sequence-type fingerprinting for indoor localizationhuwei/doc/ipin15_sequence_locate.pdf ·...

Sequence-Type Fingerprinting for IndoorLocalization

Wei Hu∗, Yongcai Wang∗ and Lei Song∗∗Institute for Interdisciplinary Information Sciences

Tsinghua UniversityBeijing, China

Email: [email protected], [email protected], [email protected]

2015 International Conference on Indoor Positioning and Indoor Navigation (IPIN), 13-16 October 2015, Banff, Alberta, Canada

Abstract—Location fingerprinting is a widely used techniquefor indoor localization. Traditional fingerprinting methods aregenerally in point-type, where the received signal strength indi-cators (RSSI) at discrete points are trained in the offline phaseand used as reference in the online phase. This type of radio maprequires many human efforts to calibrate and does not take intoaccount the spatial relationship among the discrete points.

In this paper, we propose a novel sequence-type fingerprintingmethod, which is easy to train and provides more accurate andmore robust indoor localization performance. The sequentialRSSIs are offline trained when a user moves along indoorroutes. Then a segmentation method is used to store the radiomap as a graph. In the online phase, the user’s sequentialfingerprints within a short time window are measured, and thenmatched with the sequential fingerprints extracted from the graphby subsequence dynamic time warping algorithm. We conductsimulation to verify the performance improvement of sequence-type fingerprinting over traditional fingerprinting methods.

I. INTRODUCTION

Location fingerprinting method based on Wi-Fi signalstrength is widely used for indoor localization due to its desiredfeatures such as universal availability, privacy protection andlow deployment cost [1], [2]. Location fingerprinting generallyconsists of an offline training phase and an online positioningphase. In the offline phase, a site survey process is carried outto obtain the received signal strength indicator (RSSI) values atdifferent known locations, which are stored in a radio map. Inthe online phase, RSSIs are measured by a mobile device andare searched in the radio map. The location whose RSSIs bestmatch the measured RSSIs will be determined as the locationof the target.

Despite its wide applicability, traditional point-type fin-gerprinting has two major drawbacks: (i) It is usually verylaborious to build the radio map. (ii) The radio map doesnot model the spatial relationship, i.e., the RSSI dependenciesamong adjacent locations. Therefore, it cannot use the indoorroute constraint to filter out infeasible location results, and thelocating results are often unstable and inaccurate.

To tackle above disadvantages of point-type fingerprinting,we propose a novel sequence-type fingerprinting method. Theidea is to make use of sequences of RSSIs measured alongdifferent routes, instead of RSSIs at different points, as fin-gerprints. In the offline phase, RSSIs are measured along a

collection of known routes. Then a segmentation algorithm isused to store the sequential fingerprints as a graph. From thisgraph, routes that are not trained in the offline phase can begenerated. In the online phase, the target moves and measuresRSSIs within a short time window. Then subsequence dynamictime warping (SDTW) algorithm [4] is used to find theoptimal alignment between this measured RSSI sequence anda sequence extracted from the graph. This gives the locationof the target. DTW can tolerate user’s irregular movements,so it can robustly find the location even if the user’s movingpattens in the offline phase and the online phase differ greatly.

Sequence-type fingerprinting method has several advan-tages: (i) In many buildings, potential locations are constrainedby routes. For example, people walk along corridors outsiderooms, and also walk along certain paths inside a room due tothe existence of furnitures. This can help to rule out infeasiblesolutions. (ii) Sequence-type method tends to be more accurateand robust. (iii) Sequence-type method is more labor-savingthan point-type method in the offline phase. Inertial navigationsystem (INS) such as OpenShoe [3] can be used; it suffices towalk relaxedly to complete all the data collection work.

The rest of this paper is organized as follows. We introducethe framework of sequence-type fingerprinting and its trainingmethod in Section II. The locating method based on SDTW isintroduced in Section III. Performance evaluation is presentedin Section IV. The paper is concluded with remarks in SectionV.

II. SEQUENCE-TYPE FINGERPRINTING: TRAINING PHASE

In this section we introduce the general framework ofsequence-type location fingerprinting and the techniques usedin its offline training phase. We will represent the RSSIsmeasured at a certain location as a vector whose i-th coordinateis the signal strength from the i-th access point.

The idea of sequence-type fingerprinting is as follows. Inthe offline phase, we measure and store sequences of RSSIsalong different routes. Namely, if Γ is a route in the givenbuilding, then a sequence Y = (y1, · · · , ym) of RSSI vectorswill be measured along Γ, where yi is the RSSI vector at thei-th measured point on Γ. Suppose that in the online phasethe RSSI sequence X = (x1, · · · , xn) is measured alonga route Γ′ which is part of Γ. Then we can use sequencematching algorithms to find an optimal match between X anda subsequence of Y . Since the location of the route Γ is known,the location of Γ′ can be estimated as the matched part on Γ.978-1-4673-8402-5/15/$31.00 c©2015 IEEE


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Trajectory

x [m]

y [

m]

Trajectory

Start point

RSSI measurements

Fig. 1. Example of estimated trajectory by OpenShoe. The red crosses arethe positions where RSSIs are measured.

If the RSSI fingerprints on all potential routes in the targetarea are obtained in the offline phase, then in the online phaseany route that is close to a segment of a fingerprinted routecan be located.

Note that there could be many different routes. CollectingRSSI fingerprints on all these routes one by one can still bevery laborious. We propose a measuring, segmentation andgraph representation framework for the offline phase. The radiomap is stored as a graph, which is easily trained and cangenerate fingerprints of all route combinations in the onlinephase. This greatly saves the training efforts.

A. Sequential data collection along a route

To label the location ground truth in the training phase, weemploy intertial navigation system (INS), such as OpenShoe[3], which enables us to accurately track the position of awalking person. When a person walks with an INS devicemounted on his foot, INS can calculate an estimate of histrajectory with high accuracy. Based on INS, the sequentialRSSI and position data are collected in the offline phase asfollows. A person walks through a predetermined route Γ withINS mounted on his foot. The INS calculates an estimate ofhis track during his walk (i.e., outputs, in high frequency,current positions). We approximate the real trajectory Γ bythe output of INS. In the meantime, we let the same devicekeep collecting RSSIs from wireless access points in thesurrounding Wi-Fi network. The positions where RSSIs aremeasured are also recorded.

We implement the above data collection method usingOpenShoe. In Fig. 1, we plot the trajectory estimated byOpenShoe during a short walk. The RSSIs are collected alongthis route, and the positions there there are RSSI measurementsare highlighted.

B. Radio map as a graph

We have seen how to collect RSSIs and positions alonga route. Then one way to build the radio map is to measureRSSIs along many routes and to store all of them. Ideally,these routes can cover all possible routes in the given rigion.However, it is sometimes infeasible or inadvisable to measureand store all possible routes separately due to the followingreasons: (i) There may be too many possible routes. It costs

too much labor, time and memory to measure all of them. (ii)There may be many common segments among possible routes.If all routes are measured separately, those common parts willbe measured multiple times, which is a waste of time andmemory.

Now we introduce a radio map structure based on graph.The motivation is that we can connect several routes togetherto form a new route. To achieve this, we store the radio mapas a graph G = (V,E). Each node v ∈ V is a position,and each edge e = (u, v) ∈ E corresponds to a measuredsegment between u and v (including trajectory and RSSIsequence). As a common notion in graph theory, a path Pin G is a list of edges (v1, v2), (v2, v3), · · · , (vk−1, vk) in E;we usually simply represent P as P = v1-v2- · · · -vk. Then anypath P = v1-v2- · · · -vk in G can be regarded as a potentialroute Γ by connecting the segments (v1, v2), · · · , (vk−1, vk)sequentially. Therefore, we can combine the data collected atedges (v1, v2), · · · , (vk−1, vk) to obtain the trajectory and theRSSI sequence along Γ.

In principle, by storing the radio map as a graph G, everypath in G will give a possible route in the given region.Although there could be many paths in G in general, forour purpose it suffices to consider a small number of them.Since in the online phase people would want to know theirlocation quickly (i.e., in a real-time manner), it makes senseto assume that the route to be located in the online phase isnot very long. Thus we can, for example, only consider pathswhich consist of at most c edges, where c is a certain constant(e.g. c = 2). Even if the route to be located is very long, wecan break it into short pieces and locate these pieces separately.

Automatic graph construction: Now we describe a segmen-tation method which constructs the graph automatically fromfingerprinted routes. Suppose that some arbitrary routes aremeasured in the offline phase. If two routes Γ1 and Γ2 intersectat a point v, v will be recognized as a node in the graph. Sincethe trajectories of all the routes are known, we are able to findall the intersections formed by these routes. Then the set ofnodes V will be the set of these intersections together withthe terminal points (i.e., starting and ending points) of all theroutes. Every route is broken into pieces by the intersectionson it, and then each such piece will be an edge in the graph.For example, suppose that along a route Γ there are nodesv0, v1, v2, · · · , vk, where v0 and vk are the terminal points ofΓ, and other vi’s (1 ≤ i ≤ k−1) are the intersections betweenΓ and other routes. Then (v0, v1), (v1, v2), · · · , (vk−1, vk) areedges in the graph. In this way, we only need to measuresome arbitrary routes in the offline phase, and the graph canbe constructed automatically by identifying the intersectionsand segmenting the routes.

An example is shown in Fig. 2, where 6 blue routes aremeasured in the offline phase. The 12 terminal points of theseroutes, together with the 7 intersections produced by them, willbe recognized as the nodes in the graph.

III. SEQUENCE-TYPE FINGERPRINTING: LOCATINGPHASE

In this section we present the locating method in sequence-type fingerprinting.


A. Dynamic Time Warping

First we briefly review dynamic time warping (DTW),a well-known technique for aligning two time-dependentsequences [4], [5]. For a positive integer n, let [n] ={1, 2, · · · , n}.

Classical DTW: Suppose we are given two sequencesX = (x1, · · · , xn) and Y = (y1, · · · , ym) whose elementsxi, yj(i ∈ [n], j ∈ [m]) are all in the same metric spaceX with a distance function d : X × X → R≥0. LetP = (p1, · · · , pl) be an alignment between X and Y , wherepk = (ik, jk) ∈ [n]× [m] for each k ∈ [l]. We say that P is awarping path if it satisfies the following conditions.

• Boundary condition:

p1 = (1, 1), pl = (n,m). (1)

• Step size condition:

pk+1−pk ∈ {(0, 1), (1, 0), (1, 1)} ∀k ∈ [l−1]. (2)

The distance between X and Y given the warping path Pis defined as

dP (X,Y ) =

l∑k=1

d(xik , yjk). (3)

A warping path P ∗ between X and Y is optimal if it achievesthe minimum distance among all possible warping paths. Thisminimum distance is called the DTW distance between X andY , denoted by

DTW(X,Y ) = min{dP (X,Y ) : P is a warping path}. (4)

To find an optimal warping path, there is a simple dy-namic programming algorithm. Consider the following pro-cedure: D(i, 1) =

∑ii′=1 d(xi′ , y1) for i ∈ [n], D(1, j) =∑j

j′=1 d(x1, yj′) for j ∈ [m], and

D(i, j) = min{D(i−1, j−1), D(i−1, j), D(i, j−1)}+d(xi, yj)(5)

for 1 < i ≤ n, 1 < j ≤ m. It is easy to see that D(i, j)stores the DTW distance between X[1,i] = (x1, · · · , xi) andY[1,j] = (y1, · · · , yj). Thus we have DTW(X,Y ) = D(n,m).The optimal warping path can be found by tracing all theiterations.

Subsequence DTW (SDTW): In many applications we wantto align a shorter sequence with a subsequence of a longersequence. Namely, there are two sequences X = (x1, · · · , xn)and Y = (y1, · · · , ym) (n � m), and the goal is to find asubsequence Y[a,b] = (ya, ya+1, · · · , yb) (1 ≤ a ≤ b ≤ m) ofY such that

(a∗, b∗) = arg min(a,b):1≤a≤b≤m

DTW(X,Y[a,b]). (6)

The solution to (6) can also be found using dynamicprogramming. The details are given in [4].

B. Locating by SDTW

As introduced in Section II-B, after the offline phase, aradio map is constructed in the format of a graph, and then wewill take a set of candidate paths from this graph. Suppose thatwe take k paths from the graph, which correspond to routesΓ(1), · · · ,Γ(k). For each s ∈ [k], let Y (s) = (y

(s)1 , · · · , y(s)ms)

be the sequence of RSSI vectors along the route Γ(s).

In the online phase, a person walks along a route Γ′ whilemeasuring RSSIs. We assume that Γ′ is part of Γ(s) for somes ∈ [k]. Let X = (x1, · · · , xn) be the RSSI sequence collectedon Γ′. Then we align the sequence X = (x1, · · · , xn) with asubsequence Y

(s)[a,b] of Y (s), and estimate the trajectory of Γ′ as

the part from measurement y(s)a to measurement y(s)b on Γ(s).

After specifying a distance function on the space of RSSIvectors (e.g. `p-norm d(x, y) = ‖x − y‖p in Rd for somep > 0), we can apply SDTW algorithm to find the optimalalignment between X and any subsequence of Y (s). DTWis suitable for dealing with time deformations and differentspeeds in time series, which makes it a natural fit for ourproblem since people may walk with different or varyingspeeds.

Since we do not know in advance which route Γ(s) is theone Γ′ belongs to, we need to find s∗ ∈ [k] such that X canbe optimally matched to a subsequence of Y (s∗). Thereforewe want to find

(s∗, a∗, b∗) = arg min(s,a,b):s∈[k],1≤a≤b≤ms

DTW(X,Y(s)[a,b]). (7)

To solve (7), we use SDTW to find for every s ∈ [k] theoptimal alignment between X and a subsequence of Y (s), andchoose s∗ as the one that achieves minimum DTW distance.

IV. PERFORMANCE EVALUATION

We perform simulation tests to evaluate the localizationaccuracy of sequence-type location fingerprinting. The sim-ulation is conducted in MATLAB environment. We use thefloorplan of the 3rd floor of Meng Mingwei Science andTechnology Building (South) at Tsinghua University, whichhas size 17×60m2. We randomly generate 20 positions in thearea for access points, and we use the radio signal propogationmodel [6]–[8] to calculate RSSIs at any position based on itsdistance to the access points. Fig. 2 shows the floorplan with20 randomly generated positions of access points.

We simulate the human walking process by cliking on thefloorplan. Each route is obtained by connecting the clickedpositions by line segments. On each route, RSSI vectors aremeasured about every 0.6m. In the offline phase, we specifyseveral routes to measure and then use the segmentationmethod (in Section II-B) to construct the madio map as agraph. Fig. 2 shows an example where 6 routes are measuredin the offline phase.

In the online phase, we also use mouse clicks to specifya route to be located. Recall that we need to take a set ofpaths in the graph as candidate routes. In our setting, weconsider all the paths which start and end at terminal nodesand contain at most one intersection. In other words, a path


Fig. 2. The floorplan used in the simulation. Red squares stand for thepositions of access points. The 6 blue routes are measured in the offline phase.They produce 7 intersections, and the radio map will be a graph of 19 nodes.

Fig. 3. Locating results given by SDTW and KNN (k = 3). The radio mapis the same as Fig. 2. The green routes are the ones that we want to locate;the magenta routes are the locating results given by SDTW; the black dashedroutes are obtained by connecting locations output by KNN.

that we take is either a measured route from the offline phaseor start from one route and turn to another route at their inter-section. Then, for the route given in the online phase, SDTW(using `2 norm as distance measure) is used to determine itslocation. To evaluate the locating accuracy of our method,we also implement k nearest neighbors (KNN)1 algorithm[9] to determine the location, which is widely-used in point-type location fingerprinting. Fig. 3 shows two examples oflocalization results. As we observe from a large number ofresults (including Fig. 3), KNN tends to be very unstable,and SDTW usually finds an accurate estimated location. Theresults illustrate the robustness of sequence-type fingerprintingmethod over point-type method.

We quantitively compare the locating accuracy of SDTWwith KNN. We use the radio map given in Fig. 2, andindependently generate 100 random testing routes as follows:(i) randomly select one path from all the candidate paths; (ii)randomly choose a segment from the route corresponding tothis path; (iii) on this segment, add a small Gaussian noise toall the fingerprinted positions, and connect these positions toobtain a testing route. For each testing routes, we use SDTWand KNN to estimate its location, and calculate the averagelocating errors (i.e., the distance between real position and

1Given an RSSI vector, KNN finds k closest RSSI vectors in the database,and outputs the average of the k corresponding locations.

0 0.5 1 1.5 2 2.5 30

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Locating error(m)

CD

F

SDTW

KNN (k=2)

KNN (k=3)

Fig. 4. The empirical CDFs of locating errors of SDTW and KNN.

estimated position) over fingerprinted points. The empiricalCDFs of locating errors are given in Fig. 4, which shows thatSDTW significantly outperforms KNN in terms of locatingaccuracy. The average locating errors of SDTW, KNN (k = 2)and KNN (k = 3) over the testing routes are 0.51m, 1.21mand 1.18m, respectively. The average error of SDTW is lessthan 44% of the error of KNN.

V. CONCLUSION AND FINAL REMARKS

In this paper we propose a new location fingerprintingmethod based on sequence. It does not require laboriouswork in the offline training phase, and is more robust andaccurate than tradition point-type fingerprinting. Our method isparticularly suitable for places constrained by routes, in whichpotential locations are almost covered by a set of routes.

In addition to simulation, we have implemented the locat-ing system using the techniques described in this paper. De-tailed results and analysis of real experiment will be presentedin our subsequent paper.

ACKNOWLEDGMENT

This work was supported in part by the National Ba-sic Research Program of China Grant 2011CBA00300,2011CBA00301, the National Natural Science Foundation ofChina Grant 61202360, 61033001, 61073174, 61361136003,and Tsinghua University Initiative Scientific Research Pro-gram.

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[5] H. Sakoe, “Dynamic programming algorithm optimization for spokenword recognition,” IEEE Transactions on Acoustics, Speech, and SignalProcessing, vol. 26, pp. 43–49, 1978.

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