RSSI-Based Localization of a Wireless Sensor Node with aFlying Robot

Frank Bohdanowicz, Hannes Frey,Rafael Funke, Dominik Mosen, and

Florentin NeumannInstitute for Computer Science

University of Koblenz-Landau, Germany{bohdan, frey, rfunke, dmosen,

fneumann}@uni-koblenz.de

Ivan StojmenovicSIT, Deakin University, Australia

andSEECS, University of Ottawa, Canada

stojmenovic@gmail.com

ABSTRACTWe consider the problem of navigating a flying robot to aspecific sensor node within a wireless sensor network. Thistarget sensor node periodically sends out beacons. Therobot is capable of sensing the received signal strength ofeach received beacon (RSSI measurements). Existing ap-proaches for solving the sensor spotting problem with RSSImeasurements do not deal with noisy channel conditionsand/or heavily depend on additional hardware capabilities.

In this work we reduce RSSI fluctuations due to noiseby continuously sampling RSSI values and maintaining anexponential moving average (EMA). The EMA values en-able us to detect significant decrease of the received signalstrength. In this case it is reasoned that the robot is mov-ing away from the sensor. We present two basic variants todecide a new moving direction when the robot moves awayfrom the sensor.

Our simulations show that our approaches outperformcompeting algorithms in terms of success rate and flighttime. In field experiments with real hardware, a flying robo-copter successfully and quickly landed near a sensor placedin an outdoor test environment. Traces show robustness toadditional environmental factors not accounted for in oursimulations.

Categories and Subject DescriptorsC.2.1 [Computer-Communication Networks]: NetworkArchitecture and Design—Wireless communication

General TermsAlgorithms, Experimentation, Measurement

KeywordsLocalization, wireless sensor networks, received signal strengthindicator, simulation, field experiments

Permission to make digital or hard copies of all or part of this work forpersonal or classroom use is granted without fee provided that copies arenot made or distributed for profit or commercial advantage and that copiesbear this notice and the full citation on the first page. To copy otherwise, torepublish, to post on servers or to redistribute to lists, requires prior specificpermission and/or a fee. Request permissions from Permissions@acm.org.SAC’15 April 13-17, 2015, Salamanca, Spain.Copyright 2015 ACM 978-1-4503-3196-8/15/04...$15.00.http://dx.doi.org/10.1145/2695664.2695873

1. INTRODUCTIONWireless sensor and robot networks typically consist of a

large set of sensor nodes which are distributed over an area.Nodes are supposed to sense certain physical phenomenaand to report their sensor readings wirelessly to one or moredata sinks. In addition, a set of mobile autonomously actingrobots move through the sensed field. They are used formaintaining the sensor network or for reacting to measuredsensor readings.

Typical maintenance examples are sensor node replace-ment in case of node failure, or sensor node relocation andaddition for improving the network structure. Examples ofrobot interaction with the sensor network data readings arefire detection with subsequent robot assisted fire extinction,and intrusion detection with subsequent robot assisted re-connaissance.

In the aforementioned examples robots have to move toa certain area in the sensor field where one single sensor ora set of neighboring sensors is located. Within this workwe consider the most basic problem, where one robot has tomove to one single sensor.

We assume that no specific hardware features like direc-tional antennas or antenna arrays are available. Moreover,we do not assume any localization technique. We want tokeep both sensor and robot hardware as simple as possible.Our vision are large scale networks of smart miniaturizedparticles, where each particle should be as small, as energyefficient, and as cheap as possible.

The only system assumption we consider is that the sensornode can send a wireless beacon signal and that the robot iscapable of measuring the received signal strength. Moreover,the robot has to be capable of turning its current movementdirection roughly by 45◦ and 90◦. Our approach does notdepend on exact turning angles.

In this work we study to what extent the problem of spot-ting a sensor can be solved by an algorithmic solution giventhese limitations on available hardware features. The al-gorithm itself should be simple enough such that it can beexecuted on particles with very limited memory and com-putational resources.

The remainder of this paper is structured as follows. InSection 2 existing algorithmic solutions for spotting a sensorand for related problems are sketched. This is followed by adiscussion of signal strength measurements for sensor local-ization solutions in Section 3. We then describe in Section 4an algorithm for spotting a sensor which requires nothing

but the aforementioned model assumptions. We then showand discuss in Section 5 the results of a simulation studyunder realistic wireless communication model assumptions.Besides simulation, we also implemented our algorithm on ahardware prototype and performed empirical studies of ouralgorithm in the field (Section 6). Finally, we conclude anddiscuss possible future research directions in Section 7.

2. RELATED WORKWe now give a brief review on related work for detection

of a radio frequency (RF) transmitter.

2.1 Hardware based approachesThere are two distinguished approaches for locating an RF

transmitter: Angle-of-Arrival (AoA) and Time-of-Arrival(ToA). With AoA the position is triangulated based on theangle of several incoming radio signals. A well-known rep-resentative of AoA is High Frequency Direction Finding(HF/DF or huffduff ) a technique which can detect the di-rection towards active transmitters. ToA is based on a veryaccurate timing synchronization under the subscribing nodes(for example, Global Positioning System (GPS) is based onToA technique). However, ToA and AoA methods requirededicated hardware and increase the requirements for size,weight, cost, and energy consumption of a device. The samealso holds for the two approaches given in [1, 5]. In [1], themobile node’s movement depends not only on GPS but alsoon a uniform (although not necessarily regular) node deploy-ment, and the mobile node in [5] uses a directional antennato locate its target.

In this paper, we consider algorithmic approaches that arebased on received signal strength (RSS) for localization ofthe RF transmitter. RSS is defined as the voltage measuredby a received signal strength indicator (RSSI) circuit. TheRSSI of RF signals can be measured by almost every receiverduring communication and therefore, additional hardwareis not required. However, the lack of accurate localizationby RSSI values is elaborated in [3, 4, 10]. The positioningaccuracy using RSSI is typically limited by the behavior ofpath-loss, fading and shadowing phenomena. Further, in theextreme of its range, RSSI gives very unreliable results [9,13]and in consequence, raw RSSI values cannot be correlatedwell with the distance. Luckily, as shown in this paper,this drawback becomes negligible if the received signals aredifferently weighted and processed with a filter method.

2.2 Algorithmic approachesThe algorithms described in [2,11,12] are essentially based

on an idea to which we refer as direct line approach (see Fig-ure 1 for an illustration). Let m denote the position of therobot and t the position of the target node. Initially, therobot moves in random directions until it finds a directionin which RSSI increases, say in direction −→my. Eventually, iteither arrives at the target t (which can be claimed, e.g., ifa certain RSSI threshold is reached), or at some position pwhere RSSI starts to decrease. Under ideal model assump-tions (i.e., RSSI increases monotonically with decreasing Eu-clidean distance and the channel is noise-free), p is a pointof intersection of the straight line passing through m andy and the orthogonal to this line which passes through t.At position p either a clockwise (cw), or counter-clockwise(ccw) rotation by 90◦, leads to target t.

Figure 1: Illustration of direct line and steepestascend direction. Point m represents the mobilenode’s initial position and t is the position of thetarget node. This figure extends Figure 5 in [14].

Sun et al. [12] as well as Sheu et al. [11] consider the casewhere the mobile node overshoots the ideal point of rotationp due to a certain velocity of the vehicle. Carvalho et al. [2]introduced a two-phased approach: As long as the robot isin the “static RSSI range”, based on geometric considera-tions a direction of move is determined that leads into the“meaningful RSSI range” (the area around the target node,where RSSI is above a certain threshold). Within the mean-ingful RSSI range, the mobile node follows the direct lineapproach. Among these three approaches, the algorithm bySun et al. [12] is the only one which does not rely on odo-metric information.

The algorithms presented in [6, 14] follow an idea whichis similar to the direct line approach and to which we referas steepest ascend direction (see Figure 1). This approachgenerally requires that the robot is provided with odometricinformation. Instead of moving from m to the point p whereRSSI decreases, the mobile node moves to a point x 6= m,where difference in RSSI is large enough to estimate thelengths of the line segmentsmt and xt. Given in addition thedistance covered between m and x, the robot can computethe rotation angle Θ. Then, a clockwise or counter-clockwiserotation by Θ◦ leads towards target t.

Zhang et al. proposed two solutions for distance estima-tion: Algorithm rotation angle based on range and cosinealgorithm (RAC) makes use of a database, created from ex-perimental data, for mapping RSSI values to Euclidean dis-tances. Algorithm iterative maximum a posteriori (IMAP),uses Bayes’ formula to deduce the target node’s probabil-ity density distribution in the local target region from RSSIvalues. Then, the robot takes the point with the maximumprobability density as the estimated location [14]. The nav-igation algorithm by Lee et al. [6] assumes that the robot isequipped with an ultrasonic transceiver for distance estima-tion. In the second approach, they propose a different metricfor distance estimation: Essentially, nodes of a WSN com-pute their average of neighbors’ hop-counts which representdistances to the target node. Besides odometric informa-tion, all of these approaches assume error-free movement ofthe mobile node.

Algorithm Effective Movement Procedures (EMP) by Liet al. [7] differs from all of the aforementioned approaches.For RSSI based distance estimation, they make use of thelog-distance signal propagation model. In each iteration,EMP makes fixed length movements (half of the estimateddistance between current position and target position) inall four directions of the compass, while no actual positive

(a) Radiation pattern ac-cording to the Tmote Skydata sheet [8].

Far distance - tmote sky pattern

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(b) Heat map over averageRSSI values.

Figure 2: Radiation pattern and derived RSSI valueheat map.

progress has been detected. If no positive progress can bemade, the mobile node makes a move in random directionand continues with the next iteration.

3. RSSI MODEL AND MEASUREMENTSIn this work we consider RSSI value changes to align the

moving direction of a receiving mobile robot. The value ofthis measured variable highly depends on mutual alignmentof sender and receiver, attenuation along the communicationpath, and furthermore is subject to measurement errors atthe receiver antenna.

3.1 Mutual alignment of sender and receiverThe antenna radiation pattern highly depends on many

factors, like small differences between the individual nodes,the influence of reflections, and even small differences in dis-tance, height and node alignment between two identical fieldtests. We do not assume that the mobile node is alwayspointing exactly towards the sender node on the ground;actually then the sensor would already be spotted. In con-trast, the mobile node is moving in a certain direction notchanging its bearing. That means that the average RSSIvalues measured by the mobile node depend not only on onesingle radiation pattern but on the superposition of two, thesender’s and the receiver’s patterns, while the relative align-ment between those two patterns changes when the mobilerobot is moving.

In Figure 2(b) we depict a heat map over the averageRSSI values to be expected by the mobile robot at differentlocations around a node in the center of the map. The valueswere obtained as follows. We have used for both sender andreceiver the same radiation pattern (the pattern depicted inFigure 2(a), which is taken from the data sheet of the TmoteSky sensor nodes [8] used in our field experiments). For eachmeasurement point, the mobile robot was always aligned inone direction (e.g., always pointing to the north). We thencomputed the total antenna gain resulting from the senderand receiver antennas on a regular grid of sample locations.From these sample grid points the heat map was generated.

The figure shows the typical pattern we also obtained forother radiation pattern orientations and other sources likethose we obtained from own radiation pattern measurements

-60 -40 -20 0 20 40 60 80-100

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Ausrichtung 0° Ausrichtung 90°

Figure 3: Average RSSI values in dBm over com-munication distance in meters. Two measurementruns with different receiver node orientations (onewith 0◦ and one with 90◦).

with Tmote Sky sensor nodes in our field experiment set-tings. We always observed a general pattern where severalelliptical lobes are originating at the center. In all observedpatterns the lobes are mainly leading with increasing aver-age RSSI values towards the center.

3.2 Attenuation in the experimental settingFor the experimental setting with transmissions in the 2.4

GHz range, the mobile node has a small operating rangewhen spotting the sensor by merely listening to signal trans-missions from the sensor. To gain an insight which operatingrange we could expect in our experimental settings, we madea trivial measurement, measuring an average of around 200RSSI values with increasing distance to the sender node.Distances were increased on a line in 2 meter intervals. Fig-ure 3 shows the measured average RSSI values for two pos-sible orientations of the receiver node. The maximum dis-tance is reached when the average RSSI values are around−92 dBm (which is between the minimum receiver sensi-tivity of −90 dBm and the nominal receiver sensitivity of−94 dBm from the Tmote Sky data sheet). The differencesbetween maximum distance to the left and maximum dis-tance to the right is due to the different antenna gains causedby different antenna orientations.

We observed that beyond those distances (i.e., below anRSSI average of −92 dBm) transmissions were very oftenunsuccessful. Moreover, below an RSSI average of −86 dBmsuccess of transmissions began to degrade significantly inour experimental setting. Roughly, this was for a distanceat least beyond 30 meters (depending on the relative orien-tation of the sender and receiver antenna patterns).

3.3 Measurement errors at the receiverAlthough antenna gains originating from superimposed

radiation patterns should vary only in case of node mobility,measured RSSI values are noisy even if the receiver node isnot moving. To get an insight how far RSSI values are vary-ing in our field tests, we did several RSSI measurementswith increasing distance to the sender (the measurementswere done with two Tmote Sky sensor nodes). At each dis-tance we measured about 200 RSSI values over a period of20 seconds. Table 1 shows the result for one of those tests.The numbers are similar to those we got from other test runswith the same setting.

Table 1: Average and standard deviation of mea-sured RSSI values.

distance average standard deviation

0 m -60.93 dBm -66.7 dBm5 m -63.28 dBm -69.4 dBm10 m -67.24 dBm -75.3 dBm15 m -68.82 dBm -76.2 dBm20 m -80.76 dBm -88.0 dBm25 m -82.83 dBm -91.0 dBm30 m -86.28 dBm -91.4 dBm

An increasing distance should yield an increase in stan-dard deviation of average RSSI values since the received sig-nal strength decreases while the thermal noise at the receiverstays unaffected by the communication distance. At 11◦ Coutside temperature and 2 MHz communication bandwidthof IEEE 802.15.4, thermal noise at the receiver is around−111 dBm1.

The difference between the minimum RSSI values mea-sured here (which was around −86 dBm) and thermal noiseis thus around 25 dB, i.e., thermal noise is insignificant com-pared to the received signal strength. It follows that vari-ations of RSSI at the receiver antenna can only be due toother factors than thermal noise. Thus variations in RSSIvalues at a fixed location are mainly due to small distur-bances in node orientation and node positions (the nodewas mounted on a long bar and manually held in 3 metersheight). We observed similar fluctuations in RSSI values inthe field test with the flying robot, which was a quadcopterhovering in around 5 meter height. Due to many factors,this device never had an exact fixed location and orienta-tion. Though the device in principle stays at one place, dueto the aforementioned variations, RSSI values are subject tofast fading.

The experiments were performed outdoor, on an emptyfield and at adequate distance from possible other sourcestransmitting at the same frequency band. Thus, RSSI valuescould not deviate significantly above the signal strength afterpath loss. However, since signal strength can become arbi-trarily close to 0 (when in a deep fade), standard deviationdecreases over the distance since received signal strengthdecreases. For the measurement results depicted in Table 1(and for all other experiment runs we performed) we ob-served that the difference between average in dBm and stan-dard deviation in dBm seems to be independent on the dis-tance between sender and receiver (always measured to bearound 6 dB).

4. ALGORITHMSOur algorithms are aimed at coping with problems arising

with realistic signal propagation, while making minimal as-sumptions on the system’s hardware and initial positioning.

4.1 AssumptionsThe assumptions underlying our algorithm are as follows:

(i) The robot is equipped with sense of direction (e.g. itis equipped with a compass) that allows it to changethe direction of move, e.g., by 90◦.

1The thermal noise is computed by kT0B where k is theBoltzmann constant, T0 is the temperature of the systemand B is the utilized bandwidth.

Algorithm IterativeDirectLine

Input: threshold

1: Choose dir uniformly at random . Random initial direction2: rot_count ← 1 . For counting # of rotations3: while true do4: while indicator is non-decreasing do5: Move towards direction and return if

indicator > threshold . Arrived at destination6: end while7: dir ←rotate(dir,rot_count) . Compute rotation8: rot_count ← rot_count+ 19: end while

10: procedure rotate(dir,rot_count) . HalfPlaneExcluder11: if rot_count is uneven then12: return dir+ 90◦

13: else14: return dir+ 135◦ . −135◦ for LobeTracker15: end if16: end procedure

Figure 4: Pseudocode description of algorithm Iter-ativeDirectLine.

(ii) Initially the robot and the target node are in mutualtransmission range.

In particular, for the mobile robot we do neither assumeavailability of (geographic) location information, nor ad-ditional hardware that allows for determination of vehiclespeed or distance traveled, i.e., no odometric information isrequired. Assumption (ii) is quite natural and can be re-moved, when allowing the robot to move at random untilreceiving a beacon from the target node.

4.2 Algorithm descriptionAt first, we present a generalized version of algorithm di-

rect line (discussed in Section 2.2), called IterativeDirect-Line, from which we derive two instances, namely, the algo-rithms HalfPlaneExcluder and LobeTracker.

IterativeDirectLine proceeds as follows (see Figure 4 fora pseudocode description). Initially, the direction of moveis chosen uniformly at random, because without further as-sumptions, RSSI measurements do not allow to do any bet-ter. Afterwards, the robot always continues in current direc-tion of move until either a decrease of RSSI can be observed,or RSSI exceeds a certain threshold, an input parameter ofthe algorithm. In the latter case, a position near the targetis claimed and the algorithm terminates. In the former case,a suitable rotation is computed to change the current direc-tion of move by invoking procedure rotate. This procedureencapsulates the entire logic and can be used for arbitrarilycomplex rotation decisions (e.g., involving statistics on thehistory of RSSI, former rotation decisions, etc.).

We propose the following technique for detection of a de-crease in RSSI. The robot continuously samples RSSI val-ues. At algorithm start and at the beginning of each itera-tion of the main loop, the robot first collects sample sizemany RSSI values. It then computes the average RSSIvalue. This average is used to set up an exponential movingaverage (EMA). Every newly sampled RSSI value is usedto update the EMA. A decrease of RSSI is detected oncebad signal count many EMA values in a row are lower thanthe maximum value EMA has attained since its setup. SeeSection 5 & 6 for suitable choices of the parameters sam-

(a) (b)

Figure 5: In point c, HalfPlaneExcluder makes a cw135◦ rotation (dashed arrow), whereas LobeTrackermakes the corresponding ccw rotation (dotted ar-row).

ple size and bad signal count .Our first algorithm based on the above approach is called

HalfPlaneExcluder. It makes use of the number of rota-tions that have been performed so far. In case this number(rot_count) is uneven, a clockwise (cw) rotation by 90◦ isperformed, otherwise, a cw rotation of 135◦.

The idea behind this rotation strategy is illustrated by

Figure 5(a). Assume that−→ab is the current direction of move

(e.g., by initial random choice) and the number of performedrotations (rot_count) is currently uneven when entering theloop in line 4 of the pseudocode given in Figure 4. Eventu-ally, in some point b, a decrease of RSSI is observed. Thehalf-plane H1 being ahead and orthogonal to the current di-rection of move, is excluded from the search space and therobot performs a clockwise (cw) rotation by 90◦ and contin-ues moving. Eventually, in some point c the RSSI decreasesagain. The half-plane H2 being ahead and orthogonal to thecurrent direction of move is also excluded from the searchspace. This way, the search space is reduced to a 90◦ sector.The robot makes a cw rotation by 135◦ and moves alongthe remaining sector’s bisecting angle. It is worth notingthat without further assumptions on RSSI, the static sen-sor is not necessarily contained in the remaining sector fromsearch space. However, under the given assumptions andwithout additional knowledge on signal propagation, search-ing in this area is a sound decision.

The idea of our second approach, algorithm LobeTracker,is motivated by observations regarding the route producedby algorithm HalfPlaneExcluder, when applied under modelassumptions as described in Section 3. Consider the situa-tion depicted in Figure 5(b). The robot enters the yellowlobe and detects an RSSI decrease in point b and performsa cw 90◦ rotation. At point c RSSI deceases again. The cwrotation into the remaining search space can cause loops.In such cases it is beneficial to perform a counter-clockwiseinstead of a clockwise rotation. That is, to get algorithm Lo-beTracker, in the pseudocode provided in Figure 4, line 14has to be replaced accordingly and results in rotations assketched in Figure 5(a).

5. SIMULATIONThe problem of finding sensor nodes by RSSI measure-

ments becomes challenging due to the above-mentioned real-world effects like lobe-style antenna patterns and noise. Thegoal of our simulations is to assess the performance of variousalgorithms under the influence of the most significant effects.We extend the OMNeT++/MiXiM simulation frameworkby our empirically determined antenna pattern and set itup to employ the antenna gains and our empirically deter-mined noise characteristics together with a simple channelmodel and PHY layer. In a broad simulation study we com-pare our algorithms LobeTracker and HalfPlaneExcluder tothe algorithms EMP [7] and the algorithm by Sun et al [12].Here the algorithm by Sun et al. is a representative of direct-line algorithms introduced in Section 2 and EMP is the onlyother algorithm that requires no additional hardware capa-bilities, besides odometry. The results show that our algo-rithms outperform the other algorithms in terms of successrate and flight time.

5.1 Scenario and implementationOur simulation scenario consists of a flying robot and a

target node. The target node does not move and sends abeacon with 1 dBm power every 100 ms. The robot is ini-tially put at a random position within a circle of 40 m radiusaround the target node and moves in a random directionwith a constant speed of 1 m/s. Whenever the robot re-ceives a beacon, it determines the RSSI, updates the expo-nential moving average (EMA) of the RSSI values and exe-cutes an algorithm iteration. The algorithm decides whetherthe robot should continue to fly in the same direction orshould make a cw or ccw turn with a given angle. The turnis executed immediately and accurate. If the EMA of thereceived beacons’ RSSI values exceeds −60 dBm, the simula-tion finishes and the simulation run is considered successful.If the flight time of the flying robot exceeds 10 minutes, thesimulation run is aborted and considered as failed run.

We implemented the antenna pattern channel model as anextension to the SimplePathLoss model in MiXiM, which isequivalent to the Friis free space model. Our channel modeluses an antenna radiation pattern as input for the calcula-tion. We use the pattern of the Tmote Sky node, shown inFigure 2(a), that was reverse engineered from the radiationpattern plot for horizontal radiation in the Tmote Sky datasheet [8]. Each node has an absolute angle of orientation onthe ground. Using this angle and the senders’ and receivers’positions, we determine the relative angles, the receivers’ an-gle from the senders’ point of view and vice versa (mutualalignment of sender and receiver). Using the radiation pat-tern, this gives us two antenna gain values that are addedto the path loss.

We modified the PHY layer to implement the noise wedetermined empirically, as described in Section 3. We foundthat the standard deviation has a constant offset to the meanvalue of roughly 6 dB, i.e., the standard deviation is 6 dBless than the mean value. In the simulation we exploit thiscorrelation and model the standard deviation of the noise asa constant offset of the received noiseless signal. We simulatewith different offset values to evaluate the influence of thenoise intensity on the algorithms’ performance.

5.2 EvaluationIn a pre-evaluation we found the best alpha value for the

EMA to be 0.15 for our algorithm HalfPlaneExcluder and0.2 for our algorithm LobeTracker.

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Figure 6: Rate of runs that successfully termi-nated within the time limit of 10 minutes. Lobe-Tracker (LT) and HalfPlaneExcluder (HPE) are al-ways above 95%.

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Figure 7: Average travelled distance for runs thatsuccessfully terminated within the time limit of 10minutes.

We ran our simulation 1000 times for each parameter set.To assess the algorithms in different conditions, we ran thealgorithms with different noise standard deviation offsets be-tween 2 and 7 dB, where 2 is the strongest noise. The aver-aged results are shown with 95% confidence intervals.

Figure 6 shows the rate of successful runs. The successrate of our algorithms LobeTracker (LT) and HalfPlaneEx-cluder (HPE) is always above 95%. For strong noise (stan-dard deviation offsets of 2 to 4 dB) these algorithms signi-ficantly outperform the other algorithms. For weaker noise,the algorithm by Sun et al. is comparable to LobeTrackerand HalfPlaneExcluder and all three nearly reach 100%.

Figure 7 shows the travelled distance (covered distance)and Figure 8 shows the flight time (average execution time),for successful runs. Our algorithms LobeTracker and Half-PlaneExcluder perform equally good in terms of travelleddistance and flight time and outperform the other algorithmsin nearly all cases. Only for the weakest noise (offset 7 dB),the algorithm by Sun et al. reaches the target with slightlyless travelled distance.

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Figure 8: Average flight time for runs that success-fully terminated within the time limit of 10 minutes.

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Figure 9: Average distance from target at the mo-ment of successful termination.

Figure 9 shows the average distance of the robot from thetarget node at the moment of successful algorithm termi-nation. When comparing the results for weak and strongnoise, for our algorithms HalfPlaneExcluder (HPE) and Lo-beTracker (LT) there is a low increase in distance of at most0.5 m when the noise increases from offset 7 dB to offset 2 dB.For the other algorithms the distance increases by 1.5 to2 m. We believe that the generic trend of increasing dis-tance with increasing noise (decreasing noise offset) can beexplained because the impact of noise to the signal strengthincreases. Thus, there is a higher chance that signal strengthvariations due to noise will cause the threshold for successfultermination to be exceeded. Therefore, our interpretation ofthe divergent results between our algorithms and the otheralgorithms for low noise margins is that our algorithms getfaster closer to the center which reduces the chance of pre-mature termination due to noise rising the RSSI above thetermination threshold.

6. FIELD EXPERIMENTSThis section describes experiments that were conducted

to examine the performance of our LobeTracker algorithmunder real conditions. To minimize interference, we con-

(a) MK Quadro XL (b) Tmote Sky

Figure 10: Hardware

ducted our experiments in free terrain with the target nodebeing slightly elevated from the ground. Moreover, we paidattention to mild weather conditions to further reduce envi-ronmental influences.

We tested our algorithm using a quadcopter (copter) ofthe type MK Quadro XL, depicted in Figure 10(a), withGPS support for tracking of flight paths. The copter wasequipped with a BeagleBoard single-board computer thatwas responsible for the execution of our algorithm. Further-more, the BeagleBoard was connected to an IEEE 802.15.4compliant Tmote Sky node for sensing RSSI values receivedfrom another Tmote Sky node acting as target node (seeFigure 10(b)), and a Wi-Fi adapter to interact with the Bea-gleBoard from an external computer.

In all performed experiments, the copter was placed on theground within a range of 25 to 28 m apart from the targetnode, which was sending a broadcast packet every 100 mswith a power of 1 mW. The experiments were started froma laptop connected to the BeagleBoard via Wi-Fi while thecopter was standing on the ground.

Our first attempts revealed that the parameters deter-mined in the simulation were too strict for application inthe real experiments. Therefore, the flight speed was re-duced from 1 m/s to 0.7 m/s and the bad signal count wasincreased from 11 to 22. Furthermore, the threshold indi-cating if the target node has been detected was increasedto -45 dBm to achieve an acceptable approximation. Thesample size of 20 and the EMA’s alpha value of 0.2 wereinherited from the simulation. Finally, the copter’s altitudewas set to 3 m.

In two out of six experiments the copter took off, followedthe target node’s signal and landed in its vicinity in lessthan four minutes completely autonomously. The four re-maining flights did not reach the threshold of -45 dBm butalso succeeded in approaching the sensor. The results fromthe experiments are summarized in Table 2. For flights thatdid not reach the given threshold, we determined the bestEMA values reached and included the results for this situa-tion.

It is especially interesting that lower thresholds do not au-tomatically indicate better approximations as can be seenwhen comparing flight #1 and #5, or flight #2 and #6.These diverse results confirm irregular signal patterns de-scribed in Section 3 (e.g., if the copter advances through asignal lobe it reaches the threshold earlier and stops with ahigher distance to the target node as opposed to not hittinga lobe).

Figure 11 shows the final stage of experiment #2. Thecopter’s route to the target node (red circle) is drawn as a

Table 2: Results of the field experiments

# initial reached air target timedistance threshold route distance

1 26.06m -45 dBm 23.85m 9.78m 46 s2 27.53m -45 dBm 145.31m 2.94m 3min 45 s3 27.72m -46 dBm 79.37m 2.80m 2min 24 s4 26.36m -55 dBm 222.91m 11.68m 8min 1 s5 25.21m -49 dBm 50.96m 6.68m 1min 46 s6 27.86m -47 dBm 60.00m 2.28m 1min 49 s

-72 dBm-71 dBm-70 dBm-69 dBm-68 dBm-67 dBm-66 dBm-65 dBm-64 dBm-63 dBm-62 dBm-61 dBm-60 dBm-59 dBm-58 dBm-57 dBm-56 dBm-55 dBm-54 dBm-53 dBm-52 dBm-51 dBm-50 dBm-49 dBm-48 dBm-47 dBm-46 dBm-45 dBm-44 dBm

Figure 11: Final stage of experiment #2. White ar-rows indicate calculated directions of move. Actualflight paths deviate due to technical and environ-mental effects.

colored line indicating the received signal strength. Chrono-logically numbered black circles mark the positions wherethe copter was advised to stop. White arrows starting froma white circle (points of rotation) on the route denote theplanned flight direction produced by the algorithm after astop. Starting from the bottom of the figure the copter fliesnorthwards and reaches the first stopping position (causedby a drop in signal). At this point, the algorithm startsto collect 20 RSSI values. As the copter does not immedi-ately react to the issued stop command, it still flies furthernorthwards, which explains the drift between the black andthe white circle. This is interrupted by the collection of the20th RSSI value occurring at the white circle. At this point,the copter is instructed to do a 90° turn to the right andto follow the resulting direction. Simultaneously, the copterstarts to compute the exponential moving average (EMA)over the received RSSI values where the first EMA value isinitialized with the average over the just collected 20 RSSIvalues. The copter follows the current direction until 22EMA values in a row are lower than the best EMA seenso far since the last direction change. This is the case atthe second stopping position where the procedure outlinedabove is repeated, but this time performing a 135° turn tothe left. Three more turns (90° right, 135° left, 90° right)follow until the fixed threshold of -45 dBm is finally reached.

It can be observed that the stopping positions (black) andpoints of rotation (white) do not coincide and the tracing of

the planned flight directions is inaccurate. These deviat-ing movements emerge from the copter’s navigation controlcoping with environmental influences like inertia, wind andinaccuracy of the compass. Additionally, sudden movementsof the copter were transferred to the attached RSSI sensorand therefore caused unexpected fluctuations of the receivedsignal level misleading to wrong decisions (e.g. the copterchanges the direction of move too early). Due to these fac-tors and other real-world influences, the problem at handwas even harder to solve in the field experiments. Never-theless, the copter still managed to fly close to the targetnode, which indicates a certain robustness of our proposedalgorithm.

7. CONCLUSIONWe have considered an algorithmic solution for the local-

ization of a sensor node with a mobile robot by just usingnoisy signal strength measurements. Our studies show thatthis problem can be tackled by a simple algorithm with ahigh success rate and within short flight times. For practicalapplicability, however, it is most important to take irregular-ities in signal strength measurements seriously into account.We have implemented one of our localization algorithms ona quadcopter and we have demonstrated its functionality ina real-world test scenario.

For future research there are many interesting related prob-lems. A generalization of our problem statement would bethe localization of a set of neighboring sensors by a robot.Beacon signals of all these sensors could be used to improvesuccess rate and shortest path dilation of the robot. A fur-ther generalization would be to use several robots to localizeone or a set of sensors as a cooperating team. The corre-sponding algorithms need to be developed. Further, we as-sumed in this work that the robot already receives the signalof the sensor from the very beginning. However, in a largesensor field this is probably not the case. Thus, finding asensor would require cooperating with intermediate sensornodes. Our approach could be used as one building blockfor a more complex algorithm spotting the sensor or the setof sensors under consideration by multihop communication.

AcknowledgmentsThis work was supported in part by the German ResearchFoundation (DFG), grant “FR 2978/1-1”, by Humboldt Re-search Award for Ivan Stojmenovic, and by NSERC.

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