Localization of Mobile Users Using Trajectory Matchinggraphics.stanford.edu/~wicke/publications/localization/lwkg-lomuut… · Localization of Mobile Users Using Trajectory Matching

Localization of Mobile Users Using Trajectory Matching

HyungJune Lee, Martin Wicke, Branislav Kusy, and Leonidas GuibasStanford University, Stanford, CA, USA

{abbado,wicke,kusy}@stanford.edu, [email protected]

ABSTRACTWe present an algorithm enabling localization of mov-ing wireless devices in an indoor setting. The methoduses only RF signal strength and can be implementedwithout specialized hardware. The mobility of the usersis modeled by learning a function mapping a short his-tory of signal strength values to a 2D position. We useradial basis function (RBF) fitting to learn a reliable es-timate of a mobile node’s position given its past signalstrength measurements.

Even though we deal with extremely noisy measure-ments in a cluttered indoor setting, nodes are not re-quired to be stationary during measurement or learn-ing. We evaluate our algorithm in a real indoor settingusing MicaZ motes, achieving an average localizationaccuracy of 1.3 m. In our experiments, using histori-cal data improves the localization accuracy by almost afactor of two compared to using only the most currentmeasurements.Categories and Subject DescriptorsC.2.4 [Computer-Communication Networks]: Dis-tributed SystemsGeneral TermsAlgorithms, ExperimentationKeywordsLocalization, Mobility, RSSI, Sensor Network

1. INTRODUCTIONWith the advent of ubiquitous wireless networks, sup-

porting mobility of users has become a key topic in net-work research. Localizing users moving through a net-work is a fundamental problem in this area. Accurateestimates of users’ locations enable more efficient rout-ing strategies in the presence of mobile nodes. Location-dependent network services, with application examplesranging from building automation to targeted adver-tising or augmented reality, first and foremost requirereliable localization techniques.

The field of localization has therefore been studied ina wide variety of research communities. Triangulation

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methods [12, 14] are among the most common. Thesemethods estimate positions from a number of distanceor angle measurements to beacon nodes, utilizing mod-els that describe how acoustic or radio signals propagatein space (such as the inverse-square law). Even thoughrelatively accurate models [20] for open areas exist, theyare of limited use indoors, where model inaccuracies dueto reflections and signal fading can lead to significantposition errors. Since no accurate and efficient mod-els of indoor signal propagation are available, a numberof methods pre-compute a signal-strength map of thecoverage area [1, 10]. These methods estimate positionof a node by comparing the signal-strength signatureof beacon nodes to the map. However, both acousticand radio signals indoors tend to be highly variable overtime, especially so for mobile users, resulting in reducedaccuracy of these algorithms.

In this paper, we focus on the problem of using re-ceived signal strength indicator (RSSI) measurementsto localize mobile users in indoor environments. Asthe structure of the environment is unknown, no goodtransmission model is available. However, in an indoorsetting, the user’s mobility is restricted by the environ-ment (we cannot go through walls), and we can assumethat not all possible movements within space are actu-ally realized. Rather, the users move along a limitedset of typical trajectories, suggesting that we can learnthe structure of the space of possible movements fromrepeated observation. We can use this inferred knowl-edge to locate users, and extrapolate our observationsto unknown trajectories.

One of the main problems when using signal strengthdata for localization is the large variance in these mea-surements. Our experimental data shows that the vari-ance due to reflections is particularly severe when eithertransmitter or receiver are moving, even at low speeds.Systems that use RSSI readings for localization there-fore use averages or require the nodes to be stationaryduring the measurement [1, 9, 10]. We propose to use afunction fitting and interpolation scheme to learn a po-sition function in the high-dimensional space of signalstrength measurements. We not only use the currentset of RSSI values for reachable nodes, but also a num-ber of past samples, thereby matching a trajectory insignal strength space to a position.

The learning process handles noisy input data grace-fully by computing a smooth approximation to the in-put samples. After a learning phase which requires posi-tion ground truth, queries to the localization subsystem

reduce to a simple function evaluation. We evaluateseveral versions of this algorithm, exploring differenttradeoffs between the memory requirements, commu-nication overhead, and localization accuracy. Our re-sults clearly indicate benefits of user movement history,almost cutting the position error in half compared tousing current measurements only. We also compare theaccuracy of our algorithm for three different link qualityestimators: received signal strength indicator (RSSI),link quality indicator (LQI), and packet reception ratio(PRR). Even though RSSI measurements are clearly su-perior, other link quality measures perform reasonablywell.

The rest of this paper is organized as follows: aftergiving an overview of related work in Sec. 2, we formallydefine the problem that we are solving in Sec. 3. Sec. 4describes our solution. We evaluate the performance ofour algorithm in Sec. 5 before concluding in Sec. 6.

2. RELATED WORKThe problem of localization and tracking has been ex-

tensively studied in robotics literature. Several variantsof the localization or tracking problem with or withoutlandmarks, with or without access to a map, and usingvarious forms of sensor input have been explored. Agood overview of the field is given in the introductionof [19]. While most of these approaches use visual orrange finding sensors, some are applicable to the prob-lem of locating users within a wireless network.

Spatial relations between nodes can be found usinga number of techniques, such as time of flight [14], an-gle of arrival of a signal [13], walking GPS [17], ultra-wideband [15], or Doppler shift ranging [8]. The local-ization problem is then solved using optimization tech-niques, for example [2, 4]. However, these techniquesoften require sophisticated hardware. In contrast, weassume that nodes are equipped with very basic hard-ware that only allows us to measure some kind of radiolink quality estimate.

Approximate point in triangle (APIT) [6] and DV-hop [11] are two representatives of range free algorithms.These algorithms estimate locations using simple radioconnectivity information from multiple beacon nodes lo-cated in the proximity of the unknown node. APITlocalizes nodes at an intersection of triangular regionsdefined around beacon nodes, whereas DV-hop trian-gulates the location using hop counts that estimate dis-tances between nodes. These approaches, however, weredesigned for static networks and thus do not supportmobility well. Moreover, their accuracy is often limitedby requiring dense deployment of sensor nodes.

RSSI pattern matching algorithms (RADAR [1], Mote-Track [10]) are closely related to our approach. Usersare localized inside a building using RSSI measurementsfrom fixed beacon nodes. As no reliable radio propaga-tion model is available, these techniques do not esti-mate Euclidean distances from the measured RSSI val-ues. Instead, they learn the properties of radio signalsfor a particular position. The location of the unknownnode is found by matching the current RSSI signature

of nearby beacons to this empirical model. This pro-cess was shown capable of eliminating multipath andshadowing effects, achieving meter-level localization ac-curacy.

Ladd et al. [9] proposed an indoor localization algo-rithm achieving an average error of 1.5 m. Similarlyto our approach they sense RF signal strengths usingstandard hardware (Ethernet cards). However, theirapproach suppresses mobility related variation of radiosignals, rather than utilizing it to its benefit: the train-ing algorithm requires a person to stand still for a fewmoments or requires filtering to calibrate mobile users.

The LOCADIO system [7] explicitly models movingvs. stationary users in a probabilistic framework. Ourmethod goes one step further: we are interested in mo-bile users and therefore explicitly use the history of theusers movement in the localization algorithm.

3. PROBLEM FORMULATIONThis paper describes an approach to the indoor local-

ization problem using signal strength measurements asinput. Given information about the connection qual-ity to close-by infrastructure nodes, we infer the posi-tion of a mobile device. In our experiments, connectionquality is measured by RSSI values that are providedby the wireless hardware. As some radio chips do notsupport RSSI measurements (e. g., the Nordic NRF903used in [16]), it is important to note that our approachdoes not depend on the presence of this specific typeof measurement. Packet reception ratios, which can beextracted in all wireless networks, can be used instead(see Sec. 5).

We assume that a mobile user moves through a net-work spanned by a set N , |N | = N cooperating infras-tructure nodes. The mobile node regularly broadcastsradio packets allowing for RSSI measurements. We as-sume that these packets are dedicated beacon packets,however, we believe that aggressive suppression of bea-con packets will enable virtually zero-cost localizationand tracking in practical applications, if regular networktraffic to and from the mobile node is present.

Whenever such a beacon packet is received by the in-frastructure nodes, we extract RSSI information, yield-ing values ri(t) that measure the signal strength of thepacket sent at time t, received by the infrastructurenode with ID i. For localization, we will not only con-sider the most recent RSSI values, but utilize historicaldata as well. For our computations, we assemble thesevalues into a vector

r(t) =

r1(t− 0∆t)

...r1(t− k∆t)

T

. . .

rN (t− 0∆t)...

rN (t− k∆t)

T . (1)

r(t) defines a point in the space Xk,N of sampled trajec-tories through RSSI space, in which most of our com-putations will take place. The localization problem canthen be described as finding a function L : Xk,N → R2

which maps a trajectory from Xk,N to its end positionin world space.

4. LOCALIZATION ALGORITHMOur approach learns function L defined in the previ-

ous section from examples that we obtain in a trainingphase. During the training phase, ground truth loca-tions of the mobile user are required, however, locationsof infrastructure nodes are not needed. We use radialbasis function fitting to compute a function that ap-proximates the (noisy) input examples and is able toextrapolate from those examples in a smooth fashion inthe localization phase.

4.1 Training PhaseIn a training phase, a mobile node explores the phys-

ical space that is covered by the network. While mov-ing around in space, both world space position p(t) =[px(t), py(t)]T and signal strength measurements ri(t)are recorded at discrete times tj . We then assemble thesampled trajectories r(tj), and form Ns pairs (r(tj),p(tj))that we use as training data. These pairs are samplesof the function L that we are trying to find, and imposeconstraints of the form

L(r(tj)) = p(tj). (2)

We use RBF fitting to compute a smooth function thatapproximates these constraints.

4.1.1 RBF FittingDue to space constraints, we will only briefly review

RBF fitting here, and refer the reader to [3] for an in-depth treatment of the subject.

We express the function L = [Lx, Ly]T as a weightedsum of kernel functions φ plus a polynomial Pα in r

Lα(r) =Nc∑i=1

wαi φ(‖r− ci‖) + Pα(r), (3)

where α = {x, y}. The number, Nc, and the placementof the kernel centers ci are free parameters. In ourimplementation, we use a linear polynomial Pα(r) =〈aα|r〉+bα. The kernel function φ determines propertiesof the solution, such as its smoothness. We use thecommon multiquadric φ(d) =

√1 + d2/σ2, with σ = 1.

To compute weights wαi , we minimize the quadratic

error at the constraints (2) by solving two linear systemsof equations for the variables [Wα,aα, bα]T

φ0,0 . . . φ0,Ncr(t0)T 1

.... . .

......

...φNs,0 . . . φNs,Nc

r(tNs)T 1

1c1

. . .

. . .1

cNc

0

[Wα

aα

bα

]=

pα(t1)

...pα(tNs

)0

, (4)

in a least-squares sense. Here, φi,j = φ(‖ri − cj‖) andWα = [wα

1 , . . . , wαNc

]T . If the number of constraintsequals the number of degrees of freedom, the computedsolution is exact and the function L interpolates thetraining values. For Nc < Ns, a least-squares approxi-mation the training data is computed. In our case, the

Figure 1: A map of the experiment area. Its sizeis approximately 30 m × 25 m. Shown are theinfrastructure node locations. Areas that wereaccessible to us are shaded.

training data is very noisy, and a smoother, approxi-mate solution is desirable. The optimal number of cen-ters depends on the complexity of L, in our case, 3000centers were optimal (see Sec. 5.2).

Since our kernel functions φ have global support andno singularities, the exact position of the centers ci haslittle impact on the quality of the solution as long as therelevant parts of Xk,N are well sampled. We place thecenters along the path by using a subset of the trainingsample positions as centers.

4.2 LocalizationOnce training is complete, we can use L to compute

the position of the mobile node given measured datar(t) along the trajectory of the node. The RSSI mea-surements that are the components of r(t) are noisy, andtherefore the computed position p = L(r(t)) is not re-liable enough. We remedy this by prefiltering the RSSImeasurements, in particular, by replacing r(t) by a low-pass filtered version r̄(t).

However, this introduces a bias in the localization:the computed position trails the true position as changesin the RSSI values r(t) gradually impact the low-pass fil-tered version r̄(t). We solve this by requiring the mobilenode to send a burst of b packets in a rapid succession(we use b = 5 packets in 50 ms) and using low-pass filterof width b. In our implementation, we use a simple boxfilter. This ensures that r̄(t) is rapidly updated, keepingthe position bias to a minimum.

5. EVALUATIONWe have validated our localization method in a small

indoor testbed. Fig. 1 shows a map of the space. We dis-tributed 11 MicaZ motes [5] in the area. A mobile motesends beacon packets in regular intervals. Infrastruc-ture nodes receive these packets and record sequencenumbers, timestamps, and various signal strength in-dicators. MicaZ’s CC2420 radio chip [18] allows us tomeasure RSSI and LQI for each received packet. Addi-tionally, we compute a packet reception ratio (PRR) bycounting the number of received packets in each burst.

1 : �

2 : ×3 : �

4 : N

5 : �6 : ◦7 : +

8 : �

9 : 410: •

t [s]

t [s]

RSS

I[×

102

dBm

]R

SSI

[×10

2dB

m]

0 20 40 60 80-1

-0.9

-0.8

-0.7

-0.6

-0.5

0 20 40 60-1

-0.9

-0.8

-0.7

-0.6

-0.5

Figure 2: Localization for routes (f) and (g). Figures on the left show recorded RSSI measurementsfor all nodes, figures on the right show estimated and ground truth locations (blue and red dots,respectively), corresponding pairs connected by a line.

As mentioned before, our method can be applied to anyindicator, as long as it gives some information about thedistance between transmitter and receiver. To studythe effect of measurement noise on the localization ac-curacy, the mobile node transmits a burst of 30 packets,rather than a single beacon packet. This allows us to ex-periment with different filtering techniques to improvethe input signal. Further, we chose ∆t=0.6 s in our ex-periments, i. e., the mobile node transmits one burst ofpackets every 0.6 s.

In the training phase, we require pairs (r(t),p(t)) asdescribed in Sec. 4.1. Therefore, we move the mobilenode along a predefined route through the experimentarea. We store timestamps for predefined waypoints,while continually recording RSSI and LQI at all nodes.The training positions p(t), which will also be usedas ground truth, are estimated using linear interpola-tion between the waypoints. Fig. 2 shows some of theroutes and associated RSSI measurements. In our ex-periments, we never use the same route for both trainingand evaluation.

5.1 Error MeasuresIn order to evaluate our algorithm, we compute two

error measures along the path. The position error

epos(ti) = ‖L(r(ti))− p(ti)‖ (5)

gives us information about the general performance ofthe localization algorithm. We also compute the dis-tance to the closest point on the path

e⊥(ti) = minp∈P

‖L(r(ti))− p‖, (6)

where P is the ground truth path that we are testingagainst. This error measure does not contain errors dueto imperfect timing information used for ground truthcomputation. It also contains information on how ac-curately a world-space trajectory can be reconstructedusing the localization data.

5.2 ParametersOur algorithm accepts several parameters that can

be tuned for optimal performance. The number of pastmeasurements k determines how much historical infor-mation about the trajectories is available. As can beseen in Fig. 3 (a), a value of k = 4 is optimal in ourcase. Note that this significantly outperforms the casek = 0, in which our algorithm reduces to a traditionallocalization method based on averaged RSSI measure-ments.

The properties of the fitted RBF function depend onthe number of kernel functions (centers) used. Varyingthe number of kernel functions, we see that using around3000 kernels is optimal in our setting (Fig. 3 (b)). De-creasing the number of centers degrades the qualityof the RBF approximation, while increasing it furtheryields a function that interpolates the constraints toofaithfully. Since the input data is very noisy, interpo-lation is not desirable. The optimal number of RBFcenters depends on the complexity of the environmentin which localization is attempted.

As described in Sec. 4.2, the function L is queriedwith a low-pass filtered RSSI vector r̄. Fig. 3 (c) showsthe influence of the width b of the box filter on the local-

× — position error◦ — path error

0

2

[m] 4

0 1 2 3 4 5 6 7 8 9 k

(a)

1

[m] 2

1000 2000 3000 4000 5000 Nc

(b)

0

1

[m] 2

1 5 10 15 20 25 30 b

(c)

0

1

2

[m] 3

RSSI LQI PRR(d)

Figure 3: Position error (epos, red) and path er-ror (e⊥, blue) depending on algorithm param-eters. The graphs show the mean error, errorbars represent 75% and 25% quantiles. (a) His-tory size k. (b) The number Nc of RBF centers.(c) Low-pass filter width b. (d) Measurementtype: RSSI, LQI, or PRR with 5 burst packets.

Figure 4: Routes used. (a)–(e) for training, (f)–(i) for testing.

ization results. Our experiments show that a moderatefilter width of b = 5 performs best. While lower valuesof b yield noisy measurements, high values of b smoothout important details and degrade the localization ac-curacy.

Unless otherwise noted, all results were obtained us-ing k = 4, Nc = 3000, and b = 5, as described above.

5.3 ResultsWe use a training set of 5 routes (a) - (e), each of

which we recorded 5 times. All errors are computed for4 different routes (f) - (i), each recorded several timesto obtain a total of 24 test routes. Although the routesused for testing are composed of path segments seenduring training, none of the testing and training routesare the same (see Fig. 4).

Table 1 summarizes the localization results. Overall,our method is able to localize a mobile node with a meanposition error of less than 1.3 m. If radio contact is lostentirely, we do not predict a location. Note that by lin-early interpolating position values between waypoints,we implicitly assume that the motion of the mobile nodeis of constant speed between waypoints. This assump-tion is generally not true in our experiments. We movedthe mobile device by carrying it while walking, and theroutes involved opening doors, and at one point, enter-ing a 6 digit access code. Given perfect ground truth,our results would probably improve further.

We can see in the experimental data that errors aremore likely to be along the path than perpendicular tothe path (c. f. Fig. 2). We attribute this in part to thesystematic timing errors in the ground truth. Table 1also contains the path error e⊥, which is not affected bytiming problems with the ground truth. However, it isalso invariant to other errors.

As mentioned above, our algorithm does not requireRSSI measurements, and can operate using LQI or ap-proximate PRR measurements (see Fig. 3 (d)). Us-ing these measures, the mean position error, measuredacross all test routes, then increases to 1.7 m and 2 mrespectively. Comparing the three measures, the reason

epos 2.5% 25% 50% 75% 97.5% max avg(f) 0.18 0.67 1.07 1.64 4.40 5.63 1.32(g) 0.14 0.58 0.98 1.58 3.40 4.88 1.20(h) 0.19 0.68 1.09 1.70 3.76 6.92 1.32(i) 0.20 0.58 0.97 1.64 4.30 8.22 1.25All 0.18 0.64 1.03 1.65 4.09 8.22 1.28e⊥ 2.5% 25% 50% 75% 97.5% max avg(f) 0.09 0.30 0.52 0.86 2.24 4.97 0.68(g) 0.07 0.23 0.34 0.51 1.46 4.03 0.44(h) 0.09 0.28 0.47 0.74 1.75 3.03 0.57(i) 0.08 0.26 0.38 0.65 2.47 4.36 0.56All 0.08 0.26 0.43 0.71 2.13 4.97 0.58

Table 1: Summary of localization results (in me-ters).

for the inferior performance of LQI and PRR measure-ments is easy to see: the LQI values remain high when-ever there is radio coverage and drop sharply as soonas connectivity is about to be lost. Therefore, thesemeasurements are good as an indicator for link quality,but contain only little information about distance ofthe neighboring node. PRR measurements have similarproblems: as long as no packets are lost, PRR provideslimited information about distance. As packets startbeing lost, the measurement is necessarily discrete. Inour case, we used averaging over only five packets, giv-ing us only a very rough idea of how good, or bad, thelink really is. In this light, the results for PRR are as-tonishingly good.

6. CONCLUSION AND FUTURE WORKWe have presented a novel method for locating mobile

users within a network using RSSI measurements. Thealgorithm uses not only the current RSSI measurementfor localization, but takes advantage of past values. Us-ing historical values significantly increases the stabilityof the localization. This is particularly important in in-door settings, where RSSI measurements are extremelynoisy, in particular for mobile nodes. Using trajectoryinformation in RSSI space allows us to locate mobileusers even while they are moving.

This research leaves ample room for future work. Thedimension of the RSSI trajectory space grows linearlywith the number of nodes. Therefore, exploiting localityis crucial to ensure the scalability of the algorithm. Lo-cal, overlapping localization areas can be used to solvethis problem.

Since we use past measurements at fixed time inter-vals, we implicitly assume that the speed of the mobileuser at a given position is similar during training andlocalization. Although the method can be trained fordifferent speeds, explicitly handling speed differences,for example using dynamic time warping, would be aninteresting extension.

7. ACKNOWLEDGMENTSThe authors would like to acknowledge their funding

sources: HyungJune Lee is funded by a Samsung Schol-arship. Branislav Kusy is a member of the Army High

Performance Computing Research Cluster TA3. Mar-tin Wicke is a postdoctoral fellow of the Max PlanckCenter for Visual Computing and Communication.

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