Building Optimal Radio-Frequency Signal Maps - Semantic Scholar

Building Optimal Radio-Frequency Signal Maps Piotr Mirowski∗† , Tin Kam Ho∗ and Philip Whiting∗‡ ∗ Bell

Laboratories, Alcatel-Lucent, 600 Mountain Avenue, Murray Hill, NJ 07974, USA † Microsoft Bing, 100 Victoria Street, London, SW1E 5JL, UK ‡ Macquarie University, Balaclava Road, Sydney, NSW 2109, Australia Email: [email protected]

Abstract—A popular way for using radio-frequency (RF) signals (e.g. WiFi) to position people or device indoors is by matching received radio signal strength (RSS) to fingerprints that are spatial signatures of such measures. Traditionally such signal maps are built by manual collection of repeated measurements at predefined locations following a spatial sampling scheme. Recently, such labor intensive processes are being replaced by robotbased automation or crowd-sourced simultaneous localization and mapping (SLAM). These new approaches produce timestamped trajectories along with time-stamped RSS as the human or robot moves freely about the building. However, they require an additional procedure to segment the continuous RF samples into fingerprint cells to produce a robust signal map. In this paper, we explore several strategies for building optimal signal maps from RSS collected along robotic or pedestrian trajectories. We compare two clustering algorithms with a baseline strategy that divides the trajectories into a hierarchy of fixed-size grids. We study the trade-off between the spatial extent of the fingerprint cells and the differentiability of the RSS distribution in each cell, as well as their impact on localization accuracy and on fingerprint storage. We experimented with traces collected by an autonomous robot exploring a large multi-floor office building. Keywords—signal processing; mapping; localization; robotics

I.

I NTRODUCTION

Recent advances in mobile communication and computing stimulated the need for frequently locating a mobile device, which allows data streams from the device to be tagged with position and location specific information and services to be sent to the device user. While GPS (Global Positioning Systems) can serve this need in an outdoor environment, positioning within buildings remains a challenge because of the lack of GPS signal indoors. Many schemes have been proposed for indoor positioning [13]. One of the popular schemes is to use Radio-Frequency (RF) fingerprinting, where Received Signal Strength (RSS) measures in some RF band are collected and compared to a map of previous collected signals [1]. The map stores location-specific signatures of similar RSS measures known as fingerprints. Because of their locality, ubiquity and low cost of deployment, WiFi signals from Wireless Local Area Networks (WLAN) are often used to produce such signal maps. A traditional way of building such signal maps is by manually collecting repeated RSS measurements at predefined locations in a building. This is however labor intensive and time consuming. Recently, alternative approaches have been developed that rely on fingerprinting while moving, through robot-based automation [9], [11], [12], or through crowdsourced WiFi-based simultaneous localization and mapping (SLAM) [2], [5], [10], [14], [16]. Typically, these approaches

produce time-stamped trajectories along with time-stamped RSS, as the robot or human moves freely about the building while collecting the RSS. Whereas robot collection is more likely a dedicated process, human-conducted collection can be done while the device user carries on other normal activities, and therefore can go on continuously and produce frequent updates.

An important need in such automated or semi-automated approaches is to convert RSS measures along a continuous trajectory to position-specific fingerprints that are robust and stable to be used as a signal map. In this scenario, the signal traces consist of time-stamped pairs of spatial coordinates and RSS measurements. Because the data are collected when the device is moving, only one single sample is available as the device visits each spatial point. Typically, because of random, complex fluctuations in the signal, a single sample is not enough to represent the RSS distribution at that position. One way to address this problem is to assemble samples from a small spatial neighborhood, or from repeated visits through the same neighborhood, into a small aggregate that allows the estimation of a more stable distribution useful for matching with future samples. This requires a suitable procedure to segment the signal traces and to cluster neighboring samples to form fingerprints.

In this paper, we explore several strategies for building optimal signal maps from RSS collected along robotic or pedestrian trajectories. Our baseline consists in naive fixedsize grids: we gather all the WiFi samples collected by a freely moving robot and falling into a specific spatial location cell (e.g., 1m by 1m) into that fingerprint. We then investigate clustering the RSS top-down into cells of increasingly smaller size using decision trees in the signal space. Finally, we propose an iterative bottom-up approach that aggregates smaller-size fingerprint cells into larger grid cells, based on the probability of pair-wise confusion between fingerprint cells. We study the trade-off between the spatial extent of RSS fingerprint cells and the differentiability of the RSS distribution in each cell, as well as their impact on localization accuracy and on fingerprint data storage. We evaluate these strategies on a large dataset of WiFi RSS collected by an autonomous robot exploring a large multi-floor office environment (about 100m by 100m over 3 floors), where 1m accuracy can be obtained with dense signal mapping. We investigate which signal map building strategies are optimal for localization accuracy and suitable for WiFiSLAM.

II.

AUTOMATED DATA ACQUISITION

A. Signal Collection using an Autonomous Surveying Robot In a recent effort to study the spatial-temporal variation of radio signals in indoor environment, we developed a surveying robot that is equipped with many sensors for experimenting with localization [9], [11], [12]. The robot can carry different payloads of radio measurement equipment and can navigate a building in both planned and autonomous motions. In the autonomous mode the robot can follow hallways and avoid obstacles, as well as move in random routes in open spaces. The robot provides a stable, consistent, and reliable platform for repetitive measurements that allows us to isolate different impacts on radio signals due to different operators, different orientations of the receiver antenna, alternative configurations of network settings, as well as other disturbances in the environment. It provides baselines for studying other errors that may be present with another inherently noisier measurement process such as crowd-sourcing. The robot is a modified electric wheel chair and is equipped with a wheel odometer, an Inertial Measurement Unit (IMU) consisting of a 3-axis accelerometer, 3-axis gyroscope and 3axis magnetometer, front and back sonar sensors, a Kinect color and depth camera and an on-board WiFi router (see Figure 1). The Kinect camera is used as a proximity sensor to enable obstacle avoidance and as a detailed depth range sensor to support Simultaneous Localization and Mapping (SLAM).

and angular drifts of IMU-derived bearings. Therefore a second step uses a particle filter (as a Monte-Carlo Localization algorithm) along with pre-loaded building blueprints to make iterative predictions about the robot’s next position (using odometry estimates) and corrects the belief in the robot’s position using range sensor measurements and an existing map [4]. A third, final, step registers the robot’s position onto a global coordinate system using a set of calibration points. These are self-describing visual landmarks (QR codes) that encode their own geographical positions in a few strategic locations of the building. When the robot observes a QR code landmark in an RGB-D image, the relative position of the robot w.r.t. the QR code can be geometrically estimated from the depth image to estimate the actual robot’s position [9]. Additional bundle adjustments (a-posteriori corrections) can be made by optimizing the robot’s pose graph [6], [10]. The time-stamped trajectories, along with synchronized radio RSS measurements, are input to the fingerprint generation algorithm discussed in this paper, and are also used to evaluate the quality of the obtained fingerprints. B. Crowd-Sourcing From Hand-Held Devices Some variants of the algorithms developed for positioning the robot and calibrating its trajectories can be adapted to work for a hand-held device (e.g. smartphone) that is equipped with similar sensors [10]. Our methods for building signal maps are intended to apply to signal traces collected from such devices as well; the main difference between a robot and a smartphone resides in resorting to Pedestrian Dead Reckoning (based on inertial step counting and magnetic heading estimation) instead of precise inertial- and wheel-based odometry. In such applications, the maps are expected to be noisier because of less precision in device tracking. This means a more significant role for data sample aggregation, fingerprint and map construction, and more careful choices of the matching algorithms during real-time tracking. III.

Fig. 1.

Two views of an autonomous surveying robot.

In movement, the robot collects time-stamped traces of data from the wheel odometer and the inertial sensors, color and depth images from the Kinect sensor, as well as radio measurements from the equipment in the payload. The sensor data are used to reconstruct the paths as the robot traverses the building. Details of the reconstruction methods are described in [11]. The method consists of several steps. First, during movement, the robot’s instantaneous position and orientation (x, y; θt ) are estimated using the following simple motion equations, where vt is the forward/backward motion at time t (provided by the wheel encoder) and dθ is the left/right rotation: xt yt θt

= xt−1 + vt cos(θt−1 ) = yt−1 + vt sin(θt−1 ) = θt−1 + dθ

(1) (2) (3)

The paths consisting of these estimated positions may suffer from accumulated errors due to inexact wheel encoding

C ONSTRUCTING F INGERPRINTS FROM S IGNAL T RACES

The RSS data samples collected on-the-fly while the robot is moving, even after trajectory correction and calibration, require further processing before they can be used for localization. An important reason is that radio RSS often fluctuates between a certain range even if the receiver stays at a fixed position, and a single sample is rarely sufficient to characterize the complex distribution of the signal strengths. Traditionally researchers attempted to overcome this problem by collecting repeated measurements at each fixed position, thereby capturing the statistical characteristics. In many cases the signals from multiple Access Points (APs) are observed or assumed to follow a multivariate Gaussian distribution [3][7]. However, others [8][15] reported that this is not always the case: the signal can be multimodal, different recording devices can measure quite different distributions at the same location, and simple changes in antenna orientation can impact the RSSI by as much as 10dBm. In our scenario of dynamic data collection, we impose a fixed time budget for measurements at each position, which would not allow for many repeated measurements. Therefore a method is needed to approximate the signal distribution by assembling samples from nearby

points included in a small time window while the robot is moving. This is especially needed in the case of crowdsourcing from handheld device users, where we want the users to be able to move naturally, but not stay at fixed positions for dedicated measurements. The extent to which the signal map can represent accurately the statistical distribution of the RSS measurements directly impacts the quality of results in its eventual use in real-time localization and tracking. The problem we are solving is one of segmentation, or clustering, where we need to divide a set of spatially distributed samples into regions that share a common RF signal strength distribution. The signal distribution at each position, known as a fingerprint, is stored in a map with its corresponding spatial coordinates. The intention is that in real-time tracking, measured RF samples from a device can be compared to the signal distribution stored in the map, with the best match being the one at the true position of the tracked device. Details of the fingerprint-based localization are provided in section III-A. There are several concerns in the creation of the fingerprints. Because the results are meant to be used in localization, the fingerprints should be spatially small, so as to support higher precision in localization. However, because of the use of dynamic data collection, an overly small spatial neighborhood will contain very few samples which may fail to fully capture the statistical characteristics of the RF signal strength distribution. There are also practical concerns about the storage needed for a signal map with many fingerprints, and the computational cost in matching with them during tracking time. In order to investigate these tradeoffs, we developed three different approaches to construct fingerprints from our continuous signal traces, namely a subdivision of the space with a regular grid (see section III-B), merging adjacent fingerprint cells bottom-up using fingerprint similarity criteria (see section III-C) and a subdivision of the space top-down using decision trees with criteria on fingerprint similarity (see section III-D). We present the methods and evaluate them in an extensive trial in two areas with different geometrical features in a large, complex office building.

P (ˆ x, yˆ, zˆ) =

k(S, S(i) )(xi , yj , zi ) PN (i) i=1 k(S, S )

i∈N

(5)

While the hyper parameters α and K should be crossvalidated on the training set of fingerprints, as in [8], we observed that the localization accuracy on test data is typically consistent for large ranges of values of α ∈ [0.001, 0.1] and numbers of nearest neighbors between 3 and 10. Therefore we decided to fix these parameters for all fingerprint cell subdivisions. B. Regular Grid Subdivision The first method is simple spatial subdivision following a regular grid, defined using the building coordinates. We explored various resolutions for the fingerprint grid size: 1m, 2m, 3m, 4m, 5m, 7.5m and 10m. Samples falling in the same spatial cell were gathered and associated with the cell ID. The robot was moving at a maximal speed of 0.2m/s while sampling WiFi at about 2Hz. Because of the irregular nature of the robot’s movements, the number of WiFi samples vary from cell to cell. For instance, if one uses 1m-wide fingerprint cells, then all the WiFi measurements that were collected when the robot’s position was between x and x+1 on the X axis and between y and y+1 on the Y axis, where x and y are multiples of 1m, belong to the same fingerprint cell. Once we have attributed all the positions and the corresponding RF signals {(xt , yt ); St }t∈I that were collected at times t in the disjoint time interval I associated to a specific grid cell l, we can compute the average position (xi , yi ) inside that cell as well as the distribution qi of the RF signal. This method gives a set of fingerprints at each resolution. A finer, denser fingerprint grid gives more precise position information, but has fewer RF samples in each cell so the representation of the RF signal distribution is less reliable. A coarser fingerprint grid has more RF samples in each cell, but would allow for less precise localization. The cells at the finest resolution, i.e., 1m2 in size, are used as building blocks for the fingerprints to be created using the other two methods. C. Cell Merging

A. Fingerprint-based Localization The RF fingerprint-based localization algorithm is based on the weighted nearest neighbor regression [1], expressed as a weighted kernel regression form as in [8]. For a collection of T multivariate RSS samples S collected at runtime from P access points, where S can be seen as a matrix S = (st,j )t∈[1,T ],j∈[1,P ] of size T × P , a signal similarity is computed with all the M signal fingerprints {S(i) }i∈[1,M ] (i.e., with a set of M signal fingerprint matrices). We decided to use the simplest metric, which is the Euclidean distance between the vectors of mean values of the signal strength for each access point (see Eq. 4). The localization algorithm itself is weighted kernel regression with K nearest neighbors. By noting N such a set of nearest neighbors and (xi , yi , zi ) the spatial positions of the signal fingerprint cells, the predicted location (ˆ x, yˆ, zˆ) is expressed in Eq. 5.

k(S, S(i) ) = e

−α

PP j=1

(i)


2

E[S.,j ]−E[S.,j ]

(4)

A second method that we investigated is to start with the finest spatial cells (say, with edge length 1m), and iteratively examine all pairs for potential merges according to a criterion. The goal is to avoid ambiguous situations where two fingerprints that are spatially distant share similar signal information and cause spurious matches. In [8], the authors demonstrated, using probabilistic bounds on the number of signal samples needed to obtain good localization accuracy, that the main reason for weak localization performance is due to underdetermined fingerprints, i.e., cells containing an insufficient number of RSS samples to derive robust statistics. When one cannot collect more RSS information, the only work-around is to merge a cell that is ambiguous in signal space with one of its spatially neighboring cells, in the hope that the union of RSS samples will contribute to a unique RF signature. The algorithm works by iteratively finding the pair (i, j) of fingerprints that are the worst offenders (i.e., spatially distant and with the most RF similarity, which we measure using the KL-divergence [8] between the two AP visibility distributions). If the KL-divergence value is smaller

then pair up the cells with one from either side of the cut, and than a threshold, the pair is a candidate for disambiguation. compute all the distances between their centroids. Here the In that case, the Manhattan distance is computed between distances are taken to be the Euclidean distances between the the coordinates of the cells, and if the distance is above a centroid vectors. The merit score is defined to be the maximum threshold, we merge one of the fingerprints i or j with its plus the minimum of such distances, as described in pseudoimmediate neighbors that has the minimum KL-divergence. code 2. This is so chosen because even though the maximum Figure 2 shows a set of fingerprints resulting from such a distance usually determines the best signal separation, in the merging process. Note that with this method, we do not merge case of 196 several candidate cuts having the same maximum cells across different floors. Merge criterion: 0.010000, 293Merge fps criterion: 1.000000, fps distances, the addition of the minimum distance can serve 40 to pick out the one that minimizes confusion. A remark should be made here that the signal strength is not necessarily monotonically increasing or decreasing with distance to the AP 35 due to complex reflections in indoor environment, therefore the maximum inter-cut distances do not necessarily occur between cells that are farthest apart spatially. 30

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Fig. 2. Example of a set of fingerprints resulting from a cell merging process, 20 cells (marked in red). Right: merged fingerprints using a 1m grid. Left: original (marked in red), with original fingerprints marked in blue.

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D. Decision Tree Construction

The candidate X or Y cut with the best merit score is chosen to split the node. The procedure continues recursively, until only a single grid cell remain, or when the merit score for the best candidate cut drops below a pre-selected threshold m. The node will be taken as a leave. Different thresholds can be chosen to produce trees with different spatial resolution. Figure 3 shows an example set of x,y cuts chosen to split the collection of cells marked with a red cross, which resulted in the fingerprints whose center positions are marked with a blue dot.

A third approach to constructing fingerprints is by way 10 of a decision tree. This is a top-down method to generate a hierarchy of grid cells. The tree is split at the top to different floors. Then, at each branch corresponding to a single 5 floor, a tree is constructed with the procedure described in the following. Notice that this process is different from the Fingerprints on 1m grid Fingerprints on 1m grid typical decision tree construction process in the context Fingerprints of Fingerprints after merging after merging classification. In classification, the first need is to enforce 0 0 a15node.5The 10 25 15 the 20 35 25 40 30 45 35 40 45 20 distribution 30 class feature 5similarity10within of label across a split is a response of that, and the merit of Fig. 3. Left: example set of x,y cuts. Right: positions of cells in the entire a split is defined to promote the best separation of the class collection (blue) on one of the floors and positions of the fingerprints generated distribution. In our current process, the evaluation is the other by tree (red). way around: we first need to preserve spatial continuity of the node, because this is required of a fingerprint to be used for Algorithm 1 MakeTree(I, {S(i) , xi , yi }i∈I ) tracking. The signal distribution across a candidate split is a response of that, therefore the merit of a split is defined to (x∗ , Mx∗ ) = arg maxx∈X Merit(Il,x , Ir,x , {S(i) , xi , yi }i∈I ) promote the dissimilarity of the signals. (y ∗ , My∗ ) = arg maxy∈Y Merit(Id,y , Iu,y , {S(i) , xi , yi }i∈I ) if Mx∗ ≤ m and My∗ ≤ m then At each internal node, we look for the best split on either Add {S(i) , xi , yi }i∈I to fingerprints the X or the Y axis, and the cuts along the X and Y axes are else evaluated in turn. We start from a collection of M atomic cells if Mx∗ ≥ My∗ then (e.g., 1m size) noted I = {1, 2, . . . , M }. Each cell is defined (i) (i) MakeTree(I , {S(i) ,ofxiMATLAB , yi }i∈Il,x∗ ) l,x∗Version by signal S and centroid (xi , yi ): {S , xi , yi }i∈I . Student An X Version of MATLAB Student (i) ∗ MakeTree(Ir,x , {S , xi , yi }i∈Ir,x∗ ) cut at coordinate x results in left set Il,x = {i ∈ I : xi ≤ x} else and right set Ir,x = {i ∈ I : xi > x}. Similarly, an Y cut MakeTree(Iu,y∗ , {S(i) , xi , yi }i∈Iu,y∗ ) along coordinate y results in down and up sets Id,y∗ = {i ∈ ∗ ∗ I : yi ≤ y } and Iu,y∗ = {i ∈ I : yi > y }. Pseudo-code MakeTree(Id,y∗ , {S(i) , xi , yi }i∈Id,y∗ ) 1 details the recursive nature of the algorithm. Note that for end if speed-up, we evaluate at most 9 candidate cuts (into at most end if 10 sections) per dimension, using quantiles of the coordinates of cells’ centroids. Algorithm 2 MeritFunction(I1 , I2 , {S(i) , xi , yi }i∈I=I1 ∪I2 ) The candidate cuts are evaluated using a merit score that is dmin = mini∈I1 ,j∈I2 ||E[S(i) ] − E[S(j) ]||2 computed as follows. For each cut that is chosen, the cells in the node are divided into two halves on either side of the cut. dmax = maxi∈I1 ,j∈I2 ||E[S(i) ] − E[S(j) ]||2 The centroid E[S(i) ] of the vectors of measured RSS from the return M = dmax + dmin Access points in each cell i is taken to represent the cell. We 40

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IV.

E VALUATION OF S IGNAL M AP Q UALITY

To investigate the trade-offs between the various concerns regarding the signal maps constructed with the proposed approaches, we designed a series of experiments in a large office complex featuring different spatial geometry. We selected two areas in the building, one with the layout of traditional office buildings with long hallways and many small offices on the side (see section IV-A), and another with a large, open atrium with a high ceiling (see section IV-B). The RF signal characteristics are known to be very different in these areas. We use the autonomous survey robot as described in the paper to collect the WiFi signal strengths in the environment along with their position associations in time-stamped traces. We used the existing WiFi Access Points and, in the case of the open atrium, we installed additional WiFi routers dedicated for this experiment. We did not install additional APs in the office corridor environment. The RF data were sampled by a smartphone (Samsung Nexus S) placed on the robot.

the atrium. The area covered by the robot was about 40m by 50m, on a single floor. Figure 5 shows the layout of the area and the robot trajectories. One of the trajectories, path 1, with multiple small loops, was used for defining the fingerprints. The path included 3961 measurements in 306 cells of 1m2 in size. Two other trajectories (paths 2 and 3) were acquired later that same day, on February 28, 2013, towards the end of the business day when there were occasional people moving around the robot. The figure shows an additional Path 4 from an earlier test which was not used in the experiment described in this paper. There were 72 WiFi Access Points visible in this area. 45 40 35 30 25 20 15 Path 1 (fingerprinting) Path 2 (test run) Path 3 (test run)

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A. Multi-Floor Office Building with Many Hallways

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The first area where we conducted the experiments includes 3 floors each with several long hallways with many small offices on the side. As the robot moved around this area, a total of 104 WiFi Access Points were seen, therefore the received signal strength vectors have 104 components. Figure 4 shows a part of one floor in this area and some robot trajectories. The robot made multiple traversals on each floor. Over the 3 floors, 22397 signal measurements in a total of 1049 cells of 1m2 were used to construct the fingerprints with the three investigated approaches. Additional measurements in the remaining traces were used to evaluate the resultant signal maps.

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Fig. 4. Layout of a part of the office building overlaid with two robot trajectories.

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Layout of the atrium and the robot trajectories.

C. Experimental Results The results of tracking accuracy using fingerprints created by the three investigated methods in both of the test areas are presented in Tables IV-C and IV-C. In each table, the column for process and parameter gives the method used. For regular subdivision, the parameter is the length of the edge of each cell in meters. For the other two methods, the parameters are the Student Version of MATLAB values used the merging and splitting criteria. For each trial and test tracks, we give the median error and the 90th percentile error in meters. The error is measured as the distance between the true position of the device and the position predicted by the K-nearest neighbor regression algorithm (see Eq. 5). In each column of errors, the minimum (i.e., the best result) is highlighted in boldface. In the first, multi-floor, set of experiments, the floor prediction accuracy was consistently 100%. TABLE I.

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T RACKING ACCURACIES IN HALLWAYS .

Process/ Param regular 1 regular 2 regular 3 regular 4 regular 5 regular 7.5 regular 10 merge tree 15 tree 20 tree 25

# FPs 1049 492 297 212 168 109 78 206 727 594 491

Median Error (m) 2.56 2.54 2.67 2.6 2.74 3.11 3.33 2.66 2.2 2.39 2.36

90th %-tile Error (m) 7.21 7.64 6.87 7.74 7.68 6.58 7.04 7.21 7.78 7.07 7.44

B. An Atrium with Open Spaces D. Discussion The second area for the experiments is the atrium of the Student Version of MATLAB Student Version of MATLAB same office complex. There is a small conference center with From Tables IV-C and IV-C, it can be seen that each of the several rooms, a long walkway with a high, slanted ceiling, three fingerprint construction methods has its own merits. One and both are connected to a 5-story atrium. The robot moved can see that the finest grid of 1m does not necessarily yield around in the conference center as well as in the open areas in optimal results and that reducing the number of fingerprints

TABLE II. Process/ Param regular 1 regular 2 regular 3 regular 4 regular 5 regular 7.5 regular 10 merge 0.1 merge 0.5 merge 0.75 merge 1.0 tree 60 tree 80 tree 100

# FPs 306 127 77 48 37 22 13 276 224 203 196 287 271 239

T RACKING ACCURACIES IN ATRIUM . Track 1 Median 90th %-tile Error (m) Error (m) 1.67 5.19 1.76 4.8 1.98 4.84 2.16 4.64 2.04 4.91 2.89 6.49 3.3 8.23 1.64 5.21 1.7 5.33 1.62 5.38 1.62 5.38 1.72 5.27 1.74 5.19 1.78 5.58

Track 2 Median 90th %-tile Error (m) Error (m) 1.07 3.08 0.99 3.13 1.27 3.32 1.54 2.98 1.58 4.43 2.7 7.01 3.93 8.34 1.04 3.31 1.1 2.94 1.09 2.94 1.08 2.83 1.04 3.46 1.07 3.59 1.16 4.11

be attempted with the merging or tree splitting algorithms, there is room for further optimizing the utilization of RF signal measurements acquired with dynamic collection processes. Better utilization of data collected in this manner can help realize the benefits of crowd-sourcing, opening the way for continuous, passive signal map updates without incurring heavy data collection costs. ACKNOWLEDGEMENTS The authors would like to acknowledge the helpful contributions by Ravishankar Palaniappan, Ivan Dryanovski and Hao Tong during the experimental (data acquisition) phase. R EFERENCES

can be beneficial. The best median accuracy in tracking tends to occur either with a specific regular grid (2m for the Atrium experiments) or with the merging or the tree method using a parameter that created fewer fingerprints than the finest grid in regular subdivision. For example, reducing the number of fingerprints using either a coarser grid or the tree or merging methods gave slightly better median tracking accuracy in the Atrium dataset (where the signal data were rich) and better median accuracy in the hallways dataset, where the regular grid at 1m size made over 1000 fingerprints yet with them tracking incurred larger errors. This is desirable because the advantages are doubled in both better accuracy and requiring less storage and matching time. Figure 6 shows a typical cumulative distribution of tracking errors. Fingerprints that minimize tracking error at at a particular percentile may be desirable depending on the requirements of the tracking application.

[1] [2]

[3]

[4]

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[7]

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[9]

[10] Fig. 6. Cumulative distribution of tracking errors in the atrium using fingerprints created with the tree method using a parameter value of 20. [11]

V.

C ONCLUSION

We investigated, for fingerprint-based indoor localization, how to utilize RF signal measurements acquired while the receiving device is moving, as in the use of an autonomous survey robot with a limited time budget, or in crowd-sourcing from ordinary users who are carrying out their routine activities. We described three methods for creating a signal map that contains RF fingerprints of various spatial scopes. The methods were tested in a large, complex office building feature both ordinary hallways and irregular open spaces. The results demonstrated that the careful thinking that went into the more sophisticated methods for fingerprint generation produced some desirable advantage. Those methods hold the potential for improving the quality of signal maps beyond that obtained by the most obvious method (regular grid subdivision). Since there are still other design choices that can

[12]

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