Vision-Enabled Node Localization in Wireless Sensor Networks

Transcription

1 Vision-Enabled Node Localization in Wireless Sensor Networks Huang Lee and Hamid Aghajan Wireless Sensor Networks Lab Department of Electrical Engineering Stanford University, Stanford, CA and Abstract We introduce novel localization techniques for wireless image sensor networks. Based on visual observations between the image sensor nodes or simultaneous observations of a moving object by several nodes, the proposed schemes employ simple image processing functions to obtain angular bearing information between the nodes in a neighborhood and solve for the node positions. We will first propose a technique to localize nodes relative to a coordinate system defined by two reference nodes and propagate the topology information throughout the network. In a different scheme, we consider cases where simultaneous observations from a moving target are used by several image sensors to jointly estimate the coordinates of the nodes as well as those of the target. We will also propose a technique in which the assumption of a simple motion pattern for the target allwos for a collaborative scheme for finding relative location information between the nodes. In a fourth scheme, assistance from a moving beacon knowing its location information is used to localize a network of image sensors. The proposed algorithms are based on in-node processing and local collaboration between the nodes and hence are scalable to large networks. Simulation and experimental results are provided to verify the performance of the proposed techniques. I. INTRODUCTION Wireless sensor networks are an emerging technology for monitoring the physical world [] []. In a sensor network application, large numbers of tiny sensor nodes may be deployed and collaborate to gather data from the environment. Each node is equipped with a sensing modality, such as an image sensor, and has the capability to communicate over wireless channels. Such wireless sensor networks find applications in smart environments, surveillance, environmental monitoring, wildlife observation and tracking, and others. Most applications in sensor networks rely on the knowledge of sensor positions. However, manual location entry results in high deployment cost and is unrealistic in large networks. In addition, since sensor nodes are energy constrained, solutions like GPS are not recommended. Furthermore, in many applications based on the use of image sensors, information about the orientation angle and coverage area of each image sensor is also necessary to perform event and target tracking. Such information cannot be provided by the GPS technology. Node localization therefore is a fundamental problem in sensor networks [3] [] [5] []. Recently, research on image sensor networks has received large interest; however, only limited study of the localization problem has been reported for these networks [7] [8]. In image sensor networks, each node is usually equipped with a low-resolution camera because of the complexity and cost limitations. Furthermore, calibration in multi-camera systems is impractical in large networks [9]. Hence, a localization algorithm that can utilize low-resolution images and requires low computational power and minor sensor calibration is very much desired. Topology discovery in a wireless sensor network is often needed for system-level functions such as routing as well as application specific activities requiring location information. The use of signal strength of the RF signal has been used for estimating distances between the nodes for localization [] []. While the technique is attractive from a device cost perspective, experience has shown that such measurements yield poor distance estimates []. Much improved accuracies can be obtained by time-of-flight measurements when acoustic and RF signals are used together [3] at additional hardware cost. Visual information obtained through the use of image sensors deployed for various applications enables novel approaches to the node localization process. Given a camera model, a node can map its image plane information to angles in the two-dimensional system plane. In the localization methods presented in this paper, nodes share information regarding common observations of either other nodes or of a moving target to solve for their position and orientation information. If assistance is available from a moving beacon agent that defines a relative coordinate system for the network, a decentralized method can be employed in which each node calculates its own location and orientation using visual observations of the beacon. We will also discuss how topology information can propagate throughout the network based on local information obtained within clusters of nodes. The remainder of the paper is organized as follows. In section II we describe the model used for visual observations. Then, in sections III, IV, V, and VI the proposed localization techniques based on four different observation models are presented. Simulation and experimental results are discussed in each corresponding section. Some concluding remarks are included in section VII. In Proc. of Cognitive Systems and Interactive Sensors (COGIS), Paris, March.

2 II. SYSTEM MODEL We will present and discuss four image-based localization methods in this paper. We will refer to these methods based on the types of observations used, which are listed below: ) Node-based method: Observations between network nodes ) Target-based method: Common observations by nodes of a moving target with arbitrary motion 3) Target path model-based: Common observations of a moving target moving with fixed velocity vector ) Beacon-assisted method: Observations by nodes of a moving beacon knowing its coordinates. In all cases the network coordinate system in which the location and orientation of the image sensor nodes are estimated is a two-dimensional space. Table I lists how the sensor image planes are situated with respect to the network coordinate system plane. The system is modeled in the two-dimensional plane, assigning both position and orientation parameters to each image sensor. We use a pinhole camera model (Fig. (a)) described by the equation ϕ =tan ( d D tan ( )) ψ, () where ϕ represents an observed object s angular displacement from the camera s orientation direction, d represents the distance from the center of the image plane in pixels, D represents the image plane dimension in pixels, and ψ represents the field-of-view angle of the image sensor. During network localization and topology discovery steps, nodes utilize visual information to determine their own position with respect to the position of surrounding nodes and the base station. III. METHOD USING OBSERVATIONS BETWEEN NODES A. The Algorithm We consider the two-dimensional localization problem shown in Fig. (b). Choosing one node as the origin of the relative coordinate system, a neighboring node is used to define the unit length. It is assumed that these two reference nodes can observe each other and by doing so they determine their orientations θ and θ with respect to the relative coordinate system. The rationale for making this assumption will be discussed when we describe a protocol for propagation of the topology information in Sec. III-B. The two reference nodes then identify a third unlocalized node which is in the visual ranges of both. Each reference node uses image processing techniques to identify the angular offset of the unlocalized node (e.g. via an RF and LED beaconing scheme), and the angles are labeled φ and φ. The two observed angles are then related by S + λ e jθ e jφ = S + λ e jθ e jφ, () where S and S represent the positions of the two reference nodes and λ and λ represent their respective distances from the unlocalized node. TABLE I RELATIVE SITUATION OF IMAGE PLANES FOR THE PROPOSED LOCALIZATION SCHEMES. Method Node-based Target-based Target path model-based Beacon-based Image Plane Orientation Perpendicular to coordinates plane Perpendicular to coordinates plane Perpendicular to coordinates plane Parallel to coordinates plane By separately considering the real and imaginary parts, the equation can be rewritten as λ cos(θ + φ ) λ cos(θ + φ )=Re{S S }, (3) λ sin(θ + φ ) λ sin(θ + φ )=Im{S S }. () Thus the problem can be written as a system of linear equations with two unknowns: [ ][ ] [ ] cos(θ + φ ) cos(θ + φ ) λ Re{S S = }. sin(θ + φ ) sin(θ + φ ) λ Im{S S } (5) Using the solution for λ, the location of the third node, S, can be written as the sum of vector S and the vector from S to the node, and takes the form S = S + λ e jθ e jφ. () To complete the localization process, the unlocalized node must determine its orientation by observing one of the two reference nodes. As the position of both nodes are known, the orientation can be easily found using basic trigonometry. B. Propagation of Topology Information Topology discovery in a wireless sensor network is often needed for system-level functions such as routing as well as application specific activities requiring interpretation of collected data. Relevance of the location information in many sensor networks applications, possible lack of global identification for the nodes, and the need to employ scalable (geographic) routing protocols all call for employing a network localization technique to obtain the position information for the nodes during network setup. The node-based localization technique begins with nodes close to the base station and continues recursively to more distant nodes until all are localized. The base station initiates the process by requesting a response from all unlocalized neighboring nodes. The first to reply becomes the designated helper node. The distance between the base station and the helper node defines the unit length in the system-wide coordinate system in which the base station s position is the designated origin. Thus, the helper node s (, ) location is established and it proceeds to determine its orientation with respect to the base station. This can be achieved, for example, through the use of an LED mounted on the base station which is illuminated at the designated time. After localization of the first node is complete, the base station and the helper attempt to localize other neighboring

3 ψ φ Φ Θ S Target λ λ λ Φ S Θ Θ Θ d S Reference D S Nodes Φ Φ Φ Θ Φ Θ S Reference Nodes S (a) (b) (c) Fig.. (a) Pinhole camera model. (b) Model for localization using observations between nodes. (c) Model for localization using common observations of a moving target. nodes. A variety of schemes can be used to order the nodes. The simplest method of identifying neighbors is to use the order of response to the base station s initial broadcast. The chosen unlocalized neighbor is asked to illuminate its LED and attempts are made to localize the node using the described method. The base station regulates radio communication during the entire process and assigns unique labels to each node. The first round of localization concludes when all base station neighbors have acted as helper nodes to attempt to localize common neighbors. The second round involves nodes which cannot see the base station but can be observed by two previously localized nodes. The base station first chooses a localized node, identified by its localization order. This node requests a helper and attempts to localize neighboring nodes in a similar fashion. Once a new node is localized in the local coordinate system, a simple coordinate transformation yields the desired global position information. The process continues recursively, each node determining the base station s angular positioning as mapped to its own image plane with the help of two previously-localized nodes. Notifications sent to the base station after the localization of each node allows the base station to regulate the entire process, ensuring that no more than one node illuminates its LED at any time. C. Simulation Results We now simulate the effect of input noise on the propagated position information for the node-based localization scheme. For this simulation, to ensure participation from all the considered nodes, we assume the cameras are omnidirectional, and the positions and orientations of the nodes are set randomly. The effect of observation noise on the node-based localization method is shown in Fig.. Observation noise in degrees is modeled as a uniformly distributed variable and is added to the observation angle towards the observed node. The input noise is added to observations made by all the participating nodes. As Fig. (a) indicates, for localization using observations between the nodes, the resulting errors are comparable with the observation noise for all the simulated networks. The effect of error propagation per number of hops away from the base station is shown more directly in Fig. (b). Sensor orientation error (degrees) Sensor orientation error (degrees) Beacon: Nodes Beacon: 5 Nodes Beacon: 5 Nodes No Beacon: Nodes No Beacon: 5 Nodes No Beacon: 5 Nodes 3 5 Observation noise (degrees) 5 3 Beacon: degrees Beacon: 3 degrees Beacon: degree No Beacon: degrees No Beacon: 3 degrees No Beacon: degree (a) 3 Distance from base station (hops) (b) Fig.. (a) Effect of observation noise on sensor orientation error. (b) Effect of number of hops to base station on sensor orientation error in presence of observation noise. IV. METHOD BASED ON OBSERVATIONS OF A MOVING TARGET A. The Algorithm A moving beacon traverses the network where it is observed by two reference nodes at each stage as well as other unlocalized nodes. It is assumed that all nodes participating at each stage can observe the moving target simultaneously. This can be achieved by a synchronization signal broadcast, which can emanate from the base station or from the beaconing moving

4 agent. This synchronization concept is similar to [], and provides adequate accuracy if the moving beacon stops at the observation instance or moves slowly. After constructing the relative coordinate system, we define the sensor orientations θ, θ for the reference nodes and θ for a third, unlocalized node, as in Fig. (c). More than one unlocalized node can participate in the operation, each of which calculating its position by communicating only with the reference nodes. We assume that the orientations of the two reference nodes, θ and θ, are known. This is easily accomplished if the two nodes can observe each other or when the reference nodes are previously localized by other nodes. This assumption can greatly simplify the model and allows for efficient computation of the localization information. An observation of the target is made at the unlocalized node at the same time instance as the two reference nodes. The observed angle of the nodes at the nth observation is denoted by φ n, φn, and φn and the unknown distance between each sensor and the target is denoted by λ n, λn, and λn. Two independent equations can be obtained from each observation by relating the positions of the unlocalized nodes, the target, and both reference nodes. Thus for N observations we have S = λ n e jθ e jφn λ n e jθ e jφn, n =,...,N (7) S = λ n e jθ e jφn λ n e jθ e jφn +, n =,...,N (8) where S = le jδ is the position of the unlocalized node in polar coordinates, and n represents the nth observation. For N observations, there are a total of 3N ++(λ n, λn, λn, θ, l, δ) unknown parameters and N equations which come from the real and imaginary parts of (7) and (8). Hence, we need at least N 3 observations to solve for all the unknown parameters. When the orientations (θ, θ ) of the reference nodes are known, observations made at the two reference nodes are sufficient to locate the target by triangulation. Therefore, the whole algorithm can be decomposed into two stages. In the first stage, we use the observations from reference nodes to obtain the target coordinates. Given φ n and φn from image planes at the reference nodes, the distances between the target and the reference nodes at the nth observation are derived by λ n sin (φ n = ) sin (φ n φn + θ θ ) (9) λ n = sin (φ n + θ ) sin (φ n φn + θ θ ). () The estimated target coordinates are then given by λ n ej(φn +θ) sin (φ n + θ ) = sin (φ n φn + θ θ ) ej(φn +θ). () After obtaining the target coordinates, we can linearize the equations. Assume that the estimated target positions at time instances n and m are given by p n and p m.wehave le jδ = p n λ n e jθ e jφn = pm λ m e jθ e jφm. () This equation can be rearranged as e jθ (p n p m ) λ n e jφn + λ m e jφm =. (3) 5 Fig. 3. Group 7 Reference node hand-off. 3 Group The unknown variables in the equation are θ, λ n, and λ m. Once we obtain these values, we can find the sensor coordinates le jδ. B. Reference Node Hand-off In a large network, the moving target may travel through different groups where the nodes in the same group can observe the target at the same time. Each group has its own reference nodes; therefore, each group may have its own relative coordinate system. If the reference nodes are different from other sensor nodes and are equipped with global positioning system, the relative coordinates can be transferred to absolute coordinates, and locations in different groups will be readily consistent. However, if we assume that none of the sensor nodes in the network is equipped with global positioning system, each group will only know about its own coordinate system. In order to unify the coordinates among all groups, the adjacent groups must have at least a common member node. For example, group shown in Fig. 3 contains nodes to, and group contains nodes to 7. The target moves from group to group. Since node 3 and know their relative coordinates and orientations in both groups, the coordinates of these two groups can be unified. C. Topology Propagation Protocol Topology propagation scheme for the target-based method is similar to that for the node-based method. The process begins with nodes close to the base station and continues recursively to more distant nodes in the network. However, unlike the node-based method, the propagation direction is determined by the beacon s path instead of node response times to the base station. In this scenario, only neighbors that observe the moving beacon respond to requests. After localization, nodes may not know the positioning of all of their neighbors. To share this information, nodes can broadcast their position information to their neighbors. D. Simulation Results These methods employ local node collaborations to find the relative positioning of the nodes in a neighborhood. We first provide simulated examples of how these methods work, and then will consider the effects of observation noise on the resulting location estimates. Since a propagation protocol is used to link the local position information between neighboring

5 observations observations 5 observations observations observations 5 observations.9 3 observations observations 5 observations.7.8 Target position error (unit length) Sensor position error (unit length) 5 3 Sensor direction error (radians) Fig.. noise (radians) noise (radians) noise (radians) (a) (b) (c) Noise influences on the target position estimation. (a) Error in target position. (b) Error in node position. (c) Error in node orientation. regions of the network, a study of how an error in estimating the location of the object in the image plane can propagate throughout the network is also included for these techniques. ) Noise Effect Analysis: We assume that there is an additive noise in the observed angles resulting from image processing operations at each node. The noise in image sensor k is modeled by the uniform random variable U ( a k,a k ), where a k is varied between and. (radians) for all the nodes in the simulation. The simulation results are shown in Fig.. The minimum number of required observations is three. It can be observed that we can only improve the node location and orientation estimation results by increasing the number of observations. This is because each target position is located only using the corresponding common observations for that position. ) Noise Effects on Propagation of Topology Information: We now simulate the effect of input noise on the propagated position information for the target-based localization scheme. For this simulation, to ensure participation from all the considered nodes, we assume the cameras are omnidirectional, and the positions and orientations of the nodes as well as the target coordinates are set randomly. The effect of observation noise on the target-based localization method is shown in Fig.. Observation noise in degrees is modeled as a uniformly distributed variable and is added to the observation angle towards the target. The input noise is added to observations made by all the participating nodes. Fig. (a) indicates that error is comparable to the observation noise only for networks of 5 or fewer nodes. One way to improve the performance in this case is to increase the number of target observations for each localization effort. The effect of error propagation per number of hops away from the base station is shown more directly in Fig. (b). E. Experimental Results We now set to verify the performance of the proposed targetbased localization algorithm via experiments in an indoor environment. A set of 5 Agilent Technologies ADCM 7 image sensor modules are deployed in an indoor environment. The localization algorithm is programmed in MATLAB and runs on laptop computers. All nodes communicate with each other over wireless channels where IEEE 8.b is adopted (a) 8 8 Fig. 5. (a) The moving target. (b) Experimental localization results using common observations of a moving target. as the underlying protocol. The experiments use API libraries and MATLAB functions developed for controlling image sensors and performing packet transmission over wireless channels [5]. The image sensors have a field-of-view of approximately 5 degrees. We assume that the orientations of the reference nodes are known and perpendicular to the unit line. We apply a background subtraction method to detect the moving target, which in this experiment is a remote-controlled car (Fig. 5 (a)). While the target travels in the network, the reference node at the origin broadcasts synchronization signals regularly. The sensor nodes can therefore acquire images of the target simultaneously. The reference nodes then broadcast the positions of the target on their image planes. When enough observations are made, the localization algorithm is run at each unlocalized node. Experimental results are shown in Fig. 5 (b), and indicate a set of estimates very close to the actual measured quantities. V. METHOD BASED ON TARGET MOTION MODEL A. The Algorithm In this approach, we consider the use of a motion model for the target in the localization algorithm. The technique is applicable to various target tracking applications, but we use the content of a roadway traffic monitoring application to derive the algorithm. The sensor nodes can work in pairs to estimate their relative orientations and positions by making observation of a moving target and exchanging information. This can be done based on the mere assumption that the target (b)

6 Fig.. Sensor Moving target λ λ 3 λ λ w Sensor Network coordinates in method based on fixed velocity for the target. moves with a fixed (but unknown) velocity. For example, in the case of traffic monitoring, the movement of a vehicle moving with fixed speed along a highway lane can be used to localize the network of image sensor nodes. We will use the terms target and vehicle interchangeably in this section to refer to the moving object. Once the sensor pair is localized, it can start to estimate the object s positions and velocities by triangulation. In addition, the sensors can also keep refining the orientation and position estimations while tracking different objects. The image sensors are assumed to be deployed as shown in Fig.. We can choose sensor as the origin, and define a coordinate system as shown in the figure. When the sensors are deployed, we do not know the sensor positions and orientations and the second sensor may not be on the x-axis. To perform relative localization, each node needs to make four observations of the moving vehicle. We may assume that several vehicles pass through the network with different velocities, but each vehicle with a fixed velocity vector v = v e j v during the observations. Given sampling time t, we can use three equations to describe the relationship of the four observations at sensor : λ n ejφn e jθ + v t = λ n+ e jφn+ e jθ, n =,, 3 () where θ is the orientation of the sensor, λ n is the distance from the sensor to the location of the moving object at the nth observation, and φ n is the nth observed angle. By rearranging the equations, we can remove the unknown term v te jθ. Thus the unknown distances can be described by cos φ cosφ cos φ 3 λ cosφ cosφ 3 cos φ λ sin φ sinφ sin φ 3 λ 3 =. sinφ sinφ 3 sin φ λ (5) We can obtain the values λ n which are the normalized nonzero solutions of (5) by singular value decomposition (SVD). The λ n can be considered the normalized values of λ n = c λn, where λ n represents the estimate of λn and c is the normalization factor. We can now show how to obtain the sensors orientations. In the context of traffic monitoring, if the moving vehicle moves parallel to the highway lane, the orientations of the two sensors relative to the lane can be readily obtained using the set of estimated values for λ n k, where k indicates the kth sensor. In a more interesting case, if we assume that the network observes several vehicles each of which generally (but not necessarily exactly) moves parallel to the highway lane, we can model the movement direction v as a random variable with a mean π, which indicates a velocity parallel to the highway lane. The orientation of each sensor can then be estimated by averaging the values obtained from observations made of different vehicles: [ θ k = average ( λn+ tan k sin φ n+ k λ )] n k sin φn k λ n+ k cos φ n+ k λ n k cos φn k () where k indicates the kth sensor. Up to now each sensor would perform its own calculations and can estimate its orientation angle with respect to the direction of the object s motion path. To find the distance between the pair of sensor nodes, the two sensors need to exchange information. In order to define a measure of length, we can use the distance w, which is the normal distance between the two lines passing through the sensor locations and parallel to the direction of the object s motion. Using this measure of distance, we can find the factors c k,k =, that appear in the normalized solutions λ n k = c k λ n k for the two sensors. Once we have these factors, we can derive the positions of the vehicle related to sensor i as p n i = λ n i ejφn i e jb θi, n =,, 3, ; i =,. (7) Although p n can be used to estimate the vehicle s velocity, it requires four observations of each moving vehicle. If the two sensors collaborate, we can conserve sensing energy by taking two observations on each moving vehicle to estimate its velocity by triangulation. If the two sensors are reasonably synchronized, they can take images simultaneously, and we will have p n = pn + s, where s is the polar coordinates of sensor and is unknown. With this information, the second sensor position is derived by ŝ = average [ λn e jφn e j b θ λ n e jφn e j b θ ], (8) in which averaging is performed over all the observations. Based on the above results, each vehicle s position at observation index n is given by sin (φ n p n + θ ) Re (ŝ ) cos (φ n + θ ) Im (ŝ ) = sin (φ n φn + θ θ ) e j(φ n + θ) b (9) and the vehicle s velocity between the two observation instances n and n is obtained by v n = pn p n. () t B. Simulation Results We now discuss the simulation results for the algorithm based on the assumption of a fixed velocity vector for the moving object. The simulation considers a traffic monitoring scenario, in which the velocity vectors of vehicles are assumed

7 Sensor orientation error (degree) 5 5 Number of observed cars (a) Sensor position error (meter) Number of observed cars Fig. 7. Simualtion results for node localization using observations of vehicles moving with fixed velocity vectors. (b) (a) 8 y Field of View x 8 Fig. 9. (a) Simple diagram showing a mobile beacon assisting in localization of a network of image sensors. (b) The coordinates of an image sensor in a plane parallel to the ground (top view). θ (b) Fig. 8. A snapshot of a traffic monitoring simulation in which the orientation of the image sensors and the speed of passing vehicles are estimated. to be of a speed v and direction v. These two numbers are modeled by two uniform random variables U (5, 5) (m/sec) and U (π/, 3π/) (radians), respectively. We also add noise modeled by U (.5,.5) (radians) to the observed angle by each camera towards the vehicles. The sensor orientation and position estimation errors are shown in Fig. 7 (a) and (b), respectively. It can be observed that the estimation errors decrease with increasing number of observed vehicles. We developed a simulation based on this scheme in which first the orientations of a number of image sensor nodes are estimated in an iterative method using observations from the first few vehicles moving through the network. Then, the node orientation estimates are used to track and estimate the speed of new vehicles. Four sensors are deployed on a three-lane road as shown in Fig. 8. In this simulation, we randomly generate cars with different sizes and velocities. Each sensor first estimates its orientation, and than estimates the car positions and velocities. On the left screen, the red short lines and the dot indicate the estimated sensor orientations and the car s position. It can be observed that the red lines are overlapped with the true orientation lines (in blue). The right screen is the speed meter where the blue and pink bars are the true and estimated vehicle speeds, respectively. A demonstration video can be downloaded from VI. BEACON-ASSISTED LOCALIZATION METHOD A. The Algorithm In this section we propose to use a beacon agent that defines a coordinate system and provides a set of observations for the network. This method leads to a decentralized network localization scheme, in which each image sensor uses a few observations of the beacon to estimate its own coordinates, orientation angle, and the height from the -D plane on which the beacon moves. In this model the image sensors are assumed to be deployed on the ceiling and looking down, with their image planes parallel to the ground (Fig. 9 (a)). The image planes could however have an unknown rotation angle θ as shown in Fig. 9 (b). We assume the beacon moves around and makes stops throughout the network such that each image sensor observes it on at least two different spots. At each spot the beacon broadcasts its location relative to an initial point of reference it defines and hence provides the network with a relative coordinate system. In particular, the x and y axes and the unit length of a -D coordinate system are defined by the beacon. When the agent stops and broadcasts its coordinates, the image sensors in its communication range each acquire a frame from their respective field-of-views. The agent may be observed by a few image sensors, each of which then detects the beacon s location on its image plane by simple frame subtraction using an initial background frame. More specifically, at time step i, the robot broadcasts its coordinates denoted by a vector s i. These coordinates can be transferred into the coordinates on the image plane of the image sensor via y i = αr (s i p)+n i, i =,...,N b, () where y i is the vector of observed coordinates on the image plane, the vector p is the unknown coordinates of the sensor, the vector n i is the noise modeled by a Gaussian random variable, α is an unknown[ scaling factor indicating ] cos θ sin θ the height of the camera, and R = is the sin θ cos θ rotation matrix representing the unknown sensor orientation θ. To solve for the unknown variables α, θ, and p, we first rearrange () to cancel the vector p between pairs of observations and obtain y i+ y i = αr (s i+ s i )+(n i+ n i ), i =,...,N b. () We define vectors s i, ỹ i, and ñ i as s i = s i+ s i, i =,...,N b, (3)

8 8 8 Fig.. Results of the beacon-assisted method simulated for a network of image sensors. The path taken by the beacon and the observation points are shown along with the true and estimated coordinates and orientations of the image sensors and each node s field-of-view. ỹ i = y i+ y i, i =,...,N b, () ñ i = n i+ n i, i =,...,N b. (5) Then () can be rewritten in the matrix form as ỹ () s () s () ỹ () s () s () [. =. v. w ỹ Nb () s Nb () s Nb () ỹ Nb () s Nb () s Nb () ] + ñ () where ñ =[ñ (), ñ (),...,ñ N (), ñ N ()] T, and v = α cos θ and w = α sin θ are the unknown variables. We can solve for v and w in () by the standard least-square technique, which leads to a closed-form solution here since only a matrix inversion is needed in our model. After obtaining the estimation results v and ŵ, we can estimate α, θ and R. The sensor coordinates p can then be derived by p = N b si α R y i. (7) Having estimates for image sensor s coordinates, height, and orientation allows us to create a visual coverage map of the environment. After each image sensor has calculated its own location parameters, the nodes can take turn to broadcast their parameters to all nodes within their communication range. B. Simulation Results Fig. shows a simulated network of image sensors deployed randomly with different orientations for their image planes. The path and the locations that the moving agent makes stops to be visually observed by the cameras are also shown. Each image sensor needs to observe the agent on at least two stop points to be able to solve for its own location parameters. The estimates for the coordinates and the orientations of the image sensors are superimposed on the actual positions, and each camera s field-of-view is also drawn based on the estimated orientation and the estimated height of the sensors. VII. CONCLUSIONS This work addressed the localization problem in a novel way, in that only visual observations made by image sensors from a set of other nodes, a moving target, or a beacon agent are used to find solutions for the network node coordinates. The schemes proposed in this paper employ exchange of information between the network nodes or broadcasts from a beacon agent to formulate collaborative or decentralized processing schemes for the image-based localization problem. The information being exchanged is of low data rate nature and the schemes do not require transmission of raw images between the nodes. Application areas in which the image sensor node location and orientation information can be used include target detection and tracking, robot tracking and control, estimation of traffic speed in roadways, and implementing geographic routing schemes for wireless sensor networks. VIII. ACKNOWLEDGMENTS The authors wish to thank the support provided by Agilent Technologies. REFERENCES [] I. F. Akyildiz, W. Su, Y. Sankarasubramaniam, and E. Cayirci, A survey on sensor networks, IEEE Commun. Mag., vol., no. 8, pp., Aug.. [] C.-Y. Chong and S. P. Kumar, Sensor networks: evolution, opportunities, and challenges, Proc. IEEE, vol. 9, pp. 7 5, Aug. 3. [3] J. C. Chen, K. Yao, and R. E. Hudson, Source localization and beamforming, IEEE Signal Processing Mag., vol. 9, no., pp. 3 39, Mar.. [] L. Hu and D. Evans, Localization for mobile sensor networks, in Proc. of the ACM MobiCom, Sept.. [5] A. Galstyan, B. Krishnamachari, K. Lerman, and S. Pattem, Distributed online localization in sensor networks using a moving target, in in Proc. of the Third International Symposium on Information Processing in Sensor Networks, Apr., pp. 7. [] C. Savarese, J. M. Rabaey, and J. Beutel, Locationing in distributed adhoc wireless sensor networks, in Proc. ICASSP,, pp. 37. [7] W. Mantzel, H. Choi, and R. G. Baraniuk, Distributed alternating localization-estimation of camera networks, in Proceedings of the 38th Asilomar Conference on Signals, Systems, and Computers, Nov.. [8] D. Agathangelou, B. P. Lo, J. L. Wang, and G.-Z. Yang, Selfconfiguring video-sensor networks, in Proceedings of the 3rd International Conference on Pervasive Computing, May 5. [9] F. Pedersini, A. Sarti, and S. Tubaro, Multi-camera parameter tracking, in in IEE Proceedings Vision, Image and Signal Processing, vol. 8, Feb., pp [] P. Bergamo and G. Mazzini, Localization in sensor networks with fading and mobility, in Proc. of IEEE PIMRC,, pp [] F. Mondinelli and Z. M. Kovacs-Vajna, Self localizing sensor network architectures, IEEE Transactions on Instrumentation and Measurement, pp , April 3. [] J. Hightower, R. Want, and G. Borriello, Spoton: An indoor 3d location sensing technology based on rf signal strength, University of Washington UW CSE --, Feb.. [3] L. Girod and D. Estrin, Robust range estimation using acoustic and multimodal sensing, in Proc. of IEEE/RSJ Int. Conf. on Intelligent Robots and Systems (IROS),. [] J. Elson, L. Girod, and D. Estrin, Fine-grained network time synchronization using reference broadcasts, in Symp. on Operating Systems Design and Implementation,. [5] Stanford Wireless Sensor Networks Lab: WiSNAP,