The impact of sensor errors and building structures on particle filter-based inertial positioning

Pervasive and Mobile Computing 8 (2012) 764–776

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Pervasive and Mobile Computing

journal homepage: www.elsevier.com/locate/pmc

The impact of sensor errors and building structures on particlefilter-based inertial positioningThomas Toftkjær 1, Mikkel Baun Kjærgaard ∗

Department of Computer Science, Aarhus University, IT-parken, Aabogade 34, DK-8200 Aarhus N, Denmark

a r t i c l e i n f o

Article history:Received 5 January 2011Received in revised form 7 April 2011Accepted 12 July 2011Available online 23 July 2011

Keywords:Inertial positioningParticle filterGPSError sources

a b s t r a c t

Positioning systems that do not depend on in-building infrastructures are criticalfor enabling a range of applications within pervasive computing. Particle filter-basedinertial positioning promises infrastructure-less positioning, but previous research has notprovided anunderstanding of how the positioning accuracy of such systemsdepends on thesensor errors and the building structure. This paper evaluates the impact of sensor errorsand building structures on the positioning accuracy using a waist-mounted system namedPro-Position. We analyze results from deploying the system in regular and open spacedoffice buildings as well as in a shopping mall. The results show that differences in accuracycan be explained by error sources of the sensor and the constraints provided by buildingstructures. Additionally, we present and evaluate methods for using GPS positioning withparticle filter-based inertial positioning to improve accuracy in large open areas and toprovide seamless handover when entering buildings.

© 2011 Elsevier B.V. All rights reserved.

1. Introduction

Applying the visions of pervasive computing to a variety of domains require indoor positioning independently of localinfrastructures. Examples of such domains are fire fighting [1], search and rescue, health care and police work. Many otherposition-based applications would, furthermore, benefit from indoor positioning technologies, that do not depend on a localinfrastructure [2]. Another motivation for avoiding local infrastructure-based positioning systems is the costs for installing,maintaining and calibrating the systems, e.g., for WiFi [3,4], Powerline [5], GSM [6] or Ultra-wide band positioning [7] orthe requirement that other nodes should be present for radio-based ad-hoc positioning [8]. A third reason is that in manyindoor areas satellite systems such as GPS do not provide pervasive coverage and provide a problematic accuracy whenavailable [9].

Pedestrian inertial positioning is a technology promising infrastructure-less positioning by depending solely on sensingmovement. The primary focus has been devoted to foot-mounted and waist-mounted inertial systems. The waist-mountedsystems such as the one presented by Judd [10] have the advantage that they can be naturally worn attached to a belt andcan easily be re-mounted on another person. The system proposed by Constandache et al. [11] also suggests that this type ofsystemwill be feasible for smart phones. Recent researches from Foxlin [12] and Beauregard [13] have argued for using foot-mounted inertial-based systems for tracking pedestrians, due to the possibility of using zero velocity updates to improveaccuracy.

In this paper we focus on waist-mounted systems, which have slightly lower accuracy than the foot-mounted systems.In principle the error growth for both types of system is linear with time [10,14] with just the magnitude being different.Therefore our results forwaist-mounted systems are also indicative for foot-mounted systems. Earlier research has provided

∗ Corresponding author. Tel.: +45 89425674; fax: +45 89425601.E-mail addresses: [email protected] (T. Toftkjær), [email protected] (M. Baun Kjærgaard).

1 Current address: Systematic A/S, Søren Frichsvej 39, 8000 Aarhus C, Denmark.

1574-1192/$ – see front matter© 2011 Elsevier B.V. All rights reserved.doi:10.1016/j.pmcj.2011.07.001

T. Toftkjær, M. Baun Kjærgaard / Pervasive and Mobile Computing 8 (2012) 764–776 765

evidence that the accuracy of foot-mounted systems can be improved, when combined with particle filters informed bybuilding models [15,14]. Our contribution here is evidence that the same factor of improvement can be realized with waist-mounted sensors, and furthermore provides seamless handover from outdoor positioning, e.g., from GPS to indoor inertialpositioning.

For particle filter-based inertial positioning to become a widely usable indoor positioning technology, it has to workin any type of building structure. For existing systems [15,14] only evaluations in office buildings with narrow corridors2–3 m wide and small rooms approximately 16 m2 were considered. Because these particle filters use walls as constraints,such office buildings provide many constraints that can help improve accuracy. These office buildings are, however, notrepresentative of common buildings such as shopping malls, open-spaced office buildings or public schools and thereforean understanding of the relationship between the building structures in general and the performance of particle filter-basedinertial positioning is needed. Such an understanding is critical to help guide the design of new particle filter-based inertialpositioning solutions that can be pervasively deployed.

Previous research [15,14] did not consider the important problem of starting outside from a GPS determined position.However, this is unfortunately not a trivial problem. Since, depending on the building structure and the entering and exitpoints, the particle cloud might avoid or only partially enter or exit the building under scrutiny. If the cloud does not fullyenter the building, the outside part will quickly grow because of fewer outdoor restrictions compared to indoor. We presenta solution to the problem using GPS as an indoor versus outdoor sensor.

We make the following contributions in this work: First, we present Pro-Position, a waist-mounted inertial and GPS-based system that uses particle filters informed by building models. We evaluate the proposed system, for the purpose ofshowing that the system can provide an accuracy that is comparable to that of foot-mounted systems given the buildingstructures. Second, we report findings for a regular office building, an open spaced office building and a shopping mall toprovide evidence for how the positioning accuracy depends on the sensor errors and the building structure. We propose toclassify the impact of building structures by considering the unconstrained area surrounding a pedestrian. Third, we presentand evaluate methods for using GPS positioning with particle filters to improve accuracy in large open areas, to provideseamless handover when entering buildings and to avoid outside rapid particle growth. The evaluation, furthermore, takesdifferent thresholds for when to use GPS measurements into account.

2. Related work

Tracking pedestrians with inertial sensors have been a long standing research goal. The classic double integration basedsystems successful in vehicular and flight applications are too bulky and power consuming to use for pedestrians. Researchhas therefore proposed systems for pedestrians using different sensors, sensor placements and algorithms and recentsystems have made use of a priori information concerning buildings with the purpose of improving accuracy.

An early system proposed by Judd [10] is worn on the torso. The system uses tri-axial accelerometers to detect stepsand tri-axial magnetometers for tilt-corrected headings. It includes a Kalman filter that can make use of an external GPS ifavailable and a barometric altimeter, where the latter is not further described.

Placing sensors on the foot enables zero velocity updates during the resting phase of the foot where one can assume thatthe foot is notmoving. The application of zero velocity updates replaces the cubic error growth over timewith a linear growthfor the number of steps. An early evaluation by Randell et al. [16] studied several foot-mounted systems, where motion wassensed by detecting steps and their magnitude provided from accelerometer readings. Each step was then directed in theheading provided by the used compass. Amoremature system named NavShoe is proposed by Foxlin [12], and is also a foot-mounted system using tri-axial accelerometers, magnetometers and gyros. For this system Foxlin proposed an algorithmbased on a Kalman filter with zero velocity updates to fight drift. Godha et al. [17] has furthermore evaluated a comparablesystem.

BothWoodman andHarle [14] andWidyawan et al. [15] propose to combine foot-mounted inertial sensors with buildingmodel informed particle filters. The building model is used to provide constraints for the particle filter to allow particles tomove through doors and up stairs and to disallow them to pass through walls. Based on step events measured by the foot-mounted inertial sensor, the particle filter applies building constraints. Woodman and Harle report an accuracy below onemeter for a 450 m2 area consisting of narrow corridors and small rooms, and only after the particle cloud has converged toa single cluster. In [18] the authors note that such convergence is often delayed by symmetry and could even in some casesbe prevented.

The systempresented byWidyawan et al. [15] uses amore computational heavy backtracking particle filter, but a simplerstep detection algorithm compared to the system by Woodman and Harle [14]. In their evaluation Widyawan et al. startoutside a building at a manually surveyed point and orientation, which provides an artificial help for their system, and thewalk into an approximately 1100 m2 large building. With a detailed building model they achieve a mean accuracy of 1.3 m.They also consider removing the interior of the building, which decreases the mean accuracy to 1.8. Once again in this casethe building is rather small and with narrow corridors.

In comparison this paper report findings for a particle filter-based waist-mounted system in a 1967 m2 regular officebuilding, a 3162 m2 open spaced office building and a 33, 462 m2 shopping mall, where the later includes a single 3749 m2

shop. Based on the results from these buildings, we provide evidence that the positioning accuracy depends directly onthe sensor errors and the building structure and that a particle filter-based waist-mounted system can provide an accuracy

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Fig. 1. Overview of Pro-Position with sensors, building models and particle filter.

comparable to that of foot-mounted systems given the building structures.We propose to analyze the building structures bycomputing the unconstrained area surrounding the pedestrian.We considermethods for using GPS positioningwith particlefilters to improve accuracy in large open areas and to provide seamless handover when entering buildings.

3. Positioning using Pro-Position

In this paper we present Pro-Position, a particle filter-based inertial positioning system for both indoor and outdoorpositioning. Pro-Position consists of three elements: Firstly, sensors that measure movement and absolute position, i.e., awaist-mounted inertial sensor and a high sensitivity GPS receiver, secondly, building models in 2.5 dimensions consistingof a 2D plane for each floor and, thirdly, a particle filter (see Fig. 1).

3.1. Sensors

The sensor part of the system is realized using a waist-mounted inertial sensor and a high sensitivity GPS receiverboth connected to a small form-factor computer. The inertial sensor used, is a waist-mounted Honeywell DRM 4000 dead-reckoningmodule [19], which contains tri-axial accelerometers,magnetometers and gyros aswell as a barometric altimeter.The module is low-power and comparable in price to the Xsens sensors used by both Widyawan et al. [15] and WoodmanandHarle [14]. Themodule usesmotion classification algorithms to analyzewalkingmotion and compensate, when the useris running or just fidgeting in place. An automatic compass orientation algorithm provides accurate azimuth information,when the user is upright or prone, and the gyros are used to compensate for transient magnetic disturbances and transientaccelerations, that may interfere with compass operation. The barometric altimeter provides vertical positioning. Themodule provides displacement vectors and altitude readings to our system. The DRM 4000 module is used with factorysettings to avoid making any assumptions of the environment or person wearing it. Finally as the GPS receiver, we use thehigh sensitivity receiver U-Blox EVK-5H [20].

3.2. Building model

The system requires the use of building models to constrain movement with a particle filter. It will be impossible forbuilding models to include all the obstacles that constrains a pedestrian’s movement in a building and we will thereforerestrict the information to permanent walls, doors and stairs. For instance, the evaluated shopping mall includes a lot ofnon-permanent walls and other interiors, which are not modeled, since it does not seem feasible to keep such informationup-to-date.

We furthermore assume that a two and a half dimensional model will be sufficient to model a building, as also arguedfor byWoodman and Harle [14]. The model contains a plane for each floor, which can be connected to each other. Wemakethe assumption that permanent walls are impassable except through openings, such as doors. Rooms are represented bypolygons and doors by placing an opening on the edge of a room polygon and linking this to the opening of another roompolygon. Openings in the outer building polygons can have connections to the outside instead of another polygon. Eachpolygon exists fully in the plane of the floor, it is assigned to, but opening connections may connect to openings of otherfloor planes to represent stairs. To represent complex rooms, that contain other rooms, the model allows polygons to haveinternal boundaries defined by other polygons. The building model also allow modeling the thickness of walls by placingthe polygons appropriately apart.

3.3. Particle filter

Several papers have established the particle filter as a well suited Bayesian filtering technique for positioning [14,15].The particle filter in this paper is based on the descriptions in these articles. The Pro-Position filter is a SamplingImportance Resampling (SIR) algorithm using a fixed number of particles in each resampling step, which is done tomaintain

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Fig. 2. A particle cloud inside the shopping mall building. Permanent walls are shown in grey and openings in red. (For interpretation of the references tocolour in this figure legend, the reader is referred to the web version of this article.)

approximately the same computational speed for all iterations of the algorithm. The resampling strategy chosen is thesystematic resampling algorithm [21].

The particle filter is an recursive algorithm, that in this context fuses streams of position sensor data, corrects for variousconstraints and bounds, e.g., building models, and gives an estimate of the position of an entity either in the form of aprobability density function, or a position. This is visualized in Fig. 1.

3.3.1. The algorithm step by stepAs the name implies a particle filter uses the concept of particles to represent an approximation of probability density

function. Each particle has a position and a weight, which is the probability that the position of the particle corresponds tothe pedestrian’s actual position. Fig. 2 shows the distribution of particles at a certain iteration from the mall experiment. Inthe Pro-Position system we initialize the particles by using a GPS or groundtruth fix. The particles are positioned accordingto a Gaussian distribution with the fixpoint as a mean and an appropriate standard deviation.

For each displacement vector (l, δθ ) received from the dead-reckoning module, each particle is propagated by a vector vwhere l is the estimated step length and δθ is the heading change. The particle propagation vector v is for each individualparticle generated from (l, δθ ) by adding white Gaussian noise. For the step length l according to an error distribution forstep length estimation and for the heading change δθ according to an error distribution for compass noise.

The correction part of the algorithm adjusts the particle weights according to the constraints such as the building. Thisis primarily done by penalizing particles that have passed through walls. One might ask whether maintaining expressivepower in the particle cloud by changing the path of such particles to a path that is valid in the context of the building model,i.e., bouncing the particles of walls, is a good idea. This could be a valid approach if the system could depend on other sensorsto correct the weight of the particles away from a bad hypothesis, but since this is not the case for Pro-Position, wewill haveto use the collision with walls as evidence of a bad hypothesis. This approach is also used by Woodman and Harle [14], andactually the localization technique in that paper would not work without it. To address the critical problem of outside rapidparticle growth Pro-Position uses a GPS receiver as an indoor/outdoor sensor, i.e., killing off all particles that are outsideaccording to the building models, when no GPS signals have been received for an appropriate time period.

As mentioned earlier the particle filter resamples using a systematic resampling algorithm and resamples in a way thatensures that the size of the particle set remains constant. Resampling is done to avoid a high variance in the set of particles.If the variance increases too much, the probability density function, that the set of particles represents, would be poorlyapproximated at the most probable positions.

The particle set is evaluated for the best position estimate, which is usually done by doing a simple mean calculationor by calculating the position of the largest cluster of particles. Afterwards a new iteration of the particle filter commenceswith new measurements.

4. Experimental setup

We have evaluated Pro-Position in three buildings: a 1967 m2 regular office building, a 3162 m2 open spaced officebuilding and a 33, 462 m2 shopping mall. These buildings were selected because they offer different conditions forpositioning both in terms of building type and availability of GPS. The building layout of the three buildings are shownin Figs. 3–5 together with the evaluation paths and the sizes of the buildings. The regular office building consists of corridors2–3 m wide with offices 12–55 m2 in size connected to them. The open spaced office building has a few corridors 2–4 mwide, but consists mainly of a 1120 m2 open space connected with offices from 15 to 30 m2. The shopping mall consists of5–6 m wide corridors and shops from 143 to 3749 m2. Each building was modeled in the building model described in thesection named ’Building Model’ from blueprints of the buildings.

For each building three paths starting outdoor going indoor through different areas of the buildings and out again wereselected and manually surveyed. In the regular office building the paths were 293 m, 294 m and 308 m, respectively. In theopen spaced office building the paths were 204 m, 237 m and 177 m, respectively and in the shopping mall the lengths ofthe paths were 403 m, 389 m and 504 m, respectively.

For the evaluation, the Honeywell DRM 4000 inertial sensor was mounted on a pedestrian’s waist using a commerciallyavailable runners belt. To achieve the best performance from the inertial sensor it was placed right above the coccyx, as this

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Fig. 3. Ground truth for shopping mall (242 m × 143 m).

Fig. 4. Ground truth for open spaced office building (62 m × 51 m).

is themost directionally steady position on the human torso [10]. It should be noted that theDRM4000 uses amagnetometerfor estimating directions of vectors. At the side of the runners belt a U-blox GPS receiver was placed and at the front thestandard U-blox antenna. Both the inertial sensor and the GPS receiver were connected via USB to an Asus tablet PC runningWindows Vista. The tablet PC uses a UMTSmodem to connect to the internet for receiving A-GPS information for the U-bloxreceiver.

For evaluating the system, a person walked the chosen paths pressing a button on the tablet PC, when passing selectedpoints, where a change in the pedestrian’s speed or direction seemed likely, e.g., stops, turns andwhen opening closed doors.For each button press the current system time was recorded together with the point coordinates as ground truth data forthe evaluation. Between data points constant movement speed is assumed and therefore a linear interpolation was applied

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Fig. 5. Ground truth for regular office building (100 m × 41 m).

to get ground truth data for the periods between button presses. This should provide an acceptable ground truth accuracybelow half a meter. During evaluation inertial sensor events and GPS events were logged on the tablet PC together with thecurrent system time. The logged data was then later processed in real-time by a particle filter implemented in Java runningon a laptopmimicking a server computing platform. The laptop had an Intel Core 2 Duo CPU 2.20 GHz and 3 Gb RAM runningWindows XP service Pack 2. The particle filter ran with a particle limit of 5,000 particles, which allowed it to run in real-time and finish each iteration within the 2,000 ms time slot given, before the next time event was triggered. From initialexperiments the following system parameters were selected for the dead-reckoningmodule: a standard deviation of 15° forthe error distribution for the heading change and 12 cm for the error distribution for the step length estimation.

5. Accuracy of waist-mounted systems

In this sectionwewant to present results to compare the improvements that particle filter based positioning can providefor foot and waist-mounted sensors. We use the results from our measurement campaign in three different buildings usingPro-Position with a waist-mounted sensor. The results are presented in Table 1 for each path divided into raw sensor andPro-Position and with the median and the 95% error. The positioning error is calculated as the Euclidean distance betweenthe ground truth and the estimated position. In both cases the first ground truth measurement was used for initialization,which means that the initial error is zero, the initialization is done this way for evaluation purposes and in the live systeminitialization is done with GPS. The raw sensor error is calculated by comparing the dead reckoning vector measured at timet with the ground truth vector formed by the previous ground truth position at time tprevious and the current ground truthposition at time t , the difference is the raw sensor error.

The raw waist-mounted sensor has in the two office buildings a median accuracy of 8.0–11.3 m which is comparableto the 8.0 m reported by Widyawan et al. [15] for their foot-mounted sensor. However, in the longer mall experiments theerror for the waist-mounted sensor adds up to 17.5–25.3 m. The particle filter developed by Widyawan et al. [15] is able tominimize the average error to 1.5 m for the foot-mounted sensor readings whereas Pro-Position in the best case is able todecrease themedian error to 2.5m.Woodman andHarle [14] are ablewith their foot-mounted sensor using particle filteringto minimize the error below 0.5 m but do not state the error of their raw sensor. Therefore one can conclude that the rawsensor reading of our waist mounted sensor is in three of our experiments as good as a foot-mounted but in the remainingsix it is not. Furthermore, Pro-Position was able to considerably improve the accuracy of the waist-mounted readings butnot as much as has been demonstrated for foot-mounted sensors. It is, however, unclear how the foot-mounted systemswould perform in large open buildings such as the mall because both Woodman and Harle [14] and Widyawan [15] didtheir measurements in office buildings.

To analyze the accuracy in the different buildingswe here discuss our results for the 95% quantile. For theMall the overall95% quantile error is around 15m, one path in particular affects this errorwhich is the longest one.2 This path is also the paththat enters a large shop which means fewer constraints for the particle filter. Otherwise the error is around nine meters forthemall. The open spaced office has an overall error of around 13mwhich is less than in themall. This difference is expectedas the paths in the open spaced office are shorter and the constraints are tighter. There is one path though that sticks outwitha 95% error of 15.4 m. Further analysis has shown that this can be attributed to a large sensor error that occurred midwaythrough this path. Even though with this anomalous event the overall accuracy is still around two meters better than in themall. For the regular office the errors are significantly smaller. This is as expected, we anticipated that the regularity of theconstraints in the buildings and the layout would have an influence on the performance of the system.

To provide a better understanding of the impact of the different error factors we will in the following section considersensor errors and the impact of the building structure in more detail.

2 The length of the individual paths can be seen in the Experimental Setup section.

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Table 1Median and 95% quantile results for the raw sensor and Pro-Position (PP).

50% (m) 95% (m)Sensor PP Sensor PP

Mall 1 18.34 3.41 28.71 9.60Mall 2 17.47 4.27 32.81 8.70Mall 3 25.28 5.12 32.81 15.98Mall total 21.40 4.61 31.88 15.06Open office 1 8.03 2.95 11.65 8.41Open office 2 11.27 8.58 32.46 15.36Open office 3 10.56 3.87 14.33 7.68Open office total 9.19 4.84 31.72 13.16Regular office 1 9.12 2.52 26.23 5.39Regular office 2 10.59 3.09 16.17 6.59Regular office 3 8.48 3.87 22.68 9.50Regular office total 9.30 3.08 24.54 7.55

6. Error factors of particle filter-based inertial positioning

In this section we will analyze the factors that influence the performance of particle filters. There are a number of errorfactors that directly influence the performance and some that only indirectly impact it such as the properties of the chosenbuilding or properties of the chosen path for the experiments. We will in the following try to give a thorough listing ofperformance factors and then go into more detail with two of them.

The reason for using particle filters is to estimate position while we have noisy data from the inertial sensors, which isthe major source of positioning errors. The noisy data covers both physical properties of the surrounding materials suchas for example magnetic anomalies, difference in gait from person to person and the internal error and noise in the sensoritself.

Another overall contributor to the performance of a particle filter-based system is the building structures. A direct errorsource is the accuracy of the building model, e.g., walls that are not there, that the entire building is fixed slightly off inone direction, or that the hallways are modeled to narrow or wide. The building model contributes with constraints but theconstraints it provides depend on the layout of the building. It is essential how regularly the constraints appear and if theyexperience any form of symmetry. In this work we considered different buildings and their structures whereas evaluatingthe accuracy and correctness of themodel as the building is changed over time and special cases of symmetry is left as futurework.

Reported performance of particle filters will also be affected by the choices that are made when building andexperimenting with them: the strategy chosen to initialize the particle filter, type of particle filter, resampling strategyof the particle filter, the movement pattern and length of the paths chosen. Motivated by the results from our measurementcampaign we will in the following two sections focus in more detail on sensor errors and the building structures whereas,e.g., evaluating different individual motion patterns are left as future work.

6.1. Sensor errors

We have computed the raw absolute sensor errors and in Table 2 the average absolute sensor error per reading is givenfor each data set. The absolute sensor error is calculated by comparing the dead reckoning vector measured at time t withthe ground truth vector formed by the previous ground truth position at time tprevious and the current ground truth positionat time t , the difference is the raw sensor error. The numbers show a large difference between the mall and especially theopen spaced office. Wewill further characterize this difference by the number of doors passed through, the number of turnsmade and the distance to the walls.

The presence of doors that have to be passed will change a pedestrian’s movement pattern because for every closed doora couple of sidesteps, maybe even a backwards step have to bemade. As the sensor is less accurate for such type of steps thepresence of doors will increase the error for every door. The mall paths have two to four doors but they open automaticallyso no sidesteps are necessary. The open office building paths have between 6 and 10 doors requiring not only sidesteps butalso entering of codes on a sidepanel and the regular office building paths have four doors that require opening. Thereforedoors contribute to the sensor errors in the office buildings.

In the Figs. 3–5 it is possible to count the number of turns made on each of the paths, for mall 1 and 2 the numbers are 5and 6, for mall 3 with the largest sensor errors the number is 10. For the open spaced office building the numbers are 12, 12,and 14. For the regular office building the numbers are 8, 8 and 14. As the sensor is less accurate when turning every turnwill add to the error.

If the distances to walls from the sensor are large there is a lower chance that buildings materials will interfere withthe sensor, especially the compass is sensitive to, e.g., iron. In summary, the three factors seem in combination to offer anexplanation for the results in Table 2.

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Table 2Average sensor error per sensor reading.

Average sensor errors (m)

Mall 1 0.22Mall 2 0.23Mall 3 0.30Open office 1 0.38Open office 2 0.41Open office 3 0.43Regular office 1 0.30Regular office 2 0.29Regular office 3 0.31

Fig. 6. Accuracy and sensor error over time for open space office building path 2.

Fig. 7. Size of the unconstrained area around a point for a given maximum distance.

To further analyze path 2 in the open office building where a large sensor error influenced the accuracy, Fig. 6 shows theaccuracy and the sensor error over time for each step of the particle filter. As can be seen from the figure the largest errorcurve starts at sixty seconds with a number of errors of around one to two meters. A closer inspection of the data revealedthat these errors were all biased in the same direction. The error occurred in an open space that meant that there were noconstraints tomitigate the anomalous error. Therefore not only themagnitude of errors canmatter but also the pattern theyappear in.

6.2. Building structures

The building structure has an impact on the performance of particle filter-based inertial positioning, as it providesthe constraints that help the particle filter improve accuracy. Therefore the regularity of building constraints should beindicative for the accuracy for such systems. Previous work by Woodmann and Harle [18] has motivated that in addition tothe regularity of building constraints the accuracy also depends on whether the constraints experience either translationalor rotational symmetry. The existence of symmetry can both prevent particle clusters to converge to a single cluster andmake them split into several clusters. What makes constraints symmetrical is either that they are lacking or that they aresymmetric with respect to another part of the building.

To classify points within a building with respect to regularity of constraints, we want to calculate the size of theunconstrained area around each point. This is motivated by the relation between the size of the unconstrained area and thenumber of constraints and how close they are. Fig. 7 illustrates the unconstrained area around a point for a given maximum

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Fig. 8. Particle filter error distance compared to size of unconstrained area for mall 3.

Table 3Median Pro-Position accuracy compared to the size of theunconstrained area.

Pro-Position Unconstrained area50% (m) (m2)

Mall 1 3.41 824Mall 2 4.27 831Mall 3 5.12 1555Open office 1 2.95 132Open office 2 8.58 165Open office 3 3.87 171Office 1 2.52 78Office 2 3.09 61Office 3 3.87 70

distance. Using the size of the unconstrained area will classify points in a large open room as very unconstrained and pointsin a narrow hallway as very constrained. The metric can also capture that an area with few constraints will have a higherchance of being symmetric with respect to other areas, however, it does not capture the more subtle types of translationaland rotational symmetry which is an interesting topic for future work.

We calculate the unconstrained area around a point in the following steps:• Given a pointm = (x, y).• Calculate the intersection point ij = (xj, yj) with the closest constraint for 36 equally spaced angles 10° times j :=

(1, . . . , 36).• If no intersection point exists at a maximum distance of fifty meters then the intersection point with a circle of radius

fifty meters is used.• Form the polygon P of the points (i1, . . . , i36).• Calculate the area of the polygon P .

The intersection point is computed by an intersection function supported by our building model.To analyze the impact of building structures in terms of the size of the unconstrained area, we have computed the size

for every ground truth position for all our data sets. Fig. 8 shows the size of the unconstrained area compared to the particlefilter error during the mall 3 walk. One can notice from the figure how the unconstrained area is large in the beginning andthe end as the person is outside the mall. When entering the building the size decreases but with some variation, whenpassing intersections and as the person enters the largest shop in the mall there is a significant increase. Comparing theerror distances with the size of the unconstrained area one can notice that many times, when the size of the unconstrainedarea increases, so does the error distance with one exception around fifty seconds which can be attributed to a 180° turnwith high sensor error, which makes the particle cloud lag after the person for 20–30 s.

We have for each of our data sets computed the average size of the unconstrained area, which is listed in Table 3 togetherwith median accuracy of the particle filter. As expected the mall has the highest average sizes in a range from 824 to 1555and for the open spaced and the regular office they are considerably smaller in the range from 132 to 171 and 61 to 78,respectively. Comparing the median accuracy with the size of the unconstrained area, one can notice that in many cases anincrease in the size of the unconstrained area also means a higher median error. There are some exceptions to this such asOpen office 2 where other error factors significantly impact the result, as discussed in the section named ’Sensor Error’.

6.3. Comparing error sources

The preceding sections have discussed the error factors of sensor errors and building structures. To make a quantitativecomparison of their impact on the resulting positioning accuracy, we have used linear regression. The linear model has two

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Table 4Variable parameters estimated using linear regression.

% quantile Sensor errors Unconstrained area

50 0.65 0.5675 0.65 0.6195 0.64 0.63

Fig. 9. Path for ground truth and results for the inertial sensor and Pro-Position with and without GPS positioning for path 3 in the shopping mall.

variables — one for the average sensor error and one for the square root of the average unconstrained area.3 The parametersof the variables in the model have been constrained to take values from zero to one. As data for the regression, we haveused normalized values between zero and one calculated for the average sensor errors as given in Table 2 and for theunconstrained areas given in Table 3 compared to both the median, the 75% quantile and the 95% quantile particle filtererrorswhere two of themare given in Table 1. The results listed in Table 4 suggest that the sensor error has the largest impacton the resulting accuracy because it is weighted highest by the regression. However, for the 75% and the 95% quantile theweight of the unconstrained area is increasing suggesting that the building structure has a higher impact when consideringhigher quantiles.

7. Improving accuracy using GPS

In many use cases pedestrians will be walking from the outside into a building, which means that we can use the GPS tofind our initial position. In some buildings indoor GPS reception is also possible as studied by Kjærgaard et al. [9] and mightbe used to improve accuracy, for instance, in large open areas, which are challenging surroundings for particle filter-basedinertial positioning because of fewer constraints. An example of such a large open area is the 3749 m2 shop that the thirdpath in the shopping mall passes through.

We have extended Pro-Position tomake use of GPSwhen available, firstly, for providing the initial position and, secondly,to correct the particles. For correction the particle filter will update the particle weights according to their distance from theGPS position. The correction is only applied if there are any GPS events and in the case ofmultiple events the system uses theone with the lowest GPS receiver estimated horizontal error. The correction is applied by creating a Gaussian distributionwith mean zero and the GPS receiver estimated horizontal error as standard deviation. Using this distribution a likelihoodp is calculated from the distance between the particle and the GPS position. The weight of the particle is then updated bymultiplying the former weight with p. However, to control how bad GPSmeasurements are used, we filter out GPS positionswith an estimated error higher than a certain threshold parameter.

3 The square root is applied to linearize the data.

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Fig. 10. Cumulative error distribution for the inertial sensor and Pro-Position with and without GPS positioning for path 3 in the shopping mall.

Fig. 11. RMS accuracy versus the threshold for GPS estimated error.

Fig. 12. Number of used GPS measurements versus the threshold for GPS estimated error.

It is only in the shopping mall that there is a significant amount of indoor GPS fixes and therefore we will focus on thisbuilding. To visually compare the accuracy versus nearbywall constraints, Fig. 9 for path 3 in themall plots the ground truthand the result for the inertial sensor, and Pro-Position without GPS and with GPS using a threshold of 30 m. From this figureone might notice how the use of the GPS improves the accuracy in the large shop by moving the estimated positions moretowards the ground truth path. Furthermore, a cumulative error distribution is shown in Fig. 10 highlighting a decrease ofthe overall median accuracy with 2.5 m compared to not using the GPS and an even higher decrease of 10.7 m for the 95%quantile. To evaluate which threshold for the GPS estimated error works best, we have plotted RMS errors with respect toGPS thresholds in Fig. 11. From the results one can notice that in the shoppingmall there is an accuracy improvement for thethird path of 2.5 m and a smaller improvement for the first and the second path of around 0.5–1 m. In general a thresholdof 30 m seems to provide a good performance.

To understand how many measurements are used with each threshold, Fig. 12 plots the number of used GPSmeasurements for each threshold. In the shopping mall a large amount of GPS measurements are available actually nearlyhalf of the time during each path. The selected threshold of 30 mwill for the shopping mall measurements filter out around25% of the worst estimated measurements. Using a threshold higher than 30 m does not seem to provide a major decreasein the RMS errors. This is mainly due to that the estimated accuracy is used by the particle filter when updating the weights.

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Therefore one can conclude that if GPS is available in a building it can be used to improve accuracy, even when large indoorerrors are present.

8. Discussion

In this section wewould like to discuss based on our results how inertial particle filter-based positioning relates in termsof advantages to other positioning technologies, which types of applications the technology is most well suited for andwhatlessons to take from our results.

8.1. Positioning technologies

The primary advantage of inertial particle filter-based positioning is that it can be used without preparation of thebuilding in focus which is necessary for both infrastructure-based UWB [7] and WiFi positioning [3,4]. In comparison, toinfrastructure-based positioning, where the coverage area is the primary cost factor, for inertial systems it is the number oftargets that is the most influential cost factor. In terms of errors our results indicate that sensor errors, lack of constraints,doors and turns are the main factors that limit the accuracy of inertial particle filter-based positioning. This is, for instance,different from infrastructure-based UWB positioning where the main error factors are due to the existence of constraintsand the number of obstacles within rooms. Therefore inertial particle filter-based positioning is a relevant technology toconsider as it fills a gap where infrastructure-based technologies are less suitable.

8.2. Applications

Given the error and cost considerations mentioned earlier the primary use cases for inertial particle filter-basedpositioning are scenarios where a few external people enter a building not owned by their home organization. In everydaycases this could be guards or other service people entering large premises, or in more extreme cases fire fighters or policepersonnel. Howgood the positioningwill be then depends on the error factorsmentioned earlier. Given the results presentedin this paper the technology does not provide the level of accuracy required for safety of life operations, and reliability is notguaranteed due to the discussed error factors. Therefore the current state of the technology suggests that everyday types ofuse cases seem the most feasible starting points for deploying this type of technology.

8.3. Lessons

The lessons that can be drawn from this work is that the accuracy of inertial particle filtering-based positioning dependson a number of error factors. That absolute positioning technologies can help fight these errors when available includingusing GPS as an indoor versus outdoor sensor. There are types of errors linked to building specific movements that havepreviously not been given much attention. E.g., that a person needs to press codes and open doors to access a certain partof a building or take an escalator. One method that might help improve the particle filtering approach to better handle suchmovements is by modeling them as part of the particle filtering approach. This is an interesting path of future work.

9. Conclusion

In this paper we have presented Pro-Position a waist-mounted inertial and GPS-based system using particle filtersinformed by building models. We evaluated the system in a regular office building, an open spaced office building anda shopping mall to show that the system provides a median accuracy of 2.5–8.6 m depending on the sensor errors andbuilding structures compared to 8.0–25.3 m with pure inertial positioning. The accuracy is therefore comparable to that offoot-mounted systems given the building structures.We provide an understanding of how the positioning accuracy dependson the sensor errors and the building structure and propose to classify the impact of building structures by consideringthe unconstrained area around the pedestrian. This understanding will help build new particle filters that directly targetcommon sensor errors and differences among building structures. Furthermore, we presented and evaluated methods forusing GPS positioning with particle filters to enable a seamless handover from outdoor positioning, avoiding the outdoorrapid particle growth problem and to improve accuracy in large open areas which provided an increase in accuracy of 2.5 mfor the median and 10.7 m for the 95% quantile.

In our ongoingworkwe are trying to address several issues. Firstly, to implement a system that uses the inertial sensors ofsmart phones. Secondly, to analyze the dependency between positioning accuracy and peoples’movement patterns. Thirdly,to extend the evaluation with a foot-mounted sensor to compare the sensors in the buildings. Fourthly, to improve theparticle filtering approachbasedon the results, e.g., bymodeling building specificmovements for pressing codes andopeningdoors, and taking escalators or elevators. Fifthly, to evaluate the impact of the building model accuracy and correctness ofthe model as the building is changed over time and special cases of symmetry.

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Acknowledgment

The authors acknowledge the financial support granted by the Danish National Advanced Technology Foundation for theproject Galileo: A Platform for Pervasive Positioning under J.nr. 009-2007-2.

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