Location Fingerprint Positioning Based on Interval-valued Data FCM Algorithm

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1 Available online at Physis Proedia 5 (01 ) International Conferene on Solid State Devies and Materials Siene Loation Fingerprint Positioning Based on Interval-valued Data FCM Algorithm Fang Li, Weiming Tong, Tieheng Wang Shool of Eletrial Engineering and Automation Harbin Institute of Tehnology Harbin, Heilongjiang Provine, China Abstrat In order to redue positioning alulation power onsumption of ZigBee module, a fingerprint positioning method was proposed in the paper based on interval-valued data fuzzy -means algorithm. Fingerprints were regarded as interval-valued data whih ould reflet its unertainty aused by measurement error and interferene. In highdimensional feature spae spanned by interval midpoint and length, fingerprints were lustered by FCM algorithm to lower omputation omplexity. Compared with traditional lustering tehnologies, suh as -mean, the method got better lustering results of loation fingerprints in the positioning experiment designed in the paper. Results from the lustering and positioning experiments show that the method provides a feasible solution to derease the positioning alulation power onsumption of ZigBee module remarkably, as well as ensures the positioning preision Published by Elsevier Ltd. B.V. Seletion and/or peer-review under responsibility of of [name Garry organizer] Lee Open aess under CC BY-NC-ND liense. Keywords:ZigBee, loation fingerprint, fuzzy lustering, interval-valued data, positioning 1. Introdution Reently, the researh fous of ZigBee positioning system based on loation fingerprint method is how to improve the preision. However, omplex algorithms an redue the positioning error and onsume more wireless node energy at the same time whih an not be ignored. Energy-saving tehnology is the basis of all kinds of tehnologies in ZigBee network [1]. It is very important to derease positioning alulation power onsumption to prolong network lifetime, espeially positioning is served as an assistive funtion in the ZigBee network. Referene [] lassified loation fingerprints by lustering tehnology to derease alulation ost. It grouped fingerprints whih were measured from the same aess points into the same luster. However, when all or most of sampling loations an be overed by the signals of aess points, it has little hange of omputational amount before and after lustering. A positioning method based on -means lustering Published by Elsevier B.V. Seletion and/or peer-review under responsibility of Garry Lee Open aess under CC BY-NC-ND liense. doi: /j.phpro

2 1940 Fang Li et al. / Physis Proedia 5 ( 01 ) was proposed in [3]. The Eulidean distane between fingerprint and luster enter was used as lustering riterion in the method. But, the use of average value of reeived signal strength to get the similarity an not reflet the influene on sampling aused by the interferene in the environment. At the same time, - means lustering belongs to a kind of hard partition and divides every fingerprint into a luster absolutely. So, the fingerprints on the boundaries of different lusters have bad lustering results whih an lower the positioning preision at last. A loation fingerprint lustering algorithm based on Gaussian mixture model was put forward in [4]. Fingerprint was supposed as a mixture of multidimensional normal distributions whih approximated to distributions of signal strength. Beause of using probability distribution of signal strength to luster the fingerprint, the method has better restrain effet on noise during lustering proeeding than the methods mentioned above. Whereas, distribution of signal strength an not be replaed by normal distribution exatly on some environments and statistial distribution is subjet to sampling frequeny. In this paper, we present a new method for estimating the loation with low omputational requirements in the ZigBee network using FCM algorithm [5]. The sampling value of signal strength is regarded as interval-valued data whih an desribe its unertainty and is lustered by fuzzy -means lustering algorithm. We have evaluated the method in an indoor spae spanning a 750 square meter. Results obtained show that the method has better lustering effet of fingerprint than it of -means algorithm and ensures the aeptable positioning preision.. Researh of Methodology We begin with a desription of our experimental testbed. We then disuss the data olletion proess, inluding tools we developed for this purpose. Finally, based on analysis of statistial harateristi of signal strength sample, we desribe the reason of treating fingerprint as interval-valued data and using FCM algorithm to luster it..1 Experimental Testbed Our experimental testbed is loated on the entrane hall of a teahing building. The layout of the floor is shown in Fig. 1. The floor has dimension of 30 m by 5 m, an area of 750 sq. m. Four ZigBee beaons (b1, b, b3 and b4) fixed at the height of meters an provide even four-overlap overage in all portions of the hall. Eighty alibration points where the ZigBee mobile nodes signal strength were olleted are denoted by the solid blak dots. And the diretions of arrows indiate the sampling route.. ZigBee Module We applied a ZigBee module adopted TI s single-hip.4ghz IEEE ompliant RF transeiver CC40 and Mirohip s enhaned Flash miroontroller PIC18F460. We used RS-3 to transport ommands and information between b b b4 b m 10 Figure 1. Layout of the experimentation environment

3 Fang Li et al. / Physis Proedia 5 ( 01 ) laptop and modules suh as network finding, assoiation and disassoiation. The module adopted.4ghz 50 ohm inverted-f antenna whih got 1.1dB gain [6]..3 Signal Strength Statistial Charateristi We sampled the signal strength of all beaons at every loation and generated the fingerprint database. The sampling proess per loation lasted 180 seonds at 1 Hz. Fig. shows the signal strength distribution of beaon 1 at random loation in the testbed. It is onluded that multi-path fading and people s ativities make the signal strength flutuate, instead of fixed value, whih makes it diffiult to operate sampling value of signal strength as a real vetor. So, in most ases, sampling value of signal strength is impreise and the bigger range in whih sampling value flutuates, the more impreise it is. In order to study this kind of impreise data lustering, we regarded fingerprint as interval-valued data and got interval midpoint and length through further feature extration to desribe distribution and unertainty of fingerprint. At last, we lustered fingerprints by FCM algorithm to lower omputation omplexity in high-dimensional feature spae spanned by interval midpoint and length. 3. Fingerfrint FCM Clustering Figure. Histogram of the signal strength of beaon 1 sampled at random loation Suppose there are k beaons and n sampling loations. At eah loation fingerprint vetor is RSS i = (rss i1,,rss ik ), where i {1,,,n}. rss ik is signal strength sampling value of the k th beaon at the i th sampling loation. In the paper, we deal with rss ik as interval-valued data and transform it to [min(rss ik ), max(rss ik )] to desribe the hange range of it. After further feature extration of [min(rss ik ), max(rss ik )], we an get rss ik and.. rssik Where rss ik is interval midpoint and rss ik vetor RSS i after further feature extration. min( rssik ) max( rssik ) ik rss rssik max( rssik ) min( rssik ) is interval length. Aording to (1), we an get new fingerprint.. RSS i ( rssi1,..., rssik, rssi1,..., rssik) (1) () Where is weighting fator, we an use it to ontrol influene of interval length on the lustering result.

4 194 Fang Li et al. / Physis Proedia 5 ( 01 ) If we luster n fingerprints into lusters using FCM, the lustering objetive funtion is n m Jm( U, P) ( ij) ( dij) i1 j1 s. t. U M f Where ij is the membership of the i th fingerprint to the j th luster and generates membership matrix U= [ ij ] n... p ( p,..., p, p,..., p ) is luster enter and generates enter matrix P = (p T 1,, p T j ) j j1 jk j1 jk where j {1,,,}m is smooth parameter. The similarity between the i th fingerprint and the j th luster enter is (3) ( d ) RSSi p (4) Where A is a positive definite matrix. And when it is a unit matrix, d ij denotes Eulidean distane. Our goal is to minimize the objetive funtion (3). Beause all parts of matrix U are independent, we an get the min{j m } as follows ij n m min{ Jm( U, P)} min{ ( ij) ( dij) } i1 j1 n m = min{ ( ij ) ( dij ) } i1 j1 j A (5) The solution of (5) is an optimization problem under equality onstraint Lagrangian funtion as follows j 1 1. We an onstrut a ij The first-order neessary onditions of (6) is m L ( ) ( d ) ( 1) ij ij ij j1 j1 (6) L m d ij L ij 10 j 1 m1 ( ij ) ( ij ) 0 (7) Aording to (7), we an get membership of RSS i to the j th luster and luster enters 1 dij m1 ij ( ) l 1 dil n n m m pj ( ij) RSSi ( ij) i1 i1 Iteration stopping riterion is P (t) -P (t+1) < or U (t) -U (t+1) <. Where t is iteration times. 1 (8)

5 Fang Li et al. / Physis Proedia 5 ( 01 ) Results and Analysis 4.1 Clustering Results Analysis In order to verify lustering validity of the method, we seleted two groups of ZigBee beaons randomly and 80 fingerprints per group in the testbed shown in Fig. 1. Two groups are aording to beaon group 1 (b1, b and b3) and beaon group (b1, b and b4) respetively. On the onditions of = 1, m = 1, = 3 and A = E, FCM lustering results of two beaon groups fingerprints are shown in Fig. 3 and Fig. 5 respetively. We an see that every fingerprint is assigned to the luster in whih it has the biggest membership. It is also onluded from the figures that all fingerprints are assigned to three lusters learly and there are little overlaps between different lusters. Beause the loations of beaons are distributed around the testbed, fingerprints in the same luster an reflet the distane relationship between sampling loations on whih they were sampled and loations of beaons. In Fig. 5, there are some obvious overlaps on the loations of 1,, 3, 18, 19 and 0. This is beause that b4 has no line of sight with these loations and signal strength of b4 is lower omparatively. When Eulidean distane is adopted as lustering riterion, these fingerprints are assigned to luster 3 instead of luster 1 in whih the signal strength of b4 is higher than it of luster 3. We also implemented -means algorithm of fingerprints with the same parameters to ompare the lustering results whih are shown in Fig. 4 and Fig. 6. It is shown that in the same test onditions, fingerprints in the same luster distributed onfusedly in spae. The reason is that -means algorithm uses average value of signal strength to alulate the similarity between the fingerprint and luster enter, whih is suseptible to noisy data. At the same time, -means lustering is a hard partition and divides every fingerprint into a group absolutely. So, the fingerprints on the boundaries of different lusters have bad lustering results. Figure 3. FCM lustering result of fingerprints of beaon group 1 Figure 4. -means lustering result of fingerprints of beaon group 1

6 1944 Fang Li et al. / Physis Proedia 5 ( 01 ) Figure 5. FCM lustering result of fingerprints of beaon group Figure 6. -means lustering result of fingerprints of beaon group 4. Positioning Results Analysis We used Bayesian inferene [7] to estimate the loations of ZigBee mobile nodes based on FCM lustering results of fingerprints. Through the positioning result, we an verify the influene on preision and ost before ould after FCM lustering. We seleted 48 loations in the testbed randomly at whih signal strength of beaon group 1 were sampled. We also implemented Bayesian inferene (method 1), Bayesian inferene based on -means algorithm (method ) and Bayesian inferene based on intervalvalued data FCM algorithm (method 3) to ompare the positioning results. Fig. 7 shows the orresponding relationship between positioning errors and their probabilities. We an see that positioning preision of method 3 present in the paper is better than method. Method 3 deals with fingerprint as interval-valued data and desribes the distribution and unertainty of signal by interval midpoint and length. Not only similarities of fingerprints are taken into aount, but also influene of disturbane in the environment. At the same time, loations at boundaries of different lusters have similar memberships generally. Fuzzy lustering adopted by method 3 an get memberships of fingerprints attahed to different lusters, whih an get higher probable loation estimation. Although positioning preision of method 3 is slightly worse than method 1 s, it is in favor of dereasing alulation ost and time after lustering. Fig. 8 shows time ost of single loation in different lusters. The alulation time is tested on ZigBee module whih CPU runs at 16MHz and single instrution yle is 50ns. We an see that fingerprint grouped in luster 3 onsumed the least positioning time. Moreover, fingerprint un-lustered onsumed the most. In the test, the positioning time onsumption (3.65s) of 48 loations of method 1 is approximately.6 times it of method 3 (1.41s). But the preision improvement is inonspiuous. Mathematial expetation of positioning time of method 3 is ni Et () ti (9) n Where is the number of lusters. t i is the positioning time per loation in the i th luster. n i is the number of sampling loations in the i th luster. n is the number of all sampling loations. i1

7 Fang Li et al. / Physis Proedia 5 ( 01 ) Figure 7. Comparison of positioning errors and their probabilities between three methods Figure 8. Comparison of positioning time onsumption per loation in different luster 5. Conlusions We used interval-valued data FCM algorithm to luster fingerprint to derease the positioning energy ost of ZigBee module. Pratial lustering results prove that this method an lessen influene aused by interferene. By omparison with -means algorithm, lustering results of this method aord with relationship between signal strength and propagation distane refleted by fingerprint muh more. At last, we implemented Bayesian inferene based on fingerprint lustering. Positioning results indiate that this method an derease positioning alulation ost and improve positioning effiieny remarkably with the guarantee of positioning preision. 6. Aknowledgment We thank for the support of a grant from NSF of China under grant number and a grant from the NSF of Heilongjiang Provine under grant number E Referenes [1] Peng Y G, Li Y L, Lu Z C, et al. Method for saving energy in Zigbee network. In: WiCom '09 5th International Conferene on Wireless Communiations, Networking and Mobile Computing, Beijing, China,

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