Lightweight Map Matching for Indoor Localisationusing Conditional Random Fields

Zhuoling Xiao, Hongkai Wen, Andrew Markham, Niki TrigoniDepartment of Computer Science, University of OxfordWofson Building, Parks Road, Oxford, OX1 3QD, UK

Email: {zhuoling.xiao, hongkai.wen, andrew.markham, niki.trigoni}@cs.ox.ac.uk

Abstract—Indoor tracking and navigation is a fundamentalneed for pervasive and context-aware smartphone applications.Although indoor maps are becoming increasingly available, thereis no practical and reliable indoor map matching solutionavailable at present. We present MapCraft, a novel, robustand responsive technique that is extremely computationally ef-ficient (running in under 10 ms on an Android smartphone),does not require training in different sites, and tracks welleven when presented with very noisy sensor data. Key to ourapproach is expressing the tracking problem as a conditionalrandom field (CRF), a technique which has had great successin areas such as natural language processing, but has yet tobe considered for indoor tracking. Unlike directed graphicalmodels like Hidden Markov Models, CRFs capture arbitraryconstraints that express how well observations support statetransitions, given map constraints. Extensive experiments inmultiple sites show how MapCraft outperforms state-of-the artapproaches, demonstrating excellent tracking error and accuratereconstruction of tortuous trajectories with zero training effort.As proof of its robustness, we also demonstrate how it is able toaccurately track the position of a user from accelerometer andmagnetometer measurements only (i.e. gyro- and WiFi-free). Webelieve that such an energy-efficient approach will enable always-on background localisation, enabling a new era of location-awareapplications to be developed.

I. INTRODUCTION

Whereas GPS is the de facto solution for outdoor position-ing, no clear solution has as yet emerged for indoor positioningdespite intensive research and the commercial significance.Applications of indoor positioning include smart retail, nav-igation through large public spaces like transport hubs, andassisted living. The ultimate objective of an indoor positioningsystem is to provide continuous, reliable and accurate posi-tioning on smartphone class devices. We identify maps as thekey to providing accurate indoor location; this is a reasonableassumption given that indoor mapping is a high priority forcompanies, such as Google, Microsoft, Apple, Qualcomm, andso on. A map can be viewed in the broadest sense as a spatialgraph which provides constraints. At the simplest level thistakes the form of a floor plan of a building. This constrains theallowable motion of a user - people cannot walk through wallsand can only enter a room through a door. Other maps (meta-maps essentially) provide additional constraints or features,such as the positions of access points, radio fingerprints, signalstrength peaks or distorted geomagnetic fields. Based on atime-series of observations, such as inertial trajectories orRF scans, the goal is to reconcile the observations with theconstraints provided by the maps in order to estimate the most

feasible trajectory of the user, i.e. the sequence that violatesthe fewest constraints.

Existing map matching techniques, based on recursiveBayesian filters, such as HMMs, Kalman and particle filters,have been successfully applied to the location estimationproblem, but are limited in two ways: Firstly, they are com-putationally expensive, and are thus typically delegated tothe cloud to run. Not only does this lead to lag and serviceunavailability in connection-poor areas, it has the side-effectof leaking detailed sensor data and precise location to a thirdparty. Secondly, they typically require high fidelity sensor datato estimate accurate trajectories, leading to power drain.

Motivated by these pressing problems, we present a freshapproach to indoor positioning that is lightweight and com-putationally efficient, but also robust to noisy data, allowingit to provide always-on and real-time location information tomobile device users. The goal of the proposed approach is toachieve similar or better accuracy as existing techniques, butwith fewer computational, space and sensor resources. Unlikeexisting techniques that model the problem using directedgraphical models, the proposed MapCraft algorithm uses anundirected graphical model, known as linear chain conditionalrandom fields (CRFs). The CRF model is particularly flexibleand expressive, allowing a single observation to be relatedwith multiple states and for multiple observations to informa single state. This allows us to capture correlations amongobservations over time, and to express the extent to whichobservations support not only states, but also state transitions.

In terms of performance, MapCraft is two to three ordersof magnitude more computationally efficient than competingtechniques, running in less than 10 msec on an Android phone,enabling real-time location computation online. The secondadvantage of MapCraft is that it offers high location accuracyeven when it uses ultra low power sensors (e.g. accelerometerand magnetometer), whereas existing approaches rely heavilyon power hungry sensors like frequent WiFi scans to monitorthe local radio environment, or gyroscopes running at highsampling rates to capture turns and steps. Until recently, be-cause of the dominant cost of the main processor, deactivatingthese sensors had little impact on overall power consumption.However, with the advent of motion tracking devices, wesee a clear trend of low power digital motion processors(DMPs), e.g. InvenSense MPU-6000/MPU-6050, able to taskand process inertial data in bursts, while the system processorremains in a low-power sleep mode. In this new regime, thedominant cost will not come from the processor, but from thepower hungry sensors, such as WiFi and gyroscope. Another

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ObservationsObservations

SensorsSensors

MotionMotionMotion

AccelerometerAccelerometer

MagnetometerMagnetometer

GyroscopeGyroscope

MotionRFRF

WiFiWiFi

BluetoothBluetooth

FM radioFM radio

ProcessingProcessing

MotionMotionMotion

Dead ReckonDead Reckon

IMUIMU

MotionRFRF

PropagationPropagation

ConstraintsConstraints

Floor planFloor plan

RF fingerprintRF fingerprint

AP locationAP location

LandmarksLandmarks

CRF ModelCRF Model

Viterbi AlgorithmViterbi Algorithm

Location Location

Ψ1

Ψ2

Fig. 1. System architecture.

reason for gyro-free motion sensing is the anticipated growthof the wearable device market, in which many ultra low powerchips (e.g. KMX61 and LSM303C) are not equipped withgyroscopes. Thus, algorithms that can afford not to use thesesensors are key to offering an always-on positioning service fora large range of low power devices. In summary, this paper’skey contributions are:

• Lightweight map-matching: The proposed MapCrafttechnique enables computationally efficient, real-timemap-matching using sensor data from multiple sourcesand a floor plan.

• Robust and accurate indoor tracking with noisy tra-jectories: We demonstrate excellent performance evenin the presence of bias, noise and distortions. Asan extreme case, we show accurate tracking can beobtained from gyro-free dead reckoning.

• Extensive real-world validation: We achieve hightracking accuracy in multiple environments (office,museum, market). MapCraft outperforms existing mapmatching techniques even without training.

The remainder of this paper is organized as follows: Sec. IIoutlines the system architecture and Sec. III overviews existingtechniques. Sec. IV introduces the CRF model and Sec. Vproposes MapCraft, a map matching solution that uses CRFsfor indoor tracking. Sec. VI extensively evaluates MapCraftin three indoor settings, and compares it with competingtechniques. Sec. VII concludes the paper and discusses ideasfor future work.

II. SYSTEM MODEL

The system architecture is shown graphically in Fig. 1,and is described through the use of an example. When a userenters a building and launches the tracking application, theapplication requests a floor plan (along with other meta-data

Fig. 2. The power consumption gap between gyro-free and gyro-aided sys-tems will increase with the emergence of digital motion processors (assuming1000mAh battery, gyro-free current of 0.5mA and gyro-aided 4.3mA).

as generated by other systems, which could include fingerprintmaps) from the server, if not already within the cache. Notethat this is the only time that a user needs to reveal anydata about their coarse position to a third party. Sensorson the user’s phone collect data about the motion and (ra-dio) environment. Motion sensors can include accelerometers,magnetometers and gyroscopes. Radio sensors can includeWiFi, Bluetooth (low energy), FM radio and so forth. Rawsensor data is typically not immediately usable and needs to beprocessed. In the case of motion data, this could include deadreckoning trajectories based on counting steps and estimatingheading, or using full IMU tracking in the case of foot mountedsensors. For RF data, a channel/propagation model can beused to relate received signal strengths to physical distances.Alternatively, raw signal strengths may be directly forwardedto the CRF model, to be later combined with RF fingerprintmap data if available.

Maps and observations are combined using conditionalrandom fields, an undirected graphical model described inSec. IV. The CRF model is particularly well suited to thissequential problem because it allows us to flexibly definefeature functions that capture the extent to which observationssupport states and state transitions, given map constraints.As a user moves through the building, certain paths becomeunlikely, as they violate map constraints. The Viterbi algorithmis used to efficiently find the most likely sequence of statesthrough the transition graph, culminating in an estimate of theuser’s location and quality thereof.

III. BACKGROUND

Before presenting our novel approach, we will first positionour work wrt the literature. We focus on techniques thatmake use of widely available infrastructure, such as inertialsensors embedded in mobile devices and wireless access pointsin buildings, which we divide into three classes: 1) motionsensing techniques that use magnetometer, accelerometer andgyroscope data; 2) RSS-based techniques that make use ofreceived signal strength readings from wireless Access Points(APs), and 3) Bayesian fusion of inertial and RSS sensor data.

A. Motion sensing

Motion sensing involves fusing data generated by inertialmeasuring units (IMUs) to compute the user trajectory relativeto her initial position. Some techniques assume that IMUs are

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mounted on the foot of the person [9], [12], [31], whereas oth-ers obtain data from IMUs embedded in consumer electronicdevices, such as smartphones [26]. Inertial motion sensing isperformed by iteratively repeating the following three tasks:1) Motion Mode Recognition, which uses accelerometer datato distinguish between different modes of movement (e.g.static, walking and hand texting, walking with phone in a bag,etc.) [26]; 2) Orientation Tracking, which uses magnetome-ter, accelerometer and, optionally, gyroscope data to estimatethe device orientation [11], [25]; 3) Step Length Estimation,which uses accelerometer data to estimate step length [20].Practical challenges in motion sensing, such as the sensitivityto phone position and the variability in user walking profiles,are explored in [17]. In cooperative scenarios, accuracy canfurther be improved by fusing inertial data with user encounterinformation [7], [27]. A major challenge with motion sensing isdealing with orientation errors due to magnetic field distortionsand sensor biases. This problem will be exacerbated whentrying to infer orientation without gyroscope, which will beincreasingly power-efficient with the advent of digital motionprocessors (Fig. 2).

B. RSS-based localisation

RSS-based fingerprinting is another popular method due tothe wide availability of wireless APs, and the cost benefits ofnot having to install and maintain special-purpose infrastruc-ture. Existing techniques, such as Radar [3], PlaceLab [16]and Horus [33], typically involve a training phase, in whicha building is surveyed and the signal strengths received ateach location from the various APs are recorded in a radiomap. Once a map is available, people can use it to deter-mine their own location by comparing the signal strengthsthat they receive from APs with those in the map. Furthertechniques have been developed to deal with heterogeneouswireless clients [13] or to exploit additional features of theenvironment, e.g. FM signals [6], sound, light and color [2].The main disadvantage of these methods is that they requirelabour intensive surveying of the environment to generate radiomaps. To address this problem, there have been a numberof simultaneous localisation and mapping efforts recently thataim to automatically build the radio map, by fusing RSS withmotion sensor data, as discussed in the next subsection.

C. Bayesian fusion of motion and RSS data

Existing fusion algorithms, such as Hidden Markov Model-s, Kalman and Particle Filters, are typically based on Bayesianestimation. They represent the conditional dependence struc-ture between observation and state variables using directedgraphical models (top of Fig. 3). It is often assumed that thesensor measurements are conditionally independent of eachother given the state. This is the basis of the Naive Bayesmodel (top left of Fig. 3). The extension of this model to asequence of states linked through transition probabilities leadsto recursive Bayesian models, such as HMMs (top center ofFig. 3). The joint probability distribution between all stateand observation variables is decomposed into a product ofconditional distributions (top right of Fig. 3).

p(S0:T , Z0:T ) = p(S0)p(Z0|S0)T∏i=1

[p(Si|Si−1)p(Zi|Si)] (1)

where S0, . . . , ST are the variables representing the real statesof a system (e.g. the locations of a person) over a time horizon0, . . . , T , and Z0, . . . , ZT are the observation variables over thesame time period. The problem of indoor localisation is eithercast as a filtering problem (find p(St|Z1:t)), or as a smoothingproblem (p(St−k|Z1:t), where k > 0) if the user can toleratesome delay, or as the inference problem of finding the mostlikely trajectory S0:T given observations Z0:T .

Hidden Markov Models (HMM) is a special class of arecursive Bayesian model where state variables are discrete,and the transition model p(Si|Si−1) is a matrix. HMMs havebeen widely used for map matching and location estimation,both outdoors using road maps [10], [18], [28] as well asindoors [23], [30], and they come in two flavours: one is thefirst order HMM where states represent user locations. Analternative is to model the transitions between pairs of locationsas the state itself. A limitation of both models is that theydo not take into account correlations between nearby inertialobservations, for example correlated magnetometer bias due tothe metal disturbances in the earth’s magnetic field. Section VIshows how this limitation impacts the accuracy of 1st [23], [28]and 2nd-order HMM algorithms [10].

Kalman Filters: An alternative approach is to consider thelocation of a user as a continuous variable and resort to aKalman Filter variant (e.g. [5]). Sensor fusion is typicallyperformed in two steps. First, the Kalman Filter estimates theposition of a moving node after taking into account its previousposition and the inertial sensor data. Then, RSS data are used toupdate the node’s position, abiding by map constraints. Similarto first order HMMs, Kalman Filters are effective when radiosignal strengths are periodically sampled from various accesspoints, and fused with inertial data; however, their performancedeteriorates when we solely make use of inertial sensors andthe building’s floor plan.

Particle Filters: Another common technique for performingonline map matching is to use a particle filter [1], [4], [17],[19], [31]. The key idea of particle filters is to approximate thedistribution p(St−1|Z1, . . . , Zt−1) by a set of particles. In eachround, these are first moved according to the transition model,their weights are then updated according to the observationmodel, and particles are then re-sampled according to theirweights. Over time, the particles typically converge to themost likely position of the user. One of the major issues ofthe particle filter is the computation time, as a large number ofparticles are typically required to ensure good estimation of thecontinuous probability distribution, especially when dealingwith noisy inertial data and large maps. Sec. VI shows thatour particle filter implementation (inspired by [19]) often failsto converge when using gyro-free dead reckoned data due toerrors in orientation estimates. When it uses the full suite ofIMU data and WiFi, it converges but at much higher cost.

WiFi SLAM: Other approaches such as WiFi-based SLAMfuse RSS and motion sensor data to simultaneously build amap of the environment and locate the user within this map [8],[21], [22].Recently, [32] proposed a SLAM approach that doesnot exploit the full power of dead reckoning but only measureswalking steps. SLAM approaches can be seen as orthogonal toour work: first, we assume that basic maps, i.e. floor plans, areavailable and there is no need to discover them; second, weview SLAM techniques as map generators providing optional

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( | ) ( | )( )Bayes Model Hidden Markov Model HMM Factor Graph

p(z2[2]|s2)

s0 s0 s1 s2 s0 s1 s2

p(s1|s0) p(s2|s1)p(s0)

z0 [1] z0 [2] z1 [1] z1 [2] z2 [1] z2 [2] z0 [1] z0 [2] z1 [1] z1 [2] z2 [1] z2 [2]z0 [1] z0 [2]

Linear Chain CRF Factor Graph

Linear Chain Conditional Random Field

Max. EntropyModel

s0 s0 s1 s2 s0 s1 s2

Ψ1 Ψ2

p

z0 z z

Fig. 3. Directed generative graphical models (top) vs. undirected discriminative models (bottom).

input to our map matching algorithm, e.g. radio fingerprintmaps [8], or organic landmark maps [24], [29]. Once floorplans (and optionally radio maps) are available, our focus is ondesigning sensor fusion techniques that make the best possibleuse of sensor measurements and maps in a way that is bothlightweight and robust.

In summary, existing techniques require either rich sensorsor intensive computation to yield good accuracy. In this paper,we propose a novel approach to resource-efficient localisationbased on conditional random fields.

IV. CONDITIONAL RANDOM FIELDS

CRFs are undirected probabilistic graphical models intro-duced by Lafferty et al. [15]. They have been successfullyapplied to a number of tasks in computer vision (e.g. clas-sifying regions of an image), bioinformatics (e.g. segmentinggenes in a strand of DNA), and natural language processing(e.g. extracting syntax from natural-language text). In allof these applications, the input is a vector of observationsZ = {Z0, . . . , ZT }, and the task is to predict a vector of latentvariables S = {S0, . . . , ST } given input Z.

Maximum Entropy Model: In order to introduce CRFs, wemust first introduce the Maximum Entropy Model (MEM). Achain CRF is an extension of MEM for state sequences, inthe same way that a HMM extends a naive Bayes model, asillustrated in Fig. 3. The Maximum Entropy Model assumesthat given incomplete knowledge of the probability distributionp(S0|Z0), the only unbiased estimate is a distribution that is asuniform as possible given training data (consisting of several(Z0, S0) values). This implies finding the model that has thelargest possible conditional entropy:

p∗(S0|Z0) = argmaxp(S0|Z0)∈P

H(S0|Z0) (2)

where P is the set of all models consistent with the trainingmaterial. To explain the meaning of consistency, let’s considera set of m features f1, . . . , fm, each one of which is a functionof observation and state variables. A model is consistent withthe training material when the expected value of each featurein the empirical distribution (training dataset) is equal toits expected value in the model’s distribution. Each feature

thus introduces a constraint, and finding p∗(S0|Z0) becomesa constrained optimisation problem. For each constraint aLagrange multiplier λi is introduced; the optimal solution inthe maximum entropy sense is log linear [14], [15]:

p∗λ(S0|Z0) ∝ exp(m∑i=1

λi ∗ fi(S0, Z0)) (3)

The conditional probability distribution of states givenobservations is thus proportional to the exponentiated sum ofweighted features.

Linear Chain Conditional Random Fields can be viewedas the sequence version of Maximum Entropy Models, in thesame way that HMMs is an extension of the naive Bayes clas-sifier model. In linear chain CRFs, the conditional probabilityof states given observations is proportional to the product ofpotential functions that link observations to consecutive states,as expressed in the equation below and shown in Fig. 3 (bottomright).

p∗λ(S|Z) ∝T∏j=1

Ψ(Sj−1, Sj , Z, j) (4)

where j denotes the position in the observation sequence, andΨ are potential functions. A potential function is composedof multiple feature functions fi, each of which reflects ina different way how well the two states Sj−1 and Sj aresupported by the observations Z.

Ψ(Sj−1, Sj , Z, j) = exp(m∑i=1

λi ∗ fi(Sj−1, Sj , Z, j)) (5)

Differences between HMMs and CRFs: HMMs are directedgenerative graphical models: they are trained to maximize thejoint probability distribution of observation and state variables,which they compute as a product of state priors and conditionalprobabilities of observations given states (top right of Fig. 3).In contrast to HMMs, CRFs are undirected discriminativemodels: they are trained to directly maximise the condition-al probability of state variables given observation variables,which they compute as a product of potential functions (bottomright of Fig. 3). Thus, unlike HMMs, in CRFs there is no

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need to model the exact conditional probability distributionsof observations given states (or state transitions). Instead oneonly has to define feature functions, as discussed in Sec. V-B.

Furthermore, the power of CRFs over HMMs lies in howthey link observations to each other and to states. CRFs areable to model both: 1) how observations relate to individual s-tates, as well as 2) how they relate to transitions between states.This is very convenient for tracking systems that make use ofinertial sensor data, which naturally depend on the transitionbetween two locations rather than on a single location. Usinginertial observations in a HMM would complicate things byeither having to use an input-output first order HMM, wheretransition probabilities depend on inertial data, or having tomodel the problem as a second-order HMM, where a staterepresents a transition between locations.

In HMMs observations at a given timestamp are typicallyconsidered independent of each other given the state (naiveBayes assumption), whereas in CRFs, it is possible to definefeatures that capture these dependencies. In addition, in H-MMs, observations generated at a given step only depend onthat step’s state. In CRFs, we are flexible to define featuresthat link an entire chain of observations (of arbitrary length)with a state or a state transition. This is useful when nearbyobservations are perturbated with correlated errors, e.g. when alocal distortion of the magnetic field affects several consecutiveheading observations. It is further useful when using RSSlandmarks for tracking; for instance, several RSS observationsmust be received after time t before deciding if the observationat time t is a peak value.

Finally, in CRFs, it is possible to define more than onefeature function that captures the dependency between a sub-chain of observations and a state (or state transition). Newfeature functions can be used to accommodate new sensingmodalities in a natural way.

V. MAP MATCHING USING CRFS

We are now in a position to describe our algorithm, calledMapCraft, which makes use of CRFs to track people in indoorenvironments1. MapCraft involves four distinct steps: 1) Mappre-processing; 2) Definition of states and feature functions;3) Training to determine feature weights; and 4) Inference toestimate location over time. The first three steps are performedonce for each building by either a mobile phone or a servicein the cloud. The fourth step is performed online on the user’ssmartphone to track themselves.

A. Map pre-processing

This step takes a floor plan as input, and produces a graphthat 1) encodes a set of discrete states (locations), and 2)represents physical constraints between discrete states imposedby the map. This information will then be fed to the secondstep, to help us define the CRF’s states and feature functions. Inour implementation, such information is obtained from mapsin various image formats. The main task is to extract edgesfrom the image needed to perform map structure recognition

1Since we assume that a floor plan (and optionally a radio map) is readilyavailable, we interchangeably refer to the tracking problem as the mapmatching problem.

or reconstruction, using standard edge detection algorithms.A graph is built on the reachable region of the map. Wefirst divide the graph into identical squares with edge lengthe. Small e increases the computational cost while large edegrades the map matching accuracy. A suitable choice of ein our system is the average step length of the trajectory tobe matched, e.g. 0.8 m. The neighbours of a target vertexare vertices which have a common geographical border withthe target vertex and pass the connectivity test as well. Theremoval of unreachable vertices is important to the systemperformance, because there is typically a large number ofvertices in the map that cannot be reached from the legalregion. The process of map generation and graph constructiononly happens once when a new map is used in the system.

B. Definition of states and feature functions

The output of the previous step directly allows us to definethe state space of the CRF, as the set of discrete locationsencoded in the vertices of the generated graph. We are nowin a position to introduce the set of feature functions usedby MapCraft. Recall that a feature function fi defines thedegree to which observations Z support our belief about twoconsecutive states (St−1 and St); the stronger the support, thehigher the value of the feature function fi(St−1, St, Z). Notethat in CRFs, we are free to use any subset of observations,generated at a single or multiple time steps, though in mostcases, the observations that matter are those temporally closeto time t. In what follows, we specify for each feature thesubset of observations that it uses, and how it relates them tostate transitions or, in some cases, to individual states.

The first feature in our system expresses the extent to whichan inertial measurement Zint supports the transition betweenstates St−1 and St:

f1(St−1, St, Zint ) = I(St−1, St) (6)

× (fθ1 (St−1, St, Zθt ) + f l1(St−1, St, Z

lt))

where I(St−1, St) is an indicator function equal to 1 whenstates St−1 and St are connected and 0 otherwise. The inertialobservation Zint has two components: the measured length Zltand angle (heading) Zθt of displacement, which are assumed tobe independent. fθ1 and f l1 are the functions to relate the angleand length to the underlying graph, respectively. The functionfθ1 is given as

fθ1 (St−1, St, Zθt ) = ln

1

σθ√

2π− (Zθt − θ(St−1, St))2

2σ2θ

(7)

where θ(St−1, St) is the orientation of the edge between statesSt−1 and St, and σ2

θ is the heading variance of the observationZθt . The feature function f l1 is defined likewise.

The purpose of the second feature is to handle correlationsin heading errors in a recent time window. It does so bymeasuring how well a corrected inertial measurement Zint (θ̂),derived by rotating Zint by angle θ̂, supports the transitionbetween states St−1 and St:

f2(St−1, St, Z0:t) = f1(St−1, St, Zint (θ̂)), (8)

The rotation angle θ̂ is estimated as the average headingdifference between the estimated and measured headings from

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time stamp t− w to t, where w is a window size parameter.

θ̂ =w∑i=1

Θ(SMLEt−i − SMLE

t−i−1 , Zθt−i)/w, (9)

where Θ represents the angle between two vectors, and SMLEt

is the maximum likelihood estimate (MLE) of the state at timet taking into account all measurement from 0 to t. MLE stateestimates are computed efficiently using the Viterbi algorithmas explained in Sec V-D.

The third feature function is optional, and it takes intoaccount the signal strength observations in conjunction with aradio fingerprint map, if it is available in a building. Unlike theprevious two feature functions, that constrain state transitions,this feature constraints individual states.

f3(St, ZRSSt ) = −(St − µt)

T (Σt)−1(St − µt), (10)

in which the observation ZRSSt is the estimated mean µt andcovariance Σt of current position given RSS fingerprint data.This feature measures the negative squared Mahalanobis dis-tance between the state and the RSS-based position estimate.

The CRF model used by MapCraft combines the threefeatures above into a potential function Ψj(Sj−1, Sj , Z, j),which is computed as the exponentiated function of theirweighted sum as shown in Equation 5. The way that weightsλi are determined is explained in the next subsection (Trainingstep). However, as we will show in Section VI, in typicalindoor environments, the training step is not strictly required,as using equal weights typically yields comparable locationaccuracy to that obtained after careful weight training. Hence,in practice the following training step can be skipped and equalweights can be assigned to the three features above.

The power of the CRF model is that it does not constrainus to only use the features above. Depending on the sensordata available and the maps available, it might be useful toextend the list of features. For example, suppose that we are inpossession of a radio map, denoted with PeakPointInMap(St),that contains the locations where the RSSI from an access pointtakes a local peak value (e.g. provided by [24]). We could thendefine a fourth feature as follows:

f4(St, Zt−w:t+w) =

{1 if Zt = max(Zt−w:t+w)

and PeakPointInMap(St)0 otherwise

(11)

In case the building is equipped with cameras, additionalfeatures could be added to incorporate visual sensor data. Ingeneral, CRFs provide a flexible model where a number ofdifferent observations can be fused into the model.

C. Training to determine feature weights

In many scenarios where CRFs are applied, the freedomof being able to define a number of different features comesat the cost of needing to estimate their weights. This steprequires training material T , which consists of one or more truetrajectories, paired with respective sequences of sensor obser-vations. Training the CRFs to estimate weights is performedby maximising the log-likelihood on the training material T :

Lλ(T ) =∑

((S,Z)∈T )

log p∗λ(S|Z) (12)

By taking the partial derivative of the log likelihoodfunction with respect to each feature λj and setting it to 0,we get the maximum entropy model constraint:

ET (fi)− E(fi) = 0 (13)

that is, the expected value of the i-th feature under theempirical distribution ET (fi) is equal to its expected valueunder the model distribution E(fi).

Setting the gradient to zero does not always give us ananalytical solution for the weights λi. This requires resortingto iterative methods, such as iterative scaling or gradient-basedmethods. Independent of the method used, one needs to be ableto compute E(fi) and ET (fi) efficiently. This is easily donefor ET (fi), since all we have to do is go over each trainingsequence, sum up the weighted sum of feature functions overall time steps, and sum up the result for all training sequences.

ET (fi) =∑

(S,Z)∈T

T∑j=1

fi(Sj−1, Sj , Z, j) (14)

Computing E(fi), however, is slightly more complicatedand requires the use of a dynamic programming approach,known as the Forward-Backward algorithm, similar to theone typically used for Hidden Markov Models. The details ofhow this algorithm is applied to CRFs can be found in [14].The time complexity of the Forward-Backward algorithm isO(|S|2T ), where T is the length of the sequence and |S| isthe number of discrete states.

The goal of the training is to tune the feature weights λi inEqn. 5 in order to make the features best support the trainingdata. The weight actually reflects how much we trust thecorresponding feature. For instance, if we set a large weight,e.g. 5, for feature f1(St−1, St, Z

int ), we can see from Eqn. 7

that it is equivalent to decreasing the length variance σ2l and

angle variance σ2θ much smaller, which means we consider

the length and angle measurements to be more accurate thanindicated by these variances defined in Eqn. 7. Therefore, itis not necessary to tune the weights from training data if thevariances of measurements are well defined.

It is also worth noting that large feature weights should beavoided, because they amplify slight differences in the featurevalues of two tracking solutions into significant differences inthe potential function ψ, due to the exponential function inEqn. 5. We suggest that all feature weights should be chosenfrom [0.5, 2], which works well in all our experiments indifferent environments. It is also demonstrated in Sec. VI withour empirical results from three different indoor environmentsthat the training step only has slight impact (< 10%) onlocalisation accuracy. The default setting of weights equal to 1for all features yields similar performance to weights derivedfrom training. Hence, in practice we do not need trainingmaterial (ground truth trajectories); we can directly proceedto the location inference step described below.

D. Inference to estimate location over time

The final step is finding the most likely sequence of hiddenstates, i.e. the most likely trajectory S∗. This requires solvingthe following optimisation problem:

S∗ = argmaxS

p(S|Z), (15)

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The Viterbi algorithm, a dynamic programming algorithm,offers an iterative solution with a worse case time complexityof O(|S|2T ), where T is the length of the trajectory in stepsand |S| the number of states. It is similar to the Forward-Backward algorithm used in each learning iteration, with thesubtle difference that it applies a maximisation instead of asumming operation in each induction step. More specifically,in each step, it evaluates the highest score δj(s) along a pathat position j that ends in each possible value s for state Sj ,as follows, and gradually fills a lattice with these values:

δj(s|Z) = maxs′∈S

δj−1(s′)Ψj(s′, s, Z, j) (16)

In the case of on line real-time tracking, the most recentlyfilled column of the lattice, which represents a discrete distribu-tion p(Si|Z1:i) is normalised and converted into a 2D Gaussiandistribution and displayed on the user’s map. If MapCraftis extended to employ features that use a few observationsafter the current step (e.g. feature f4), a slight delay will beintroduced in displaying a user’s location. In the case of delaytolerant off line tracking, it is possible to wait until the locationaccuracy is high before performing the path backtracking stepof the Viterbi algorithm, and computing the optimal path formthe lattice.

In our implementation, we introduced two additionalheuristics. First, we observed that in steps when the estimatedlocation accuracy is high it is beneficial in practice to replacethe current step’s discrete distribution with its Gaussian ap-proximation. This helps remove low probabilities far awayfrom the true location, and move them closer to the truelocation thus slightly extending the estimated error ellipse. Asa result, our algorithm became more robust to slight over- orunder- estimation of step length which, after several steps, canmake the estimated position drift away from the true position.The second optimisation was to use the inference step notonly for location tracking, but also to estimate heading ateach step. More specifically, when we have high confidencein a backtracked path generated by the Viterbi algorithm, wegenerate estimates of heading and compare them with theraw heading data provided by our inertial sensors, in order toestimate the bias of the gyroscope. We can close the loop bycorrecting the gyroscope’s bias when we have high confidencein our location estimates; we have observed that this feedbackloop further improves localisation accuracy.

VI. EVALUATION

Sites: To demonstrate the real world applicability of thetracking system, our map matching algorithm is evaluated andcompared against competing approaches in three real-worldsettings, namely an office building, a market, and a museum.All of these have different floor plans as shown in Fig. 8 andmethods of construction which affect the obtained sensor data.The office environment (65×35m2, where the majority of thetests have been conducted) is a multi-storey office buildingwith a stone and brick construction, reinforced with metalrebars - testing was conducted on the fourth floor. The market(108 × 53m2) consists of a number of small shops, laid outover a single floor. Construction is mainly brick and mortar,with a metal roof. The museum (109×89m2) is a multi-storeystone building with large, open spaces. Testing was conducted

on the ground floor. Overall, 500 trajectories of average length200 m were collected over 15 days.

Participants: The variations between different people aretaken into account by acquiring data from 20 people ofdifferent genders, heights, and ages. They may not appearin all three sites, but each one of them has participated inthe experiments in at least two different sites. During theexperiments, the subjects held the mobile phones in their handsand then walked anywhere in the building without plannedroutes, to realistically capture real pedestrian motion, ratherthan artificial, constant speed trajectories.

Devices and Implementation: Different types of mobilephones and pads are involved in experiments, including LGNexus 4, Asus Nexus 7, Samsung Nexus S, Samsung Galaxy SIV, Samsung Galaxy S III, Samsung I9100G Galaxy S II, HTCHero S and Huawei U8160. These mobile phones differ greatlyin terms of sensors, functionality and price. But one thing incommon is that they all run the Android operating systemno earlier than version 2.3.6. A snapshot of our applicationprototype has been shown in Fig. 1.

Ground truth: To provide accurate ground truth, numberedlabels were placed along corridors and within rooms on a3 m grid. Using the device’s camera, these were filmedat the same time experiments were conducted. The time-synchronized video streams were then mapped to locationson the floorplan, and intermediate locations interpolated usingfootstep timing, also obtained from the video.

Training: Fig. 7(c) shows the impact of training on theperformance of MapCraft. Training alters weights for thevarious input features, away from the nominal case of weights1 for all features (when the training iteration is 0). Severaliterations of training were run on a set of training trajectoriesobtained from the office environment. The weights from eachtraining iteration were then applied to each of the three datasets (trajectories from the office, museum, and market) forcross validation. Note that the RMS error of the trajectoriesin the office environment, where training was performed, isdecreased with the number of training iterations, but onlyslightly (up to 9%). The RMS error of market and museumtrajectories also do not vary much; it can even slightly increasebecause the training is performed in a different environmentthan testing. This implies that training is not critical to goodperformance and in practice, it can be skipped. The remainderof experiments, which are conducted with weights 1 for allfeatures, show that MapCraft is accurate without requiringcareful training to a particular environment.

Competing Approaches: We compare MapCraft with severalstate-of-the-art map matching algorithms. For readability, theirnames reveal the underpinning Bayesian estimation techniquewith references that point to source papers with implementa-tion details: 1) HMM [28]: This algorithm uses a first orderHMM, where states represent discrete positions, with equaltransition probabilities between neighboring states (regardlessof the vertex degree). An typical example is VTrack [28] whichworks very well using ground truth position estimates fromGPS as observations. Seitz et al. [23] extends VTrack andobtains the underlying graph of HMM from RSS rather thanGPS, by also exploiting position estimates from the inertialtrajectory as observations; 2) HMM-IO [23]: This is an Input-

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Fig. 4. Matched trajectories using MapCraft and competing approaches with gyro-free and gyro-aided simple raw trajectories.

Output first order HMM; the difference from the first orderHMM is that inertial data is not used to generate observationsat each step, but to calculate the transition probability betweenconsecutive states; 3) HMM2 [10]: In the second-order HMM,states are path segments connecting two locations in the map.Observations encompass both inertial displacement vectorsand RSS-based position estimates. Transition and observationmodels are defined as in AutoWitness [10]; 4) PF: This algo-rithm uses a particle filter implementation similar to Zee [19].Specifically, A total number of 2000 particles are used. Wealso implement similar step counting algorithm and exactlythe same particle update as Eqns. (3) and (4) in [19] withthe stride length variation δi uniformly distributed within±30% of the estimated stride length and heading perturba-tion βi ∼ N (0, 10◦). Generally speaking, these competingapproaches work well with simple structure trajectories, e.g.those generated in major corridors in a building, as shown inFig. 4. It is demonstrated below that the accuracy of theseapproaches decrease dramatically with tortuous trajectoriesshown in Fig. 8.

A. Performance Comparison

Accuracy/Sensor Tradeoff: The goal of the first experiment,which was conducted in the office site, is to explore thetradeoff between sensor usage and position accuracy. Differentsensors provide different accuracy in location or headingestimations. For instance, gyro sensors help improve headingestimates, esp. in the presence of magnetic field distortions,as are typically encountered in indoor settings. WiFi scansprovide helpful information about absolute location. Fig. 5shows three different regimes of map matching with increasinglevels of sensor usage: 1) accelerometer and magnetometeronly; 2) full inertial sensing: accelerometer, magnetometer,

and gyroscope (no WiFi; 3) full inertial sensing with periodicWiFi RSS measurements. Notice that MapCraft significantlyoutperforms competing algorithms under all three regimes,typically resulting in errors two to three-fold lower thanthe next best approach (2000 particles are used in PF-basedapproach).

Specifically, Fig. 5(a)) shows the error CDF with onlyaccelerometer and magnetometer measurements, such as wouldbe used in a system aiming to consume minimal energy. Thelack of gyro readings makes the heading estimation very inac-curate, especially in areas with high concentrations of metal.As a consequence, the whole raw trajectory is very noisy.These distorted trajectories greatly deteriorate the performanceof existing methods whilst our approach remains robust tonoisy sensors. One of the key reasons is the use of featuref2 that handles heading error correlations. Fig. 5(b) showsthe error distributions with full inertial measurements. Thegyroscope provides more accurate heading estimation over ashort period of time. However, over time, the accumulated errorbecomes excessively large. However, due to the features in oursystem, the accumulated error is gradually reduced in eachstep, which guarantees the accuracy of the heading estimationand yields accurate matching results. Fig. 5(c) shows theerror CDF with periodic WiFi measurements, taken every 16seconds. These are used, in conjunction with a radio finger-print map, to provide absolute position estimates. With thesemeasurements, the performance of HMM and PF improvessignificantly. However, the performance of MapCraft increasesfurther still with the combination of relative and absolutemeasurements. This is because it captures more features ofthe measurements across both time and space.

Execution time and memory use: Next, we investigate thecost of MapCraft on a mobile phone (LG Nexus 4). We

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Fig. 5. Error CDFs for various map matching approaches with increasing number of sensors a) gyro-free and b) gyro-aided and c) wifi- and gyro-aided.

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Fig. 6. Comparisons of (a) execution time, (b) memory usage and (c) convergence distances of the various map matching approaches.

show that, not only it is more accurate, but it also offerssignificant computational and memory savings compared toexisting approaches. This makes it lightweight and practical torun on resource-constrained mobile devices such as phones andwearable sensors. For a highly responsive pedestrian trackingapplication, the processing time for each step should be lessthan 300ms. Meanwhile, the memory limit for a single appli-cation on current Android platform is 20 MB. Any algorithmwith requirements exceeding these limits is not suitable forreal-time pedestrian tracking with existing hardware. Fig. 6shows the execution time and RAM usage of the various mapmatching algorithms2. Time (ms) in Fig. 6(a) is estimated asthe average time to process a single step over the trajectoriesgenerated in the office site. Approaches using Viterbi decoding(CRFs, HMM, HMM2) have a time complexity of O(N2T ) intheory (N is the number of vertices). But different formulationsof graph have different sparsity degree, resulting in varyingrun time costs. Note that MapCraft outperforms the otherapproaches, with an execution time of 10 ms, whilst obtainingthe lowest RMS error.

The memory requirements of the various approaches areshown in Fig. 6(b). HMM2 in its current form cannot bedeployed on an Android device due to the very high RAMusage of approximately 50 Mbyte. This is because it is based

2The execution time and memory usage of MapCraft are first tested in LGNexus 4. All algorithms including MapCraft are implemented and tested inMatlab. Then the execution time and memory usage of other approaches arescaled relative to the values from the MapCraft real tests.

on a second order HMM which leads to exponential memoryusage with the number of states as the entire transition matrixneeds to be stored. HMM(Seitz) and PF are close to thelimits of an Android application. HMM(VTrack) and MapCraftconsume a similar amount of RAM (4 Mbytes), but the RMSEof VTrack is considerably higher.

Convergence distance: The proposed and competing algo-rithms are designed for online tracking. However, in theabsence of WiFi measurements and without knowledge of theinitial pose, they initially incur a convergence cost, whichwe measure as the average minimum distance needed forthe algorithm to find the correct location within an errorof 3 m. Fig. 6(c) shows that for 97% of cases, MapCraftconverges within 50 m and the next best, HMM2, within 60 m.The HMM (Seitz) and PF approach show considerably worseperformance, in some cases never converging. Even with avery large number of particles (100k), the PF approach failsto converge in many cases due to impoverishment. VTrack isunable to estimate the correct location, as it requires a goodinitial starting point estimation. Note that when WiFi-aidingis used, all algorithms provide a good location estimate after2-4 m.

Discussion: The underlying reason for the superiority ofMapCraft in tracking accuracy is the ability to model dis-placements of inertial trajectories without prior assumptions,as we have discussed in Section IV. The first-order HMMmatches the locations rather than the displacements of the

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raw trajectory to possible location sequences in the map,and thus its performance can be easily degraded with avery noisy raw trajectory due to the increasingly accumulatedlocation error from the inertial measurements. We have tomake prior assumptions on the transition and observationprobability distributions for HMM and HMM2, which are onlyapproximations of the real world scenarios. In addition, theHMM category (HMM, HMM2, and HMM-IO) all assume theindependence of observations given the state but unfortunatelydifferent observations are likely to be correlated, both spatiallyand temporally. As explained in Section IV, CRF makes nosimilar assumptions, which makes it easy to capture thesedependence and accurately model the tracking process as itis. As a result, CRF has better accuracy in general, especiallywith torturous trajectories in long-term tracking.

The PF approach is sensitive to motion sensing errors,especially the heading bias caused by magnetic disturbance ofmetallic objects, which is ubiquitous in indoor environments.In our experiments, the magnetic disturbance from one bigmetallic object usually lasts for 5 to 15 meters and can be aslarge as 30 degrees, which is very likely to mislead all particlesinto the wrong room, especially with very tortuous trajectoriesgenerated in our experiments. Since the PF approach onlyhas local information about the region covered by particles,if all particles enter a wrong room it is hard to recover to thecorrect position. Furthermore, if the heading bias comes at thebeginning of the tracking process, it is difficult for the particlefilter to converge without knowledge of the initial pose of thepedestrian.

The MapCraft is lightweight in both running time andmemory usage because it neither stores transition or emis-sion matrices (only several feature functions) nor performsexpensive matrix operations. The HMM category, especiallyHMM2 whose state space is much bigger, take more runningtime and memory for processing transitions and emissions. Therunning time and memory usage of HMM-IO are comparableto MapCraft when the number of features is small, e.g. 2or 3 in our experiments because the transition and emissionprobabilities are computed in a real-time manner.

The running time and memory usage of particle filter large-ly depends on the number of particles. The major computationcost comes from checking whether the position update of eachparticle violates the map constraints. The results shown inFig. 6 are obtained with 2000 particles.

B. Robustness

The next set of experiments are performed to examinethe robustness of MapCraft and its applicability to real worldscenarios. It must be emphasized that all these results are forthe WiFi-free case, i.e. the only input to the system is a floorplan and IMU data. The results that we had with WiFi wereeven better, but we do not show them for space reasons.

Long-term tracking: First, we studied the repeatability ofaccuracy results as we run MapCraft for long time periods,resulting in inertial trajectories that are increasingly distortedwith respect to the true trajectory. Fig. 7(a) shows the resultsof an experiment where the same route was followed 50 timesin the office environment by different people with differentmobile phones and the resulting trajectories calculated. Note

that although the raw inertial measurements are significantlydifferent each time, the map-matched trajectories are verysimilar. This shows that the map matching process is ableto accurately reconstruct the correct trajectory, in spite ofexcessive and varying metal-induced distortions to the headingestimation.

Multi-site performance: We then studied the robustness ofMapCraft in a variety of environments, namely an officebuilding, a museum and a supermarket.

Very complex and tortuous trajectories typically are theweakness of inertial tracking systems, due to drift and theabsence of absolute anchor measurements. However, by usingthe map matching approach, very accurate reconstruction canbe provided even when the user executes a complex trajectory.This is shown in Figure 8. The cumulative distribution functionof location errors in the three environments are shown inFig. 7(b).

The room-level accuracy, defined as the percentage ofmatched trajectories entering the correct room, and overall 97percentile accuracy is shown in Table I. The room level accu-racy is above 90% in all environments, which demonstrates theapplicability of our approach to tackling real-world navigationproblems. This compares well with other approaches based onextensive and multimodal radio fingerprinting [6].

TABLE I. RMS ERROR, 97 PERCENTILE ACCURACY ANDROOM-LEVEL ACCURACY OF MAPCRAFT IN THREE SITES.

Site office museum marketRMS error (m) 1.69 1.14 1.83

97 percentile (m) 4.10 2.37 4.53Number of rooms 20 15 29Room entry-events 357 360 82

Room identification (%) 93.0 100 96.3

Impact of training: Finally we studied the impact of trainingon the tracking accuracy of MapCraft. Consistent with what wehave discussed in Section IV, the feature weights trained fromground truth trajectory do not provide significant accuracyimprovements, as shown in Fig. 7(c). To demonstrate therobustness of MapCraft over the feature weights, we onlytrain the model with ground truth trajectories from the officeenvironment and apply the same weights to all three exper-iment sites. It is observed from Fig. 7(c) that the changein accuracy after ten iterations are less than 30 percent.Note that there is a slight increase in the museum site aftertraining over five iterations. and then the accuracy remainsunchanged henceforth. Fig. 7(c), feature weights used in allthree experiment site are the same weights trained from theground truth trajectories in office environment.

VII. CONCLUSION

We demonstrated the merit of a novel map matchingtechnique, based on the application of conditional randomfields. We have shown how it is robust, being able to operatewith very noisy sensor data; lightweight, running in under 10ms on a smartphone; and accurate, achieving the lowest RMSerrors compared with other state-of-the-art approaches. It doesnot require per-site training, which will allow for easy andwidespread adoption, as the only information that is requiredto use our approach is a floorplan. In the future, our system has

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the potential to make crowd-sourcing of WiFi fingerprints prac-tical, without requiring time-consuming manual scans. This isbecause MapCraft is able to establish a user’s position usingonly dead-reckoned trajectories and a floorplan, without anyexternal information such as a starting location or knowledgeof WiFi access point locations. We believe that MapCraft haswidespread application to a number of domains, as this singleapproach can be used with a wide variety of sensors andmap information. One particularly relevant area is estimatinglocation online and in real-time in resource-constrained body-worn sensors. In summary, we have presented a system thataddresses the very pressing problem of providing accurate, lowpower, indoor tracking, that is responsive, robust and scalable.

ACKNOWLEDGMENT

The authors would like to thank the anonymous reviewersfor their invaluable comments and suggestions. The authorsalso thank Prof. Phil Blunsom from University of Oxfordand Dr. Andrew Symington from University College Lon-don for the useful information and helpful discussions. Thiswork is also partly supported by the HARPS EPSRC project(EP/L00416X/1).

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