A pedestrian navigation system using a map-based angular motion model for indoor and outdoor environments

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A pedestrian navigation system usinga map-based angular motion model forindoor and outdoor environmentsSusanna Kaiser a , Mohammed Khider a & Patrick Robertson aa DLR , Oberpfaffenhofen, Weßling , GermanyPublished online: 22 Jun 2012.

To cite this article: Susanna Kaiser , Mohammed Khider & Patrick Robertson (2013) A pedestriannavigation system using a map-based angular motion model for indoor and outdoor environments,Journal of Location Based Services, 7:1, 44-63, DOI: 10.1080/17489725.2012.698110

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Journal of Location Based Services2012, 1–20, iFirst

A pedestrian navigation system using a map-based angular motionmodel for indoor and outdoor environmentsy

Susanna Kaiser*, Mohammed Khider and Patrick Robertson

DLR, Oberpfaffenhofen, Weßling, Germany

(Received 5 December 2011; final version received 4 April 2012; accepted 25 May 2012)

By incorporating known floor-plans in sequential Bayesian positioningestimators, such as particle filters, long-term positioning accuracy can beachieved as long as the map is sufficiently accurate and the environmentsufficiently constrains pedestrians’ motion. Instead of using binarydecisions to eliminate particles when crossing a wall, map-based angularprobability density functions (PDFs) are used in this article that are capableof weighting the possible headings of the pedestrian according to localinfrastructure. In addition, we will include outdoor maps by processingsatellite images of the region. We will show that the angular PDFs will helpto obtain better performance in critical multi-modal navigation scenariosand in the outdoor area when including maps.

Keywords: indoor positioning; multi-sensor navigation; particle filtering;human motion models; maps

1. Introduction

With the development of small, low-cost and light-weight sensors, the market forpedestrian navigation is growing rapidly. Especially, indoor navigation is an excitingresearch and development area that promises new applications for many aspects ofour lives. A number of approaches have been followed in indoor positioning rangingfrom high-sensitivity Global Navigation Satellite System (GNSS) receivers, dedi-cated wireless systems to inertial navigation, as well as various combinations (Liu2007, Mautz 2009, Koyuncu and Yang 2010). In this article, we will focus on inertial-measurement-unit (IMU)-based navigation for pedestrians in combination withother sensors. The application is continuous and online metre-level-accuracypositioning with either foot mounted sensors (Foxlin 2005) or other suitable formsof pedestrian dead reckoning (PDR) (Mezentsev et al. 2005, Kourogi et al. 2009).The aim of PDR is detecting and estimating individual steps of a person. To estimatethe distance travelled a simple step counter can be used (Crouter et al. 2003), and ifheading changes are also estimated then the relative location change over time can bedetermined. In this study, we perform a true six degrees of freedom navigation

*Corresponding author. Email: [email protected] of this study has been published in the Proceedings of International Conference onIndoor Positioning and Indoor Navigation (IPIN), 2011, by IEEE Xplore at ‘http://ieeexplore.ieee.org/xpl/mostRecentIssue.jsp?punumber¼6062621’.

ISSN 1748–9725 print/ISSN 1748–9733 online

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© 2013 Taylor & Francis

Journal of Location Based Services, 2013Vol. 7, No. 1, 44-63, http://dx.doi.org/10.1080/17489725.2012.698110

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integration, aided during resting phases using the well-known zero velocity update(ZUPT) (Foxlin 2005).

Every form of PDR suffers from cumulative errors which can be modelled, forinstance, as angular and distance random walks (Angermann et al. 2010). The resultis a random walk error in relative location which implies that the estimated locationdrifts over time. In this article, the cascaded Bayesian estimation architectureproposed in Krach and Robertson (2008) is used to handle these drifts. Here, a lowerextended Kalman filter (EKF), with integrated ZUPTs, that performs PDR and anupper particle filter (PF) that can handle floor-plans are cascaded. A PF usuallydraws importance samples according to a proposal density function and updates theparticle’s weight upon the arrival of the measurements. The resulting discretedistribution is an approximation to the true posterior distribution. Resampling theparticles after weighting is often done periodically to ensure a sufficient particlediversity.

When performing particle filtering with accurate PDR, one typically uses thelikelihood PF (LPF). The LPF uses an importance density that is based on thelikelihood measurement and uses the state transition prior to weight the particles(Arulampalam et al. 2002). In this article, it draws particles according to a proposaldensity that reflects the step measurement (PDR output of the lower Kalman filter)and weights the particles with the state transition (human motion) model. This articlewill address how such a model can be computed given the knowledge of walls (floor-plans) and outdoor maps.

The posterior distribution of the estimated user position can be multi-modal.In Beauregard et al. (2008), Krach and Robertson (2008) and Woodman and Harle(2008), the authors used walls to weight the particles (i.e. particles that cross wallsreceive very low weights). In such case, it has been shown that few particles (or evenjust one) that happen to be erroneously remaining in another (larger) room with noeffective wall constraints may result in multi-modality and eventually in very largepositioning errors. This is because these particles will not suffer from running intowalls and, therefore, will always receive high weights, whereas some of the ‘correct’particles will be subject to receive low weights due to wall crossings. Resampling willeliminate these particles with low weights and regenerate a part of them within thelarge room. Since PF estimates are computed based on the number of particles andtheir weights, loosing particles at the walls results in erroneous estimates andeventually estimator divergences.

In this article, the proposed location-dependent angular PDFs that are based onmaps are used to weight the particles in the upper LPF. With the use of the angularPDFs (Kaiser et al. 2011) we compute the particle weights with a more realisticmotion model, as opposed to binary weighting. Our experimental results show thatthe above-mentioned multi-modality problem can be successfully addressed. Theangular PDFs can also be used in applications when the prediction of heading isneeded – e.g. in a movement model – with known floor-plans/maps where thepossible headings are constrained due to obstacles or walls.

In addition to the results addressing the multi-modality problem, we propose inthis article to use outdoor maps for refining angular PDFs in outdoor areas. Theoutdoor layout can be obtained by processing satellite images of the region. With thisinformation, we will show that the performance will be improved, especially whenthe GPS measurements are not accurate.

2 S. Kaiser et al. Journal of Location Based Services 45

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The rest of this article is organised as follows: we begin by presenting scenarioswith multi-modal posterior distributions. After that, we describe the angular PDFsthat are used in the weighting stage of the LPF. Then, we describe the algorithm forobtaining the outdoor layout. Finally, the experimental setup is briefly presentedfollowed by showing how the proposed model can overcome failures associated withusing binary weights and how it can improve the performance in outdoor areas.

2. Scenarios with multi-modal posterior distributions

When using no angular PDFs, the transition model in the LPF is based on binaryweighting: if a particle crosses a wall then its weight is set to zero (or close to zero),otherwise it is set to one and weighted solely by the likelihood functions of any othernon-PDR sensors (e.g. GPS, compass). This approach works only when thepedestrian is moving within a building with small rooms or corridors, as explained inKaiser et al. (2011), since in this case all particles suffer comparable elimination rates.The use of known building layouts helps to constrain the particles to walkable areas.However, during the estimation process it may happen that the particle cloud splitsinto two sub-groups due to a wall – so they enter two different rooms. If the roomsizes differ, the bigger room has the advantage that particles will not run into walls asfast or as often as inside the more constrained room.

For example, let us consider a particular scenario where the particles are split intotwo groups due to wall constraints (Figure 1, the ‘Y-scenario’). In this example, acorridor splits into two directions – a Y-constellation. The large corridor splits intotwo almost parallel corridors heading to two different building parts (or twobuildings). The difference between the two building parts are their respective wallconstraints: Building part A consists of a narrow loop corridor and more

ParticlesTruetrack

BuildingPart B

BuildingPart A

SplitPoint

Figure 1. The ‘Y-Scenario’: particles will be split into two groups if the heading differencebetween the two paths is small. Due to the denser wall constraints in building part A, theparticles there will suffer a higher loss rate (wall collisions) and the incorrect group will survivein area B.

Journal of Location Based Services 346 S. Kaiser et al.

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constraining walls, whereas building part B has fewer wall constraints. The true

trajectory leads to building part A. The thickness of the particle trajectories depictsthe particles’ contribution to the posterior density. At first, the correct group ofparticles is expected to receive a higher weight, due to a better match between the

actual heading and the PDR, perhaps aided with a magnetic compass. But afterentering the building parts, particles in area A will suffer a stronger reduction in theirpopulation. Particles that enter area B will suffer less reduction and will dominate the

posterior over time – leading to a significant error.Another example of multi-modality is the following case: again, the considered

building consists of two parts, one area with no wall constraints (Figure 2, buildingpart A) and one with a small corridor (Figure 2, building part B). The two parts are

connected to each other through a small corridor. The true track (given in green) is aloop through the corridor in building part B. We assume that the starting position of

a pedestrian is not known to a high degree of accuracy (perhaps only a very roughestimate is available from mobile radio positioning). We choose for simplicity thatthe particles will be randomly arranged at the beginning. Again, the difference in the

average elimination rates of particles will lead to the incorrect mode dominating orsurviving outright.

To show a very realistic example based on our own office environment and onreal measurement data, we modified the correct floor-plan by removing few walls in

the lower right area (only in the map database) to create a large unconstrained area(large room, see Figure 3) and an area with a corridor and small rooms. It is worth

mentioning that our walk was compatible with this modified floor-plan, so the walkmay just have well taken place within this (modified) building. The real track of thepedestrian is given in blue. The user was requested to walk through a pre-defined

specific path starting outdoors where GPS was available, walking through thebuilding (3 loops, no GPS) and coming out again. This path passes through several

pre-defined ground truth points (GTPs, red crosses in Figure 3) and through many ofthe rooms in our office building. After the straight walk from outside to inside andturning to the right, the particle cloud splits into two competing groups of particles

because of the wall of the corridor: one group enters the very large room and theother group enters the small corridor. The second group is actually close to the

pedestrian’s true location and following her track. Both groups of particles will

Building Part A Building Part BTrueTrack

Figure 2. Example of multi-modality when beginning estimation – i.e. the starting position isnot accurately known.


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follow the relative motion of the pedestrian, but the second group of particles will

suffer a significant reduction in its population – those of its members that explore the

PDR error state space but run into walls. The first group, however, will not suffer

such losses and will dominate. The second group will more often run into a wall

before it has a chance to dominate the particle population. Actually, in a long-term

usage scenario in environments with different constraints it is only a matter of time

before such events may occur, resulting in very large and probably permanent

position errors until a second source of location can be obtained (e.g. GNSS or

wireless localisation). The underlying problem with the aforementioned approaches

for weighting particles in an LPF is the fact that they do not correctly model human

motion with respect to the constraints in buildings. To combat these failures, the use

of angular PDFs is proposed in this article.

3. Angular PDFs based on maps

Our objective is to derive a motion model that assigns a probability to a step of a

human being. Since we assume that our PDR is very good at estimating the distance

travelled during this step, we can assume that all particles explore steps with similar

distances – hence in this study we shall not weight according to the distance each

particle travels. We shall only consider the likelihood of the pedestrians’ step with

respect to the specific direction of that step, originating at the previous location of

the particle.The proposed angular PDFs are derived from a diffusion algorithm based on

maps that can also be used as a movement model (Khider et al. 2009). In Khider

et al. (2009), the diffusion algorithm taken from Kammann et al. (2003) is applied,

which is extended for using additionally maps and for handling floor-plans in three

dimensions. The principle of the computation of the 2D-diffusion matrix based on

maps is described in Section 3.1. Section 3.2 describes the calculation of the angular

PDFs.

ground truth pointpathof the test user

Start/End

Location where theparticle cloud splitsinto two groups

Large room

Figure 3. Floor-plan and trajectory of the scenario with one big room and constrained areas.


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3.1. Calculation of the diffusion matrix based on maps

The idea of the diffusion algorithm – which is a standard solution for path finding ofrobots (Schmidt and Azam 1993) – is to have a source continuously effusing gas thatdisperses in free space and gets absorbed by walls and other obstacles. In Kammannet al. (2003) and Khider et al. (2009), the diffusion model is used with the assumptionto have a source effusing gas which is one of the possible destination points. Here, apath finder is needed to find the path to that destination point. Contrary to that, inthis article we assume that the source of the gas is the current waypoint, and wecalculate an angular PDF out of the gas distribution. No path-finding algorithm isneeded anymore and the weighting is independent of the choice of destination points.

The computation of the diffusion matrix based on maps can be found in Khideret al. (2009). However, instead of computing the diffusion values for the whole area,we use a sliding squared window of size Nx �Nx, where the current waypointðxm, ymÞ is the middle point of that window (Kaiser et al. 2011):

ðxm, ymÞ ¼Nx

2

� �,

Nx

2

� �� ð1Þ

where Nx is odd-numbered and represents the size of the sliding squared window.Depending on the grid size and the size of the squared window, the resolution of theangular PDF can be varied. The central assumption for defining the angular PDFs isthat the possible headings are following the gas distribution, if the current waypointis the source of the gas.

For each waypoint a so-called diffusion matrix D is pre-computed. The diffusionmatrix for a particular waypoint – that represents the middle point of the slidingwindow – contains the values di,j for the gas concentration for each other possiblelocation ði, j Þ within the window when gas effuses from that waypoint. Theadvantage of taking the actual waypoint instead of destination points as the sourceof the gas is that we can get a weighting function directly from the gas distribution.Another advantage is that the weighting is totally independent from the choice of thelocation of destination points. In addition, we can restrict the rectangular area to asmall area around the actual position, so that the computational effort is muchlower. Finally, one can think of evaluating the PDF values during runtime instead ofpre-computing the PDFs for the whole area.

3.2. Calculation of the angular PDFs based on maps

Figure 4(a) shows the gas distribution (diffusion matrix) from one waypoint within aportion of a floor-plan. One can see that the gas is restricted through walls to theareas where it can flow. From this diagram we can choose a threshold to get acontour line of the gas distribution. From this contour line we get directly theangular PDF using the distance to the contour line. When the gas is reaching a wall,the contour ends at the wall and the distance is equal to the distance to the wall.Figure 5 shows the polar diagram of the angular PDF for that waypoint. The weightis higher for those directions in which people may walk. Since it is possible to stay infront of a wall, a small distance is applied for the directions to the wall in the casethat the current position is close to the wall. Additionally, when particles cross awall, their weight is set to a very small value, regardless of the angular PDF.


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Figure 4. (a) Diffusion matrix for a squared area and the current waypoint in the middle, and(b) contour line (shown in dark red) of the diffusion values.

Figure 5. Polar chart of the angular PDF.


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Details of the calculation of the angular PDF can be found in Kaiser et al. (2011)

and are given next. The contour line of the diffusion matrix represents our angular

PDF. Therefore, we have to determine this contour line first. Here, we specify a set C

of Nc contour line points for the diffusion area:

c1, . . . , cNc

� �¼ x1, y1ð Þ, . . . , xNc

, yNc

� �� : ð2Þ

The contour line points can be obtained by checking all the diffusion values to be

below a certain threshold T. If a diffusion value dk,l at position ðk, l Þ is below that

threshold:

dk,l 5T ð3Þand the diffusion value of at least one neighbouring point (direct neighbourhood) is

greater than the threshold T:

dkþo,lþp 4T 8o, p : o ¼ �1, 0,þ1,

p ¼ �1, 0,þ1, o 6¼ p 6¼ 0ð4Þ

then the position ðk, l Þ is part of the contour line:

ci ¼ ðk, l Þ 2 C: ð5ÞWalls are included in this computation since for a point on the wall the following

equation holds:

dk,l ¼ 0 if ðk, l Þ is on wall: ð6ÞFigure 4(b) shows the contour line of the diffusion values marked in dark red

(T was set to 0.0001).The value of the angular PDF for an angle � is obtained via the distance of the

current waypoint ðxm, ymÞ to the contour line point that lies in the direction of that

angle �. Here, � is the absolute angle when drawing a line from the contour point to

the waypoint ðxm, ymÞ in a Cartesian coordinate system. In our evaluation we used

discrete values for angle �. The angle spacing was 5� and we had 72 different values

for computing the weighting function. These values seemed to be enough to obtain a

smooth weighting function. With this, we have also taken into account the trade-off

between the amount of data to be stored, precision of the angular PDF and the

influence of the precision of the PDF on the results.The distance bci between the current waypoint and the point of the contour line

ci ¼ ðk, l Þ is defined as:

bci ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiðxm � kÞ2 þ ð ym � l Þ2

q: ð7Þ

Since for a specific range of � more than one contour point can be found, the

value for the non-normalised weighting function ~wð�Þ is obtained by the maximum of

possible distances to points of the contour line within a specified range of �:

~wð�Þ ¼ maxci¼ðk,l Þ’ðk,l Þ2�

bci ð8Þ

where ’ðk, l Þ is the absolute angle between the contour point ci ¼ ðk, l Þ and the

actual waypoint ðxm, ymÞ, assuming the same north-oriented coordinate system for

the map and the waypoints.


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Additionally, it is checked if the direct line of the waypoint to the contour linepoints crosses a wall. Those contour line points that cross a wall are not consideredin the computation of the angular PDF, since the directions to points behind wallsshould not be favoured.

Finally, the weighting function is normalised as follows:

wð�Þ ¼ ~wð�ÞP2��¼0 ~wð�Þ

: ð9Þ

Angles are normally not independent from previous directions. To incorporatethe dependence of the angle to the previous angle, one possibility is to consider onlythe possible directions in the range of �� 90� � � ��þ 90� (normalised half histogram)or of smaller ranges. In this article, we used the normalised half histogram since itresults in better performance. Investigating other possibilities of considering previousangles is very interesting and foreseen for further studies.

To adapt the weighting function to the speed of the pedestrian, the followingequation is applied to the weight wð�Þ:

w0ð�Þ ¼ wð�Þs ð10Þ

where S is the step length of the particle. The step length depends on the odometrymeasurement and is estimated by the lower EKF. With this, more weight is given tosmaller steps and less weight is applied to large steps. This is done because weightingis multiplicative over time, and the weight change should be normalised to a givendistance travelled (here corresponding to 1m, when S¼ 1). Otherwise, particlestravelling a given distance in a larger number of shorter steps would be weightedmore often than a particle travelling the same distance in fewer steps.

Finally, it should be noted that the angular PDFs can be pre-computed andstored to reduce the computational effort during position estimation.

4. Generating outdoor-layouts from satellite images

In addition to the advantages of using angular PDFs for navigation in indoor areas,it can be shown that map-based angular PDFs will also improve the performance inoutdoor areas. For outdoor areas usually there exists no public informationdescribing walkable areas, fields, flower beds, etc. Street maps may help to obtaininformation about the streets, but the ways in front of the buildings are not covered.For outdoor areas information about the exact location and texture of paths, fields,meadow, forest or flower beds is needed. To obtain a layout for the outdoor area, inthis article we propose to extract the layout information from satellite images of theconsidered area. The layout is used for calculating the diffusion matrix andrepresents values of different accessibility (Kaiser et al. 2011):

li,j ¼1

�if li,j is accessible, � ¼ 1 . . . 255

0 if li,j is not accessible

8<: 8 i, j : i, j ¼ 0, . . . ,Nx

where the values of � represent the accessibility levels. The most accessible areas willhave a value � of 1 whereas the least accessible area will have a value � of 255.


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According to the accessibility of a specific area, the value � lies between 1 and 255.

We have chosen the values to be between 0 and 255 because of the memory-efficient

representation of a single-byte representation. In our evaluations, the values were

chosen to be less than 5 because otherwise the gas decelerated too much in front of

meadows, flower beds, etc., which might be crossed by pedestrians. With large values

of � the diffusion values will become very low for a specific accessibility level,

resulting in high differences across the accessibility levels. Then, the computed

angular PDF at the borders of an area of equal accessibility will have very low

values, resulting in a behaviour that is similar to that in front of a wall.Let us consider our office environment that is depicted in Figure 6(a) and (b),

where 6(b) is a portion of 6(a) showing our office building. From this image we

obtain walkable areas by analysing different colours of the image. For instance, the

Figure 6. Satellite photo or our office environment (provided by ‘DLR/DigitalGlobeprovided by European Space Imaging’). (b) is a cutout of (a) showing our office building.


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forest area is usually shown in dark green, meadows are given in light green and

streets and paths are given in light grey.From the satellite image we obtain the accessibility information directly from the

different colours. First, we did this in a simple way: we decided from the colour, the

type of area that the respective image part belongs to. Figure 7(a) gives the results for

this decision for our office area. Here, we assumed to have two different accessibility

levels: one for walkable areas (e.g. streets, paths; white colour areas in Figure 7a) and

one for less accessible areas (e.g. forest, flower beds; dark grey areas in Figure 7b).

The floor-plan of the building (black lines) is mapped into the image and detected

accessibility levels inside the building are masked out.Since the colours of the satellite images are sometimes darkened through

shadows, there are some areas that are not correctly detected. In addition, very small

areas of different accessibility levels appeared due to very small colour differences in

Figure 7. Layout generated from the satellite photo (Figure 6b) with (a) and without (b)smoothing. Walkable area is given in white, less accessible area in dark grey and the walls ofour floor-plan are given in black.


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some parts of the image. Hence, areas that are too small and with surrounding pixelsof another colour should be cancelled. Here, we cancelled out single pixels, areas ofsize 2� 2 pixels and of size 3� 3 pixels. The result of cancelling such small imageareas from Figure 7(a) is given in Figure 7(b). This approach leads to smoothed areasand a more useful outdoor map for applying the motion model.

Finally, shadows can be detected by investigating the colour that shadows aregetting among other dark areas. Figure 8 shows the results of marking shadows inour layout and light grey is used for that. Since in shadowed areas one might notknow the accessibility level, we decided to apply an accessibility level betweenwalkable areas (white colour) and forest and flower beds (dark grey).

For showing the advantages of using maps in the outdoor area, measurementswere analysed for a test user that was asked to do a long outdoor walk, then enter thebuilding and finally come out again to the starting position after one loop insidethe building. The true path is depicted in Figure 9 with blue arrows and the GTPs aregiven in red.

5. Experimental setup and results

The developed model was tested and evaluated using an already available distributedevaluation and demonstration indoor/outdoor environment for positioning. Theenvironment is based on sequential Bayesian estimation techniques and allowsplugging-in different types of sensors, Bayesian filters and transition models.

The sequential Bayesian positioning estimator that is used to evaluate theperformance of our weighting function is based on a PF fusion engine and uses thefollowing sensors: commercial GPS, electronic compass and a foot-mounted IMUassisted with ZUPTs (Krach and Robertson 2008).

Figure 8. Layout generated from the satellite photo (Figure 6b) with marked shadows.Walkable area is given in white, less accessible area in dark grey, shadowed area in light greyand the walls of our floor-plan are given in black.


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5.1. Experiments addressing the multi-modality problem

To illustrate the benefits of the use of the angular PDFs, the scenario with different

wall constraints described in Section 2 is used, where the particle cloud splits into two

groups during estimation. When classical binary weighting based on floor-plans is

used, the correct particle group is unfortunately eliminated due to the wall

constraints in the restricted (correct) area and the incorrect group survives in all

evaluation runs. In contrast, the use of our weighting function compensates the loss

of particles due to wall crossings. As time elapses, the correct particle group is

continuously rewarded and resampling results in eliminating the incorrect group. As

long as we, on average, reward more than the average proportion of particles lost

due to the walls, the correct hypothesis will remain strong.The path of the real track of the pedestrian is given in Figure 3. The GTPs

(shown in Figure 3) of the path are: 1, 2, 3, 4, 5, 6, 7, 8, 9, 3, 4, 5, 6, 7, 8, 9, 3, 4, 5, 6,

7, 8, 9, 3, 2, 1. Whenever the test user passed across one of the GTPs, the estimated

position at that point was compared with the true position. The GTPs were carefully

measured to the sub-centimetre accuracy using a Total Station (Leica Smart Station

TPS 1200). Errors between the true and estimated pedestrian positions were recorded

with and without the use of the angular PDFs.Figure 10 shows the average position error for 100 evaluation runs of the

investigated scenario. The positioning error at the starting position (GTP1) is due to

inaccuracies of the GPS measurement close to the building. Comparing the case of

no angular PDFs (red curve) with that of the angular PDFs (blue curve), we can

realise from the position error differences after GTP4 (at time �75 s) – the location

where the particle cloud splits into two groups – that the correct group survives when

using the angular PDFs for weighting. When using only walls to weight the particles

(binary weighting), the correct particle group was eliminated and the positioning

error became large. Later on, the incorrect group stayed inside the large room due to

the wall constraints when using only walls for weighting, whereas the correct group

Figure 9. True path of the test user. This environment is used when simulating the effects ofusing maps outdoor.


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of particles correctly enters the large room through the corridor when using angularPDFs. Since in both cases the particles are highly spread within the large room, theposition error is similar at GTP9 (at time �220 s), but the heading error is larger forthe erroneous wrong group. Therefore, the position error gets higher again afterleaving the large room for this group. As expected, the scenario where the map-basedweighting function is used shows much lower average position error compared to thecase where only binary weighting from wall crossings is used.

Visual representations of the posterior particle distribution from our LPF-basedestimator are shown in Figures 11 and 12 for the use of binary weighting and the useof the angular PDFs, respectively. For both cases the same total number of particlesis used for performance comparison (5000 particles). In each of the small images weshow the floor-plan of our office environment, particles, GTPs marked in red, theMMSE position and heading (blue dot with arrow) and the latest received GPSmeasurement (green dot) with a green arrow for the compass measurement.

From Figures 11, we can see that the lack of a correct motion model resulted in theincorrect group of particles surviving and the correct group being eliminated aftersome time. Due to the fact that the particle cloud is very large and a bit behind the trueposition due to GPS positioning inaccuracies at the beginning, the particles split at thecorridor entrance (Figure 11d, GTP4, at time �75 s). The particles do not split afterGTP4 in loops 2 (at time �260 s) and 3 (at time �410 s) because the particles are notwidely spread in front of the large room and are more concentrated at the entrance ofthe corridor. From Figure 11(e) we can see that the cloud spreads after entering thelarge room and the wall in the direction of the trajectory – actually a constraint withinthe large room – eliminates only a part of the erroneous particles. The correct group iseliminated in Figure 11(g) and (h), and hence the MMSE is seen to be far from theGTPs. From image 11(h) we can see that the cloud is again close to the coming GTP9(at time �220 s) due to the wall constraints in Figure 11(g), but the estimated headingis incorrect, and accordingly an erroneous position estimation follows.

The results for weighting with the angular PDFs are given in Figure 12. One cansee that the proper motion model compensates the loss of particles due to wall

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Figure 10. Average position error for the scenario with a large room.


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Figure 11. Visual representations of the posterior of the particles at different consecutive timeinstances of the first loop. No angular PDFs were used for weighting.


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Figure 12. Visual representations of the posterior of the particles at different consecutive timeinstances of the first loop. Weighting was done with the use of the angular PDFs.


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crossings and results in the survival of the correct particle group. As time elapses, thecorrect particle group is continuously rewarded; resampling then results ineliminating the incorrect group. In Figure 12(h), we can also see that the positionof the particle cloud is similar to that of Figure 11(h) – this reflects the similar valuesat GTP9 (at time �220 s) shown in the error curve. But at this point the direction(represented by the blue arrow) is more correct when using the angular PDFs.Therefore, the position accuracy is higher during the following loops. Due to the factthat the large room has few constraints, the position estimate is not very accuratewithin this room. It should be noted that this is a critical scenario because of thelarge unconstrained area. No GPS signal is available inside the building to correctthe IMU drifts and the compass might be heavily disturbed by magnetic fields fromelectrical cables and the presence of metallic objects and structures. Theseinaccuracies may deteriorate the position estimation accuracy. This can be the casewhen too few particles leave the large room using the correct door. From Figure 3,we can see that the large room has two exits on the left side. If the wrong exit ischosen by many particles due to heading drift, the following estimations will also beincorrect. This is reflected in the high-error peaks at GTP3 in loop 2 (at time �250 s)and in loop 3 (at time �400 s).

Table 1 gives the rate of incorrect estimations in our 100 evaluation runs. Anestimation is considered to be incorrect when the estimated position is more than 5mdistant to the true track (e.g. outside the building or in other corridors/rooms).Within the first loop the use of no angular PDFs for weighting results in 100% ofincorrect position estimations, whereas the use of the angular PDFs results infollowing the true track in all evaluation runs. For the second and third loops – theestimation is worse now due to the missing wall restrictions within the large room –the rate of incorrect position estimation is reduced from 50% to 8% by the use ofweighting with angular PDFs.

5.2. Results addressing the outdoor area

To show the benefits of the angular PDFs with outdoor maps, we chose the trackwith a long walk in the outdoor area of Figure 9. The GTPs (shown in Figure 9) ofthe path are: 1, 2, 3, . . . , 20, 7, 6, 5, 4, 3, 2, 1. Figure 13 gives the results for 100evaluation runs of the investigated scenario. In this walk, the first GPS measure-ments are not very accurate and accordingly the starting position is not very well

Table 1. Rates of incorrect estimations of the scenario with the large room.

Algorithm

Location of incorrect position estimation

Incorrect positionin first loop

Incorrect position insecond/third loop

Angular PDFs (%) 0 8No angular PDFs (%) 100 50

Note: An estimation is considered to be incorrect when the estimated position ismore than 5m distant to the true track.


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known. The position estimation will only be refined when the pedestrian enters thebuilding with the help of the foot-mounted IMU odometry measurements assistedwith floor-plans. Because the estimations are more accurate before entering thebuilding, when using angular PDFs including maps, the estimations inside thebuilding also start more accurate. Inside the building, both estimators (with andwithout angular PDFs) perform similarly due to the strong wall constraints. Butwhen leaving the building, the position estimation using angular PDFs is again moreaccurate. As can be seen from Figure 13, the average position error can be improvedfrom 3.09m in the case of no use of angular PDFs to 2.45m when using angularPDFs. It should be noted that most inaccuracies in this scenario come from noisyGPS measurements at the beginning. However, after the 10th GTP, the overall erroris below 2m.

Results for another walk along the same trajectory are given in Figure 14. As inthe previous walk, the performance is better before the pedestrian enters the buildingwhen using angular PDFs. After coming out again, only small improvements can beseen due to noisy GPS measurements at the end of the walk. For longer outdoorwalks, the performance gain would be more visible. Here, we achieved an overallaverage improvement of 0.2m.

The above example shows that the use of maps and floor-plans in a non-binary way can improve position estimation. From a Bayesian estimationperspective, it should be noted that a proper movement model should accuratelymodel the likelihoods of a person following different paths with respect toconstrained and unconstrained areas. We believe our estimator to be moreaccurate in this sense.

6. Conclusions

In this article, we presented a transition model for pedestrians that uses a knownbuilding layout to construct an angular PDF for a pedestrian’s step direction. We

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Figure 13. Average position error for the scenario with a long walk outside the building –walk 1.


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have demonstrated that a simple PF that uses only the knowledge of walls toconstrain particles can diverge if the particles’ distribution is multi-modal and acompeting, erroneous particles group is in an area with few limiting walls in theirvicinity. It has been shown that weighting with the angular PDFs performs betterthan binary weighting in multi-modal scenarios. In addition, it has been shown thatthe use of angular PDFs including different accessibility levels in outdoor areas willresult in an improved performance. The layout with different accessibility levels canbe obtained from satellite images. Further work should focus on analysing more datasets in different environments (wall arrangements) to prove the reliability of theposition estimation algorithm including weighting with the angular PDFs in allsituations. Furthermore, the applicability of generating layouts from satellite imagesshould be investigated in terms of accuracy of the proposed algorithm. Finally, thepotential use of angular PDFs in other applications such as simultaneous localisationand mapping with foot-mounted sensors (FootSLAM (Robertson and Angermann2009)) is foreseen for future work.

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Figure 14. Average position error for the scenario with a long walk outside the building –walk 2.


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Documents

A pedestrian navigation system using a map-based angular motion model for indoor and outdoor environments