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A Tracking System for Wireless EmbeddedNodes Using Time-of-Flight Ranging

Evangelos B. Mazomenos, Jeff S. Reeve, Senior Member , IEEE ,

Neil M. White, Senior Member , IEEE , and Andrew D. Brown, Senior Member , IEEE

Abstract—In this work, we present the design, development, and evaluation of a real-time target tracking system for wireless

embedded nodes, capable of effectively tracking manoeuvring targets. The proposed tracking system is designed to operate solely on

range measurements obtained with the use of a two-way time-of-flight method without the need for additional hardware being

incorporated in the nodes. To address the challenge of coping with manoeuvring targets, the tracking problem is formulated as a

dynamical estimation problem where an adaptive multiple-model approach is employed to represent the motion pattern of

manoeuvring targets. The ranging observations are produced in real time and used as inputs to a particle filter algorithm that produces

the estimates of the target’s kinematic variables. Simulations are provided to assess the effect of several factors on the system’s

performance. Ultimately, the entire system is implemented on commercially available hardware and tested in an outdoor deployment. A

total of 25 experiments demonstrate an average RMS accuracy of 2.6 m for position and 1.9 m/s for velocity, in a 15 m 15 m area.

Such performance, which is additionally confirmed from simulation results, reveals the potential of the proposed range-only system in

application scenarios where real-time tracking of mobile targets is needed.

Index Terms—Wireless sensor networks, real-time and embedded systems, target tracking

Ç

1 INTRODUCTION

AFTER a decade of continuous evolution and develop-ment, wireless sensor networks (WSNs) have earned a

prominent spot among pervasive computing technologies.The flexibility they offer, by encompassing various sensormodalities, low-power wireless communication and proces-sing ability, in a limited-sized hardware platform, initiated

research in various interdisciplinary directions for exploit-ing this novel technology in a number of applicationdomains [1]. Examples include environmental monitoring,smart structures, habitat monitoring, military defenseapplications, surveillance and security, mobile robotics,healthcare and medical applications, agriculture and assetmanagement [2], [3].

Locationing and tracking objects of interest is consideredto be a pivotal functionality for a number of applicationdomains. WSNs are considered to be a technology able toprovide innovative solutions for locationing and trackingapplications. They offer the possibility of employing a large

number of observers, tasked with monitoring the samephenomena, an approach that enables decentralized sen-sing, distributed computing and collaborative signal pro-cessing [4]. An abundant amount of information isaccumulated from the network with high spatial andtemporal resolution. For locationing and tracking, this isof particular interest, facilitating the development of more

robust, flexible, and cost-effective tracking systems [5], [6].The basic concept for target tracking with WSNs is todeploy a number of cooperative embedded nodes tomonitor a specific region of interest. Whenever a target ispresent, the nodes interact with the target and collect usefulinformation for the tracking operation. Generally, in

tracking systems, the target’s dynamics are inferred byprocessing specific information, associated with the target’skinematic variables (position, velocity, direction of move-ment). For example, from various sensor readings(e.g., acoustic energy), the relative distance between thesource (target) and the sensor (anchor) can be derived.The collected data are then imported into the “trackingalgorithm,” which produces an estimate of the target’skinematic variables.

Under this context, the work presented in this paperattempts to exploit the capabilities of embedded WSNs indeveloping a real-time, range-only target tracking system.

The range-only characterization of the system pertains tothe type of data that the system utilizes to infer the target’skinematics. The proposed system operates exclusively onrange observations acquired with the use of a two-waytime-of-flight (ToF) ranging method. Our choice of employ-ing ToF ranging differentiates the proposed system from anumber of approaches that employ additional types of observations (bearings, velocity) which may require addi-tional hardware (micro RADARS, directional antennas) to be installed on the wireless nodes.

The tracking problem is theoretically formulated as adynamical system with the objective being the real-time

estimation of the target’s kinematic variables based onrange observations. The proposed system is intended toeffectively track manoeuvring targets, which is the case inthe majority of real-world tracking scenarios. For this, a

IEEE TRANSACTIONS ON MOBILE COMPUTING, VOL. 12, NO. 12, DECEMBER 2013 2373

. The authors are with the School of Electronics and Computer Science,University of Southampton, Building 59, Highfield Campus, SouthamptonSO17 1BJ, United Kingdom.E-mail: {ebm07r, jsr, nmw, adb}@ecs.soton.ac.uk.

Manuscript received 14 Mar. 2012; revised 31 Aug. 2012; accepted 8 Sept.2012; published online 2 Oct. 2012.For information on obtaining reprints of this article, please send e-mail to:[email protected], and reference IEEECS Log Number TMC-2012-03-0128.Digital Object Identifier no. 10.1109/TMC.2012.209.

1536-1233/13/$31.00 2013 IEEE Published by the IEEE CS, CASS, ComSoc, IES, & SPS

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multiple-model approach is used to represent the dynamicsof manoeuvring targets. Such an approach diversifies theproposed system from other approaches in the area thatonly consider a constant velocity (CV) model for describingthe target’s dynamics, thus providing limited support formanoeuvring targets [7], [8], [9]. Due to the nonlinearity between the range observations and the kinematic vari-ables, the resulting system is nonlinear. To solve thissystem, an adaptive multiple-model particle filter (PF)tracking algorithm is proposed. By applying multiplemodels to represent the evolution of the target’s dynamicsin time, we demonstrate that our design tracks manoeuvr-ing targets efficiently. Simulation results of applying theproposed framework on manoeuvring targets can be foundin our previous work [10]. As an expansion of this work, themultiple-model approach is verified through a simulationcomparison against the CV model for a manoeuvringscenario. Moreover, we study and quantify the effect of two important parameters on the performance of thetracking system, namely the number of particles and thesampling interval. We also calculate the Cramer-Rao lower bound (CRLB) and utilize it as a benchmark to assess theperformance of our system. This analysis is based on theaccuracy obtained by the ToF ranging method that is alsoanalyzed here and incorporated in the tracking system.

As a final extension to our previous work, in this paperwe present a working prototype of our system, implemen-ted on commercially-off-the-self (COTS) hardware. The T.I.EZ430-RF2500 platform was used for this. In our prototype,three types of node are designated; the anchor nodes, thetarget node, and the central node. For each different class of nodes, a separate piece of software was developed. In

addition, the tracking algorithms were implemented asMATLAB routines, which collect the ranging data andproduce an estimate of the targets trajectory in real time.The system was deployed in a 15 m 15 m outdoors area,and multiple experiments were executed with the targetmoving in a variety of trajectories. The results obtained arecompared to simulations that verify the achieved perfor-mance. These prominent outcomes justify the choice of arange-only tracking system for embedded nodes and alsoreveal that the proposed system satisfies the three mainobjectives of accuracy (1 percent of the area), real-timeoperation, and tracking of manoeuvring targets.

The rest of the paper is structured as follows: Section 2summarizes related work in the literature. The two-wayToF ranging method is discussed in Section 3. In Section 4,we provide the mathematical formulation of the trackingproblem as a nonlinear estimation problem and introducethe models that account for the motion dynamics as wellas the observations. In addition, this section reviews thePF tracking algorithms. Simulation results are presented inSection 5 alongside the calculation of the CRLB that isused as a benchmark to compare the systems perfor-mance. Section 6 presents the implementation on COTShardware of the tracking system. Results obtained from

the outdoors experimentation of the full system areprovided in Section 7 alongside a comparison to simula-tion results. In the final section, concluding remarks andfuture directions are discussed.

2 RELATED WORK

Many ideas regarding tracking and locationing with WSNsare presented in the relevant literature. We will restrainourselves to the tracking systems that were implementedand demonstrated at full scale. Coates et al. consider aclustered WSN for tracking, comprising of class-B sensornodes that measure, either the range or the bearing of the

target and class-A cluster heads that aggregate the datagathered from the class-B nodes. Each of the class-A clusterheads runs its own local PF, based on the data acquiredfrom the class-B nodes in its neighborhood (cluster). Theweights for each particle are then calculated based oninformation from all cluster heads. Each cluster headrepresents a particle with a certain weight associated withit and a global estimation can then be extracted [11], [12].The drawback of such an approach is that there is a need fora large number of cluster heads particles (>200) andsubsequently even larger for class-A nodes, to achieveaccurate performance, resulting in a network that involves

an excessive number of nodes.The CRICKET indoor locationing system [13] developedat MIT consists of beacons that are attached to the ceilingof a building, and receivers, called listeners, that requirelocationing. The beacons periodically transmit their loca-tion information in an RF message and an ultrasonicpulse. The listeners listen to beacon transmissions andcompute their own locations by calculating the TDoA of the two signals emitted from nearby beacons. The user’slocation is determined in relation to the already knownlocation of the mounted nodes [14]. The CRICKET locationing method is used in a centralized localizationand tracking algorithm named LaSLAT . LaSLAT algorithmreported a few centimeters of error in an 7 m 7 mindoor area and approximately 0.5 m error in an 27 m 32 m dense outdoor deployment [15].

RADAR is another indoor locationing system that is based on low-power WSNs. A number of infrastructurenodes, placed in known locations, are used to generate RSSIvalues for different positions in the coverage area and builda signal strength database. Whenever a blind node requirespositioning, its RSSI value is measured by the closestinfrastructure nodes. The observations are fused to a centralserver, which examines the signal strength map to obtainthe best fit for the current transmitter position. The achieved

accuracy is between 2 to 3 meters [16]. Ahmed et al. addressthe combined problem of target detection and tracking.Target presence or absence is modeled by a probabilityfunction. The tracking algorithm that is used estimates,apart from the target’s state vector, an extra binary variablethat indicates the presence of the target [17]. In theprototype system, a dense network of MicaZ nodesprovided range readings inferred by measuring the acousticintensity and a PF algorithm, which employs a largenumber of particles (5,000), produces both the target’sdynamics as well as decides on the presence of the target.The reported results are in the area of 0.1-0.25 m in an

indoors 1 m 3 m area with the use of at least eight anchornodes [18].

Radio interferometry was presented as a ranging methodfor embedded nodes in [19]. Kusy et al. [20] employ this

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method in the inTrack tracking system. In inTrack, the targetnode is programmed to transmit an unmodulated highfrequency sine wave. One stationary infrastructure node,positioned in known coordinates, transmits a similar signalsimultaneously with the target. The resulting compositesignal demonstrates a phase offset, which when measured atother infrastructure nodes depends only on the in-nodedistance between the participating nodes. The targetsposition is inferred, by employing multiple anchors tomeasure the phase offset. An extension of inTrack, ispresented, where the Doppler shift of the transmitted sine-

wave is also measured at the infrastructure nodes and is usedto estimate the target’s velocity. A tracking algorithmcombining the extended Kalman filter and a constrainednonlinear least-squares optimization method is used to inferthe target’s position and velocity. The reported accuracy of the system increases with increasing number of participatinganchor nodes [21]. A deployment of eight infrastructurenodes in a 50 m 30 m area reported results of 1.3-2.2 m forposition and 0.13-0.35 m/s for velocity [22], [23].

Previous research considered a linear model to representthe target’s motion dynamics. However, this approachcannot effectively cope with alterations in the position andvelocity vectors of a manoeuvring target. To achievetracking of manoeuvring targets, adaptive estimationalgorithms and a multiple-model approach to describe thedevelopment of the target’s dynamics in time are investi-gated in this work.

Two-way time transfer is an established method, devel-oped in the 1960s for acquiring the range between twowirelessly communicating devices. It is extensively used insatellite communications. In recent years, a number of attempts in designing two-way ToF methods for ranging inWSN have been presented [24], [25], [26]. Inspired by this,we have opted to employ a ToF method in the proposedtracking system that yields several advantages over acoustic

ranging methods. The systems that are based on acousticranging not only require a dense deployment of anchornodes even in small areas, but also have the need foradditional hardware like ultrasound transceivers to beattached on the WSNs nodes. If audible acoustic signals areused, the target must itself produce these acoustic signals.Different to the interferometric ranging method thatrequired the target node and another node to transmit sinewaves simultaneously, the proposed ToF ranging schemeonly has a calibration requirement.

3 TWO-WAY TIME-OF-FLIGHT RANGING

In this section, we highlight the major aspects of the ToFranging technique used in the proposed range-onlytracking system. For a detailed analysis, the reader is

directed to our previous work that was focused entirely onthis method [27]. In principle, ToF methods attempt toestimate the transit time of a signal. The a priori knowl-edge of the signal’s velocity allows the approximation of the distance between transmitter and receiver. The devel-oped method intends to quantify the distance between apair of unsynchronized wireless nodes and is considered to

be ideal for the range-only tracking system that weconsider. The fundamental idea is to achieve an estimationof the distance between the two nodes by conductingmultiple two-way message exchanges and calculating themean ToF value.

The objective is to estimate the distance between nodes Aand B (Fig. 1). A local timer on node A is employed toprovide the ToF timing values. Initially, node A sends thefirst ranging signal and captures the time of its timer (ttAB ).Node B receives the signal and after a period of time, thatcorresponds to node B swapping its state, from receiver totransmitter (as well as a number of other delays) node B

sends a ranging signal back to node A. Following, node Areceives the reply signal and stores the time of its reception(trBA). The timer in node A measures tA ¼ trBA ttAB

multiple times.Within tA, the delay related to the ranging message being

processed at node B is included. To measure the amount of time that corresponds to delays that occur during the two-way message exchange process and remove it, we introducea calibration stage. This is accomplished by placing thetransceivers at a very close distance (<0:2 m), so the ToFperiod is minimal and executing multiple transactions thatare averaged to produce the minimum time (tmin) that is

required to complete a message exchange. This amount of time corresponds to a minimal ToF period and reveals allthe hardware and software delays that occur during a two-way ranging transaction. This calibration step is deemed to be more efficient in capturing all the delays that occurduring a two-way message exchange than simply measur-ing, using a local timer, the amount of time that the messagespends in node B. We make the assumption that thesedelays remain constant and are independent of the distance between the nodes. Subsequently, only the propagationdelay will increase the two-way time transfer value as thenodes are placed at greater distance.

Fig. 2 illustrates a timing diagram of a message exchange between the two nodes. Send and receive occurs on therising edge of the nodes clocks. Assuming that for a givendistance, the tT oF will be the same and the delay T B proc that

MAZOMENOS ET AL.: A TRACKING SYSTEM FOR WIRELESS EMBEDDED NODES USING TIME-OF-FLIGHT RANGING 2375

Fig. 1. Proposed two-way ToF ranging.

Fig. 2. Timing diagram of a two-way message exchange.

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node B requires to process the ranging signal and submitthe reply is constant, the only ambiguity will be inserted bythe delays associated with the clocks phase shift andfrequency drift. Given that the two clocks are unsynchro-nized and have a small difference in frequency, the phaseoffset between the devices will oscillate, thus the delays T d 1

and T d 2 will follow a similar varying pattern. By over-sampling, we capture a normally distributed set of multiple

timing transactions centered around the mean ToF value.Therefore, capturing a sufficiently large number of timingvalues will allow us to extract the mean ToF value that can be, linearly associated with the distance between the nodes.

Following the completion of the required number of two-way transactions, node A enters the calculation phase.The calculation phase involves the extraction of the ToFout of the multiple stored timer values. In the event thatone, or in general a small fraction of these n transactionshas produced erroneous timing, including them in theaverage calculation will result in distorting the correctmean value. To avoid this, the following procedure isfollowed. Let us assume that we obtain n two-way ToFvalues tn. Initially, the mean etT oF and standard deviationof the n values are calculated.

In the following step, we calculate the absolute differenceof each one of the n values from etT oF . Ultimately, out of then collected ToF values, we exclude the ones that fall outsidethe one deviant limit. The final btT oF value is calculated byaveraging the remaining m values. It is then converted todistance by first subtracting from it the calibration value(tmin), then dividing the calibrated value by two, to get asingle-way ToF time (tT oF final

¼ 12

ð btT oF tminÞ) and finallymultiplying the previous value by the speed of light in air(c/1.0003) to convert time to distance

3.1 Implementation and Evaluation

The ranging system was implemented on the T.I EZ430-RF2500 platform, and two types of nodes were designatedand programmed with different pieces of software. Arequester node, which is in essence node A, that initiates theentire tracking operation, logs the two-way timing valuesand executes the calculation phase and a responder that actsas the relay node B. The clock on node A was set to themaximum possible frequency of 16 MHz. We carried outexperiments in various environments outdoors and in-doors with 1,000 ranging transactions at data rate settings

250 and 500 kbps. The achieved accuracy was in the area of 1-3 m RMS.

To verify the distribution of the measurements that theproposed ToF ranging system yields, an experiment is

designed were two nodes are placed in short distance(2 m) indoors and a vast number of ToF estimates islogged over a period of time. Approximately 10,000 ToF

estimations were logged. Fig. 3 depicts the histogram of theobtained values, and it is clear that they can be consideredas normally distributed. However, considering a noise-freescenario with no timing uncertainties, the lower bound of the standard deviation of the measurements, for a setdistance, is extracted from the unit uniform distribution.This is given from T oF ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffið1=12Þ

p ¼ 0:28 cc (cc:clock

cycles). In practice, the standard deviation of the measure-ments is expected to be higher.

In our implementation, the node performed the calcula-tion phase whenever 100 two-way transactions werecompleted. Part of the process is the calculation of the

standard deviation for these 100 transactions to exclude thetiming values that fall outside the single deviant boundary.This procedure is repeated 10 times to reach the required1,000 transactions. From all the experiments carried out, thestandard deviation of the timing values was initially inthe range of 1.4-1.8 cc for the 500 kbps setting and 2.4-3 cc at250 kbps. After averaging the values (excluding the onesoutside the one deviant limit), the deviation was reduced to0.3-0.9 cc at both 500 and 250 kbps.

The deviation in the outdoors experiments was found to be smaller than the one indoors. Particularly, for the500 kbps data rate setting, which is used in the trackingsystem, the standard deviation that the two-way rangingvalues exhibit was approximately 0.4 cc on average.Dividing this by 2, we get T oF ¼ 0:2 cc. This value isexpressed in clock cycles and a single clock cycle of the16 MHz timer is (1/16 MHz) ¼ 62:5 ns. Thus, the standarddeviation of the proposed system can be approximatedas T oF ¼ 12:5 ns. This translates to a standard deviation of approximately 3:7 m calculated from ranging ¼ c tof .

4 TRACKING SYSTEM OVERVIEW

The theoretical foundation of the proposed range-onlytracking system is provided here. We consider a scenario

where a dedicated WSN is deployed in an area, to track atarget of interest. A number of anchor nodes are consideredto be deployed in known positions. Fig. 4 illustratesthe envisioned setup. The proposed tracking system is


Fig. 3. Timing histogram of 10,000 two-way values at 500 kbps.

Fig. 4. Tracking system overview.

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formulated as a dynamic state estimation problem in thediscrete-time state-space domain. Here, we focus on themathematical formulation of the tracking problem assum-ing that the range observations become available from theToF scheme analyzed in the previous section. We alsoanalyze the developed tracking algorithms that are used tosolve the dynamic problem and infer the target’s kinematic

variables. To begin with, the state vector is populated fromthe target’s kinematic variables that the system attempts toestimate. Since we consider ground targets, we choose toestimate the target’s planar coordinates and two-axisvelocity. Thus, the state vector is given as

x ¼ ½x y vx vyT : ð1Þ

Next, we consider that the target’s motion pattern can bedescribed with the following dynamic model:

xðtÞ ¼ Fxðt 1Þ þ wðt 1Þ ð2Þ

.

where

¼

T 2s =2 0

0 T 2s =2

T s 0

0 T s

26643775; ð3Þ

. T s: is the sampling period.

. wðt 1Þ: is a 2 1 i.i.d process noise vector withdimension of acceleration m=s2, sampled from aknown distribution that represents any mismodelingeffects or disturbances in the motion model

.

and xðtÞ: is the state vector, defined in (1).We follow two different approaches in populating the

motion matrix F in (2). In the first approach, F is formedaccording to the constant velocity model under which, thetarget is assumed to be constantly moving with velocityaround a certain value. In this case matrix, F is given as

F ¼

1 0 T s 0

0 1 0 T s0 0 1 0

0 0 0 1

26643775: ð4Þ

One of the main objectives of the proposed tracking

system is to provide enhanced support in trackingmanoeuvring targets. To achieve this, we adopt anapproach where the state-update equation is modeled withthe use of multiple switching dynamic models. This methoddescribes more accurately the pattern of a manoeuvringtarget and effectively captures the sudden changes in thevelocity vector that manoeuvring targets exhibit. In thiscase, our system is modeled using three switching dynamicmodels. The models we consider are the CV modeldescribed previously and two coordinated turn models.

An integer parameter, termed as regime variable, isintroduced in the multiple-model case. The regime variable

rðtÞ dictates which of the three state models (regimes) is inuse during the time interval ðt 1; t. The regime variablerðtÞ is modeled as a time homogeneous, three-state, first-order Markov chain with transitional probability matrix

given by mn ¼4

ProbfrðtÞ ¼ m j rðt 1Þ ¼ ng. The probabil-ity matrix indicates the probability of a regime transitionoccurring, between consecutive sampling steps, as well asthe probability of the system remaining on the same regime(Fig. 5). In the multiple-model case, the state updateequation is formulated as follows:

xðtÞ ¼ FðrðtÞÞxðt 1Þ þwðt 1Þ: ð5Þ

The state transition matrix F at time t is definedaccording to the value of the regime variable rðtÞ,(FðrðtÞÞ). For r ¼ 1, F(1) is given from the constant velocity

motion model (4). For r ¼ 2 and r ¼ 3, F is definedaccording to the following coordinating turn models.The first coordinated turn model defined as

Fð2Þ ¼

1 0 sinð!T sÞ=! ðcosð!T sÞ 1Þ=!0 1 ð1 cosð!T sÞÞ=! sinð!T sÞ=!0 0 cosð!T sÞ sinð!T sÞ0 0 sinð!T sÞ cosð!T sÞ

26643775: ð6Þ

The second coordinated turn model given as

Fð3Þ ¼

1 0 sinð!T sÞ=! ðcosð!T sÞ 1Þ=!0 1 ð1 cosð!T sÞÞ=! sinð!T sÞ=!0 0 cosð!T sÞ sinð!T sÞ0 0 sinð!T sÞ cosð!T sÞ

2664

3775

: ð7Þ

T s denotes the sampling interval and w is the turningrate, expressed in rad/s and considered to be constant. Thetwo coordinated turn models are used to model turningmanoeuvres in the anticlockwise and the clockwise direc-tion, respectively. These type of motion modeling has beenused previously in scenarios involving bearings onlytracking as well as in aircraft navigation [28], [29].

4.1 Observations Model

The measurements vector obtained at each time stepcontains an estimation of the distance between the target’sposition and the position of each one of the N s anchornodes. These range estimations are produced with the useof the two-way ToF ranging method. Subsequently at eachtime step, the complete measurements vector is given asziðtÞ ¼ ½z 1; z 2; z 3 . . . z N s ; i ¼ 1; 2 . . . ; N s.

The completion of the dynamical system requires thedefinition of the measurements equation, which mathema-tically relates the observations zðtÞ and the state-vector xðtÞ.Since we consider ranging measurements, the equation isformed with the use of the euclidean norm:

ziðtÞ ¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiðyðtÞ yiÞ2 þ ðxðtÞ xiÞ2

q þ vðtÞ; ð8Þ

where i ¼ 1; . . . ; N s and xðtÞ, yðtÞ are the target’s x-ycoordinates at time t, and xN s , yN s are the coordinates of the anchor nodes, and vðtÞ is a N s 1 noise vector sampled


Fig. 5. Regime probability transitions.

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from a known distribution that represents the observationsnoise. From our ranging experiments, we see that theobservations error follows a Gaussian distribution withzero mean and 3.7 m standard deviation. The observationsnoise is the main source of error that affects theperformance of the tracking system. A detailed analysis of the factors that affect the accuracy of the ranging method isprovided in [27].

4.2 Tracking Algorithms

Based on the state model (single, multiple) that is used, wedevelop an algorithmic framework for the recursive solutionof the formulated tracking system. Considering the non-linear nature of the system, we choose to employ PF as the basis of our tracking algorithms. PF are a class of recursiveBayesian estimation methods inspired by the techniques of importance sampling and Monte Carlo integration [30], [31].In the Bayesian estimation framework, an unknown state (inthis case, the state vector xðtÞ) is estimated in a two-stageprocedure given the incoming measurements (observations)

and a mathematical process model [32].To calculate a state estimate at time t given the sequence

of measurements zðtÞ up to that time, the posteriorprobability density function (pdf) pðxðtÞ j zðtÞÞ of the stateat time t should be estimated. After obtaining the posteriorpdf pðxðtÞ j zðtÞÞ, an estimation of the state vector can then be produced with the use of a certain criterion like theminimum mean square error (MMSE). In PF-based algo-rithms, to estimate the pdf pðxðtÞ j zðtÞÞ at time t; N particlesare generated from a proposal distribution q ðxðtÞ jzðtÞÞ. Letus denote the generated particles at time t as xðtÞi and theircorresponding weights as wðtÞi. The weights are calculated

from wðtÞ

i

/ pðxðtÞ

i

j zðtÞÞ=q ðxðtÞ

i

j zðtÞÞ. After obtainingthe weight for each particle, an estimation of the desiredpdf at time t can be produced from: pðxðtÞ j zðtÞÞ ¼PN

i¼1 wðtÞi ðxðtÞ xðtÞiÞ, where is Dirac’s delta function.A well-known issue of concern in PF is the degeneracy

problem. In practical terms, after a number of iterations all but one particles have negligible weights. Thus, a sub-stantial amount of computation is devoted in updatingparticles with minimal contribution to the approximation of the pdf. To avoid this, a measure, called effective samplesize N eff , is introduced (N eff ¼ 1=

PN i¼1ðwðtÞiÞ2). A resam-

pling step is carried out whenever N eff is found to besmaller than a predefined threshold N thr. Resamplingeliminates samples with low importance weights whilemultiplies samples with high importance weights [30].

4.3 Range-Only Tracking Particle Filter Algorithm(ROT-PF)

The algorithm described in this section is intended for atracking scenario where the targets motion is represented bythe CV model. To begin with, we considered that both thestate and measurements noise follow known distributionsthat can be sampled. The transitional prior pðxðtÞjxðt 1Þ) ischosen as the importance density function to sampleparticles from. Initial particles (at time t ¼ 0) are drawn

from a distribution pðx0Þ that represents the system’s priorknowledge regarding the target’s initial state condition.

To produce a sample from the transitional prior, a noisesample wðt 1Þi is initially generated and used in (2) to

produce a sample xðtÞi distributed accordingly to thetransitional prior. Upon receiving a new measurement, theweight for each particle is computed. Because the transi-tional prior is chosen as the importance density function,the calculation of the weight for each particle simplifies to~wðtÞi / pðzðtÞjxðtÞiÞ which is the likelihood of the measure-ment vector (real observation) zðtÞ ¼ ½z 1; z 2 . . . z j, given thepredicted observation zðtÞi, calculated from (8), using thesampled particle xðtÞi. Since the measurements zðtÞ follow aGaussian distribution N ðv; vÞ, the weight ~wðtÞi for particlexðtÞi is calculated from

~wðtÞi ¼YN s

j¼1

1 ffiffiffiffiffiffiffiffiffiffi2 2v

p exp ðzðtÞ zðtÞiÞ2

2 2v

!: ð9Þ

The final step in the ROT-PF algorithm involves resam-pling, whenever N eff is found to be smaller than N thr.

4.4 Range-Only Tracking Multiple-Model ParticleFilter Algorithm (ROT-MMPF)

To recursively estimate the state vector in the multiple-model case, a multiple-model PF algorithm is employed.The state vector in the multiple-model case is theaugmented state vector that contains both the state xðtÞand the regime variable rðtÞ. The augmented state vector isdenoted as yðtÞ ¼ ½xðtÞ rðtÞ.

In this case, initial particles are drawn from twodistributions pðr0Þ and pðx0Þ. Particles for the state xðtÞare sampled from the transitional prior similar to the ROT-PF algorithm, while particles for the regime variable aresampled according to the transitional probability matrix ¼ ½mn. As with the ROT-PF algorithm, whenever a newmeasurement vector becomes available, the weight for eachparticle is computed by using the likelihood function pðzðtÞ j yðtÞiÞ, which in this case depends on the augmentedstate vector. Similar to the ROT-PF algorithm, the predictedobservation z ðtÞi is calculated based on the sampledparticles of the state vector xðtÞi using (8). The final stepof the ROT-MMPF algorithm includes the resampling stepwhenever it is necessary.

An iteration of the ROT-PF and the ROT-MMPFalgorithms is given in Fig. 6.

5 SIMULATION EVALUATION

This section provides results from simulating the proposedtracking system under various two-dimensional scenarioswhere a single target is considered. We aim to compare themultiple-model approach against the single-model one andinvestigate the effect on the achieved accuracy that thesampling interval and number of particles have. Moreover,we derive the theoretical CRLB of the proposed system andcompare it with results obtained from simulations. Toquantify the accuracy achieved in estimating the target’scoordinates, the root mean square error

RMSE ¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1=T XT

t¼1

ðxðtÞ xðtÞÞ2 þ ðyðtÞ yðtÞÞ2v uutis used. x and y denote the algorithm’s estimates of thetarget’s x and y coordinates, respectively, and T the total time.


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5.1 Multiple Model versus Single Model

Here, a comparison of the two approaches (single andmultiple models) that are employed to form the stateequation takes place. A scenario where the target performs

a predefined trajectory that involves a quick two-turnmanoeuvre is simulated with both state formulations. FromFig. 7, it is clear that the MMPF-ROT algorithm cansuccessfully track the target’s manoeuvres, while the PF-ROT algorithm keeps track of the target during the first turn but looses focus in the second turn and requires some timeto converge back to the target’s trajectory.

5.2 Sampling Interval—Number of Particles

Two of the system parameters that affect the accuracy of the proposed system in a real-world scenario are thesampling period (T s) and the number of particles (N ) the

PF algorithms employ to approximate the state vector.Increased T s translates to smaller number of observations becoming available to the system within a specific amountof time. T s is heavily dependent on the amount of time

required by the anchor nodes to collect and fuse the rangingestimates. Moreover, T s is also affected by the time the

system requires to run the tracking algorithm and producean estimate. Conversely, increasing N results in increasedaccuracy since the posterior pdf is approximated withhigher precision. To evaluate the effect of these twoparameters, we initially simulate the system for constantN ¼ 500 but with increasing T s ¼ 2; 3; 4; 5; 6; 7 sec andfollowing we maintain T s ¼ 2 sec and use a varying particlesize N ¼ 500; 1; 000; . . . ; 4; 000. For each set of values,100 Monte Carlo trials are conducted. At each execution,the RMSE for position was calculated, and finally, theaverage RMSE was calculated for the total of 100 runs. Fig. 8illustrates average RMSE results against both of theseparameters for the ROT-PF (a,b) and ROT-MMPF (c,d)

algorithms, respectively.5.3 Posterior Cramer-Rao Lower Bounds

The Cramer-Rao lower bound is a theoretically derivedlower bound of the second-order error of an unbiasedestimator, frequently utilized as a benchmark for evaluatingthe performance of dynamic estimation algorithms [33],[34]. In the majority of the situations, the CRLB is calculatedrecursively with the use of the Fisher information matrix.This bound is called “posterior” because it is applicable insystems modeled with nonzero process noise [35]. Wecompute the posterior CRLB for the two approaches used toformulate the state dynamics of the proposed range-only

tracking system. Moreover, simulations are presented toassess the performance of the proposed system against thetheoretically derived lower bound. For a dynamicalestimation problem, the covariance matrix PðtÞ of an


Fig. 7. Comparison of the two models under a manoeuvring scenario.

Fig. 8. The effect of the sampling interval and the particle size on the systems accuracy: (a) and (b) ROT-PF algorithm. (c) and (d) MMPF-ROTalgorithm.

Fig. 6. Pseudocode of the ROT-PF and ROT-MMPF algorithms.

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unbiased estimator xðtÞ of the state vector at time k has alower bound (CRLB) expressed in (10), where JðtÞ is theFisher’s information matrix

PðtÞ ¼4

IEfðxðtÞ xðtÞÞðxðtÞ xðtÞÞT g JðtÞ1: ð10Þ

5.3.1 CRLB for the ROT-PF Algorithm

In this case, the state equation is modeled with the use of theCV model. Considering the process noise to be zero

(wðtÞ ¼ 0), which means a purely deterministic trajectory,

matrixJðtÞ is recursively calculated from:JðtÞ ¼ ½F1T Jðt

1ÞF1 þPN s

i¼1 H ðtÞT i RðtÞ1

i HðtÞi, where N s is the number of

anchors, H ðtÞi is the Jacobian of the measurements equation

(rxðtÞz iðtÞ) with respect to the state vector, evaluated at the

true value of xðtÞ, and RðtÞ1i is the inverse of the

observations noise covariance matrix [36]. Since the initial

density to sample particles is chosen to be Gaussian

( pðx0Þ ¼ N ðx0; o;P0Þ), the iteration begins with J0 ¼ P10 .

The Jacobian matrix of the measurements equation zðtÞ is a

1 4 matrix given in

H ðtÞi½1; 1 ¼ ðxðtÞ xiÞ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

ðxðtÞ xiÞ2 þ ðyðtÞ yiÞ2q ;

H ðtÞi½1; 2 ¼ ðyðtÞ yiÞ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

ðxðtÞ xiÞ2 þ ðyðtÞ yiÞ2q ;

H ðtÞi½1; 3 ¼ 0;

H ðtÞi½1; 4 ¼ 0:

ð11Þ

To compare the ROT-PF algorithm against the CRLB,

we simulate the following scenario. Four anchor nodesare considered deployed at coordinates s1 ¼ ½10 0;

s2 ¼ ½50 0; s3 ¼ ½10 25; s4 ¼ ½50 25. In line with the theore-

tical assumptions, the process noise is considered

zero, while the observations noise is considered Gaussian

with v ¼ 3:7 m. The target’s initial state vector is x0 ¼

½10 m 10 m 0:1 m=s 0:1 m=s and initial particles are sampled

from a Gaussian distribution with 0 ¼ x0 þ N ð0; 1Þ and

covariance matrix S0 ¼ J10 ¼ diag ½1 1 1 1. This scenario

was simulated for 400 time steps for a total of 500 Monte

Carlo runs and the CRLB for position was calculated as:

CRLB pos ¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiJðtÞ1½1; 1 þ JðtÞ1½2; 2q ;

where JðtÞ1½1; 1 and JðtÞ1½2; 2 are the diagonal ele-ments of the information matrix corresponding to the

CRLB for x and y coordinates, respectively. Results areillustrated in Fig. 9, from where it is clear that theachieved RMS error follows a similar to the CRLB trendand is bounded by it.

5.3.2 CRLB for the ROT-MMPF Algorithm

In the multiple-model case, the derivation of CRLB is beingdone using the same approach as for the single-model casepresented previously. Consequently, taking into account azero process noise system, the CRLB is computed recur-sively for a sequence of regime variables [37].

Considering a specific sequence of regime variables

rðtÞl ¼4

frð1Þl; rð2Þl; . . . ; rðtÞlg, with l ¼ 1; 2; . . . ; st being the

possible regime values up to time t, the covariance of an

estimator of the state vector is given by (10) conditioned on

the particular regime sequence. Thus, PðtÞ ¼4

IEfðxðtÞ

xðtÞÞðxðtÞ xðtÞÞT jrðtÞlg ½JðtÞl1.

Fisher’s information matrix JðtÞl is computed for

the specific regime variable sequence rðtÞl from the same

equation as in the ROT-PF case. The conditional (on theregime sequence rðtÞl) CRLB is given as known from the

inverse of the information matrix, CRLB lðxðtÞÞ ¼4

½JðtÞl1.

Considering that at time k the regime variable can be any of

the possible sk different permutations, the unconditional

CRLB is calculated as the expectation of the conditional

bounds [37], CRLB ðxðtÞÞ ¼Psk

l¼1 prðrðtÞlÞ½JðtÞl1, where

prðrðtÞlÞ is the forward probability of a particular sequence

of regimes, of the first-order Markov chain defined by the

transition probability matrix ¼ ½ij.

Nevertheless, the computational complexity of the

CRLB, in this case, increases exponentially with time andrequires the enumeration of the growing regime sequences.

As a result, this bound can only be calculated for small

numbers of t [38]. For this, in a number of works on target

tracking [39], [40], an a priori known regime sequence RðtÞ

is considered. This sets the probability of that particular

sequence to “1” and the probability of any other regime

sequence to “0” in the CRLB equation. As a result, it is

simplified to: JðtÞ ¼ ½½Fðt 1Þ1T Jðt 1Þ½Fðt 1Þ1 þPN s

i¼1 ½H ðtÞ;iT RðtÞ1

i HðtÞi .

The evaluation of the CRLB for the MMPF took place both with the enumeration method as well as for a purely

deterministic trajectory (absent process noise, a prioriknown regime sequence). The simulation setup wassimilar to the one for the investigation of the CRLB for theROT-PF algorithm. The target’s initial state vector is x0 ¼½10 m 10 m 1 m=s 1 m=s. The manoeuvring turning rate wasset to wr ¼ =3. Initial particles for the regime variable weresampled with equal probability P 0 ¼ ½1=3 1=3 1=3, and thetransitional probability is set to m ¼ 0:95.

A realization of a regime sequence for K ¼ 100 timesteps was produced, and it was used to calculate the CRLBin a deterministic way for that particular regime sequence.This scenario was simulated for a total of 500 Monte Carlo

runs, and the results are shown in Fig. 10b. For theenumeration method, the total time steps were set toK ¼ 12. Results of 500 Monte Carlo runs are illustrated inFig. 10a. From Figs. 10a and 10b, it is clear that the RMSE of


Fig. 9. CRLB for the ROT-PF algorithm.

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the MMPF-ROT system follows a similar trend as thetheoretical CRLB for both cases.

6 SYSTEM IMPLEMENTATION AND

EXPERIMENTATION

In the prototype implementation of the complete trackingsystem, we designate three different types of wirelessembedded nodes. For each different class of nodes, a specificpiece of software was developed to implement the node’soperation. The T.I. EZ430-RF2500 hardware was used.

6.1 Anchor Nodes

The anchor nodes are a number of embedded nodesdeployed in known locations, and their mission is tointeract with the target node in order for the ranging datato be produced from the two-way ToF technique. Ourapproach is to designate the anchor nodes as respondernodes and have them operate in the exact way that the

responder node operates in the two-way ToF method.6.2 Target Node

The target node is the mobile object of which the trajectorythe system attempts to estimate. For the two-way ToFranging method we employ, it was deduced that the role of requester would be suitable for the target node. In theresulting system, the target initiated the communication between itself and the anchors. Initially, the target engagesin a ranging process with the first anchor node; as soon asthe nominal number of transactions is achieved and thetwo-way ToF estimate is calculated, the value is fused tothe central node and the target node carries on and executes

the ranging routine with the next anchor node. A data cycleis completed when the target node has acquired oneranging estimate from every anchor node. The fourestimates are sequentially fused to the central node at themoment of their production. The target node mustexchange ranging transactions on a one-to-one basis witheach one of the anchors within a single sampling period. Toguarantee this, and prevent message collisions between thetarget and the anchors, each anchors CC2500 radio isprogrammed to operate on a different communicationchannel. This approach allows the target node to completethe ranging process with a specific anchor without the risk

of another anchor node intercepting it that would result infaulty time readings. The target node is aware of thecommunication channel that each anchor operates on andloops through these during each sampling interval.

6.3 Central Node

The central node is responsible for the collection of rangingestimates and for the execution of the tracking algorithm.Several important challenges were considered in the designof the central-node software. First, the issue of timesynchronization between the data acquired and the

estimates produced. As soon as the central node acquiresthe required data from the anchor nodes, the execution of the tracking algorithm is initialized and the state estimatesare produced. Following, a new set of observations will beavailable at the central node, and the algorithm is executed based on the new set of data to produce the next stateestimate. It is imperative to ensure that both the operationsof continuous data accumulation and execution of thealgorithm will run in the central node effectively.

Under these conditions, a choice was made to employ alaptop as the platform to execute the PF trackingalgorithm. An EZ430-RF2500 node connected to a USBport acts as the bridge between the target node and thelaptop. The central EZ430-RF2500 node forwards eachranging estimate to its UART port that is connected to thelaptop and then the software running on the laptop takesover for further processing.

The tracking algorithm (either MMPF-ROT or PF-ROT)is implemented as a MATLAB routine. A top-level scriptinitializes the procedure, and it is there where all therelevant system parameters are set. These involve the noiselevels, the distribution from which the initial particles aresampled, the target’s initial location, the anchor’s positions,and the connection parameters with the EZ430-RF2500central node are all defined before the initialization of the

tracking operation. The front-end script monitors the serialport where the central node is connected and is pro-grammed to signal an interrupt whenever the requiredamount of bytes (i.e., four range estimates) is accumulated.The tracking algorithm routine is scheduled to runwhenever such an interrupt is raised. After the trackingalgorithm runs to completion, the results are stored andthe program waits for another set of ranging data to become available.

Different to our simulation experiments, the samplinginterval for the real-world experiments was not set to aconstant value. The sampling interval is the time elapsed

between two successive executions of the tracking algo-rithm or in terms of the state-space model, the time elapsed between the current and the previous state vectors. It is aparameter that has a significant effect on the system’s


Fig. 10. CRLB for the MMPF-ROT algorithm: (a) using the enumeration method and (b) using a predefined trajectory.

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performance as it was revealed through the simulationsinvestigation. In the real-world experiments, the samplinginterval is affected primarily by the amount of timerequired to collect a ranging estimate from all the anchors.Using an oscilloscope setup, we have measured that a singleranging estimate of the ToF method (100 two-way transac-tions), between a pair of nodes, requires approximately152 ms to be produced with the nodes placed close to eachother on the requester node. Subsequently, a systemsampling interval of less than 1 s (0.7-0.8 s) is expected inthe presence of four anchors, if no delays are introduced.

Nevertheless, in the event that the connection betweenthe target and the anchors is not ideal, retransmissions of the ranging messages may be required to reach the nominalnumber of 100 two-way transactions, which is required toobtain a ToF range estimate between the target and therespective anchor. Subsequently, this will result in anincrease of the sampling interval since more time isrequired to obtain the range estimates. To avoid using anerroneous sampling interval in our model, an adaptivescheme is employed. The sampling interval is calculated inMATLAB as the required amount of time to obtain the fourrange estimates (time when the interrupt is raised). Thevalue of a real-world clock is captured whenever aninterrupt is raised. By subtracting the previous value of that clock, the sampling interval can be calculated. Usingthis method, we guarantee that the state-update model thatis employed takes into account the varying amount of timethat has lapsed between two successive executions of thetracking algorithm.

7 EXPERIMENTS EXECUTION AND RESULTS7.1 Preliminaries

In the experiments carried out, the four anchors wereplaced in known positions in the corners of a 15 m 15 msquare area. The central processing node was placed on thetop of the square area. In our experiments, we restrained intracking a single mobile node. The target mobile node wascarried in the hands of a person who was walking withvarying speed (1.3-1.8 m/s) in the designated square area.Finally, the nodes were elevated from the ground (1 m) toavoid potential deflection of the RF signals from theground. The target node was carried at a similar height as

the anchor nodes. Fig. 11 illustrates the layout of theexperimental deployment. An area that allowed excellentLoS conditions was chosen. LoS is a requirement posed bythe ranging method, because its performance degrades innon-LoS conditions due to physical obstacles, causingmultipath propagation as well as diminishing the qualityof the link connection. As we showed in [27], the accuracyof the ranging method decreases in indoor conditions thatare expected to contain several physical obstacles (e.g.,walls, doors). Since the performance of the tracking systemis dependent on the accuracy of the ranging observations, itis expected that will deteriorate in indoor environments.

In all experiments, the nominal number of two-wayranging transactions with each anchor node was set to 100.The reason for choosing 100 two-way transactions toestimate the range between the target and each anchor is

related to the required real-time system operation.The EZ430-RF2500 does not have enough memory to storemore than 100 timing values, which means that to utilizemore than 100 transactions the ranging routine should beexecuted multiple times. This can done in situations (e.g.,ranging between nodes) where the real-time operation isnot a critical component. However, in the tracking systemwhere the ranging estimates must reach the central node ina timely manner with minimum delay, such an approachwould add significant latency that would hinder the abilityfor real-time operation. Due to the these issues, we chose toproceed with setting the nominal number of ranging

transactions to 100. With this setting, the minimumobserved value of the sampling interval during theexperiments was around 0.8 s, which verifies the scenariowhere no delays exist, and the maximum one around 2.2 s.

The rest of the parameters for the tracking algorithmswere defined as follows: The state noise was defined as zero-mean white Gaussian noise with w ¼ 0:5. Similarly, theobservations noise is also defined as zero-mean whiteGaussian with v ¼ 3:7. The targets initial state was known.The sampling interval was set as described previously(Section 6.3). In the implementation of the PF trackingalgorithms, the particle size was set to N ¼ 1; 500 to provide

robustness in case the sampling period increased. Thedistribution to sample the initial particles was a Gaussiandistribution with zero mean and unity covariance. Finally,the transition probability for the regime variable was set atm ¼ 0:8 for the MMPF-ROT algorithm. The constant turningrate was set at =4 rad=s. The data rate was set to 500 kbps.

To calculate the proposed system’s tracking accuracy, theoutput obtained from the system is compared with respectto the ground truth of the target. To effectively measure theground truth, the target’s trajectory was predefined beforethe experiments and divided into individual segments atwhich the target moved at a straight line with approxi-

mately constant speed. During the execution of theexperiment, we recorded the times when the ranging datafrom all nodes were collected (reached the central node).Additionally, the total time of each individual straight line


Fig. 11. The deployment of the anchor nodes and the dimensions of theexperimental area.

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segment was recorded. This facilitated the computation of the target’s true velocity in each segment of its trajectory. Byknowing the estimation times, we were able to interpolateand calculate the target’s ground-truth position and velocityat the time of the execution of the algorithm. Following this

approach, the state estimate produced by the system could be compared against an accurate enough approximation of the true target variables.

7.2 Experimental Results

In this section, we present results from a number of experiments that were carried out with the proposedtracking system. The experiments are categorized in threegroups based on the target’s trajectory; straight linetrajectories, trajectories involving one or two manoeuvres,trajectories involving more than two manoeuvres. Examplesof tracking results are illustrated in Fig. 12. The position andvelocity errors are calculated, for a total of 25 tracking

experiments, with respect to the ground truth. Thecollective performance results are illustrated in Table 1.

7.2.1 Comparison to Simulation Results

Here, we present a comparison between the resultsobtained from the full-scale experiments with simulationsresults obtained after simulating multiple times a trackingscenario similar to the one we experimented with in the full-scale experiments. Four anchors were considered placedin coordinates ((0 m, 0 m), (15 m, 0 m), (0 m, 15 m), (15 m,15 m)) exactly as in the outdoor deployment. The systemparameters (target’s initial state, distribution to sampleinitial particles), the PF algorithm parameters (particle size),and the noise levels were the same as in the full-scaleexperiments. To approximate the behavior the systemdemonstrated in the full-scale experiments, we used variedsampling interval. From the experiments, the observersampling interval value was in the range of 0.8-2.2 s.To approach this in our simulations, we randomizedthe sampling interval variable between 0.8 and 2.2 s. The

simulations were run for 30 time steps and with each stephaving varying sampling interval. This approach resulted insimulation executions that run for a total time similar to theone that the real-world experiments lasted for. Wesimulated this scenario for 100 runs and included both

random and deterministic trajectories. The deterministictrajectories were the same as the ones used in the full-scaleexperiments and included straight line trajectories as welltrajectories with predefined manoeuvres. The averageRMSE obtained from the simulation analysis is 2.5 m, aresult that is very close to the one (2.6 m) observed in ourreal-world experiments. Additionally, the accuracy in thevelocity estimation obtained from simulations is 1.89 m/sthat again is similar to the one obtained in the full-scaleexperiments (1.9 m/s). The histogram of the RMSE forposition, from 100 runs of this simulation setup, isillustrated in Fig. 13.

8 CONCLUSIONS

In this paper, we presented the design, implementation, andevaluation of a real-time, range-only target tracking systemfor wireless embedded nodes. The motivating idea of thiswork considers a small number of wireless embeddednodes (anchors) to be deployed in known coordinatestasked with acquiring ranging information and a centralnode that receives the accumulated data and executes thetracking algorithm in real time, to estimate the target’sposition and velocity. The proposed system aims to achieveaccurate performance, real-time operation as well asprovide support for manoeuvring targets. Tracking of targets is based on range observations produced byutilizing a two-way ToF ranging method. To provide


TABLE 1Accuracy Results from 25 Experimental Executions

Fig. 13. Histogram of RMSE evaluated from 100 simulations undersimilar conditions with the real-world experiments.

Fig. 12. Tracking results on various trajectories. Ground truth is given in black and the filter estimate in gray. Markers indicate position and arrowsvelocity. (a) Straight line trajectory. (b) and (c) Trajectories involving turning manoeuvres.

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enhanced support for manoeuvring targets, the targetspattern is modeled with the use of multiple switchingmotion models. Two PF-based algorithms were designed torecursively estimate the target’s dynamics. Simulations areconducted to quantify the effect that two important systemparameters, the number of particles and the samplinginterval have on the systems accuracy. Compared to theCRLB theoretical bound, the system’s performance is

shown to follow a similar trend. Finally, we implementedthe tracking system on T.I. EZ430-RF2500 hardware andconduct experiments in an outdoor area of 225 m2. From atotal of 25 experiments, an average accuracy of 2.6 mfor position and 1.9 m/s for velocity was observed.Additionally, the simulation investigation attests andverifies the accuracy levels and the system’s performance,as it was demonstrated in the real-world experiments.

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Evangelos B. Mazomenos received a diploma(five year degree) in electrical and computerengineering from the University of Patras,Greece, and the PhD degree from the Schoolof Electronics and Computer Science (ECS),University of Southampton, United Kingdom, in2006 and 2012, respectively. He received the2009 IET Leslie H. Paddle fellowship on post-graduate studies for his PhD research on real-time target tracking in WSN. Since January

2011, he has been a research fellow in ECS. His research interests arein the area of WSNs with a focus on positioning and tracking, biomedicalsignal processing, and Bayesian estimation.

Jeff S. Reeve received the PhD degree intheoretical physics from the University of Alber-ta, Canada, in 1976. He is a senior lecturer atthe School of Electronics and ComputerScience, University of Southampton, UnitedKingdom. He has previously worked as aconsultant in the communication and controlgroup of Plessey, Auckland, New Zealand, andin the Airspace division of Marconi Radar,Chelmsford, United Kingdom, where he worked

on tracking algorithms for primary and secondary radar. He has alsoworked with the Parallel and Distributed Computing and the Commu-nications Group within the School. He works in the Electronic Systemand Devices Group. He has more than 100 publications in distributedcomputing, network security, and network management. His currentresearch interests include wireless ranging and positioning and novelalgorithms in distributed and parallel computing. He is a charteredphysicist, a member of the IoP, and a senior member of the IEEE.

Neil M. White received the PhD degree from theUniversity of Southampton in 1988 for a thesisdescribing the piezoresistive effect in thick-filmresistors. He is the head of the Electronics andComputer Science (ECS) Department at theUniversity of Southampton. He was appointedas a lecturer within ECS in 1990 and promotedto senior lecturer in 1999, reader in 2000, andwas awarded a personal chair in 2002. Hisresearch interests include thick-film sensors,

intelligent instrumentation, MEMS, self-powered microsensors, andsensor networks. He has published more than 200 scientific papers inthe area of sensors and instrumentation systems and holds 10 patents.He received the 2009 Callendar silver Medal, awarded by the Institute ofMeasurement and Control for his “outstanding contribution to the art ofinstruments and measurement.” He is a senior member of the IEEE.

Andrew D. Brown received the first degree inphysical electronics at Southampton Universityin 1976, and the PhD degree in microelectronicsin 1981. He has been a member of academicstaff at Southampton since 1980 and became aprofessor in 1999. He spent time at IBM HursleyPark UK as an IBM visiting scientist in 1983, atSiemens NeuPerlach, Munich, as a visitingprofessor in 1989 and at Multiple AccessCommunications Ltd., as part of the Senior

Academics in Industry Scheme in 1994. He was appointed as anestablished chair of electronics at Southampton University in 1999. In2000, he spent a sabbatical at LME Design Automation working oncryptographic synthesis; in 2002, he received a Royal Society industrialfellowship for two years; in 2004, he spent six months in Trondheim,Norway, and in 2008, in Cambridge, United Kingdom, both sabbaticalsas a visiting professor. He has published more than 130 papers andedited a book in the field of design automation as applied to VLSI. He isa fellow of the IEE and the BCS, a chartered engineer, and a registeredEuropean engineer. He has been involved in two DTI TeachingCompany schemes, and numerous conferences in various capacities.He is a senior member of the IEEE.

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