Accuracy Indicator for Fingerprinting Localization Systems

Accuracy Indicator for Fingerprinting Localization Systems Vahideh Moghtadaiee, Andrew G. Dempster, Binghao Li School of Surveying and Spatial Information Systems University of New South Wales Sydney, Australia Abstract Fingerprinting is a technique that records vectors of received power from several transmitters, and later matches these to a new measurement to position the new user. This paper proposes a new mechanism to calculate the (Dilution of Precision) DOP-like value and error estimation for fingerprinting localization by investigating relationship between real distance and vector distance between fingerprints used in earlier fingerprinting experiments in Wi- Fi and FM radio networks. However, because fingerprinting algorithms use nearest neighbor techniques, the relationship between real distance and vector distance of these nearby fingerprints was also examined and found to more helpful when estimating the position. The proposed method used only the information from the training stage of fingerprinting and when compared with previous literature, it was found to give the improved results. Keywords-indoor localization; fingerprinting; DOP I. INTRODUCTION Indoor positioning has become highly important because of the difficulties satellite-based technology or Global Positioning System (GPS) experiences operating in such areas such as low received signal power and low visibility of satellites. Non-GNSS technologies, therefore, are essential for indoor localization. Utilizing signals of opportunity is a reassuring alternative navigation for GPS technology due to much higher power levels and wider coverage in indoor environments [1]. Many studies have usefully employed wireless networks for indoor localization based on the Received Signal Strength (RSS)-based location fingerprinting technique [2]. Unlike almost all other radio-navigation techniques, fingerprinting is not geometrical. In other words, the position solution does not rely on the angle to or distance from the transmitters. Instead, it requires a survey of Radio Frequency (RF) signal strength vectors to be made ahead of the system s use for localization. The fingerprinting technique stores the locationdependent characteristics of a signal collected at Reference Points (RPs) in a database and applies pattern matching algorithms to find the best match between the fingerprint of the user and the database, and eventually estimates the position of the user based on good matches. The matching methods are based on deterministic [3] and probabilistic [4] algorithms which have been used in Wi-Fi [2], FM radio [5], and mobile phone [6] networks. The measurements of the Received Signal Strength (RSS) values at one location can vary considerably, but in deterministic location fingerprinting the average value is stored for the post processing and position determination stage. In geometrical systems, a measure that relates the positioning error and the measurement (range or angle) error is known as Dilution of Precision (DOP). It generally indicates the effect of receiver-transmitter geometry on positioning accuracy. The DOP value can be calculated for Time of Arrival (TOA) [7], Time Difference of Arrival (TDOA) [8], [9], and Angle of Arrival (AOA) [10] systems by utilizing statistical methods. However, DOP for fingerprinting has not been evaluated. DOP can be used in a number of ways. First, it can be used predictively, i.e. given a network of transmitters (e.g. satellites for GPS), a value for DOP can be calculated that indicates whether a sound (i.e. low error) position is likely to be able to be calculated at a particular location. Similarly, it can be used when designing a network to place transmitters in locations that can ensure good positioning over a region. Secondly, a calculation of DOP that accompanies a particular position calculation can give an indication as to how much confidence a user can have in that calculation. Most research on indoor fingerprinting has focused on the calculation of position estimates, while the calculation of the expected error of the system has largely remained unexplored. There has not been very much published in the area of estimating errors in fingerprinting systems either. There are incomplete descriptions of how to estimate errors when using a probabilistic algorithm in [11] and [12]. Another study proposed some methods to estimate the errors, the best of which uses the best nearest neighbors returned from a deterministic positioning algorithm [13]. The result of this paper will be compared with the algorithm in [13]. In range-distance positioning calculations, the DOP is measured for a network of transmitters (e.g. satellites for GPS or Base Transceiver Stations (BTSs) for mobile phonebased positioning) in order to evaluate the high positioning accuracy locations within the area encompassed by the transmitters. In the location fingerprinting technique, however, the geometry of the transmitters such as Access Points (APs) in Wi-Fi-based positioning is not as significant as in range-distance navigation methods, due to the complexity of signal propagation in the indoor environments. In addition, the fingerprinting technique does not

fundamentally need any information about the transmitters locations. Therefore, in this paper, we investigate errors and the behavior of the signals at different points for an indoor localization system based on the network of RPs and the exact positions of them not the geometry of the transmitters, with the ultimate aim of evaluating something conceptually equivalent to DOP for the fingerprinting method. The location of the RPs are known and pre-recorded in the database. The rest of the paper is organized as follows. Section II is an overview of fingerprinting localization. Section III presents the investigation of the relationship between real distance and vector distance between fingerprints. The suggested mechanism to calculate DOP and the estimated errors, and the estimated positioning error comparison between the proposed method and previously proposed methods is described in Section IV. Finally, the conclusions of the work are discussed in Section V. II. FINGERPRINTING LOCALIZATION OVERVIEW If the propagation environment in which the system operates is known, the absolute distance between the transmitter and receiver can be calculated in an accurate manner. However, the point of fingerprinting is that it does not require knowledge either of the transmitters location, or the characteristics of the environment. Only the measurements which imply the characteristics of the environment, that is the RSSs, are needed. When recording the database of fingerprints associated with RPs, many individual RSSs are recorded, and these can vary significantly. A typical fingerprint is the average of the recorded RSSs. The fingerprint can also include information about the distribution, either a histogram for each transmitter or a more simplified parameter such as variance. Once the database of fingerprints exists, a device calculates position by recording a fingerprint and matching to the database. This usually consists of measuring a distance between the recorded RSS fingerprint and each RP fingerprint in the database. We will refer to this distance as the vector distance which has units related to dbm (as opposed to geometric distance in meters between the Test Point (TP) and an RP). Simple vector distance measures are Manhattan and Euclidean, the L1 and L2 norms. Once this vector distance is calculated, an interpolation algorithm can be used to provide location with respect to the RPs. Nearest Neighbor (NN) simply selects the RP with shortest vector distance. A K-Weighted average of Nearest Neighbors (KWNN) gives improved results [2], [5], [14]. III. NETWORK ANALASYS The experiments are carried out in an indoor environment consisting of office-like rooms and a corridor. Two sets of fingerprints are taken in this environment employing two different kinds of signals of opportunity, Wi-Fi signals and FM broadcast signals, for indoor position estimation. The fingerprinting technique for Wi-Fi positioning has been widely applied; however, that for FM positioning has not been studied thoroughly. The fingerprinting localization is chosen for indoor FM-based positioning, as fingerprinting can defeat some of the difficulties of using FM signals. It is an economical method, as it does not need any additional hardware or infrastructure [15]. Secondly, since FM signals do not carry any timing information, fingerprinting is more readily implemented than a time-independent method such as TDOA. Finally, not only does it not suffer from the effects of multipath and Non-Line-of-Sight (NLOS) signals compared to the time-dependant range-distance methods but it effectively exploits multipath because it gives high local variability to the RSS measurements [16]. More information on the layout and the RPs can be found in our earlier work [5], [14]. Table I also reports some details about them. Existing data from location fingerprinting experiments is used to help gain some insight into the nature of errors arising in this process. It should be noted that it is possible for two or more remote locations to have near-identical sets of RSS values, and a location estimate may consequently be totally inaccurate. Hence, the investigation of the relationship between real distance and vector distance is significant. This relationship has been firstly introduced for Manhattan distance in Wi-Fi positioning in our previous work [17], while most of the studies are based on the relationship between geometric distance from an AP and the RSS from that AP [18]. In this work, however, the relationship between real distance and RSS distance is investigated based on Euclidean distance and compared for both Wi-Fi-based and FM-based localization cases. Assume we have a set of n RPs in a desired area, the positions of which are known as loc x,y and are stored in the database along with the RSS vector of all the APs or FM channels at all RPs. We consider every RP as a TP once and all the other n-1 points as RPs. The Euclidean distance between fingerprints defined as: (1) where P is the number of FM channels in FM positioning or the number of APs in Wi-Fi positioning, i.e. the number of elements in the fingerprint vectors. RSS RP and RSS are the RSS vector at one RP and the TP respectively. Fig. 1 shows the Euclidean distance distribution versus the real distance between 119 RPs in both Wi-Fi- and FMbased positioning. The variation of the RSS over the desired area for Wi-Fi signals is higher than that for FM signals as expected, for two reasons: Wi-Fi signals are short-ranged and they change rapidly when distance increases from the Wi-Fi AP; Wi-Fi signals have much shorter wavelengths, so short-distance variation due to fading is more serious. Therefore, the lower variation of the FM radio signal is anticipated to result in a greater DOP value for the location estimation compared to Wi-Fi-based localization. TABLE I. THE SUMMARY OF FM AND WI-FI POSITIONING Number of RPs Number of transmitters std. of RSS Mean Positioning error FM 119 17 Channels 1.8 dbm 3.57 m Wi-Fi 119 5 APs 3.4 dbm 1.44 m

Figure 2. Different neighbourhood for one RP defined by circles with radius from 1m to 5m. Figure 1. Distribution of Euclidean distances between 119 RPs shown in [14] versus the real distance between the RPs in both Wi-Fi- and FM-based positioning. Linear regressions are also shown. This figure also demonstrates that the inferred relationship between the vector distance and the real distance is not as strong as we might like. By studying the Euclidean distance between the RP fingerprints and comparing them with real distance, it can be seen that there is a definite trend, i.e. that they are related. However, the spread that is shown in the figure is due to the power measurements varying much more erratically than would allow good prediction, due to the specifics of the indoor environment, signal fading, and features such as walls between the RPs. The significant point here is that we cannot estimate the user position by the linear regression in Fig. 1. The reason for this is that while Fig. 1 gives a good indication of how vector distance between RP fingerprints indicates real distance, the positioning algorithms tend to match to nearest neighbors so behavior of distant RPs is not relevant. Furthermore, the presence of walls in an indoor environment makes the nearest RPs more influential. Hence, the investigation of the nearest neighborhood is more essential. For this purpose, we examine the relationship between vector distance and the geometric distance in closer areas. Five different areas defined by circles around each RP are considered. As can be seen in Fig. 2, in our experiment, the radii of the circles are from 1m to 5m. We consider the minimum radius to be one meter because some RPs do not have any neighbor RPs within one meter circle as the RPs are not gridded evenly. The maximum radius of five meters is chosen since it is well above the achieved positioning accuracy (1.44m for Wi-Fi and 3.57 for FM). Fig. 3 depicts the variation of Euclidean distance over real distances for one typical RP and the RPs inside the different radius of circles in both FM and Wi-Fi positioning. The linear regression has been shown over the RPs within the five radii. It should be noted that this point has no RP within the area with 1m radius, so there is no information for r = 1m for this RP. The slopes of the linear regression defined as: Figure 3. The variation of the Euclidean distance over geometric distance between one typical RP and the RPs within five-meter circle. Linear regressions are shown when different radii are chosen. (dbm/m) (2) where ED is Euclidean distance and RD is real geometric distance. Higher slopes indicate that even nearby points have such distinct RSS values, which makes the points more recognizable. The more distinguishable the points the better accuracy can be achieved in localization. This feature is more highlighted in Wi-Fi signal compared to FM radio, which is confirmed by the slopes shown in Fig. 3. The considerably higher slopes for Wi-Fi signals compared with that of FM radio indicate a better accuracy should be achieved using Wi-Fi signal, which agrees with Table I. The slopes of the distribution of RPs in Fig. 3 based on five radii are reported in Fig. 4 for both FM radio and Wi-Fi signal. The mean of the linear regression slopes at different radii of the circles for all RPs of the mentioned area for both FM and Wi-Fi positioning is demonstrated in Fig. 5. This figure indicates that by increasing the neighborhood area for the RPs, the linear regression slope decreases, which results in lower accuracy at the end. The first reason for this is that the fingerprinting technique actually works because there is a

clear correlated relationship between ED and RD when RD is relatively small, so when RD gets larger the more number of disturbing RPs are considered which will increase the positioning error. In [14], we also mentioned that four nearest neighbors gives the minimum error in the KWNN algorithm for both FM and Wi-Fi positioning and the accuracy will be degraded when more number of nearest RPs are being taken into account. IV. THE ERROR ESTIMATION METHOD DOP for fingerprinting basically provides the level of confidence that a user can have in the position calculation. It is basically produced by evaluating the variation of the positioning error over the measurement error for one point or over a region or similarly by examining the effects of the errors in the measurement on the final state estimation. The definition of DOP is: (3) Figure 4. The linear regression slopes at different radii of the circles at one typical RP in both FM and Wi-Fi positioning. which has the unit of m/dbm in fingerprinting localization (whereas in TOA or TDOA systems, DOP is unitless). Unlike an FM signal, a Wi-Fi signal is more sensitive to the environment and the movement of people, so the measurement errors in Wi-Fi positioning are higher than those in FM-based positioning. Furthermore, utilizing Wi-Fi signals gives lower positioning error than employing FM signals (see Table I). Hence, considering the definition of DOP and the (3), the DOP for FM signals must be higher than for Wi-Fi in the same environment and the same RP arrangement. In other words, for FM positioning we need to put more RPs in the area in order to achieve the same level of accuracy of Wi-Fi. The relationship between RP density and accuracy is discussed in [2], [5]. Here we suppose the DOP-like value of fingerprinting to be an inverse of the slope we defined in previous section, which is a reasonable assumption based on the concept of DOP and the slope discussed earlier. By making this assumption, the estimated error is found by division of standard deviation of measurements error with the slope as below:. This can be generated for all RPs separately to find the estimated error at each point or it can be just applied over the whole area to find the mean estimated error. Here we just provide the mean estimated error in the environment to compare that with the mean positioning error in Table I. As was mentioned earlier, four nearest neighbors gives the minimum error in the KWNN algorithm for both FM and Wi-Fi positioning [14]. By finding four nearest RPs (four RPs with the shortest vector distances) for all RPs, we can calculate the real distances between the RPs and their four nearest RPs and take the average of all to find the average real distance of the nearest neighbors for the whole area. Here we can then find the related average slope based on Fig. 5 in our experiment. The average real distances of nearest neighbors for FM positioning found to be 5 meters and for Wi-Fi positioning is 2.5 meters. Therefore, the slopes are 0.37 and 1.9, which results in DOP-like value of 2.70 and 0.53 for FM and Wi-Fi. Standard deviation of measurements errors are also shown in Table I. The estimated errors achieved for FM and Wi-Fi utilizing this mechanism are 4.86m and 1.79m respectively (see Table II). Fig. 6 is the comparison of the mean calculated error (which we already have from the previous work [14] and the mean estimated errors using the proposed mechanism and the best candidate set method proposed in [13]. As can be seen from this figure, the new proposed method is better than the former error estimation in [13]. (4) Table II. THE MEAN ESTIMATED ERROR FOR FM AND WI-FI POSITIONING Figure 5. The mean of linear regression slopes at different radii of the circles for all RPs in both FM and Wi-Fi positioning. Mean RD (m) Slope mean (dbm/m) DOP-like value (m/dbm) Mean Est. Err (m) FM 5 0.37 2.7 4.86 Wi-Fi 2.5 1.9 0.53 1.79

Figure 6. Comparison of calculated error and estimated error using a proposed mechanism and the best candidate set method proposed in [13] V. CONCLUSION Existing data from fingerprinting experiments has been used to help gain some insight into the nature of errors arising in this process. The overall relationship between real distance and vector distance the distance between fingerprints is investigated and found to be relatively poor. However, where real distances are short between fingerprints, this relationship improves so that severalnearest-neighbor algorithms are able to supply reasonable results. A new mechanism to calculate the DOP and error estimation is also proposed for fingerprinting positioning using only the information from the training stage of fingerprinting (including RP locations and RSS values). By estimating the positioning error for different fingerprinting localization system, the quality of service of the systems may be improved in order to guaranty the integrity and the continuity of service. [8] D-H Shin and T-K Sung, Comparisons of Error Characteristics between TOA and TDOA Positioning, IEEE Trans Aerospace &Elect Sys, vol 38, no 1, Jan 2002, pp307-311 [9] B. Li, A. G. Dempster, J. Wang, 3D DOPs for Positioning Applications Using Range Measurements, Wireless Sensor Network, Volume 3, Number 10, pp. 334-340, 2011. [10] A. G. Dempster, Dilution of precision in angle-of-arrival positioning systems, Electronics Letters, vol 42, no 5, 2 Mar 2006, pp291-292 [11] P Kontkanen et al, Topics in probabilistic location estimation in wireless networks, Proc Personal, Indoor and Mobile Radio Communications PIMRC 2004, 5-8 Sep 2004, vol 2, pp 1052-1056. [12] P Myllymaki et al, Error estimation concerning a target device s location operable to move in a wireless environment, US patent 7,209,752 B2, 24 April 2007. [13] H. Lemelson, M. B. Kjærgaard, R. Hansen, and T. King, Error Estimation for Indoor 802.11 Location Fingerprinting, Proc. of the 4th Int. Symposium on Location and Context Awareness, 2009, pp. 138-155. [14] V. Moghtadaiee, A.G. Dempster, S. Lim, Indoor Positioning Based on FM Signals and Wi-Fi Signals, Proc. of IGNSS, Sydney, Australia, 2011. [15] S.-H. Fang, J.-C. Chen, H.-R. Huang, and T.-N. Lin, Is FM a RFbased positioning solution in a metropolitan-scale environment? A probabilistic approach with radio measurements analysis, IEEE Transactions on Broadcasting, vol. 55, no. 3, pp. 577 588, 2009. [16] T. King, T. Haenselmann, and W. Effelsberg, Deployment, calibration, and measurement factors for position errors in 802.11- based indoor positioning systems, in Proc. Location-and Contextawareness, 2007, pp. 17 34. [17] A. G. Dempster, B. Li, I. Quader, Errors in Determinstic Wireless Fingerprinting Systems for Localisation, Proc. Of International Symposium on Wireless Pervasive Computing, 2008, pp. 111-115. [18] B. Li, A. G. Dempster, C. Rizos, J. Barnes, Hybrid method for localization using WLAN, Spatial Sciences Conference, Melbourne, Australia, 12-16 September, pp. 341-350, CD-ROM procs REFERENCES [1] J. Raquet and R. K. Martin, Non-GNSS radio frequency navigation, in Proc. of IEEE ICASSP, 2008, pp. 5308 5311. [2] B. Li, Y. Wang, H.K. Lee, A.G. Dempster and C. Rizos, "Method for yielding a database of location fingerprints in WLAN," Proc. IEE Communications, vol. 152, no. 5, pp. 580 586, Oct 2005. [3] P. Bahl and V. N. Padmanabhan, RADAR: An In-Building RF-based User Location and Tracking System, Proc IEEE Conference on Computer Communications (INFOCOM), 2000. [4] T. Roos, P. Myllymaki, H. Tirri, P. Misikangas, J. Sievanen, A Probabilistic Approach to WLAN User Location Estimation, Int J Wireless Info Networks, vol 9, no 3, July 2002, pp155-164. [5] V. Moghtadaiee,A. G. Dempster, S. Lim, Indoor Localization Using FM Radio Signals: A Fingerprinting Approach, Proc. IEEE Indoor Positioning Indoor Navigation, Sep. 2011, pp. 1-7. [6] B. Li, A. G. Dempster, J. Barnes, C. Rizos, D. Li, Probabilistic algorithm to support the fingerprinting method for CDMA location, Int. Symp. On GPS/GNSS, Hong Kong, 8-10 Dec 2005, paper 9C-05, CD-ROM procs. [7] Elliott D Kaplan and Christopher J Hegarty (eds), Understanding GPS, 2nd ed., Artech House, 2006.