Bayesian Fusion for Indoor Positioning Using Bluetooth Fingerprints
Wireless Pers Commun DOI 10.1007/s11277-012-0777-1
Bayesian Fusion for Indoor Positioning Using Bluetooth Fingerprints 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) applied to fingerprinting method in a Bluetooth network for indoor positioning. A Bayesian fusion (BF) method is proposed to combine the statistical information from the RSSI measurements and the prior information from a motion model. Indoor field tests are carried out to verify the effectiveness of the method. Test results show that the proposed BF algorithm achieves a horizontal positioning accuracy of about 4.7 m on the average, which is about 6 and 7 % improvement when compared with Bayesian static estimation and a point Kalman filter method, respectively. Keywords Bayesian fusion · Indoor positioning · Fingerprints · Bluetooth · Motion model
L. Chen (B) · L. Pei · H. Kuusniemi · Y. Chen · T. Kröger · R. Chen Department of Positioning and Navigation, Finnish Geodetic Institute, Kirkkonummi, Finland e-mail: [email protected] L. Chen · L. Pei · H. Kuusniemi · Y. Chen · T. Kröger · R. Chen Geodeetinrinne 2, P.O. Box 15, 02431 Masala, Finland L. Pei e-mail: [email protected] H. Kuusniemi e-mail: [email protected] Y. Chen e-mail: [email protected] T. Kröger e-mail: [email protected] R. Chen e-mail: [email protected]
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1 Introduction Indoor navigation is becoming a more sought-after utility for various mobile services and applications. Bluetooth, as widely supported by mobile devices, is a proprietary open wireless technology for exchanging data over short distances. Recently, the updated specifications have been developed for the relatively longer range of transmission. New Bluetooth products, such as Bluegiga AP 3201, have an effective transmission range up to 200 m while the Bluegiga 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 indoor positioning [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 strong reflections and scattering conditions indoors, RSSI measurements are seriously attenuated by multipath of signal propagation. Therefore, it is a challenging task to estimate the position using RSSI measurements with the prevailing various fading effects. Fingerprinting is a feasible technique for positioning using RSSI measurements. The basic idea of the fingerprinting method is to match elements in a database to a particular signal strength fingerprints in the area at hand. The method operates in two phases: the training phase and the online positioning phase. In the training phase, the radio map is created based on the reference points within the area of interest. The radio map implicitly characterizes the RSSI position relationship through the training measurements at the reference points with known coordinates. In the online positioning phase, the mobile device measures RSSI observations and the positioning system uses the radio map to obtain a position estimate. The fingerprinting method has been widely discussed for indoor positioning. Various factors that affect fingerprinting are thoroughly summarized in [11]. Different fingerprinting algorithms are compared for indoor wireless local area networks (WLAN) positioning in [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 area of interest. Based on the RSSIs measured from the Bluetooth APs, we present a Bayesian fusion (BF) method, which combines the posterior estimation from the RSSI measurements with the information from the prior motion model. Field tests are carried out indoors to verify the effectiveness of the method. The paper is organized as follows. In Sect. 2, the mathematical formulation of the radio map 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 a performance 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 Bluetooth APs at the reference points for a certain period of time. Then, the fingerprint can be generated and stored by RSSI measurements collected at each reference point. Collecting all the fingerprints, the radio map is constructed. Denote R as the radio map, Ri as the ith fingerprint, then the radio map can be formulated as R = {R1 , . . . , R M }, where M is the total number of reference points. Define the ith fingerprint Ri has the form:
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Ri = ci , ai, j , a¯ i, j , σi,2 j , j ∈ {1, . . . , N } where ci is the coordinate of th ith reference point and ai j holds the l RSS values measured from the access point AP j , i.e. ai, j = {ai,1 j , ai,2 j , . . . , ai,l j }. a¯ i, j and σi,2 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-dimenT sional Cartesian plane. The position at time tk , denoted as xk = xk yk corresponds to 2D position coordinates. Denote z k, j as RSSI values measured from the jth Bluetooth AP at time epoch tk and zk = [z k,1 , . . . , z k, j ], where j ∈ N . The idea of Bayesian static localization is to 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 the posterior 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 z k, j from different AP j are independent and a Gaussian probability density function (pdf) can be approximated to the histogram of ai, j , then the likelihood p(zk |xk ) in (2) can be expressed as lk,i = p(zk |xk = ci ) =
N
p(z k, j |xk = ci )
j=1
where
p(z k, j |xk = ci ) =
N(z k, j ; a¯ i, j , σi,2 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 numerical computation, 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 xˆ rk and the covariance Prk are
where l¯k,i
M ¯ lk,i ci xˆ rk = i=1 r M ¯ Pk = i=1 lk,i (ˆxrk − ci )(ˆxrk − ci )T
M = lk,i / i=1 lk,i .
(3)
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 the velocity 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 covariance Q = (Vmax ∗ t)2 ∗ I2 , where I2 the 2 × 2 matrix and Vmax is the maximum velocity for pedestrian indoors. 4.2 Bayesian Fusion Suppose at time tk−1 , the mean and covariance of xk−1 is xˆ k−1 , Pk−1 . Then, according to the stationary state model (4), the predicted mean and covariance is m xˆ k|k−1 = xˆ k−1|k−1 m Pk|k−1 = Pk−1|k−1 + Q
(5)
At time tk , fusing the two Gaussian distributions estimated from (3) and (5), the result is still a Gaussian density function with the updated mean xˆ k|k and covariance Pk|k as [13, pp. 47] m (Pk|k )−1 = (Pk|k−1 )−1 + (Prk )−1
m m xˆ k|k = Pk|k (Pk|k−1 )−1 xˆ k|k−1 + (Prk )−1 xˆ rk
(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 and the others are on the third floor. The Bluetooth RSS data collecting system consists of a hardware evaluation kit and a self-developed data collecting application. The core component of the evaluation kit is the Bluegiga WT41 module, which is a class 1 Bluetooth 2.1 plus an Enhanced Data Rate (EDR) module optimized for long range applications. The effective scanning range is approximately 800 m. The evaluation kit is powered by a laptop through a USB connection. A self-developed application is applied to control the Bluetooth module to scan the APs nearby, collect the RSS from the detected APs and send the measurements to the laptop via a serial port. The sampling interval could be adjusted within 4–11.25 s according to the scanning priority chosen. A reference trajectory, used as the ground truth trajectory, is obtained via NovAtel’s highaccuracy 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 corridors back and forth with the test cart. Test 1 lasted for about 6 min, while Test 2 only lasted for 3 min with a relatively faster speed. The scanning priority of Bluetooth is set to 6, which corresponds to the sampling interval t ≈ 9 s. We compare the proposed BF method with the 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 0 −5
North (m)
−10
calibration point SPAN reference BSE PKF BF
−15 −20 −25 −30 −35 −50
−40
−30
−20
−10
0
East (m) Fig. 2 Position estimation in Test 1
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Pos. Error (m)
25 BSE PKF BF
20
15
10
5
5
10
15
20
25
30
35
40
time epoch k (Δ tk = 9 s) Fig. 3 Position error versus time epoch in Test 1 0 −5
North (m)
−10
calibration point SPAN reference BSE PKF BF
−15 −20 −25 −30 −35 −50
−40
−30
−20
−10
0
East (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 and the 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 show the results from Test 2, where Figs. 2 and 5 show the estimated trajectories of 3 different algorithms in a North-East coordinate frame including also the SPAN reference track as the ground truth. Figures 3 and 6 demonstrate the position error versus time epoch of the three algorithms. Figure 4 shows the estimation mean and covariance at k = 13 in Test 1 and Fig. 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 the results obtained by the BSE. Based on the prior motion model, the estimation errors are reduced. However, the improvement of the PKF is very slight, only 0.1 m. The reason is that,
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Bayesian Fusion for Indoor Positioning 0 calibration point SPAN reference BSE PKF BF
−5
North (m)
−10 −15 −20 −25 −30 −35
−50
−40
−30
−20
−10
0
East (m) Fig. 5 Position estimation in Test 2
22 20
Pos. Error (m)
18 BSE PKF BF
16 14 12 10 8 6 4 2 2
4
6
8
10
12
14
16
18
20
time epoch k (Δ t = 9 s) k
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 the Bluetooth. Thus, the prior information from the motion model has low weight on the position estimation at each epoch. Although the BF method uses the same motion model as the PKF, the final estimation of BF 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 m less than the PKF. The performance gain of BF is shown in Figs. 4 and 7. In both figures, the BSE gives relatively large estimation errors, while the PKF has almost the same estimation results as the BSE. But the significant improvements are observed in the BF method, which indicates the effectiveness by fusing the two moments in the prior prediction from the motion model and the posterior estimation from the measurements.
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North (m)
−10
calibration point SPAN reference BSE PKF BF
−15 −20 −25 −30 −35 −50
−40
−30
−20
−10
0
East (m) Fig. 7 Position estimation at k = 7 in Test 2
Table 1 Position error comparison
Test 1
2
Stat.
BSE
PKF
BF
Mean (m)
5.0
4.9
Std (m)
5.8
5.7
4.6 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 4.9
Mean (m)
5.2
5.1
Std (m)
6.2
6.0
5.6
Max (m)
22.6
21.8
22.6
95th (m)
13.0
18.5
18.3
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, 38 in Test 1 and k = 5 in Test 2. This is because, in such time epochs, the estimations of the BSE have relatively small covariance, though the estimation mean has large errors. Thus, the fusion results depend largely on the estimation from the BSE, while the BSE method is only based on the RSSI measurements from the Bluetooth APs and the radio map constructed before-hand. Therefore, the effective methods to build the radiomap and extract information from 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. Fingerprints of 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 from a motion model. Indoor field tests were carried out to verify the usefulness of the proposed indoor positioning approach. Field tests showed that the proposed method was effective and achieved the best accuracy 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, the approaches are also viable for any similar wireless network and thus the results are transferable 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 and implementation of a Bluetooth signal strength based location sensing system. In IEEE radio and wireless conference, Atlanta, pp. 319–322. 3. Sheng, Z., & Pollard, J. K. (2006). Position measurement using Bluetooth. IEEE Transactions on Consumer Electronics, 52(2), 555–558. 4. Damian, K., Sean, M., & Terry, D. (October 2008). A Bluetooth-based minimum infrastructure home localization system. In Proceedings of 5th IEEE international symposium on wireless communication systems, Reykjavik, pp. 638–642. 5. Pei, L., Chen, R., Liu, J., Tenhunen, T., Kuusniemi, H., & Chen, Y. (2010). Using inquiry-based Bluetooth 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 of the 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 international conference on distributed computing systems workshops (pp. 480–483). 8. Bargh, M., & Groote, R. (September 2008). Indoor localization based on response rate of bluetooth inquiries. In Proceedings of the first ACM international workshop on mobile entity localization and tracking in GPS-less environments. 9. Jevring, M., Groote, R., & Hesselman, C. (2008). Dynamic optimization of Bluetooth networks for indoor localization. In Proceedings of the first international workshop on automated and autonomous sensor networks. 10. Naya, F., Noma, H., Ohmura, R., & Kogure, K. (September 2005). Bluetooth-based indoor proximity sensing for nursing context awareness. In Proceedings of the 9th IEEE international symposium on wearable computers (pp. 212–213). 11. Kjærgaard, M. B. (2007). A taxonomy for radio location fingerprinting. Lecture Notes in Computer Science (pp. 139–156). Berlin: Springer. 12. Honkavirta, V., Perä lä, T., Ali-Löytty, S., & Piché, R. (2009). Location fingerprinting methods in wireless local area network. In Proceedings of the 6th workshop on positioning, navigation and communication 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 information processing from Southeast University, China, in 2009. From 2009 to 2010, he worked as a postdoctoral researcher at Tampere University of Technology, Department of Mathematics, Finland. From 2011, he is a Senior Research Scientist at the Department of Navigation and Positioning in the Finnish Geodetic Institute. He also holds a Postdoctoral Researcher position from Academy of Finland. His research interests include statistical signal processing for positioning, sensor fusion algorithm for indoor positioning and wireless positioning using signals of opportunity. Email: [email protected] Present address: Finnish Geodetic Institute, PO Box 15 (Geodeetinrinne 2), FIN-02431, Kirkkonummi, Finland.
Ling Pei received his Ph.D. degree in test measurement technology and instruments from the Southeast University, China, in 2007, joining the Finnish Geodetic Institute as a senior research scientist at the same year. Now, he is a specialist research scientist and a group leader in the Navigation and Positioning Department at the FGI. He has authored or co-authored over 40 scientific papers and book chapters. He is also an inventor of 6 patents and pending patents. His research interests include indoor/outdoor seamless positioning, ubiquitous computing, wireless positioning, mobile computing, context-aware applications and location-based services. Nowadays, he has been session chairs, research chair, advisory chair, and technical program committee members of some international conferences. Moreover, he is an editorial board member of the International Journal of Advanced Robotic Systems Editorial Board, a referee for IEEE Pervasive Computing, Sensors, International Journal of Geographical Information Science, and various 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 Department of Navigation and Positioning at the Finnish Geodetic Institute and a Lecturer at the Department of Surveying Sciences at Aalto University, School of Engineering, Finland. She received her M.Sc. degree in 2002 and D.Sc. (Tech.) degree in 2005 from Tampere University of Technology, Finland. Her doctoral studies on personal satellite navigation were partly conducted at the Department of Geomatics Engineering at the University of Calgary, Canada. From 2005 to 2009 she worked as a GPS Software Engineer in research and development at Fastrax Ltd. Her research interests cover various aspects of GNSS navigation, quality control, multi-sensor fusion algorithms for seamless outdoor/indoor positioning, and GNSS interference mitigation methods. Email: [email protected]. Present address: Finnish Geodetic Institute, PO Box 15 (Geodeetinrinne 2), FIN-02431, Kirkkonummi, Finland.
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Bayesian Fusion for Indoor Positioning Yuwei Chen received his B.Sc. from the Electronics Engineering Department of Zhejiang University (China 1999), M.Sc. from the Information and Electronic Department of Zhejiang University (China 2002), and a Ph.D. in Circuit and System from the Shanghai Institute of Technical Physics (SITP), Chinese Academy of Science (China 2005). He is now working at the Finnish Geodetic Institute as a Specialist Research Scientist in the Department of Navigation and Positioning. He has authored in over 60 scientific papers on personal navigation and remote sensing and holds 5 patents. Email: [email protected]. Present address: Finnish Geodetic Institute, PO Box 15 (Geodeetinrinne 2), FIN-02431, Kirkkonummi, Finland.
Tuomo Kröger received his Master degree in electronics from University 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 Institute, PO Box 15 (Geodeetinrinne 2), FIN-02431, Kirkkonummi, Finland.
Ruizhi Chen holds a Ph.D. degree in Geophysics, a M.Sc. degree in computer science and a B.Sc. degree in Surveying Engineering. He is Head of the Department of Navigation and Positioning at the Finnish Geodetic Institute and an adjunct Professor in the Department of Computer Systems at Tampere University of Technology. Dr. Chen worked in Nokia as an engineering manager from 1998-2001. He has been involved in research of multi-sensor positioning for mobile devices since 2001. Dr. Chen is the member of the editor board of the Journal of Global Positioning Systems. He has published one book, four book chapters and more than 120 scientific articles. He is the chair of the IEEE conferences “Ubiquitous Positioning, Indoor Navigation and Location-Based Service,” 2010 and 2012. Dr. Chen is also a board member of the Nordic Institute of Navigation. email: [email protected]. Present address: Finnish Geodetic Institute, PO Box 15 (Geodeetinrinne 2), FIN-02431, Kirkkonummi, Finland.
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Bayesian Fusion for Indoor Positioning Using Bluetooth Fingerprints 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) applied to fingerprinting method in a Bluetooth network for indoor positioning. A Bayesian fusion (BF) method is proposed to combine the statistical information from the RSSI measurements and the prior information from a motion model. Indoor field tests are carried out to verify the effectiveness of the method. Test results show that the proposed BF algorithm achieves a horizontal positioning accuracy of about 4.7 m on the average, which is about 6 and 7 % improvement when compared with Bayesian static estimation and a point Kalman filter method, respectively. Keywords Bayesian fusion · Indoor positioning · Fingerprints · Bluetooth · Motion model
L. Chen (B) · L. Pei · H. Kuusniemi · Y. Chen · T. Kröger · R. Chen Department of Positioning and Navigation, Finnish Geodetic Institute, Kirkkonummi, Finland e-mail: [email protected] L. Chen · L. Pei · H. Kuusniemi · Y. Chen · T. Kröger · R. Chen Geodeetinrinne 2, P.O. Box 15, 02431 Masala, Finland L. Pei e-mail: [email protected] H. Kuusniemi e-mail: [email protected] Y. Chen e-mail: [email protected] T. Kröger e-mail: [email protected] R. Chen e-mail: [email protected]
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1 Introduction Indoor navigation is becoming a more sought-after utility for various mobile services and applications. Bluetooth, as widely supported by mobile devices, is a proprietary open wireless technology for exchanging data over short distances. Recently, the updated specifications have been developed for the relatively longer range of transmission. New Bluetooth products, such as Bluegiga AP 3201, have an effective transmission range up to 200 m while the Bluegiga 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 indoor positioning [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 strong reflections and scattering conditions indoors, RSSI measurements are seriously attenuated by multipath of signal propagation. Therefore, it is a challenging task to estimate the position using RSSI measurements with the prevailing various fading effects. Fingerprinting is a feasible technique for positioning using RSSI measurements. The basic idea of the fingerprinting method is to match elements in a database to a particular signal strength fingerprints in the area at hand. The method operates in two phases: the training phase and the online positioning phase. In the training phase, the radio map is created based on the reference points within the area of interest. The radio map implicitly characterizes the RSSI position relationship through the training measurements at the reference points with known coordinates. In the online positioning phase, the mobile device measures RSSI observations and the positioning system uses the radio map to obtain a position estimate. The fingerprinting method has been widely discussed for indoor positioning. Various factors that affect fingerprinting are thoroughly summarized in [11]. Different fingerprinting algorithms are compared for indoor wireless local area networks (WLAN) positioning in [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 area of interest. Based on the RSSIs measured from the Bluetooth APs, we present a Bayesian fusion (BF) method, which combines the posterior estimation from the RSSI measurements with the information from the prior motion model. Field tests are carried out indoors to verify the effectiveness of the method. The paper is organized as follows. In Sect. 2, the mathematical formulation of the radio map 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 a performance 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 Bluetooth APs at the reference points for a certain period of time. Then, the fingerprint can be generated and stored by RSSI measurements collected at each reference point. Collecting all the fingerprints, the radio map is constructed. Denote R as the radio map, Ri as the ith fingerprint, then the radio map can be formulated as R = {R1 , . . . , R M }, where M is the total number of reference points. Define the ith fingerprint Ri has the form:
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Ri = ci , ai, j , a¯ i, j , σi,2 j , j ∈ {1, . . . , N } where ci is the coordinate of th ith reference point and ai j holds the l RSS values measured from the access point AP j , i.e. ai, j = {ai,1 j , ai,2 j , . . . , ai,l j }. a¯ i, j and σi,2 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-dimenT sional Cartesian plane. The position at time tk , denoted as xk = xk yk corresponds to 2D position coordinates. Denote z k, j as RSSI values measured from the jth Bluetooth AP at time epoch tk and zk = [z k,1 , . . . , z k, j ], where j ∈ N . The idea of Bayesian static localization is to 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 the posterior 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 z k, j from different AP j are independent and a Gaussian probability density function (pdf) can be approximated to the histogram of ai, j , then the likelihood p(zk |xk ) in (2) can be expressed as lk,i = p(zk |xk = ci ) =
N
p(z k, j |xk = ci )
j=1
where
p(z k, j |xk = ci ) =
N(z k, j ; a¯ i, j , σi,2 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 numerical computation, 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 xˆ rk and the covariance Prk are
where l¯k,i
M ¯ lk,i ci xˆ rk = i=1 r M ¯ Pk = i=1 lk,i (ˆxrk − ci )(ˆxrk − ci )T
M = lk,i / i=1 lk,i .
(3)
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 the velocity 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 covariance Q = (Vmax ∗ t)2 ∗ I2 , where I2 the 2 × 2 matrix and Vmax is the maximum velocity for pedestrian indoors. 4.2 Bayesian Fusion Suppose at time tk−1 , the mean and covariance of xk−1 is xˆ k−1 , Pk−1 . Then, according to the stationary state model (4), the predicted mean and covariance is m xˆ k|k−1 = xˆ k−1|k−1 m Pk|k−1 = Pk−1|k−1 + Q
(5)
At time tk , fusing the two Gaussian distributions estimated from (3) and (5), the result is still a Gaussian density function with the updated mean xˆ k|k and covariance Pk|k as [13, pp. 47] m (Pk|k )−1 = (Pk|k−1 )−1 + (Prk )−1
m m xˆ k|k = Pk|k (Pk|k−1 )−1 xˆ k|k−1 + (Prk )−1 xˆ rk
(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 and the others are on the third floor. The Bluetooth RSS data collecting system consists of a hardware evaluation kit and a self-developed data collecting application. The core component of the evaluation kit is the Bluegiga WT41 module, which is a class 1 Bluetooth 2.1 plus an Enhanced Data Rate (EDR) module optimized for long range applications. The effective scanning range is approximately 800 m. The evaluation kit is powered by a laptop through a USB connection. A self-developed application is applied to control the Bluetooth module to scan the APs nearby, collect the RSS from the detected APs and send the measurements to the laptop via a serial port. The sampling interval could be adjusted within 4–11.25 s according to the scanning priority chosen. A reference trajectory, used as the ground truth trajectory, is obtained via NovAtel’s highaccuracy 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 corridors back and forth with the test cart. Test 1 lasted for about 6 min, while Test 2 only lasted for 3 min with a relatively faster speed. The scanning priority of Bluetooth is set to 6, which corresponds to the sampling interval t ≈ 9 s. We compare the proposed BF method with the 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 0 −5
North (m)
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East (m) Fig. 2 Position estimation in Test 1
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Pos. Error (m)
25 BSE PKF BF
20
15
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5
5
10
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30
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time epoch k (Δ tk = 9 s) Fig. 3 Position error versus time epoch in Test 1 0 −5
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East (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 and the 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 show the results from Test 2, where Figs. 2 and 5 show the estimated trajectories of 3 different algorithms in a North-East coordinate frame including also the SPAN reference track as the ground truth. Figures 3 and 6 demonstrate the position error versus time epoch of the three algorithms. Figure 4 shows the estimation mean and covariance at k = 13 in Test 1 and Fig. 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 the results obtained by the BSE. Based on the prior motion model, the estimation errors are reduced. However, the improvement of the PKF is very slight, only 0.1 m. The reason is that,
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time epoch k (Δ t = 9 s) k
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 the Bluetooth. Thus, the prior information from the motion model has low weight on the position estimation at each epoch. Although the BF method uses the same motion model as the PKF, the final estimation of BF 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 m less than the PKF. The performance gain of BF is shown in Figs. 4 and 7. In both figures, the BSE gives relatively large estimation errors, while the PKF has almost the same estimation results as the BSE. But the significant improvements are observed in the BF method, which indicates the effectiveness by fusing the two moments in the prior prediction from the motion model and the posterior estimation from the measurements.
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Table 1 Position error comparison
Test 1
2
Stat.
BSE
PKF
BF
Mean (m)
5.0
4.9
Std (m)
5.8
5.7
4.6 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 4.9
Mean (m)
5.2
5.1
Std (m)
6.2
6.0
5.6
Max (m)
22.6
21.8
22.6
95th (m)
13.0
18.5
18.3
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, 38 in Test 1 and k = 5 in Test 2. This is because, in such time epochs, the estimations of the BSE have relatively small covariance, though the estimation mean has large errors. Thus, the fusion results depend largely on the estimation from the BSE, while the BSE method is only based on the RSSI measurements from the Bluetooth APs and the radio map constructed before-hand. Therefore, the effective methods to build the radiomap and extract information from 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. Fingerprints of 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 from a motion model. Indoor field tests were carried out to verify the usefulness of the proposed indoor positioning approach. Field tests showed that the proposed method was effective and achieved the best accuracy 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, the approaches are also viable for any similar wireless network and thus the results are transferable 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 and implementation of a Bluetooth signal strength based location sensing system. In IEEE radio and wireless conference, Atlanta, pp. 319–322. 3. Sheng, Z., & Pollard, J. K. (2006). Position measurement using Bluetooth. IEEE Transactions on Consumer Electronics, 52(2), 555–558. 4. Damian, K., Sean, M., & Terry, D. (October 2008). A Bluetooth-based minimum infrastructure home localization system. In Proceedings of 5th IEEE international symposium on wireless communication systems, Reykjavik, pp. 638–642. 5. Pei, L., Chen, R., Liu, J., Tenhunen, T., Kuusniemi, H., & Chen, Y. (2010). Using inquiry-based Bluetooth 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 of the 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 international conference on distributed computing systems workshops (pp. 480–483). 8. Bargh, M., & Groote, R. (September 2008). Indoor localization based on response rate of bluetooth inquiries. In Proceedings of the first ACM international workshop on mobile entity localization and tracking in GPS-less environments. 9. Jevring, M., Groote, R., & Hesselman, C. (2008). Dynamic optimization of Bluetooth networks for indoor localization. In Proceedings of the first international workshop on automated and autonomous sensor networks. 10. Naya, F., Noma, H., Ohmura, R., & Kogure, K. (September 2005). Bluetooth-based indoor proximity sensing for nursing context awareness. In Proceedings of the 9th IEEE international symposium on wearable computers (pp. 212–213). 11. Kjærgaard, M. B. (2007). A taxonomy for radio location fingerprinting. Lecture Notes in Computer Science (pp. 139–156). Berlin: Springer. 12. Honkavirta, V., Perä lä, T., Ali-Löytty, S., & Piché, R. (2009). Location fingerprinting methods in wireless local area network. In Proceedings of the 6th workshop on positioning, navigation and communication 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 information processing from Southeast University, China, in 2009. From 2009 to 2010, he worked as a postdoctoral researcher at Tampere University of Technology, Department of Mathematics, Finland. From 2011, he is a Senior Research Scientist at the Department of Navigation and Positioning in the Finnish Geodetic Institute. He also holds a Postdoctoral Researcher position from Academy of Finland. His research interests include statistical signal processing for positioning, sensor fusion algorithm for indoor positioning and wireless positioning using signals of opportunity. Email: [email protected] Present address: Finnish Geodetic Institute, PO Box 15 (Geodeetinrinne 2), FIN-02431, Kirkkonummi, Finland.
Ling Pei received his Ph.D. degree in test measurement technology and instruments from the Southeast University, China, in 2007, joining the Finnish Geodetic Institute as a senior research scientist at the same year. Now, he is a specialist research scientist and a group leader in the Navigation and Positioning Department at the FGI. He has authored or co-authored over 40 scientific papers and book chapters. He is also an inventor of 6 patents and pending patents. His research interests include indoor/outdoor seamless positioning, ubiquitous computing, wireless positioning, mobile computing, context-aware applications and location-based services. Nowadays, he has been session chairs, research chair, advisory chair, and technical program committee members of some international conferences. Moreover, he is an editorial board member of the International Journal of Advanced Robotic Systems Editorial Board, a referee for IEEE Pervasive Computing, Sensors, International Journal of Geographical Information Science, and various 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 Department of Navigation and Positioning at the Finnish Geodetic Institute and a Lecturer at the Department of Surveying Sciences at Aalto University, School of Engineering, Finland. She received her M.Sc. degree in 2002 and D.Sc. (Tech.) degree in 2005 from Tampere University of Technology, Finland. Her doctoral studies on personal satellite navigation were partly conducted at the Department of Geomatics Engineering at the University of Calgary, Canada. From 2005 to 2009 she worked as a GPS Software Engineer in research and development at Fastrax Ltd. Her research interests cover various aspects of GNSS navigation, quality control, multi-sensor fusion algorithms for seamless outdoor/indoor positioning, and GNSS interference mitigation methods. Email: [email protected]. Present address: Finnish Geodetic Institute, PO Box 15 (Geodeetinrinne 2), FIN-02431, Kirkkonummi, Finland.
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Bayesian Fusion for Indoor Positioning Yuwei Chen received his B.Sc. from the Electronics Engineering Department of Zhejiang University (China 1999), M.Sc. from the Information and Electronic Department of Zhejiang University (China 2002), and a Ph.D. in Circuit and System from the Shanghai Institute of Technical Physics (SITP), Chinese Academy of Science (China 2005). He is now working at the Finnish Geodetic Institute as a Specialist Research Scientist in the Department of Navigation and Positioning. He has authored in over 60 scientific papers on personal navigation and remote sensing and holds 5 patents. Email: [email protected]. Present address: Finnish Geodetic Institute, PO Box 15 (Geodeetinrinne 2), FIN-02431, Kirkkonummi, Finland.
Tuomo Kröger received his Master degree in electronics from University 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 Institute, PO Box 15 (Geodeetinrinne 2), FIN-02431, Kirkkonummi, Finland.
Ruizhi Chen holds a Ph.D. degree in Geophysics, a M.Sc. degree in computer science and a B.Sc. degree in Surveying Engineering. He is Head of the Department of Navigation and Positioning at the Finnish Geodetic Institute and an adjunct Professor in the Department of Computer Systems at Tampere University of Technology. Dr. Chen worked in Nokia as an engineering manager from 1998-2001. He has been involved in research of multi-sensor positioning for mobile devices since 2001. Dr. Chen is the member of the editor board of the Journal of Global Positioning Systems. He has published one book, four book chapters and more than 120 scientific articles. He is the chair of the IEEE conferences “Ubiquitous Positioning, Indoor Navigation and Location-Based Service,” 2010 and 2012. Dr. Chen is also a board member of the Nordic Institute of Navigation. email: [email protected]. Present address: Finnish Geodetic Institute, PO Box 15 (Geodeetinrinne 2), FIN-02431, Kirkkonummi, Finland.
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