Location estimation using received signal

Performance Improvement of Location Estimation Using Deviation on Received Signal Strength In Wireless Sensor NetworksKoichi Miyauchi a, Eiji Okamoto b, and Yasunori Iwanami cGraduate School of Engineering, Nagoya Institute of TechnologyGokiso-cyo, Syowaku, Nagoya 466-8555, Japana miyauchi@rose.elcom.nitech.ac.jp c b,{okamoto, iwanami}@nitech.ac.jpAbstract- We propose a performance improvement schemeof location estimation using received signal strength (RSS)method in wireless sensor networks. Reference nodes insensor networks receive RSS from a target node whoselocation is unknown, calculate the RSS deviation score, andeliminate the scattered RSS of edge-score. This improvesthe estimation accuracy which is not high in RSS methodsin general. The simulation results show that the proposedscheme enables better location estimation than theconventional scheme under the small number of pre-RSS measurement situations.Keywords- Received Signal Strength, Location Estimation, Deviation, Maximum Likelihood EstimationI. INTRODUCTIONRecently, ad-hoc network communication systems, which do not require specific access points but provide various services, are drawing much attention. Especially, the wireless sensor network, in which the localization of a device is done by radio measurement and an advanced localized service is provided based on the estimated location, has been much studied [1-3]. In the location estimation, the received signal strength (RSS) method in which the location of unknown device (called ‘target node’) is estimated by multiple RSS at location known devices (called ‘anchor node’), is popular because this method is available for almost all wireless environments and the RSS mechanism is simple and low-cost [4,5]. However, RSS is not stable and the RSS value is changed even if the transmitter sends at a same power due to the influence of channel. It significantly degrades the performance of localization but there are few studies to tackle this problem. Therefore, we propose an improved location estimation scheme of RSS in which the deviation score of RSS is calculated and the RSS of edge-score is eliminated. The location is estimated by using the log-likelihood function based on the selected RSS. This scheme achieves less measurement of RSS and accurate estimation which enables low power consumption. In the following, we describe the algorithm of the proposed scheme and evaluate the performance through computer simulations.iP i Prelatively high for largeiPFig. 1. RSS probability model of exponential distribution ati-th anchor node.II. RSS MODELThe RSS can be modeled by probability distribution. If two-dimensional sensor field is assumed,the distance between the target node and i-th anchor node can be given by22)()(iiiyyxxr(1) where ),(y xT is the location of the target node and ),(iiyx is the i-th of N anchor node location. Using this distance i r, the probability of RSS (received power) i P at anchor node i and the average RSS (average received power)iP calculated by the probability model are given byED iirP, )exp(1)|(iiiiir PPPrPp (2) where D and E are the channel coefficients configured by the sensor field environments [2]. From the left equation of (2), we can see that the average RSS i P is modeled by the target-anchor distance i r, and thus, the right equation shows what distance i r is likely when RSS i P is received at anchor node i. i r is changed according to the location of ),(yxT and the probability)|(i irrPp of i-th anchor node is also changed even if the same level of i P received. Fig. 1 shows an example of)|(iir rPp. From the exponential distribution property of (2), i P becomes nearly the average value of i P with high probability, but the probability of large value is not zero and sometimes the received RSS become large. This characteristic coincides the practical RSS model. The RSS method utilizes this difference of probability distribution and calculates the estimated location from multiple anchor nodes (at least three nodes).III. MAXIMUM LIKELIHOOD LOCATIONESTIMATION USING RSSEach measured RSS of every anchor node modeled by (2)is assumed as independent. The joint probability of p where the number of anchor nodes is N and i -th anchor node receives the poweri P is derived asmultiplication of (2) by)|()|()|()|(2211N N r P p r P p r P p P p " T(3)This equation is a likelihood function and has a maximum value when T is most likely for the measured i P . In (3), each probability )|(i i r r P p is a function of the distance i r and this i r is determined by the position of target node ),(y x T . Hence, the likelihood function of (3) becomes maximum at the most likely position. The logalithm function )(T L of (3) after M times measurements of i P is given by¦¦°¿°¾½°¯°®­¸¸¹·¨¨©§ Ni i Mk iki P MP P ML 11)1log()(T(4)where ik Pis the k -th received power of i -th anchornode. The )ˆ,ˆ(ˆy xT which has the maximum )(T L is the estimated location. Here, as shown in (4), equations of (2) and (3) can be represented using the sampling averagepower ¦ Mk ik M P 1instead of the receive RSS i P . This is the maximum likelihood (ML) estimation of RSS localization.IV . PROPOSED ESTIMATION SCHEMEAs shown in (2), the probability distribution of RSS is an exponential distribution with the mean i P and variance 2i P . From (2), D and E are constant and 2i P have large values as i r is shortened. Fig. 2 shows an example of five RSS samples causing the estimation error. An extremely large receive RSS (e.g.2i P in Fig. 2) enlarges the difference between the average power i P of the modelin (2) and the sampling average power ¦ Mk ik M P 1. From (4), this difference makes a fluctuation of )(T L for T . Thus, when a scattered RSS from the mean i P is obtained in measurement, )|(i i r P r p is affected and the accuracy of (4) is degraded. This is the problem of the RSS localization scheme decreasing the accuracy and is expected to be solved. Therefore, we consider the elimination of noisy RSS. For each anchor node i after M times measurements of ik P , the deviation score ik T of ik P can be derived using the sample average¦ Mk ik i M P 1P and the standard deviation i V of the sample byM k Ni P T ii ik ik ,...,1,...,1)(10V P (5)ikP sampling average power of model average power in (2) iP 1i P 2i P This gap degrades the estimation accuracyextremely large RSSiP 04i P 3iP 5i PFig. 2. Example of receive RSS samples degradingestimation accuracy where M=5.:model average power 1i P 2i P eliminating outside of the effective diviation range.iP 0effective range of deviationi P gap is decreasedmax T min T 1i T iP :sampling average power of ikP :sampling average power after eliminating ineffective RSS.4i P 3i P 5i P 4i T 3i T 5i T 2i TFig. 3. Elimination of ineffective RSS where M=5.We introduce the upper and lower limits as max T and min T , respectively, for ik T . The receive RSS ik P whose ik T is within the range between min T and max T is used for calculation of (4) and the accuracy can be improved without an extra measurement. Fig. 3 shows the example of eliminating effect. By eliminating the receive RSS having extremely large or small value, the samplingaverage power ¦ Mk ik M P 1approaches the model average i Pand the gap is decreased. This improvement will raise the estimation accuracy of location.V 㸬ALGORITHM OF PROPOSED SCHEME ANDNUMERICAL RESULTSA. Performance comparison with regard to RSSmeasurementsThe algorithm of proposed scheme is illustrated in Fig. 4. Using this algorithm, the performance is evaluated in the 4 x 4 m sensor field with linear anchor node location as shown in Fig. 5. The range of deviation score is 85max T and 15min T , and the channel parameters are assumed as 71026.5 u D and 5.2 E This deviation range is configurated by a heuristic search. The actual location of target node is set to )5.1,5.1(),( Y X M . In this simulation,the root mean square error (RMSE) between M and T ˆis compared as the evaluation function which is given by22)ˆ()ˆ(y Y xX RMSE (6) The RMSE performance for each measurement number M from 3 to 12 is calculated by the average of 10000 times trial. Table 1 shows the simulation conditions and Table 2 shows the simulation results.RSS measurement Standard score calculationIs within threshold?YesNoik T Remove fromlikelihood function and M ĺM-1ik P Is all checked?NoYesEstimation RMSE calculationik T 1k k 1kFig. 4. Algorithm of proposed scheme.4[m]4[m](0.0,3.5)(0.0,0.5)(0.0,1.5)(0.0,2.5)(0.5,0.0)(1.5,0.0)(2.5,0.0)(3.5,0.0)Target node Anchor node(1.5,1.5)Fig. 5. Sensor field in the study.Table 1. Simulation condition of location estimation at(1.5,1.5) of target node.Size of Sensor field4[m] x 4[m] Target node location (1.5,1.5)Number of anchor node N =8Anchor node location Fig. 5Trans. mode parameters 5.2,1026.57 u E D Effective deviation range max T =85, min T =15Number of RSS measurement M =3 to 12Number of trial to calculate RMSE10000 timesTable 2. Comparison of RMSE between two schemes.M:Number of RSS measurementRMSE of conventional ML[m]RMSE of proposed ML w/ removing RSS[m]30.2839924 0.279515740.2388926 0.236479350.2079692 0.207790360.1889015 0.188784670.1734935 0.173493580.1624253 0.162425390.1539064 0.1539064100.1453188 0.1453188110.1392523 0.1392523120.13276330.1327633The results of the performances of the proposed scheme are better than conventional ML with M from 3 to 6. This means that in the less measurement situation, the noisy RSS degrades the performance and the proposed scheme effectively eliminates them so that the probability model at anchor nodes becomes closer to (2). Meanwhile, after sufficient measurements over 7 of M , the performances of both schemes coincide because the distribution model of measured RSS is already close to (2). By this fact, the performance is not improved even if the edge RSS is eliminated. Therefore, the proposed scheme contributes the performance improvement in relatively fewer measurements.B. Performance comparison with regard to target nodelocationFrom the results of the previous simulation, it is found that the performance of the propose scheme is better at a less RSS measurement region. Then, we compare the performance with regard to anchor node location at a small number of RSS measurements. The performance of algorithm of Fig. 4 is calculated and compared with the conventional ML scheme under the condition of Table 3. The location of target node ),(y x T changes throughout the sensor field per 0.1[m] in x and y directions, and the effective region where the RMSE of the proposed scheme is smaller than conventional scheme is drawn.Table 3. Simulation conditions for calculating effectiveregion at M =3, 5, and 7.Size of Sensor field4[m] x 4[m] Grid size of simulation0.1[m]Number of anchor node N=8Anchor node location Fig. 5Trans. Mode parameters 5.2,1026.57 u E DEffective deviation range(a)max T =85, min T =15(b)max T =85, min T =25Number of RSS measurement M =3, 5, and 7.Number of trial to calculate RMSE10000 timesFig. 6. Effective region of proposed scheme where M =3and the deviation range is (a).Fig. 7. Effective region of proposed scheme where M =5and the deviation range is (a).Fig. 8. Effective region of proposed scheme where M =7and the deviation range is (a).Fig. 9. Effective region of proposed scheme where M =7and the deviation range is (b).Fig. 6 to 9 show the results. At M =3 of Fig. 6, the small number of RSS samples makes its distribution unstable (see Fig. 3) and the proposed eliminating scheme works well. As a result, the effective region is large as shown Fig. 6, especially at a far side from anchor nodes. As the number of RSS measurements increase, the effective region gradually becomes smaller as shown in Figs. 7 and 8. Although the values of RMSE are decreased in both schemes, the sampling average power gets closer to the model average power i P and the effect of the proposed scheme is decreased. However, we can see that the proposed scheme works well at the far side of sensor field even with M =7, and it is expected the proposed scheme is effective where the target node is not close to anchor nodes.In Fig. 8, the performance is not improved at the center area of the censor field because the sampling average power is stable there. From the simulation result, it is found that )(T L of the target node which is approximately equally distant from anchor nodes is stable. Therefore, we enhanced the elimination range of RSS deviation and calculated the performance. Fig. 9 shows the result of elimination range extension from Fig. 8 of M=7. The effect of elimination is raised and the performance is improved. Thus, the parameter optimization may enhance the efficiency of the proposed scheme.VI. CONCLUSIONIn this study, we proposed a performance improvement scheme of RSS location estimation in wireless sensor networks. By adopting the deviation score of receive RSS and eliminating the scattered values, the accuracy of localization is improved in a few measurement cases without an extra measurement. Numerical results showed that the performance was better than the conventional scheme at several RSS measurement cases and the deviation range optimization raised the performance. In future studies, a performance improvement scheme for various power distributions other than exponential model and an autonomous elimination range control along to environments will be developed.AcknowledgmentThis research was partially supported by KDDI foundation.References[1] A.Savvides, H.Park, and MB. Srivastava, ’The Bits and Flops of the N-hop Multilateration Primitive For Node Localization Problems.’, in Proc. Intl. Workshop on Sensor Nets. Apps.,pp.112-121, Sept.2002. [2] D.-P.Zha, M.Takashima, Yanagisawa, J.Taketugu, K.Fukui, .Fukunaga, S.Hara, and K.Kitayama, ’ A Maximum Likelihood Estimation Method of Localization using RSSI in Wireless Sensor Networks’, IEICE technical report 104(690), 409-414, 20050225.[3] Ismail Guvenc and Ghia-Chin Chong,’A Survey on TOA Based Wireless Localization and NLOS Mitigation Techniques’,IEEE Communications Surveys & Tutorials, V ol. 11, No. 3. (21 August 2009), pp. 107-124.[4] Charalampos Papamanthou, Franco P Preparata, and Roberto Tamassia,’Algorithms for Location Estimation Based on RSSI Sampling’, Fourth International Workshop, ALGOSENSORS 2008, Reykjavik, Iceland, Revised Selected Papers, p.72-86, July 2008.[5] C.Savarese, J.Rabaey, and J.Beutel, ’Locationing in Distributed Ad-Hoc Wireless Sensor Networks.’, In Proc. ICASSP, pp.2037-2040, May.2001.。