This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the IEEE Globecom 2010 proceedings.
Optimal KNN Positioning Algorithm via Theoretical Accuracy Criterion in WLAN Indoor Environment Yubin Xu, Member IEEE, Mu Zhou, Weixiao Meng, Member IEEE, and Lin Ma Communication Research Center, Harbin Institute of Technology, 150001, China
[email protected],
[email protected],
[email protected],
[email protected] Abstract—This paper proposes the optimal K nearest neighbors (KNN) positioning algorithm via theoretical accuracy criterion (TAC) in wireless LAN (WLAN) indoor environment. As far as we know, although the KNN algorithm is widely utilized as one of the typical distance dependent positioning algorithms, the optimal selection of neighboring reference points (RPs) involved in KNN has not been significantly analyzed. Therefore, in order to fill this gap, the optimal KNN positioning algorithm based on the best TAC is introduced. And this algorithm is beneficial to construct the reliable WLAN indoor positioning system and provide the efficient location based services (LBSs). The relationship among theoretical expectation accuracy, unit interval of neighboring RPs and dimensions of target location region is also revealed. Furthermore, the feasibility and effectiveness of optimal KNN positioning algorithm are verified based on the experimental comparisons respectively in the regular office room, straight corridors, static positioning and dynamic tracking situations. Keywords-accuracy criterion; WLAN; positioning algorithm; radio fingerprint; expectation error
I.
INTRODUCTION
Along with the ubiquitous application requirements of the next generation wireless personal networks (WPN) and the increase interests of location based services (LBS), much attention has been paid for outdoor and indoor positioning systems in recent ten years [1]. Although Global Positioning System (GPS) and cellular location system (CLS) can guarantee high positioning accuracy in outdoor environment [2], [3], they are not beneficial to be utilized for indoor location applications because of serious signal attenuation and requirements of special infrastructure [4], [5]. Therefore, various WLAN indoor positioning systems have been presented not only because of its lower cost, but also by the reason of non-registered 2.4GHz ISM band and free wireless license for IEEE 802.11 b/g protocol. Microsoft Research’s RADAR system is the first sophisticated WLAN positioning system [6]. CMU–PM and CMU–TMI positioning systems based on the pattern matching method are developed by Carnegie Mellon University [7]. Massachusetts Institute of Technology’s cricket location system suggests a viable practical solution to the three goals of scalability, privacy, and tracking agility [8]. Artificial neural network (ANN) for positioning was discussed by [9]. Castro and Chiu’s Nibble is one of the original systems utilizing probabilities [10]. Youssef’s Horus system is the archetype of probabilistic
positioning systems by Bayes theorem [11]. Depended on the theory of hidden Markov model, RSS Markov Localiser (RML) was presented by RWTH Aachen University [12]. In general, fingerprint-based and model-based algorithms are the two typical types of WLAN indoor positioning algorithms [13]. The former algorithm outperforms the latter one in the aspect of location accuracy, environmental adaptation and system expandability. Furthermore, the fingerprint algorithm consists of the pattern matching algorithms, like ANN, support vector machine (SVM) and Kalman filter [14], and distance dependent algorithms, such as KNN et al. No matter for the pattern matching or distance dependent algorithms, there are two phases called off-line and on-line phases, respectively [15]. In the off-line phase, RPs are calibrated in the target location region and the radio signal strength (RSS) is also recorded at each RP as the fingerprint for the intelligent system training. Then, the Euclidean distance between new recorded RSS and pre-stored fingerprints is calculated in the on-line phase. Although the pattern matching algorithms hold the merits of nonlinear mapping, parallel distributed processing and adaptive self-learning abilities, location performance extremely depends on the characteristics of training samples, iterative learning algorithms and system generalization ability. Then, distance dependent algorithms are extensively utilized for the current indoor positioning systems [16]. However, to the best of our knowledge, the KNN’s optimal parameter has not been theoretically analyzed. In order to improve the algorithm adaptability and expansibility, TAC is presented to evaluate the accuracy performance of KNN algorithms with different selections of neighboring RPs and in separate environmental. This paper is outlined as follows: Section 2 gives an overview of the fundamental model of KNN positioning algorithm, related presumptions and parameters. In Section 3, TAC is presented respectively for KNN algorithms with different numbers of neighboring RPs. In order to compare the accuracy performance and positioning efficiency of the optimal KNN algorithm, Section 4 presents the experiments for static positioning and dynamic tracking situations respectively in regular office room and straight corridors. Our conclusions are summarized in Section 5.
This work is supported by National High-Tech Research & Development Program of China under Grant 2008AA12Z305
978-1-4244-5637-6/10/$26.00 ©2010 IEEE
II.
FUNDAMENTAL MODEL
This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the IEEE Globecom 2010 proceedings.
A. Mathematical Model of KNN Algorithm Basically, KNN algorithm shown in Eq.(1) is the fundamental model for any distance dependent positioning algorithm. And in this case, two parameters, the number of neighbors k ∈ N + and distance type q ∈ R + , should both be significantly considered. 1 ⎧ N AP q ⎞q ⎛ ⎪ρ = S new ,t − S pre,i ,t ⎟ , i = 1, " , N RP ⎪ i ⎜⎝ ∑ ⎠ t =1 ⎪ ⎪ S new = S new ,1 , " , Snew , NAP , Spre,i = S pre,i ,1 , " , Spre,i , NAP ⎪⎪ ⎨Γ D = { ρi , i = 1, " , N RP } ⎪ ⎪ Ψ k = R j = ( x j , y j ) : ρ j ∈ Φ k ( Γ D ) , j = 1, " , k ⎪ k ⎞ 1 k 1⎛ k ⎪ * * * C x y x y , , = = ( ) ⎜ ∑ j ∑ ∑ Rj j ⎟ = ⎪ k ⎝ j =1 j =1 ⎠ k j =1 ⎩⎪
(
)
(
{
Euclidean distance between A` and Oc .
D1
Rj
( j = 1,
" , N RP )
The j-th RP.
r dj
( j = 1,
" , N RP )
Unit interval between neighboring RPs. Euclidean distance between R j and Oc . d j = jr . The TP.
T dT
Actual Euclidean distance between T and Oc .
d T*
Estimated Euclidean distance between T and Oc .
δ ,ϕ
Uniform distribution in range of [ 0, r ] .
P0
)
Pj
(1)
}
where, S new and S pre,i denote the signal vectors at new recorded and i-th RP, respectively. N AP and N RP are the dimensions of
Transmitting power of APs.
( j = 1,
" , N RP )
PT
Received power at T .
fs
WLAN signal frequency. f s ≈ 2.4 GHz .
Prob ( x )
Probability of variable x .
Eδ ( f )
Expectation of function f with respect to δ .
Ed j ( f )
⎛ 1 O⎜ ⎜d ⎝ j
⎞ ⎟⎟ ⎠
Expectation of function f with respect to d j . t
consists of the front k elements ascending order.
{ρ , j
j = 1, " , k } in
+
III.
•
Attenuation characteristic can be approximated by signal propagation model in free space to avoid the influence of multi-path effect.
⎞ ⎟⎟ ⎠
TAC FOR KNN ALGORITHM
⎧ ⎪ PT = P0 − ⎡⎣32.45 + N lg ( dT − D1 ) + 20 lg ( f s ) ⎤⎦ ⎨ P = P0 − ⎡⎣32.45 + N lg ( d j − D1 ) + 20 lg ( f s ) ⎤⎦ ⎩⎪ j
Oc
Rj
A1
dj
dT
δ d j +1
r Ws = N RP r + ϕ
Figure 1. Mathematical model in the linear condition
Positions of RPs obey the uniform and central symmetrical distributions.
•
Compared with the dimensions of target location region, the unit interval between two neighboring RPs can be ignored.
•
•
Positions of test point (TP) satisfy the uniform and random distributions in the target location region.
Substitution of Eq.(2) into Eq.(3) leads to
Parameters
Description
Ws
Dimensions of the target region which limit the coordinate extents of APs, RPs and TP.
Oc
Origin of the coordinate system.
Ai ( i = 1, " , N AP )
The i-th AP.
(2)
R j +1
T
•
PARAMETERS FOR ACCURACY DEDUCTION PROCESS
.
Relationship among P0 , PT , Pj and Pj +1 can be described in the following by the presumption of free space condition.
Access points (APs) satisfy the independent and omnidirectional radiation properties with equal transmitting power.
TABLE I.
t −1
A. KNN Algorithm with k=1
B. Presumptions and Parameters In order to effectively simplify accuracy deduction process and extract the main factors which significantly influence the accuracy performance of KNN positioning algorithm, the following five presumptions should be satisfied. •
⎛ 1 Higher order terms of ⎜ ⎜d ⎝ j
( t ∈ N \ {1})
signal characteristics and number of RPs. C * and R j are the estimated position and j -th RP. Φ k ( Γ D ) is the set that
Received power at R j .
According to the Eqs.(1) and (2), there are two sub cases for this situation as listed below
d T* = R j with positioning error δ . Then, Pj − PT ≤ PT − Pj +1
D1 ≤ d j −
δ2 r − 2δ
,
0 ≤ δ ≤ d 2j + d j r − d j
(3)
(4)
Random variable δ depends on d j , so in the first step, calculate g (d j ) = Eδ ⎡⎣ f (δ , d j ) ⎤⎦ , and then, the confidence probability is obtained by calculating Ed j ⎡⎣ g ( d j ) ⎤⎦ .
978-1-4244-5637-6/10/$26.00 ©2010 IEEE
This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the IEEE Globecom 2010 proceedings.
between Pj and Pj + 2 should satisfy
⎛ ⎛ δ2 ⎞ δ2 ⎞ Eδ ⎜ d j − ⎟ = Eδ ( d j ) − Eδ ⎜ ⎟ r − 2δ ⎠ ⎝ ⎝ r − 2δ ⎠ r Δ r r2 = dj + + − ln 4 4 8Δ r − 2Δ
Pj − PT ≤ PT − Pj + 2
(5)
From Fig.1, one obtains D1 ≤ d j −
where, Δ = d 2j + d j r − d j . The corresponding confidence probability Prob1,δ ( ε ) for this case is presented by Eq.(6). ⎡1 ⎛ δ2 Prob1,δ ( ε ) = Ed j ⎢ Eδ ⎜ d j − r − 2δ ⎝ ⎣⎢ d j =
1 N RP
⎞⎤ ⎟⎥ ⎠ ⎦⎥
⎛ r r2 r ⎞ Δ + + − 1 ln ⎜ ∑ ⎜ 4d j 4d j 8Δd j r − 2Δ ⎟⎟ j =1 ⎝ ⎠ N RP
r − 4 N RP
N RP
ln d j
j =1
dj
∑
⎛ 1 + O⎜ ⎜d ⎝ j
⎞ ⎟⎟ ⎠
2
r r E1,δ ( ε ) = Ed j ⎡⎣ Eδ (δ ) ⎤⎦ = − 4 16 N RP
r ( ε ) = Ed 2,2, d +
⎛ 1 1 +O⎜ ∑ ⎜ j =1 d j ⎝ dj
⎞ ⎟⎟ ⎠
1 = N RP
2
Prob
(8)
E1, r −δ
Prob1, r −δ ( ε ) =
r 4 N RP
r − 8 N RP
N RP
ln d j
j =1
dj
∑
⎛ 1 1 + O⎜ ∑ ⎜d j =1 d j ⎝ j
r 2,2, d j + 2
⎞ ⎟⎟ ⎠
2
E
(9)
(ε ) = 1 +
⎛ 1 ⎛ r ⎞ NRP 1 ⎜⎜ 3 + 4 ln ⎟⎟ ∑ + O ⎜⎜ 2 ⎠ j =1 d j ⎝ ⎝ dj
N RP
ln d j
j =1
dj
∑
⎞ ⎟⎟ ⎠
2
(10)
(15)
2,2, d j +
(ε )
r 2
r ⎞ NRP 1 ⎛ ⎜ 3 + 2 ln ⎟ ∑ 2 ⎠ j =1 d j ⎝
N RP
ln d j
j =1
dj
∑
2,2, d j +
r 2
( ε ) = Ed
j
•
dT* =
2,2, d j +
r 2
⎛ 1 + O⎜ ⎜d ⎝ j
(ε )
⎞ ⎟⎟ ⎠
(16)
2
is given by
r ⎞ ⎤ ⎪⎫ ⎪⎧ ⎡ ⎛ ⎨ Eδ ⎢ ( d j + δ ) − ⎜ d j + ⎟ ⎥ ⎬ 2 ⎠ ⎦ ⎪⎭ ⎝ ⎪⎩ ⎣ ⎛ 1 ⎞ 1 + O⎜ ⎟ ∑ ⎜d ⎟ j =1 d j ⎝ j⎠ N RP
(17)
2
1 3r d j +1 + d j + 2 ) = d j + . Then, ( 2 2 Pj − PT > PT − Pj + 2
Based on the complementary property, E (11)
Prob
2,2, d j +
E
B. KNN Algorithm with k=2 dT* =
d 2j + 2d j r , Prob
r 4 N RP
r r2 ≈ − 4 4 N RP
E1 ( ε ) = Prob1,δ ( ε ) E1,δ ( ε ) + Prob1, r −δ ( ε ) E1, r −δ ( ε ) r r2 + 4 8 N RP
is
⎛ Θ r r2 r ⎞ ln + − ⎜⎜1 + ⎟ ∑ 4d j 2d j 2Θd j r − Θ ⎟⎠ j =1 ⎝
Furthermore, expectation error E
Finally, the expectation error for this case satisfies
≈
(ε )
r 2
N RP
r − 2 N RP
By complementary property, E1,r −δ ( ε ) and Prob1, r −δ ( ε ) for this case are respectively presented by Eq.(9) and (10).
•
j
2
2,2, d j +
(14)
becomes
N RP
N RP
(13)
⎧⎪ 1 ⎡ δ 2 ⎤ ⎫⎪ − E d ⎨ ⎥⎬ δ ⎢ j 2 ( r − δ ) ⎦⎥ ⎭⎪ ⎢⎣ ⎩⎪ d j
dT* = R j +1 with location error r − δ . Then,
3r r2 (ε ) = + 4 16 N RP
0 ≤ δ ≤ d 2j + 2d j r − d j
By the Taylor expansion of
And also, the expectation error for this case is
•
Prob
(7)
2
,
where, Θ = d 2j + 2d j r − d j . Probability Prob
j
⎛ r ⎞ N RP 1 ⎜⎜ 3 + 4ln ⎟∑ 2 ⎟⎠ j =1 d j ⎝
2(r − δ )
⎡ δ2 ⎤ r Θ r r2 Eδ ⎢ d j − ln ⎥ = dj + + − 2 ( r − δ ) ⎦⎥ 4 2 2Θ r − Θ ⎣⎢
(6)
be obtained by Eq.(7). r Prob1,δ ( ε ) = 1 + 8 N RP
δ2
Therefore,
d 2j + d j r , Prob1,δ ( ε ) can
Based on Taylor expansion of
(12)
1 ( d j + d j +1 ) = d j + 2r . Then, 2
3r 2
(ε )
2,2, d j +
(18) 2,2, d j +
3r 2
(ε )
and
are
3r 2
As a necessary and sufficient condition, the relationship
978-1-4244-5637-6/10/$26.00 ©2010 IEEE
5r r2 (ε ) = + 4 4 N RP
⎛ 1 ⎞ 1 + O⎜ ⎟ ∑ ⎜d ⎟ j =1 d j ⎝ j⎠ N RP
2
(19)
This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the IEEE Globecom 2010 proceedings.
Prob
2,2, d j +
r = 2 N RP
3r 2
(ε )
N RP
ln d j
j =1
dj
∑
⎛ 1 ⎞ r ⎛ r ⎞ NRP 1 − ⎜ 3 + 2 ln ⎟ ∑ + O ⎜⎜ ⎟⎟ 4 N RP ⎝ 2 ⎠ j =1 d j ⎝ dj ⎠
2
(20)
Finally, expectation error for this case E2,2 (ε ) satisfies r 2
+ Prob
( ε ) E2,2,d + r (ε ) j
j
r r2 ≈ + 4 2 N RP
2
3r ( ε ) E 3r ( ε ) 2,2, d + 2,2, d + 2
N RP
ln d j
j =1
dj
∑
j
•
2
B. Static Positioning Positioning accuracy respectively in regular office room and straight corridor environments is shown in Fig.3. 6
N1
neighboring RPs satisfying
d s < d j +1
( s = j − N1 + 1, j − N1 + 2, " , j ). •
Exist
N2
dt > d j +1
( t = j + 2, j + 3, " , j + N 2 + 1 ).
3 2
5 4.5 4 3.5
TP6 TP7 TP8 Mean
3 2.5 2 1.5
1
1 KNN(k=2) KNN(k=3) KNN(k=4) KNN algorithm with different neighboring RPs
0.5 KNN(k=5) KNN(k=1)
KNN(k=2) KNN(k=3) KNN(k=4) KNN algorithm with different neighboring RPs
KNN(k=5)
(a) TP1, 2, 3, 4 and 5 in straight corridors (b) TP6, 7 and 8 in office room Figure 3. Accuracy performance in office room and straight corridors
Then, dT* can be calculated by Eq.(22). N 2 − N1 ξ r = d j +1 + r , 2 2
ξ ∈N
•
KNN with k = 1 and 2 outperform the other KNN algorithms. In other words, accuracy performance can not be consequentially improved by the increase of k . This result is in accordance with previous discussion.
•
Mean positioning error in straight corridor can be approximately improved by 16.3% compared to the office room environment because of the better signal coverage performance and less interference by human body and infrastructures.
(22)
From Eq.(22), if ξ = −2 or 0 , positioning accuracy for this situation is equivalent to NN algorithm. If ξ = −1 or 1 , the accuracy performance equals KNN with k = 2 . And also, for the other ξ , positioning error will be significantly deteriorated because of the range of value dT ∈ ⎡⎣ d j , d j +1 ⎤⎦ . IV.
4
0 KNN(k=1)
neighboring RPs satisfying
dT* = d j +1 +
TP1 TP2 TP3 TP4 TP5 Mean
5
Number of neighboring RPs k = N1 + N 2 + 1 . Exist
(b) Straight corridors
Figure 2. Layout of target location regions
C. KNN Algorithm with k>2 In this situation, let •
(a) Office room
(21)
Positioning error (m)
2,2, d j +
Positioning error (m)
E2,2 ( ε ) = Prob
EXPERIMENTS AND COMPARISON
A. Layout of Experimental Environment The target location regions are shown in Fig.2. 9 Linksys WAP54G APi ( i = 1, " , 9 ) supporting 802.11 b/g protocols are fixed 2m height on the same floor. ASUS A8F laptop with Intel PRO/Wireless 3945ABG network connection wireless card is utilized as the MT. In the target region 1 ( Nr. 01 ), 12 RPs and 3 TPs are selected. And the intervals of neighboring RPs in X and Y directions are respectively 2m and 3m. In target region 2 ( Nc. 01, 02 & 03 ), 67 RPs and 5 TPs are also calibrated. And the interval of neighboring RPs is 1m. Origin of the coordinates is selected at RP21 (see Fig.2(b)). 180 RSS samples per each detectable AP at each RP are recorded to establish the radio map in the off-line phase. And the sampling rate is 2 samples per second.
C. Dynamic Tracking MT’s real motion trajectory is presented in Fig.4.
Figure 4. MT’s real motion trajectory for dynamic tracking situation
Positioning rate 1 k s means only one estimated position is calculated out in k seconds or by 2k RSS samples.
978-1-4244-5637-6/10/$26.00 ©2010 IEEE
This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the IEEE Globecom 2010 proceedings.
and inexpensive terminals. And the situations with serious multi-path interference will be analyzed in future work.
14
Coordinates in Y direction (m)
Coordinates in Y direction (m)
20
15
10
Estimated position with rate 1/1s (NN) Real trajectory of MT
5
0
12 10
Estimated position with rate 1/2s (NN) Real trajectory of MT
8 6 4
ACKNOWLEDGMENT
2 0 -2 -4
-5 -10
-5
0
5
10
Coordinates in X direction (m)
-6 -10
15
14
12
12
10
Estimated position with rate 1/5s (NN) Real trajectory of MT
8 6 4 2 0 -2
10
15
The authors would like to thank the reviewers for useful comments and corrections. This work was supported in part by the National High-Tech Research & Development Program of China under Grant 2008AA12Z305.
Estimated position with rate 1/10s (NN) Real trajectory of MT
8
REFERENCES
6 4 2
[1]
0 -2 -4
-6 -10
-5
0
5
10
Coordinates in X direction (m)
-6 -6
15
(c) KNN(k=1) with rates 1/5s
-4
-2
0
2
4
6
Coordinates in X direction (m)
8
10
12
14
[2]
(d) KNN(k=1) with rates 1/10s
20
20 Estimated position with rate 1/2s (KNN, k=2) Real trajectory of MT
Coordinates in Y direction (m)
Estimated position with rate 1/1s (KNN, k=2) Real trajectory of MT
Coordinates in Y direction (m)
5
10
-4
15
10
5
0
-5
15
[3]
10
5
[4]
0
-5
-10
-5
0
5
10
Coordinates in X direction (m)
15
-10
(e) KNN(k=2) with rates 1/1s 14
12
12
10 8
Estimated position with rate 1/5s (KNN, k=2) Real trajectory of MT
6
-5
0
5
10
Coordinates in X direction (m)
15
(f) KNN(k=2) with rates 1/2s
14
Coordinates in Y direction (m)
Coordinates in Y direction (m)
0
Coordinates in X direction (m)
(b) KNN(k=1) with rates 1/2s
14
Coordinates in Y direction (m)
Coordinates in Y direction (m)
(a) KNN(k=1) with rates 1/1s
-5
4 2 0 -2 -4
[5]
10 8
Estimated position with rate 1/10s (KNN, k=2) Real trajectory of MT
6
[6]
4 2 0 -2
[7]
-4
-6 -8
-6
-4
-2
0
2
4
Coordinates in X direction (m)
6
8
(g) KNN(k=2) with rates 1/5s
10
12
-6 -8
-6
-4
-2
0
2
4
Coordinates in X direction (m)
6
8
10
12
(h) KNN(k=2) with rates 1/10s
[8]
Figure 5. Relationship between real and estimated motion trajectories
•
With the increase of time cost or recorded samples, tracking performance can be significantly improved. In other words, there exists some tradeoff between realtime capacity and positioning accuracy.
•
Because of the better coverage condition, lower multipath interference and slighter shielding effect by human body, performance in corridor outperforms the office room environment. V.
[9]
[10] [11]
[12]
CONCLUSION
TAC significantly depends on the parameters r , N RP and d j . Then, in order to construct the efficient and reliable indoor KNN positioning system, the establishment of radio map and optimal selection of KNN parameters with minimal expectation error should both be seriously considered. Furthermore, KNN with k = 1 and 2 outperform the other KNN algorithms. Accuracy performance in straight corridor can be improved by 16.3% compared with the office room. Because of the tradeoff between accuracy and time cost for the dynamic tracking, the KNN(k=2) algorithm with rate 1/2s performs best. However, there is also a need to consider the computation complexity based on the requirements of portable
[13]
[14] [15] [16]
Y. Y. Gu, A. Lo, and I. Niemegeers, “A survey of indoor positioning systems for wireless personal networks,” IEEE Communications Surveys & Tutorials, vol. 11, no. 1, pp. 13–32, First Quarter. 2009. T. H. Chang, L. S. Wang, and F. R. Chang, “A Solution to the IllConditioned GPS Positioning Problem in an Urban Environment,” IEEE Trans. Intelligent Transportation Systems, vol. 10, no. 1, pp. 135–145, Mar. 2003. A. J. Weiss, “On the accuracy of a cellular location system based on RSS measurements,” IEEE Trans. Vehicular Technology, vol. 52, no. 6, pp. 1508–1518, Nov. 2003. M. Lashley, D. M. Bevly, and J. Y. Hung, “Performance analysis of vector tracking algorithms for weak GPS signals in high dynamics,” IEEE J. Selected Topics in Signal Processing, vol. 3, no. 4, pp. 661–673, Aug. 2009. L. M. B. Winternitz, W. A. Bamford, and G. W. Heckler, “A GPS receiver for high-altitude satellite navigation,” IEEE J. Selected Topics in Signal Processing, vol. 3, no. 4, pp. 541–556, Aug. 2009. P. Bahl and V. N. Padmanabhan, “RADAR: an in-building RF-based user location and tracking system,” in Proc. 19th IEEE Computer and Communications Societies Conf., vol. 2, pp. 775–784, Mar. 2000. A. Smailagic and D. Kogan, “Location sensing and privacy in a contextaware computing environment,” IEEE Wireless Communications, vol. 9, no. 5, pp. 10–17, Oct. 2002. A. Smith, H. Balakrishnan, M. Goraczko and N. Priyantha, “Tracking moving devices with the cricket location system,” in Proc. 2rd International Mobile Systems, Applications and Services Conf., pp. 190– 202, Jun. 2004. S. H. Fang and T. N. Lin, “Indoor location system based on discriminant-adaptive neural network in IEEE 802.11 environments,” IEEE Trans. Neural Networks, vol. 19, no. 11, pp. 1973–1978, Nov. 2008. P. Castro, P. Chiu, T. Kremenek, and R. Muntz, “A probabilistic room location service for wireless networked environments,” in Proc. Ubiquitous Computing Conf., pp. 18–34, Mar. 2003. M. A. Youssef, A. Agrawala, and A. U. Shankar, “WLAN location determination via clustering and probability distributions,” in Proc. 1st IEEE Pervasive Computing and Communications Conf., pp. 143–150, Mar. 2003. M. Wallbaum and T. Wasch, “Markov localization of wireless local area network clients,” Lecture Notes in Computer Science, vol. 2928, pp. 135–154, Feb. 2004. S. P. Kuo and Y. C. Tseng, “A scrambling method for fingerprint positioning based on temporal diversity and spatial dependency,” IEEE Trans. Knowledge and Data Engineering, vol. 20, no. 5, pp. 678–684, May. 2008. M. Brunato and R. Battiti, “Statistical learning theory for location fingerprinting in wireless LANs,” Computer Networks, vol. 47, no. 6, pp. 825–845, Apr. 2005. S. H. Fang, T. N. Lin, and K. C. Lee, “A novel algorithm for multipath fingerprinting in indoor WLAN environments,” IEEE Trans. Wireless Communications, vol. 7, no. 9, pp. 3579–3588, Sep. 2008. X. Y. Chai and Q. Yang, “Reducing the calibration effort for probabilistic indoor location estimation,” IEEE Trans. Mobile Computing, vol. 6, no. 6, pp. 649–662, Jun. 2007.
978-1-4244-5637-6/10/$26.00 ©2010 IEEE
