Pervasive and Mobile Computing 5 (2009) 165–181

Contents lists available at ScienceDirect

Pervasive and Mobile Computing

journal homepage: www.elsevier.com/locate/pmc

Target localization in camera wireless networksRyan Farrell a, Roberto Garcia c, Dennis Lucarelli b, Andreas Terzis c,∗, I-Jeng Wang ba Computer Science Department, University of Maryland, College Park, United Statesb Applied Physics Lab, Johns Hopkins University, United Statesc Computer Science Department, Johns Hopkins University, United States

a r t i c l e i n f o

Article history:Received 16 October 2007Received in revised form 1 March 2008Accepted 7 April 2008Available online 22 April 2008

Keywords:Multi-modal sensor networksCamera Sensor NetworksTarget detection and localization

a b s t r a c t

Target localization is an application of wireless sensor networks with wide applicability inhomeland security scenarios including surveillance and asset protection. In this paper wepresent a novel sensor network that localizes with the help of two modalities: camerasand non-imaging sensors. A set of two cameras is initially used to localize the motesof a wireless sensor network. Motes subsequently collaborate to estimate the locationof a target using their non-imaging sensors. Our results show that the combination ofimaging and non-imagingmodalities successfully achieves the dual goal of self- and target-localization. Specifically, we found through simulation and experimental validation thatcameras can localize motes deployed in a 100 m × 100 m area with a few cm error.Moreover, a network of motes equippedwithmagnetometers can, once localized, estimatethe location of magnetic targets within a few cm.

© 2008 Elsevier B.V. All rights reserved.

1. Introduction

The prevailing notion of a sensor network is a homogeneous collection of communicating devices capable of sensingits environment. This architecture offers several benefits including simplicity and robustness to individual node failures.While a number of heterogeneous designs have also been proposed that incorporate multiple classes of devices they, byand large, are intended to address data storage and dissemination objectives. An emerging concept is a sensor network thatexploits heterogeneity in sensing, especially by using cameras (e.g. [1]), in which the weaknesses of one sensing modalityare overcome by the strengths of another.The use of networked cameras is gaining momentum for key applications such as surveillance, scientific monitoring,

location-aware computing and responsive environments. This is primarily because it is far easier for users to glean contextand detail from imagery than other sensing modalities. Moreover, many applications from homeland security, to birdwatching require an image to perform the sensing task. At the same time, the drawbacks of ad-hoc vision networks arewell known: cameras consume considerable power and bandwidth and despite some recent hardware innovations (e.g. [2])these limitations are still largely unresolved. Thus, cameras should be engaged only when absolutely necessary.This paper presents a complete system that integrates vision networkswith a non-imagingmote network for the purpose

of target localization and tracking. Specifically, the system initially uses two Pan-Tilt-Zoom (PTZ) cameras to localize thenetwork’s motes. Once localized, motes employ non-imaging sensors (e.g. magnetometers), to detect the existence andestimate the location of targets traversing the deployment area. Themotes subsequently task the cameras to capture imagesof those targets. We argue that the combined system offers performance and efficiencies that cannot be achieved by a singlemodality working in isolation. Our solution is also self contained in the sense that all operational aspects of the system are

∗ Corresponding author. Tel.: +1 4105165847.E-mail address: terzis@jhu.edu (A. Terzis).

1574-1192/$ – see front matter© 2008 Elsevier B.V. All rights reserved.doi:10.1016/j.pmcj.2008.04.004

166 R. Farrell et al. / Pervasive and Mobile Computing 5 (2009) 165–181

handled by the two sensing modalities and no additional elements are needed to perform target detection, acquisition andverification.The successful integration of the camera and mote networks requires that the sensor field be located within the field of

view of an ad-hoc deployment of cameras. One solution would be to localize the nodes through other means and solve forthe transformation between the two coordinate systems. Alternatively, we solve for all location variables (mote locationsand camera orientations/locations) simultaneously in one efficient algorithm. This approach establishes a common frameof reference, such that the location of objects detected by a camera can be described in the spatial terms of the networkand vice-versa. The use of PTZ cameras allows the entire sensor network space to be mapped into the camera’s pan-tiltparameterization. Arguably the greatest advantage of the system we propose is the ability to rapidly deploy a wirelesssensor network in an ad-hoc fashion without regard to camera field-of-view. Moreover, the mote network serves to limitthe use of the camera systemwhich is used only during the initial phase of the network’s deployment. In addition to simplecuing, target classification by the mote network is the primary means of preserving power. Only high probability targets areengaged by the camera network.The rest of the paper is structured as follows. Section 2 reviews previouswork in the areas of self- and target-localization.

In Section 3 we present an outline of the proposed framework. Section 4 describes how the network can self-localize withthe help of two PTZ cameras, while Section 5 presents the target localization algorithms. Both aspects of the localizationproblem are evaluated in Section 6, which presents results from simulations and experiments with mote hardware. Finally,we close in Section 7 with a summary.

2. Related work

The work related to our system falls under two general categories: work in the area of target detection and localizationand work in the area of self-localization, especially using imaging sensors.Target detection is one of the compelling applications that drove much of the initial research in sensor networks. The

pioneeringwork by Stankovic et al. [3,4] and Arora et al. [5] among others proved that sensor networks can effectively detecttargets over large geographic areas. While those networks used magnetometers, to the best of our knowledge, they wereused only for target detection and not localization. On the other hand,we use information collected from themagnetometersto estimate the distance and the heading of ferrous targets as they move over the sensor field. Oh et al. have recently usedmagnetometers to localize targets in a multiple-target tracking algorithm [6]. That work assumed that mote locations areknown in advance. Then, the target’s location is estimated as the centroid of the locations of all the motes that detectedthe target, normalized by the signal strength measured by each of the motes. This approach has low accuracy because itassumes that the strength of the magnetic field is only a function of the distance between the target and the magnetometer,an assumption that is not valid as we show in Section 5.1.More recent work by Taylor et al. also proposed a method to localize the nodes in a sensor network while concurrently

tracking the location of multiple targets [7]. There are two main difference between that work and our approach. First,Taylor et al. localize the network using one or more co-operating mobile targets that periodically emit radio and ultrasoundsignals. This level of mobility enables the system to collect a large number of ranging estimates that can be used to localizethe nodes. On the other hand, our proposal is range-free since it requires only angular information from a small number ofstatic cameras. Second, we detect the location of uncooperative targets through the changes they generate on the ambientmagnetic field.Several innovative approaches have been suggested for the problem of self localization. Various technologies such as

ultrasound ranging, acoustic time of flight, radio signal strength and interferometry, are used to acquire good pairwisedistance estimates, often incorporating the acquired range measurements into a planar graph (see [8] and surveys [9,10]).Poduri et al. however showed that when nodes are placed in three dimensions, the number of neighbors of an average nodegrows dramatically [11]. This observation suggests the need to investigatemethodswhich do not rely on pairwise distances.To address the limitations of peer-to-peer localization techniques, a number of proposals have investigated the use of

cameras to localize a sensor network. Funiak et al. recently proposed a distributed camera localization algorithm to retrievethe locations and poses of ad-hoc placed cameras in a sensor network by tracking a moving object [12]. Unlike this previouswork, we use cameras to estimate the locations of static nodes in the sensor field in addition to their own locations. Alongthe same lines, Rahimi et al. used a network of cameras to track the locations of moving targets while at the same timecalibrating the camera network [13]. In our case cameras are used only during the initial phase to estimate mote locations.Furthermore, instead of tracking the trajectory of the target using the cameras, we use non-imaging sensors to estimatethe location of magnetic targets. The proposed localization algorithm is versatile enough to run at a central location or in adistributed fashion on the actual motes.In the Computer Vision community, the problem of simultaneously localizing both camera and objects or scenery is

frequently referred to as Structure from Motion. Representative work includes Hartley’s eight-point algorithm [14,15], andDellaert et al.’s [16] approach which avoids explicit correspondence. These approaches are generally applied to fixed field-of-view cameras, either a stereo pair of static cameras or a camera inmotion. As our approach utilizes pan-tilt-zoom camerasto provide a full field of view, we can handle arbitrary, ad-hoc deployments, evenwhen the sensors are scattered on all sidesof the camera.

R. Farrell et al. / Pervasive and Mobile Computing 5 (2009) 165–181 167

Lymberopoulos et al. recently considered the use of epipolar geometry to perform localization, using LEDs to assist thevisual detection of sensors [17]. We also use LEDs connected to the motes in our network to indicate their presence tothe associated cameras. However, unlike the solution proposed by Lymberopoulos et al. we do not require any distanceinformation from the cameras to estimate the mote locations. Even though the only information available in our case arethe angular locations of the motes relative to each camera, our solution has comparable localization error.Probably the work most closely related to ours is the Spotlight system [18]. This system employs an asymmetric

architecture in which motes do not require any additional hardware for localization while a single Spotlight device usesa steerable laser light source to illuminate the deployedmotes. The primary difference between our approach and that worklies in our focus on truly ad-hoc deployment. We assume that the cameras will have unknown location and orientationwhereas the Spotlight system relies on accurate knowledge of both camera position and orientation. Furthermore, individualmotes in Spotlight must know when the laser light source is supposed to illuminate them, a design that requires timesynchronization.

3. Outline

The proposed system consists of a network of cameras connected to non-imaging sensors, specifically magnetometers,that are used to detect the presence and estimate the location of ferrous targets. However, target localization requires thatmote locations are known in advance. In our system the task of mote localization is undertaken by a number of Pan-Tilt-Zoom (PTZ) cameras that scan the deployment area to detect the locations of the network’smotes. In this sectionwe providean overview of the proposed system and outline its components.

• Pre-deployment phase: The intrinsic parameters of the cameras and the magnetometers are calibrated prior todeployment. We present a procedure for calibrating the magnetometers in Section 5.4.• Initialization phase: The network is localized using two cameras and a base station performing non-linear least squaresoptimization. At the end of this phase the cameras learn their location and orientation and themotes know their location.Section 4 describes the proposed method.• Target localization: At the end of the initialization phase the system is operational and able to detect the presenceand estimate the location of targets traveling through the deployment area. Section 5 describes the target localizationalgorithm we developed for the sensing modality we use.

We made a conscious decision to use the cameras only during the initialization phase and after the network’s moteshave localized a target, to reduce the energy required to power the cameras. This decision wasmotivated by the high energyconsumption of PTZ cameras and the need to rapidly deploy this system using only battery power. The same approach ofexploiting waking up the cameras on demand was suggested by Kulkarni et al. in [1].As part of our previouswork,we investigated the benefits of combiningmodalities for target localization [19]. Specifically,

we showed that feedback from the cameras can be used to calibrate the motes’ magnetometers and thereby improvelocalization accuracy.

4. Optical self-localization

Wedescribe the underlying theoretical basis of our self-localization approach and discuss potential numerical techniquesfor solving the system of multivariate nonlinear equations resulting from our analysis.

4.1. Deriving the nonlinear formulation

Let us consider a planar network of wireless sensor nodes, N = {p1, p2, . . . , pn}, where pi = (pxi, pyi, 0) denotes thelocation of node i. For the cameras, we must describe both position and orientation. With each camera j, we thereforeassociate a position cj =

(cxj, cyj, czj

)and a 3 degree-of-freedom (DOF) rotation2j =

(θxj, θyj, θzj

). As we focus on ad-hoc

deployment, the values for pi, cj, and 2j are all unknown. We remove the restriction of having all the nodes on the sameplane in Section 4.2 and explore the benefits of having multiple cameras in Section 4.3, but for ease of exposition we firstpresent the solution with two cameras and nodes on the same plane.Without any notion of geodetic location or scale, the best that we can hope to recover is a local and relative coordinate

frame. Rather than pick some arbitrary scale, we have chosen to normalize the coordinate frame based on the distancebetween the two cameras. The camera locations are thus c1 = (0, 0, cz1) and c2 = (1, 0, cz2). The camera elevationsremain unknown as do the orientation parameters. Fig. 1 depicts the normalized coordinate frame (note that the nodes arenot constrained to lie within the unit square).The only values we are able tomeasure are the angular location of a given node relative to each camera.We parameterize

the camera’s pan-tilt space with coordinates (α, β), in radians. Camera j observes node i at location(αij, βij

), indicating that

camera jwould need to pan by αij and tilt by βij in order to aim directly at node i.We now derive a relationship between these measurements and the unknown values we wish to determine. In

considering the relationship between camera j and node i, for convenience we define the offset vector vij = pi − cj. As

168 R. Farrell et al. / Pervasive and Mobile Computing 5 (2009) 165–181

Fig. 1. Normalized Coordinate Frame. Illustrates the sensor networkN = {p1, p2, . . . , pn}, pi = (pxi, pyi, 0), with two active cameras, respectively locatedat c1 and c2 . Geodetic locations are normalized such that the cameras are separated by unit distance in the plane, thus c1 = (0, 0, cz1) and c2 = (1, 0, cz2).The illustration also depicts node pi localized at pan-tilt coordinates (αi1, βi1) relative to the first camera.

a vector can also be decomposed into the product of its magnitude with a unit vector in the same direction, we can writevij = ‖vij‖ · vij. The unit vector vij can be expressed in two ways. The first expression is obtained by simply dividing vij by itsmagnitude, ‖vij‖, yielding

vij =vij‖vij‖

=pi − cj‖vij‖

=1‖vij‖

(pxi − cxjpyi − 00− czj

). (1)

The second expression is found by rotating the optical axis of camera j such that it passes through pi. The standard cameramodel used in Computer Graphics (e.g. [20], p. 434) defines the local coordinate frame with the camera looking downwardalong the z-axis at an image plane parallel to the x–y plane. The optical axis thus points in the −z direction in the localcoordinate frame. To transform from the camera’s local frame into world coordinates, wemust apply the three-axis rotationR2j defined by the angles2j. To now point the optical axis at pi, we pan and tilt the camera with the rotations Rαij and Rβij ,respectively corresponding to the angles αij and βij. At length, we find the second expression

vij = RαijRβij︸ ︷︷ ︸pan−tilt

· R2j︸︷︷︸world

·(−z)︸ ︷︷ ︸

local

. (2)

Now, we equate these two expressions for vij. Merging Eq. (1), in terms of pi and cj, with Eq. (2), in terms of αij, βij and2j, we derive a relationship between the observations and the unknowns we wish to solve for:

1‖vij‖

(pxi − cxjpyi − 00− czj

)= RαijRβij · R2j ·

( 00−1

)(3)

where ‖vij‖ =√(pxi − cxj

)2+ py2i + cz

2j .

This relationship embodies three constraints per node-camera pair, one each in x, y and z. As only twomeasurements areused, however, the three constraints cannot be independent. So, each node-camera pair contributes only two to the rank ofthe system for a total rank of 4n. We have 2n + 8 variables or unknowns to solve for: elevation and 3-DOF orientation (4parameters) for each camera, and the 2-D position of each of the n nodes. For the system to be sufficiently constrained, wemust have 4n ≥ 2n+8 which yields n ≥ 4. Thus, measurements from at least 4 nodes must be used or the resulting systemof nonlinear equations (constraints derived as the components of Eq. (3)) will be under-determined. However, as wewill seein Section 6.1, using larger numbers of nodes is preferable, as it helps mitigate the presence of noise in the measurements,greatly improving localization accuracy.So far, we have derived a system of geometric constraints that govern the relationship between the relative configuration

of nodes and cameras and the angular locations of the nodes measured by each camera. The localization problem thenbecomes a problem in nonlinear optimization. An analytical expression of the system’s Jacobian was obtained and used toinstantiate a Newton-Raphson solver. As with other techniques, Newton’s method is prone to convergence at local extremadepending on the initial search location. Our implementation is therefore been based on a globally convergent Newton’sapproach from Numerical Recipes [21] which uses multiple restarts and attempts to backtrack if it reaches a non-globaloptimum.

4.2. Extending to three dimensions

Thus far, we havemaintained the assumption that all nodes in the network lie in some common plane, in our normalizedcoordinate frame, that is ∀i, pzi = 0. While this may suffice or even be a good approximation for most scenarios, in general,

R. Farrell et al. / Pervasive and Mobile Computing 5 (2009) 165–181 169

we would like to remove this restriction. Doing so requires minimal change to our model, simply making pzi an unknownwhich modifies Eq. (3) to produce

1‖vij‖

(pxi − cxjpyi − 0pzi − czj

)= RαijRβij · R2j ·

( 00−1

)(4)

where ‖vij‖ =√(pxi − cxj

)2+ py2i +

(pzi − czj

)2.As before, we would still have 4n measurements, only now we wish to solve for 3n + 8 variables. This implies that we

must have measurements for n ≥ 8 nodes before the system will be determined.

4.3. Extending to multiple cameras

Thus far, we have been working under the assumption of just two cameras, c1 and c2. While our approach is based onsolving the nonlinear system of equations derived from the angular locations observed in a pair of pan-tilt cameras, it is notinherently limited to two cameras. While a systemwith many cameras would require consideration of practical issues suchas node and camera densities, range of visibility, etc., it has the potential for scalable localization of much larger networks.The primary challenge, of course, is in ‘‘stitching’’ together all the pairwise coordinate systems into a single global

coordinate frame. While we have considered techniques such as least squares or absolute orientation [22] for constructinga global frame, we have presently deferred this to future work. We feel that a more accurate and robust technique shouldbe developed which incorporates not just the estimated local coordinate frames, but the local measurements as well. Whileadditional cameras will likely increase localization accuracy, we have not yet demonstrated this experimentally.

5. Target localization

After the network has self-localized with the help of the cameras, it can estimate the location of targets moving throughthe sensor field using its non-imaging sensors. A number of different sensing modalities can be used for this purpose, suchas acoustic or seismic sensors. We chose to usemagnetometers which are sensors that detect the presence of ferrous targetsthrough the changes they create to the earth’s magnetic field. Our choice was based on a number of factors. First, it hasbeen proven experimentally that magnetometers can detect the presence of metal objects at distances up to tens of feet [5,4]. Second, magnetometers can implicitly focus only on ’interesting’ objects moving through the sensor field (e.g. personscarrying large metallic objects). Finally, magnetometers can provide a rich set of information about the target that can beused for classification. For example, the authors of [23] outline an applicationwhich usesmagnetometers to classify vehiclesbased on their magnetic signatures.

5.1. Magnetic signal strength model

Because we use magnetometers to detect and localize targets, we model these targets as moving magnets. Note that theferrous targets we are interested in, do not have to carry actual magnets to be detected, because the changes they generateto the earth’s magnetic field can be detected in the same way.At a high level, the magnetometers measure the strength and the direction of the magnetic field generated by the target

and translate those measurements to a heading and distance. This translation requires a model that describes the magneticfield at an arbitrary location in space around the magnet. For this purpose, we adopted the model described in [24] (p. 246),which describes the strength of the magnetic field created by a magnetic dipole m at distance r and angles θ, φ from thelocation of the dipole, as:

B(Er) =µ0m4πr3

(2 cos θ r + sin θ θ) = Br + Bθ (5)

where r, θ are unit size vectors in the direction of the radius r and angle θ respectively. The parameterµ0 is the permeabilityof free space, whilem describes the dipole’s magnetic moment, which indicates the dipole’s relative strength.As Fig. 2 illustrates, B(Er) can be described as the sumof two vectors: Br that is parallel to the radius connecting themagnet

to point (x, y, z) and Bθ that is perpendicular to Br . Note that Eq. (5) does not depend on φ since themagnetic field is uniformat all points at distance r and angle θ .

5.2. Model validation

We validated the applicability of Eq. (5) by comparing its predictions with measurements collected by aMicaZmote [25]equipped with the MTS310 sensor board from Crossbow [26].The MTS310 sensor board includes an HMC1002 2-axis magnetometer manufactured by Honeywell [27]. Each of the

two axes of this magneto-resistive sensor is aWheatstone bridge, whose resistance changes according to the magnetic field

170 R. Farrell et al. / Pervasive and Mobile Computing 5 (2009) 165–181

Fig. 2. Magnetic field of ideal magnetic dipolem pointing at the z-direction.

Fig. 3. Voltage differential generated by the HMC 1002 magnetometer as a function of the applied magnetic field strength.

applied to it. This change in resistance causes a change in the voltage differential of the bridge which can be measured bythe mote’s Analog to Digital Converter (ADC) circuit. According to the manufacturer’s specification, the recorded voltagedifferential1V generated by the magnetometer is equal to:

1V = s · B · Vcc + o (6)

where s is themagnetometer’s sensitivity (inmV/V/G), B is the strength of the appliedmagnetic field (in G), Vcc is the voltagesupplied to the magnetometer, and o is the bridge offset (in mV).While we can measure 1V directly, we are interested in the magnetic field strength B. However to derive B we need

to estimate the values of s and o which are device-specific. To do so, we placed a MicaZ with its MTS310 sensor boardinside a Helmholtz coil, which is essentially a copper coil attached to an electrical source. As current passes through thecoil, it generates a uniformmagnetic field that is perpendicular to the coil’s plane. The mote was placed inside the coil suchthat themagnetic field was alignedwith each of the sensor’s axes. We thenmeasured the generatedmagnetic field B using acalibrated industrial magnetometer and recorded the1V values from themagnetometer’s X- and Y -axis for different valuesof Bwhile keeping Vcc constant.The relationship between B and 1V for the Y -axis is plotted in Fig. 3. It is clear from this figure that 1V and B have

a linear relationship as described in Eq. (6). Moreover, the parameters of this linear relationship can be derived by linearinterpolation of the collected data points.1

Next, we keep the strength B of the magnetic field constant while supplying a variable Vcc . The results from Fig. 4 verifythat1V is indeed linearly related to Vcc .

1 The HMC1022 magnetometer actually provides circuitry for self calibration, where magnetic fields of known magnitudes are generated that can beused to derive s and o using linear interpolation. Unfortunately the MTS310 board that we used, did not expose this functionality and thus we had to resortin calibrating the sensor using the Helmholtz coil.

R. Farrell et al. / Pervasive and Mobile Computing 5 (2009) 165–181 171

Fig. 4. 1V as a function of supplied voltage Vcc .

Fig. 5. Recorded magnetic field strength as a function of distance between magnetometer and magnetic target.

Given the derived values of s and o we can estimate B from 1V for any magnetic field applied to the magnetometer.Specifically, we derive the Bx and By values for the magnetometer’s two axes and then calculate the magnitude of the

magnetic field B, as B =√B2x + B2y , since the two axes are perpendicular to each other.

We performed two experiments to test the validity of Eq. (5). First, we varied the distance r between the MicaZ anda Neodymium magnet with nominal strength of 5000 G, while keeping θ constant. Fig. 5 presents the results of thisexperiment. It is evident that field strength decays with the cube of distance r , in accordance with Eq. (5).For the second experiment, we kept r constant while rotating themagnet around themagnetometer at 22.5◦ increments.

Fig. 6 plots the raw magnetometer readings (i.e.√1V 2Y +1V

2X ) collected at the different angles, coupled with the values

predicted by Eq. (5). It is clear that there is good match between the model and the experimental data across all values of θ .

5.3. Simplified localization algorithm

Weuse Eq. (5) to estimate the location of amagnetic target located inside a lattice ofmotesMi, d distance units apart fromeach other. Such a lattice with four magnetometers and one magnetic target is illustrated in Fig. 7. For now, we assume thatall motes are arranged in such a way that their Y -axes are all aligned and point North. The exact direction is not important,but rather all magnetometers’ directions must be aligned. We will remove this restriction in Section 5.4.The strength of the magnetic field recorded at mote Mi has two components recorded by the magnetometer’s X- and

Y -axes, respectively. From Fig. 7 one can see that Xi is the sum of Xri and Xθi which are the projections of Bri and Bθi on theX-axis.

Xi = Xri + Xθi (7)

Xi = Bri sin(φ + θi)+ Bθi cos(φ + θi) (8)

172 R. Farrell et al. / Pervasive and Mobile Computing 5 (2009) 165–181

Fig. 6. Measured magnetic field strength as a function of the angle between the device and a magnetic target. Also shown is the predicted field strengthaccording to Eq. (5).

Fig. 7. Magnetic target and magnetic field strength measured at magnetometersM1 andM2 .

Xi = Bri(sinφ cos θi + cosφ sin θi)+ Bθi(cosφ cos θi − sinφ sin θi) (9)

Xi = 2Ci cos θi(sinφ cos θi + cosφ sin θi)+ Ci sin θi (cosφ cos θi − sinφ sin θi) (10)...

Xi =Ci2(3 sin(φ + 2θi)+ sinφ) (11)

where Ci =µ0m4πri3

.

Likewise, we can express Yi as follows:

Yi = Yri − Yθi (12)

Yi = Bri cos(φ + θi)− Bθi sin(φ + θi) (13)...

Yi =Ci2(3 cos(φ + 2θi)+ cosφ) . (14)

R. Farrell et al. / Pervasive and Mobile Computing 5 (2009) 165–181 173

Fig. 8. Generalized target detection problem.

Since each mote measures its own Xi, Yi, Eqs. (11) and (14) offer four equations for each mote pair. We have however fiveunknowns: r1, r2, φ, θ1, θ2. Fortunately, there is another relationship that we can utilize:

d2 = r21 + r22 − 2r1r2 cos(θ2 − θ1) (15)

which is none other than the generalized Pythagorean theorem for triangleMM1M2.Analogous sets of equations can bewritten for all other mote pairs that detect themagnetic targetM . We found it helpful

in practice to add explicit constraints to ensure that the location corresponding toM1+Er1 is the same as that ofM2+Er2. Toderive these constraints, we simply equate the X- and Y -components as follows:

r1 sin(φ + θ1) = r2 sin(φ + θ2) (16)d− r1 cos(φ + θ1) = −r2 cos(φ + θ2). (17)

For kmagnetometers detecting the target, we thus have 2k+ 3(k2

)nonlinear equations: two equations for the X and Y

magnetometer readings of each node and three equations (the generalized Pythagorean equation and the two ‘‘consistency’’constraints) for each magnetometer pair.

5.4. Generalized localization problem

The algorithm presented in the previous section assumes that all the motes are aligned. As it turns out, we can removethis limitation and support placing motes at arbitrary headings φi as long as these headings are known.In turn, it is possible to estimate the mote’s orientation by taking advantage of the earth’ magnetic field and treating

the magnetometer as an electronic compass (as a matter of fact one of the intended uses of the HMC1002 is in compassingapplications). Assuming that the earth’s magnetic field points north (with some offset depending on the location in whichthe system is deployed), one could derive during the initialization phase the heading of the mote φi in degrees using theformulas outlined below:

φi =

90− arctan

(BxBy

)·180π, By > 0

270− arctan(BxBy

)·180π, By < 0

180, By = 0, Bx < 00, By = 0, Bx > 0

where Bx and By are the magnetic field strengths recorded by the magnetometer’s X- and Y -axis respectively.Givenmote headingsφi estimated by themechanismdescribed above, the generalized version of the localization problem

can be solved. As Fig. 8 illustrates, the target magnet is located at (xm, ym) and has orientation φm. Each magnetometerMi islocated at (xi, yi) and has orientation φi. The angle from the magnet to each magnetometer relative to the magnet’s axis isdenoted by θi. Instead of adding the magnetometer orientation as a third unknown on top of ri and θi, we now express thequantities ri and θi in terms of the known position (xi, yi) and the unknown magnet parameters (xm, ym) and φm.

ri =√(xi − xm)2 + (yi − ym)2 (18)

θi = arcsin(xi − xmri

)− φm (19)

and as before

Ci =µ0m4πr3i

. (20)

174 R. Farrell et al. / Pervasive and Mobile Computing 5 (2009) 165–181

Fig. 9. Calibration target used to calculate the intrinsic parameters of each camera.

Thus, instead of using three unknowns for each magnetometer, we have only one unknown, φi. The equations relating themagnetometer readings are relatively unchanged, differing only by the incorporation of φi:

Bxi =Ci2(3 sin(2θi + φm − φi)+ sin(φm − φi)) (21)

Byi =Ci2(3 cos(2θi + φm − φi)+ cos(φm − φi)). (22)

Interestingly, the generalized Pythagorean equation and the two ‘‘consistency’’ constraints are no longer useful as theycontribute no rank to the Jacobian matrix used to solve the system of non-linear equations.

6. Evaluation

6.1. Self-localization

Our primary objectives in evaluating the proposed self-localization technique are to quantify its accuracy and confirmits scalability. We first employed a network of 12 MicaZ motes to examine the localization accuracy of our approachunder realistic conditions. To overcome the limitations of this small network, we also experimented with a simulatednetwork of 100motes and found that larger networks offer improved accuracy despite theirmodest increase in computationoverhead.

6.1.1. Camera calibrationIn order to accurately determine the pan-tilt coordinates of an image point, it is necessary to know the intrinsic or

internal characteristics of the camerawhich include focal length, principal point (the true center of the image) and distortionparameters. Both cameraswe usedwere individually calibrated at theirwidest field-of-view.Many frames of a checkerboardcalibration target (see Fig. 9) at different positions andorientationswere used as input to the Camera Calibration Toolbox [28]for MATLAB. The points of intersection between neighboring squares on the calibration target are located in each frameand these points are collectively used to estimate the camera’s internal parameters. These parameters are stored in aconfiguration file and read into the system at run-time.As the PTZ cameras can also zoom, we first calibrated one camera at various focal lengths. It became obvious that some

parameters such as the principal point were not constant across focal lengths, so re-calibrationwas indeed critical. Themostinteresting discovery in the calibration process, however, was that even with per-zoom-level calibration, the computationof pan-tilt coordinateswas error-prone for all but thewidest field-of-view zoom.We eventually concluded that the center ofrotation coincides with the focal point only for the widest field-of-view. Other zoom levels therefore introduce a translationas the camera pans or tilts about the center of rotation.

6.1.2. Experimental deploymentOur experimental platform consists of a network of 12 MicaZ motes equipped with omni-directional LEDs and two PTZ

cameras: a Sony EVI-D100 and a Sony SNC-RZ25N (see Fig. 10). Our application software, written primarily in Java, runs ona standard laptop, using JNI to integrate native code for image processing and for controlling the EVI-D100. Communicationwith the sensor network is facilitated by a mote wired directly to the laptop. A core component of our system, the nonlinearsolver consists of a Java implementation of the globally convergent Newton’s method found in Numerical Recipes [21]. Oursolver is substantially (20− 25×) faster than MATLAB’s Optimization toolbox which we used in initial simulations.To self-localize a network of n nodes, the system follows the procedure outlined below:• A subset of k nodes, namely Sk = {pi1 , . . . , pik} is selected.• The nodes in Sk are sequentially interrogated, each ascending an omni-directional LEDwhich the cameras use to pinpointthe node’s location in their individual pan-tilt parameterization.

R. Farrell et al. / Pervasive and Mobile Computing 5 (2009) 165–181 175

Fig. 10. Experimental platform: MicaZ sensor network, laptop, 2 PTZ cameras.

• After finding the pan-tilt location for each node p, the corresponding nonlinear systemof equations is solved numerically,yielding location estimates for ∀p ∈ Sk.• Many such subsets, S(1)k , S

(2)k , . . . , S

(T )k , are randomly chosen and location estimates for each subset S

(t)k is determined as

above.• When this process completes, we have several location estimates for each node ( Tkn expected) and average them to derivethe final location estimate for each given node.

As will be demonstrated below, increasing the size of the subsets reduces the localization error. While a singlecomputation using all of the motes’ measurements yields the minimal localization error, we have adopted the approachusing smaller subsets (of size k) because the smaller optimization problems (i) can be solved much faster and with lessmemory, (ii) can be distributed amongst the nodes in the network and run in parallel, and (iii) quickly approach theminimallocalization error (which would be achieved using all motes).In the event that a node is not seen by a camera, perhaps due to visual occlusion, that node is not factored into the

computation. The computation could then either replace the occluded nodes with mutually-visible ones or proceed witha subset of fewer than k nodes. Even if a node is occluded in one camera, its location may still be estimated once the finalcamera parameters have been determined, simply by projecting the pan-tilt location onto the plane.Fig. 11 presents sample results for our network of 12 MicaZ motes. Each dot in these graphs shows an estimated mote

location over the unit square [0, 1]2, as calculated by the system. In Fig. 11(a), the localization results for subsets of sizek = 6 are shown, on the left colored by subset ID and on the right colored by mote ID. Fig. 11(b) shows analogous resultsfor subsets of size k = 9, hinting at the improvement in accuracy by using larger subsets. While the absence of ground truthlocalization prevents us from determining precise localization errors, we can see how the solutions for random subsetscollectively suggest an accurate location estimate.

6.1.3. Empirically verified noise modelWhile we could acquire planar ground truth locations for the nodes with relative ease, it is difficult to obtain accurate

ground truth values for the camera’s orientation and the location of the focal point inside the camera.We nonetheless hopedthat we could characterize the observed noise in such amanner that wemight produce similar measurements synthetically.Instead of generating the exact pan-tilt measurements that would result from the ground truth locations, we apply anangular perturbation ∼N(0, ζ ) to each measurement, akin to the model proposed by Ercan et al. [29,30], using ζ = 0.1◦.We generate synthetic measurements using the mean locations derived from the experimental network using subsets ofsize k = 6. Fig. 12 presents a comparison between the real and synthetic data. The synthetic noise model closely reflects theerror characteristics of the observed data.

6.1.4. SimulationTo demonstrate the improved localization accuracy obtained with larger subsets, we turned from our small physical

deployment to a larger simulated network. Simulated networks provide us with ground truth for mote locations, essentialto properly addressing the question of localization error.As we noted before, localization accuracy is associated not with the size of the network, but with the subset size k. So,

whether the network has tens, hundreds or thousands of nodes, the localization accuracywill be same for a given subset sizek assuming the number of estimates per node is fixed. For a fixed k, the required computation time grows linearly with thesize of the network. If the number of estimates per node L is fixed, then the number of random subsets required to produceL estimates for each of the n nodes is Lnk , indicating a linear relationship.Our simulated network distributed 100 nodes uniformly at randomwithin a unit square [0, 1]2. The cameraswere placed

at the same normalized heights as in our experimental setup, the first above the origin (0, 0), the second above (0, 1). Thesame process of selecting subsets described in Section 6.1.2, angularly locating the motes and solving the nonlinear systemis used to find location estimates within the plane. The noise model used is the same described in Section 6.1.3.In Fig. 14 we present results for a 100-node network choosing subsets of size 5, 10, 20, and 50. To articulate these results

in real-world terms, ifwe imagine the deployment area is 100m×100m, then these errorswould be as depicted in Fig. 13 andTable 1. Remarkably, with two cameras positioned 100 meters apart, the system can localize every node to within 15.82 cmof its true location. Moreover, it localizes a majority of them with errors less than 5 cm.

176 R. Farrell et al. / Pervasive and Mobile Computing 5 (2009) 165–181

(a) Results with subsets of size k = 6 nodes.

(b) Results with subsets of size k = 9 nodes.

Fig. 11. Self-localization results for our experimental 12-mote network. (a) Shows simultaneous plots of localization from 100 randomly selected 6-motesubsets, on the left colored by subset ID, on the right by mote ID. (b) Shows analogous results for 9-mote subsets.

Table 1Errors for 100 m× 100 m 100-node network

Subset size 50% confidence 95%confidence

5 nodes 6.70 m 96.25 m10 nodes 43.57 cm 2.14 m20 nodes 5.26 cm 17.19 cm50 nodes 4.85 cm 11.73 cm

6.2. Target localization

6.2.1. SimulationPrior to conducting any experiments with actual magnets, wewere able to use a virtual sensor network to simulate noisy

magnetometer readings, generated by adding white noise to the magnetic field strength provided by Eq. (5), and comparethe localization accuracy aswell as the orientation estimates. Certain intrinsic properties of the system emerged not throughtheoretical analysis, but rather through simulation. One such property is the inherent ambiguity in orientation whereas themagnetometer readings will be identical if both the target and network nodes are rotated by 180◦ (see Fig. 15(a)). Fig. 15(b)shows the simulated target-localization accuracy for various configurations (different numbers of nodes detecting the target,constrained/unconstrained orientation, etc.).

R. Farrell et al. / Pervasive and Mobile Computing 5 (2009) 165–181 177

(a) Observed. (b) Synthetic.

(c) Compared.

Fig. 12. Empirically validated noisemodel. (a) Plots the solutions for 100 subsets using actualmeasurements obtained from the experimental system (samedata displayed in Fig. 11(a)). (b) Plots the solutions for 100 subsets using simulated measurements obtained using the synthetic noise model. (c) Shows acomparison between the the observed and the synthetic data. The mean location for each mote along with the error ellipse indicating 95%-confidence aredepicted. As in the first two plots, blue is used for the observed data, red for the synthetic data.

Fig. 13. Localization error distributions. For a simulated 100 × 100 m deployment containing 100 nodes, the curve showing the percentage of nodeslocalized within any given error is shown for 5-, 10-, 20- and 50-node subsets.

178 R. Farrell et al. / Pervasive and Mobile Computing 5 (2009) 165–181

(a) Solution, k = 10. (b) Solutions, k = 50.

(c) 95% errors, k = 10. (d) 95% errors, k = 50.

Fig. 14. Simulated large-scale network. (a)–(b) Present localization results for 10- and 50-node subsets, respectively. (c)–(d) Present the mean of thesolutions for each node together with the ellipse of 95% confidence. Each node is plotted in a unique color and a black error line is drawn between eachnode’s ground truth location and the mean of its solutions.

Table 2Experimental target localization results

Min error Avg. error Median error Std. deviation

1.9 cm 13.8 cm 9.5 cm 14 cm

6.2.2. Experimental resultsWe designed an experiment to test mote localization in the following way. First, we selected random locations on a

1 m× 1 m level surface to place a set of six pre-calibrated motes. We then selected a set of fifty target locations by placinga magnet of known strength at each of these locations.Each of the network’s motes initially collects measurements about the ambientmagnetic field and subtracts these values

from subsequent measurements. Doing so, cancels the contribution of any environmental effects to the target localizationprocess. The collected measurements are finally relayed to a base station which executes the generalized localizationalgorithm described in Section 5.4.Table 2 presents our initial target localization results from the network of sixMicaZmotes. The average localization error

was∼14 cm while the minimum localization error was much smaller.Fig. 16 presents the distribution of localization errors across all experiments. A number of interesting observations can be

made from this figure. First, there is good correlation between the experimental results and the simulation results shown in

R. Farrell et al. / Pervasive and Mobile Computing 5 (2009) 165–181 179

Fig. 15. Magnetometer simulations. (a) Shows the 180◦ orientational ambiguity inherent in many of the solutions. (b) Shows the cumulative errordistributions for 4-, 6- and 8-motes with arbitrary orientation detecting the target and compares them to 3 motes with aligned headings.

Fig. 16. Cumulative density function of the target localization error. The median localization error is less than 10 cm.

Fig. 15.b. Second, the majority of cases result in low localization error. There are however a few cases with high localizationerror, indicating that some positions did not localize well.The most likely cause behind these disparities is the calibration process described in Section 5.4. The resolution of the

industrial magnetometer is 0.1 G, while the HMC1002magnetometer on theMTS310 board has a resolution of 200µG. Sincewe calibrate each mote independently to within .1 G, it is possible that any two motes will be off from each other by .2 G.Given that measurements at the fringes of the magnetometers’ sensing range are in the order of few mGauss, the lack ofaccuracy accounts for the cases with large localization error, especially considering that magnetic field strength decreaseswith the cube of distance.To validate this hypothesis, we investigate whether some motes contribute inaccurate measurements thus skewing the

results. To do so, after running the localization experiment, we generate( nk

)measurement combinations where n is the

number of motes participating in the experiment and k is a subset of these motes. Fig. 17 presents the localization error CDFfor the best

( nk

)combination, when k ≤ 2, 3, 4. It is evident that for positions that localize well, different k values do not

produce sizable performance differences. On the other hand, small k values produce better results for positions that localizepoorly. The underlying cause for this seemingly counter-intuitive result is that using small k values provides the opportunityto remove faulty measurements that skew the final result. This result indicates that robust estimation techniques, suchas trimmed mean and M-estimates can be used to remove measurement outliers, which are likely to be small magnitudemagnetometer readings.

6.3. In-network target localization

Since themotes have been pre-calibrated and each knows its ownheading,we should in theory be able to detect and eventrack a target with a knownmagnetic ‘‘signature’’ (i.e.magnetic dipole moment). The target has three unknowns, its x and y

180 R. Farrell et al. / Pervasive and Mobile Computing 5 (2009) 165–181

Fig. 17. Effect of selecting different measurement subsets on localization error.

location on the plane and the orientation of its magnetic axis, φm. It would seem that the four measurements provided by apair of nearby motes with two-axis magnetometers should provide enough information to recover these target parameters(xm, ym, φm).Thus far, the numeric solution of the nonlinear equations describing the localization task occurs at a central location

(e.g., at a laptop connected to the sensor network). However, it would preferable if, once the motes know their orientation,they could perform target detection and tracking entirely within the network. We have done just this by implementing anumerical solver in TinyOS that allows mote pairs to collaborate in localizing a target.Our TinyOS implementation is based on levmar, an implementation of the Levenberg-Marquardt algorithm [31]. By

hand-coding the required matrix inversion, we were able to pack this powerful solver into a single TinyOS task. Due tohardware limitations such as fixed-point arithmetic we expected very little in the way of performance but were quitesurprised to see theMicaZ perform approximately 30 iterations of the solver per second (i.e., 33milliseconds per iteration). Ifthe initial estimate used to initialize the solver is close to the true location, the solver typically converges in 8–15 iterations,just more than half a second with communication overhead, etc. However, our results here are preliminary as we are stillworking to carefully measure the localization error with this method.

7. Summary

We present a comprehensive solution to the problem of localization inmulti-modal sensor networks. First, two Pan-Tilt-Zoom (PTZ) cameras are used to estimate the locations of the network’smotes. Unlike previous solutions, only angular infor-mation from the cameras is used for self-localization. Results from an experimental implementation, coupled with resultsfrom larger simulated networks indicate that the accuracy of the proposed localization algorithm increases with the size kof the nodes collectively localized in the same batch. This result, coupled with the fact that localization accuracy does notdegrade as the size of the network increases, makes the proposed approach very attractive for large scaleWSN deployments.Once the network has self-localized, it can detect the presence and estimate the location of ferrous target moving over

the sensor field, with the help of magnetometers connected to the network’s motes. We present two variations of the targetlocalization algorithm, onewhich assumes that motes are deployed on a regular lattice and a generalized version that workswith arbitrary (but known) mote headings φi. We have implemented this second version of the localization algorithm onthe MicaZ motes of our testbed and evaluated its accuracy through experiments with actual magnets as well as large scalesimulations. We find that the generalized version performs almost as well as the version requiring regular mote formationsas the number of motes detecting the target increases. Furthermore, early results from our experimental evaluation indicatethat it is possible to locate magnetic targets with average localization error in the order of a few cm in a 1 m× 1 m field.

Appendix. Derivation of simplified magnetometer equations

A handful of simple trigonometric identities allow us to derive Eqs. (11) and (14). We here show just the derivation forXi (Eq. (11)) as Yi (Eq. (14)) follows the same approach.

Xi = 2Ci cos θi (sinφ cos θi + cosφ sin θi)+ Ci sin θi (cosφ cos θi − sinφ sin θi) (≡ 10)= Ci sinφ

(2 cos2 θi − sin2 θi

)+ 3Ci cosφ sin θi cos θi

= Ci sinφ((32+12

)cos2 θi −

(32−12

)sin2 θi

)+3Ci2cosφ (2 sin θi cos θi)

R. Farrell et al. / Pervasive and Mobile Computing 5 (2009) 165–181 181

=Ci2sinφ

(3(cos2 θi − sin2 θi

)+ 1

(cos2 θi + sin2 θi

))+3Ci2cosφ (2 sin θi cos θi)

=3Ci2sinφ cos 2θi +

Ci2sinφ +

3Ci2cosφ sin 2θi

Xi =Ci2(3 sin(φ + 2θi)+ sinφ) . (≡ 11)

References

[1] P. Kulkarni, D. Ganesan, P. Shenoy, Q. Lu, SensEye: A multi-tier camera sensor network, in: Proceedings of the 13th Aannual ACM internationalconference on Multimedia, 2005, pp. 229–238.

[2] M. Rahimi, R. Baer, O. Iroezi, J. Garcia, J. Warrior, D. Estrin, M. Srivastava, Cyclops: In situ image sensing and interpretation inwireless sensor networks,in: Proceedings of the 3rd ACM Conference on Embedded Networked Sensor Systems, SenSys, 2005.

[3] L. Gu, D. Jia, P. Vicaire, T. Yan, L. Luo, A. Tirumala, Q. Cao, T. He, J.A. Stankovic, T. Abdelzaher, B. Krogh, Lightweight detection and classification forwireless sensor networks in realistic environments, in: Proceedings of the 3rd ACM Conference on Embedded Networked Sensor Systems, SenSys,2005.

[4] T. He, S. Krishnamurthy, J.A. Stankovic, T.F. Abdelzaher, L. Luo, R. Stoleru, T. Yan, L. Gu, J. Hui, B. Krogh, An energy-efficient surveillance system usingwireless sensor network, in: MobiSys, 2004.

[5] A. Arora, P. Dutta, S. Bapat, V. Kulathumani, H. Zhang, V. Naik, V. Mittal, H. Cao, M. Demirbas, M. Gouda, Y.-R. Choi, T. Herman, S.S. Kulkarni,U. Arumugam, M. Nesterenko, A. Vora, M. Miyashita, A line in the sand: A wireless sensor network for target detection, classification, and tracking,Computer Networks (2004) 605–634.

[6] S. Oh, L. Schenato, P. Chen, S. Sastry, A scalable real-timemultiple-target tracking algorithm for sensor networks, Tech. Rep. UCB//ERLM05/9, Universityof California, Berkeley, Feb. 2005.

[7] C. Taylor, A. Rahimi, J. Bachrach, H. Shrobe, A. Grue, Simultaneous localization, calibration, and tracking in an ad hoc sensor network, in: Proceedingsof the Fifth International Conference on Information Processing in Sensor Networks, IPSN, 2006, pp. 27–33.

[8] D. Moore, J. Leonard, D. Rus, S.J. Teller, Robust distributed network localization with noisy range measurements, in: Proceedings of the 2nd ACMConference on Embedded Networked Sensor Systems, SenSys, 2004, pp. 50–61.

[9] J. Hightower, G. Borriello, Location systems for ubiquitous computing, IEEE Computer 34 (8) (2001) 57–66. URL: http://citeseer.ist.psu.edu/article/rey01location.html.

[10] N. Patwari, J.N. Ash, S. Kyperountas, A.O.H. III, R.L. Moses, N.S. Correal, Locating the nodes: Cooperative localization in wireless sensor networks 22 (4)(2005) 54–69.

[11] S. Poduri, S. Pattem, B. Krishnamachari, G.S. Sukhatme, Sensor network configuration and the curse of dimensionality, in: Workshop on EmbeddedNetworked Sensors, EmNets, 2006. URL: http://cres.usc.edu/cgi-bin/print_pub_details.pl?pubid=495.

[12] S. Funiak, C. Guestrin, M. Paskin, R. Sukthankar, Distributed localization of networked cameras, in: Proceedings of the Fifth International Conferenceon Information Processing in Sensor Networks, IPSN, 2006, pp. 34–42.

[13] A. Rahimi, B. Dunagan, T. Darrell, Simultaneous calibration and tracking with a network of non-overlapping sensors, in: Proceedings of CVPR, 2004.[14] R. Hartley, In defense of the eight-point algorithm, IEEE Transactions on Pattern Analysis and Machine Intelligence 19 (6) (1997) 580–593.[15] R.I. Hartley, A. Zisserman, Multiple View Geometry in Computer Vision, 2nd edition, Cambridge University Press, ISBN: 0521540518, 2004.[16] F. Dellaert, S. Seitz, C. Thorpe, S. Thrun, Structure from motion without correspondence, in: Proceedings of the IEEE Computer Society Conference on

Computer Vision and Pattern Recognition, 2000, pp. II: 557–564.[17] A. Barton-Sweeney, D. Lymberopoulos, A. Savvides, Sensor localization and camera calibration in distributed camera sensor networks, in: Proceedings

of IEEE BaseNets, 2006.[18] R. Stoleru, T. He, J.A. Stankovic, D. Luebke, A high-accuracy, low-cost localization system for wireless sensor networks, in: Proceedings of the 3rd ACM

Conference on Embedded Networked Sensor Systems, SenSys, 2005, pp. 13–26.[19] M. Ding, A. Terzis, I.-J. Wang, D. Lucarelli, Multi-modal calibration of surveillance sensor networks, in: Proceedings of MILCOM 2006, 2006.[20] D. Hearn, M.P. Baker, Computer Graphics, 2nd ed., Prentice-Hall, Inc., Upper Saddle River, NJ, USA, 1994.[21] W.H. Press, S.A. Teukolsky, W.T. Vetterling, B.P. Flannery, Numerical Recipes, in: C: The Art of Scientific Computing, Cambridge University Press, New

York, NY, USA, 1992. URL: http://www.library.cornell.edu/nr/bookcpdf/c9-7.pdf.[22] B.K.P. Horn, Closed-form solution of absolute orientation using unit quaternions, Journal of the Optical Society of America (1987).[23] Honeywell Corporation, Application note AN218: Vehicle detection using AMR sensors. Available at: http://www.ssec.honeywell.com/magnetic/

datasheets/an218.pdf.[24] D.J. Griffiths, Introduction to Electrodynamics, Prentice Hall, 1999.[25] Crossbow Corporation MICAz Specifications. Available at: http://www.xbow.com/Support/Support_pdf_files/MPR-MIB_Series_Users_Manual.pdf.[26] Crossbow Corporation, MICA2 Multi-Sensor Module (MTS300/310). Available at: http://www.xbow.com/Products/Product_pdf_files/Wireless_pdf/

MTS_MDA_Datasheet.pdf.[27] Honeywell Corporation, HMC1002 Linear Sensor. Available at: http://www.ssec.honeywell.com/magnetic/datasheets/hmc1001-2&1021-2.pdf.[28] J.-Y. Bouget, Camera calibration toolbox for matlab. Available at: http://www.vision.caltech.edu/bouguetj/calib_doc/.[29] A. Ercan, A.E. Gamal, L. Guibas, Camera network node selection for target localization in the presence of occlusions, in: SenSysWorkshop onDistributed

Cameras, 2006.[30] A. Ercan, D. Yang, A.E. Gamal, L. Guibas, Optimal placement and selection of camera network nodes for target localization, in: DCOSS, 2006, pp. 389–404.[31] M. Lourakis, levmar: Levenberg-Marquardt nonlinear least squares algorithms in C/C++. Available at: http://www.ics.forth.gr/∼lourakis/levmar/.

Andreas Terzis is an Assistant Professor in the Department of Computer Science at Johns Hopkins University. He joined the facultyin January 2003. Before coming to JHU, Andreas received his Ph.D. in computer science from UCLA in 2000. Andreas heads theHopkins InterNetworking Research (HiNRG) Groupwhere he leads research inwireless sensor network protocols and applicationsas well as network security.