Radio Map Fusion for Indoor Positioning in Wireless Local Area Networks

Transcription

1 2005 7th International Conference on Information Fusion (FUSION) Radio Map Fusion for Indoor Positioning in Wireless Local Area Networks A. Kushki, K.N. Plataniotis, A.N. Venetsanopoulol Multimedia Laboratory University of Toronto 10 King's College Road, Toronto, Canada {azadeh, C. S. Regazzoni Biophysical & Electrical Engineering University of Genova Via dell Opera Pia 11, 16100, Genova, Italy Abstract- This paper addresses the problem of indoor location estimation (LE) in a Wireless Local Area Network (VLAN) using received signal strength (RSS). The difficultly of the problem lies in the complexity of the indoor propagation channel at operating WLAN frequency of 2.4GHz, resulting in nonlinear and non-gaussian spatio-temporal RSS properties. The first contribution of this paper is the introduction of a nonparametric Nadaraya-Watson estimator for LE using location fingerprints to capture the spatial distribution of RSS. Secondly, a novel method is proposed based on fusion of multiple location fingerprints at each survey location to cope with multimodal temporal probability distributions of RSS. Experimental results using real data collected in an office environment indicate that the proposed multiple-map method outperforms the KNN-based LE methods in terms of root mean square error. I. INTRODUCTION The recent shift from a computer-centric design paradigm to a user-centric philosophy has led to the advent of a plethora of context-aware applications. Context-awareness refers to utilization of information about a user's environment and actions to custom-tailor the system response to the situation at hand. Context-aware applications include emergency services (e.g. E-911 in cellular systems), health-care and surveillance, and commercial personalized services. An indispensable piece of knowledge in context-aware applications is the location of users of the system. Location estimation (LE) in outdoor environments has been studied widely using various technologies such as the Global Positioning System (GPS) [1], and cellular network-based techniques [2]. Indoor location systems have also been proposed based on various technologies such as proximity sensors, radio frequency (RF) badges, and Wireless Local Area Network (WLAN) radio signals. The latter offers two main advantages over other location estimation methods. First, WLANs are widely deployed in office and home environments and provide ubiquitous coverage in a large area. Second, Network Interface Cards used on receivers provide Received Signal Strength (RSS) measurements without the need for any additional hardware, hence reducing installation and equipment costs and labor. Location estimation using RSS in indoor environments is particularly challenging due to the complexity of indoor radio channel. This stems from severe multipath and shadowing conditions as well as non-line-of-sight propagation due to presence of walls, humans, and other rigid objects. Moreover, the IEEE WLAN operates on a frequency of 2.4GHz which is the same as cordless phones, microwaves and the resonance frequency of water. This leads to interference from such devices and signal absorption by the human body. This complex environment gives rise to non-gaussian and timevarying RSS densities at fixed locations in space, making the estimation problem particularly challenging. Many location estimation systems collect representative (fingerprint) RSS values for a set of known locations during a training phase to build a radio map of the environment. Online RSS measurements are then compared against the fingerprints to compute location estimates. The map consist of single, deterministic location fingerprints or RSS probability distributions at fixed locations. Because of the time-varying nature of indoor propagation, a single RSS fingerprint generally does not provide a sufficient representation of the data. The alternative probabilistic methods store RSS histograms for each location and thus incur high computation and storage costs. Furthermore, long term data collection is needed to produce close approximations. The first contribution of this paper is the use of a nonparametric Nadaraya-Watson estimator to capture spatial distributions of RSS with any prior assumptions. Secondly, a novel method for building a small set of radio maps from the training data to capture the temporal variation of RSS at fixed locations. Lastly, a novel distance fusion technique is introduced for comparing online measurements against the set of maps. Outline of the proposed system is shown in Fig. 1. The rest of this paper is organized as follows: Section II provides an overview of existing literature. The proposed method is presented in Section III. Section IV reports on experimental results and Section V concludes the paper and provides directions for future work. II. PREVIOUS WORK The two stages in map-based radio location techniques are offline training and online estimation. During these stages some feature of the radio signal is collected, stored, and compared to incoming measurements from the mobile. An overview of the existing works on each component follows /05/$ IEEE 1311

2 Fig. 1. Overview of proposed method. A. Radio Signal Features Four features of radio signals can be used in location estimation in wireless networks [2]: Angle of Arrival (AoA), Time of Arrival (ToA), Tine Difference of Arrival (TDoA), and Received Signal Strength (RSS). Although there have been a few works exploring the use of ToA [3] and AoA [4], most LE systems rely on RSS as the main feature. This is because RSS measurements can be obtained relatively effortlessly and inexpensively without the need for additional hardware. Spatio-temporal properties of RSS have been studied in several works. Approaches such as [5] and RADAR [6] assume a prior model for the characteristics of indoor radio propagation as a function of distance from the access point. This model is generally stated as a path loss model relating the loss in transmitted signal as a function of distance. One problem with this approach is that constant signal strength contours are generally anisotropic [7], [8]. That is, increasing distance from an access point results in RSS attenuation at different rates in different directions. This phenomenon can be attributed to the asymmetry of the propagation environment (walls, furniture, doors, etc.). Furthermore, orientation of the mobile station with respect to the access point severely affects the RSS. For example, at a fixed location, a difference of nearly 9dBm in RSS is reported for various orientations in [9]. This is due to the fact that the signal absorbtion by the human body introduces additional signal loss if the user's body is positioned between receiver and transmitter. Lastly, it is important to note that the dependency between RSS measurements and distance is not a deterministic one [101. The time-varying nature of the environment leads to time-varying interference, shadowing, NLOS propagation and multipath effects. This dynamic nature of the indoor environment leads to temporal variations in the received signal. Several works have aimed to characterize these variation by studying the probabilistic RSS distributions at fixed spatial locations. Traditionally, RSS is assumed to be log-normally distributed. However, results of measurements over various time periods presented in [8], [9] show that this assumption is not always true. In fact, distributions are reported to be left-skewed (as a results of range limitations), and possibly multimodal in presence of users. In [9] it is concluded that the RSS can be assumed to be stationary over small time scales. B. Offline Training Generally, LE approaches that employ RSS can be divided into two categories: model-based and radio-map (location fingerprinting). In model based approaches, training RSS measurements are used to determine parameters of a propagation model. These methods, however, suffer from the shortcoming discussed previously. In contrast to model-based techniques, map-based methods collect RSS fingerprints at known locations during the training. These RSS-location pairs constitute what is known as a radio map. In the online stage, live measurements are compared to the radio map and a location estimate is returned. Existing map-based methods vary in the way they construct the radio map (i.e. their definition of location fingerprints) as well as the methods used to perform the online comparisons. We discuss representative techniques for each case in the rest of this section. During the offline phase, the RSS values are measured at a fixed locations for a certain period of time (ranging from several minutes to hours in different works). This set of time measurements is collected and processed to extract various information on the density of RSS. Techniques such as RADAR [6] and [11] extract a single RSS fingerprint from the available RSS samples over time (at a fixed location). This value is generally the time average (mean) of RSS measurements for a given location. The time average, however, only provides a complete representation of RSS variations in the case of zero variance in the data. In LEASE [7] signals from stationary emitters with known positions are used are to capture time variations in RSS at during online operation. An alternative approach is to model RSS as a random variable that is statistically dependent on the location. This corresponds to approximating the conditional probability density f(rjp) or the likelihood. Here, r = [RSSaP,..., RSSP'k] contains the RSS measurements from each of the k access points and p = (x, y) denotes the 2-dimensional position in Cartesian coordinates. Various suboptimal solutions to the problem of likelihood density estimation have been used in the literature. Parametric methods operate on the assumption that a known class of densities (e.g. Gaussian) can be used to approximate temporal RSS characteristics. The estimation procedure is reduced to detenmine parameters of this density family (e.g. required moments). Unfortunately, normal assumption for RSS distribu- 1312

3 tions has been contradicted in several cases [8], [12]. Another common approach is to build a histogram of RSS values for known locations and obtain a discrete version of densities [12]-[15]. Lastly, a non-parametric shaping filter is used in [8] to generate the likelihood. Once the likelihood density f(rlp) is obtained, the posterior density f(plr) is obtained through Bayes theorem and knowledge of the prior density f(p). Specifically, fp f (rlp)f(p)dp( The posterior density, represented as a discrete histogram, is then stored in the radio map for each survey location. We denote the radio map mathematically as follows: MA4 = {Pi, (R1, a,)},..., {PN, (RN, an)}i (2) 1 1~~~~~~~~0 - survey point 1 survey point N In Equation (2), N is the number of survey points and the M x k matrix Ri = [r1,..., rm] contains the set of M RSS vectors needed to produce a fingerprint at the ith survey point. Finally, aor contains any other parameters needed in the representation. For example, in systems using deterministic sample mean, M - 1, ri is the mean RSS value from the access points and ao is null. Similarly, for systems with the log-normal distribution assumption, M = 1, ri is the RSS mean whereas ao contains the covariance of the distribution. Lastly, in histogram-based methods, M > 1, ri corresponds to the histogram bins and ai contain their relative frequencies. C. Online Location Estimation After building the radio map defined in Equation (2), the online measurement from mobile stations are compared to the map and a location estimate is obtained. For the case of deterministic radio maps, the incoming RSS measurement is compared against the deterministic stored value (e.g. mean) using the Euclidean distance or its variations [6], [l1]. Either the survey point with smallest distance is returned as the user location, or the k top matches are average to obtain the estimate. The stochastic-based systems exploit the stored posterior together with an optimality criterion estimate the location of the mobile user. For example, the well known Minimum Mean Square Error (MMSE) [15] and Maximum a Posteriori (MAP) [14] estimates are obtained as follows: PMMSE = E{plr} = J f(plr)dp (3) PMAP =argmaxf(pjr) argmaxf(pijr) (4) p Pi III. PROPOSED NON-PARAMETRIC ESTIMATION METHOD The first contribution of this paper is the proposal of the Nadaraya-Watson estimator for indoor location estimation. This method uses the set of location fingerprints to approximate the joint density f(p, r) and ultimately provide the MMSE estimate of the location as a weighted average of the survey points. The second contribution is the use of a multi-valued radio map and a novel fusion technique for representation of multimodal distributions. The rest of this section describes the details of the proposed methods. A. Offline Map Construction As depicted in Figure 1, the offline stage of the proposed method corresponds to the construction of the radio map. The purpose of radio map building is to detennine the pairs {pi,(ri,ai)} for i = 1,...,N as in Equation (2). In doing this, several issues are considered and discussed below. 1) Survey points: A set of survey points {pi} with known locations are needed where RSS fingerprints will be produced. The spatial distribution of these points and their number N affect the performance of a radio-map based techniques. Since no prior information is available on the location of the mobile user, a uniform grid is assumed for the survey points. The number of survey points N is also an important parameter. If this number is too large, fingerprint locations may report redundant information whereas a small number may result in insufficient resolution. The work of [2] provides a theoretical upper-bound on the number of needed survey points. Furthermore, experiments with varying number of points are reported in Section IV. 2) Extraction of location fingerprints: Given the survey locations {pi}' 1, we proceed to determine the fingerprints (ri, ai) at each location. In order to capture some of the time-varying properties of RSS, a set of RSS measurements are collected over a short duration (around 5 minutes) at each survey location. From these measurements, a histogram approximation is built to the density of RSS at each pi. Note that this results in a suboptimal approximation for several reasons. First, RSS measurements over sampling periods in order of seconds are correlated [16]. Second, RSS is not stationary over long time intervals [9]. Clearly, the fingerprint at each location depends on properties of RSS distributions such as those discussed in Section II. Since RSS is nonstationary, the fingerprint derived from a short-time window may not be suitable for use at a later time. To this end, it is encouraging to note that the results of [8] suggest that the long term (several hours) time average is similar to the short term (ten minutes) sample mean for the distributions. Unfortunately, however, the distributions are generally reported to be non-gaussian. More specifically, they are mainly asymmetric (mostly left-skewed) and possibly multimodal [8], [9], [12], [13]. This means that the sample mean may not provide the best possible representation. Section IV reports on various fingerprints derived from the series. Namely, we consider the sample mean, median, and various trimmed means. The possible multimodality of the distributions leads consideration of multiple fingerprints at a given location. We propose achieve this multi-valued representation by extracting a set of dominant values from the RSS distribution at a fixed location. To this end, the kmeans algorithm [17] is used to produce C clusters from the time measurements at each location. In this 1313

4 case, R C and ris correspond to the cluster means in the radio map of Equation (2). Note that this clustering technique ignores the time correlation of the RSS measurements and is thus suboptimal. At this stage, it is not clear what the optimum value of C should be. Since multimodal distributions arise in the presence of users and severe noise conditions, we may conclude that this value is dependent on the environmental conditions. Experiments for determining the best value of C are reported in Section IV. Based on our experimental data this value is generally small (C < 5). B. Online Non-parametric Estimation During the online phase, a vector of RSS measurements is received from the mobile client, compared to the radio map, and a location estimate is returned. As shown in Equations (3) and (4), both MMSE and MAP estimates of the location require knowledge of the posterior pdf f(plr). Since the shape of this density is unknown in many cases, our approach strays away from parametric techniques. Instead, a non-parametric kernel estimator is used to estimate the density from the fingerprints at survey points. This technique does not require any assumptions on the functional form of the density function. 1) Kernel Estimator: Given the RSS fingerprints derived in the previous section and the assumption of their independence, the joint density of location and RSS measurements is estimated as follows [18]: fpr) in r h h E (hp)2(h,)k ( jp K (' 'r), (5) where k is the dimension of rcorresponding to the number of access points. K(-) is a zero mean kemel function with unit area, and hp and hr are smoothing parameters [18]. Two well known exammples of kernel functions include the Gaussian (K(x) = (27r)-2TJCJ-2 exp (_-1xTC-1x)) and Exponential (K(x) = 2 exp (-l IxI j)) functions. The smoothing parameters are used to control the width of the kernels, or the region of influence of each survey value. As it is evident from the form of the kernel functions under consideration, the smoothing parameter hr has a direct relationship to the variance of the measurements [2]. The choice of these parameters is not trivial and is done manually using the training data for the proposed system. Theoretical methods for choosing the smoothing parameters can be found in [18]. Using (5) and a non-parametric estimate of f(r), the MMSE estimate of location becomes: N p = E wipi7 i--= K ( r Zzi1K (hr) The estimator of Equation (6) is known as the Nadaraya- Watson estimator. The location estimate is a weighted average of the survey points with weights determined by the kernel function and the smoothing parameter, hr. Note that the non-parametric version of the MAP estimator corresponds to the nearest neighbour matching method used in the literature. In that case, p = pj, where j -arg min Ir - ril2 (7) Properties of the Nadaraya estimator in terms of bias and variance have been well studied and a detailed account can be found in [19]. Furthermore, theoretical performance of the estimator in the context of location estimation in cellular networks has been investigated in [2], [20]. In the interest of space, we refrain from repeating these results. 2) Estimation with a Multi-valued Map: The kernel estimator of (6) uses one RSS fingerprint per survey location to produce the appropriate weight for that location. We propose to determine the weight for each survey point in the average of Equation (6) by fusion of multiple fingerprints. Specifically, the ith survey point pi, the weight is obtained by fusing a set of weights {w(c)cl1 based on each of the C fingerprints. That is, K (r-r(c) (c) _h Wi E (r- ) D c? =?.... C. (8) The fusion of weights for each pi must be performed in a flexible manner to take into account varying degrees of noise present at different survey locations. To this end, we use a compensatory operator to perform this aggregation [21]. That is, Wi = -yi min(w$ ) + (1 - -Yi) max(wjc)). (9) In this operator, -Yi is a parameter that can adjust the logical behaviour of this operator. The extreme case of ty = 0 leads to a logical OR operator. In this case, a given survey point receives a high weight if the measurement matches any of the clusters for the location. A pure disjunctive aggregation, however, may be too optimistic in the sense that the measurement may be deemed "close" to many survey points. At the other extreme, -y = 1 corresponds to a logical AND operator. For all other values of -y the result is a compromise between the two extremes. The next section experiments with various values of -y and the effect on accuracy of location estimation. Using the aggregation operator in (9), it is also possible to assign unequal importance to each cluster. For example, clusters that contain majority of the data points can receive a higher weight. This would mean that an observation that matches a cluster with the majority of data points at a given location receives a higher score than an observation matching a cluster with very few elements at that location. We have adopted an exponential weighing scheme [22] such that w(c)= (w(c))w- where wc oc Nc. Here, N, is the number of measurements in cluster c and Nt is the total number of time measurements. The weights obtained,from Equation (9) for each survey point pi are then used in the weighted averages of Equation (6) to yield the final estimate. 1314

5 IV. EXPERIMENTAL RESULTS Evaluation of WLAN based positioning systems is not trivial due to the lack of standardized test environments and performance measures. In this section, we report on the accuracy of the proposed methods for 2-dimensional absolute (as opposed to symbolic) location estimation in an indoor office environment. Details of our experimental setup as well as the adopted figure of merit are presented in sections that follow. A. Setup The experiments were carried out on the third floor of a five story office building at the University of Genova with approximate dimensions of 25mx 14m. The map of this floor is shown in Fig.2. On the map, the location of the three access points are indicated by diamonds whereas survey and test points are depicted as black circles and 'x' marks, respectively. The tests were carried out using three access points; two Cisco Aironet 1100 Series1 with Integrated 2.2 dbi diversity dipole antennae, and one Lucent ORiNOCO AP with an omni-directional antenna of 2-3dBi gain. The WLAN was operating at 2.4GHz at a data rate of 11 Mbps. The measurements were made on an IBM ThinkPad T42 equipped with an Intel Centrino processor, an integrated Intel PRO/Wireless 2200BG wireless card, and Windows XP operating system. The RSS measurements were obtained by a publicly available network sniffer software, NetStumbler3. The RSS values reported by this software are in units of dbm and quantized to integer values with unit spacing. A typical range of RSS measurements is [-80,-10] dbm. The sampling rate was 2 samples per second and RSS values were recorded for 5 minutes, resulting in 600 samples per survey point. Measurements were collected for a total of 33 survey points, covering a laboratory and a hallway as shown in Fig.2. As explained later, only 19 of the survey points are used during the operation of the system. The points were separated by 1 meter on a uniform grid where not restricted by physical constraints such as steps and walls as shown in Fig. 2. The access points were positioned at heights of 160cm, 125cm, and 105cm respectively. The height of the laptop was 120cm placed on carton boxes. Moreover, the orientation of the laptop kept towards the west for training and test measurements. This was done to eliminate effects of user orientation on the results. During the experiments, people were present and working in the laboratory. The training and test points were collected from 12p.m. to 9p.m. on a Saturday to exploit minimized human traffic and interference from other devices. For testing purposes, measurements were collected for the set of 10 test points marked as 'x' in Fig.2. This data was collected on the same day as the training data. For each point, the laptop was held statically by a user for 10 seconds resulting 1 2http:// 3http:// in 20 test samples per test point. The orientation of the user remained towards the west as in the training phase4. B. Figure of Merit A positioning system's performance can be evaluated in terms of various metrics such as location error, accuracy, timeliness, and cost [23]. Since we address the problem of static positioning in this paper, only positioning accuracy is considered in the subsequent section. Note that the computational complexity of the proposed method during the online stage is a direct function of the choice of kernel function and number of survey points. Positioning error is generally considered to be the Euclidean distance between the true position and its estimate. When multiple test points are involved, the overall error is an aggregation of the positioning error at each point. Examples include the mean, median, and various percentile errors. We have adopted the Root Mean Square Error (RMSE) criterion for evaluation of our system. Given the set of test points {p1,... pn} and their estimates {P1,... Pn}, the RMSE is calculated as follows: where - C. Results II RMSE = q-e -Pill'7 Ti- indicates the Euclidean distance. (10) In this section, the effects of system parameters on positioning accuracy are investigated. In addition, the performance of the system is compared to that of the popular KNN-matching method. As previously mentioned, the four important parameters that affect the performance of the proposed system are 1) shape of the kernel, 2) survey point values, 3) number of survey points, and 4) smoothing parameter. In terms of kernel functions, the Gaussian and Exponential kernels are considered in our experiments. Table I shows the RMSE obtained using different combinations of kernels and fingerprints. Based on these results, the exponential kernel used with the time average of the training RSS samples at each location provides the lowest RMSE. This combination is used for the rest of the experiments. TABLE I RMSE VALUES IN METERS FOR VARIOUS COMBINATIONS OF KERNELS AND FINGERPRINTING TECHNIQUES. Gaussian Exponential mean median % trimmed mean % trimmed mean % trimmed mean The measurements as well as their statistical analysis are available online at

6 9m f ZMT7pt I a mIU}TJ 2.1n4. r.x7. H, * X.8..X9. x. 10K 24m Fig. 2. Map of the experimentation environment. For both kernels, the RMSE is plotted as a function of the smoothing parameter and the results are depicted in Fig. 3(a). This parameter seems to have a great effect on the accuracy of the system and can be chosen during the training phase. For our data, a value of unity shows the best performance over all spatial locations in the test area. Fig. 3(b) shows the RMSE as a function of number of survey points. The results show that the system is able to provide accurate result with a minimum spacing of 2m between the survey points (19 points). Fig. 4(a) depicts RMSE results for three extreme values of -y, namely, -y E {0, 0.5, 1}, for each of the 10 survey points. As it is seen, the optimum values that minimizes the error varies for each location. This further stresses the benefits of using a family of aggregators such as the compensatory operator as opposed to a fixed method such as the arithmetic average. A general observation is that for the positions insides the room (test positions 1 to 6), values close to zero work well whereas the values close to unity are more appropriate for the hallway. This can be contributed to the more severe noise conditions, both in terms of multipath and shadowing by human bodies, near the staircase. RSS distributions near such points exhibit multimodality in contrast to unimodal distributions inside the room. These results suggest that an AND-like behaviour is more desirable in noisy environments where multimodal distributions are present. The effect of number of clusters C on the accuracy of the algorithm is shown in Fig.4(b) for each test point. The results indicate that C = 4 yields the best results for the given data-set. It should also be noted that under-clustering or overclustering can severely compromise the performance of the system. Lastly, the performance of the proposed single and multimap techniques is compared with the popular KNN matching approach and the results are reported in Fig 4(c). The singlevalued map and the KNN method have nearly similar performance. The KNN methods provides the location estimate as the arithmetic average of the three nearest points with closest survey values to the observation. This should be contrasted to the proposed techniques where all survey points contribute to the final estimate with different weights. The proposed methods, thus, eliminate the need for sorting operations during the online phase. The multi-valued map technique clearly outperforms the other two methods. The improved performance, however, comes the price of increased storage requirements. In this case, 4 floating points numbers are to be stored for each survey points as compared to the single value need for the other two methods. V. CONCLUSION The use of a non-parametric kernel estimator has been proposed in this paper for location estimation with RSS fingerprints. This has eliminated the need for any assumption regarding the spatial distribution of the signal strength. Additionally, the fusion of multiple fingerprints has been proposed to deal with multimodalities in temporal distributions of signal strength. Our results demonstrate the ability of the proposed method in providing accurate results with a relatively small number of survey points and fingerprints. At this stage, parameter optimization for the system has be done based on the training data. Further theoretical analysis of the system, however, will be performed in the future to better understand the effect of relevant parameters and automatically determine their optimal values. ACKNOWLEDGMENT The authors would like to acknowledge the kind assistance of Ms. R. Singh in collection of the WLAN experimental data at the University of Genova site. This work was supported by the University of Genova grant for foreign graduate students Rector's Decree #2545 of 10 June 2004, FIRB Vicom project, and Natural Sciences and Engineering Research Council of Canada. REFERENCES [1] P. Enge and R Misra, "Special issue on global positioning system,' Proceedings of the IEEE, vol. 87, no. 1, [2] M. McGuire and K. Plataniotis, "Dynamic model-based filtering for mobile terminal location estimation," IEEE Trans. on Vehicular Technology, vol. 52, no. 4, pp ,

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