Range-based Mobility Estimations in MANETs with Application to Link Availability Prediction

Transcription

1 Range-based Mobly Esmaons n MANETs wh Applcaon o Ln Avalably Predcon Zhuoqun L, Lngfen Sun and Emmanuel C. Ifeachor School of Compung, Communcaons and Elecroncs Unversy of Plymouh Drae Crcus, Plymouh, PL4 8AA, Uned Kngdom {Zhuoqun.L, L.Sun, E.Ifeachor}@plymouh.ac.u Absrac The qualy of communcaons n moble ad-hoc newors s largely deermned by he opologcal sably. Characerzng he mobly of moble nodes (e.g. how ofen hey move away from each oher) would enable he measuremen of he frequency of newor reconfguraons for predcng sably. In hs paper, we frs defne a rple V, Θ, Ψ whch consss of mobly parameers ha are drecly correlaed wh he sably of a newor (e.g. ner-node relave speeds/orenaons and epoch me). Based on our prevous sudy on range-based velocy esmaons, we hen propose a new scheme o esmae he mobly parameers n realme. In conras o exsng mehods ha are based on eher localzaon sysems or feaures of wreless channel, he proposed scheme esmaes he parameers V, Θ, Ψ only from he me-varyng ner-node dsance nformaon whle reanng s relably and accuracy even n nosy envronmens. The performance of he proposed scheme s valdaed n compuer smulaons agans an exsng mehod under dfferen newor sengs. We also apply he proposed scheme o ln avalably esmaon as a more lghwegh way of obanng mobly parameers usng an exsng ool. Prelmnary resuls for varous scenaros show ha, wh he proposed scheme, he ool acheved a comparable performance o when a pror nowledge of nodal mobly s used. Index Terms Mobly, Ln duraon, Ln avalably, Epoch me, GPS-free, MANET I. INTRODUCTION A ypcal moble ad-hoc newor s a collecon of wanderng moble nodes whch form nfrasrucureless newors from emporary wreless lns. The qualy of communcaons n moble ad-hoc newors suffers from frequen opologcal changes caused by he relave movemens beween moble nodes. Accurae and relable approxmaon of nodal mobly (e.g. relave speeds and orenaons beween moble nodes and her average epoch me ) n realme s necessary for predcng he sably of he newor opology for dfferen confguraons/mobly models. For example, nowledge of he relave velocy beween mobles nodes and he average epoch me s useful n predcng ln avalably [2] and provsonng of adapably for roung schemes [3]. Convenonally, he mobly of a moble node,.e. s velocy and epoch me, can be nferred from s changng posons [4] wh he help of a localzaon sysem, such As defned n [], an epoch s a segmen of a moble node s pah, durng whch he node ravels n a consan drecon a a consan speed. The me a node spen on one epoch s defned as he epoch me. as he Global Posonng Sysem (GPS) or a GPS-free posonng sysem [5]. However, he GPS sgnal s normally oo wea o be of any use ndoors. The GPS-free posonng sysems [5] [6] may be used as alernaves o GPS. Bu such localzaon sysems requre he presence of sable anchor nodes, whch may no exs n ad-hoc newors where every node s movng consanly. In addon, hese sysems are oo complex and compuaonally expensve us for racng nodal mobly. Some echnques specalzed n velocy esmaons mae use of characerscs of he wreless channel and/or receved sgnal. For example, Doppler frequency s ulzed n [7] [8] [9] for moble velocy esmaon. The frs momen of he nsananeous frequency of he receved sgnal s used n [] o yeld beer performance. Bu hese echnques have a common problem,.e. hey rely on precse nowledge of he properes of specfc wreless channels or receved sgnal. Ths lms her applcably o only scenaros where he paern of sgnal propagaon s consan. The relave movemens beween nodes cause he nernode dsance o change over me. In a recen sudy [] a Ln Predcon Algorhm (LPA) s presened o predc ln breaage by ulzng he me-varyng ner-node range nformaon, nsead of he properes of wreless channel, for velocy esmaons. However, hs mehod assumes he measured range nformaon o be nose-free [], whch maes no feasble n normal nosy communcaon envronmens. In prevous wor [2], we suded Range-based relave Velocy Esmaons (RVE) for moble ad-hoc newors. Usng barely he nformaon of he ner-node dsance measured n realme by echnques such as Tme-of-Arrval (ToA) [3], he RVE esmaors are less dependen on sgnal characerscs and are more robus n nosy scenaros. In hs paper, we frs defne a rple V, Θ, Ψ o represen mobly parameers (e.g. he ner-node relave speed/orenaon and he epoch me) ha are drecly correlaed wh he opologcal sably,.e. ln avalably [] [2]. Based on our wor on he RVE esmaors, we hen propose a new scheme of mobly esmaons, whch allows moble nodes o derve V, Θ, Ψ n realme. The performance of he proposed scheme s valdaed by compuer smulaons n newors of dfferen properes. We also apply he proposed scheme o a ool for ln avalably esmaon [2] as a more lghwegh way of obanng mobly parameers. Prelmnary resuls show ha,

2 2 wh he proposed scheme, he performance of he ool for newors of dfferen mobly models (e.g. Random WayPon and Random Wal [4]) s comparable o when he nodal mobly s assumed o be nown a pror. The organzaon of hs paper s as follows. In Secon II, we presen he new scheme of mobly esmaons ncludng he mehods for esmang he relave speed and orenaon as well as epoch mes. The smulaon model used for performance evaluaon of he scheme and he resuls are nroduced n Secon III. In Secon IV, we demonsrae how he proposed scheme s appled o ln avalably predcons and hen dscuss he prelmnary resuls. Fnally, we conclude he paper n Secon V. II. THE SCHEME OF RANGE-BASED MOBILITY ESTIMATIONS In hs secon, we nroduce he proposed scheme of mobly esmaons based on he RVE esmaons (e.g. RVEd) presened n [2]. In a moble ad-hoc newor of N nodes, we assume ha each node perodcally measures he dsances o s one-hop neghbors by means of eher receved sgnal srengh (RSSI), me-of-arrval (ToA) or me-dfference-ofarrval (TDoA) measuremens. Whou ang he effec of Non-Lne-of-Sgh (NLOS) condons no accoun, a dsance esmae produced by any of hese mehods a me, ˆd can be smply modeled as: ˆd = d + ɛ () where d s he rue value of he dsance and ɛ s he measuremen nose ha can be modeled as a zero-mean Gaussan random varable wh varance σ 2 ɛ. Every node also repors s collecon of dsance esmaes o all of s one-hop neghbors. Thus, every node nows no only he dsances o s one-hop neghbors bu also hose beween s neghborng nodes whn he one-hop neghborhood. The measuremens and exchanges of dsance nformaon are carred ou a a frequency of /, whch can be fnely uned accordng o he resoluon requremen of he mobly esmaon. Le R be he se of node s one-hop neghbors ha are also one-hop away o each oher. In he proposed scheme, we defne V, Θ, Ψ as a rple of mobly parameers for a node, where V = {ˆv R } and Θ = {ˆθ R } are he ses of esmaed s speeds and orenaons relave o s one-hop neghbors, respecvely. Ψ = {ψ n n =, 2,..., C} s he collecon of C pas epoch me of node. A. Esmang ner-node Relave Speeds and Orenaons As shown n Fg., gven he presence of a leas wo neghbors whn he rado coverage ((, ) R ) ncludng a deparng node (he defnon and speed esmaon of a deparng node s gven n he Appendx),.e. node, a node can derve ˆv and ˆθ n realme usng he RVEd mehod as descrbed below. The relave posons and dsances among he hree nodes, and are changng over me due o her relave movemens. The changes n he dsances among hese nodes also cause her ncluded angles o vary over me. As hese nodes θ Fg.. he changes n he ranges and he orenaons beween node, and caused by her relave movemens durng me slo perodcally exchange wh each oher he dsance nformaon o her one-hop neghbors, node s able o calculae hese me-varyng ncluded angles a every me slo (e.g. ). Le I be he dsance beween node and measured a me. Le K and J be node s dsance o and measured a he same me, respecvely. Accordng o he Cosne Rule, he ncluded angle of K and J, ϕ, s gven by: ϕ = cos K2 + J 2 I 2 2K J (2) Smlarly, gven he dsance esmaes among, and sampled a me (e.g. I, K and J ), he ncluded angle ϕ can be calculaed by: ϕ = cos K2 + J 2 I 2 2K J (3) The change of he angle ϕ o ϕ from me o s he resul of boh node s and s movemens relave o durng. Assumng ha durng and does no cross each oher 2, here could a mos be 4 possble relave movemen paerns among node, and n he me slo (see Fg.2). Le ϕ M be he ncluded angle of K and K and ϕ X be he ncluded angle of J and J. The varous relave movemen paerns demonsraed n Fg.2 resul n 4 dfferen relaonshps beween ϕ, ϕ, ϕ M and ϕ X, whch can be summarzed n Eq.4 as: ϕ X = { ϕ ϕ ϕ M ϕ ϕ ϕ ϕ + ϕ M ϕ < ϕ where ϕ s he ncluded angle of J and K. From Eq.4, we could oban he value of ϕ X for dervng node s velocy relave o durng f ϕ M and ϕ s nown. As node s a deparng node and he relave speed of, ˆv, s nown (see Appendx), we can calculae ϕ M (ϕ M ) by: (4) ϕ M = cos K2 + K 2 M 2 2K K (5) where M (M = ˆv ) s he dsance ha node moved durng relave o. However, s very dffcul o calculae 2 The cases when node and cross each oher s no dscussed, as hey rarely happen f he me slo s shor (e.g. second). Even f he wo nodes do cross each oher on some occasons, hey can be deeced and reaed as excepons.

3 3 (a) (c) (b) (d) Fg. 2. Four possble movemen paerns of node and relave o durng me slo. as s oppose sde connecng a me and a me s no measurable. Whou nowng ϕ, we wll have wo values of ϕ X from Eq.4 wh one of hem beng he rue value. The rue ϕ X can be denfed from wo ses of values of ϕ X. One can produce he second se by usng he same mehod wh anoher velocy-nown node or wh node a me laer 3. Le ϕ A X (ϕa, ϕ a ) and ϕ B X (ϕb, ϕ b ) be he wo ses of values produced by he RVEd mehod wh wo velocynown nodes or wo me slos. We can deermne he rue value of ϕ X by: ϕ X = ϕ A X ϕ B X (6) ϕ Therefore, we can esmae s speed relave o node durng me slo, ˆv by: ˆv = M = (J cosϕ X J ) 2 + (J snϕ X ) 2 and he relave orenaon ˆθ by: B. Esmang Epoch Tme (7) ˆθ = cos J 2 + M 2 J 2 2J M (8) The epoch me ψ n of node (ψ n Ψ ) can be deermned by recordng he me when he node sars a new epoch (or fnshes he las epoch). Whou he help of any localzaon sysems or any speed meers, a node can no deec he changes n s own movng speed or orenaon. Neverheless, provded he presence of 2 or more neghbors mos of he me, a node can sll deec he sar/end pon of an epoch accordng o he fac ha he changes n s movng drecon/speed affec s relave speeds/orenaons o all of s neghbors. The pseudo code for he mplemenaon of he algorhm for esmang epoch me n a node s lsed n Fg.3. 3 Supposng ha node does no change s velocy durng he pas 2 me. Fg. 3. Velocy_Change_Coun = ; for n n Neghbor_Se R Curr_v n = Esmae_Relave_Speed ( n ) ; Curr_ n = Esmae_Movng_Orenaon ( n ) ; f ( Prev_v n!= Curr_v n Prev_ n!= Curr_ n ) Velocy_Change_Coun++; Prev_v n = Curr_v n ; Prev_ n = Curr_ n ; end f end for f ( Velocy_Change_Coun == Number_of_Neghbors_n_R ) Epoch_Tmes [++] = Curren_Tme Las_Epoch_Tme; Las_Epoch_Tme = Curren_Tme ; else Curr_Epoch_Elapsed = Curren_Tme Las_Epoch_Tme; end f Pseudo Code for Esmaons of Epoch Tmes In he mplemenaon, node nalzes a couner wh value a he begnnng of updang ses V and Θ. The value of he couner s ncreased by f a change n he speed or orenaon o a neghbor n se R s deeced. Afer hs round of relave speed and orenaon updaes, curren me s recorded as a sarng pon of a new epoch f he value of he couner equals R,.e. he number of node s onehop neghbors whose veloces have been esmaed usng he RVEd mehod. Therefore, epoch me s obaned from nervals beween he sarng pons of consecuve epochs. Elapsed me of he curren epoch s also recorded. The use of hs nformaon for ln avalably esmaon s gven n Secon IV. III. PERFORMANCE EVALUATION OF THE SCHEME OF MOBILITY ESTIMATIONS To valdae he performance of he proposed scheme of mobly esmaons, we deploy he ns-2 smulaor o smulae varous newor scenaros of dfferen speed lms and mobly models n wo expermens. A. Smulaon Model The smulaed moble ad-hoc newor consss of N = 4 nodes movng around n a square area wh he sze of L L. The rado radus r of a node s fxed a 25m. Usng boh of he mobly modellng ools descrbed n [5] and [6], he smulaons cover a wde range of nodal mobly characerzed by he Random Waypon Model [4] and an enhanced verson of he Random Wal model [6]. For boh of he mobly models, he pause me s ep a o produce connuous movemen. The speed of a moble node s unformly dsrbued over [v mn, v max ], where v mn s fxed a 3.5m/s and v max ranges beween 5m/s and 4m/s. A moble node measures he dsance o s one-hop neghbors and exchanges hs nformaon wh all of s neghborng nodes a nervals of = second. The esmaes of ner-node dsance have measuremen nose ha are modeled by a zero-mean Gaussan dsrbuon wh varance σ 2 ɛ. The

4 4 maxmum value of σ ɛ s se o be 4m, whch s reasonable for off-he-shelf producs [3]. The mobly esmaons are carred ou n a duraon of 9 seconds sarng afer 5 seconds of warm-up perod. In he fgures generaed from he smulaon resuls, each daa pon corresponds o a mean of 3 repeaed expermens wh dfferen random seeds. B. Expermenal Resuls ) Expermen : The frs expermen s o compare he speed esmaes produced by he proposed scheme, he Ln Predcon Algorhm LPA [] and he acual resuls colleced from smulaons. In hs expermen, he mobly model s fxed as Random WayPon 4 and he sde lengh of he newor area L s 8m. The maxmum speed lm v max s ncreased from 5m/s o 4m/s (wh a sep of 5m/s). The ner-node relave speed s esmaed usng he RVEd and he LPA mehods. Gven a fxed 2m of σ ɛ, he predced resuls as well as he acual values measured wh he localzaon module of he smulaor are gven n Fg.4. As shown n Fg. 4, he RVEd esmaor performs much beer han he LPA mehod n erms of predcon accuracy regardless of he speed lms. In order o examne he robusness of he RVEd and he LPA mehods n nosy envronmens, we furher compared he performance of he wo mehods (n erms of he normalzed bas beween her esmaes and he rue values) agans varous nose levels by ncreasng σ ɛ from.5m o 4m. The Normalzed Bas of he speed Esmaes (NBE) s gven by: NBE = E[ˆv] v (9) where v s he mean of he rue values of relave veloces measured from smulaon and E[ˆv] s he mean of he velocy esmaes. NBE ndcaes how close he speed esmaes are o he rue values. The resuls colleced from boh low (v max =m/s) and hgh mobly scenaros (v max =3m/s) are ploed n Fg.5. From Fg.5, we can observe ha he LPA mehod s sensve o boh he levels of nose and nodal mobly. The normalzed bas of s esmaes can be up o 2. Whereas he RVEs mehod demonsraes sgnfcan accuracy by lmng he normalzed bas whn he range of [-.6,.6] n all he scenaros of varous nose devaons or speed lms. 2) Expermen 2: The second expermen s o compare he epoch me esmaed by he proposed scheme wh he acual values measured wh he negraed localzaon module n he smulaons. Boh he Random WayPon and he Random Wal mobly models are nvolved n hs expermen. In hese wo models, moble nodes are bounced bac when hey reach he boundary of he newor area. For he scenaros of Random WayPon mobly, he sde lengh of he newor area s vared from 4m o 8m for an ncreasng lengh of average epochs. The average duraon of acual epochs n he newor and he esmaes provded 4 The resuls obaned for he Random Wal model are no presened here as he RVEd esmaor s ndependen of he mobly model ha moble nodes are followng. Iner Node Relave Velocy (m/s) Acual RVEd LPA[] Maxmum Speed Lm (m/s) Fg. 4. Iner-node Relave Speed Vs. Maxmum Speed Lm (σ ɛ = 2m) Normalzed Bas RVEd vmax=m/s RVEd vmax=3m/s LPA[] vmax=m/s LPA[] vmax=3m/s σ ε (m) Fg. 5. Normalzed Bas of he Range-Based Velocy Esmaor Vs. he Sandard Devaon of Nose by he proposed scheme are gven n Fg.6. As shown n Fg.6, he acual values of average epoch me agree wh her esmaes regardless of he speed lms or he sde lenghs. In he scenaros wh 4m and 6m of sde lenghs he esmaes seems o be slghly overesmaed. Ths may due o ha n smaller areas moble nodes are bounced bac more ofen, whch decreases he accuracy of he proposed mehod. In he Random Wal model, he epochs of a moble s movemen s exponenally dsrbued wh a mean of ψ. Fg.7 gves he acual and esmaed epoch me n scenaros of Random Wal mobly wh varous speed lms and mean epoch me (e.g. 2s, 4s and 6s). We can see from Fg.7 ha he esmaes produced by he proposed scheme mach he acual values agan wh he Random Wal mobly. I should be noed ha boh he measured and he esmaed epoch me are shorer han he specfed mean ψ. Ths s because a moble ofen sars a new epoch even he curren one s no fnshed due o ha has reached he newor boundary and s beng refleced bac. The frequency of such reflecons s ncreasng wh he nodal speed.

5 5 9 8 Measured L=8m Measured L=6m Measured L=4m Esmaed L=8m Esmaed L=6m Esmaed L=4m r T p v Average Epoch Tme (s) n+ (lengh n me) n d + d θ v Maxum Speed Lm (m/s) Fg. 6. Average Epoch Tme Vs. Maxmum Speed Lm, Random WayPon Mobly Fg. 8. n- Epochs Epochs and Ln Duraon Resuled from Node and s movemens Average Epoch Tme (s) Measured ψ=6s Measured ψ=4s Measured ψ=2s Esmaed ψ=6s Esmaed ψ=4s Esmaed ψ=2s Maxum Speed Lm (m/s) Fg. 7. Average Epoch Tme Vs. Maxmum Speed Lm, Random Wal Mobly IV. LINK DURATION AND AVAILABILITY ESTIMATIONS WITH V, Θ, Ψ In hs secon, we apples he proposed mobly esmaon scheme o a ool of ln avalably predcon presened n [2]. The purpose s o demonsrae ha he proposed scheme can be used o provde neworng ools/proocols wh mobly nformaon (e.g. relave speeds and epoch dsrbuons) ha are normally obaned from complex localzaon/movemen racng sysems or assumed o be nown a pror. A. he Predcon-Based Ln Avalably Esmaon Jang e al. [2] proposed he predcon-based ln avalably esmaon, whch nvolves wo consecuve sages: frsly, he esmaon of he proeced ln lfe me (denoed as T p ), whch s he connuous perod from he me when he esmaon s made unl he ln s broen, assumng he relave speed and orenaon are consan durng hs perod. Secondly, as he real ln lfe may no really las o T p f eher of he wo nodes changed her epochs (see Fg.8), he predcon of he probably (denoed as L(T p )) ha he real ln lfe wll be T p or over. For esmang he proeced ln lfe me T p beween wo nodes (e.g. node and n Fg.8), he auhors n [2] recommended he use of velocy nformaon obaned from GPS or a measuremen-based predcon usng 3 samples of he ner-node dsance. For he predcon of L(T p ) beween and, one can use he followng expresson proposed n [2]: L(T p ) = L (T p ) + L 2 (T p, φ) () where L (T p ) represens he case ha neher of he wo nodes changed her epochs whn me T p. Le A (x) = P{ψ x} denoe CDF of node s epoch me. For a ln connecng node and, L (T p ) s gven by: L (T p ) = A (T p )A (T p ) () L 2 (T p, φ) represens he case ha eher of he wo nodes change her veloces a me φ whn T p (φ < T p ). L 2 (T p, φ) can be calculaed as [2]: L 2 (T p, φ) = φ + p(t p φ)a (T p φ)a (T p φ) T p +ε (2) where p=.5 s he smplfed probably ha he wo nodes wll approach each oher afer an epoch change occurs. ε s an esmae of he probably ha here are more han epoch changes snce φ (whn T p ) and he conrbues of hese epoch changes o he ln avalably s posve. The value of ε s suggesed o be measured n realme due o he dffculy of s exac calculaon [2]. B. Esmang Ln Duraons wh V and Θ Wh he mobly parameers V, Θ, Ψ esmaed by he proposed scheme, we can approxmae he proeced ln lfe T p whn 2 me slos, nsead of 3 as suggesed n [2] and []. Ths shorens he amoun of me ha a moble needs o wa unl can have an esmaon of T p, especally when he ner-node dsances are sampled over long me nervals. As shown n Fg.8, d and d are he dsance esmaes beween and sampled a me and +, respecvely. v (v V ) s he relave speed and θ (θ Θ ) he relave orenaon beween and esmaed a +. Accordng o he Cosne Rule, we have he followng equaon: cosˆθ = d2 + (T p + ) 2ˆv 2 r2 2d (T p + )ˆv (3)

6 6 As T p + >, he proeced ln lfe me T p beween node and can be derved from Eq.(3) as: d 2 T p = cos2 ˆθ ˆv 2 (r2 d 2 ) + d cosˆθ (4) ˆv 2 C. Ln Avalably Predcons wh Ψ In [2] and [3], he auhors assumes ha he dsrbuons and he mean lengh of epochs are nown o a moble node. Ths assumpon s unrealsc as he newor confguraons are normally no nown o a moble especally o hose us oned he newor. Wh he proposed scheme of mobly esmaons, a moble can now approxmae he epoch lenghs and dsrbuons n newors of unnown confguraons, whou he help of any movemen racng sysems. If a moble node (e.g. ) has recorded suffcen number (e.g. over 3 [7]) of s pas epoch me, can esmae he CDF of s epochs for Eq. and Eq.2 as follows: A (x) = P{ψ x} = Ψx Ψ (5) where he subse Ψ x = {ψ Ψ ψ > x}. For he calculaon of L 2 (T p ) usng Eq.2, an expeced me φ a whch frs epoch change occurs whn T p (denoed as φ) can be also approxmaed n realme as: φ = Ψ s + Ψs ( ψ Ψ s F(ψ, τ ) + ψ Ψ s F(ψ, τ )) (6) where he subse Ψ s = {ψ Ψ ψ < T p +τ }, τ denoes he elapsed me of curren epoch of 5, and F(ψ, τ) = ψ τ (ψ > τ) or (ψ τ). We denoe he ln avalably esmaon based on he realme esmaon of V, Θ, Ψ as L r (T p, Ψ). We have L r (T p, Ψ) = L (T p, Ψ) + L 2 (T p, Ψ). Noe ha n a newor where he dsrbuon of epochs of a node s homogeneous, Ψ can be approxmaed by Ψ n he above equaons, and vce versa. D. Prelmnary Resuls In a hrd expermen, we es he performance of ln avalably predcons wh mobly parameers (e.g. V, Θ, Ψ ) esmaed by he proposed scheme n newors wh Random Waypon or Random Wal mobly. For each esmaed T p we measured he acual resdual ln lfe me (denoed as T r ). The resulng T r /T p s he acual ln avalably. Smlar o [2], le L mn (T p, Ψ) = L r (T p, Ψ) ε be he conservave ln avalably whou consderng he facors represened by ε. From m pars of (T r /T p, L mn ) of dfferen values colleced from smulaons, we measure ε as: ε = m m ( T r, L mn (T p,, Ψ, )) ( N ) (7) T p, = 5 Denoed as Curr Epoch Elapsed n he pseudo code lsed n Fg.3. Ln Avalably Acual T r /T p Predcon L r (T p, Ψ), ε=.44 Predcon L(T p ), ε= Proeced Ln Lfe Tme T p (s) Fg. 9. Predced Resdual Ln Lfe Tme Vs. Ln Avalably, Random WayPon Mobly L = 8m Ln Avalably Acual T r /T p Predcon L r (T p, Ψ), ε=.36 Predcon L(T p ), ε= Proeced Ln Lfe Tme T p (s) Fg.. Predced Resdual Ln Lfe Tme Vs. Ln Avalably, Random Wal Mobly ψ= 45s Fg.9 and Fg. plo he s averages 6 of he acual ln avalably T r /T p and hose of L r (T p, Ψ), as well as L(T p ) wh arfcally gven parameers [2] for Random WayPon and Random Wal mobly, respecvely. Noe ha he values of L r (T p, Ψ) and L(T p ) ha are bgger han afer addng ε are approxmaed as. As shown n boh Fg.9 and Fg., he performance of he realme predcon L r (T p, Ψ) s comparable o ha of L(T p ). In Fg.9 when T p s beween 5s and 35s, he curve of L r (T p, Ψ) even has smlar flucuang endency wh ha of acual resuls. In some cases when he acual ln avalably drops, as hose observed a T p over 35s n Fg.9 or a T p over 6s n Fg., L r (T p, Ψ) does no mach well wh he realy. Ths s due o he fac ha here are less daa colleced from he smulaed newor when T p s large whle ε s an average of many evens mang L r (T p, Ψ) more accurae for frequenly occurrng evens. A smlar phenomenon and s explanaon can be found n [2]. 6 As L r (T p, Ψ) or L mn (T p, Ψ) are based on epoch nformaon colleced n realme, nsead of a fxed epoch dsrbuon as n [2], her values are flucuang as hose of T r/t p do. s averages of hese daa are ploed o show her endency whle eepng a ceran degree of accuracy.

7 7 V. CONCLUSIONS In he emergng wreless moble ad-hoc newors, he opologcal sably has sgnfcan mpac on he qualy of communcaons. Knowledge of he mobly of mobles, such as her relave speeds and orenaons as well as her epoch me, s mporan as hese parameers are closely correlaed wh he frequency of opologcal reconfguraons n he newor. Convenonal ways of measurng he nodal mobly nvolves complex localzaon sysems such as he cosly GPS or sascal approaches ha rely on precse nowledge of he characerscs of sgnal propagaon. In hs paper, based on our recen sudy on range-based velocy esmaons, we propose a new scheme o esmae n realme he mobly of a moble node (e.g. s relave speeds and orenaons o s neghbors and s pas epoch me) usng only he me-varyng ner-node dsance nformaon. Represened by a rple V, Θ, Ψ, hese mobly parameers are drecly correlaed o he sably of newors. In conras o exsng mehods, he proposed scheme s less dependen on sgnal characerscs and s more robus n nosy envronmens. The performance of he proposed scheme s valdaed by compuer smulaons agans an exsng mehod n scenaros of varous speed lms. As an applcaon example, he proposed scheme s appled o an exsng ool o provde mobly nformaon for predcng ln avalably. Prelmnary resuls from varous newor scenaros show ha, wh he proposed scheme, he ool acheved a comparable performance o when hardcoded parameers are used. ACKNOWLEDGMENT The wor repored here s suppored n par by he BIOPAT- TERN EU Newor of Excellence (EU Conrac 5883). REFERENCES [] A. B. McDonald and T. F. Znab, A mobly-based framewor for adapve cluserng n wreless ad hoc newors, IEEE Journal on Seleced Areas n Communcaons, vol. 7, no. 8, pp , Augus 999. [2] S. Jang, D. He, and J. Rao, A predcon-based ln avalably esmaon for roung mercs n manes, IEEE/ACM Transacon on Neworng, vol. 3, no. 6, pp , December 25. [3] S. Jang, Y. Lu, Y. Jang, and Q. Yn, Provsonng of adapably o varable opologes for roung schemes n manes, IEEE Journal on Seleced Areas n Communcaons, vol. 22, no. 7, pp , Sepember 24. [4] Z. R. Zad, B. L. Mar, and R. K. Thomas, A wo-er represenaon of node mobly n ad hoc newors, n Proc. of IEEE Inernalonal Conference on Sensor and Ad Hoc Communcaons and Newors (SECON), Ocober 24. [5] S. Capun, M. Hamd, and J. Hubaux, GPS-free posonng n moble ad-hoc newors, Cluser Compung, vol. 5, Aprl 22. [6] D. Nculescu and B. Nah, Poson and orenaon n ad hoc newors, Elsever ournal of Ad Hoc Newors, vol. 2, no. 2, pp. 33 5, Aprl 24. [7] A. Sampah and J. M. Holzman, Esmaon of maxmum doppler frequency for handoff decsons, n Proc. of IEEE Vehcular Technology Conference, pp , May 993. [8] R. Narasmhan and D. C. Cox, Esmaon of moble speed and average receved power n wreless sysems usng bes bass mehods, IEEE Transacons on Communcaons, vol. 49, no. 2, pp , December 2. [9] T. G. Basavarau, C. Puamadappa, M. A. Gouam, S. K. Sarar, and B. Ramesh, Doppler locaon algorhm for moble ad hoc newors, n Proc. of Newor and Communcaon Sysems, 26. [] G. Azem, B. Senad, and B. Boashash, Moble un velocy esmaon based on he nsananeous frequency of he receved sgnal, IEEE Transacon on Vehcular Technology, vol. 53, no. 3, pp , [] L. Qn and T. Kunz, Increasng pace delvery rao n DSR by ln predcon, Inernaonal Conference of Hawa Sysem Scence, pp. 3 39, January 23. [2] Z. L, L. Sun, and E. C. Ifeachor, Range-based relave velocy esmaons for newored moble devces, Submed o IEEE Transacons on Vehcular Technology, Augus 26. [3] J. Werb and C. Lanzl, Desgnng a posonng sysem for fndng hngs and people ndoors, IEEE Specrum, vol. 35, no. 9, pp. 7 78, 998. [4] T. Camp, J. Boleng, and V. Daves, A survey of mobly models for ad hoc newor research, Wreless Communcaon & Moble Compung (WCMC), vol. 2, no. 5, pp , 22. [5] C. de Waal and M. Gerharz, Bonnmoon: a mobly scenaro generaon and analyss ool, hp:// [6] J. Y. Le Boudec and M. Vonovc, Perfec smulaon and saonary of a class of mobly models, n Proc. of INFOCOM, Mam, FL, March 25. [7] D. C. Mongomery and G. C. Runger, Appled sascs and probably for engneers (second edon), John Wley, 999. APPENDIX DETERMINING THE RELATIVE SPEED TO A deparng node When a node s passng hrough a neghborng node s rado coverage, s dsance o he neghborng node s frs decreasng before reaches he closes pon and hen ncreasng unl exceeds he node rado radus. We refer a node s neghbors whose dsance s ncreasng as deparng nodes. If hs node does no change s pah when s passng by hs neghbor, s raecory s a sra lne and s perpendcular o he close dsance beween hese wo nodes. As shown n Fg., d e s node s rue dsance o node a he me when reached s rado coverage. ˆde s s esmae. ˆdp, ˆdp and ˆd p+ are he dsance esmaes sampled a consecuve me slos (e.g. p, p and p + ). ˆdp can be used o approxmae he closes dsance beween node s raecory and node f sasfes { ˆd p > ˆd p ˆd p+ > ˆd p }, assumng hs relaonshp s no affeced by measuremen nose. Fg.. e d e p - p p + dp- d p d p+ Esmaon of relave velocy - he RVEs mehod Le M be he movemen of relave o from me e o me p, we have M = v ( p e ). Accordng o he heorem of Pyhagoras, we can oban ˆv, he esmae of v, by: ˆv = M p e = ˆd2 p ˆd 2 e p e (8)