (ER) NLS (x) by usng the complete set of measured energy ratos. A popular approach to solve the problemstheunconstranedleastsquaresmethod.snce every par of hyperspheres (wth double ndces replaced by a sngle par ndex for the sake of brevty) x c m = m and where P P J (ER) LS (x) = ut p x ζ p + wt p x ψ p, () p = p = u m κ ζ m κ m j κj, m j κj. () The closed-form soluton of the above unconstraned least squares formulaton makes ths method computatonally attractve; however, t does not reach the Cramer-Rao bound. In [7], energy-based localzaton s formulated as a constraned least squares problem, and some well-known least squares methods for closed-form TDOA-based locaton estmaton are appled, namely, lnear ntersecton [8], sphercal ntersecton [9], sphere nterpolaton (SI) [3], and subspace mnmzaton [3]. In [3], an algebrac closed-form soluton s presented that reaches the Cramer-Rao bound for Gaussan measurement nose as the SNR tends to nfnte. The authors n [33] formulated the localzaton problem as a convex feasblty problem and proposed a dstrbuted verson oftheprojectonontoconvexsetsmethod.adscussonof least squares approaches s provded n [9], presentng a low-complexty weghted drect least squares formulaton. A recent revew of energy-based acoustc source localzaton methods can be found n [8]. 4. TOA-Based Localzaton Typcally, a WASN sound source locaton setup assumes that there s a sound-emttng source and a collecton of fxed mcrophone anchor nodes placed at known postons. When the sound source emts a gven sgnal, the dfferent mcrophone nodes wll estmate the tme of arrval (TOA) or tme of flght (TOF) of the sound. These two terms may not be equvalent under some stuatons. The TOF measures the tme that t takes for the emtted sgnal to travel the dstance between the source and the recevng node; that s, η c m x s. (3) In fact, when utlzng TOA measurements for source localzaton, t s often assumed that the source and sensor nodes cooperate such that the sgnal propagaton tme can

6 6 Wreless Communcatons and Moble Computng be detected at the sensor nodes. However, such collaboraton between sources and sensor nodes s not always avalable. Thus, wthout knowng the ntal sgnal transmsson tme at the source, from TOA alone, the sensor s unable to determne the sgnal propagaton tme. In the more general stuaton when unknown acoustc sgnals such as speech or unexpected sound events are to be localzed, the relaton between dstances and TOAs can be modeled as follows: τ =η +t s +ε, (4) where t s s an unknown transmsson tme nstant and ε s the TOA measurement nose. Note that the tme t s appears duetothefactthattypcalsoundsourcesdonotencodea tme stamp n ther transmtted sgnal to ndcate the startng transmsson tme to the sensor nodes and, moreover, there s not any underlyng synchronzaton mechansm. Hence, the sensor nodes can only measure the sgnal arrval tme nstead of the propagaton tme or TOF. One way to tackle ths problem s to explot the dfference of parwse TOA measurements, that s, tme dfference of arrval (TDOA), for source localzaton (see Secton 5). Although the dependence on the ntal transmsson tme s elmnated by TDOA, the measurement subtracton strengthens the nose. To overcome such problems, some works propose methods to estmate both the source locaton and ntal transmsson tme jontly [34]. WhentheTOAandtheTOFareequvalent(.e.,τ =η ), for example, because there are synchronzed sound-emttng nodes, the source-to-node dstances can be calculated usng the propagaton speed of sound [35]. Ths may requre an ntal calbraton process to determne factors that have a strong nfluence on the speed of sound. The computaton of thesourcelocatoncanbecarredoutnacentralnodeby usng the estmated dstances and solvng the trlateraton problem [36]. Trlateraton s based on the formulaton of one equaton for each anchor that represents the surface of the sphere (or crcle) centered at ts poston, wth a radus equaltotheestmateddstancetothesoundsource.the soluton to ths seres of equatons fnds the pont where all the spheres ntersect. For D localzaton, at least three sensors are needed, whle one more sensor s necessary to obtan a 3D locaton estmate. 4.. Trlateraton. Let us consder a set of N sensor TOA measurements τ that are transformed to dstances by assumng a known propagaton speed: r =c τ, (5) where c s the speed of sound (343 m/s). Then, the followng system of equatons can be formulated: m x s =r =,...,N. (6) Each equaton n (6) represents a crcle n R or a sphere n R 3,centeredatm wth a radus r.notethattheproblem s the same as the one gven by (5). Thus, solvng the above system s equvalent to fndng the ntersecton pont/ponts of a set of crcles/spheres. Agan, the trlateraton problem s not straghtforward to solve due to the nonlnearty of (6) and the errors n m and r [37]. A number of algorthms have been proposed n the lterature to solve the trlateraton problem, ncludng both closed form [37, 38] and numercal solutons. Closed-form solutons have low computatonal complexty when the soluton of (6) actually exsts. However, most closed-form solutons only solve for the ntersecton ponts of n spheres n R n. They do not attempt to determne the ntersecton pont when N > n,where small errors can easly cause the nvolved spheres not to ntersect at one pont [39]. It s then necessary to fnd a good approxmaton that mnmzes the errors contaned n (6) consderng the nonlnear least squares cost functon: J (TOA) NLS (x) = x (TOA-NLS) s N = = arg mn x ( m x r ), J (TOA) NLS (x). (7) Numercal methods are n general necessary to estmate x (TOA-NLS) s.however,comparedwthclosed-formsolutons, numercal methods have hgher computatonal complexty. Some numercal methods are based on a lnearzaton of the trlateraton problem [4 4], ntroducng addtonal errors nto poston estmaton. Common numercal technques such as Newton s method or steepest descent have also beenproposed[38,4,4].however,mostofthesesearch algorthms are very senstve to the choce of the ntal guess, and a global convergence towards the desrable soluton s not guaranteed [39]. 4.. Estmatng TOAs of Acoustc Events. As already dscussed, localzng acoustc sources from TOA measurements only s not possble due to the unknown source emsson tme of acoustc events. If the sensors are synchronzed, the dfferences of TOA measurements can be used to cancel out the common term t s,sothatasetoftdoasareobtaned andusedasdscussednsecton5.alow-complextymethod to estmate the TOAs from acoustc events n WASNs was proposed n [43], where the cumulatve-sum (CUSUM) change detecton algorthm s used to estmate the source onset tmes at the nodes. The CUSUM method s a lowcomplexty algorthm that allows estmatng change detecton nstants by maxmzng the followng log-lkelhood rato: k τ = arg max ln ( p(x (t),θ ) ). (8) τ k p(x (t),θ ) t=τ The probablty densty functon of each sample s gven by p(x (t), θ), whereθ s a determnstc parameter (not to be confused wth the DOA of the source). The occurrence of an event s modeled by an nstantaneous change n θ, so that θ = θ before the event at t = τ and θ = θ when t τ. To smplfy calculatons at the nodes, the samples beforetheacoustceventareassumedtobelongexclusvelyto a Gaussan nose component of varance σ,whlethesamples after the event are also normally dstrbuted wth varance

7 Wreless Communcatons and Moble Computng 7 Central node Central node EW TOA TOA EW TOA EW TOA EW TOA EW: event warnng (a) (b) Fgure 3: Node communcaton steps n CUSUM-based TOA estmaton. (a) One of the nodes detects the sound event and sends an event warnng alert to the other nodes. (b) The nodes estmate ther TOAs and send t to a central node. σ >σ. These varances are estmated from the begnnng and tal of a wndow of samples where the nodes have strong evdence that an acoustc event has happened. The advantage of ths approach s twofold. On the one hand, the estmaton of the dstrbuton parameters s more accurate. On the other hand, the CUSUM change detecton algorthm needs only to berunwhenanacoustceventhasactuallyoccurred,allowng sgnfcant battery savngs n the nodes. The detecton of acoustc events s performed by assumng that, at least, one of the nodes has the suffcent SNR to detect the event by a smple ampltude threshold. The node (or nodes) detectng thepresenceoftheeventwllnotfytherestbysendngan event warnng alert n order to let them know that they must run the CUSUM algorthm over a wndow of samples (see Fgure3).Theampltudethresholdselectonscarredoutby settng ether the probablty of detecton or the probablty offalsealarmgvenanntalestmateoftheambentnose varance σ. Note that synchronzaton ssues stll persst (all τ must have a common tme reference), so that the nodes exchange synchronzaton nformaton by usng MAC layer tme stampng n the deployment dscussed n [43]. 5. TDOA-Based Localzaton When each sensor conssts of multple mcrophones, localzaton can be accomplshed n an effcent way demandng as much as possble of the processng to each node and then combnng measurements to yeld the localzaton at the central node. When nodes are connected through low btrate channels and no synchronzaton of the nternal clocks s guaranteed, ths strategy becomes a must. Among all the possble measurements, a possble soluton can be found n the tme dfference of arrval (TDOA). 5.. TDOA and Generalzed Cross Correlaton. Consder the presence of M nodes n the network. For reasons of smplcty n the notaton, all nodes are equpped wth N mcrophones. The TDOA refers to the dfference of propagaton tme from thesourcelocatontoparsofmcrophones.ifthesources located at x s,andtheth mcrophone n the mth sensor s at m (m) =,...,N,theTDOAsrelatedtothedfferenceofthe ranges from the source to the mcrophones and j through τ (m) = r(m) c = x s m (m) x s m (m) j c =,...,N, j=,...,n,, =j, m=,...,m. (9) Throughout the rest of ths subsecton we wll consder pars of mcrophones wthn the same node, so we wll omt the superscrpt (m) of the sensor. The estmate τ of the TDOA τ can be accomplshed performng the generalzed cross correlaton (GCC) between the sgnals acqured by mcrophones at m and m j,asdetalednthefollowng. Under the assumpton of workng n an anechoc scenaro and n a sngle source context, the dscrete-tme sgnal acqured by the th mcrophone s x (t) =α s(t η )+ε (t), =,...,N, () where α s a mcrophone-dependent attenuaton term that accounts for the propagaton losses and ar absorpton, s(t)

8 8 Wreless Communcatons and Moble Computng sthesourcesgnal,η s the propagaton delay between the source and the th mcrophone, and ε (t) s an addtve nose sgnal. In the dscrete-tme Fourer transform (DTFT) doman, the mcrophone sgnals can be wrtten as X (ω) =α S (ω) e jωη +E (ω), =,...,N, () where S(ω) and E (ω) are the DTFTs of s(t) and ε (t),respectvely, and ω Rdenotes normalzed angular frequency. Gven the par of mcrophones and j, wth = j,the GCC between x (t) and x j (t) canbewrttenas[] R (τ) π π π X (ω) X j (ω) Ψ (ω) e jωτ dω, () where X (ω) s the DTFT of x (t), s the conjugate operator, and Ψ (ω) s a sutable weghtng functon. The TDOA from the par () s estmated as τ = arg max τ R (τ) F s, (3) where F s sthesamplngfrequency.thegoalofψ (ω) s to make R (τ) sharper so that the estmate n (3) becomes more accurate. One of the most common choces s to use the PHAse Transform (PHAT) weghtng functon; that s, Ψ (ω) = X (ω) Xj (ω). (4) In an array of N mcrophones, the complete set of TDOAs counts N(N )/ measures. If these are not affected by any sort of measurement error, t can be easly demonstrated that only N of them are ndependent, the others beng a lnear combnaton of them. It s common practce, therefore, to adopt a reference mcrophone n the array and to measure N TDOAs wth respect to t. We refer to the set of N measures as the reduced TDOA set. Wthout any loss of generalty, for the reduced TDOA set, we can assume the reference mcrophone be wth ndex, and the TDOAs τ j n the reduced set, for reasons of compactness n the notaton, are denoted wth τ j, j=,...,n. 5.. TDOA Measurement n Adverse Envronments. It s mportant to stress the fact that TDOA measurements are very senstve to reverberaton, nose, and the presence of possble nterferers: n a reverberant envronment, for some locatons and orentaton of the source, the peak of the GCC relatve to a reflectve path could overcome that of the drect path. Moreover, n a nosy scenaro, for some tme nstants the nose level could exceed the sgnal, thus makng the TDOAs unrelable. As a result, some TDOAs must be consdered outlersandmustbedscardedfromthemeasurementset before localzaton (as n the example shown n Fgure 4). Several solutons have been developed n order to allevate the mpact of outlers n TDOAs. It has been observed that GCCs affected by reverberaton and nose do not exhbt a sngle sharp peak. In order to dentfy outlers, therefore, some works analyze the shape of the GCC from whch GCC-PHAT GCC-PHAT GCC-PHAT GCC-PHAT Range dfference (cm) Range dfference (cm) 3 Range dfference (cm) 3 3 Range dfference (cm) GCC-PHAT GT Peak Fgure 4: Examples of GCCs measured for pars of mcrophones wthnthesamenode.itspossbletoobservethatformostof theabovegccsthemeasuredtdoa(peak)sveryclosetothe ground truth (GT). Ths does not happen for one measurement, due to reverberaton. Note also that TDOA values have been mapped to range dfferences. they were extracted. In [], authors propose the use of the functon ρ τ D R (τ) τ D R (τ), (5) to detect GCCs affected by outlers. More specfcally, the numerator sums the power of the GCC samples wthn the nterval D centered around the canddate TDOA and compares t wth the energy of the remanng samples. When ρ overcomes a prescrbed threshold, the TDOA s consdered relable. Two metrcs of the GCC shape have been proposed n [3, 44]. The frst one consders the value of the GCC at the maxmum peak locaton, whle the second compares the hghest peak wth the second hghest one. When both metrcs overcome prescrbed thresholds, the GCC s consdered relable. Another possble route to follow s descrbed n [] and s based on the observaton that TDOAs along closed paths of mcrophones must sum to zero (zero-sum condton) and that there s a relatonshp between the local maxma of the

9 Wreless Communcatons and Moble Computng 9 autocorrelaton and cross correlaton of the mcrophone sgnals (raster condton). The zero-sum condton on mnmum length paths of three mcrophones wth ndexes, j, and k, n partcular, states that m k (l) τ +τ jk +τ k =. (6) By mposng zero-sum and raster condtons, authors demonstrate that they are able to dsambguate TDOAs n the case of multple sources n reverberant envronments. In [7] authors combne dfferent approaches. A redundant set of canddate TDOAs s selected by dentfyng local maxma of the GCCs. A frst selecton s operated by dscardng TDOAs that do not honor the zero-sum condton. A second selecton step s based on three qualty metrcs relatedtotheshapeofthegcc.thethrdfnalstepsbased on the nspecton of the resduals of the source localzaton cost functon: all the measurements related to resduals overcomng a prescrbed threshold are dscarded. It s mportant to notce that all the referenced technques for TDOA outler removal do not nvolve the cooperaton of multple nodes, wth clear advantages n terms of data to be transmtted Localzaton through TDOAs. In ths secton we wll consder the problem of source localzaton by combnng measurements comng from dfferent nodes. In order to dentfy the sensor from whch measurements have been extracted, we wll use the superscrpt (m).fromageometrc standpont, gven a TDOA estmate τ (m), the source s bound to le on a branch of hyperbola (hyperbolod n 3D), whose foc are n m (m) and m (m) j,andwhosevertcesarec τ (m) far apart. If source and mcrophones are coplanar, the locaton of thesourcecanbedeallyobtanedbyntersectngtwoormore hyperbolas [4], as n Fgure 5 and some prmtve solutons for source localzaton rely on ths dea. It s mportant to notce that when the source s suffcently far from the node, the branch of hyperbola can be confused wth ts asymptote: n ths case the TDOA s nformatve only wth respect to thedrectontowardswhchthesourceslocatedandnotts dstance from the array. In ths context t s more convenent to work wth DOAs (see Secton 6). In general, ntersectng hyperbolas s a strongly nonlnear problem, wth obvous negatve consequences on the computatonal cost and the senstvty to nose n the measurements. In[]asolutonsproposedtoovercomethsssue,whch reles on a projectve representaton. The hyperbola derved from the TDOA τ (m) as a (m) x +b (m) xy + c (m) where the coeffcents a (m) at mcrophones m (m) y +d (m), b (m) and m (m) j s wrtten x+e (m) y+f (m) =, (7), c (m), d (m), e (m), f (m) are.equaton determned n closed form by m (m), m (m) j,and τ (m) (7) represents a constrant on the source locaton. In the m m (l) x s m j (l) Fgure 5: The source les at the ntersecton of hyperbolas obtaned from TDOAs. presence of nose, the constrant s not honored and a resdual can be defned as ε (m) (x) = V (m) (a (m) +e (m) y+f (m) ), x +b (m) xy + c (m) y +d (m) x (8) where V (m) = for all the TDOAs that have been found relable and otherwse. The resduals are stacked n the vector ε(x),andthesourceslocalzedbymnmzngthecost functon J (TDOA) HYP (x) =ε(x) T ε (x). (9) If TDOA measurements are affected by addtve whte Gaussan nose, t s easy to demonstrate that (9) s proportonal to the ML cost functon. It has been demonstrated that a smplfcaton of the localzaton cost functon can be brought f a reference mcrophone s adopted, at the cost of the nodes sharng a common clock. Wthout loss of generalty, we assume the reference to be the frst mcrophone n the frst sensor (.e., =and m=),andwealsosetm () = ;thats,theorgnof the reference frame concdes wth the reference mcrophone. Moreover, we can drop the array ndex m upon assgnng a global ndex to the mcrophones n dfferent sensors, rangng from j = to j = NM.Inthscontext,tspossbleto lnearze the localzaton cost functon, as shown n the next paragraphs. By rearrangng the terms n (9) and settng =, t s easy to derve x s r j = x s m j, (3) where r j = c τ j. In [45] t has been proposed to represent the source localzaton problem n the space-range reference frame: a pont x =[x,y] T n space s mapped onto the 3D space-range as x T,r] T where r= x s x x s. (3)

10 Wreless Communcatons and Moble Computng r y Most LS estmaton technques adopt ths cost functon and they dffer only for the addtonal constrants. The Unconstraned Least Squares (ULS) estmator [6, 3, 3, 47, 48] localzes the source as x x (ULS) s = arg mn x s,r s J (TDOA) SP (x s,r s ). (38) C C s [x s,r s ] T C It s mportant to notce that the absence of any explct constrant that relates x s and r s provdes n many applcatons a poor localzaton accuracy. Constraned Least Squares technques, therefore, rentroduce ths constrant as Fgure 6: In the space-range reference frame the source s a pont on the surface of the cone C s and closest to the cones C. We easly recognze that, n absence of nose and measurement errors, r s the range dfference relatve to the source n x s between the reference mcrophone and a mcrophone n x. If we replace r s = x s, (3) we can easly nterpret (3) as the equaton of a negatve half-cone C j n the space-range reference frame, whose apex s [m T j, r j] T,andwthapertureπ/4, andthesourcepont [x T s,rt s ] les on t. Equaton (3) can be terated for j=,..., N M,andthesourcesboundtoleonthesurfaceofallthe cones. Moreover, the range r s of the source from the reference mcrophone must honor the constrant r s = x s, (33) whch s the equaton of a cone C s whose apex s n [m T,]T and wth aperture π/4.themlsourceestmate,therefore,s the pont on the surface of the cone n (33) closest to all the cones defned by (3), as represented n Fgure 6. By squarng both members of (3) and recognzng that (3)canberewrttenas x s +y s r s =, (34) x j x s +y j y s r j r s (x j +y j r j )=, (35) whch s the equaton of a plane n the space-range reference frame, on whch the source s bound to le. Under error n the range dfference estmate r j, (35) s not satsfed exactly, and therefore a resdual can be defned as e j =x j x s +y j y s r j r s (x j +y j r j ). (36) Based upon the defnton of e j, the LS sphercal cost functon s gven by [46] J (TDOA) NM SP (x s,r s )= j= e j. (37) x (CLS) s = arg mn J (TDOA) x s,r s SP (x s,r s ) (39) subject to r s = x s. Based on (39), Sphercal Intersecton [9], Least Squares wth Lnear Correcton [49], and Squared Range Dfference Least Squares [5] estmators have been proposed, whch dffer for the mnmzaton procedure, rangng from teratve to closed-form solutons. It s mportant to notce, however, that all these technques assume the presence of a global reference mcrophone and synchronzaton vald for all the nodes. Alternatve solutons that overcome ths technologcal constrant have been proposed n [7, 5]. Here the concept of cone propagaton n the space-range reference has been put atadvantage.inpartcular,n[5],thepropagatoncones defned slghtly dfferent from the one defned n (3): the apexsnthesourceandr s =. As a consequence, n absence of synchronzaton errors, all the ponts [x (m)t j, r (m) j ] T. j =,...,N, m =,...,M must le on the surface of the propagaton cone. If a sensor exhbts a clock offset, ts measurements wll be shfted along the range axs. The shft can be expressed as a functon of the source locaton, and therefore t can be ncluded n the localzaton cost functon at a cost of some nonlnearty. The extenson to the 3D localzaton cost functon was then proposed n [7]. 6. DOA-Based Localzaton When each node n the WASN ncorporates multple mcrophones, the locaton of an acoustc source can be estmated based on drecton of arrval (DOA), also known as bearng, measurements. Although, such approaches requre ncreased computatonal complexty n the nodes n order to perform the DOA estmaton they can attan very low-bandwdth usage as only DOA measurements need to be transmtted n the network. Moreover, they can tolerate unsynchronzed nput gven that the sources are statc or that they move at a rather slow rate relatve to the analyss frame. DOA measurements descrbe the drecton from whch sound s propagatng wth respect to a sensor n each tme nstant and are an attractve approach to locaton estmaton also due to theeasenwhchsuchestmatescanbeobtaned:avarety of broadband DOA estmaton methods for acoustc sources are avalable n the lterature, such as the broadband MUSIC algorthm, [5] the ESPRIT algorthm [5], Independent ComponentAnalyss(ICA)methods[53],orSparseComponent Analyss (SCA) methods [54]. When the mcrophones

11 Wreless Communcatons and Moble Computng Fgure 7: Trangulaton usng DOA estmates (θ θ 4 ) n a WASN of 4 nodes (blue crcles, numbered to 4) and one actve sound source (red crcle). Fgure 8: Trangulaton usng DOA estmates contamnated by nose ( θ θ 4 ) n a WASN of 4 nodes (blue crcles, numbered to 4) and the estmated locaton of the sound source (red crcle). at the nodes follow a specfc geometry, for example, crcular, methods such as Crcular Harmoncs Beamformng (CHB) [55]canalsobeappled. Inthesequel,wewllfrstrevewDOA-basedlocalzaton approacheswhenasnglesourcesactventheacoustcenvronment. Then, we wll present approaches for localzaton of multple smultaneously actve sound sources. Fnally, we wll dscuss methods to jontly estmate the locatons as well as thenumberofsources,aproblemwhchsknownassource countng. 6.. Sngle Source Localzaton through DOAs. In the sngle source case, the locaton can be estmated as the ntersecton of bearng lnes (.e., lnes emanatng from the locatons of the sensors at the drectons of the sensors estmated DOAs), amethodwhchsknownastrangulaton. An example of trangulaton s llustrated n Fgure 7. The problem closely relates to that of target moton analyss, where the goal s to estmate the poston and velocty of a target from DOA measurements acqured by a sngle movng or multple observers. Hence, many of the methods were proposed for the target moton analyss problem but outlned here n the context of sound source localzaton n WASNs. Consderng a WASN of M nodes at locatons q m = [q x,m q y,m ] T, the functon that relates a locaton x =[x y] T wth ts true azmuthal DOA estmate at node m s θ m (x) = arctan ( y q y,m x q x,m ), (4) where arctan( ) s the four-quadrant nverse tangent functon. Note that we deal wth the two-dmensonal locaton estmaton problem; that s, only the azmuthal angle s needed. When nformaton about the elevaton angle s also avalable, locaton estmaton can be extended to the three-dmensonal space. In any practcal case, however, the DOA estmates θ m, m =,...,M, wll be contamnated by nose and trangulatonwllnotbeabletoproduceaunquesoluton, cravng for the need of statstcal estmators to optmally tackle the trangulaton problem. Ths scenaro s llustrated n Fgure 8. When the DOA nose s assumed to be Gaussan, the ML locaton estmator can be derved by mnmzng the nonlnear cost functon [56, 57]: J (DOA) ML (x) = M m= σ m ( θ m θ m (x)), (4) where σ m s the varance of DOA nose at the mth sensor. As nformaton about the DOA error varance at the sensors s rarely avalable n practce, (4) s usually modfed to J (DOA) M NLS (x) = ( θ m θ m (x)), (4) m= whch s termed as nonlnear least squares (NLS) [58] cost functon. Mnmzng (4) results n the ML estmator, when the DOA nose varance s assumed to be the same at all sensors. Whleasymptotcallyunbased,thenonlnearnatureof the above cost functons requres numercal search methods for mnmzaton, whch comes wth ncreased computatonal complexty compared to closed-form solutons and can become vulnerable to convergence problems under bad ntalzaton, poor geometry between sources and sensors, hgh nose, or nsuffcent number of measurements. To surpass some of these problems, some methods form geometrcal constrants between the measured data and result n better convergence propertes than the maxmum lkelhood estmator [59] or try to drectly mnmze the mean squared

12 Wreless Communcatons and Moble Computng locaton error [6] nstead of mnmzng the total bearng error n (4) and (4). Other approaches are targeted at lnearzng the above nonlnear cost functons. Stansfeld [6] developed a weghted lnear least squares estmator based on the cost functon of (4) under the assumpton that range nformaton r m s avalable and DOA errors are small. Under the small DOA errors assumpton θ m θ m (x) canbeapproxmatedbysn( θ m θ m (x)) andthemlcostfunctoncanbemodfedto where J (DOA) ST (x) = (Ax b)t W (Ax b), (43) sn θ cos θ A = [.., ] [ sn θ M cos θ M ] q x, sn θ q y, cos θ b = [., ] [ q x,m sn θ M q y,m cos θ M ] r σ r W = σ, [ d ] [ r M σ M] whch s lnear and has a closed-form soluton: (44) x (ST) s = (A T W A) A T W b. (45) When range nformaton s not avalable, the weght matrx W can be replaced by the dentty matrx. In ths way, the Stansfeld estmator s transformed to the orthogonal vectors estmator, alsoknownasthepseudolnear estmator [6]: x (OV) s =(A T A) A T b. (46) Whlesmplenthermplementatonandcomputatonally very effcent due to ther closed-form soluton, these lnear estmators suffer from ncreased estmaton bas [63]. A comparson between the Stansfeld estmator and the ML estmator n [64] reveals that the Stansfeld estmator provdes based estmates. Moreover, the bas does not vansh even for a large number of measurements. To reduce that bas varous methodshavebeenproposedbasedonnstrumentalvarables [65 67] or total least squares [57, 68]. Motvated by the need for computatonal effcency, the ntersecton pont method [69] s based on fndng the locaton of a source by takng the centrod of the ntersectons of pars of bearng lnes. The centrod s smply the mean of the set of ntersecton ponts and mnmzes the sum of squared dstances between tself and each pont n the set. To ncrease robustness n poor geometrcal condtons, the method ncorporates a scheme of dentfyng and excludng outlers that occur from the ntersecton of pars of bearng lnes that are almost parallel. Nonetheless, the performance of the method s very smlar to that of the pseudolnear estmator. To attan the accuracy of nonlnear least squares estmators and mprove ther computatonal complexty, the grdbased (GB) method [7, 7] s based on makng the search space dscrete by constructng a grd G of N g grd ponts over the localzaton area. Moreover, as the measurements are angles, the GB method proposes the use of the Angular Dstance takng values n the range of [, π] as a more proper measure of smlarty than the absolute dstance of (4). The GB method estmates the source locaton by fndng thegrdpontwhosedoasmostcloselymatchtheestmated DOAs from the sensors by solvng x (GB) s J (DOA) M GB (x) = [A ( θ m,θ m (x))], (47) m= = arg mn x G J (DOA) GB (x), (48) where A(, ) denotes the angular dstance between the two arguments. To elmnate the locaton error ntroduced by the dscrete nature of ths approach, a very dense grd (hgh N g )s requred. The search for the best grd pont s performed n an teratve manner: t starts wth a coarse grd (low value of N g ) and once the best grd pont s found accordng to (47) anewgrdcenteredonthspontsgenerated,wth a smaller spacng between grd ponts but also a smaller scope.then,thebestgrdpontnthsnewgrdsfound andtheproceduresrepeateduntlthedesredaccuracys obtaned, whle keepng the complexty under control, as t does not requre an exhaustve search over a large number of grd ponts. In [7] t s shown that the GB method s much more computatonally effcent than the nonlnear least squares estmators and attans the same accuracy. 6.. Multple Source Localzaton. When consderng multple sources, a fundamental problem s that the correct assocaton of DOAs from the nodes to the sources s unknown. Hence, n order to perform trangulaton, one must frst estmate the correct DOA combnatons from the nodes that correspond to the same source. The use of DOAs that belong to dfferent sources wll result n ghost sources, that s, locatons that do not correspond to real sources, thus severely affectng localzaton performance. Ths s known as the data-assocaton problem. The dataassocaton problem s llustrated wth an example n Fgure 9: nawasnwthtwonodes(bluecrcles)andtwoactvesound sources(redcrcles),letthesoldlnesshowthedoasto thefrstsourceandthedashedlnesshowthedoastothe second source. Intersectng the bearng lnes wll result n 4 ntersecton ponts: the red crcles, that correspond to the true sources locatons and are estmated by usng the correct DOA combnatons (.e., the DOAs from the node that correspond

13 Wreless Communcatons and Moble Computng 3 Fgure 9: Illustraton of the data-assocaton problem. A twonode WASN wth two actve sound sources. The sold lnes show the DOAs to the frst source, whle the dashed lnes show the DOAs to the second source. Intersectng the bearng lnes from the sensors wll result n 4 possble ntersecton ponts: the true sources locatons (red crcles) that are estmated by usng the correct combnaton of DOAs and the ghost sources (whte crcles) that are the results of usng the erroneous DOA combnatons. to the same source) and the whte crcles that are the result of usng the erroneous DOA combnatons ( ghost sources). Also,wthmultpleactvesources,somearraysmght underestmate ther number, especally when some nodes are far from some sources or when the sources are close together n terms of ther angular separaton [54]. Thus, mssed detectons can occur, meanng that the DOAs of some sourcesfromsomearraysmaybemssng.asllustratedn [7], mssed detectons can occur very often n practce. In the sequel, we revew approaches for the data-assocaton and localzaton problem of multple sources whose number s assumedtobeknown. Some approaches tred to tackle the data-assocaton problem by enumeratng all possble DOA combnatons fromthesensorsanddecdngonthecorrectdoacombnatons based on the resultng locaton estmates from all combnatons. In general, f C s denotes the number of sensors that detected s sources, the number of possble DOA combnatons s N comb = S s= s C s. (49) The poston nonlnear least squares (P-NLS) estmator developed n [73] ncorporates the assocaton procedure n the ML cost functon, whch takes the form J (DOA) M P-NLS (x) = m= mn θ m, θ m (x), (5) where θ m, s the th DOA estmate of sensor m. To mnmze (5), N comb ntal locatons are estmated (one for each DOA combnaton) usng a lnear least squares estmator, such as the pseudolnear transform of (46). Then, the cost functon (5) s mnmzed usng numercal search methods N comb tmes, each tme usng a dfferent ntal locaton estmate. Each tme, for each sensor the DOA closest to the DOA of the ntal locaton estmate s used to take part n the mnmzaton procedure. In that way, for all ntal locatons, the estmator s expected to converge to a locaton of a true source. However, as llustrated n [7], n the presence of mssed detectons and hgh nose the approach s not able to completely elmnate ghost sources. The multple source grd-based method [7] estmates an ntal locaton for each possble DOA combnaton from the sensors by solvng (47). It then decdes whch of the ntal locaton estmates correspond to a true source, heurstcally by selectng the estmated ntal locatons whose DOAs are closer to the DOAs from the combnaton used to estmate that locaton. Other approaches focus on solvng the data-assocaton problem pror to the localzaton procedure. In ths way, the correct assocaton of DOAs from the sensors to the sources s estmated beforehand and the multple source localzaton problem decomposes nto multple sngle source localzaton problems. In [74] the data-assocaton problem s vewed as an assgnment problem and s formulated as a statstcal estmaton problem whch nvolves the maxmzaton of the rato of the lkelhood that the measurements come from the same target to the lkelhood that the measurements are falsealarms. Snce the proposed soluton becomes NP-hard for more than three sensors, suboptmal solutons tred to solve the same problem n pseudopolynomal tme [75, 76]. Anapproachbasedonclusterngofntersectonsofbearng lnes n scenaros wth no mssed detectons s dscussed n [77]. It s based on the observaton that ntersectons between pars of bearng lnes that correspond to the same source wll be close to each other. Hence, ntersectons between bearng lnes wll cluster around the true sources, revealng the correct DOA assocatons, whle ntersectons from erroneous DOA combnatons wll be randomly dstrbuted n space. Permttng the transmsson of low-bandwdth addtonal nformaton from the sensors can lead to more effcent approaches to the data-assocaton problem. The dea s that the sensors can extract and transmt features assocated wth each source they detect. Approprate features for the dataassocaton problem must possess the property of beng smlar for the same source n the dfferent sensors. Then, thecorrectassocatonofdoastothesourcescanbefound by comparng the correspondng features. In [78] such features are extracted usng Blnd Source Separaton.Thefeaturesarebnarymasks[79]nthefrequency doman for each detected source that when appled to the correspondng source sgnals they perform source separaton. The extracton of such features reles on the W- dsjont orthogonalty assumpton [8], whch states that n a gven tme-frequency pont only one source s actve, an assumpton whch has been showed to be vald especally for speech sgnals [8]. The assocaton algorthm works by fndng the bnary masks from the dfferent arrays that correlate the most. However, the method s desgned for scenaros wth no mssed detectons and, as llustrated n [7], performance sgnfcantly drops when mssed detectons

14 4 Wreless Communcatons and Moble Computng y (cm) y (cm) x (cm) x (cm) (a) (b) Fgure : Example of (a) narrowband locaton estmates and (b) ther correspondng hstogram for a scenaro of two actve sound sources (the red X s). The narrowband locaton estmates form two clusters around the true sources locatons, whle ther correspondng hstogram descrbes the plausblty that a source s present at a gven locaton. occur. Moreover, the assocaton algorthm s desgned for the case of two sensors. The desgn of assocaton features that are robust to mssed detectons s consdered n [7] along wth a greedy assocatonalgorthmthatcanworkwthanarbtrarynumber of sources and sensors. The assocaton features descrbe how the frequences of the captured sgnals are dstrbuted to the sources. To do that, the method estmates a DOA φ(ω, k) n each tme-frequency pont, where ω and k denote the frequency and tme frame ndex, respectvely. Then, a tmefrequency pont (ω, k) s assgned to source s f the followng condtons are met: A(φ(ω, k), θ s (k)) <A(φ(ω, k), θ q (k)), q=s, (5) A(φ(ω, k), θ s (k)) <ε, (5) where θ s (k) s the DOA estmate at tme frame k for the sth source at the sensor of nterest and ε s a predefned threshold. Equatons (5) and (5) mply that each frequency s assgned to the source whose DOA s closest to the estmated DOA n ths frequency, as long as ther dstance does not exceed a certan threshold ε. The second condton (see (5)) adds robustness to mssed detectons as t rejects the frequences wth DOA estmates whose dstance from the detected sources DOAs s sgnfcantly large Source Countng. Assumng that the number of sources s also unknown and can vary arbtrarly n tme, other approaches were developed to jontly solve the source countng and locaton estmaton problem. In these approaches, the central dea s to utlze narrowband DOA estmates for each tme-frequency pont from the nodes n order to estmate narrowband locaton estmates. Approprate processng of the narrowband locaton estmates can nfer the numberandlocatonsofthesoundsources.thelocatonfor each tme-frequency pont s estmated usng trangulaton basedonthecorrespondngnarrowbanddoaestmates from the sensors at that tme-frequency pont. Fgure shows an example of such narrowband locaton estmates and ther correspondng hstogram, whch also descrbes the plausblty that a source s at a gven locaton. The processng of these narrowband locaton estmates s usually done by statstcal modelng methods: n [8], the narrowband locaton estmates are modeled by a Gaussan Mxture Model(GMM),wherethenumberofGaussancomponents corresponds to the number of sources, whle the means of the Gaussans determne the sources locatons. A varant of the Expectaton-Maxmzaton (EM) algorthm s proposed that ncorporates emprcal crtera for removng and mergng Gaussan components n order to determne the number of sources as well. A Bayesan vew of the Gaussan Mxture Modelngsadoptedn[83,84],whereavarantoftheKmeans algorthm s utlzed that s able to determne both thenumberofclusters(.e.,numberofsources)andthe cluster centrods (.e., sources locatons) usng splt and merge operatons on the Gaussan components. 7. SRP-Based Localzaton Approaches based on the steered response power (SRP) have attracted the attenton of many researchers due to ther robustness n nosy and reverberant envronments. Partcularly,theSRP-PHATalgorthmstodayoneofthe most popular approaches for acoustc source localzaton usng mcrophone arrays [85 87]. Bascally, the goal of SRP methods s to maxmze the power of the receved sound

15 Wreless Communcatons and Moble Computng 5 source sgnal usng a steered flter-and-sum beamformer. To ths end, the method uses a grd-search procedure where canddate source locatons are explored by computng a functonal that relates spatal locaton to the TDOA nformaton extracted from multple mcrophone pars. The power map resultng from the values computed at all canddate source locatons (also known as Global Coherence Feld [88]) wll show a peak at the estmated source locaton. Snce SRP approaches are based on the explotaton of TDOA nformaton, synchronzaton ssues also arse when applyng SRP n WASNs. As n the case of source localzaton usng DOAs or TDOAs, SRP-based approaches for WASNs have been proposed consderng that multple mcrophones are avalable at each node [89 9]. In these cases, the SRP method can be used for acqurng DOA estmates at each node or collectng source locaton estmates that are merged by a central node. Next, we descrbe the fundamentals of SRP- PHAT localzaton. 7.. Conventonal SRP-PHAT (C-SRP). Consder a set of N dfferent mcrophones capturng the sgnal arrvng from a sound source located at a spatal poston x s R 3 n an anechoc scenaro, followng the model of (). The SRP s defned as the output power of a flter-and-sum beamformer steered to a gven spatal locaton. DBase [85] demonstrated that the SRP at a spatal locaton x R 3 calculated over a tme nterval of T samples can be effcently computed n terms of GCCs: J (SRP) C N (x) = T N =j=+ R (τ (x))+ N = R (), (53) where τ (x) s the tme dfference of arrval (TDOA) that would produce a sound source located at x;thats, τ (x) = x m x m j. (54) c The last summaton term n (53) s usually gnored, snce t s a power offset ndependent of the steerng locaton. When GCCsarecomputedwthPHAT,theresultngSRPsknown as SRP-PHAT. In practce, the method s mplemented by dscretzng the locaton space regon V usng a search grd G consstng of canddate source locatons n V andcomputngthefunctonal of (53) at each grd poston. The estmated source locaton s the one provdng the maxmum functonal value: x (C-SRP) s = arg max x G J (SRP) C (x). (55) 7.. Modfed SRP-PHAT (M-SRP). Reducng the computatonal cost of SRP s an mportant ssue n WASNs, snce power-related constrants n the nodes may render mpractcal ts mplementaton n real-world applcatons. The vast amount of modfed solutons based on SRP s amed at reducng the computatonal cost of the grd-search step [9, 93]. A problem of these methods s that they are prone to dscard part of the nformaton avalable, leadng to some performance degradaton. Other recent approaches are based on analyzng the volume surroundng the grd of canddate source locatons [87, 94]. By takng ths nto account, the methods are able to accommodate the expected range of TDOAs at each volume n order to ncrease the robustness of the algorthm and relax ts computatonal complexty. The modfed SRP-PHAT collects and uses the TDOA nformaton related to the volume surroundng each pont of the search grd by consderng a modfed functonal [87]: J (SRP) M N (x) = N = j=+ L u (x) τ=l l (x) R (τ), (56) where L l (x) and Lu (x) are the lower and upper accumulaton lmts of GCC delays, whch depend on the spatal locaton x. The accumulaton lmts can be calculated beforehand n an exact way by explorng the boundares separatng the regons correspondng to the ponts of the grd. Alternatvely, they can be selected by consderng the spatal gradent of the TDOA τ (x) =[ xτ (x), yτ (x), zτ (x)] T,whereeach component γ {x,y,z}of the gradent s γτ (x) = c ( γ γ x m γ γ j x m ). (57) j For a rectangular grd where neghborng ponts are separated a dstance r g andthelowerandupperaccumulaton lmts are gven by L l (x) =τ (x) τ (x) d g, L u (x) =τ (x) + τ (x) d g, (58) where d g = (r g /) mn(/ sn(θ) cos(φ), / sn(θ) sn(φ), / cos(θ) ), and the gradent drecton angles are gven by θ=cos ( zτ (x) ), τ (x) φ=arctan ( yτ (x), xτ (x)). (59) The estmated source locaton s agan obtaned as the pont n the search grd provdng the maxmum functonal value: x (M-SRP) s = arg max x G J (SRP) M (x). (6) FgureshowsthenormalzedSRPpowermapsobtaned by C-SRP usng two dfferent grd resolutons and the one obtaned by M-SRP usng a coarse spatal grd. In (a), the fne search grd shows clearly the hyperbolas ntersectng at thetruesourcelocaton.however,whenthenumberofgrd ponts s reduced n (b), the SRP power map does not provde a consstent maxmum. As shown n (c), M-SRP s able to fx

16 6 Wreless Communcatons and Moble Computng 4 C-SRP (r g =cm). 4 C-SRP (r g =cm) y (m) y (m) x (m) x (m) (a) (b) 4 M-SRP (r g =cm) y (m) x (m) (c) Fgure : Example of SRP power maps obtaned by C-SRP and M-SRP for a speech frame n anechoc acoustc condtons usng dfferent spatal grd resolutons. Yellow crcles ndcate the node locatons. ths stuaton, showng a consstent maxmum even when a coarse spatal grd s used. An teratve approach of the M-SRP method was descrbed n [95], where the M-SRP s ntally evaluated usng a coarse spatal grd. Then, the volume surroundng the pont of hghest value s teratvely decomposed by usng a fner spatal grd. Ths approach allows obtanng almost the same accuracy as the fne-grd search wth a substantal reducton of functonal evaluatons. Fnally, recent works are also focusng on hardware aspects n the nodes wth the am of effcently computng the SRP. In ths context, the use of graphcs processng unts (GPUs) for mplementng SRP-based approaches s specally promsng [96, 97]. In [98] the performance of SRP- PHAT s analyzed over a massve multchannel processng framework n a mult-gpu system, analyzng ts performance as a functon of the number of mcrophones and avalable computatonal resources n the system. Note, however, that theperformanceofsrpapproachessalsorelatedtothe propertes of the sound sources, such as ther bandwdth or ther low-pass/pass-band nature [99, ]. 8. Self-Localzaton of Acoustc Sensor Nodes Methods for sound source localzaton dscussed n prevous sectons assume that q m for m =,...,M, the locatons of

17 Wreless Communcatons and Moble Computng 7 x x 3 x x =. m y =.5 m z =.7 m Fgure :Illustraton of a WASN comprsed wthm=node and S=4loudspeakers for self-localzaton scenaro. the acoustc sensor nodes, or m for =,...,N,thoseof mcrophones, are known to the system and fxed n tme. In practcal stuatons, however, the precse locatons of the sensor nodes or the mcrophones may not be known (e.g., for the deployment of ad hoc WASNs). Furthermore, n some WASN applcatons, the node locatons may change over tme. Due to these reasons, self-calbraton for adjustng the known node/mcrophone locatons or self-localzaton of unknown nodes of the WASNs becomes necessary. The methods for self-localzaton of WASNs can be dvded nto three categores []. The frst one uses nonacoustc sensors such as accelerometer and magnetometers, thesecondoneusesthesgnalstrength,andthethrdone uses the TOA or TDOA of acoustc sgnals. In ths secton, wefocusonthelastcategorysncethasbeenshownto enable localzaton wth fne granularty, centmeter-level localzaton [], and requres only the acoustc sensors. The TOA/TDOA-based algorthms can be further dvded nto two types dependng upon whether the source postons are known for self-localzaton. Most of the early works addressed ths problem as mcrophone array calbraton [ 5] wth known source locatons. The general problem of jont source and sensor localzaton was addressed by [5] as a nonlnear optmzaton problem. The work n [6] presented a soluton to explctly tackle the synchronzaton problem. In [7], a soluton consderng multple sources and sensors per devce was descrbed. Thssectonwllfocusonalgorthmsthatassumeknown source postons generatng known probe sgnals wthout the knowledge of the sensor postons as well as the synchronzaton between the sensors and the sources. Ths approach allows all processng to take place on the sensor node for self-localzaton. The system llustraton for ths problem s gven n Fgure. The remander of ths secton descrbes the TOA/TDOA-based methods for acoustc sensor localzaton bymodelngthenaccuratetoa/tdoameasurementsfor robust localzaton, followed by some recent approaches. 8.. Problem Formulaton. Consder a WASN comprsed of S sources and M nodes. The mcrophone locatons m (m),for =,,...,N,atnodeq m can be determned wth respect to the node locaton, ts orentaton, and ts mcrophone m x 4 confguraton. So we consder the sensor localzaton of fndng the mcrophone locaton m (m) asthesameproblem asfndngthenodelocatonq m n ths secton. Wthout lossofgeneralty,wecanconsderthecasewthonlyone node and one mcrophone (M = N = )becauseeach node determnes ts locaton ndependently from others. In addton, we consder that the sources are the loudspeakers of the system wth fxed and known locatons n ths scenaro. Let m and x s be the sngle mcrophone poston and the poston of the sth source for s S {,,...,S}, respectvely. The goal s to fnd m by means of S receved acoustc sgnals emtted by S sourceswherethelocatonof each source x s s known. The TOF η s from the sth loudspeaker to the sensor s defned as η s c m x s, (6) where c s the speed of sound. Note that ths equaton s equvalent to (3) except that we consder a sngle mcrophone (m), multsource ({x s })casefors S; thusthetofs ndexed wth respect to s nstead of. From (6), t s evdent that m canbefoundfasuffcentnumberoftofsareknown. In practce, we need to rely on TOAs nstead of TOFs due to measurement errors. In order to remove the effect from such unknown factors, thetdoacanbeusednsteadoftoa,whchsgvenby τ s s η s η s = m x s m x s, (6) c regardng a par of sources s,s S. Pleasenotethatthe subscrpts for the TDOA ndcate the source ndexes that are dfferent from those defned for sensor ndexes n (9). Snce the probe sgnals generated from the sources along wth ther locatons are assumed to be known to the sensor nodes, the dervatons of the self-localzaton methods hereafter rely on the GCC between the probe sgnal and the receved sgnal at the sensor. Provded that the drect lne-ofsght between the source and the sensor s guaranteed, then the tme delay found by the GCC n () between the probe sgnal and the sgnal receved at the sensor provdes the TOA nformaton. 8.. Modelng of Tme Measurement Errors. Two man factors asynchrony and the samplng frequency msmatch between sources and sensors can be consdered for the modelng of tme measurement errors. When there exsts asynchrony between a source and a sensor, the TOA can be modeled as τ s =η s +Δη s, (63) where η s sthetruetoffromsth source to the sensor and Δη s s the bas caused by the asynchrony. If there exsts samplng frequency msmatch, then the samplng frequency at the sensor can be modeled as F s +ΔF s,wheref s s that of the source. Consderng these and gnorng the roundng of the

18 8 Wreless Communcatons and Moble Computng dscrete-tme ndex, the relatonshp between the dscretetme TOA τ s and the actual TOF η s s gven by τ s = η s +Δη s = η s +Δη s ( ), (64) F s +ΔF s F s +ΔF s /F s whch can be further smplfed for ΔF s F s as τ s α η s +β s, (65) where α (F s ΔF s )/F s, η s η s /F s,andβ s Δη s (F s ΔF s )/F s. If the sources are connected to the playback system wth the same clock such that the sources share the common playback delay, then β s =βfor all s S. Therefore where a=c/αand b = cβ/α. m x s =cη s a τ s +b, (66) 8.3. Least Squares Method. Gven a suffcent number of TOA or TDOA estmates, the least squares (LS) method can be used to estmate the sensor poston. The TOA-based and the TDOA-based LS methods proposed n [, ] are descrbed n ths subsecton TOA-Based Formulaton. Motvated by the relaton n (66), the localzaton error e s correspondng to the sth loudspeaker can be defned as e s (a τ s +b) m x s, s S. (67) If we defne the error vector as e (TOA) [e e e S ] T wth unknown parameters a, b, and m, then the cost functon can be defned as J (TOA) LS (m,a,b) = e(toa). (68) Then the localzaton problem s formulated as m (TOA) LS = arg mn m,a,b whch does not have a closed-form soluton. J (TOA) LS (m,a,b), (69) TDOA-Based Formulaton. We can consder the frst loudspeaker for s = as the reference loudspeaker, whose TOAandpostoncanbesetto τ and x =. Gven a set of TDOAsntheLSframework,tcanbeusedwth(66)as a τ s +b=(a τ s a τ )+(a τ +b) a τ s + m, (7) where τ s s the TDOA between the sth and the frst loudspeakers. Wth the frst as the reference, we can defne length S vectors e s (a τ s + m ) m x s,for s =,3,...,Sand e (TDOA) LS [ e, e S ] T,thecostfuncton canbedefnedas J (TDOA) LS and the LS problem can be wrtten as m (TDOA) LS (m,a) = e(tdoa) LS, (7) = arg mn m,a J (TDOA) LS (m,a). (7) Note that the TDOA-based approach s not dependent upon the parameter b unlke the TOA-based approach LS Solutons. For both the TOA- and TDOA-based approaches, the error vector can be formulated as e = HΘ g, where the elements of the vector Θ are unknown and those of the matrx H and the vector g are both known to the system. The error vectors for both approaches n ths formulaton can be expressed as follows []: x T τ τ b m e (TOA) = [... m. ] [ a ] [ x T S τ S τ s ] [ ab ] x [., ] [ x S ] τ x T τ m a e (TDOA) = [.. x. ] [ m ] [.. ] [ τ S x T S τ S] [ a ] [ x S ] (73) Although the elements of the vector Θ are not ndependent from one another, the constrants can be removed for computatonal effcency [5, ], then the nonlnear problems n (69) and (7) can be consdered as the ULS problem as follows: mn Θ e, (74) whch has the closed-form soluton gven by Θ (H T H) H T g. (75) It has been shown that t requres S 6to fnd the closedform soluton for both approaches []. For the case when a=c, that s, no samplng frequency msmatch wth known speed of sound, the TDOA-based approach can be further smplfed as c τ x T e = [.. [ m [ x c τ [[[ ] m ]., (76) ] [ c τ S x T S ] [ x S c τ S] whch s related to the methods developed for the sensor localzaton problem [5, 8]. The self-localzaton results of the LS approaches are hghly senstve to the estmated values of TOA/TDOA. If they are estmated poorly, then the localzaton accuracy may sgnfcantly suffer from those naccurate estmates. In order to address ths ssue, a sldng wndow technque s proposed to mprove the accuracy of TOA/TDOA estmates [].

19 Wreless Communcatons and Moble Computng Other Approaches. More recently, several papers have tackled the problem of how to desgn good probe sgnals betweensourceandsensorandhowtomprovetofestmaton; n [], a probe sgnal desgn usng pulse compresson technque and hyperbolc frequency modulated sgnals s presented that s capable of localzng an acoustc source and estmates ts velocty and drecton n case t s movng. A matchng pursut-based algorthm for TOF estmaton s descrbed n [9] and refned n []. The jont localzaton ofsensorandsourcenanadhocarraybyusnglow-rank approxmaton methods has been addressed n [3]. In [4] an teratve peak matchng algorthm for the calbraton of a wreless acoustc sensor network s descrbed n an unsynchronzed network by usng a fast calbraton process. The method s vald for nodes that ncorporate a mcrophone and a loudspeaker and s based on the use of a set of orthogonal probesgnalsthatareassgnedtothenodesofthenetwork. The correlaton propertes of pseudonose sequences are exploted to smultaneously estmate the relatve TOAs from multple acoustc nodes, substantally reducng the total calbraton tme. In a fnal step, synchronzaton ssues are removed by followng a BeepBeep strategy [6, ], provdng range estmates that are converted to absolute node postons by means of multdmensonal scalng [4]. 9. Challenges and Future Drectons 9.. Practcal Challenges. Some real-world challenges arse n the desgn of localzaton systems usng WASNs. To buld a robust and accurate localzaton system, t s necessary to ensure a tradeoff among aspects related to cost, energy effectveness, ease of calbraton, deployment dffculty, and precson. Achevng such tradeoff s not straghtforward and encompasses many practcal challenges as dscussed below Cost-Effectveness. The potentalty of WASNs to provde hgh-accuracy acoustc localzaton features s hghly dependent on the underlyng hardware technologes n the nodes. For example, localzaton technques based on DOA, TDOA, or SRP need ntensve n-node processng for computng GCCs as well as nput resources permttng multchannel audo recordng. Wth the advent of powerful sngle-board computers, hgh-performance n-node sgnal processngcanbeeaslyacheved.nonetheless,mportant aspects should be consdered regardng cost and energy dsspaton, especally for battery-powered nodes that are massvely deployed Deployment Issues. Localzaton methods usually requre a predeployment confguraton process. For example, TOA-based methods usually need to properly set up synchronzaton mechansms before startng to localze targets. Smlarly, energy-based methods need nodes wth calbrated gans n order to obtan hgh-qualty energy-rato measurements. All these tasks are usually complex and tmeconsumng. Moreover, they tend to need human supervson durng an offlne proflng phase. Such predeployment phasecanbecomeevenmorecomplexnsomeapplcaton envronments where nodes can be accessed by unauthorzed subjects. Moreover, WASNs are also appled outsde of closed buldngs. Thus they are subject to daly and seasonal temperature varatons and correspondng varatons of the speed of sound [35]. To cope wth ths shortcomng, calbraton needs to be automated and made envronment adaptve System Reslency. Besdes predeployment ssues, a WASN should also mplement self-confguraton mechansmsdealngwthnetworkdynamcssuchasthoserelated to node falures. In ths context, system desgn must take nto account the number of anchor nodes that are needed n the deployment and ther placement strategy. The system should assure that, f some of the nodes get out of the network, the rest are stll able to provde locaton estmates approprately. To ths end, t s mportant to maxmze the coverage area whle mnmzng the number of requred anchor nodes n the system Scalablty. Dependng on the specfc applcaton, the WASN that needs to be deployed can vary from a very small andsmplenetworkofafewnodestoverylargewasnswth tens or hundreds of nodes and complex network topologes. For example, n wldlfe montorng applcatons a very large number of sensors are utlzed to acoustcally montor very large envronments, whle the topology of the network can be constantly changng due to sensors beng dsplaced by the wnd or by passng anmals. The challenge n such applcatons s to desgn localzaton and self-confguraton methodsthatcaneaslyscaletocomplexwasns Measurement Errors. It s well known that RF-based localzaton n WSNs are prone to errors due to rregular propagaton patterns nduced by envronmental condtons (pressure and temperature) and random multpath effects such as reflecton, refracton, dffracton, and scatterng. In the case of WASNs, acoustc sgnals are also subject to smlar dstortons caused by envronmental changes and effects produced by nose and nterferng sources, reflected echoes, object obstructon, or sgnal dffracton. Other errors are related to the aforementoned predeployment process, resultng n synchronzaton errors or naccuraces n the postons of anchor nodes. These errors must be analyzed n order to flter measurement nose out and mprove the accuracy of locaton estmates Benchmarkng. In terms of performance evaluaton, so far there are no specfc benchmarkng methodologes and datasets for the locaton estmaton problem n WASNs. Due to ther heterogenety n terms of sensors, number of sensors and mcrophones, topology, and so on works comparng dfferent localzaton methods usng a common sensor setup are dffcult to fnd n the lterature. The defnton of formal methodologes n order to evaluate localzaton performance and the recordng of evaluaton datasets usng real-lfe WASNs stll reman a bg challenge.

20 Wreless Communcatons and Moble Computng 9.. Future Drectons 9... Real-Lfe Applcaton. Inourdays,theneedforreallfe realzatons of WASN wth sound source localzaton capabltes s becomng more a more evdent. An mportant drecton n the future wll thus be the applcaton of the localzaton methodologes n real-lfe WASNs. In ths drecton, the ntegraton of methodologes from a dverse range of scentfc felds wll be of paramount mportance. Such felds nclude networks (e.g., to desgn the communcaton and synchronzaton protocols), network admnstraton (e.g., to organze the nodes of the network and dentfy and handle potental falures), sgnal processng (e.g., to estmate the sources locatons wth many potental applcatons), and hardware desgn (e.g., to desgn the acoustc nodes that can operate ndvdually featurng communcaton and multchannel audo processng capabltes n a power effcent way). Whle many of these felds have flourshed ndvdually, the practcal ssues that wll arse from ther ntegraton n practcal WASNs stll reman unseen and the need for benchmarkng and methodologes for ther effcent ntegraton s becomngmoreandmoreurgent Machne Learnng-Based Approaches. One of the practcal challenges for the deployment of real-lfe applcatons sthehugevarabltyofacoustcsgnalsrecevedatthe WASNsduetotheacoustcsgnalpropagatonnthephyscal doman as well as the naccuraces caused at the system level and uncertantes assocated wth measurements of TOAs and TDOAs. Wth the help of large datasets and vastly ncreased computatonal power of off-the-shelf processors, these varabltes can be learned by machnes for desgnng more robust algorthms.. Concluson Sound source localzaton through WASNs offers great potental for the development of locaton-aware applcatons. Although many methods for locatng acoustc sources have been proposed durng the last decades, most methods assume synchronzed nput sgnals acqured by a tradtonal mcrophone array. As a result, when desgnng WASN-orented applcatons, many assumptons of tradtonal localzaton approaches have to be revsted. Ths paper has presented a revew of sound source localzaton methods usng commonly used measurements n WASNs, namely, energy, drecton of arrval (DOA), tme of arrval (TOA), tme dfference of arrval (TDOA), and steered response power (SRP). Moreover, snce most algorthms assume perfect knowledge on the node locatons, self-localzaton methods used to estmate thelocatonofthenodesnthenetworkarealsoofhgh nterest wthn a WASN context. The practcal challenges and future drectons arsng n the deployment of WASNs have also been dscussed, emphaszng mportant aspects to be consdered n the desgn of real-world applcatons relyng on acoustc localzaton systems. 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