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A Pocket Guide to Indoor MappingPascal Bissig, Roger Wattenhofer, Samuel Welten,

Distributed Computing Group - ETH Zurich,firstname.lastname@tik.ee.ethz.ch

Abstract—In this paper, we present a way to obtain accurateWLAN signal strength maps in indoor environments, withoutdedicated hardware, and without a time consuming and compli-cated training process. We need two contributions towards thisend. First, we present a novel dead-reckoning technique, to gatheraccurate user motion estimates. This motion data is combinedwith information about the signal strength of access points ofthe wireless infrastructure. Our second contribution lies in theefficient integration of this complementary information into asystem that allows for easy mapping and requires nothing buta smartphone. All the required data is gathered from peoplewalking casually around in an area of interest while carrying asmartphone in their pocket.

Index Terms—Spatial signal strength distribution; motionestimation; localization; SLAM, Graph-SLAM;

I. INTRODUCTION

Today, GPS is an essential component of the global informa-tion infrastructure. Similarly to the Internet, its applications areaffecting many aspects of modern life. Although GPS satellitescover our globe, and current smartphones are equipped withsuitable receivers, GPS based localization still has its blindspots, in particular if a user enters a building. Often, navigatinginside an unknown building can be just as hard (if not harder!)than navigating outside, in free space.

WLAN signal strength based indoor localization is widelyused today. However, for such a system to work, knowledgeabout the spatial signal strength distribution is required. Inthis paper, we present a way to obtain accurate WLAN signalstrength maps that can be used to localize any WLAN enableddevice localization similar to GPS also in indoor environments,without dedicated hardware, and without a time consumingand expensive training process.

Our paper has two main contributions. The first contributionis a novel motion estimation technique that allows us to gatheraccurate user motion data in an unobtrusive way. The requiredsensors, a 3-axes accelerometer and a 3-axes gyroscope, canbe found in many modern smartphones. Using these sensormeasurements, we show how the direction of the leg andhip can be accurately estimated, independent of how thesmartphone is placed in the trouser pocket. Based on theseestimates, we can track the heading as well as the distanceof each step the user takes. This motion model is tailored tofit the requirements of tracking users in indoor environmentsand therefore does not utilize the (often unreliable) magneticfield to determine the absolute heading. Instead, the change inheading between steps is estimated. We evaluate the perfor-mance of this motion model and show that despite our non-restrictive sensor placement and the lack of absolute heading,we still manage to get a qualitatively high motion tracking

performance. We also show how the motion model is able toextrapolate from a single configuration parameter to work atdifferent walking speeds. As we will show, our motion data islocally highly accurate, i.e. short walks with a smartphone doexhibit a small relative positioning error.

The positioning error is growing with distance though, sowe use information about the signal strength of access pointsof the wireless infrastructure to globally correct that. Oursecond contribution lies in the integration of the complemen-tary information – the locally accurate motion data and theglobally accurate signal strength data – into a system thatallows for easy mapping with nothing but a smartphone inthe pocket. More precisely, we obtain additional positioningconstraints between locations that the user has visited whilewalking around in the area of interest. We use the common(least-squares) Graph-SLAM technique to obtain correctedpositions for all the signal strength measurements that a userrecorded. Compared to the Monte-Carlo technique which ismost commonly used for such applications, the Graph-SLAMmethod leads to maximum likelihood estimates of the signalstrength measurement locations. Furthermore, Monte-Carloapproaches have to back-propagate newly gained insights afterloop closure; this is not required when using least squaresand greatly improves performance when combining data frommultiple measurement sessions or users. As a result, the systemis capable of recovering accurate relative positions of thesignal strength measurements from data that was captured bymultiple users walking through an area at different times. Weshow a qualitative example for the mapping performance in alarge university building.

II. RELATED WORK

Crowd-sourcing Localization. Recent work presented by Raiet al. [1] shows the high interest in localization solutionsrelying on crowd sourced data rather than time consumingtraining. The introduced system [1] can provide localizationinformation using only crowd-sourced information. Motionestimates and WLAN signal strength measurements are fusedusing a particle filter approach which also requires a floorplan map. As a result, the locations of the signal strengthmeasurements within the floor plan can be estimated. Highlocalization accuracy is achieved. However, the required floorplan map has to fulfill strict requirements in order for theparticle filter to converge to the correct WLAN signal strengthmeasurement locations. The probability density that has to beestimated with a particle has four dimensions which impliesa high computational complexity on the mobile device. Ourapproach does not require a map and the use of efficient sparse

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non linear solvers that are readily available, the computationalcomplexity is lower.

Signal Strength Mapping. The problem of acquiring signalstrength maps in an unsupervised manner has been approachedby Chintalapudi et al. [2]. The system they presented allowsWLAN signal strength based localization without annotatedtraining data. No motion data is used in the process. Instead,the relative positions of WLAN Access Points and mobile nodelocations are modeled as a function of the received signalstrengths. The resulting set of overdetermined geometricalconstraints is solved using a genetic algorithm. OccasionalGPS location measurements are used to obtain location infor-mation in the global frame. However, GPS measurements arehard to obtain in indoor environments and may be erroneous.The received signal strengths are the only indication forgeometrical distance. Due to non-line of sight effects in indoorenvironments the complexity of this relationship is beyond thereach of the simple model used in the paper. This shortcomingbecomes evident as the localization accuracy drops if theaccurate locations of the access points are provided in thetraining phase. Therefore, the model might be accurate enoughto provide localization capabilities, but the estimated map willin reality never converge towards the accurate access pointdistribution. In our approach, a person’s motion is estimatedin order to get geometrical distance information. The measuredsignal strengths are only utilized to recognized previouslyvisited locations. Therefore, even if associations are incorrect,our maps converge to the accurate signal strength distributionbecause the increasing number of unbiased distance estima-tions from our motion model.

Motion Estimation. The dead-reckoning method we presentin this paper is the enabling factor that allows us to createsignal strength maps. Many such methods to estimate humanmotion using foot-mounted sensors have been described inthe literature [3], [4], [5], [6]. These solutions rely on the footbeing stationary when in contact with the ground. This zero-velocity interval can be used to counteract the velocity esti-mation drift caused by integrating the accelerometer signals.An overview of different methods to estimate motion basedon foot-mounted sensor measurements have been comparedby Skog et al. [7]. Another approach, relying on sensors fixedon a helmet was presented by Beauregard [8]. As our goalis to perform mapping in an unobtrusive way, we desire tomeasure user motion based on its natural location when usersare casually walking around. Therefore, all motion estimationmethods that require dedicated hardware such as bodily fixedsensors are useless if we want to allow a wide range of usersto contribute in the mapping process. Our motion estimationmethod only requires a modern smartphone being placed in atrouser pocket which makes it tangible for many people now,and even more so in the future. A motion estimation methodthat is seemingly similar to the one presented in this paperwas described by Blanke and Schiele [9]. This method anda selection of others that are equally nonrestrictive about thepositioning of the sensors have been experimentally comparedby Steinhoff and Schiele [10]. While the motion direction isestimated using the available sensor measurements, the step

length was assumed to be constant and even manually setfor each track. The presented evaluation does not allow us toquantitatively benchmark our approach because the evaluationresults are distance- and orientation error quantities for eachstride. The results are median stride length errors of more than10cm and median orientation errors of more than 5◦ whereaswe achieve mean localization errors of below 10% of thetraveled distance. However, the argument that an estimationerror of 10cm per stride is already more than 10% of thetraveled distance is highly questionable. Partly due to measure-ment errors in the ground truth but also because our approachestimates not only step- heading and count but also distance.Also our motion model can cope with different walking speedswithout requiring the stride length to be manually configured.In addition to this, our approach does not rely on the useof magnetic field sensors to determine the absolute headingdirection. Due to the large magnetic disturbances that mayinterfere with finding the correct direction towards north,using magnetometers in indoor environments is questionableand may incur large and unexpected errors. As a result, ourapproach is not able to estimate absolute headings for thesteps, but only the change in heading for consecutive steps.Another system that is seemingly similar to ours, but requiringtwo separate, fixed sensors to estimate motion based on theorientation of the thigh was presented by Lee and Mase [11].

SLAM. In the robotics community, the Simultaneous Local-ization and Mapping Problem (SLAM) has been an activeresearch topic for over twenty years. Bailey and Durrant-Whyte [12], [13] summarized the most important results andsolution ideas. To apply these SLAM solutions, two comple-mentary information sources are required. Firstly, the motionof the measurement device has to be estimated. Secondly,previous locations have to be recognizable if visited again.Both requirements can be met with off-the-shelf smartphones.The known SLAM solutions already have been applied to theindoor mapping problem in several instances. Ferris et al. [14]introduced a method to build signal strength maps in in-door environments based on Gaussian Process Latent Variablemodels. Motion information is integrated with signal strengthobservations to estimate the signal strength distribution whichcan be used for localization. While the approach is ableto reconstruct topologically correct maps, the true geometricshape of the building could not be captured. Comparing theirreconstructed maps to ours (see Figure 6) clearly indicates thesuperior mapping accuracy of our approach. Huang et al. [15]presented an adaption of the Graph SLAM method whichuses WLAN signal strengths as observations. Pedometer andgyroscope measurements are used to estimate the user’s mo-tion. The results show that signal strength measurements aresufficient to recognize previously visited locations. We followthis approach and formulate a sparse non-linear optimizationproblem based on the motion estimates and signal strengthmeasurements. This has the advantage that many highly ef-ficient solvers are available and can directly be applied tosolve the mapping problem. Also this problem formulationallows us to combine motion and observation information frommultiple walks or even users. In the publication of Huang et

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al. [15], the resulting pose distribution is only shown for asmall building that allows for many loop closure constraints.Also, it is unclear how to crowd source the required dataas the motion estimation approach is assumed to be known.Our motion estimation approach allows us to present resultsfor larger buildings with sparser loop closure opportunities.Additionally, our approach requires only a smartphone as wellas existing wireless infrastructure.

III. MOTION

The algorithm we present to track the motion of a userrequires a 3-axes gyroscope and a 3-axes accelerometer to beplaced loosely in a trouser pocket. Modern smartphones notonly contain the required set of sensors, but are likely to belocated in a user’s trouser pocket. Additionally, the proximity-and light-sensors can be used to determine if the phone mightbe located in- or outside the pocket. The method is splitinto three parts which are described in the three followingsubsections. Firstly we show how the orientation changes ofthe phone can be estimated using the gyroscopes only. Theseorientation estimates are then used to track the motion of theusers thigh which allows us to find the exact moments in timewhen the leg reaches its extreme orientations as depicted inFigure 2. We then estimate the length and the direction of eachstep based on two consecutive orientation extrema.

Orientation. In indoor environments, the earth magneticfield is heavily disturbed by power cables, concrete rein-forcements and such. In addition, magnetic disturbances arecaused by varying electrical currents in the sensor frameitself. To complicate the use of these magnetic field sensorseven more, infrequent recalibration of the sensors occurredwithout notification. Since these errors are hard to accuratelymodel, we decided to not use the magnetic field sensor tocounter the heading drift caused by the gyroscopes. We foundthat the heading drift caused by the gyroscopes is nearlytime independent and can be effectively corrected with theobservation model presented later on. Therefore, we onlyuse the gyroscope measurements (ωx, ωy, ωz) to estimate theorientation quaternion q which can be computed using theHamilton product:

qt = qt−1 · (1,ωx

2,ωy

2,ωz

2) (1)

This orientation estimate relates the sensor frame to an arbi-trarily chosen coordinate frame which has an offset to theearth coordinate frame that is governed by the gyroscopedrift. While the orientation estimate drift leads to errors inthe motion estimates, knowledge of the absolute orientationin the earth coordinate frame is not required.

Rotation Based Step Detection. The following step detectionand estimation is based on the assumption that a smartphonethat is placed in a trouser pocket approximately follows themotion of the thigh. We use this assumption to infer theevolution of the orientation of the thigh and the axis aroundwhich it rotates (the hip axis). We then use these vectorsto find orientation extrema which we use to determine stepdirection and distance. The most relevant vectors that are

used in the following discussion are shown in Figure 2. Inthe following discussion, all vectors are expressed in sensorcoordinates. The acceleration of the earth’s gravitational fieldg is transformed into the sensor coordinate frame using theorientation quaternion q from Equation 1. In a first step, the

φ(tmin)φ(tmax)

Fig. 2. The most important vectors used to find φ(t) are shown for a minimumof φ(t) and a maximum of φ(t) respectively. The leg direction L is shown inred, the hip direction H is shown in green (points out of the image), the earthgravitational force g is shown in blue, the inclination angle φ(t) is shown inyellow and the vector used to find the inclination L × H is drawn in black.

direction of the leg L in the sensor coordinate frame can beestimated using a low-pass filter:

L = LC · L + (1− LC) · g

The cutoff frequency LC =√L · g is chosen to allow

the leg estimate to quickly converge whenever the deviceorientation relative to the thigh changes. During normal use, Lis oscillating around g and the leg estimate is not significantlyconverging towards g. The normalized estimate L

|L| can beused to determine the rotation axis between the leg and thedirection of the gravitational force:

r = g × L

Based on the rotation axis r, we estimate the direction of thehip H using a low-pass filter:

H = HC · H + (1−HC) · r (2)

The cutoff frequency HC = |sin(|r|)| is chosen to increasethe influence of the rotation axis r on the hip estimate H if theangle between L and g grows. The reason for this is the fact,that the rotation axis can be determined with higher accuracy ifthe angle between the two vectors is larger. In case the rotationaxis is pointing into the opposite direction of the hip estimate,the rotation axis is reversed (r = r · signum(r · H))before applying the low-pass filter in Equation 2. The hip axisH converges to one of the two (opposing) main rotation axesof the leg. In the absence of absolute heading information, thetwo convergence possibilities of H deliver equal estimation

4

t [s]

a[m s2

]

15 20 258

10

12

14

t [s]

φ(t

)[r

ad]

15 20 251

1.5

2

Fig. 1. A comparison of the accelerometer magnitude (left) and inclination angle φ (right) during several steps on a threadmill. The treadmill setting for themeasurements was set to 1 km

h. Clearly the inclination φ is suitable to detect steps.

performance and results. The hip- and leg-direction estimatesare then used to find φ(t):

φ(t) = arccos ((L × H) · g) (3)

The evolution of φ(t) is used to find the points in timewhere the the thigh is maximally displaced. Figure 1 visualizesφ(t) and for comparison also shows the evolution of theacceleration magnitude signal a(t). In phi(t) the minima andmaxima are easy to detect whereas in the accelerometer signal,it is extremely hard to extract isolated steps. Each minimumand maximum in φ(t) corresponds to the end of the last stepand the beginning of the next. With accelerometer based stepdetection methods, counting steps gets increasingly difficult atlow walking speeds, as the foot impact gets less articulated inthe accelerometer signal. In addition to this, φ(t) allows us notonly to count steps, but also to find the orientation extrema ofthe leg swing which allows us to accurately estimate the steplength and direction.

Step Estimation. The direction and length of each step isestimated based on the smartphone orientations recorded inthe minima and maxima of φ(t). The change in orientationbetween minima and maxima can be expressed as axis aand angle α. Because absolute heading information is notavailable, a can be used as the walking-direction. The angleα can be used to estimate the step length.

s =a

|a|· c · sin

(α2

)(4)

The constant c is user dependent and has to be configured.

IV. OBSERVATION

In addition to the motion data, the smartphone is able torecord the evolution of received signal strength indicators(RSSI) for all visible access points. In indoor environments,inferring distance from received signal strengths is infeasible.Non-line of sight effects and antenna imperfections lead to aspatial signal strength distribution which cannot be capturedin a function that depends on the distance between senderand receiver. This is why we use these signal strength mea-surements not to infer physical distance, but to recognizepreviously visited locations only. We achieve this recognitionby comparing two landmarks L1 and L2 using the following

signal space distance measure:

s(L1, L2) =1

|M1 ∩M2|∑

e=M1∩M2

|M1(e)−M2(e))|

+1

|M1 \M2|∑

e=M1\M2

|M1(e)− lmin)|

+1

|M2 \M1|∑

e=M2\M1

|lmin −M2(e))|.

(5)

The sets of visible access points are denoted as M1 and M2

respectively. Access points that report an RSSI lower than lmin

are neglected. In addition, access points that are only visible inthe other landmarks are considered to be received with signalstrength lmin. Two landmarks assumed to be captured in thesame location (associated) if their distance measure s(L1, L2)is lower than a threshold sth.

V. FUSION

The complementary characteristics of the motion- and ob-servation association constraints can be exploited to counteractthe divergence of integrating motion estimates using the ob-servation associations. THe similar to finding the equilibriumpoint of a system of springs and masses. The visited locationscorrespond to the masses and are described as point in spaceas well as current motion heading xi = (x, y, φ). The motionand association constraints correspond to the springs. Thestiffness of the springs corresponds to the confidence level ofthe estimates. Whereas the association constraints are modeledas springs with equilibrium length zero and do not constrainthe heading difference, the motion constraints are modeled assprings with equilibrium length equal to the estimated steplength that also constrain the change in heading φ betweenconsecutive poses.

xi = fi(xi−1, ui) + wi. (6)

The pose xi is linked to the previous pose xi−1, using thesensor readings ui. The model uncertainty is captured in theGaussian noise term wi. Landmark associations are describedas follows:

0 = ||xik − xjk ||+ vk. (7)

This captures the fact that if we associate two landmarks, weexpect them to be recorded in spatially close locations. TheGaussian noise term vk may vary depending on the association

5

Treadmill speed [kmh ]

Spee

des

timat

e[ms

]

3 4 5 60.5

1

1.5

2

Fig. 3. Comparing the motion model speed output to the ground truth(Treadmill speed setting). Clearly, the motion model output linearly dependson the actual walking speed which means that when properly configured, themotion model will work at different walking speeds.

quality where k addresses one specific association betweentwo poses xik and xjk . The optimization problem is definedas follows:

Θ∗ = argminΘ

[ M∑i=1

||fi(xi−1, ui)− xi||2Λi

+

K∑k=1

||xik − xjk ||2Σk

].

(8)

For simplicity, the notation ||e||Σ = eᵀΣ−1e was used. Thesolution is the set of poses Θ that minimizes the givencost function based on the constraints obtained from themotion- and observation model. We solve the sparse non-linearoptimization problem using iSAM [16].

Compared to a particle filter based approach, this non-linear least squares problem allows us to overcome the lack ofabsolute heading information as well as heading drift withoutincreasing the computational complexity. Note that a particlefilter would need to sample the joint probability functionof spatial location, heading offset and heading drift. Addingdimensions to the probability distribution causes the numberof particles to grow exponentially.

VI. EXPERIMENTS AND RESULTS

The following experiments were carried out using a Sam-sung Nexus S smartphone. In a first step, the motion- andobservation models are evaluated separately because the mo-tion model will deliver user specific performance whereas theobservation model will be largely user independent.

Motion. Firstly the speed estimation is compared to the actualwalking speed. A single user was walking on a treadmill whosespeed setting was used as the ground truth walking speed.The results shown in Figure 3 indicate a linear dependancebetween actual speed and motion model estimate. This is thedesirable outcome since it indicates that the motion modelcan be configured for a specific user with only one parameterand deliver accurate speed estimates over a variety of walkingspeeds. The variances shown for each treadmill speed settingindicates a large variance of of the speed estimates even thoughthe treadmill- and therefore walking speed was very constantduring the experiment. The results shown in Figure 3 wereused to find the parameter c from Equation 4.

Acc

umul

ated

erro

r[m

]

Track length [m]80 100 120 140 160 180 200

0

5

10

15

20

25

Fig. 4. Relating the traveled distance with the resulting motion modelintegration error.

The distance estimation was evaluated with eleven peoplethat were asked to walk down a 51 meter long straight hallway.The motion model output had a mean of 51.7 meters and astandard deviation of 4.4 meters. This result indicates, thatthe motion model may be adapted for different users. Toevaluate the motion model accuracy in a more realistic settingin which people were walking through hallways, doors andbends, the same eleven people were asked to walk along fourpredefined tracks with increasing lengths (51m, 81m, 120m,154m, 195m). All the tracks ended in their starting point whichmeans, the localization error after each track is captured inthe distance between start- and estimated end-point. Figure 4shows the increasing localization error caused by accumulatingmotion estimation errors. As expected, the localization errorincreases as the traveled distance grows. A large portion of theerror is caused by the drifting heading estimate which couldnot be corrected using the magnetic field sensors. Althoughthe closed tracks facilitate evaluating the localization error,note that this evaluation scheme does not capture the fact thatthe motion model might systematically over- or underestimatethe step lengths for different users. However, combined withthe results shown in Figure 3 and the distance measurementaccuracy of the straight hallway experiment we conclude thatthe motion model works for a variety of people walking atdifferent speeds only requiring to be configured at one speed,or even only using the users body height.

Observation. Observations are associated to each other iftheir mutual signal space distance is below a given threshold.Therefore, we require the signal space distance to be low fortwo spatially close fingerprints. On the other hand, comparingspatially distant fingerprints should lead to a high signal spacedistance. To evaluate how well this requirement is met by thesmartphone WLAN observations, we carried out the followingexperiment. We collected a large number of fingerprints bywalking at constant speed through office building hallways.The hallways are are forming a rectangle (50m x 10m) whichis traversed twice during the experiment. The distance measurefor all the pairs of recorded fingerprints are shown in Figure 5.Note that the distance measure is commutative and therefore,the distribution is symmetric. Also, elements that are close tothe diagonal indicate signal space distances of two fingerprintsthat have been recorded within a short period of time. Thefarther away from the diagonal, the larger the time spanbetween the two recorded fingerprints. Because the experiment

6

i

j

100 200 300 400

100

200

300

4005

10

15

20

25

30

35

Fig. 5. While walking around a set of rectangular shaped (50m x 10m) setof hallways twice, roughly 420 fingerprints were collected. This figure showsthe fingerprint signal space distance for all pairs i, j of recorded fingerprints.

was conducted while walking at constant speed, this alsomeans that the time span in which two fingerprints wererecorded linearly translates to a spatial distance. Since the goalof this experiment is to get an idea of how well our signalspace distance measure is able to distinguish fingerprints thatare far from fingerprints that are close, it is desirable to havelow distance measures along the diagonal, but high distancemeasures the further away from the diagonal. In addition to themain diagonal, two secondary diagonals which are originatefrom the second round through the rectangular set of hallways.Similar to the main diagonal, we desire low distance measuresclose to the secondary diagonals but high distance measuresthe further away we get. Clearly the secondary diagonalsare less clear than the main diagonal especially, the offdiagonal elements are less distinguishable from the diagonalelements. The four by four checkerboard pattern is a resultof the rectangular track and shows that fingerprints recordedin the two opposite long hallways have a large signal spacedistance. However, within one hallway, the spatial distanceof fingerprints with small signal space distances can growlarge. Due to this shortcoming, erroneous associations haveto be expected. In addition, the similarity between fingerprintswithin one hallway will impede localization performance.

Fusion. Fusing motion- and association data by non-linearoptimization leads to a map of fingerprints. The quantitativeevaluation of the map quality is difficult as long as no local-ization scheme is used to measure localization performancebased on the generated fingerprint map. Figure 6 shows thefingerprint distribution resulting from the fusion step for theETH main building. The recorded fingerprints are drawn asblue dots. The received signal strengths for two distinct (nonoverlapping) access points are indicated in blue to red coloredareas around the corresponding fingerprints. The relative fin-gerprint positions are the result of the fusion step. The floorplan as well as the rotation and translation between floor planand fingerprint distribution is not automatically obtained butadded by hand. The fingerprint locations obtained in the fusion

x [m]

y[m

]

0 20 40 60 80 100 120

102030405060708090

100110

Fig. 6. Fingerprint distribution for ETH Zurich main building (HG). Finger-print locations are indicated as blue dots. Signal strengths for selected accesspoints are shown in blue to red colors

step resemble the true shape of the building with with fewexceptions (intersection on the right side).

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