Sea Depth Measurement with Restricted Floating Sensors

Transcription

1 Sea Depth Measuremet with Restricted Floatig Sesors Zheg Yag, Mo Li, ad Yuhao Liu Hog Kog Uiversity of Sciece ad Techology {yagzh, limo, Abstract Sea depth moitorig is a critical task to esure the safe operatio of harbors. Traditioal schemes largely rely o labor-itesive work ad expesive hardware. This study explores the possibility of deployig etworked sesors o the surface of sea, measurig ad reportig sea depth of give areas. We propose a Restricted Floatig Sesors (RFS) model, i which sesor odes are achored to the sea bottom, floatig withi a restricted area. Distiguished from traditioal statioary or mobile sesor etworks, the RFS etwork cosists of sesor odes with restricted mobility. We costruct the etwork model ad elaborate the correspodig localizatio problem. We show that by locatig such RFS sesors, the sea depth ca be estimated without the help of ay extra ragig devices. A prototype system with Telos sesor odes is deployed to validate this desig. We also examie the efficiecy ad scalability of this desig through large-scale simulatios.. Itroductio We coducted a field study i H. H. Harbor, which is curretly the secod largest harbor for coal trasportatio i Chia. It has experieced rapid developmet over the past years, ad its coal trasportig capability has icreased from.6 millio tos per year i to 6.7 millio tos per year i 6. However, this harbor curretly suffers from the icreasigly severe problem of silt depositio alog its sea route. H. H. Harbor has a sea route that is 9 autical miles log ad 8m wide at the etrace, icludig a ier route ad a outer route. The sea route is desiged to have a water depth of.m to allow for the passage of ships that weigh over thousad tos. Sice the sea route has bee i operatio, it has always bee threateed by the movemet of silt from the shallow sea area withi 4 autical miles outside the route etrace. I the evet that the sea route is silted up, ships of large toages must wait for eterig the harbor to prevet groudig, ad ships of small toages eed Figure : Restricted floatig sesors o the sea be piloted ito the harbor. Moitorig the extet of siltatio reliably is critical i order to esure the safe operatio of H. H. Harbor. The ucertaity ad the high istat itesity of the siltatio make moitorig the extet of siltatio extremely expesive ad difficult. The amout of siltatio i H. H. Harbor is affected by may factors, amog which tide ad wid blow are the most domiatig. While the tides produce a periodic ifluece o the movemet of silt, the highly variable ature of wid brigs more icidetal ad itesive effects. For example, records show that strog wids with wid forces of 9 to o the Beaufort scale hit H. H. Harbor from Oct. th to Oct. th i. The storm surge brought 97,m of silt to the sea route, which suddely decreased the water depth from 9.m to.7m ad blocked most of the ships weighig more tha thousad tos. The harbor admiistratio hired three boats equipped with active soars to cruise the 8km shallow sea area aroud the harbor for several days. Moitorig sea depth costs this harbor more tha 8 millio US dollars per year. I this work, we explore the possibility of deployig etworked sesors o the sea surface for sea depth measuremet. Differet from deploymets o groud, sesor odes, i this sceario, will geerally ot be statioary at their origial deployed places, but float by may factors, e.g. ocea curret, wid blow, ad tide

2 etc. Therefore, we achor the sesor odes to the sea bottom by ropes to restrict their floatig movemets. Otherwise, they may float out of our iterested moitorig area. We call them the Restricted Floatig Sesors (RFS). Figure illustrates a RFS etwork deployed i a sea area. As show, differet sea depths result i differet sizes of floatig areas. To map sea depth, both geographic positios ad water depths are ecessary. We fid that such measuremets ca be acquired by figurig out sesors floatig areas. Sectio details the process how we obtai water depth from the localizatio results of floatig areas without ay extra ragig devices. Thus our problem chages to determiig the floatig area of each sesor. Sice the sesor odes i the RFS etwork ca float aroud, the traditioal localizatio approaches for statioary sesors caot work. O the other had, simply treatig the RFS etwork as a mobile sesor etwork ad blidly applyig those localizatio approaches for mobile WSNs does ot capture the special ature of the RFS etwork. I the RFS etwork, sesor odes float withi restricted areas, providig us possibilities to capture their mobility models. By uderstadig RFS mobility behaviors, we ca achieve higher accuracy with reduced overhead. I this paper, we give a elaborate aalysis o the localizatio problem i the RFS etwork. We build etwork models ad establish the localizatio objective as locatig the floatig area of each sesor ode. We equip a small portio of the etwork odes with exteral locatig devices such as GPS receivers, called seed odes; while others are o-seed odes. All sesor odes estimate their distaces from each other. Our approach applies differet computatio schemes for efficietly localizig the floatig areas of the seed ad o-seed odes based o rage distace estimatios. By locatig the sesor odes, we ca accordigly ifer the sea depth at the achor positios i a practical way, which prevets relyig o other expesive specialized devices like soar pigers. We validate our desig by lauchig a prototype system with Telos sesor odes off the seashore i HKUST campus. The results show that our prototype achieves less tha.m sea depth estimatio error averagely. We coduct a large scale simulatio to further test the system performace ad scalability uder various etwork settigs. With precise distace measuremets assumed, we ca obtai the sea depth estimatio with a average relative error withi %. The rest of the paper is orgaized as follows. I Sectio, we formally defie the RFS etwork model ad formulate the localizatio problem for RFS. We describe our localizatio approaches for seeds ad o-seeds i Sectio ad Sectio 4. I Sectio, we discuss measurig sea depth based o the floatig area localizatio. We preset the experimets ad the results i Sectio 6. We summarize related work i Sectio 7 ad coclude this work i Sectio 8.. The Network Model I this sectio, we first give a defiitio of the more geeral Restricted Mobile Sesor (RMS) etwork. DEFINITION. RMS etwork. A sesor is called a restricted mobile sesor, if it is capable of movemet but its movemet is restricted withi a local area of the applicatio field. A etwork composed of restricted mobile sesors is called a RMS etwork. The RFS is a typical RMS etwork. Oce achored at a poit, the sesor ode floats o the sea surface but withi a restricted area. DEFINITION. Floatig area. I a RMS etwork, the movemet of a sesor is limited i a restricted area. The restricted area may have differet shapes due to differet costraits of RMS etworks. I the RFS etwork, each sesor ode floats o the sea surface withi a disk area cetered at its achor. This disk area is called the floatig area of the sesor. We use o(c, r) to deote a disk floatig area, where c ad r represet the cetre ad radius of the disk area, respectively. I practice, c is the achored positio of each sesor ad r is determied by the legth of the rope ad the sea depth at the achored positio. DEFINITION. Floatig model. I the RFS etwork, each sesor floats withi its floatig area. The movemet is affected by may factors, e.g. ocea curret, wid blow, tide etc. The factors above ca hardly be modeled ad mostly affect with radomess. I this case, the curret positio of a sesor is cosidered idepedet of its previous positios uder oegligible itervals betwee cosecutive samplig times. Each sesor is assumed to appear i the floatig area uder uiform distributio ad the probability distributio of the sesor positio is give by:, ( x, y ) o ( c, r ) f( x, y) = π r, otherwise DEFINITION.4 RFS etwork model. The targeted RFS etwork N(S, O) cosists of a set of sesors S ad the correspodig set of floatig areas O. Each sesor s i moves withi its floatig area o i uder the floatig model. The floatig areas of differet sesors are assumed o-overlapped, i.e. s i, s j S withi floatig area o i (c i, r i ) ad o j (c j, r j ), dist(c i, c j ) > r i + r j. This assumptio prevets the possibility that two sesors get too close ad their ropes become twisted with each other. This assumptio is realistic i practice as

3 the sesor commuicatio rage is usually multiple times the radius of sesor floatig area. DEFINITION. Neighborhood of RFS. I traditioal sesor etworks, the eighbors of a sesor s are defied as the set of sesors that have direct commuicatios with s. While the eighborhood is relatively stable i static sesor etworks, it is highly dyamic i mobile sesor etworks. As a restricted mobile sesor etwork, RFS etwork shares similarity with traditioal mobile sesor etworks i that each sesor ode has dyamic coectios with its eighborig odes. However, the locality of sesor movemet i the RFS etwork costrais this dyamic effect. Therefore, we are able to itroduce a more proper defiitio of eighborhood for RFS. Sesor s i ad s j are defied to be eighbors iff. they ca commuicate with each other i their etire floatig areas. Each ode has direct commuicatio with its eighbor odes at ay time. Uder this defiitio, we obtai a stable eighborhood i RFS etworks. DEFINITION.6 Floatig area localizatio. I RFS etworks, sesor odes move withi their floatig areas uder the probabilistic floatig model. The localizatio issue i RFS etworks is to obtai the floatig areas istead of the istataeous locatios. The floatig area localizatio i the RFS etwork idicates the process of locatig the floatig area o(c, r) of each sesor, icludig the cetral achor positio c ad the radius r. I the followig, localizatio meas floatig area localizatio if ot elsewhere specified. DEFINITION.7 Error. Let o(c, r) be the floatig area of sesor s ad ocr ˆ(,) ˆ ˆ be the estimated floatig area. The localizatio error icludes two parts: () error o the estimated achor positio e c = dist(,) cˆ c ; () error o the estimated radius e r = rˆ r. The relative error of floatig area o(c, r) is defied as a D vector E( oo ˆ, ) = (e c /r, e r /r). The average localizatio error of a RFS etwork N(S, O) is defied as E( N) = E( oˆ, o) O o. O We desig the Floatig Area Localizatio Algorithm (FALA) to localize sesor odes i a RFS etwork. I the localizatio process, all sesor odes are able to measure the distaces betwee themselves through RSS measuremets. Other superior techiques like TOA, TDOA ad AOA ca be applied for higher ragig accuracy. As a statistic based algorithm, FALA yields the localizatio result after a series of data samplig. Durig each samplig process, seeds collect their locatios ad o-seeds process the distace measuremets. FALA applies differet schemes for locatig seeds ad o-seeds. Although seeds are able to kow their istataeous locatios, further computatio based o the locatio iformatio is eeded to determie their floatig areas. For o-seeds, FALA derives their floatig areas from distace iformatio through a sequetial process. FALA icludes four steps: samplig, seed floatig area computig, o-seed floatig area computig, ad cotiuous date collectio ad accuracy improvemet.. FALA for Seeds As equipped with localizatio devices, seeds are aware of their istat positios. We carry out a series of sampligs o seed positios. After a period of time, each seed ode records a set of positios it resides i at differet time. We estimate the floatig area of seed odes from the positio sets. Obviously, all sampled positios of a seed are certaily i its floatig area uder the floatig model. I other words, its floatig area should be a disk area at least cotaiig all sampled positios. Thus, we ca trasform the localizatio problem to figurig out a disk area which covers a set of positios. Apparetly, there are may feasible disk areas, amog which the smallest oe should be cosidered the maximum likelihood estimatio because it provides the highest probability of the occurrece of a set of positios. Thus, the smallest oe is the cosidered the estimatio of the floatig area of the seed. As the sampled positios accumulate, the floatig area is asymptotically approached. The problem is formulated as follows. Give a set P of poits i the plae, fid the smallest eclosig disk for P, that is, the smallest disk that cotais all the poits of P. For simplicity, we assume that o three poits are colliear ad o four poits are cocircular. I computatioal geometry, this problem is ofte called the Miimum Eclosig Disk (MED) problem. It is ot difficult to fid a brute force solutio to the problem which takes O( 4 ) ruig time. However, such a algorithm itroduces itesive computatioal cost which is likely ot suitable for the resource restricted sesor odes. A radomized algorithm[9, 7] for MED problem has bee proposed i computatioal geometry domai, which takes O() expected ruig time. It is observed that whe a poit is outside the MED of all other poits, it must lie i the boudary of MED of all poits. The followig theorem [9] illustrates this observatio.

4 Theorem: Let P be a set of poits i the plae. Let R be a possibly empty set of poits with R P = φ. Let D(P, R) deote the miimum eclosig disk of P that cotais R o its boudary. The we have, (a) If a poit p D(P\{p}, R), the D(P, R) = D(P\{p}, R); (b) Otherwise D(P, R) = D(P\{p}, R {p}). Probability = = = = = Based o this theorem, the radomized algorithm RMED computes the MED of a give set P of positios. At the very begiig, we have o idea about which poit lies o the boudary of MED, so the seed rus RMED(P, ull) as a start. Algorithm RMED(P, R) : if P = φ or R =, : the D := the disc defied by R. : else choose a radom p P, 4: D := RMED(P\{p}, R); : If p D, 6: the D := RMED(P\{p}, R {p}). 7: retur D. The RMED algorithm ca be chage to work i a icremetal maer [9]. That is to say, beig iformed the curret positio from its positioig device at each samplig time, a seed updates its existig miimum eclosig disk ad obtais a refied approximatio of the floatig area. I this olie versio of algorithm, seeds ca start localizatio as early as possible without waitig for all samplig positios collected. This feature well suits the data acquisitio patter of seed samplig process. Moreover, the updatig process takes oly O() expected ruig time. Accordig to our algorithm, the approximated floatig area ô is always smaller tha the real oe o. The error betwee o ad ô keeps decreasig durig the updatig processes i which ô expads towards o. To miimize the estimatio error, the seed eeds to collect more sample data. However, a large sample capacity usually implies a log period of samplig. Therefore, we eed to properly choose a sample capacity aimig for a acceptable accuracy. We coduct a simulatio to aalyze the error of our estimatio at differet sample capacities of =,,, ad. The simulatio results are show i Figure. We fid that whe the umber of sampligs is, 8% of cases have less tha % relative error of radius estimatio ad whe the umber of sampligs is, 9% of cases have less the % error. I most applicatios, a umber ragig from to iduces a acceptable sample capacity for seeds to compute their floatig areas Ratio of Estimate to Real Radius Figure : Cumulative distributio fuctio of the estimated to real radius ratio 4. FALA for No-seeds Whe seeds have localized their floatig areas, we eed to utilize them as referees to locate o-seeds. Trilateratio from referees is a widely used method to localize static odes i statioary sesor etworks. However, due to the dyamic property, directly usig trilateratio for RFS leads to poor accuracy. I this sectio, we propose a ew scheme for locatig oseeds based o statistical measuremets. 4.. The Framework of No-seed FALA Before lookig iside the o-seed FALA, we first defie two cocepts about computed ad computable sesor odes. DEFINITION 4. Computed ad computable sesor odes. We call a sesor ode computed if its floatig area is already kow. If a o-computed sesor ode has k (k ) computed eighbors, it is a computable sesor ode. The o-seed FALA is a iterative process, gradually trasformig computable sesors to computed sesors. Figure plots a deploymet of four sesors: a o-seed s, with the floatig area o ukow, ad its three eighbors {s i i }. Assume all s i are computed odes, that is, their floatig area o i (c i, r i ) are kow. Let d i deote the distace betwee s ad s i. Our goal is to estimate the floatig area o of s. Clearly, with oe time measuremet there exists ucertaity for floatig area computatio. As show i Figure, aother disk area o differet from o is also possible to be a cadidate of the floatig area of s, because the curret positio of s which satisfies all distace costraits also resides i o. We caot distiguish the real area from o ad o at this stage. That meas, it is impossible to calculate the floatig area of s uder a sigle time observatio of d i.

5 Figure : No-seed localizatio for explorig the relatioship betwee sample statistics ad the hidde parameters, based o the geometrical relatioship ad regressio aalysis respectively. I step, although sesor odes are mobile, their achored positios are static. Thus, it is possible to solve a typical poit localizatio problem for locatig achored positios. O the premise that the distaces from a ukow achor positio to three kow achored positios are obtaied, trilateratio ca be coducted to calculate the ukow achored positio. With c ad r, this step completes the floatig area computatio of s ad s becomes a computed sesor ode. 4.. Geometrical Relatioship Figure 4: Achor distace estimatio The distace measuremet d i varies all the time due to the movemet of s ad s i. We observe that multiple sampligs ca alleviate the ucertaity for localizatio. If we treat o ad o as two sets of poits i plae, whe s moves to some positio i o - o, the distace samplig iformatio egates the possibility of o beig the floatig area. Furthermore, we kow that d i oly depeds o o(c, r) ad o i (c i, r i ), irrespective of ay other floatig areas o j (j i). Hece, the sample distributio is determied by r i, r, ad the distace betwee two achored positios d i = dist(c, c i ), idicatig that, to some extet, the samples statistics ca imply r i, r, ad d i. Therefore, the relatioship betwee the sample statistics ad the parameters r i, r, ad d i is of great importace, based o which o-seeds ca localize their floatig areas. Without loss of geerality, we oly cosider s ad a calculated eighbor s i, as show i Figure 4. For simplicity, we use d ad d istead of d i ad d i to elaborate the o-seed FALA. We kow d varies all the time while d is a static value. Let D deote the radom variable of d ad let d i deote the observed value of D at samplig time t i. Three steps are icluded i the floatig area computatio of o-seed s, described as below.. A o-seed s samples the distace measuremets d betwee s ad its eighbors.. Based o sample statistics, s calculates d ad r.. If s is computable, it calculates the achor positio c by trilateratio based o d. I step, the o-seed s carries out a samplig process. I step, s estimate the hidde parameters based o distace samples. We cosider two methods A simple method for estimatig d ad r is to explore the geometrical relatioship betwee the two floatig areas of s ad s i. We defie d max = max(d) ad d mi = mi(d) as the miimum ad maximum values of D. As show i Figure 4, d max ad d mi are obtaied i two extreme situatios. Accordig to the geometrical relatioship, we have: d mi ' max + d d = dmax dmi r = r. i Such a method is simple to implemet ad takes little computatio cost. I practice, it is reasoable to regard max(d i ) ad mi(d i ) as the estimatio of d max ad d mi respectively. However, the extreme cases may ot occur i samplig, uder which we will get bad estimatios of d max ad d mi. I additio, o-egligible ragig errors of existig approaches also heavily degrade the effectiveess of the method. O the cotrary, the statistical method, based o samplig distributios, less suffers from this. 4.. Regressio Aalysis As we have observed, the distributio of D, to some extet, reflects the hidde parameters r ad d. This fact allows us to desig a method to estimate r ad d based o sample statistics. I our aalysis, sice r i is a kow parameter, we itroduce two coefficiets θ ad θ, such that r = θ r i ad d = θ r i. The sample statistics iclude the mea ˆμ ad the stadard deviatio ˆ σ of samples, defied by ˆ μ = di i=

6 ˆ σ = ( d ˆ i μ). i= A simulatio study is coducted to explore the relatioship betwee hidde parameters (θ ad θ ) ad sample statistics ( ˆμ ad ˆ σ ). Figure gives us a importat ituitio about the relatioship, that is, there exists liear relatio betwee the parameters ad the sample statistics. We ow sythetically take accout of the impact of both θ ad θ by usig multiple regressio aalysis. Let β be a coefficiet matrix, our geeral form of two-variable liear regressio equatio is as follows: θ ˆ μ ˆ σ = β θ. Usig least squares techique, we have β = I summary, a ode s first collects sample distaces betwee itself ad its eighbor s i, ad the calculates the statistics ˆμ ad ˆ σ. Accordig to the regressio model, s determies θ ad θ ; ad fially completes the estimatio of r ad d. Errors of our regressio model may come from two sources: () the residuals i regressio aalysis ad () the iaccuracy of ˆμ ad ˆ σ.the residual figure, Figure 6, illustrates that the error of our liear regressio model is relatively small if we cosider the usual values of θ ad θ. The iaccuracy of ˆμ ad ˆ σ is usually due to a small sample capacity. Takig error aalysis of ˆμ as a example, the size of sample ca be determied by the accuracy costrais. The ormality test of sample data, Figure 7, suggests the samplig distributio is almost ormal. Thus, the statistic ˆ μ μ ˆ σ / possesses a t-distributio. The we get ˆ σ ˆ σ P( ˆ μ t ˆ α/, < μ < μ+ tα/, ) = α, ad the iterval estimatio of μ ˆ σ ˆ σ ( ˆ μ t ˆ α/,, μ+ tα/, ) is a ( - α) % cofidece iterval for the mea μ. The legth of the iterval is ˆ σ l = t. α /, Probability Sample Statistic Residuals Residuals Mea Value Std. Dev. 4 6 θ Sample Statistic Mea Value Std. Dev θ Figure : Hidde parameters vs. sample statistics 4 Case Number 4 Case Number Figure 6: Residuals of regressio aalysis Sample Data Figure 7: Normal probability plot of sample data Accordig to the t-distributio, = deserves a 9% cofidece iterval with a acceptable accuracy l =.64 ˆ σ.. Sea Depth Measuremet by FALA The ultimate goal of this work is to estimate the depth of the sea. By utilizig FALA, we ca efficietly localize the sesor odes i the etwork. Whe we use a rope with legth L to achor the sesor ode o the sea of depth h (L > h), the sesor ode floats withi the disk area of radius r = L h, as show i Figure 8. After localizatio, we obtai the floatig area of a ode, achievig its ceter c as well as its radius r. We ca the easily calculate the sea depth at positio c. This calculatio ivolves either extra measuremets or hardware costs.

7 Figure 8: Geometrical structure of sea depth measuremet Figure 9: Prototype system deploymet Whe the sea depth of a moitorig regio is deep, loger ropes are ecessary. I this situatio, the gravity of ropes caot be igored. Whe sesor odes are o the boudaries of their floatig areas, ropes caot be straight but form a curve with steep upper part ad mild lower part. Such a curve ca be see as a part of cateary. We ca calculate the see depth accordig to localizatio results ad the equatio of cateary []. 6. Performace Evaluatio We first examie the effectiveess of our desig by deployig a prototype system off the seashore. A large scale simulatio is further coducted to test the system scalability uder varied etwork parameters. We evaluate FALA usig three metrics: E(c) = e c /r, E(r) = e r /r, defied i Sectio, ad E(h) = hˆ h /h to evaluate the error of sea depth measuremet. I some previous literatures, the locatio error is represeted relative to the hop size (the maximum commuicatio rage of a ode) [6, 7]. However, for FALA evaluatio, if we use the commuicatio rage as a bechmark to measure locatio error, a m error cotributes the same impact to a small floatig area as to a large floatig area, i.e. a m radius area ad a m radius area. To dimiish this ufairess, we adopt the relative error agaist the radii of floatig areas i the evaluatio. Sice the commuicatio rage of each sesor ode is usually ~ times larger tha the radius of its floatig areas i our experimet, the estimate errors are usually several times tha they are agaist the sesor commuicatio rage. 6. Prototype Experimet To better uderstad the systematic behaviors of FALA, we deploy a prototype with odes off the seashore o uiversity campus. The hardware layer of the prototype is costructed o the Telos motes with Atmel8 processor ad CC4 trasceiver. We fit each ode with a lightweight supportig shelf, which floats o the sea surface ad raises the sesor ode cm high above the sea surface. such assembled floatig odes are achored o a m m sea area where the water depth is aroud 4~7m. Figure 9 exhibits our deploymet. We utilize RSSI values from the trasceivers to estimate the distaces betwee odes. The trasmittig power of sesor odes is set to mw ad trasmittig rage could reach as far as 4m with more tha - 9dbm receivig sigal stregth. We costruct a distace estimator accordig to the most widely used sigal propagatio model: the log-ormal shadowig model []. Due to the coarse ad o-mootoe correspodece betwee the RSSI ad distace i the real measuremets, the relative error of the distace estimatio ca be up to %, which heavily limits the accuracy of FALA. We believe more precise distace estimatig techiques such as TDOA or TOA based approaches will help to achieve better accuracy. Figure plots the FALA performace i our prototype system. The error of achored positio, as show i Figure (a), is aroud.~ for seeds ad.~4 for o-seeds. For radius estimatio, the error is aroud.~., illustrated i Figure (b). I Figure (c), we ca see the relative error of sea depth is aroud.~.. From Figure, seeds basically outperform o-seeds i all three metrics. I practice, two factors limit our prototype from more accurate results: () the seawater ear the seashore moves a little regularly rather tha completely affected by radomess, which makes errors o our floatig model assumptios; () the large errors i our RSSI based ragig techique cotributes much to the estimatio error of FALA.

8 4 Seed No-seed.4. Seed No-seed.. Seed No-seed E(c) E(r). E(h)... Sesor Node ID Sesor Node ID Sesor Node ID (a) Error of achor positio (b) Error of radius (c) Error of sea depth Figure : FALA performace of each ode i the prototype system E(c). E(r).. E(h) Sample Capacity of No-seeds. 4 Sample Capacity of No-seeds 4 Sample Capacity of No-seeds (a) Error of achor positio (b) Error of radius (c) Error of sea depth Figure : Impact of sample capacity with precise distace measuremet E(c) E(r).4 E(h)... 4 Percetage of Seeds (%).8 4 Percetage of Seeds (%). 4 Percetage of Seeds (%) (a) Error of achor positio (b) Error of radius (c) Error of sea depth Figure : Impact of seed proportio with precise distace measuremet 6. Large-scale Simulatio We geerate etworks of 9 odes radomly distributed i a square sea regio. I our simulatio, the sea regio is desiged to be a 6m 6m square ad has a water depth aroud m. Whe a RFS etwork is deployed i this sea regio, the radii of floatig areas are ~6m, which are determied by sea depth ad rope legth. A typical commuicatio rage of the sesor odes is m ad the average degree of etwork topology is 8. I all our measuremets, we itegrate the results from etwork istaces. I our simulatio, we varied two parameters, the proportio of seeds ad the sample capacity, to examie FALA uder differet etwork settigs. We test the performaces of geometrical relatio () method ad regressio aalysis () method proposed i Sectio 4. Precise distace measuremets We first assume precise distace measuremet to explore the ideally achievable accuracy of FALA. Figure (a) plots the average error of achored positio. The error of is below., which is lower tha as the sample capacity varies i a wide rage. Whe the size of sample is larger tha, the extra gai from becomes trivial. Therefore, ca be a good choice of sample capacity cosiderig the tradeoff betwee the accuracy ad overhead. As show i Figure (b), the average radius error of cosistetly decreases as the sample size icreases; while is slightly gettig worse. outperforms whe sample capacity is larger tha. The average error of sea depth, ivestigated i Figure (c), follows the similar patter as the radius estimatio. We also examie the impact of the seed desity o FALA, highlighted i Figure. All performace metrics get better whe the seed desity icreases. There is otable gap betwee ad i Figure (a). The error of is less tha whe % seeds exist. I figure (b) we examie the radius estimatio. We observe that both ad yield smaller errors whe isertig more seeds ad is better tha whe seed proportio is larger tha %. Figure (c) shows the error o sea depth measuremets. Agai, it follows the similar patter as radius error does ad yields the error from. to. whe seed proportio varies from % to 4%.

9 E(c) E(r) E(h) Sample Capacity of No-seeds 4 Sample Capacity of No-seeds. 4 Sample Capacity of No-seeds (a) Error of achor positio (b) Error of radius (c) Error of sea depth Figure : Impact of sample capacity with oisy distace measuremet E(c) 4 Percetage of Seeds (%) E(r).. 4 Percetage of Seeds (%) E(h) Percetage of Seeds (%) (a) Error of achor positio (b) Error of radius (c) Error of sea depth Figure 4: Impact of seed proportio with oisy distace measuremet Noisy distace measuremets We further evaluate FALA uder oisy distace measuremets. I our simulatio, we itroduce a zeromea Gaussia oise with stadard deviatio of % of the real values ito distace measuremets. Agai, outperforms, as show i Figure ad 4. Compared with Figure ad, the error of all performace metrics is larger tha the correspodig errors with precise distace measuremet. Especially, for achored positio estimatio, the error ca be times larger. Clearly, a oisy distace measuremet heavily degrades the performace of FALA. I such situatios, sample data ad % seeds are ecessary for precise localizatio. 7. Related Work Recet advaces i WSNs attract the attetio of a lot of researchers [,, 6, 8] with may efforts made for locatig sesors [6, 8, ]. Accordig to the targeted eviromets, previous localizatio approaches ca be classified ito two types: for static sesor etworks ad for mobile sesor etworks. The static localizatio problem has bee extesively studied for WSNs. The proposed localizatio approaches typically use a small umber of seed odes that are aware of their locatio. Moreover, ragig measuremets [6,,, 4, 6] (i rage-based approaches) or eighborhood iformatio [4, 8, ] (i rage-free approaches) are utilized to locate o-seed odes. All these approaches assume the ivariability of sesor locatios. Oce a sesor ode kows its locatio, it ca be used as a beaco to locate other sesor odes. Such a strategy fails i our RFS cotext due to the movemet of sesors. Some of the static localizatio approaches [, 4] ca be exteded to coform to the mobile eviromet. Most of them, however, caot yield results i real time ad thus suffer from estimatio latecy ad iaccuracy brought o by sesor movemets. Bergamo ad Mazzii s [] is oe of the first works related to the localizatio problem i mobile sesor etworks. Two fixed seeds are assumed trasmittig across the etire etwork ad other odes ca measure the received sigal stregth accurately. L. Hu ad D. Evas propose a statistic based localizatio approach for mobile sesor etworks i [7] based o the MCL method [], which origiates from a mobile localizatio problem i robotics. Mobility creates obstacles to accurate localizatio, resultig i large errors ad heavy commuicatio cost. I additio, dese seed deploymet is required i that proposed approach. Noe of above schemes cosiders a restricted movemet model for sesor odes. Directly usig those localizatio approaches does ot capture the special movemet behaviors of RFS etworks. Hece, they suffer from either iaccurate localizatio results or uecessary estimatio overhead. 8. Coclusios ad Future Work We discuss a ovel sea depth measuremet applicatio usig wireless sesor etworks. We defie the localizatio problem i RFS etworks ad itroduce the cocept of floatig area localizatio, so as to determie the floatig areas of sesor odes. A statistical approach, FALA, is desiged, based o which the sea depth ca be acquired without expesive soar systems. A prototype with Telos odes is deployed o a sea surface, ad itesive large-scale simulatios are co-

10 ducted to examie the efficiecy ad scalability of the proposed approach. This work is still at its early stage. The future work leads ito followig directios. () Oe assumptio i our floatig model is that the sesors float withi their achored areas uder radomess, which i our prototype test is show to be iadequate. The seawater ear the seashore moves a little regularly rather tha completely affected by radomess. The wave may also itroduce errors of estimatios. Thus a well model of the behaviors of the sea will help dimiish their egative impact or eve make use of their regularity to achieve more accuracy. () The system scalability is also a importat issue we eed pay special attetio to. Sice the RSSI based distace measuremet bears a large error, there is a tred of error propagatio o our estimatios whe the etwork size sigificatly icreases, especially uder a small percetage of seeds. Whether or ot we are able to desig a soud collaboratig mechaism at the layer of etwork topology, so that we ca suppress the localizatio errors throughout the etwork, is a sigificat but challegig issue. () Sea depth estimatio is of great iterests ad importace for may sea moitorig applicatios. Our FALA approach yields the estimatios of sea depth by utilizig the result of the floatig area localizatios, reducig the cost. This approach, however, also has its ow limitatios, e.g. the achor of each sesor ca actually get buried by the silt, which leads to iaccurate estimatios as the time passes by. Is there ay other light-weight approach for measurig the sea depth? Due to the itesive eeds o the sea depth measuremet ad the difficulty of employig ifrastructures at sea, we believe WSN is oe of the best cadidates for this applicatio. (4) The Restricted Floatig Sesors describe a geeral model for sesor deploymet which might be suitable for may sesig applicatios carried out o the sea. Uder differet cotexts of the sesig applicatios, we might cocer differet factors of the etwork besides the locatios, such as sesor coverage, etwork coectivity, data sampligs, etc. Due to the ature of restricted mobility, the RFS etwork itroduces the itermediate dyamics betwee the static etwork ad mobile etwork. By developig mechaisms over the dyamics but takig advatage of the restrictio o the mobility, ca we achieve higher efficiecy? We believe it is o-trivial ad highly related to the cocered factors ad the applicatio cotext. We are curretly cotiuig this project for aswerig part of above questios ad deployig a real workig system together with the research group from Ocea Uiversity of Chia. Ackowledgemet This work is supported i part by the Hog Kog RGC grat HKUST669/7E, the Natioal Basic Research Program of Chia (97 Program) uder grat No. 6CB, the Natioal High Techology Research ad Developmet Program of Chia (86 Program) uder grat No.7AAZ8, ad NSFC Key Project grat No. 6. 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