Bayesian Fusion for Indoor Positioning Using Bluetooth Fingerprints

Wireless Pers CommunDOI 10.1007/s11277-012-0777-1

Bayesian Fusion for Indoor Positioning Using BluetoothFingerprints

Liang Chen · Ling Pei · Heidi Kuusniemi ·Yuwei Chen · Tuomo Kröger · Ruizhi Chen

© Springer Science+Business Media, LLC. 2012

Abstract This paper studies the use of received signal strength indicators (RSSI) appliedto fingerprinting method in a Bluetooth network for indoor positioning. A Bayesian fusion(BF) method is proposed to combine the statistical information from the RSSI measure-ments and the prior information from a motion model. Indoor field tests are carried out toverify the effectiveness of the method. Test results show that the proposed BF algorithmachieves a horizontal positioning accuracy of about 4.7 m on the average, which is about 6and 7 % improvement when compared with Bayesian static estimation and a point Kalmanfilter method, respectively.

Keywords Bayesian fusion · Indoor positioning · Fingerprints · Bluetooth ·Motion model

L. Chen (B) · L. Pei · H. Kuusniemi · Y. Chen · T. Kröger · R. ChenDepartment of Positioning and Navigation, Finnish Geodetic Institute, Kirkkonummi, Finlande-mail: [email protected]

L. Chen · L. Pei · H. Kuusniemi · Y. Chen · T. Kröger · R. ChenGeodeetinrinne 2, P.O. Box 15, 02431 Masala, Finland

L. Peie-mail: [email protected]

H. Kuusniemie-mail: [email protected]

Y. Chene-mail: [email protected]

T. Krögere-mail: [email protected]

R. Chene-mail: [email protected]

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1 Introduction

Indoor navigation is becoming a more sought-after utility for various mobile services andapplications. Bluetooth, as widely supported by mobile devices, is a proprietary open wire-less technology for exchanging data over short distances. Recently, the updated specificationshave been developed for the relatively longer range of transmission. New Bluetooth prod-ucts, such as Bluegiga AP 3201, have an effective transmission range up to 200 m while theBluegiga AP 3241 can have even a 800-meter effective transmission range in open areas [1].Thus, based on the new features developed, Bluetooth is a potential technology for indoorpositioning [2–10].

In general, the observables for positioning include angle of arrival (AOA), time of arrival(TOA), time difference of arrival (TDOA) and received signal strength indicators (RSSI),among which RSSI can be easily obtained in low cost equipments. However, due to the strongreflections and scattering conditions indoors, RSSI measurements are seriously attenuatedby multipath of signal propagation. Therefore, it is a challenging task to estimate the positionusing RSSI measurements with the prevailing various fading effects.

Fingerprinting is a feasible technique for positioning using RSSI measurements. Thebasic idea of the fingerprinting method is to match elements in a database to a particularsignal strength fingerprints in the area at hand. The method operates in two phases: thetraining phase and the online positioning phase. In the training phase, the radio map is createdbased on the reference points within the area of interest. The radio map implicitly charac-terizes the RSSI position relationship through the training measurements at the referencepoints with known coordinates. In the online positioning phase, the mobile device measuresRSSI observations and the positioning system uses the radio map to obtain a position esti-mate. The fingerprinting method has been widely discussed for indoor positioning. Variousfactors that affect fingerprinting are thoroughly summarized in [11]. Different fingerprint-ing algorithms are compared for indoor wireless local area networks (WLAN) positioningin [12].

In this study, we investigate utilizing the Bluetooth fingerprints for indoor positioning.For the investigation, we deployed totally 13 long-range access points (APs) in an office areaof interest. Based on the RSSIs measured from the Bluetooth APs, we present a Bayesianfusion (BF) method, which combines the posterior estimation from the RSSI measurementswith the information from the prior motion model. Field tests are carried out indoors to verifythe effectiveness of the method.

The paper is organized as follows. In Sect. 2, the mathematical formulation of the radiomap is presented. Sections 3 and 4 describe the BF method, which is composed of two steps,the Bayes static estimation (Sect. 3) and Bayesian fusion with the motion model (Sect. 4).In Sect. 5, the experimental platform is described in detail as well as numerical results and aperformance comparison is presented and discussed. In Sect. 6, conclusions are drawn.

2 Radio Map

In the training phase, the Bluetooth receiver collects the RSSI from the detected BluetoothAPs at the reference points for a certain period of time. Then, the fingerprint can be gener-ated and stored by RSSI measurements collected at each reference point. Collecting all thefingerprints, the radio map is constructed. Denote R as the radio map, Ri as the i th fingerprint,then the radio map can be formulated as R = {R1, . . . , RM }, where M is the total numberof reference points. Define the i th fingerprint Ri has the form:

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Bayesian Fusion for Indoor Positioning

Ri =(

ci ,{

ai, j , ai, j , σ2i, j

}), j ∈ {1, . . . , N }

where ci is the coordinate of th i th reference point and ai j holds the l RSS values measuredfrom the access point AP j , i.e. ai, j = {a1

i, j , a2i, j , . . . , al

i, j }. ai, j and σ 2i, j are the statistical

mean and variance obtained from ai, j . N is the total number of Bluetooth APs.

3 Bayesian Static Estimation

In the positioning phase, we assume a mobile device of interest moves in a two-dimen-sional Cartesian plane. The position at time tk , denoted as xk = [

xk yk]T

corresponds to 2Dposition coordinates. Denote zk, j as RSSI values measured from the j th Bluetooth AP at timeepoch tk and zk = [zk,1, . . . , zk, j ], where j ∈ N . The idea of Bayesian static localization isto estimate the posterior p(xk |zk) with only the current measurement. Using the Bayes’ rule,we get

p(xk |zk) = p(zk |xk)p(xk)

p(zk)(1)

Due to lack of specific prior information on xk , we set a uniform prior to p(xk). Then theposterior probability p(xk |zk) in (1) is equivalent to the likelihood p(zk |xk), i.e.

p(xk |zk) = p(zk |xk) (2)

Assume that the measurements zk, j from different AP j are independent and a Gaussianprobability density function (pdf) can be approximated to the histogram of ai, j , then thelikelihood p(zk |xk) in (2) can be expressed as

lk,i = p(zk |xk = ci ) =N∏

j=1

p(zk, j |xk = ci )

where

p(zk, j |xk = ci ) ={

N(zk, j ; ai, j , σ2i, j ) if AP j hearable

l0 if AP j unhearable

For unhearable AP j , the likelihood l0 should be zero. However, for the stability of numericalcomputation, the probability l0 is set to a very low value. We set l0 = 10−11 in the algorithm.

Based on the posterior p(xk |zk), the estimated mean xrk and the covariance Pr

k are

xrk = �M

i=1lk,i ci

Prk = �M

i=1lk,i

((xr

k − ci )(xrk − ci )

T)

(3)

where lk,i = lk,i/(�M

i=1lk,i).

4 Bayesian Fusion with Motion Model

4.1 Motion Model

Sequential estimation can improve the position accuracy by exploiting the motion model.A stationary state model is suitable to describe the indoor pedestrian movement where thevelocity often stays small [12]. The formulation is

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xk+1 = xk + wk, (4)

where wk is a white zero mean Gaussian noise independent of the state x(k), with covarianceQ = (Vmax ∗ �t)2 ∗ I2, where I2 the 2 × 2 matrix and Vmax is the maximum velocity forpedestrian indoors.

4.2 Bayesian Fusion

Suppose at time tk−1, the mean and covariance of xk−1 is xk−1, Pk−1. Then, according to thestationary state model (4), the predicted mean and covariance is

xmk|k−1 = xk−1|k−1

Pmk|k−1 = Pk−1|k−1 + Q (5)

At time tk , fusing the two Gaussian distributions estimated from (3) and (5), the result is stilla Gaussian density function with the updated mean xk|k and covariance Pk|k as [13, pp. 47]

(Pk|k)−1 = (Pmk|k−1)

−1 + (Prk)

−1

xk|k = Pk|k[(Pm

k|k−1)−1xm

k|k−1 + (Prk)

−1xrk

](6)

5 Tests and Results

5.1 Testing

An indoor test was carried out in a corridor on the third floor at the Finnish Geodetic Institute.13 Bluetooth APs were deployed in the whole building, with 5 APs on the second floor andthe others are on the third floor. The Bluetooth RSS data collecting system consists of a hard-ware evaluation kit and a self-developed data collecting application. The core componentof the evaluation kit is the Bluegiga WT41 module, which is a class 1 Bluetooth 2.1 plusan Enhanced Data Rate (EDR) module optimized for long range applications. The effectivescanning range is approximately 800 m. The evaluation kit is powered by a laptop through aUSB connection. A self-developed application is applied to control the Bluetooth module toscan the APs nearby, collect the RSS from the detected APs and send the measurements to thelaptop via a serial port. The sampling interval could be adjusted within 4–11.25 s accordingto the scanning priority chosen.

A reference trajectory, used as the ground truth trajectory, is obtained via NovAtel’s high-accuracy GPS/INS SPAN system including an HG1700 IMU (inertial measurement unit).Figure 1 shows the floormap and the whole indoor positioning platform.

5.2 Results

Two tests were carried out in the scenario. In both tests, a tester walked along the corridorsback and forth with the test cart. Test 1 lasted for about 6 min, while Test 2 only lasted for3 min with a relatively faster speed. The scanning priority of Bluetooth is set to 6, whichcorresponds to the sampling interval �t ≈ 9 s. We compare the proposed BF method withthe Bayes static estimation (BSE) method (Sect. 3) and the point Kalman filter (PKF) method,which uses a Kalman filter to further smooth the position results obtained by the BSE [12].In the tests, the covariance of the process noise in BF and PKF are both set as Q = 182 · I2

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Fig. 1 Floormap and the position of the Bluetooth APs

−50 −40 −30 −20 −10 0

−35

−30

−25

−20

−15

−10

−5

0

East (m)

Nor

th (

m)

calibration pointSPAN referenceBSEPKFBF

Fig. 2 Position estimation in Test 1

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5 10 15 20 25 30 35 40

5

10

15

20

25

time epoch k (Δ tk = 9 s)

Pos

. E

rror

(m

)

BSEPKFBF

Fig. 3 Position error versus time epoch in Test 1

−50 −40 −30 −20 −10 0

−35

−30

−25

−20

−15

−10

−5

0

East (m)

Nor

th (

m)


Fig. 4 Position estimation at k = 13 in Test 1

The initial position of the BF and the PKF is obtained from the first output of the BSE andthe initial covariance for position estimation is 9 ∗ I2.

Figures 2, 3 and 4 show the estimation results from Test 1 and Figs. 5, 6 and 7 showthe results from Test 2, where Figs. 2 and 5 show the estimated trajectories of 3 differentalgorithms in a North-East coordinate frame including also the SPAN reference track as theground truth. Figures 3 and 6 demonstrate the position error versus time epoch of the threealgorithms. Figure 4 shows the estimation mean and covariance at k = 13 in Test 1 andFig. 7 shows the estimation at k = 7 in Test 2. The ellipse shown covers an one sigma (68 %)confidence interval. Position errors are compared in Table 1.

From the results, the mean error of the BSE is about 5 m. The PKF smoothes further theresults obtained by the BSE. Based on the prior motion model, the estimation errors arereduced. However, the improvement of the PKF is very slight, only 0.1 m. The reason is that,

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−50 −40 −30 −20 −10 0

−35

−30

−25

−20

−15

−10

−5

0

East (m)

Nor

th (

m)


Fig. 5 Position estimation in Test 2

2 4 6 8 10 12 14 16 18 20

2

4

6

8

10

12

14

16

18

20

22

time epoch k (Δ tk = 9 s)

Pos

. E

rror

(m

) BSEPKFBF

Fig. 6 Position error versus time epoch in Test 2

the covariance matrix Q in the motion model is large due to the long sampling interval of theBluetooth. Thus, the prior information from the motion model has low weight on the positionestimation at each epoch.

Although the BF method uses the same motion model as the PKF, the final estimation ofBF incorporates covariance from the BSE, which is ignored by PKF. Thus, in comparison,the positioning error of the BF is 4.7 m on the average, about 0.4 m less than BSE and 0.3 mless than the PKF.

The performance gain of BF is shown in Figs. 4 and 7. In both figures, the BSE givesrelatively large estimation errors, while the PKF has almost the same estimation results asthe BSE. But the significant improvements are observed in the BF method, which indicatesthe effectiveness by fusing the two moments in the prior prediction from the motion modeland the posterior estimation from the measurements.

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−50 −40 −30 −20 −10 0

−35

−30

−25

−20

−15

−10

−5

0

East (m)

Nor

th (

m)


Fig. 7 Position estimation at k = 7 in Test 2

Table 1 Position errorcomparison

Test Stat. BSE PKF BF

1 Mean (m) 5.0 4.9 4.6

Std (m) 5.8 5.7 4.8

Max (m) 27.2 26.5 23.3

95th (m) 12.7 12.9 12.8

Median (m) 2.9 2.9 2.9

Min (m) 0.4 0.4 0.3

2 Mean (m) 5.2 5.1 4.9

Std (m) 6.2 6.0 5.6

Max (m) 22.6 21.8 22.6

95th (m) 18.5 18.3 13.0

Median (m) 2.5 2.5 2.6

Min (m) 0.6 0.6 0.6

However, the BF method did not effectively reduce the large errors occurring at k = 18, 38in Test 1 and k = 5 in Test 2. This is because, in such time epochs, the estimations of theBSE have relatively small covariance, though the estimation mean has large errors. Thus, thefusion results depend largely on the estimation from the BSE, while the BSE method is onlybased on the RSSI measurements from the Bluetooth APs and the radio map constructedbefore-hand. Therefore, the effective methods to build the radiomap and extract informationfrom the noisy RSSI measurements are still the basis for accurate fingerprinting positioning.

6 Conclusions and Future Works

This paper studied wireless positioning fingerprinting in a Bluetooth network. Fingerprintsof RSSI were used for localization. A Bayesian fusion (BF) method was presented, which

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combined the posterior estimation from the measurements and the prior information froma motion model. Indoor field tests were carried out to verify the usefulness of the proposedindoor positioning approach.

Field tests showed that the proposed method was effective and achieved the best accu-racy when compared with the Bayesian static estimation method and the point Kalman filter.Although the compared algorithms were tried out in a Bluetooth fingerprinting scenario, theapproaches are also viable for any similar wireless network and thus the results are transfer-able to e.g. Wi-Fi signal strength based positioning.

References

1. Specification of Bluegiga System. (7 October 2010). WT41-A/WT41-N preliminary data sheet,Vol. 7, Bluegiga.

2. Bandara, U., Hasegawa, M., Inoue, M., Morikawa, H., & Aoyama, T. (September 2004). Design andimplementation of a Bluetooth signal strength based location sensing system. In IEEE radio andwireless conference, Atlanta, pp. 319–322.

3. Sheng, Z., & Pollard, J. K. (2006). Position measurement using Bluetooth. IEEE Transactions onConsumer Electronics, 52(2), 555–558.

4. Damian, K., Sean, M., & Terry, D. (October 2008). A Bluetooth-based minimum infrastructure homelocalization system. In Proceedings of 5th IEEE international symposium on wireless communicationsystems, Reykjavik, pp. 638–642.

5. Pei, L., Chen, R., Liu, J., Tenhunen, T., Kuusniemi, H., & Chen, Y. (2010). Using inquiry-basedBluetooth RSSI probability distributions for indoor positioning. Journal of Global Positioning Systems,9(2).

6. Simon, H., & Robert, H. (May 2009). Bluetooth tracking without discoverability. In Proceedings ofthe 4th international symposium on location and context awareness.

7. Anastasi, G., Bandelloni, R., Conti, M., Delmastro, F., Gregori, E., & Mainetto, G. (April 2003).Experimenting an indoor Bluetooth-based positioning service. In Proceedings of the 23rd internationalconference on distributed computing systems workshops (pp. 480–483).

8. Bargh, M., & Groote, R. (September 2008). Indoor localization based on response rate of bluetoothinquiries. In Proceedings of the first ACM international workshop on mobile entity localization andtracking in GPS-less environments.

9. Jevring, M., Groote, R., & Hesselman, C. (2008). Dynamic optimization of Bluetooth networks forindoor localization. In Proceedings of the first international workshop on automated and autonomoussensor networks.

10. Naya, F., Noma, H., Ohmura, R., & Kogure, K. (September 2005). Bluetooth-based indoor proximitysensing for nursing context awareness. In Proceedings of the 9th IEEE international symposium onwearable computers (pp. 212–213).

11. Kjærgaard, M. B. (2007). A taxonomy for radio location fingerprinting. Lecture Notes in ComputerScience (pp. 139–156). Berlin: Springer.

12. Honkavirta, V., Perä lä, T., Ali-Löytty, S., & Piché, R. (2009). Location fingerprinting methods inwireless local area network. In Proceedings of the 6th workshop on positioning, navigation andcommunication 2009 (WPNC’09).

13. Gelman, A. B., Carlin, J. S., Stern, H. S., & Dubin, D. B. (2000). Bayesian data analysis(2nd ed.). London: Chapman & Hall.

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Author Biographies

Liang Chen received his Ph.D. degree in signal and informationprocessing from Southeast University, China, in 2009. From 2009 to2010, he worked as a postdoctoral researcher at Tampere Universityof Technology, Department of Mathematics, Finland. From 2011, heis a Senior Research Scientist at the Department of Navigation andPositioning in the Finnish Geodetic Institute. He also holds a Postdoc-toral Researcher position from Academy of Finland. His research inter-ests include statistical signal processing for positioning, sensor fusionalgorithm for indoor positioning and wireless positioning using signalsof opportunity. Email: [email protected] Present address: Finnish Geo-detic Institute, PO Box 15 (Geodeetinrinne 2), FIN-02431, Kirkkon-ummi, Finland.

Ling Pei received his Ph.D. degree in test measurement technol-ogy and instruments from the Southeast University, China, in 2007,joining the Finnish Geodetic Institute as a senior research scientist atthe same year. Now, he is a specialist research scientist and a groupleader in the Navigation and Positioning Department at the FGI. He hasauthored or co-authored over 40 scientific papers and book chapters.He is also an inventor of 6 patents and pending patents. His researchinterests include indoor/outdoor seamless positioning, ubiquitous com-puting, wireless positioning, mobile computing, context-aware appli-cations and location-based services. Nowadays, he has been sessionchairs, research chair, advisory chair, and technical program commit-tee members of some international conferences. Moreover, he is an edi-torial board member of the International Journal of Advanced RoboticSystems Editorial Board, a referee for IEEE Pervasive Computing, Sen-sors, International Journal of Geographical Information Science, andvarious IEEE international conferences. Email: [email protected]. Present

address: Finnish Geodetic Institute, PO Box 15 (Geodeetinrinne 2), FIN-02431, Kirkkonummi, Finland.

Heidi Kuusniemi is the Chief Research Scientist at the Departmentof Navigation and Positioning at the Finnish Geodetic Institute anda Lecturer at the Department of Surveying Sciences at Aalto Univer-sity, School of Engineering, Finland. She received her M.Sc. degreein 2002 and D.Sc. (Tech.) degree in 2005 from Tampere University ofTechnology, Finland. Her doctoral studies on personal satellite navi-gation were partly conducted at the Department of Geomatics Engi-neering at the University of Calgary, Canada. From 2005 to 2009 sheworked as a GPS Software Engineer in research and development atFastrax Ltd. Her research interests cover various aspects of GNSS nav-igation, quality control, multi-sensor fusion algorithms for seamlessoutdoor/indoor positioning, and GNSS interference mitigation meth-ods. Email: [email protected]. Present address: Finnish GeodeticInstitute, PO Box 15 (Geodeetinrinne 2), FIN-02431, Kirkkonummi,Finland.

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Yuwei Chen received his B.Sc. from the Electronics EngineeringDepartment of Zhejiang University (China 1999), M.Sc. from theInformation and Electronic Department of Zhejiang University (China2002), and a Ph.D. in Circuit and System from the Shanghai Institute ofTechnical Physics (SITP), Chinese Academy of Science (China 2005).He is now working at the Finnish Geodetic Institute as a SpecialistResearch Scientist in the Department of Navigation and Positioning.He has authored in over 60 scientific papers on personal navigation andremote sensing and holds 5 patents. Email: [email protected]. Presentaddress: Finnish Geodetic Institute, PO Box 15 (Geodeetinrinne 2),FIN-02431, Kirkkonummi, Finland.

Tuomo Kröger received his Master degree in electronics from Univer-sity of Kuopio. He is a research scientist in Finnish Geodetic Institute.His research interests include sensor based indoor/outdoor navigation.Email: [email protected]. Present address: Finnish Geodetic Insti-tute, PO Box 15 (Geodeetinrinne 2), FIN-02431, Kirkkonummi, Fin-land.

Ruizhi Chen holds a Ph.D. degree in Geophysics, a M.Sc. degreein computer science and a B.Sc. degree in Surveying Engineering.He is Head of the Department of Navigation and Positioning at theFinnish Geodetic Institute and an adjunct Professor in the Depart-ment of Computer Systems at Tampere University of Technology. Dr.Chen worked in Nokia as an engineering manager from 1998-2001. Hehas been involved in research of multi-sensor positioning for mobiledevices since 2001. Dr. Chen is the member of the editor board of theJournal of Global Positioning Systems. He has published one book,four book chapters and more than 120 scientific articles. He is thechair of the IEEE conferences “Ubiquitous Positioning, Indoor Nav-igation and Location-Based Service,” 2010 and 2012. Dr. Chen isalso a board member of the Nordic Institute of Navigation. email:[email protected]. Present address: Finnish Geodetic Institute, PO Box15 (Geodeetinrinne 2), FIN-02431, Kirkkonummi, Finland.

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Bayesian Fusion for Indoor Positioning Using Bluetooth Fingerprints

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