Location Fingerprint Positioning Based on Interval-valued Data FCM Algorithm

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Physics Procedia 25 ( 2012 ) 1939 – 1946

2012 International Conference on Solid State Devices and Materials Science

Location Fingerprint Positioning Based on Interval-valued

Data FCM Algorithm

Fang Li, Weiming Tong, Tiecheng Wang

School of Electrical Engineering and Automation Harbin Institute of Technology Harbin, Heilongjiang Province, China

Abstract

In order to reduce positioning calculation power consumption of ZigBee module, a fingerprint positioning method was proposed in the paper based on interval-valued data fuzzy c-means algorithm. Fingerprints were regarded as interval-valued data which could reflect its uncertainty caused by measurement error and interference. In high-dimensional feature space spanned by interval midpoint and length, fingerprints were clustered by FCM algorithm to lower computation complexity. Compared with traditional clustering technologies, such as c-mean, the method got better clustering results of location fingerprints in the positioning experiment designed in the paper. Results from the clustering and positioning experiments show that the method provides a feasible solution to decrease the positioning calculation power consumption of ZigBee module remarkably, as well as ensures the positioning precision.

Keywords:ZigBee, location fingerprint, fuzzy clustering, interval-valued data, positioning

1. Introduction

Recently, the research focus of ZigBee positioning system based on location fingerprint method is how to improve the precision. However, complex algorithms can reduce the positioning error and consume more wireless node energy at the same time which can not be ignored. Energy-saving technology is the basis of all kinds of technologies in ZigBee network [1]. It is very important to decrease positioning calculation power consumption to prolong network lifetime, especially positioning is served as an assistive function in the ZigBee network.

Reference [2] classified location fingerprints by clustering technology to decrease calculation cost. It grouped fingerprints which were measured from the same access points into the same cluster. However, when all or most of sampling locations can be covered by the signals of access points, it has little change of computational amount before and after clustering. A positioning method based on c-means clustering © 2012 Published by Elsevier B.V. Selection and/or peer-review under responsibility of Garry Lee Open access under CC BY-NC-ND license.

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was proposed in [3]. The Euclidean distance between fingerprint and cluster center was used as clustering criterion in the method. But, the use of average value of received signal strength to get the similarity can not reflect the influence on sampling caused by the interference in the environment. At the same time, c-means clustering belongs to a kind of hard partition and divides every fingerprint into a cluster absolutely. So, the fingerprints on the boundaries of different clusters have bad clustering results which can lower the positioning precision at last. A location fingerprint clustering algorithm based on Gaussian mixture model was put forward in [4]. Fingerprint was supposed as a mixture of multidimensional normal distributions which approximated to distributions of signal strength. Because of using probability distribution of signal strength to cluster the fingerprint, the method has better restrain effect on noise during clustering proceeding than the methods mentioned above. Whereas, distribution of signal strength can not be replaced by normal distribution exactly on some environments and statistical distribution is subject to sampling frequency.

In this paper, we present a new method for estimating the location with low computational requirements in the ZigBee network using FCM algorithm [5]. The sampling value of signal strength is regarded as interval-valued data which can describe its uncertainty and is clustered by fuzzy c-means clustering algorithm. We have evaluated the method in an indoor space spanning a 750 square meter. Results obtained show that the method has better clustering effect of fingerprint than it of c-means algorithm and ensures the acceptable positioning precision.

2. Research of Methodology

We begin with a description of our experimental testbed. We then discuss the data collection process, including tools we developed for this purpose. Finally, based on analysis of statistical characteristic of signal strength sample, we describe the reason of treating fingerprint as interval-valued data and using FCM algorithm to cluster it.

2.1 Experimental Testbed

Our experimental testbed is located on the entrance hall of a teaching building. The layout of the floor is shown in Fig. 1. The floor has dimension of 30 m by 25 m, an area of 750 sq. m. Four ZigBee beacons (b1, b2, b3 and b4) fixed at the height of 2 meters can provide even four-overlap coverage in all portions of the hall. Eighty calibration points where the ZigBee mobile nodes’ signal strength were collected are denoted by the solid black dots. And the directions of arrows indicate the sampling route.

2.2 ZigBee Module

We applied a ZigBee module adopted TI’s single-chip 2.4GHz IEEE 802.15.4 compliant RF transceiver CC2420 and Microchip’s enhanced Flash microcontroller PIC18F4620. We used RS-232 to transport commands and information between

b1 _b2 b4 b3 01 80 10 71 30m

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laptop and modules such as network finding, association and disassociation. The module adopted 2.4GHz

50 ohm inverted-F antenna which got 1.1dB gain [6].

2.3 Signal Strength Statistical Characteristic

We sampled the signal strength of all beacons at every location and generated the fingerprint database. The sampling process per location lasted 180 seconds at 1 Hz. Fig. 2 shows the signal strength distribution of beacon 1 at random location in the testbed. It is concluded that multi-path fading and people’s activities make the signal strength fluctuate, instead of fixed value, which makes it difficult to operate sampling value of signal strength as a real vector. So, in most cases, sampling value of signal strength is imprecise and the bigger range in which sampling value fluctuates, the more imprecise it is. In order to study this kind of imprecise data clustering, we regarded fingerprint as interval-valued data and got interval midpoint and length through further feature extraction to describe distribution and uncertainty of fingerprint. At last, we clustered fingerprints by FCM algorithm to lower computation complexity in high-dimensional feature space spanned by interval midpoint and length.

Figure 2. Histogram of the signal strength of beacon 1 sampled at random location

3. Fingerfrint FCM Clustering

Suppose there are k beacons and n sampling locations. At each location fingerprint vector is RSSi=

(rssi1,…,rssik), where i ę{1,2,…,n}. rssik is signal strength sampling value of the kth beacon at the ith

sampling location. In the paper, we deal with rssik as interval-valued data and transform it to [min(rssik),

max(rssik)] to describe the change range of it. After further feature extraction of [min(rssik), max(rssik)],

we can get . ik rss and rssik . _min( _{) max(} ₎ 2 max( ) min( ) ik ik ik ik _ik _ik rss rss rss rss rss rss ° ® ° ¯ (1) Where . ik

rss is interval midpoint and rssik

is interval length. According to (1), we can get new fingerprint vector

_____

i

RSS after further feature extraction

_____ . . 1 1 ( ,..., , ,..., ) i i ik i ik RSS rss rss Grss Grss (2) Where G is weighting factor, we can use it to control influence of interval length on the clustering result.

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If we cluster n fingerprints into c clusters using FCM, the clustering objective function is 2 1 1 ( , ) ( ) ( ) s. t. n c m m ij ij i j fc J U P d U M P ° ® ° ¯

¦¦

₍₃₎ Where Pij is the membership of the ith fingerprint to the jth cluster and generates membership matrix U=

[Pij]nhc.

. .

1 1

( ,..., , ,..., )

j j jk j jk

p p p p p is cluster center and generates center matrix P = (p1T,…, pjT)ˈ

where ję{1,2,…,c}˗m is smooth parameter. The similarity between the ith fingerprint and the jth cluster center is _____ 2 ( _ij) i _j A d RSS p (4) Where A is a positive definite matrix. And when it is a unit matrix, dij denotes Euclidean distance.

Our goal is to minimize the objective function (3). Because all parts of matrix U are independent, we

can get the min{Jm} as follows

2 1 1 2 1 1 min{ ( , )} min{ ( ) ( ) } = min{ ( ) ( ) } n c m m ij ij i j n c m ij ij i j J U P d d P P

¦¦

¦

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The solution of (5) is an optimization problem under equality constraint 1 1 c ij j P

¦

. We can construct a Lagrangian function as follows

2 1 1 ( ) ( ) ( 1) c c m ij ij ij j j L

_¦

P d O

_¦

P (6) The first-order necessary conditions of (6) is

1 2 1 ( ) ( ) 0 1 0 m ij ij ij c ij j L m d L P O P P O w °w ° ® w ° °w ¯

¦

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According to (7), we can get membership of _____

i

RSS to the jth cluster and cluster centers

1 2 1 1 1 _____ 1 1 ( ) ( ) ( ) c ij _m ij l il n n m m i j ij ij i i d d p RSS P P P _ª _º ° _« _» ° ¬ ¼ ® ° ª º ª º u ° « » « » ¬ ¼ ¬ ¼ ¯

¦

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Iteration stopping criterion is ||P(t)-P(t+1)|| < H or ||U(t)

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4. Results and Analysis

4.1 Clustering Results Analysis

In order to verify clustering validity of the method, we selected two groups of ZigBee beacons randomly and 80 fingerprints per group in the testbed shown in Fig. 1. Two groups are according to beacon group 1 (b1, b2 and b3) and beacon group 2 (b1, b2 and b4) respectively. On the conditions of G= 1, m = 1, c = 3 and A = E, FCM clustering results of two beacon groups’ fingerprints are shown in Fig. 3 and Fig. 5 respectively. We can see that every fingerprint is assigned to the cluster in which it has the biggest membership.

It is also concluded from the figures that all fingerprints are assigned to three clusters clearly and there are little overlaps between different clusters. Because the locations of beacons are distributed around the testbed, fingerprints in the same cluster can reflect the distance relationship between sampling locations on which they were sampled and locations of beacons. In Fig. 5, there are some obvious overlaps on the locations of 1, 2, 3, 18, 19 and 20. This is because that b4 has no line of sight with these locations and signal strength of b4 is lower comparatively. When Euclidean distance is adopted as clustering criterion, these fingerprints are assigned to cluster 3 instead of cluster 1 in which the signal strength of b4 is higher than it of cluster 3.

We also implemented c-means algorithm of fingerprints with the same parameters to compare the clustering results which are shown in Fig. 4 and Fig. 6. It is shown that in the same test conditions, fingerprints in the same cluster distributed confusedly in space. The reason is that c-means algorithm uses

average value of signal strength to calculate the similarity between the fingerprint and cluster center, which is susceptible to noisy data. At the same time, c-means clustering is a hard partition and divides

every fingerprint into a group absolutely. So, the fingerprints on the boundaries of different clusters have bad clustering results.

Figure 3. FCM clustering result of fingerprints of beacon group 1 Figure 4. c-means clustering result of fingerprints of beacon group

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Figure 5. FCM clustering result of fingerprints of beacon group 2 Figure 6. c-means clustering result of fingerprints of beacon group 2

4.2 Positioning Results Analysis

We used Bayesian inference [7] to estimate the locations of ZigBee mobile nodes based on FCM clustering results of fingerprints. Through the positioning result, we can verify the influence on precision and cost before could after FCM clustering. We selected 48 locations in the testbed randomly at which signal strength of beacon group 1 were sampled. We also implemented Bayesian inference (method 1), Bayesian inference based on c-means algorithm (method 2) and Bayesian inference based on interval-valued data FCM algorithm (method 3) to compare the positioning results. Fig. 7 shows the corresponding relationship between positioning errors and their probabilities. We can see that positioning precision of method 3 present in the paper is better than method 2. Method 3 deals with fingerprint as interval-valued data and describes the distribution and uncertainty of signal by interval midpoint and length. Not only similarities of fingerprints are taken into account, but also influence of disturbance in the environment. At the same time, locations at boundaries of different clusters have similar memberships generally. Fuzzy clustering adopted by method 3 can get memberships of fingerprints attached to different clusters, which can get higher probable location estimation.

Although positioning precision of method 3 is slightly worse than method 1’s, it is in favor of decreasing calculation cost and time after clustering. Fig. 8 shows time cost of single location in different clusters. The calculation time is tested on ZigBee module which CPU runs at 16MHz and single instruction cycle is 250ns. We can see that fingerprint grouped in cluster 3 consumed the least positioning time. Moreover, fingerprint un-clustered consumed the most. In the test, the positioning time consumption (3.65s) of 48 locations of method 1 is approximately 2.6 times it of method 3 (1.41s). But the precision improvement is inconspicuous. Mathematical expectation of positioning time of method 3 is

1 ( ) c i i i n E t t n u

¦

(9) Wherec is the number of clusters. ti is the positioning time per location in the ith cluster. ni is the number of

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Figure 7. Comparison of positioning errors and their probabilities between three methods

Figure 8. Comparison of positioning time consumption per location in different cluster

5. Conclusions

We used interval-valued data FCM algorithm to cluster fingerprint to decrease the positioning energy cost of ZigBee module. Practical clustering results prove that this method can lessen influence caused by interference. By comparison with c-means algorithm, clustering results of this method accord with

relationship between signal strength and propagation distance reflected by fingerprint much more. At last, we implemented Bayesian inference based on fingerprint clustering. Positioning results indicate that this method can decrease positioning calculation cost and improve positioning efficiency remarkably with the guarantee of positioning precision.

6. Acknowledgment

We thank for the support of a grant from NSF of China under grant number 50907014 and a grant from the NSF of Heilongjiang Province under grant number E200914.

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