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IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 60, NO. 10, OCTOBER 2011

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Accuracy of RSS-Based Centroid Localization Algorithms in an Indoor Environment Paolo Pivato, Graduate Student Member, IEEE, Luigi Palopoli, Member, IEEE, and Dario Petri, Fellow, IEEE

Abstract—In this paper, we analyze the accuracy of indoor localization measurement based on a wireless sensor network. The position estimation procedure is based on the received-signal-strength measurements collected in a real indoor environment. Two different classes of low-computational-effort algorithms based on the centroid concept are considered, i.e., the weighted centroid localization method and the relative-span exponential weighted localization method. In particular, different sources of measurement uncertainty are analyzed by means of theoretical simulations and experimental results. Index Terms—Centroid algorithm, localization, propagation model, wireless sensor networks (WSNs).

I. I NTRODUCTION

I

N THE last few years, the use of wireless sensor networks (WSNs) has become commonplace in different fields, ranging from environmental monitoring in harsh and hostile areas to precision agriculture, from security and surveillance to medicine and industries and, more recently, from home automation and assisted living [1]–[4]. A recent indoor application for WSNs is the localization of moving targets. This application is motivated primarily by the low cost of this solution and the lack of effective positioning and tracking systems working inside buildings. Indeed, the global positioning system solves many localization problems outdoor, where the devices can receive the signals coming from satellites, but the system is hardly usable indoor. Moreover, wireless nodes present some advantages in terms of system miniaturization, scalability, quick and easy network development, cost, and reduced energy consumption. Most of the proposed localization solutions rely on receivedsignal-strength (RSS) measurements. In fact, RSS can be used to estimate the distance between an unknown node (called a target node) and a number of reference nodes with known coordinates (called anchors or beacons). The location of the target node is then determined by multilateration [5].

Manuscript received June 24, 2010; revised February 5, 2011; accepted February 6, 2011. Date of publication May 2, 2011; date of current version September 14, 2011. This work was supported in part by the Autonomous Province of Trento, Italy, under Project “ACube—Ambient Aware Assistance” and in part by the Italian Ministry of University and Research under the 2008 PRIN Project “Methodologies and Measurement Techniques for Spatio–Temporal Localization In Wireless Sensor Networks.” The Associate Editor coordinating the review process for this paper was Dr. Z. Liu. The authors are with the Department of Information Engineering and Computer Science, University of Trento, 38123 Trento, Italy (e-mail: pivato@ disi.unitn.it). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TIM.2011.2134890

Unfortunately, some studies showed the large variability of RSS, due to the degrading effects of reflections, shadowing, and fading of radio waves [6]–[9]. As a result, localization methods using RSS are affected by large errors and lack of accuracy. However, RSS-based techniques remain an appealing approach [10]. This is mainly due to the fact that RSS measurements can be obtained with minimal effort and do not require extra circuitry, with remarkable savings in cost and energy consumption of a sensor node. In fact, most of WSN transceiver chips have a built-in RSS indicator (RSSI), which provides RSS measurement without any extra cost. In the literature, there exist many studies about RSS-based outdoor localization, most of which analyze the problem through simulations and experimental data [11], [12]. Conversely, to the best of our knowledge, less attention has been given to RSS-based indoor localization. The available results are obtained mainly by means of simulations. The models adopted in these simulations use either the same or different path-loss exponents for each link, but they usually do not account for the different nonidealities of radio transmissions in indoor environments [13]. In fact, there is a lack of experimental data, which are necessary to adequately validate the proposed solutions [14]. The aim of this paper is to investigate the accuracy of RSSbased indoor localization. Thus, we propose a deep analysis of the impact on the measurement accuracy of different disturbing phenomena such as reflections, diffraction, and scattering and the influence of the error introduced by low-computationalcomplexity localization algorithms recently proposed in the literature. Although this paper is carried out for particular classes of algorithms, we believe that the proposed methodology is by a large extent generalizable. At first, we consider a log-distance path-loss model, which is widely used for the analysis of indoor wireless channels, and characterize it with respect to a specific measurement context. In this case, our goal is the identification of channel parameters by applying linear regression to a significant set of measurements. In addition to the characterization of the adopted channel propagation model, we carry on analyzing the accuracy of the so-called weighted centroid localization (WCL) and relativespan exponential weighted localization (REWL) algorithms. The proposed metrological characterization of the RSS-based indoor localization system allows us to provide an insightful interpretation of the limitations of the approach, which can be useful for future developments. The remainder of this paper, which extends what has been presented in [15], is organized as follows. Section II contains

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related work. Section III describes the experimental framework, detailing the measurement scenario. The characterization of the indoor propagation channel is presented in Section IV, dealing with the adopted channel model and the related channelparameter estimation. In Section V, after a brief overview on the CL approach, we analyze the algorithms used in our experiments mainly on the basis of both meaningful simulation and experimental results. In Section VI, we conclude this paper. II. R ELATED W ORK As aforementioned, the vast majority of studies on RSSbased localization has been performed in outdoor environments. Conversely, the effects of spurious disturbances on the accuracy of RSS-based indoor localization have received little attention in the literature. Moreover, a small number of published papers are based on experimental results obtained from real indoor test beds. There exist several algorithms that can be used to determine the position of a target through RSS measurements: Some of them are geometric methods, such as lateration or a minimum–maximum method (min–max), whereas some others are based on statistical approaches, such as maximum likelihood. RADAR[14] provided one of the first experimental work on indoor localization using IEEE 802.11 radios for wireless local area network. It was based on an RSS mapping technique, in which a set of RSS measurements with known coordinates was collected a priori in an observation area. Then, the location of a target node was computed online by searching for the RSS values nearest to the current measurement in terms of some defined metrics. The average location error reported by RADAR was approximately 3 m. Alippi and Vanini [16] tested an RSS-based outdoor localization methodology exploiting a minimum least squares (LS) algorithm, after modeling a propagation channel. The deployment of anchors had a density of one node over 25 m2 on an area of 500 m2 . The average distance error obtained was about 3 m. In [17], an extensive indoor RSS measurement campaign was carried out in order to tune the parameters of the assumed channel model. Then, the collected RSS data have been used offline as inputs for two localization methods, i.e., the min–max and Bayesian filtering algorithms. A distance error of the order of 5 and 2 m was achieved for the two algorithms, respectively. In order to avoid the creation of RSS maps, complicate probability models, or high-computational-effort algorithms, Reichenbach and Timmermann [18] proposed approximated indoor localization based on a weighted centroid approach [19] combined with RSS measurements in an IEEE 802.15.4 sensor network. The weights were defined as inversely proportional to the RSS values measured between the target and each anchor node. The solution was tested in a square room with a side length of 3 m, using four anchor nodes displaced at the corners and one target node located in 13 different positions. The obtained relative localization error varied between 7.8% and 26%. The weighted centroid approach is one of the localization algorithm examined in the following.

Fig. 1.

Location test points within the room.

III. M EASUREMENT C ONTEXT The sensing platform used in our experimental setup was a TelosB wireless sensor node produced by Crossbow Inc. It is an open-source wireless node based on a Texas Instruments MSP430 microprocessor and equipped with an IEEE 802.15.4compliant Chipcon CC2420 radio module. The antenna is a 2.4-GHz planar inverted-F antenna printed on the dielectric substrate of the circuit board, which is fed by a coplanar waveguide. It is located on the border of one of the short sides of the node. We used this type of platform because of its remarkable popularity in the academic community and the wealth of software available. The experimental test bed was a rectangular room with a size of 5.8 × 4 m, which was furnished with a couch, a bookcase put on the wall, a table, and a settle. Therefore, the considered environment well emulated a real ambient living room. The system infrastructure was composed of one mobile node (i.e., the target), one base-station node (i.e., the sink), and 12 fixed nodes (i.e., the anchors). The mobile node was set on a dielectric support that is 50-cm high and stood upright. The linoleum floor was divided into 68 test point located on a grid with a resolution of 50 cm. They are represented with circles in Fig. 1. The 12 fixed nodes were hanged on the ceiling, which is 260-cm high. They are represented with squares in Fig. 1 and labeled with a number. The displacement of the fixed nodes formed a rectangular grid covering all the monitored environment. In the test-bed deployment phase, we experimented different placements of the nodes on the roof and the ceiling, in order to verify the existence of an optimal coverage pattern assuring the communications among all the nodes. As a matter of fact, we verified that the radio link was good in any configurations. We tested also several relative antenna orientations between target and anchor pairs, without noticing remarkable differences in the RSS values measured. Then, we arranged the mobile node and the fixed nodes, so that their antennas were mutually oriented one toward the others. The system performs the RSS measurements from the messages exchanged between the mobile node and each anchor node. The low-level communications between the nodes are carried out by the services provided by TinyOS. The mobile node sends a ping to the 12 anchor nodes requesting a response. Then, each anchor node replies in turn with a message containing the node identification and the transmitted power level. When the mobile node receives a reply message, it measures the

PIVATO et al.: ACCURACY OF RSS-BASED CL ALGORITHMS IN INDOOR ENVIRONMENT

SS through the built-in RSSI and reads the other information contained in the message. The process is repeated several times. All the measured RSS data are sent to the base station, which is connected to a laptop personal computer. Finally, the collected RSS values are processed and analyzed to extract statistical information and evaluate the result of the localization algorithms described in Section V. In order to minimize the exchange of messages and energy consumption, data collection and processing should be performed on the sensor node. We made a different choice because using a personal computer allows for an exhaustive statistical analysis, which is the main purpose of this paper, and an easier implementation of different localization algorithms. The measuring process was repeated 30 times for each of the 68 test point locations, resulting in a total amount of 24 480 RSS values collected. The achieved measurement repeatability was quite high, i.e., always within ±1 dBm.

A. Indoor Radio-Channel Propagation Model In order to characterize the indoor propagation channel, we assume that the SS follows the log-distance shadowing path-loss model proposed by Rappaport [20]. This propagation model is widely used in indoor wireless link budget and is given by:   d RSS(d) = RSS(d0 ) − 10η log +w (1) d0 where d is the transmitter–receiver distance, d0 is the reference distance, η is the path-loss exponent, i.e., the rate at which the signal decays, and w is a space-stationary zero-mean Gaussian 2 . RSS(d) is the RSS, and random variable with variance σw RSS(d0 ) is the signal received at the reference distance (both in decibel-milliwatts). An alternative formulation for (1) is as follows:   d RSS(d) = Ptx + K − 10η log +w (2) d0 where Ptx is the transmitted power (in decibel-milliwatts), and K is the attenuation factor at the reference distance d0 . Let d denote the true distance between the mobile and an anchor node, and let dˆ denote the distance estimated by inverting (2) and using the measured value for RSS(d). Under the assumptions made in (1) and applying the law of uncertainty propagation [21] to (2), we obtain that the distance estimator is biased, and its relative bias is given by (3)

whereas the relative standard deviation results as ˆ σ[d] σw  0.23 . d η

In particular, from (3) and (4), we have the following: ˆ σw b[d]  0.11 . ˆ η σ[d]

(5)

Considering η ranging between 1 and 4, as commonly occurred in practice, (5) returns values in (0.03σw , 0.11σw ). Thus, the distance estimator bias could be significant. For instance, for η = 2.3 and σw = 6.1 dB, as occurred in our ˆ ˆ  30%. experimental results, we have b[d]/σ[ d] Moreover, according to (4), the relative standard deviation of the estimated distance increases for about 5% to 20% for each decibel-milliwatt of RSS standard uncertainty. Thus, we can conclude that any distance estimator based on model (1) is very sensitive to RSS uncertainty. To the best of our knowledge, this interesting result has not been reported in the literature before.

B. Channel Parameters Estimation

IV. C HANNEL C HARACTERIZATION

ˆ σ2 b[d]  0.03 w2 d η

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(4)

Both of these formulas have been validated by simulations that are not reported here for the sake of conciseness.

The data set of RSS measurements, which is collected as described in Section III, was used to estimate the channel parameters K and η. The transmission power Ptx was set to −25 dBm in all nodes. This value was chosen because it was the minimum available power level ensuring a complete coverage of the room, thus allowing a good balance between coverage and energy consumption. The reference distance d0 , which is related to the antenna far field region, was set to be equal to 10 cm. The channel parameters were firstly estimated by applying the linear LS method (LSM) to all the 24 480 RSS values collected, obtaining K = −17.2 dB and η = 2.3. The achieved result is shown in Fig. 2(b), where the dots represent RSS measurements, and the solid line refers to the theoretical pathloss model derived by linear regression. In order to determine if the data well fit the derived parameters, we computed also the regression coefficient ρ, which resulted to be equal to 0.42. Moreover, the standard deviation of the RSS measurements was σw = 6.1 dB, leading to a relative bias on the estimated distance of 17% and a relative standard deviation of 60%, as provided by (3) and (4), respectively. As a second step, we analyzed the path-loss model considering each anchor node individually, whereas the mobile node is still moved in each of the 68 test points. The channel parameters K and η were still estimated by using the LSM for each data set of 2040 collected RSS values. Then, we considered the four anchors (i.e., anchors 1, 3, 10, and 12) located in the corners of the room and the six-anchor configuration given by the four anchors in the corners and the two anchors (i.e., anchors 5 and 8) in the middle of the room. We collected 8160 and 12 240 RSS values, respectively, and as described before, we used these values to estimate the channel parameters η and K through the LSM. Table I lists the log-distance channel parameters estimated in each case, together with the error standard deviation and the related regression coefficient. As shown, the channel-modelerror standard deviation is nearly constant for all the considered sets of anchors, whereas the resulting path-loss exponents is

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IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 60, NO. 10, OCTOBER 2011

TABLE I LOG NORMAL CHANNEL PARAMETERS

Fig. 2. RSS measurements and related channel models, considering (a) the four anchors in the corners of the room and (b) all the 12 anchors reported in Fig. 1.

quite changing. In particular, considering the channels related to each single anchor, it ranges from a minimum of 0.5 for anchor 4 to a maximum of 4.1 for anchor 12. The corresponding regression coefficients behave in a similar way, ranging from 0.15 to 0.63, respectively. From a distance estimation point of view, these anchors represent the worst and the best case, respectively. Indeed, a higher value of the regression coefficient means that the data received by the related anchor carry more information about the unknown distance. It is worth noticing that the four anchors located in the corners of the room provided the highest value of the regression coefficient; thus, they can be considered as the more informative ones. To the best of our knowledge, no previous work has reported remarkable differences of the channel parameters when considering each anchor node singularly. However, given the different locations of the anchors, the received signal is expected to be not affected by the same reflections, fading, and multipath interference, thus leading to a significant difference in the channel models. It is worth noticing that similar observations on the irregularity of the wireless communication channel were presented in [22], in which an extension to the isotropic radio model for an outdoor environment was proposed.

Fig. 3. RSS error histograms obtained, considering (a) the four anchors in the corners of the room and (b) all the 12 anchors reported in Fig. 1.

The histograms hw of the RSS error w are depicted in Fig. 3 for the case of the 4 and 12 anchors, respectively. Both distributions show a behavior far from Gaussian, which is conversely to the assumption commonly made in the literature [20].

PIVATO et al.: ACCURACY OF RSS-BASED CL ALGORITHMS IN INDOOR ENVIRONMENT

Moreover, we considered the RSS error histograms obtained for different distance intervals of equal amplitude (i.e., 50 and 100 cm). The obtained histograms noticeably differ each other, suggesting a nonstationary behavior of the RSS error with respect to the distance, which is different from what we would expect from the model suggested in [20].

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to the target, was proposed. The result is the WCL algorithm, which estimates the position of the target node as  n   · a dˆ−g i i (7) pˆ = i=1  n  dˆ−g i i=1

V. L OCALIZATION A LGORITHMS The localization problem can shortly be formalized as follows. Consider the set of nodes N = {A1 , A2 , . . . , An }, i.e., each one with a fixed and known position (hence the name anchors). In this paper, we are working with the common assumption of 2-D localization since the third dimension usually is not of primary interest in an indoor environment. Thus, the position of an anchor is a two-tuple ai = (xi , yi ), where xi and yi are evaluated with respect to origin O. Let p denote the position of a moving target node of unknown coordinates (x, y), and let RSSi denote the measured intensity of the SS from anchor ai experienced by the target. The goal of an RSSbased localization algorithm is to provide estimate pˆ = (ˆ x, yˆ) of position p given the vector [RSS1 , RSS2 , . . . , RSSn ]. We can recognize two classes of RSS-based localization algorithms: the range-based algorithm, which uses several target-to-anchor distance estimations obtained through the RSS measurements, and the range-free algorithm, which determines the position of the target node without performing distance estimation [5], [23]. In the following, we analyze two different methods: the WCL and REWL algorithms. The former belongs to the class of range-based solutions, whereas the latter is a range-free approach. Both algorithms are characterized by a low computational effort. This, combined with low transmission power, allows to significantly limit node energy consumption.

A. WCL The WCL algorithm is based on the so-called CL proposed in [24]. This solution approximates location p of the target node by calculating the centroid of the coordinates ai = (xi , yi ) of the so-called visible anchor nodes, i.e., the nodes for which a communication has been established during the measurement. More specifically, the estimated position of the target node is given by pˆ =

m 1  · ai m i=1

(6)

where m is the cardinality of subset N of visible anchors. It is worth noticing that when the target node communicates with all the anchors, i.e., all anchors are visible, the centroid results the center of the anchors coordinates. Notice that the CL approach assumes all the visible anchors equally near the target node. Since this assumption is most likely not satisfied in practice, in [19], the introduction of a function, which assigns a greater weight to the anchors closest

where dˆi is the distance between the target and anchor ai , which is estimated through RSSi of the visible anchors. Exponent g > 0 determines the weight of the contribution of each anchor. If g = 0, then pˆ is simply the sample mean of ai , and the WCL reduces to the CL approach. Increasing the value of g causes the anchors to reduce the range of their “attraction field” with respect to the mobile node, thus increasing the relative weight of the nearest anchors. The plots in Fig. 4 show the results of simulations running the WCL algorithm with 4, 6, and 12 anchors positioned as described in Sections III and IV and choosing g = 1.8. Each surface represents the algorithm error ealg in terms of the distance between the true position and the position estimated using the WCL algorithm with a grid resolution of 5 cm. The algorithm inputs were the true distances between the target and the anchors, which are calculated from their known coordinates. As shown, passing from 4 to 12 anchors, the error globally decreases, whereas it is drastically reduced in the proximity of anchor locations. Furthermore, we can observe that, using six anchors, the error tends to increase with respect to the fouranchor configuration. This is likely due to the presence of the two additional anchors placed in the center of the room, which increases the center-clustering behavior featured by algorithms based on the CL approach. Similar error surfaces were obtained assuming that additive white Gaussian noise (AWGN) with different values of standard deviation affects the RSS measurements. We noticed that, on average, the maximum values of the algorithm error are little sensitive to the noise. Otherwise, the noise affects significantly the areas with small error values, which are usually located near the center of the room, therefore increasing the centerclustering behavior of the algorithm. Tables II and III, respectively, show the mean and rootmean-square (RMS) values of the total distance error in the estimated position etot , which is achieved by running the WCL algorithm on the experimental data, with 4, 6, and 12 anchors and considering different values of exponent g within range (1, 1.8). In particular, the algorithm inputs were the distances between the target and each anchor, which are estimated by inverting (2) and using the RSS values measured in each of the 68 test points, as described in Sections III and IV. The same tables also summarize the mean and the RMS of the algorithm distance error ealg and the experimental noise distance error ew determined for the same sets of anchors and values of exponent g. The experimental noise distance error was obtained as the difference between the position estimates determined by running the WCL algorithm using both the true and estimated distances. Notice that this latter error is due to the noise component w in (2). In particular, Tables II and III show that, on the first approximation, mean μalg and RMSalg

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TABLE II WCL ALGORITHM MEAN DISTANCE ERROR

TABLE III WCL ALGORITHM RMS DISTANCE ERROR

number of anchors n and the regression coefficient ρ given in Table I, i.e.,   1 1 RMSw ∝ . (8) μw ∝ n·ρ n·ρ

Fig. 4. WCL distance error for g = 1.8, considering (a) the four anchors in the corners of the room, (b) the six anchors, and (c) all the 12 anchors reported in Fig. 1.

of the algorithm error depend little on the anchor number and decrease with the raising exponent g. This behavior is partially compensated by the noise error, whose mean μw and RMSw values increase with an increasing value of g and decrease with a raising number of anchors. As a result, the effect of the algorithm error on the total error is negligible for the four anchors, whereas it counts for 6 and 12 anchors. Considering any two different anchor configurations (e.g., 4 and 12 anchors) it is interesting to note that the ratio of the correspondent mean μw and the RMS RSSw values of the noise error reported in Tables II and III tend to be inversely proportional to the square root of the product between the

Since a growing number of anchors result in a decrease in the regression coefficient, using more anchors reduces the effect of noise by a factor that is smaller than the square root of the number of anchors. In any case, (8) can provide some useful hints on the expected effect of noise in different system configurations with changing number of anchors. Fig. 5 depicts the cumulative histograms H of the WCL estimation errors considering the four anchors in the corners of the room and all the 12 anchors. As expected, the median total estimation error is about 1 m, using 4 or 12 anchors. Indeed, the four anchors in the corners carry most of the information about the unknown distance, as shown in Section IV. Notice also that the use of 12 anchors, although does not produce a significant reduction of the average estimation error, has a beneficial effect on the maximum error. B. REWL The REWL is an RSS-based range-free localization algorithm recently proposed in the literature [25]. This algorithm is inspired by the WCL method. The weights are obtained by the relative placement of the anchor RSS value within the span of all the RSS values measured by the target node. In the estimation of the target position, the REWL algorithm favors the anchors, which exhibits higher RSS values and therefore are likely to be closer to the target node. This is obtained using

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Fig. 5. Cumulative histograms for the WCL localization algorithm errors, considering (a) the four anchors in the corners of the room and (b) all the 12 anchors reported in Fig. 1.

the weighting factor λ, according to the exponentially moving average concept [25]. The estimated target node position is given by [25] n

 (1 − λ)RSSmax −RSSi × ai

pˆ =

i=1

n 

(9) (1 − λ)RSSmax −RSSi

i=1

where RSSmax is the maximum value in the span of the RSS values measured by the target node. Suggested values for λ, which are experimentally determined, range from 0.10 to 0.20 [25]. In fact, assuming the path-loss model (1), it can be shown that in case of no noise, the REWL algorithm reduces to (7), where g ranges between 0.5 and 3.9 when η and λ assume values in (1, 4) and (0.1, 0.2) intervals, respectively (as given in the Appendix). Fig. 6 shows the surfaces representing the algorithm distance error ealg , which is obtained by running simulations of the REWL algorithm for λ = 0.15, with 4, 6, and 12 anchors and with a grid resolution of 5 cm. The inputs of the algorithm were the theoretical RSS values that might be measured by the

Fig. 6. REWL distance error for λ = 0.15, considering (a) the four anchors in the corners of the room, (b) 6 anchors, and (c) all the 12 anchors reported in Fig. 1.

target in each point of the grid in the absence of noise. These values were evaluated using the path-loss model (2), considering for each set of anchors the related channel parameters η and K reported in Table I and the true distances d between the target and the anchors, which are calculated from their known coordinates. The transmission power was assumed to be Ptx = −25 dB, and the reference distance was d0 = 10 cm. Clearly, the error tends to decrease with the increasing number of anchors. The shape of the error surfaces is substantially similar to the one of the WCL algorithm, with the exception of the four-anchor configuration that features a higher error around the center of the grid. As previously highlighted for the

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TABLE IV REWL ALGORITHM MEAN DISTANCE ERROR

TABLE V REWL ALGORITHM RMS DISTANCE ERROR

WCL, the six-anchor configuration exhibits higher algorithm error values with respect to the four-anchor configuration. Moreover, we analyzed also the error surfaces obtained by assuming the RSS values affected by AWGN. Assessment on these is similar to the ones drawn for the WCL algorithm. Tables IV and V list the mean and RMS values of the total distance error in the estimated position etot , which is achieved by running the REWL algorithm with 4, 6, and 12 anchors and considering λ = 0.10, λ = 0.15, and λ = 0.20. The algorithm inputs were the RSS values measured by the target in each of the 68 test point, as described in Sections III and IV. The same tables report also the mean and RMS values of the algorithm distance error ealg and the experimental noise distance error ew . This latter error is determined as the difference between the position estimates achieved by running the REWL algorithm on both the theoretical and measured RSS values. As shown, mean μalg and RMSalg of the algorithm error depend on the number of anchors, but they feature a different behavior as the weighting factor λ changes. In fact, with four anchors, they increase passing from λ = 0.10 to λ = 0.20, whereas with 6 and 12 anchors, they decrease significantly when λ increases. Mean μw and RMSw of the noise error decrease with an increasing number of anchors, whereas they decrease with a raising value of λ. As regard to mean μtot and RMStot of the total error, they depend little on both the anchor number and the weighting factor λ. Fig. 7 shows the cumulative histograms of the localization errors resulting when running the REWL algorithm with λ = 0.15 and for the four anchors on the corners of the room and for all 12 anchor nodes, respectively. Considerations similar to those expressed for the WCL algorithm can be done. In particular, for the 12-anchor configuration, the maximum total

Fig. 7. Cumulative histograms for the REWL algorithm errors for λ = 0.15, considering (a) the four anchors in the corners of the room and (b) all the 12 anchors reported in Fig. 1.

distance error etot is limited, whereas the algorithm distance error ealg is not negligible. VI. C ONCLUSION In this paper, we have analyzed the accuracy of indoor localization based on RSS measurements collected by a WSN. The accuracy of two classes of low-computational-effort algorithms based on the centroid concept, which are called WCL and REWL, was analyzed. The measurement system was deployed in a real indoor environment, and by the online running of the adopted algorithms, it provided the estimated position of a target node in different test points inside an observation field. At first, we characterized a wireless propagation channel using a model largely adopted in the literature. We showed that this model is affected by a quite high relative bias and standard uncertainty. Thus, we might expect that the error increases as the distance from the anchors increases. This is most likely due to the severe propagation conditions of the indoor radio channel, i.e., affected by the reflections of the signals against the walls, the floor, and the ceiling. Moreover, we noticed that the information carried by each anchor strongly depends on the anchor position. Thus, for all

PIVATO et al.: ACCURACY OF RSS-BASED CL ALGORITHMS IN INDOOR ENVIRONMENT

the considered localization algorithms, a growth of the anchor number does not necessarily improve measurement accuracy, i.e., conversely to what we would expect. Although the error introduced by the analyzed algorithms is not negligible, the measurement uncertainty is mainly due to the noise associated to the wireless propagation channel model. In any case, the measurement uncertainty is as high as few tens of percent of the size of the observed indoor environment. Although we cannot claim that this paper has provided the ultimate answer to all the questions related to RSS-based localization in an indoor environment, in our opinion, it offers some interesting insights on the topic. To the best of our knowledge, this paper first points out the relationship between absolute and relative distance errors, highlighting how the RSS uncertainty tends to propagate as a relative distance uncertainty. In addition, starting from the experimental data, we suggest that the noise component of the error is inversely proportional to the square root of the product of the anchor number and the regression coefficient of the channel propagation model. We also analyzed the uncertainty introduced by the use of approximated localization algorithms, such as WCL and REWL. In particular, we found that the error introduced by the algorithm is usually negligible compared with the uncertainty due to propagation channel model noise; nevertheless, it can become significant when the number of anchors increases. A PPENDIX A E QUIVALENCE B ETWEEN REWL AND WCL A LGORITHMS Considering the path-loss model given by (1) and assuming the noise component w negligible, the RSS experienced by the target at distance di from anchor ai can be expressed as   di RSSi = RSS0 − 10η log . (A.1) d0 According to (A1), the maximum RSSmax value of the RSS corresponds to the minimum distance dmin between the target and the anchor node, i.e.,   dmin RSSmax = RSS0 − 10η log . (A.2) d0 Subtracting (A1) from (A2) and replacing (1), we obtain   d n  10η log d i min × ai (1 − λ)

. (A.3) pˆ = i=1  n d 10η log d i min (1 − λ) i=1

From which, using the properties of logarithms, we have the following:   10η log(1−λ) n  di × a i dmin pˆ = i=1 n  . (A.4)   di 10η log(1−λ) i=1

dmin

Equation (A4) reduces to (7), defining g = 10η log(1 − λ).

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IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 60, NO. 10, OCTOBER 2011

Paolo Pivato (S’05) received the M.Sc. degree in telecommunication engineering from the University of Trento, Trento, Italy, where he is currently working toward the Ph.D. degree in embedded electronics and computing systems with the Department of Information Engineering and Computer Science, University of Trento. His main research interests include localization in wireless sensor networks and embedded system design and development.

Luigi Palopoli (M’04) received the M.Sc. degree in computer engineering from the University of Pisa, Pisa, Italy, in 1992 and the Ph.D. degree in computer engineering from Sant’Anna School of Advanced Studies of Pisa, Pisa, in 2002. He is an Assistant Professor of computer engineering with the University of Trento, Trento, Italy. His main research interests include embedded system design, particularly with resource-aware control design and adaptive mechanisms for quality-of-service management. Dr. Palopoli has served in the Program Committee of different conferences in the area of real-time and control systems.

Dario Petri (F’09) received the M.Sc. (summa cum laude) and Ph.D. degrees in electronics engineering from the University of Padova, Padova, Italy, in 1986 and 1990, respectively. He is currently the Head of the Department of Information Engineering and Computer Science, University of Trento, Trento, Italy. He is the author or coauthor of over 200 papers published in international journals or proceedings of peer-reviewed international conferences. His research interests include measurement science and technology, particularly on data-acquisition system design and testing, embedded system design and characterization, fundamentals of measurement theory, uncertainty evaluation methods, statistical inference methods, application of digital signal processing to measurement problems, and measurement for quality management systems. Dr. Petri was the Chair of the Italian Ph.D. School on Measurement and Information Society of the Italian Society of Electrical and Electronic Measurement (GMEE) from 2002 to 2005, of the Italian Research Line on Measurement for the Information Society of GMEE from 2002 to 2008, and of the Italy Chapter of the IEEE Instrumentation and Measurement Society from 2006 to 2010. He has been a Cofounder and the General Chair of the Ph.D. School of the International Measurement University of the IEEE Instrumentation and Measurement Society and General Chair of various international conferences and workshops.He is also a member of the Administrative Committee of the IEEE Instrumentation and Measurement Society. He is currently the Vice Chair of the IEEE Italy Section, which gather almost 5000 researchers from Italian universities and companies in the area of electrical and information engineering, and the Vice Chair of the GMEE, which gather researchers from universities, metrological institutes, and companies in the field of measurement and instrumentation. He is an Associate Editor of the IEEE TRANSACTIONS ON I NSTRUMENTATION AND M EASUREMENT .