Simultaneous Localization of Multiple Unknown CSMA-based Wireless Sensor Network Nodes Using a Mobile Robot with a Directional Antenna

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1 Simutaneous Locaization of Mutipe Unknown CSMA-based Wireess Sensor Network Nodes Using a Mobie Robot with a Directiona Antenna Dezhen Song, Chang-Young Kim, and Jingang Yi Abstract We use a singe mobie robot equipped with a directiona antenna to simutaneousy ocaize unknown carrier sensing mutipe access (CSMA)-based wireess sensor network nodes. We assume the robot can ony sense radio transmissions at the physica ayer. The robot does not know network configuration such as size and protoco. We formuate this new ocaization probem and propose a partice fiter-based ocaization approach. We combine a CSMA mode and a directiona antenna mode using mutipe partice fiters. The CSMA mode provides network configuration data whie the directiona antenna mode provides inputs for partice fiters to update. Based on the partice distribution, we propose a robot motion panning agorithm that assists the robot to efficienty traverse the fied to search radio source. The fina ocaization scheme consists of two agorithms: a sensing agorithms that runs in O(n) time for n partices and a motion panning agorithm that runs in O(n) time for radio sources. We have impemented the agorithm, and the resuts show that the agorithms are capabe of ocaizing unknown networked radio sources effectivey and robusty. Index Terms Radio frequency ocaization, wireess sensor network, robot navigation, partice fiter I. INTRODUCTION Consider a scenario that our enemy has depoyed a sensor network to detect troop movements in a desert. In order to neutraize the treat, we need to ocaize sensor network nodes. Since the sensor network is usuay composed of a arge number of miniature wireess sensor nodes with sefconfigurabe ad hoc networking capabiities, ocaization of those nodes manuay is difficut and time-consuming. Imagine that a mobie robot equipped with a highy sensitive directiona radio antenna has been dispatched for the ocaization task. A new research probem arises because the networked configuration and packet information of the sensor network are unknown to the robot. Due to the hardware and energy constraints, most of sensor network nodes empoy carrier sensing mutipe access (CSMA)-based Media Access Contro (MAC) protoco or its variations. This aows us to take advantage knowedge of the CSMA MAC protoco in the ocaization process. However, ocaizing an unknown wireess sensor network is different This work was supported in part by the Nationa Science Foundation under IIS D. Song and C. Kim are with Computer Science and Engineering Department, Texas A&M University, Coege Station, TX 77843, USA (emai: dzsong@cse.tamu.edu) and kcyoung@neo.tamu.edu J. Yi is with Mechanica and Aerospace Engineering Department, Rutgers University, Piscataway, NJ 8854 USA (emai: jgyi@jove.rutgers.edu) Locaized radio sources Undiscovered radio sources Fig.. Schematics of depoying a singe mobie robot to ocaize unknown wireess sensor network nodes. The nodes with dashed circes indicate that they are transmitting. and more difficut than ocaizing a constant radio beacon due to the unknown network size, transient and intermittent transmissions, and signa source anonymity. As iustrated in Fig., the robot can detect spatia distribution of radio signa strengths (RSS) as it traves in the fied of radio sources. Our approach buids on augmented partice fiters and combines a probabiistic sensing mode describing the characteristics of a directiona antenna, and a CSMA mode that can detect network configuration usefu for ocaization purposes. The partice fiters output the posterior probabiity distribution of radio sources. Based on the partice distribution, we deveop a motion panning scheme to generate robot contro commands to search and ocaize radio sources. The fina ocaization scheme consists of two agorithms: a sensing agorithm that runs in O(n) time for n partices and a motion panning agorithm that runs in O(n) time for radio sources. We have impemented the agorithm and the resuts show that the agorithms are capabe of ocaizing unknown networked radio sources effectivey and robusty. The rest of the paper is organized as foows. We begin with reated work in Section II. We present system architecture and hardware in Section III. Then we define the probem in Section IV. In Section V, we introduce our sensing mode. The robot motion panning probem is presented in Section VI. We vaidate our mode and agorithm through simuation experiments in Section VII. Finay, we concude the paper with Section VIII. II. RELATED WORK Locaization of unknown networked radio sources is reated to a variety of research fieds incuding radio frequencybased ocaization, Simutaneous Locaization and Mapping

2 (SLAM), modeing of radio antennas, and modeing of CSMAbased wireess network protocos. The recent deveopment of radio frequency-based ocaization can be viewed as the ocaization of friendy radio sources because researchers either assume an individua radio source that continuousy transmits radio signas (simiar to a ighthouse) [] [5] or assume that the robot/receiver is a part of the network which understands the detaied packet information [6] []. However, such information is not aways avaiabe in an unknown network. In a recent work [], Letchner et a. use a network of wireess access points to ocaize a mobie unit. This can be viewed as a dua version of our probem. They use mutipe static isteners to ocaize a mobie transmitter, whie we try to ocaize mutipe static transmitters using a mobie istener. In another cosey reated work [9], Sichitiu and Ramadurai ocaize sensor network nodes with a mobie beacon. Again, the mobie beacon and the sensor network nodes share the network information. In robotics research, SLAM is defined as the process of mapping the environment and ocaizing robot position at the same time [3] [7]. Athough both SLAM and our research are based on Bayesian methods, SLAM assumes that the environment is static or cose to static. Directy appying SLAM methods to our probem is not appropriate because networked radio sources create a highy dynamic environment where the signa transmission patterns change quicky. Athough recent advances in SLAM aow tracking of moving objects [8] whie performing SLAM task, the environment argey remains static. We reaize that changes of transmission pattern are traceabe because a arge number of RF networks are based on a CSMA MAC ayer protoco. Our work is inspired by partice fiter-based SLAM methods which are capabe of soving generic, non-gaussian, and noninear probems. Since a arge cass of wireess networks use a CSMA-based MAC ayer protoco [9], we assume this as prior knowedge of the network. Utiizing a CSMA mode to enhance sensing is a unique characteristic of our system. An eary work by Mahotra and Krasniewski [3] uses mutipe orthogona antennas to trianguate the position of a radio source. Athough they do not assume that the receiver understands more information other than the physica ayer, their antenna mode does not address the probems when there is ony one mobie antenna. Robot traveing constraint and perspective imitation are not the concern of their work. This paper extends our previous conference paper [] by providing detaied information on how to utiize partice fiters and how robot motion panning is conducted based on the partice fiter outcome, and presenting more experimenta resuts. This work differs from our previous work [] by considering signa retransmissions due to coisions. A. System Architecture III. SYSTEM DESIGN Fig. iustrates the system architecture. Whenever the directiona antenna intercepts a transmission, the RSS reading of the transmission enters the system aong with the current robot/antenna configuration, which refers to the position and the orientation of the antenna. The robot knows its ocaization at any time in our system. The antenna mode provides information to partice fiters regarding the potentia ocation of the radio source. The CSMA mode updates its estimated number of potentia radio sources, each of which corresponds to a partice fiter. There are mutipe parae partice fiters running with each partice fiter corresponding to the spatia distribution of a potentia radio source. Hence the spatia distribution of each radio source is represented by the partice distribution of each partice fiter. The partice fiters are updated based on the antenna mode outputs. After each update of the partice fiters the system determines if a radio sources are detected. If not, the motion generation agorithms pans robot motion to search for more radio sources. Fig.. Antenna mode CSMA mode B. Hardware Sensing Probem Antenna readings Partice fiters System architecture. Stop? Yes No Motion generation As iustrated in Fig. 3, the robot used in the system is custom made in our ab. The robot measures cm 3. The robot has two fronta drive whees and one rear cast whee and uses a typica differentia driving structure. The robot can trave at a maximum speed of 5 cm/second. The radio sources are.4ghz XBee nodes from Maxstream. Each XBee node has a chip antenna and the transmission power of mw. (a) Fig. 3. Hardware of the system. (a) the robot and the directiona antenna. (b) Radio sources The directiona antenna is a HyperGain HG45G paraboic directiona antenna with a maximum gain of 5dBm at.4ghz. It is an off-the-shef product from L-com Goba Connectivity. Using directiona antenna is an important design in acquiring bearing/directiona information of unknown signa sources. The system utiizes both the RSS readings of the (b)

3 antenna and the orientation of the antenna as inputs. Since the antenna is fixed on the robot as iustrated in Fig. 3(a), the antenna orientation is the robot orientation. It is important to point out that the unknown signa source may change the transmission power eves because this is unfriendy ocaization. For such cases, using an omni-directiona antenna cannot provide correct correspondence between distance to the active radio source and RSS. Mutipe antennas with different poarizations that form an antenna array shoud be used to find the direction of the unknown radio sources. In this case, RSS ratios between the antennas are more important that RSSs themseves. In recent work [], Kim and Chong have shown how to find the radio source using two antennas with different poarizations. Since the focus of this paper is not about an eaborated antenna or antenna array mode, we use ony one antenna to provide directiona information by assuming fixed RSSs at transmitters for brevity. However, our method is not imited to this simpe case and can be easiy extended to a robot with an antenna array. IV. PROBLEM DEFINITION We are now ready to formuate our ocaization probem. To formuate the probem and focus on the most reevant issues, we have the foowing assumptions: A. Assumptions ) The robot and radio sources are in a free and open D space. At this stage, we target at outdoor appications. ) The received signa does not contain information about the signa source. In fact, the robot usuay cannot decode the packet at the MAC eve due to the unknown network. 3) Athough the robot cannot decode the packets, it sti can sense the coision of radio transmissions by monitoring RSS and phase changes. 4) Network traffic is ight and each transmission is short. These are the typica characteristics of a ow power sensor network. Actuay, this assumption makes ocaization more difficut. If the network traffic is heavy and the transmission duration is engthy, the robot can ocaize the active radio source by simpy riding the wave. In fact, most ow power sensor nodes have a packet ength magnitude of ms. 5) The directiona antenna on the robot has high sensitivity and can isten to a traffic. This is the advantage that the robot has. 6) The radiation pattern of the radio sources is circuar. This assumption simpifies the modeing process. Later we wi show that the proposed method aso works for non-circuar radiation patterns. 7) The radio sources are stationary. At this stage, we do not consider mobie nodes. 8) A radio sources transmit at the same power eve. This assumption is not necessariy true for the most genera case. For cases with different unknown power eves, we can use a pair of orthogona antennas to extract directiona information of the radio source regardess of the variation of transmission power eve. Hence the proposed method can be easiy generaized to cases with different transmission power eves. 9) The robot can accuratey execute its motion command. Our focus here is not to study the effect of imprecise motion. Assumptions ) and 3) differentiate ocaizing an unknown wireess sensor network node from ocaizing a friendy continuous radio beacon. Due to the transient and intermittent transmission pattern aong with signa source anonymity, the robot cannot simpy trianguate the signa source. Since ony one robot is considered, the singe perspective makes it more difficut than cases with mutipe robots or receivers. B. Nomencature k: a discrete time index variabe. i: a partice index variabe, i I = {,...,n}, where n is the tota number of partices and I is the partice index set. n n max is not a fixed number, where n max is maximum number of partices. m: an index variabe for radio sources, m M = {,...,}, where is the tota number of radio sources and M is the radio source index set. x k m: the ocation of the m-th radio source at time k. The variabe is a random state variabe because we do not know the actua ocation. X k : the joint state for a radio sources at time k, X k = {x k,..., xk }. s k m : a set of partices for the m-th radio source, sk m = {wm,i k, xk m,i i I}, where each partice has an assigned reative weight wm,i k and a potentia radio source ocation x k m,i = [xk m,i,yk m,i ]T R. S k : the joint partice set at time k, S k = {s k,..., sk }. Z k : the RSS reading at time k, Z k [,55] N. Z k = {Z,Z,...,Z k }: the set of a RSS vaues at time k. u k : a robot/antenna position and orientation at time k, u k = [x k,y k,θ k ] T R S, where S = ( π,π] is the orientation ange set. C. Probem Definition Based on the assumptions, we define our ocaization probem as foows. Probem (Locaization Probem): Given a received RF signa strengths Z k, compute the number of radio sources,, and estimate the position of each radio source X k. Since we appy a partice fiter approach to address the probem, propery designed partice fiters shoud represent the spacia distribution of X k. Hence the overa probem can be broken down into the foowing two subprobems. Probem (Sensing Probem): Given a received RF signa strengths Z k, compute the number of radio sources,, and the conditiona probabiity of sensor ocations p(x k Z k ). Probem 3 (Motion Panning Probem): Given p(x k Z k ), pan u k+ for next period. 3

4 V. SENSING PROBLEM The sensing probem is to computep(x k Z k ). As iustrated in Fig., there are three major components in the sensing probem: antenna mode, CSMA modeing, and partice fiters. A. Antenna Mode From antenna theory, bearing and distance are the two most important variabes that determine the radiation pattern distribution in the D space for a given antenna. Reca that u k = [x k,y k,θ k ] T is the robot antenna configuration when the radio transmission is sensed at time k and x k m = [x m,y m ] T is the m-th radio source position. Define d k m and φk m as the distance and the bearing from robot to the m-th radio source position, respectivey, d k m = (x k x m ) +(y k y m ), φ k m = atan(x k x m,y k y m ) θ k. Aso from antenna theory [3], when the m-th radio source is transmitting, the expected RSS Z k of the directiona antenna is approximated as, E(Z k ) = {og C βog (d k m )+og s(φk m )}, () where C is a constant depending on radio transmission power and (d k m) β is the signa decay function. The directivity of the antenna is captured by the term s(φ k m ), which describes the radiation pattern of the antenna. We obtain C =.77 and the decay factor β =.65 from antenna caibration. Our β vaue conforms to the widey-accepted notion that the decay factor is between and 4 [3]. The units of E(Z k ) are dbm. From antenna theory and the resuts from antenna caibration, we perform curve-fitting to obtain the radiation pattern function, { s(φ k cos m) = (4φ k m), if φ k m cos (8 () ), otherwise. Eqs. () and () describe the expected RSS given that the radio transmission is from m-th radio source. However, the sensed RSS is not a constant but a random variabe due to the uncertainties in radio transmissions. From the antenna caibration, we know thatz k conforms to the truncated norma distribution with a density function of ) σ g(z) = f(z E(Zk σ ) F( zmax E(Zk ) σ ) F( zmin E(Zk ) σ ), (3) where the vaue of σ is 3.3 by the antenna caibration, z is the sensed RSS, f( ) is the probabiity density function (PDF) of a norma distribution with zero mean and unit variance, F( ) is the cumuative distribution function (CDF) of f( ), and z min and z max are the minimum and the maximum RSS that the antenna can sense, respectivey. Let G(z) = z z min g(z)dz (4) be the CDF of the truncated norma distribution. SinceZ k can ony take integer vaues, we obtain the antenna mode as foows, P(Z k = z x k m ) = G(z +.5) G(z.5). (5) B. CSMA Mode One critica part of the sensing probem is to estimate how many radio sources are in the network. Here we utiize the CSMA mode to estimate the potentia number of sources. Fig. 4. Successfu transmission period Packet T= a Busy period B Ide period I CSMA: transmission period anaysis. t Unsuccessfu transmission period Y a Packet Packet 3 T= a Busy period B Normaized time Fig. 4 iustrates the timing of a CSMA protoco. The time axis is aternativey divided into busy and ide periods. In the figure, a denotes the propagation deay, t is the starting time of a busy period, and t + Y is the time that the ast packet arrives between t and t+a, < Y a. B, I, and U are the durations of the busy period, the ide period, and the time during a cyce that the channe is used without conficts, respectivey. Each busy period is aso termed as a transmission period, which is further cassified as a successfu transmission period or an unsuccessfu transmission period. Without oss of generaity, we set packet ength T = in Fig. 4. A packet takes additiona time a to propagate, and a. Therefore, a successfu transmission takes time (+a). a is mainy determined by how fast the circuitry can recognize the transmission. If a radio source transmits packet at time t, then the duration between t and t+a is a vunerabe period because other radio sources cannot sense its transmission and may initiate another transmission (Packet 3), which woud ead to a coision. If each radio source transmits according to an independent Poisson process with the same packet generation rate λ, the aggregated transmission rate S is given by S = λ. Due to retransmission, the actua packet arriva rate G, caed offered traffic rate, is arger than S. By the aggregation of severa Poisson signa sources, S is aso a Poisson process. G can aso be approximated with a Poisson process. The offered traffic rate G is the sum of the source traffic rate S and the retransmission traffic rate R, thus, G = S +R. Define the busy coision probabiity P pc as the conditiona probabiity of a coision given the channe is busy. Then P pc = e ag (6) by the approximation that G is Poisson. Since the robot can isten to a traffic, G and P pc can be observed over time. Hence the unknown networked parameter a can be estimated using (6). Hence, we treat a as known in the rest of the paper. Upon each coision, there are two retransmissions schedued R = GP pc. Therefore, G = S +GP pc. (7) With G and P pc observed, we can obtain S using (7). If we know λ, then we can obtain = S/λ. However, this woud not work for the most genera cases because ) λ is usuay unknown and ) λ might not be the same across different radio sources. To hande the probem, we can envision that each 4

5 radio source can be further divided into mutipe coocated sub radio sources with each sub radio source shares the same transmission rate λ << λ min, where λ min is the smaest transmission rate of the origina radio sources. Hence we can sti appy the condition that each radio source has the same transmission rate of λ. The number wi be much bigger than the actua. However, this is not a concern because we can aways combine coocated sources after they are ocaized. For this reason, we assume each radio source shares the same transmission rate in the rest of the paper. C. Partice Fiters We now know that there are radio sources. For each radio source m, we use a partice fiter to track its spacia distribution p(x k m Zk ). This is an instance of the Bayes fitering probem which can be computed using a two-phase recursive approach: Prediction Phase: p(x k m Zk ) = p(x k m xk m, uk )p(x k m Zk )dx k m. Since positions of radio sources are static, state x k m is independent of the deterministic robot motion u k. Therefore, the prediction phase in (8) is trivia, Update Phase: (8) p(x k m Z k ) = p(x k m Z k ). (9) p(x k m Zk ) = ηp(z k x k m )p(xk m Zk ) where η is a normaizing factor. = ηp(z k x k m)p(x k m Z k ) () The partice fiter represents p(x k m Z k ) by a set of partices s k m. Reca that s k m = {wm,i k, xk m,i i =,...,n} where n is the tota number of partices, wm,i k is the assigned weight for the partice, and x k m,i = [xk m,i,yk m,i ]T R is the potentia radio source ocation. The update phase in the partice fiters is performed in two stages: importance samping and resamping. ) Importance Samping: The importance samping weights each of the sampes w k m,i = wk m,i p(zk x k m,i ) () by the sensor mode p(z k x k m,i ) that can be computed using (5). Each partice in s k m is randomy drawn from sk m proportiona to the updated weight wm,i k. The importance samping step reduces the number of ow weighted partices and increases the number of high weighted partices. ) Resamping: After a few iterations of the importance samping, the number of survived partices shrinks and utimatey becomes zero, which causes the degeneracy probem. The probem can be soved by adding more partices into s k m by resamping when the effective number of partices is beow an effective threshod number. Let n eff denote the effective number, which is computed based on weights, n eff = n i= (wk m,i ) () according to [4]. We define n t as the threshod that is determined by the experiments. If n eff < n t, we perform resamping. Resamping aso introduces the probem of oss of diversity among partices. This is because sampes are drawn from a discrete partice set rather than from a continuous distribution. In order to sove this probem, it is necessary to modify the resamping process by introducing Gaussian random noise into the resamped partices. Let N( μ r,σ r ) denote the two dimensiona Gaussian distribution where μ r and Σ r are the mean vector and the covariance matrix, respectivey, where μ r = x k m,i and Σ r is a tunabe diagona matrix determined by experiments. Therefore, partices in s k m are obtained by resamping from {w k m,i,n( xk m,i,σ r) i =,...,n}. Another probem of resamping is that there coud be no partice in vicinity of the correct state. This is known as the partice deprivation probem. To address the probem, we add a 5% randomy generated partices into s k m with an initia weight of /n each. D. Data Association For radio sources, there are partice fiters. It is important to determine which partice fiter to be updated once a RSS is perceived. This is a data association probem. We use maximum a posteriori probabiity (MAP) estimation to address the probem. Let ˆp(x k m Z k ) be the posterior probabiity estimation of the m-th partice set, n i= wk ˆp(x k m Zk m,i ) = p(zk x k m,i ) n j= i= wk j,i p(z k x k j,i ). (3) Let m be the index for the seected radio source, which is chosen by maximizing ˆp(x k m Z k ), m = argmax m Mˆp(xk m Zk ). (4) E. Stopping Time and Locaization Criterion With the MAP approach, we can seectivey update an individua partice fiter. Fig. 5 iustrates the resuts of the partice distribution with respect to the actua radio source ocation over time k. It is cear that the majority of partices converge to the vicinity of the radio source ocation. As a Monte Caro method, it is necessary to determine a stopping time that detects convergency trend of the partices as a function of each individua partice set s k m. Since partices are ocated in the D space, the spatia distribution of partices in s k m are can be described by a mean vector μ m and a covariance matrix Σ m. Hence we have, n μ k m = wm,i k xk m,i, (5) i= n i= Σ m = wk m,i [( xk m,i μk m )( xk m,i μk m )T ] n. (6) i= (wk m,i ) Define λ m and V m as the maximum eigenvaue and the corresponding eigenvector of Σ m, respectivey. According to principe component anaysis (PCA), we know that the 5

6 (a) k = (b) k = 3 (c) k = 8 (d) k = 5 Agorithm : Partice Fiter-based Sensing Agorithm input : Z k output: s k m begin Update G Estimate S and according to (7) Compute ˆp(x k m Z k ) using (3) Find m using (4) Compute wm k,i, i I, using () O(n) Normaize wm k,i, i I n c = ; s k m = end O(n) O(n) for i = to n do O(n) Draw i from s k m with probabiity wk m,i if {wm k,i, xk m,i } / sk m then s k m = sk m {wk m c,i, xk m } c,i n c = n c + n = n c Compute n eff using () if n eff < n t then for i = to 95%n max do O(n) Draw partice i from {wm k,i,n( xk m,i,σ r) i =,...,n} Add the partice to s k m n c = n c + Add 5%n max random partices to s k m n = n max Compute λ m using PCA if λ m ε then radio source m is ocaized. O(n) (e) k = 48 (f) k = Fig. 5. Sampe resuts of partice distribution with respect to actua radio source ocation over time k. There are four radio sources represented by back dots. The smaer coor dots indicate each individua partice. Four different coors represent resuts of four partice fiters. The robot performs random wak in this exampe. maximum variance of the partice distribution in the D space can be measured by its argest eigenvaue λ m. As the partice set converges to the vicinity of the radio source, λ m shoud decrease. Define ε as the threshod for λ m. We define that the m-th radio source is ocated and we can stop the corresponding partice fiter computation if F. Agorithm λ m ε. (7) The computation of the sensing mode can be summarized in Agorithm. It is cear that each iteration of Partice Fiterbased Sensing Agorithm (PFSA) runs in O(n) time for n partices. VI. MOTION PLANNING PROBLEM As iustrated in Fig. 5, the partice sets track the spatia distribution of radio sources. However, the resuts shown in Fig. 5 are based on a robot performing a random wak, which is not necessariy the best choice for robot motion panning. We need to deveop an effective robot motion panner to ensure s k m converges. We propose a two step approach. First, the robot chooses a targeted radio source m t to investigate. Then the robot determines its configuration that best ensures the convergence of s k m t. A. Choosing a Target The process of choosing a target argey depends on how we each partice set converges and the traveing distance of the robot. For m-th partice set, reca that a smaer λ m means radio source m is coser to be ocaized. Hence, the robot can ocaize the target without spending too much time. On the other hand, we woud ike the robot to trave the minimum distance to save energy. We define the foowing function to describe the tradeoff between the convergence status and the traveing distance, ω m = αλ m +( α)d μm, (8) where α is the weighting factor between convergence and distance, and d μm is the distance between the robot s 6

7 d d s d Fig. 6. Sampe robot configuration for a partice set. The gray eipsoid region represents partice distribution. The dashed red ine represents the directivity of the antenna (i.e. function s( ) in ()). current position and the estimated position of m-th radio source μ k m. A radio source with a sma ω m woud be a desirabe target for the robot. However, if we use this metric, the robot might stick with a prominent target and fai to expore other targets. To avoid this, we define a history weighting function, { if τ mc > τ max h(m c ) = (9) otherwise where m c is the current target, τ mc is the eapsed time that the robot has been with the current target, and τ max is the time threshod for the maximum investigation duration. At each step, τ mc is updated as foows, { τ mc + if m c has not change τ mc = () otherwise. Therefore, the robot is forced to investigate other targets once τ max is reached. τ max can be obtained using the transmission rate λ and a probabiity threshod p m. The probabiity that the targeted radio source does not transmit any signa duringτ max is e λτmax. If we want the probabiity to be ess than p m, we can choose m τ max = λ n( p m). () Combining convergence, traveing distance, and history, we choose the targeted radio source m t that minimizes the foowing m t = arg min h(m c)ω m. () m M B. Robot Configuration Once a target radio source m is identified, we need to identify a corresponding robot configuration that can acceerate the convergence of the partice set s k m. As iustrated in Fig. 6, an intuitive choice is to aign the most sensitive reception region of the directiona antenna with the partice set. In this way, the robot does not need to trave too cose to the radio source, the robot can reduce its trave distance, and be energy efficient. To ensure a good aignment between the antenna and the partice eipsoid describing regions with a high concentration of partices, it is necessary to aign the zero bearing ange of the antenna with the ong axis of the partice eipsoid. Reca that V m represents the eigenvector that corresponds to the maximum eigenvaue of matrix Σ m. Let v m,x and v m,y be the x- and y- components of V m, respectivey. We know that the ong axis of the eipsoid is determined by V m according to PCA. Hence, the orientation of the robot/antenna is, θ = atan(v m,x,v m,y ). (3) The remaining parameter is the distance between the robot and the center of the partices. As iustrated in Fig. 6, the distance is defined as d s. If d s is obtained, the robot position [x, y] is obtained straightforwardy, x = μ m,x d s cos(θ), y = μ m,y d s sin(θ). (4) where μ m,x and μ m,y represent the x- and y- components of μ k m, respectivey. μ k m is the center the partice set s k m according to (5). Therefore, we need to compute d s. From PCA, we know that the eipsoid in Fig. 6 is the approximation of the partice distribution. As iustrated in Fig. 6, we define d and d as the interception points of the outer and inner boundaries of the main reception area with the zero bearing axis, respectivey. The boundary functions are described in (). We woud ike to fit the ong axis of the eipsoid in between d and d, λ m = d d. (5) Since λ m is known, this aows us to find the expected signa strength using (), E(Z) = [og C βog λ m +βog ( og cos 8 β )]. (6) The expected signa strength can hep us to compute d and d and obtain d s = d + λ m. (7) Therefore, the robot configuration[x,y,θ] T is found. As more transmission are intercepted, the partices converge and λ m decreases. Consequenty, the robot adaptivey moves cose to the radio source to increase ocaization accuracy. Hence we name this approach as Greedy Adaptive Motion Panning (). C. Agorithm We summarize our agorithm in Agorithm. It is cear that the agorithm runs in O(n) time for n partices and radio sources. VII. EXPERIMENTS We have impemented the agorithms and the simuation patform using Microsoft Visua C++.NET 5 with OpenGL on a PC Desktop with an Inte.3GHz Core Duo CPU and GB RAM. The machine runs Microsoft Windows XP. We are not abe to run the actua physica experiment due to the range imitation of our oca position system for the robot. GPS is not an option due to insufficient accuracy. To vaidate the resuts in high fideity, we design a hardware-in-the-oop simuation where RSS readings are 7

8 Agorithm : Agorithm input : s k m output : [x,y,θ] T begin for m = to do Compute μ m and Σ m using (5) and (6) Perform PCA on Σ m and obtain λ m end Update τ mc using () Compute τ max using () Compute ω m using (8) Find m t according to () Compute θ using (3) Compute E(Z) using (6) Compute d and d using () Compute d s using (7) Compute [x, y, θ] using (4) end O() O(n) y (meters) Robot trajectory Actua ocations of radio sources Estimated ocations of radio sources x (meters) (a) Trajectory obtain from actua data by fixing the robot whie moving the radio source around. Therefore, the simuation is driven by actua radiation patterns (except the case where we ater the radiation pattern for testing in non-circuar transmission patterns). We ca the data gathering processing as antenna caibration where we pace the radio source at 38 different orientations and distances with respect to the antenna. In each setting, we coect readings to measure the randomness of the reception. Those data are used to drive the simuation process. For the unknown network, each radio source generates radio transmission signas according to an independenty and identicay distributed Poisson process with a rate of. packets per second. The packet ength is. seconds. The propagation deay a is 3% of the packet ength. The radio sources are ocated in a square fied with a side ength of 3 meters. For the partice fiter, we set the maximum number of partices for each radio source n max = 3, the threshod for the effective number of partices n t =, and( the covariance ) matrix for adding the Gaussian noise Σ r = 5. For 5 ocaization stopping condition, we set ε =.5. For the motion panning, we set robot speed at.5 m/sec., weighting factor α =.9, and the probabiity threshod for transmission p m =.. Those parameters are set based on the best performance derived from mutipe trias in experiments. A. A Sampe Case Fig. 7 iustrates the robot trajectory and the convergence trends for a sampe case with six radio sources. The initia position of the robot is the center of the fied. As we can see from Fig. 7(a), the robot graduay approaches each radio source. At the end of experiments, the estimated ocations of radio sources are conforma to the actua ocations of the radio sources. The ocaization process is successfu. Fig. 7(b) iustrates how λ m for each radio source converges over time. λm Radio source Radio source Radio source 3 Radio source 4 Radio source 5 Radio source Time (sec.) (b) Convergence Fig. 7. The resuting robot trajectory and the convergence trends for a sampe case with six radio sources. A λ m s successfuy converge. What is worth noting is the reationship between the robot position and the convergence trend. If we take a cose ook at radio source, we can find that it converges ast because it is the ast radio source the robot approaches. We consider the convergence speed satisfying because each radio source ony transmits at a mean rate of packet per seconds. For the sampe case, the PFSA runs in 3 miiseconds and agorithm runs in.6 miiseconds. This is not surprising because they are inear agorithms. Since computation speed is not a concern here, we skip speed tests in the rest of experiments. B. Comparison with Two Heuristic Approaches We aso compare our to two heuristic approaches, namey, a random wak and a fixed-route patro. The fixedroute patro traverses the fied using a pre-defined route. Since the robot has no knowedge of the ocaization of radio sources, the fixed route is usuay the tour that traverse the entire 8

9 Time (sec.) 5 5 proposed method. More specificay, we focus on the most restrictive assumptions, which are Poisson arriva processes, circe radiation patterns, and eveny distributed traffic among radio sources. 4 (a) Time comparison Time (sec.) Mean square error (meters) (b) Locaization accuracy comparison Fig. 8. Locaization performance comparison among the, a random wak, and a fixed route patro. region for coverage purpose. We increase the tota radio source number from to 8 to observe the performance of each method. For each tria, we randomy generate radio source ocations and test a three methods. We repeat trias for each case and compute the average time required for ocaizing a radio sources and the mean square error between estimated radio source ocations and the actua source ocations. Comparison resuts are shown in Fig. 8. A agorithms are abe to ocaize radio sources. As iustrated Fig. 8(a), is consistenty faster than the two counterparts. As for the ocaization accuracy, Fig. 8(b) shows that a methods are simiar in ocaization accuracy. The accuracy decreases as number of radio sources increases. We conjecture that this is due to the RSS resoution of the antenna and the randomness in RSS make a methods unabe to distinguish the radio sources that are cose to each other. Hence, the data association step in Section V-D might associate the radio source with a wrong partice fiter. Hence the accuracy of ocaization decreases. C. Robustness Tests Our ocaization method is derived under a set of restrictive assumptions. In this part, we are interested in testing the system performance when reaxing some assumptions. In other words, we woud ike to know the robustness of the Fig. 9. time. Mean square error (meters) (a) Time comparison (b) Locaization accuracy comparison Locaization performance comparison under Gaussian inter-arriva The first test of robustness is to reax the assumption that the packets are generated according to Poisson processes. In reaity, if a particuar routing mechanism is used, then the packet generation processes coud deviate significanty from Poisson processes. We simuate those traffic patterns by using Gaussian inter-arriva time. The Gaussian distribution has a mean of. second and a variance of. Other parameters are the same as the sampe case test in Fig. 7. Fig. 9(a) shows that our method is sti consistenty faster than its two counterparts. For ocaization accuracy, our method is sighty better. This indicates that our method is not imited to the Poisson arriva process. The second test of robustness concerns ocaization performance when the radiation pattern of the radio sources are non-circuar. Due to different surface conditions, materias, and environment infuence, the radiation pattern of a wireess sensor node is not necessariy round. To characterize this probem, we use an eipse radiation pattern to approximate the rea radiation pattern. To quantify the deviation from the circuar radiation pattern, we define axis ratio r a as the ratio 9

10 4 4 8 Time (sec.) 6 4 Time (sec.) Axis ratio r a (a) Time comparison (a) Time comparison Mean square error (meters) Mean square error (meters) Axis ratio r a (b) Locaization accuracy comparison Fig.. Locaization performance comparison for a case with 6 radio sources and non circuar radiation pattern. Fig.. (b) Locaization accuracy comparison Locaization performance comparison with uneven transmission rate. between the minor axis and the major axis of the eipse. If r a =, the radiation pattern is perfecty circuar. We vary the ratio from. to. We use a 6-radio source setup in the experiment and random trias for each axis ratio. To avoid the possibiity of faiure to converge, we set the maximum running time of the simuation as 3 sec. Fig. iustrates the resuts. Fig. (a) shows that a three methods are very sow when r a is sma and become fast when the axis ratio increases. When r a is sma, the eipse is ong and narrow. Hence the antenna mode cannot provide a reasonaby accurate prediction of the ocation of the radio sources. Our method become faster than the other two when r a >.4. Simiar resuts in ocaization accuracy are shown in Fig. (b). These resuts suggest that our method is more robust to non-circuar radiation pattern than the other two, which is desirabe. It is worth noting an eipse mode may not be abe to characterize the strong irreguarity of radiation patterns in some cases. For exampe, a bended antenna can cause its radiation pattern to be muti-moda instead of unimoda. In these cases, the agorithm has an decreased ocaization or may find some phantom sources. However, the resuts are sti usabe because they sti significanty reduce the search space of the unknown radio sources. The third test of the robustness focuses on the scenario where the traffic might be uneveny distributed in a sensor network. Due to the popuarity of custering techniques in routing, certain nodes (i.e., custer heads/routers) have much higher traffic than other nodes in the network. In this test, we set one radio source to transmit at.5 packets per second and other radio sources transmit at. packets per second. The rest of setup is the same as those in Fig. 8. Fig. iustrates the time and accuracy comparison resuts. Once again, our method is better than the other counterparts when the transmission rate is uneven. A of the tests show that our ocaization method is more robust to the vioation of assumptions than the fixed route patro and the random wak. VIII. CONCLUSIONS AND FUTURE WORK We reported how to use a singe mobie robot equipped with a directiona antenna to ocaize unknown networked radio sources. We proposed a partice fiter-based ocaization approach that combines a CSMA mode and a directiona antenna mode. We aso proposed a motion panning agorithm based on the partice distribution. The sensing agorithm runs in O(n) time for n partices and the motion panning agorithm runs in O(n) time for radio sources and n partices. We have impemented the agorithm and tested it using a rea datadriven simuation patform. The resuts show that the agorithm

11 is capabe of ocaizing unknown networked radio sources. The experiment resuts shown that the proposed ocaization method is faster, more accurate, and more robust than the two other heuristic methods. We are currenty testing our agorithm using physica experiments. We are aso interested in designing a mutiperobot ocaization scheme and wi consider an approach to ocaize moving radio sources. Another important extension is to dea with scenarios where the radio source may change its transmission power during the communication. ACKNOWLEDGMENTS REFERENCES [] P. Bah and V. N. Padmanabhan, RADAR: An in-buiding RF-based user ocation and tracking system, in INFOCOM,, pp [] J. Letchner, D. Fox, and A. LaMarce, Large-scae ocaization from wireess signa strength, in Proc. of the Nationa Conference on Artificia Inteigence (AAAI-5), 5. [3] N. Mahotra, M. Krasniewski, C. Yang, S. Bagchi, and W. Chappe, Location estimation in ad hoc networks with directiona antennas, in ICDCS 5: Proceedings of the 5th IEEE Internationa Conference on Distributed Computing Systems (ICDCS 5). Washington, DC, USA: IEEE Computer Society, 5, pp [4] M. Youssef, A. Agrawaa, and U. Shankar, Wan ocation determination via custering and probabiity distributions, in IEEE PerCom 3, 3, p. 43. [5] G. Mao, B. Fidan, and B. Anderson, Wireess sensor network ocaization techniques, Computer Networks, vo. 5, no. 7, pp , 7. [6] N. Buusu, J. Heidemann, and D. Estrin, Gps-ess ow cost outdoor ocaization for very sma devices, IEEE Persona Communications Magazine, vo. 7, no. 5, pp. 8 34, October. [7] X. Ji and H. Zha, Sensor positioning in wireess ad-hoc sensor networks using mutidimensiona scaing, in INFOCOM 4, 4. [8] K. Lorincz and M. Wesh, Motetrack: A robust, decentraized approach to rf-based ocation tracking, in Proceedings of the Internationa Workshop on Location and Context-Awareness (LoCA 5) at Pervasive 5, 5. [9] M. Sichitiu and V. Ramadurai, Locaization of wireess sensor networks with a mobie beacon, in first IEEE Internationa conference on Mobie Ad hoc and Sensor Systems, 4, pp [] N. Buusu, V. Bychkovskiy, D. Estrin, and J. Heidemann, Scaabe, ad hoc depoyabe rf-based ocaization, in Grace Hopper Ceebration of Women in Computing Conference, Vancouver, British Coumbia, Canada. University of Caifornia at Los Angees, October. [Onine]. Avaiabe: buusu/papers/buusua.htm [] D. Koutsonikoas, S. Das, and Y. Hu, Path panning of mobie andmarks for ocaization in wireess sensor networks, Computer Comunications, vo. 3, pp , 7. [] T. Sit, Z. Liu, M. A. Jr., and W. Seah, Muti-robot mobiity enhanced hop-count based ocaization in ad hoc networks, Robotics and Autonomos Systems, vo. 55, pp. 44 5, 7. [3] S. Thrun, Robotic mapping: A survey, in Exporing Artificia Inteigence in the New Mienium, G. Lakemeyer and B. Nebe, Eds. Morgan Kaufmann,. [4] M. W. M. G. Dissanayake, P. Newman, S. Cark, H. F. Durrant- Whyte, and M. Csorba, A soution to the simutaneous ocaization and map buiding (sam) probem, IEEE Transactions on Robotics and Automation, vo. 7, no. 3, pp. 9 4,. [5] D. Hähne, W. Burgard, D. Fox, K. Fishkin, and M. Phiipose, Mapping and ocaization with RFID technoogy, in Proc. of the IEEE Internationa Conference on Robotics and Automation (ICRA), 4. [6] K. P. Murphy, Bayesian map earning in dynamic environments, in NIPS, 999, pp. 5. [7] D. Fox, S. Thrun, F. Deaert, and W. Burgard, Partice fiters for mobie robot ocaization, in Sequentia Monte Caro Methods in Practice, A. Doucet, N. de Freitas, and N. Gordon, Eds. New York: Springer Verag,. [8] C. Wang, C. Thorpe, S. Thrun, M. Hebert, and H. Durrant-Whyte, Simutaneous ocaization, mapping and moving object tracking, The Internationa Journa of Robotics Research, vo. 6, no. 9, pp , September 7. [9] J. Warand and P. Varaiya, High-Performance Communication Networks, nd Edition. Morgan Kaufmann Press,. [] D. Song, J. Yi, and Z. Goodwin, Locaization of unknown networked radio sources using a mobie robot with a directiona antenna, in the American Contro Conference (ACC), New York City, USA, Juy, 7, pp [] D. Song, C. Kim, and J. Yi, Monte caro simutaneous ocaization of mutipe unknown transient radio sources using a mobie robot with a directiona antenna, in IEEE Internationa Conference on Robotics and Automation (ICRA), Kobe, Japan, May 9. [] M. Kim and N. Y. Chong, Direction sensing rfid reader for mobie robot navigation, IEEE Transactions on Automation Science and Engineering, vo. 6, no., pp , January 9. [3] R. S. Eiott, Antenna Theory and Design. The IEEE Press, 3. [4] A. Doucet and A. M. Johansen, A tutoria on partice fitering and smoothing: Fifteen years ater, Tech. Rep., 8.