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K Nearest Neighbors Based on Lateration for WLAN Location Estimation Maryam Khordad, Mina Maleki Communications Technology Institute, Iran Telecommunication Research Center, Tehran, Iran
[email protected] ,
[email protected]
Abstract— Estimating the location of people in an indoor environment poses a fundamental challenge in ubiquitous computing. K Nearest Neighbor (KNN) is a deterministic algorithm that is widely used in positioning systems but its performance depends on determining the number of neighbors and can improve extensively by employing appropriate selection algorithm. This paper presents a novel KNN-based positioning algorithm called LKNN (Laterarion and KNN) that uses distance-based positioning techniques to select the best area and best number of nearest neighbors dynamically. The performance of the proposed algorithm is compared with KNN and a locating system based on Bayesian algorithm. The superior accuracy of our approach over a number of trials is demonstrated.
I. INTRODUCTION Knowledge of users’ positions is increasingly important in today’s society. The possibilities and opportunities for location-based services (LBS) have attracted a lot attention from companies and researchers [1]. Many systems over the years have tried to overcome the problem of determining and tracking the user’s position. Examples include GPS [2], wide-area cellularbased systems [3], infrared-based systems [4], ultrasonicbased systems [5], various computer vision systems [6], physical contact systems [7], and radio frequency (RF) based systems [8-14]. Outdoor positioning, using global positioning systems (GPS) or techniques that determine the user’s position in a cellular network, have been well explored and standardized. But GPS does not work indoors and may not give enough accuracy to move around in these environments. Of these, the class of RF-based systems that use an underlying wireless data network, such as 802.11, to estimate user location has gained attention recently, especially for indoor applications. RF positioning techniques which are based on Received Signal Strength Indication (RSSI) of Access Points (APs) can be classified by the measurement strategies they employ to determine mobile user location to Radio mapbased (fingerprinting) [8-12] and Distance-based (lateration) [13-14] techniques. Radio map-based positioning technique refers to a technique that is based on the measuring and recording of RSSI from APs to describe the characteristics of propagation inside an indoor environment. It usually works in two phases: offline training phase to create a radio map of Reference Points (RPs) and their measured RSSI and online positioning phase to calculate the mobile user’s location [13,16]. To determine user’s position in positioning phase, different algorithms such as
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distribution-based methods [9-10, 16-17] and deterministic methods [8, 11-12, 18-19] have been proposed. Distance-base positioning techniques use RSSI of APs to find the distance from each AP and detect mobile user’s location. But in environments with many obstructions, such as an indoor environment, measuring the distance is not accurate because of signal propagation issues such as reflection, refraction, and multipath [13, 15] and we have an approximate area instead of an exact point. The most popular RSSI-based location fingerprinting method for WLAN-based indoor environments is a deterministic method based on K Nearest Neighbor (KNN) [8, 11-12]. But the performance of this method depends on the number of selected neighbors (i.e. RPs). If we manage to find the best neighbors the performance of the algorithm will improve [11-12]. In this paper, we present a novel KNN-based positioning algorithm that selects the best area and best number of neighbors dynamically. It utilizes the distancebased positioning techniques to determine an approximate area around user. Next, the RPs existed in the determined area are chosen as the neighbors to be employed in KNN and all unnecessary neighbors out of this area are ignored. The rest of the paper is organized as follows. In Section II, we describe the RF positioning techniques. Section III states the proposed method called LKNN. In Section IV, we describe the evaluation of our technique in the real indoor space and the obtained results. Finally, Section V concludes the paper. II.
RF-BASED POSITIONING TECHNIQUES
Popularity and use of the Radio Frequency (RF) in different applications and predominantly in the area of identification and location aware systems is growing. Its versatile qualities, easy availability and simplicity of use have led a spate of development of different systems and technologies based on Radio Frequency Identification. In this section we are going to present 2 types of RF-based positioning techniques: Radio map-based and Distancebased positioning techniques. A. Radio map-based positioning techniques Radio map-based positioning technique or fingerprinting technique refers to a technique that is based on the measuring and recording of RSSI from APs to describe the characteristics of propagation inside an indoor environment. This technique usually works in two phases: offline training phase and online positioning phase.
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During the offline phase, the signal strength received from the APs at some predefined locations (reference points (RPs)) in the area of interest is tabulated, resulting in a so-called radio map or calibration database. During the online positioning phase, the signal strength samples received from the APs are used to “search” the radio map to estimate the user location. There are different approaches for online phase. Deterministic approach is one of the most commonly used ones. Deterministic algorithms attempt to find minimum statistical signal distance between a detected RSSI location vector and the location vectors of the various calibration sample points. This may or may not be equal to the minimum physical distance between the actual device physical location and the recorded location of the calibration sample. The sample point with the minimum statistical signal distance between itself and the detected location vector is generally regarded as the best raw location estimate contained in the calibration database [13]. Deterministic approach usually uses K Nearest Neighbors (KNN) algorithm. KNN is one of the basic fingerprint based algorithms and generally used for WLAN-based indoor positioning. In this method the distance between mobile user and each RPs (neighbors), using the distance between their RSSI vectors, is calculated. K (K2) nearest neighbors (those with the shortest distance) are taken into account, the average of the coordinates of these K points can be used as the estimate of the mobile user location. Assuming there are l location fingerprints in a given area that make a reference carpet. Then, the location fingerprints, are represented by {F1 , F2 ,..., Fl } , and each have a mapping to a set of locations {L1 , L2 ,..., L1} . In the online phase, a sample RSS value S is measured from N access points, which could be averaged over a time window. The sample measurement vector is S = ( S1 , S 2 ,..., S N ) , where each element corresponds to the RSS value from a particular access point. Each location fingerprint, i on the reference carpet, can be represented by the vector Fi = ( ρ1i , ρ 2i ,..., ρ Ni ) , composed of the mean signal strength values from each access point. The nearest neighbor method then simply selects the fingerprint that is “closest” to the RSS value of the current measurement. This method simply chooses the fingerprint that has the minimum distance to the current measurement in signal space. A generalized distance function can be used to pick the fingerprint j, that minimizes the distance in signal space by (1):
Dist ( S , F j ) ≤ Dist ( S , Fk ), ∀k ≠ j
(1)
A generalized weighted distance Dp, given by (2) can be used to calculate distances in signal space. 1
p 1 N 1 DP = ( ¦ Si − ρ ij ) p N i =1 wi
(2)
where P is the norm parameter, wi is the weighting factor, (wi ≤ 1) and N is the number of access points. The weighting of RSS components can be varied by adjusting
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the bias, wi [19]. The most common metric used is the Euclidean distance [8, 15, 19]. In the Euclidean distance, p=2, and wi = 1 . There are various other distance metrics (one such being the Manhattan Distance), where p ≠ 2 [19]. In practice, determining the closest location fingerprint is not always practical, since if there are errors in the location, one would not have any idea of the possible alternatives. An improvement is to use the k nearest neighbor search, instead of the closest one [8, 19]. The final position estimate is the average of the positions returned by the k nearest neighbors. This results in a closer estimate of the current location. The location accuracy improves as the size of k grows [8]. So, location of mobile user in KNN is calculated using (3) and (4). k
x=
¦w x
i i
(3)
¦w y
(4)
i =1 k
y=
i i
i =1
( xi , yi ) is position of neighbor i. If wi shows the weight of the ith selected RP then wi can be equal to (1/k) or can be inversely proportional to the Euclidean distance according to (5). This type of KNN is called WKNN:
wi =
1 Di
(5)
k
¦
Di
i =1
Di is the Euclidean distance between input vector and neighbor i and is calculated using (6). N
Di = (
¦
2
1
S t − ρ ti ) 2
(6)
t =1
where S t is the signal strength from APt in input vector i and ρt is the signal strength from APt in neighbor i.
B. Distance-based positioning techniques This class of positioning techniques is usually called lateration. Lateration computes the position of an object by measuring its distance from multiple reference positions. Two approaches for measuring the distances required by lateration are time of flight and attenuation [1]. Time of flight refers to measuring the time difference between transmission and arrival time of an emitted signal (with a known velocity). Attenuation is based on the fact that the intensity of an emitted signal decreases as the distance from the emission source increases. The decrease relative to the original intensity is the attenuation. Given a function correlating
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attenuation and distance for a type of emission and the original strength of the emission, it is possible to estimate the distance D from an object to some point P by measuring the strength of the emission when it reaches P. In two dimensions, such calculation tells us that the object is located anywhere on a circle with a radius D (distance), centered at the transmitter. Distance can be calculated with reference to more receivers, which results in additional circles on which the object is located. The only way that the object can be located somewhere on two or more circles is if the circles intersect. The point of intersection of the circles is where the object is actually located. Because circles can intersect at more than one point, three distance measurements are needed, and similarly four different measurements are needed for a three-dimensional system. In environments with many obstructions, such as an indoor office space, measuring distance using attenuation is not accurate. Signal propagation issues such as reflection, refraction, and multipath cause the attenuation to correlate poorly with distance, resulting in inaccurate and imprecise distance estimates. On the other hand in indoor environments the intersection of three circles is not only a point and it is an area, so it is not possible to find exact location (Fig. 1). III. PROPOSED METHOD KNN takes all the k nearest neighbors into account while calculating the estimated result, therefore this algorithm depends on k and calculation of k is very important in this algorithm. On the other hand sometimes k nearest neighbors are not close to each other and they spread in the area so their average position is not helpful really. Thus finding the best number for k and the best area for neighbors is very important in KNN results. Usually when the best value of k in a domain is known, it is used for solving different problems in that domain. However, sometimes it is better to change k according to a new problem. Our method uses KNN algorithm for online indoor positioning and adjusts the value of k to handle different situations. In other word, number of neighbors (k) changes dynamically. We call our method LKNN which means our method is based on KNN and lateration. During the online phase of radio map-based positioning, we use both lateration and KNN to improve our accuracy. As said before, lateration is not an accurate solution for indoor environments. We use lateration to determine an approximate area that our solution is located in. In our algorithm we use IEEE 802.11 channel model for indoor propagation in which the received power is represented by (7). RSS i = pt − 10n log10
Di +S D0
(7)
where RSSi is the received signal strength of ith AP, Di is the distance from ith AP in meters, pt is transmitter power, n represents the path loss exponent for the environment, D0 is the reference path loss in dB for the desired frequency when the receiver-to-transmitter distance is 1 meter and S specifies the standard deviation associated
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Figure 1.
Lateration and distance estimation [14]
with the degree of shadow fading present in the environment, in dB. These parameters depend on the environment and are calculated in each environment using interpolation technique on the calibration data stored in radio map. Using this equation we estimate the distance from each of APs covered in input vector and then draw a circle around each AP with the center of (APx, APy) and radius of D. We assume that the solution is in the intersection of these circles. So we find RPs located in this intersection. However, we do not use intersection exactly. All APs are sorted according to their strength in input vector. The RPs in the first circle (the circle around strongest AP) are selected as an initial set of nearest neighbors. For each RP in the first circle, number of circles that this RP is located in is calculated. If there are z APs in input vector, RPs with less than z circles around them are deleted from initial set. If number of RPs in the initial set of nearest neighbors is less than two, the radiuses of all circles are increased by 0.2 of their length (8). This step is repeated until the number of RPs in the set of nearest neighbors get equal to or more than two. Radiusi = Radiusi + Radiusi ∗ 0.2
(8)
where Radius i is the radius of ith AP. In next step we set the value of k equal to the number of RPs selected in the previous step then using these points and KNN algorithm, the output location is found. Fig. 2 shows the pseudo code of our algorithm. 1) For i=1 to Number of APs • Get related RSSI of each AP • Find distance (Di) from each AP using Eq. (6) 2) Define circle around each AP with the center of (APxi, APyi) and the radius Di. 3) Select RPs in the smallest circle (around the strongest AP) as the Nearest_Neighbors set. 4) Filter the Nearest_Neighbors set to find the neighbors in the intersection area of all APs. 5) If the number of found neighbors in the Nearest_Neighbors set is less than 2 • Increase the radius of all APs by Eq. (8) • Go to step 3. 6) Calculate the location using existed neighbors in Nearest_Neighbors set by Eq. (3) and (4). Figure 2. Pseudo code of LKNN algorithm.
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To test the performance of the system, we used an independent test set that includes about 150 locations. To present the accuracy of different configurations of the RSSI-based fingerprinting approach, the error distance is calculated. Mean Estimation Error (MEE) is a linear distance defined by (9).
MEE =
Figure 3.
An example solved with LKNN
Fig. 3 illustrates a comparison between KNN and LKNN in selecting the neighbors. D1 and D2 are the calculated distances from AP1 and AP2, respectively. As shown in this figure, the selected neighbors by LKNN are different in numbers and places with KNN. Neighbors found by LKNN are more centralized than KNN ones. Also the number of neighbors in LKNN can change dynamically. IV. EXPERIMENTAL EVALUATION We have evaluated the performance of our method comparing it to KNN and Ekahau [21] method that is based on Bayesian algorithm. We performed our experiment in the first floor of Communication Technology (CT) building in Iran Telecommunication Research Center (ITRC). This floor has a dimension of 50 meters by 32 meters and we have 4 APs in this floor. The layout of the floor and the locations of APs are shown in fig. 4. To create a radio map in the training phase, we specify some reference points place 1.5 meters apart. Then by using the Ekahau Site Survey (ESS) software [21], we collect RSS values receive in each RP. After that, we summarize multiple signal strength samples from each AP using the sample mean. Finally, we saved these values and the real locations in our radio map database.
Figure 4. Plan of the first floor of Communication Technology Institute in ITRC and locations of APs
1 P
P
¦(x − x ) 0
2
+ ( y − y0 ) 2
(9)
where P is the numbers of test points and (x0, y0) and (x, y) are the real and estimated coordinates, respectively. Fig. 5 illustrates the mean error of KNN algorithm using different number of neighbors (k). The value of k affects the accuracy of KNN method. We also compared the result of LKNN, KNN and Ekahau algorithms and results are illustrated in Table I. In this comparison k is equal to 24. According to our experiments KNN has the most performance using this k. Table I includes the mean error by (9), accuracy (error range) and 50th, 70th, and 90th percentiles error in meters. Xth percentile error means that error of X% of the test cases were less than X. As shown, our LKNN method performs better than KNN and even Ekahau. In addition, this method does not depend on a specific k and it does not need earlier experiments to find the best k in each environment. As another experiment, we create a new radio map in which the place of reference points are about 3 meters apart. The effect of using different numbers of RPs in LKNN and KNN is depicted in Table II. It is observable from this table that the performance of KNN algorithm is degraded by decreasing the number of RPs because of more distance between nearest neighbors from each other. Also, the best numbers of k in this algorithm are about 25 and 10 for RPs with 1.5 and 3 meters apart, respectively. So, it is obvious that the performance of KNN algorithm depends on the number of RPs, too. But our LKNN algorithm has the same performance in both cases and even it performs a little better with less RPs. It shows that LKNN algorithm is independent from the number of RPs.
Figure 5.
MEE of KNN using different number of neighbors.
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[5]
Method
Mean Error
Accuracy
50%
70%
90%
LKNN
2.8832
0.3683-7.7547
2.78
3.5
4.7
KNN ( k=24)
3.113
0.2851-10.1097
2.85
3.8
5.25
Ekahau
3.06
0.198-9.425
2.73
4.225 5.155
TABLE II. MEE USING KNN AND LKNN METHODS FOR DIFFERENT NUMBERS OF RPS KNN
3.51 3.78
3.35 3.32
3.18 3.33
3.14 3.44
3.13 3.6
3.16 3.72
2.88 2.83
V. CONCLUSION We considered the indoor location determination problem using WLAN infrastructure and received signal strength of access points. KNN is a deterministic approach that is widely used in indoor positioning systems and lateration is a well performed algorithm in outdoor positioning. However both of these algorithms have some shortcomings. One of the main challenges of using KNN algorithm for positioning is determining the best number of neighbors because it depends on the environment conditions such as the number of RPs, location and number of APs and etc. We tried to solve this challenge and improve the performance of KNN algorithm integrating it with lateration method and finding the number of nearest neighbors (k), dynamically. Our experimental results show that our proposed method outperforms traditional KNN algorithm and even Ekahau that is a commercial locating system based on Bayesian algorithm. REFERENCES [1] [2]
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