Lighweight Target Tracking Using Passive Traces in Sensor Networks

Ligh w eigh t T arget T rac king Using P assiv e T races in Sensor Net w orks ∗ Andrei Marculescu † Sotir is Nikoletseas ‡ Olivi er P ow ell † Jose Ro lim † August 2 0, 202 1 Abstract W e s tudy the imp ortan t problem of trac king moving targets in wireless sensor net- w orks. W e try to o v ercome the limitations of standard state of the art trac king metho ds based on cont inuous location trac king, i.e. the high energy dissipation and co mmunica- tion o v erhead imp osed b y the activ e participation of sensors in th e trac king process and the lo w scalabilit y , esp eciall y in sparse net wo rks. In stead, our appr oac h u ses sensors in a passiv e w a y: th ey just reco rd and jud iciously sp read information ab out observ ed target presence in their v icinity; th is information is then used by t he (p o we rf u l) trac king agen t to lo cate th e target b y just f ollo wing the traces left at sensors. Ou r proto col is greedy , local, distributed, energy efficien t and v ery successful, in th e sense that (as sho wn b y extensiv e sim ulations) the tracking agen t manages to quic kly lo cate and follo w the target; also, we ac hiev e go o d trade-offs b et w een the energy dissipation and latency . 1 In tro duction Recen t adv ances in micro-electromec hanical syste ms (MEMS) and wireless communic ations hav e enabled the dev elopmen t of v ery small, smart, low cost sensing devices ([8, 1]) with sensing, data-pro cess ing a nd wireles s transmission capabilities. They are mean t to b e p erv asiv ely de- plo y ed into forming ad-ho c wireless sensor netw orks that collect information from the a m bien t en vironmen t and mak e it a v ailable to t he user. Some applications imply deploym en t in remote or hostile env ironmen ts (battle- field, t sunami, ear t h- quak e, isolated wild-life island, space explo- ration) to assist in tasks such as target track ing, enem y in tr usion detection, forest fire detection, en vironmen tal or biolo gical monitoring . Some other applications imply deplo ymen t indo ors or in urban or con trolled env ironmen ts. Examples of suc h applications are industrial sup ervising, indo or micro-climate monitoring (e.g. to reduce heating cost by detecting p o or building thermal insulation), smart-home applications, patien t-do ctor health monitoring or blind a nd impaired ∗ This work was partially suppo r ted by the IST/FET/ Global Computing Pro gramme of the E urop ean Union, under contact num b er IST-2 005-1 5964 (AEOLUS). † CUI, Univ er s it y of Genev a, Switzerland. E-mails: { Andr ei.Mar culescu, O livier .Powel l, Jose.R olim } @cui.unige.ch ‡ Computer T echnology Institute and Department of Co mputer E ngineering & Infor matics, Universit y of Patras, Greece. E-mail: nikole@ cti.gr . 1 assisting. Sensor net works imply distributed and collab orativ e dat a -pro cessing, because of the small utilit y of each sensor individually and the sev ere resource constraints, mainly with resp ect to energy but also memory and computation capabilities. 1.1 T rac king Problems and Our Approac h W e wish to solv e the problem of trac king ob jects moving in a domain o ve r a certain p erio d of time i.e. w e w an t the wireless sensor net w ork to b e a ble to detect the p o sition of a ny mo ving ob ject in t he domain at a n y time in the monitoring p erio d. L o cation trac king is t he curren t standard approac h to the tracking problem in sensor net w orks. Lo cation tra c king includes sev eral phases : target detection, distance estimation, p osition ev aluation and tra jectory estimation. The target detection is p erformed individually by sen sor nodes in the netw ork and do es not need an y sync hronizatio n. The distance estimation uses either an empiric la w (e.g. based on signal atten uation estimations) translating the sensing in tensit y in to a real v alued distance, or uses a sp ecial har dware device p erforming this translatio n. The p osition estimation phase is typically addressed with t r ila teration. A t least three no des are p erio dically chos en among the sensors lo cated next to the target. Eac h of these three no des giv es an estimate of its distance t o the target. Finally , another no de (that can b e one of the t hree) p erforms trilateration based on the distance estimates a nd computes the p osition estimate. T he p osition ev a lua tion is t hen sen t to a base-station in order to estimate the tra jectory of the mo ving ob ject. While this metho d can giv e ve ry precise r esults when the netw ork is dense enough (at least 3 no des hav e to b e lo cated next to the target as it mov es), it has sev eral dra wbac ks. F irst, this tec hnique do es not scale to the case of trac king m ultiple ob jects, for instance a gr o up of ob jects mo ving in formatio n, or sev eral individual ob jects. Proto cols designed to compute in a precise manner the p osition of an individual ta rget are not able to cop e with the question “detect an y of the mem b ers of a g iv en gr o up”. Second, the proto col o v erhead is high in terms of communication. Each time a p osition is estimated, three no des are c hosen. Then, among these three no des another no de is c hosen to p erform the p osition ev aluation. This is done through exc hange of proto col messages a nd can b e quite energy consuming. While precision ma y b e needed in some applications, o ther applications need only rough informa t io n on the lo cation area. F or instance, if the target is represen ted b y a group of sev eral ob jects, w e ma y w an t to detect j ust an arbitrar y lo cation within this area. Finally , this tec hnique assumes the existence of a base station with p ow erful computational resources, g enerally supp osed to b e fixed. Although this is sometimes realistic, m any of the trac king applications do not resp ect this h yp othesis. F or instance , soldiers trac king an enem y w ould b e movin g to f o llo w it. Another example is habitat monitoring: a group o f biologists trac king an a n telop e herd also needs to mo v e t ow ar ds the detected herd. I n fact, man y natural trac king applications actually use a mobile sink. In order to cop e with these problems w e broa den the h yp othesis defining the tra cking prob- lem: a) The target can b e an individual ob ject (e.g. a patien t in a hospital) as w ell a s a large group of sev eral ob jects (e.g. an animal herd). b) The t r a c king precision b ecomes a para meter of the problem. W e are primarily concerning ourselv es with fuzzy trac king applicable to la r ge group o f ob jects, where the degree of precision needs not b e high. But our techniq ues can use an y sort of lo cation information att a c hed to sensors to enhance our solution’s qualit y (for instance, if in a hospital sensor no des a re aw are of their lo cation in terms of building wing and ro om n um b er, a nd w e can use this informatio n for the tra c king results). c ) The sink can b e 2 either fixed or mobile and there can be more than one sin k (for instance, tro op ers or a group of biologists). As the fixed sink case is rather w ell studied, we are concerning ourselv es mainly with the mobile sink problem, whic h is useful in applications but also more c hallenging to cop e with. 1.2 Our Con tribution The main idea of our approac h is to av oid actively in v olving sensors in the trac king pro cess. Instead, w e exploit “ t r aces” o f target presence that are an yw ay left around its moving tra jectory . The role of sensors in our proto col is rather passiv e: they just lo cally decrease tra ce in tensities with time (to tak e in t o accoun t the fact that the ta rget was detected but then mo v ed aw ay) and also propagate them appropriately , in order to spread then in a balanced w ay in the net w ork at a lo w energy cost. The activ e role in our track ing approac h is p erformed by t he tra c king agen t, that greedily follows trace gradien ts to lo cate the mo ving target. As sho wn b y the sim ulation findings, o ur approac h ac hiev es significan t improv emen ts ov er w ell kn own metho ds in the state of the ar t . First, our proto col is success ful ( i.e. the ta rget is indeed lo cated), ev en in the case o f m ultiple targets and mobile sinks. Also, our proto col is v ery efficien t, since it reduces energy a lot (b y a v oiding a ctiv e sensor participation) while k eeping latency low (b y spreading trace in tensities in a w ay that “co v ers” the net w ork in a balanced w a y). 1.3 Related W ork and Comparison A standar d ce ntralized approac h to trac king ([3]), is “sensor sp ecific”, in the sense that it uses some smart p ow erful sensors that hav e hig h pro cessing abilities. In particular, this alg o rithm assumes that eac h no de is aw are of its absolute lo cation (e.g. via a GPS) or of a relativ e lo cation. The sensors m ust b e capable of estimating the distance of the target from the sensor readings. The pro cess of tracking a target has three distinct steps: detecting the presence of the ta rget, determining the direction o f motion o f the targ et and alerting appropriate no des in the netw ork. Th us, in their approa c h a v ery large part of the net w ork is a ctiv ely inv olve d in the trackin g pro cess, a fact that may lead to increased energy dissipation. Also, in contrast to our metho d that can sim ultaneously handle m ultiple targets, their proto col can only trac k one ta rget in the net w ork at an y time. O verall, their metho d has sev eral stren gths (reasonable estimation error , precise lo cation of the tr a c k ed source, real time ta r g et track ing, but there ar e w eaknesses as well (inten siv e compu tatio ns, intens iv e radio transmissions). Our metho d is entire ly differen t to the net work arc hitecture design approac h for centralize d placemen t/ distributed trac king (see e.g. the b o o k [6] f or a nice o v erview). According to that approac h, optimal (o r as efficien t as p ossible) sensor deplo ymen t strat egies are prop osed to en- sure maxim um sensing co v erage with minimal nu mber o f sens ors, as w ell as p o w er conserv atio n in sensor net w orks. In one of the cen tralized metho ds ([2]), that fo cuses on deplo ymen t opti- mization, a grid manner discretization o f the space is p erformed. Their metho d tries to find the gridp oint closest to the target, instead of finding the exact coor dinates of the target. In suc h a setting, an optimized placemen t of sen sors will guaran tee tha t ev ery gridp oint in the area is co v ered b y a unique subset of sensors. Another net w ork design approach for track ing is provide d in [5], that tries to av oid an exp ensiv e massiv e deplo ymen t of sensors, taking adv an tag e of p ossible co v erage ov elaps ov er 3 space and time, by in tro ducing a nov el com binatoria l mo del (using set co v ers) that captures such o v erlaps. The authors then use this mo del to design and analyze an efficien t appro ximate metho d for sensor placemen t and op eration, that with high proba bilit y and in p o lynomial exp ected time ac hiev es a Θ(log n ) approximation ra t io to the optimal solution. Clearly , in con trast to our direct approach to t r a c king, suc h netw ork design solutions can pro vide full trac king only when combined with collab orativ e pro cessing metho ds, to pro cess and syn thesize individual target lo cation estimations. As opp osed to centralized pro cessing, in a distributed model sensor net works distribute the computation among sensor no des. Eac h sensor unit acquires lo cal, partial, and relat ively coarse information from its environme nt. The net w ork then collab orativ ely determines a fairly precise estimate based on its co ve rage and multiplicit y of sensing modalities. Sev eral suc h distributed approac hes ha v e b een prop osed. In [4], a cluster-based dis tributed tra cking sc heme is pro vided. The sensor netw ork is logically pa r t itioned into lo cal collab orat ive groups. Eac h group is resp onsible for pro viding information o n a target a nd t rac king it. Sensors that can join tly pr ovide the most accurate information on a targ et (in this case, those that are nearest to the target) form a group. As the ta rget mo v es, the lo cal regio n m ust mov e with it ; hence groups are dynamic with no des dropping out and o thers joining in. It is clear tha t time sync hronization is a ma jor prerequisite for this approac h to work. F urthermore, this alg orithm w orks w ell for merging m ultiple trac ks corresp onding to the same target. Ho w ev er, if t w o ta r gets come very close to eac h other, then the mec hanism described will b e unable to distinguish b et w een t hem. Another nice distributed approac h is the dynamic conv oy tree-based collab oration (DCTC) framew ork that has b een pro p osed in [9]. The con v oy tree includes sens or no des around the detected target, a nd the tree progressiv ely adapts itself to add more no des a nd prune some no des as the t a rget mo ve s. In particular, as the ta rget mo v es, some no des lying upstream of the mov ing path will drift farther a w ay from the target and will be pruned from the con v o y tree. On the other hand, some free no des lying on the pro jected moving path will so o n need to join the collab orativ e tr a c king. As the tree f urt her adapts itself according to the mov emen t of the target, the ro ot will b e to o far a w ay from the target, whic h introduces the need to relo cate a new ro ot and reconfigure the conv oy tree accordingly . If the mov ing target’s trail is kno wn a priori and each no de has kno wledge ab out the global net w ork top o logy , it is p ossible for the trac king no des to agree o n an o ptimal con v oy tree structure; these are at the same time the main w eaknesses of the proto col, since in man y real scenarios suc h assumptions are unrealistic. Finally , a “mobile” agen t appro ac h is follo w ed in [7], i.e. a master ag en t is tra ve ling through the net w ork, a nd tw o sla v e agen ts are assigned the task to participate to the trilateration. As opp osed to our metho d, their approa c h is quite complicated, including sev eral sub-proto cols (e.g. election prot o cols, trilateratio n, fusion and deliv ery of trac king results, maintaining a trac king history). Although by using mobile agents, the sensing, computing and comm unication ov er- heads can b e greatly reduced, their approach is not scalable in randomly scattered netw orks and also for w ell connected irregula r net w orks, since a big amoun t of offline compu tatio n is needed Finally , t he base that receiv es the tracking results is assumed fixed (in a track ing a pplication this can b e a pro blem). The in terested reader is referred to [10 ], the nice b o o k b y F. Zhao and L. Guibas, that ev en presen ts the trac king problem as a “canonical” problem for wireless sensor net works . Also, sev eral trac king approach es are presen ted in [6 ]. 4 A ttr ibutes P ossible v alues TYPE INITIAL or SPREAD . START TIME Time at whic h the trace was initialized. START INTENSIT Y Initial in tensit y of the tra ce. INTENSITY A p ositiv e real num b er s maller than 300. PATH A list of 1 to 3 paren t traces. MAX INTENSITY 300 TARGET ID Used f or the trac king multiple targets. T a ble 1: A ttributes of tr aces 2 Our T racing Handling T rac king Proto col (THTP) 2.1 Proto col Ov erview The intuitiv e idea b ehind o ur track ing proto col is inspired b y a natural mo del: the w ay a tiger trac ks an an t elop e in a Sa v annah. An telop e traces are initially stored into the en vironmen t as the an telop e mo ve s. The intens ity of these initial traces decreases with time. These traces a r e partially spread through the Sa v annah (e.g. due to the wind action) and the in tensit y of a spread trace decreases with the distance from the initial trace. Thus , the only role of the en vironmen t is to store and to rather passiv ely spread tr a ces. It represen ts a passiv e actor of the tra c king pro cess. The activ e actor of the trac king pro cess is the tiger, whic h sense s the traces stored in to the environme nt and tries to trac k t he antelope b y followin g the trace gradien t. The correspondence to our problem is the following: the sensor netw ork is the en vironmen t, the tiger is a tracking agent and the an telop e is the tracking ob ject. Using this natural mo del has the adv antage that as long as no tracking demand is issued, no (or few resources) ar e used into the netw ork, as opp osed to the lo cation t r a c king algorithms where the net work is con tinuously trac king the ob ject in a proa ctiv e manner, hence consuming v aluable energy . A passiv e net w ork is the key to o ur energy o ptimisation. On the other hand, when the trac king is (r eactiv ely) in progress, o nly lo cal computations and very ligh t computation resources are needed in o rder to follo w the t race gradien t. When the trac king is needed, a trac king agen t starts to walk through the net w ork. This agen t follo ws the trace gradient in a greedy manner. The agen t can be either a pure soft w are agen t originated by a mobile sink , or a human pro vided with a sp ecial device commun icating with the net w ork, o r ev en a mobile rob ot in teracting directly with the net w ork. The case of a softw are agent is someho w more complicated, b ecause it has to send the results bac k to the originator of the agen t, t ypically a mobile sink. That is the reason wh y w e fo cus on the case of a softw are agent in the presen t work. 2.2 Detailed Proto col Description 2.2.1 T race storage, spreading and atten uation. Eac h trace can b e represen ted b y the follo wing record: When a sensor no de detects a ta r get, it stores a trace with the giv en TARG ET ID ( o r gro up ID or b oth, depending on t he target b eing an individual o b ject or a group), maxim um in tensit y (in our sim ulations, MAX INTENSITY = 300) and o f t yp e INITIAL . If a trace of the corresponding 5 ID already exists, its in tensity is set to MAX INTENSITY . That means that a sens or con ta ining a trace with MAX INTENSITY is a ssumed by the proto col to b e next to the ta rget. After ha ving stored the trace, it spreads it according to the spreading strategy . W e prop ose a spreading stra t egy whic h aims at co v ering a large area of the net w ork, with a small amoun t o f energy cons umption. W e try t o build a tree of degree 2 across the net work, but in a distributed manner. The no de that detects the target sends a spreading message to t w o of its neighbours. If the receiving no de has no trace of ID sp ecified in the message it stores lo cally the trace a nd forwards the message to tw o of its neigh b o urs, and so on. These tw o neigh b ours are sele cted according to a subtle heuristic that w as designed to span the net w ork efficien tly . Supp ose the no de n 0 needs to spread its trace to t w o neigh b ours n 1 and n 2 . The first neigh b our, n 1 , is selected randomly amo ng the subset V r ep ( n 0 ) of neigh b ours of n 0 farther from a repulsion p oin t than n 0 . While the second no de is also selecte d in V r ep ( n 0 ), it is not selected rando mly but deterministically as b eing the further a w ay fro m the p o in t. A t the end of the pro cess, w e obtain a tree of degree t w o spanning the net w ork. This pro cess is illustrated in figure 2.2.1, where a trace is b eing pro pagated from the cen ter of a net work of 2500 no des randomly and uniformly distributed in a 1000 × 1000 square and the comm unication radius of the no des is 100 meters. The rationale b ehind this heuristic is that the random c hoice for n 1 will help ensuring that the tree do es not leav e an y unco v ered holes inside the g lo bal co v ered region, while the idea of c ho osing n 2 according to the p oint heuristic is to ensure that the tree indeed spans through the whole net w ork. Of course this implies choosing wisely the repulsion p oin t. Also, ev en though some ov erlapping of t he branc hes of the tree is p ossible b ecause of the random nat ure o f the tr ee construction, this unpleasant p ossibilit y is r educed b y in tro ducing an inhibition mec hanism that p ermits t o limit the propagation of traces that w ould induce a branc h o v erlap. As a conseque nce, only a small amoun t of messages is required to span the net w ork since the tree branc hes do not ov erlap. The repulsion p oint In order t o insure that the tree spreads the whole net w ork, traces car r y with them a PATH v ariable. When a tra ce is of type INITIAL , the path is empty . When a tra ce is of type SPREAD the path is not empt y . In fact, only the last tw o hops of a path need to be k ept in the PATH v a riable. When a no de n 0 tries to spread a trace, it sets it’s repulsion point to be its grand-paren t in the tree ro oted whe re the INITIAL trace was created. If the PATH is not o f size tw o but of size 1, it sets the repulsion p o in t t o b e its paren t in the tree. Finally , when a trace is of ty p e INITIAL , t he repulsion p oint is the no de n 0 itself. As a consequence , the no de n 0 tends to c ho o se n 2 in a w a y t ha t preserv es some kind of inertia with resp ect to the t w o previous hops: the trace tends to go far aw a y f rom where it comes. This is balanced b y the fact that the other no de, n 1 , is c hosen randomly . The Inhibition Mec hanism T he INITIAL INTENSITY if a trace of t yp e INITIAL is initia lised to MAX INTENSITY . F urthermore, we ass ume that eac h no de has a clo c k, a nd that whenev er a trace is b eing added to a no de, the INITIAL TIME at whic h the trace has b een star t ed is recorded. Please note that w e do not require t he clo ck s of different no des to b e sync hronized. A t an y giv en time t , the INTENSITY of a trace is de fined to b e max { 0 , INITIAL INTENSITY − ( t − INITIAL TIME ) } . When a no de n “spreads a trace” T to another node n ′ , what actually happ ens is that a new trace T ′ is initialised on the receivin g no de n ′ . The PATH of T ′ is up dated b y app ending n to it. If the spreading o ccurs at time t , the INITIAL TIME of T ′ is set to t , while the MAX INTENSITY of T ′ is set to b e the INTENSIT Y of T at time t minus a “spreading p enalt y”. In our exp eriment, 6 the p enalt y w as set to b e 1. The purpose of the spreading p enalty is to ensure that a tra cking agen t follow ing a gradien t of ev er more inte nse traces will actually end up at a t r a ce of ty p e INITIAL . The spreading inhibition mec ha nism is the following. F irst of all, eviden tly , a trace is only spread if its intens ity is greater than 0. Second, if a no de n is ab out to spread a trace of in tensit y INTENSITY but that there is at least one mem b er of V r ep ( n ), the spreading is inhibited. This is how branc h o v erlapping in the t ree is reduced. Figure 1: The efficien t spanning of a trace starting at the cen ter. F urthermore, eac h no de contin uously executes a (v ery simple and lo cal) in t ensity attenuation pro cess. W e used for our experimen ts a linear atten uation: at eac h step, the trace in tensit y is decremen ted b y o ne. If the tra ce reaches the minim um v alue, it is deleted. The attenu atio n frequency (time b etw een tw o consecutiv e steps of this algorithm) has to b e low er than t he time needed by the targ et to co ver the distance of one hop. If this condition is fulfilled, the assumption that a node with maxim um trace in tensit y is on trac k alwa ys holds. W e note t ha t other attenuation functions (e.g. faster) can b e used in our proto col to b etter fit differen t scenarios and ac hiev e different trade- o ffs. 2.2.2 T racking process. W e designed an agen t -orien ted t rac king. When the sink (e.g. a biologist) wishes to disco v er the target (e.g. an antelope), it initiates a trac king agent. The tracking agen t follo ws the trace gradien t in a greedy manner. This simple pro cess only r equires fo r eac h no de to b e a ware of the in tensities of its neighbours. The decision of the agen t t o go to a no de or to ano t her is guided b y a purely distributed criterion. During the initialisation phase, while the agen t finds itself into 7 a no de without any trace, it w alks randomly to an y of the neigh b o ur s. Although the pro cess is simple a nd distributed, there are t w o p oints w e should b e aw are of. First of all, the trac king applications g enerally need a rep orting pro t o col, with reasonable resp onse delay (la tency). The random walk fr o m the initialisation stage can b e quite inefficien t. That is wh y a go o d co v erage of the spreading tec hnique is vital for the p erforma nce of the algorithm. The b etter is the trace cov erage the higher is the probabilit y of a ra ndom w alk to cross a trace path and then follo w it. On the other hand we can use a biased random w alk in order to decrease the initialisation time. T he sim plest is the following. No des are recording a sp ecial trace for the trac king agen t(s). There is no spreading for these track s, they only atten uate and v anish with time. As opp osed to the an telop e track s, these trac ks are inhibitor y for ag en ts. This can b e view ed as a pa r t ia l self-a v oiding random w alk. The second problem comes from the hill clim bing tec hnique used. As an y o ther greedy tec hnique, o ur trace follo wing is sub ject to lo cal minim um traps. T o fix this problem, a sp ecial t yp e o f inhibitory tra ce is used. When the trac king agent comes to a no de with t he largest lo cal in tensit y , it has to mov e back . Before mov ing bac k, the agen t marks this no de as b eing bad. Because as long as the trace gra dien t do esn’t c hange suc h a maxim um is a cul-de-sac, and t he no de is then a v oided by this agen t and an y other agen ts. Care m ust b e tak en if sev eral types of targets a r e trac k ed. In this case, a distinct “ bad no de” trace should b e used f or eac h t yp e of target. In o r der to optimize the tra cking pro cess, sev eral agen ts can b e sent through the net work. Let us also note that in the classical case of a fixed base statio n and con tin uous monitoring of the target, the trac king agen t can b e initiated by the first no de ha ving detecte d the target. Sending bac k the results is an easy pro cess in this case. If t r a jectory estimation is needed, three agen ts are initia ted instead of one. 2.2.3 Sending bac k the results This part of the proto col b o ils dow n to routing a message to a mobile destination (e.g. biologist). The routing no des are not a w are of the curren t p o sition o f the destination. W e call this t yp e of routing p erv asiv e routing, b ecause its results hav e t o b e av a ilable “ev erywhere in the netw ork”. W e suggest tw o p ossible strategies for solving this problem. The first strategy is to consider the p erv asiv e routing as an inv erted track ing problem. As our proto col scales w ell for sev eral targets, w e can view the trac king data destination a s such an ob ject. The return message tra c ks its destination exactly in the same manner a t r ac king agen t w ould trac k its target. This tec hnique can b e v ery efficien t when the movin g pattern of the destination is ve ry dynamic ( i.e. the destination co v ers a la rge area). The second strategy is a h ybrid b et w een the g eog raphic routing and the tra c king problem. The trac king agen t kno ws its initia l p osition, so when it is sending a return message, it is routed with geogr a phic routing to the initial po sition, and from the initial po sition the des tinatio n is trac k ed. This tec hnique can b e v ery efficien t when the mov ing pattern of the destination is almost stationary (i.e. the destination cov er a v ery small area). 3 Exp e rimen ts F or sim ulation purp o ses, w e tak e the following parameters. The netw ork is comp osed of 300 no des. The comm unicatio n radius is 10 0 meters , the detection radius is 25 meters, the target 8 seman tic sym b ol default v alue n um b er of no des n 300 sensors comm unication radius d trx 100 meters sensing radius d dtx 25 meters target sp eed detection r adius 6 km/h message pro pagation f requency f r eq 1 MSG/second net w ork densit y dens 10 / (100 2 · 3 . 14)* Mag/second T a ble 2: Sim ulation parameters sp eed is 6 km/h. The message transmission frequency is of 1 message p er second ( this determines the sp eed at whic h traces can spread through the netw ork, as w ell as the delay b et w een tw o hops of the trac king a gen t). The dens ity of t he net w ork is the n umber of sensors per square meter. Since the n um b er of sensors is fixed (300), the nodes are spread in a square region w ith side l suc h that 300 /l 2 = density . While the targ et mov es inside the net work, no des detect it. A t any giv en time, the last whic h has detected the targ et is the one with the highest in tensit y t r a ce. Call this node n best . A t the same time, the trac k er agent v isits no des. At a ny g iven time, w e can consider the no de with highest in tensity it has visited so far. Call this no de b bestE s timation . In o ur sim ulations, w e measure the distance b etw een n best and n bestE s timation . W e consider that the trac k er’s b est estimation o f the target’s lo calization is correct, i.e. the target is lo calized by the trac k er, whenev er n best = n bestE s timation . F or sim ulation purp oses, w e let some parameters c hange in the following w a y . The results o f our simulations when sim ulating an execution time of 20 min utes are presen ted below. 3.1 V arying densit y The default v alue v a lue fo r the densit y is 10 / (100 2 · 3 . 14). In the first exp erimen t set, w e test the algorithm with the follow ing densities: 7 . 5 / (10 0 2 · 3 . 14 ), 10 / (100 2 · 3 . 14 ), 20 / (100 2 · 3 . 14 ) and 40 / (100 2 · 3 . 14), Whic h means that the exp ected n um b er o f neighbours in the comm unication graph is a b out 7 . 5 , 10, 2 0 and 40 resp ectiv ely , since w e use the dis c graph mo del f o r our sim ulations (c.f. section 4), whereas eac h p oint of the netw ork can b e roughly expected to be sensing cov ered b y 7 . 5(25 / 100) 2 = 0 . 46875 to 4 0(25 / 100) 2 = 2 . 5 se nsor no des. (I.e. w e c ho ose densit y parameters which alwa ys guara ntee that the net w ork is connected with high probability , ho w ev er the sensing co v erage go es from b eing partial to dense). The results are sho wn on figure 3.1. In figure 2(a), w e see that the track er frequen tly lo calizes the target (eac h time the distance is 0), whateve r the densit y tested except for the lo w er densit y . In figure 2( b) , w e see that the total n um b er of messages p er no de is v ery r easonable for all densities. It is also in ter sting to no t ice that the n um b er of spreading me ssages seems to b e correlated with densit y . The correlatio n is not extremely strong (in reticular ab ov e a p o ssible threshold densit y), b ecause other random factors are quite imp ortant to o (lik e t he motio n pa tern of the target). Ho w ev er, w e do observ e that the n umber of messages diminish es with the densit y . This is due to the wa y the heuristic spanning tree is constructed and is a desirable feature (sp ecifically the w a y one of the no des alw a ys tries to go the further p o ssible from the repulsion p oin t, c.f. section 2.2.1). 9 (a) Distance (b) Mess ages Figure 2: V arying densities 3.2 V arying Sp eed The default v alue v a lue fo r the target speed is 6 km/h. In the second exp erimen t set, w e test the algorithm with the fo llo wing sp eeds: 5, 15, 2 5, 35 km/h. The results are sho wn o n figure 3.2. Again, we notice that for all the tested t a rget sp eeds, the target is often lo calised b y t he trac k er. This is quite nice, since it could hav e b een f ear ed that for the highest target sp eeds the trac k er w ould nev er ha v e lo calized the target. Also, the n um b er of messages is k ept lo w. When the target’s sp eed increases , more detection o ccurs and thus more traces need to b e spread, whic h explains the increased n um b er of messages with increased sp eed from fig ure 3(b) . 3.3 V arying Sensing Radius The default v alue v alue for the sensing radius is 25 m. In the third experimen t set, w e test the algorithm with the following sens ing radii: 10, 40, 7 0 , 100. The results are sho wn on figure 3.3. W e observ e the same kind of fav orable behavior. The t a rget is b eing exactly lo calised prett y often, f o r all sensing radii. F o r increasing sensing radius t here a re more detections by the sensors and thus more messages are b eing generated, but in eve ry case the n um b er of messages is k ept v ery reasonable. 3.4 V arying Message F requency The default v alue v alue for the message f r equency is 1 second, i.e. the trac king agent mov es ev ery second and traces are spread ev ery second. In t he third exp erimen t set, w e test the algorithm with the follo wing message propagation frequ encies: 1, 3, 5, 10, 20. The results are sho wn on figure 3.4. 10 (a) Distance (b) Mess ages Figure 3: V arying sp eed The most imp o rtan t observ atio n is that, not surprisingly , is that for long propagation dela ys (e.g. when a message is only sen t ev ery 20 seconds), it is more difficult to lo calise t he target. This is so b ecause with increasing message propagation delay , the tracking agen t b ecomes slo w er and is thus less efficien t at trac king the target. Still, except fo r the longest propagation delays , the target is b eing lo calised regularly . A v ery nice result is t ha t the nu mber of messages sen t increases o nly slowly with reducing propagation dela ys. That is, if messages are sen t tw ice more often, the total n um b er of messages is fa r from doubling. This is due to t he inhibitio n mec ha nism: when messages a re sen t quic kly , the spreading of a trace is mo r e lik ely to b e inhibited by a previous tr a ce whic h has not ye t v anished with time. On the contrary , when propagation delay a re long, the spreading of a new tra ce is likely to span a larger p ortion of the net work, since previous trace in tensities will b e low due to the time-in tensit y dissipation implied b y our mo del. Therefore, precision can b e traded fo r increased traffic. 4 Sim u lation Implemen t ation D etails W e us ed a ruby implemen tatio n to mak e our sim ulations. In our sim ulations, we use the unit disc graph model for building a high lev el abstratcion of the comm unication graph asso ciated with the sensor netw ork. The target mov emen t is mo delled using the random w aypoint mo del. In this model, the target c ho oses a ra ndom p oin t and mo ves t o it at the chose n sp eed (whic h w as a fixed adjustable parameter in our sim ulations). As a consequenc e, the targ et mo ves along line segmen ts. If the target is mo ving fr om p oin t A to p oin t B , starting at time t 0 and arriving at time t 1 , we used the follow ing mo del for t a rget detection by the sensor no des: if a sensor no de n is at distance d ( AB , n ) of the segmen t AB a nd that d ( AB , n ) is smaller than than the sensing radius d dtx (c.f. table 3), then the no de detects the presence of the ta r g et at t ime t , where t = d ( x,A ) d ( A,B ) ( t 1 − t 0 ), where x is the only po in t of the segmen t AB suc h that d ( x, n ) = d ( AB , n ). 11 (a) Distance (b) Mess ages Figure 4: V arying sensing radius This means that an ev en t can o ccur at times ta king v alue in the real n umbers (or at least their floating p oint r epresen tation in the programming langua g e). W e feel that this fairly complicated sim ulation en vironmen t, when compared to an approac h that w ould discretize time in rounds, is m uc h more precise. A t the cost of complicating the implemen tat io n of the sim ulation platf orm and putting higher computation loads on its execution, we th us used a fairly detailed sim ulation en vironmen t. Although ev ents o ccur at real n umber v alued times, there is only a finite nu mber of even t during each t ime interv al. W e use this to store eve nts on a n sc heduled ev ents stac k ordered by time, and execute the even ts starting at the top of the stac k. F or example, when the target starts moving from p oin t A to B , w e first compute all detections b y sensor no des and put them on the sc heduled ev en ts stack , ordered b y time. W e then “execute” the first detection b y pic king the sc heduled ev en t at the top of the stac k. The top ev en t, ass uming it is an target detection b y a sensor no de, implies initia lizing a tr a ce on the detecting no de. Because this trace will ha v e to b e spread a few seconds la ter (dep ending on the sim ulation parameters), w e create a “spreading” ev ent and insert it on the sche duled ev en t stac k and sort the stac k according to t he sc heduled execution time of the ev en t (a full sorting is no t required, since the stac k is alwa ys k ept sorted, it in f act suffices to intro duce the new ev ent at the prop er place in the stac k). Summarizing, the executing flow o f the sim ulator is (1) Pic k the ev ent at the top of the stac k, (2) Execute the ev ent (e.g initialize a trace) (3) D etermine all future ev en ts implied b y the execution and insert them on the sc heduled ev en ts stack . Start at p oin t (1) ag ain. 5 Conclus ions W e ha v e proposed a lig ht weigh t target trac king pro t o col for wireless sensor netw orks. inspired b y an analogy with the w ay a lion trac ks do wn an a n telop e in the Sav annah by follo wing it’s smell. In our proto col, targets lea ve traces b ehind them. The intens ity of those traces (lik e the o dor of the an t elop e) decreases with time. The sensor netw ork propagat es those traces (lik e the 12 (a) Distance (b) Mess ages Figure 5: V arying Message F r equencies wind propa gates the smell of the an telop e) using an inno v ativ e propagating pro cess aiming at spanning the netw ork with a tree of degree 2 with non o v erlapping branc hes. The proto col w as ev aluate trough extensiv e sim ulations under represen tativ e net w ork op eration regimes. It w as sho wn that the proto col is successful at letting a tracking agent lo calize the targ et regularly , and that the message o v erhead w as ke pt low . Mor e precisely , it w as show n that the pro t o col scales pa rticularly w ell in terms of netw ork densit y since the lo calization pro cess is efficien t and the message ov erhead is low, for all tested densities . W e also sho w that the net w ork is capable of t rac king targets movin g at differen t speeds (from slow to quite fast). W e ha ve also tested differen t sensing co v erage regimes (from no t w ell co vere d to redundantly cov ered), and sho w ed that although traffic increase s with increased sensing range, target lo calisation is ac hiev ed for all regimes with reasonable message o v erhead. Fina lly , an imp o rtan t finding is that diminishing propagation delays (e.g. b y increasing the dut y cycle of sensor no des) do es not augment to o m uc h the message ov erhead b ecause of the tra ce spreading inhibition mec hanism. References [1] I. F. Akyildiz, W. Su, Y. Sank arasubramaniam, and E. Cayirc i. Wireles s s ensor netw orks: a surv ey . Computer Netw orks, 371 , 38:39 3 422, Marc h 2002. [2] K. Chakrabarty , S. S. Iy engar, H. Q i, and E. Cho, G rid cov erage for surv eillance a nd target lo cation in distributed sensor net w orks, IEEE T rans. Comput. 51(12) (2 0 02). [3] R. 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