ARTI: An Adaptive Radio Tomographic Imaging System

Transcription

1 1 ARTI: An Adaptive Radio Tomographic Imaging System Ossi Katiokaio, Riku Jäntti Senior Member, IEEE and Nea Patwari Member, IEEE Abstract Radio tomographic imaging systems use received signa strength measurements between static wireess sensors to image the changes in the radio propagation environment in the area of the sensors, which can be used to ocaize a person causing the change. To date, spatia modes used for such systems are set a priori and do not change. Imaging and tracking performance suffers because of the mismatch between the mode and the measurements. Coecting abeed training data requires intensive effort, and the data degrades quicky as the environment changes. This paper provides a means for a radio tomographic imaging system to bootstrap to improve its spatia modes using unabeed data, iterativey improving itsef over time. A coection of tracking fiters are presented to improve the accuracy of image and coordinate estimates. This paper presents an onine method to use these estimates to instantaneousy update spatia mode parameters. Further, a smoothing method is presented to fine-tune the mode with a given finite atency. The deveopment efforts are evauated using simuations and vaidated with rea-word experiments conducted in three different environments. With respect to another stateof-the-art radio tomographic imaging system, the resuts suggest that the presented system increases the median tracking accuracy by twofod in the most chaenging environment and by threefod when the mode parameters are trained using the smoothing method. I. INTRODUCTION In received signa strength (RSS)-based device-free ocaization (DFL) systems, a wireess network is depoyed in an area to be monitored. Each device in the network broadcasts packets and stores the RSS received from the other devices in the network. When peope are ocated or move in the environment, they modify the way radio signas propagate, which is observed in the RSS measurements of the sensors in ways that can be used to ocate and monitor them [1]. Since, in this type of system, the ony source of information is the RSS provided by the radio modue of the nodes, the transceivers are commony referred to as sensors, and the network as a radio frequency (RF) sensor network []. As an exampe, such systems have been expoited for residentia monitoring [3], ambient assisted iving [], and miitary purposes [5]. Accurate ocaization is dependent on an accurate mode for RSS measurements. However, the way in which RSS is a function of the ocations of peope is highy variabe, dependent on the environment, the frequency channe, and the way in which Copyright (c) 15 IEEE. Persona use of this materia is permitted. However, permission to use this materia for any other purposes must be obtained from the IEEE by sending a request to pubs-permissions@ieee.org. Ossi Katiokaio and Riku Jäntti are with the Department of Communications and Networking, Aato University, Schoo of Eectrica Engineering, Espoo, Finand (emai:{name.surname}@aato.fi). Nea Patwari is with University of Utah, Department of Eectrica and Computer Engineering. emai: npatwari@ece.utah.edu mutipath waves interact with the environment and the peope within it [], [6], [7], [8], [], [9]. There are two widey used approaches to mode RSS and to perform ocaization: fingerprinting [1], [11], [1], and mode-based approaches [13], [1], [15], [16]. Fingerprinting methods require a database of training data abeed with a person s ocation, as the person moves to each possibe ocation in the area. During runtime, the current set of RSS measurements are compared to those in the database to estimate the current ocation. Instead of ocation-abeed training data, mode-based approaches use an a priori spatia statistica mode for the changes in RSS with respect to the ocations of the sensors and person. Locaization is typicay performed via imaging [13], [1] or sequentia Monte Caro [16], [17] methods. With sufficient abeed training data, fingerprinting methods are abe to achieve high accuracy, athough performance degrades exponentiay as the environment is atered [1]. Mode-based approaches can be depoyed quicky, but the mismatch between the a priori mode and the actua RSS changes observed as a function of ocation resuts in degraded performance. The paper focuses on mode-based approaches and we refer to them as RF tomography systems. In this paper, we present Adaptive Radio Tomographic Imaging (ARTI), a mode-based approach which bootstraps to improve its mode over time. There is a chicken-andegg probem in adapting ink RSS modes: ocation estimates using generic a priori modes are variabe and inaccurate, yet finding an accurate mode for any particuar ink requires accurate ocation estimates as abes for RSS data. ARTI soves this probem by appying a combination of 1) fitering for the RF tomographic imaging and tracking estimates, ) RSS modeing, and 3) new onine and batch-processing agorithms to adjust mode parameters. The resut is that ARTI overcomes the need for ocation-abeed training data and is capabe of providing extremey accurate ocaization. ARTI operates as iustrated in Fig. 1. In short, the system acquires RSS measurements r from S sensors of the wireess network and weights the measurements in the adaptive measurement unit. The weighted and mean-removed RSS measurements y are inputted to the RTI unit to form a discretized propagation fied image z i of the monitored area. Thereafter, z i are fitered and the person s position z t is estimated from the fitered images x i. A Kaman fiter is used to track evoution of the target s state x t which is used by the onine estimator unit to recursivey estimate the reference RSS vaue µ and expected direction of RSS change w. The smoothing/batch-training unit cacuates smoothed estimates of x i and x t which are then used by a batch-training agorithm to estimate parameters of the system.

2 !,"! SMOOTHING / BATCH-TRAINING $ % &,$ % ', ( % RF sensor network Onine estimator!,"! $ % & # Adaptive! " Image! " Estimate! " % "#!! Target $! measurement RTI KF position KF unit " "!#$,%!#$ " " #!$%,&!$% Fig. 1: System overview of ARTI TABLE I: Major notations Parameter Description r,c (k) RSS of ink on channe c at time k µ,c and w,c Reference RSS and weight of measurement system y k Input measurement vector to RTI at time k z i k and zt k Image and ocation measurement x i k and xt k Estimate of image and target states φ,c and λ,c Parameters of RSS mode for ink and channe c F and H Transition and measurement matrix Q and V Process and measurement noise The rest of the paper is organized as foows. In the foowing section, the reated work is discussed. Thereafter, the required background information is introduced and motivation for the work is presented. In Section IV, the components of ARTI are presented. In Section V, the conducted experiments are presented, experimenta findings are discussed and the system performance is evauated using simuations. In Section VI, the deveopment efforts are vaidated using data from three different environments and thereafter, concusions are drawn. In Tabe I, major notations of the paper are summarized. II. RELATED WORK RF tomography systems commony ocaize the person using an imaging approach referred to as radio tomographic imaging (RTI) [13], [1] or with a Bayesian inference approach which is typicay soved using sequentia Monte Caro methods (SMC) [17], [7]. The benefit of RTI is that it is computationay efficient, it provides a goba soution and the used spatia mode ony requires information regarding the size of the eiptic region where the person infuences the RSS, which we ca the sensitivity region. As a drawback, the tempora RSS changes are not accounted for in the tracking agorithm and information can be ost in the two-step process to first estimate the image and then the ocation. The benefit of SMC is that the tempora evoution of the measurements are directy reated to the kinematic state of the person. However, SMC is computationay more demanding, it ony gives a oca soution that can converge to a wrong trajectory and it requires a more detaied spatia mode to reate the RSS measurements to person s kinematic state, geometry and eectrica properties. In this paper, we deveop an image fiter for RTI that is used to track evoution of the propagation fied. In this way, information how the person atered the propagation fied at the previous time instant can be incuded to the tracking agorithm. Aso, smoothing fiters are presented so that the entire time horizon can be taken into account when estimating unknown states of the system. Imaging based approaches typicay rey on a Kaman fiter to track evoution of the target state, that is, coordinates and veocity of the person [9], [18], [19], [], [1]. In this paper, a Kaman fiter is aso used to track the image state. This improves the quaity of noisy images, it enabes to contro the deay in image estimates and we known smoothing fiters can be used to enhance the images even further. Imaging systems that use RSS variance [18], [1], kerne distance methods that use short- and ong-term RSS histograms [19], [], and channe diversity methods that average the RSS across the set of used channes [8], [9] a introduce a significant deay in the images because the measurements are based on a window of RSS sampes. Using RTI and the image fiter, the system can be designed so that the deay in the images is smaer than with the aforementioned methods. The used spatia mode reates RSS measurements to the person s ocation, geometry and eectrica properties and it dictates the performance of RF tomography systems. RTI uses a very simpistic mode that ony requires knowedge about the size of the sensitivity region [13]. On the other hand, SMC methods typicay rey on more detaied empirica modes such as the exponentia [17], magnitude [] or exponentia- Rayeigh [3] modes. Theoretica modes have aso been deveoped based on diffraction theory [15], [16] and singebounce refections []. If the mode parameters are propery tuned and in ine-of-sight (LoS) conditions, it has been shown that SMC methods outperform RTI [17] and the more detaied the mode is, the higher the tracking accuracy is [], [3], [16]. However, many of the aforementioned modes have been derived and vaidated ony in LoS conditions and expoiting

3 3 them in chaenging environments is difficut. The reason being, as the person obstructs the imaginary ine connecting the TX-RX pair, which we ca the ink ine, the RSS can increase or remain unchanged rather than decrease [8], [], [9]. In addition, the sensitivity region is unique for different inks [9]. These two empirica findings contradict with the modes presented in iterature because they commony assume: i) a decrease in RSS is observed when the ink ine is obstructed; ii) the parameter that tunes size of the sensitivity region is assumed constant. To overcome this imitation, we extend the exponentia mode in the context of RTI by estimating the magnitude and direction of RSS change onine and use batchtraining to fine-tune parameters of the mode. This approach is shown to be extremey effective, enabing high accuracy tracking in very difficut environments. In order for RF sensor networks to function, they require access to caibration data, i.e., RSS measurements that are not atered by the presence of a person. Typicay, measurements are gathered during a vacant period and mean of the caibration data is used as the reference RSS vaue during operation 1. However, it is not aways possibe to coect such caibration data, and the reference vaue can aso change over time [3], [], [5], [19]. In reated iterature, an exponentiay weighted moving average (EWMA) has been used to update the reference vaue and to make the system adaptive [3], [7], [19]. The drawback of using EWMA is that if the person remains stationary for a ong time period, the EWMA wi sowy converge to the current vaue and the person wi bend in to the noise of the estimated images making ocaization impossibe [3], [19]. This issue has been addressed by ony updating the reference RSS for inks that are far away from the person [] or by identifying the inks that are not atered by the person [7], [5]. We expand the work in [] by deveoping a ogic that makes the decision about parameter update. If the conditions are satisfied, the reference RSS is estimated onine using EWMA and ony inks that are far away from the estimated position are updated. On the other hand, when the person is cose to the ink ine, the magnitude of RSS change is estimated using EWMA and based on the vaue, the used measurement mode is updated. A. Preiminaries III. BACKGROUND We consider scenarios where S wireess sensors are depoyed in the monitored area. Each sensor broadcasts and receives packets from other sensor of the network. The sensors form L unique inks that are programmed to communicate over C channes. A ink is represented with a -tupe (, c) where is the ink and c the channe identifier. The monitored area is discretized using a grid of N voxes. The position of voxe n is denoted as p n = [x n y n ] T where x n and y n are coordinates of the voxe. Correspondingy, the coordinates of TX and RX of ink are denoted as p tx and p rx in corresponding order. 1 The reference vaue is not aways the mean. For exampe, [7] uses a Gaussian distribution and [19] uses a ong-term RSS histogram to describe the reference RSS measurements. The sensors communicate in TDMA fashion and the transmission sequence is based on the sensors buit-in ID numbers. One TDMA cyce consists of S transmissions, one from each sensor. After the cyce, the sensors switch synchronousy to the next frequency channe found in a ist predefined by the user and a new TDMA cyce is started. The TDMA cyces are sequentia, and a transmission from each sensor on each channe forms a communication round consisting of S C transmissions. After the communication round, the sensors switch to the first frequency channe on the ist and a new communication round is started. B. Radio Tomographic Imaging The objective of RTI is to estimate changes in the propagation fied of the monitored area and to ocate the person causing the change. This objective is fufied by monitoring the changes in RSS and forming a discretized propagation fied image using a projection matrix. The mean-removed RSS measurements for ink on channe c can be expressed as r,c (k) = r,c (k) µ,c (k). (1) where r,c (k) is the measured RSS and µ,c (k) the reference RSS vaue. In the discretized RTI mode, it is assumed that r,c (k) is a inear combination of the changes in each voxe pus noise [1] N r,c (k) = [a,n b n,c (k)] + η,c (k), () n=1 where b n,c is the RSS change in voxe n on channe c, a,n the weight of voxe n for ink, N the number of voxes and η,c (k) the measurement noise. The weighting how each voxe n impacts the RSS change of each ink is described by a geometrica eipse mode a,n = d 1/ e,n/λ, (3) where d = p tx p rx is the ink ength and denotes the Eucidean norm,,n = p tx p n + p rx p n d is excess path ength of voxe n with respect to ink and λ is decay rate of the mode defining sensitivity region of the ink. Various weighting modes have been proposed in the iterature and the readers are referred to [6], [7] and the references therein for detais about other weighting options. RTI systems that expoit channe diversity weight the channe measurements using y,c (k) = w,c (k) r,c (k), () where w,c (k) is a scaar weight. When a inks of the RF sensor network are considered, the changes in the propagation fied can be modeed as y c (k) = Ab c (k) + η c (k), (5) where y c R L 1 and η c R L 1 are the weighted measurements and noise of the L inks, b c R N 1 is the Typicay, RTI systems reduce a ink s muti-channe RSS measurements to a scaar vaue by weighting and averaging, i.e., y (k) = 1 C C c=1 w,c(k) r,c (k) [8], [3], [].

4 [m] RSS [db] sampe [k] (a) RSS vs. time RSS [db] r,c ( ),c = 17 g,c ( ),c = 17 r,c ( ),c = g,c ( ),c = [m] (b) RSS vs. Fig. : r,c (k) and g,c (k; θ,c ) as a function of time in (a) and as a function of in (b) radio tomographic image to be estimated, and A R L N is the weight matrix where each coumn represents a singe voxe of the image and each row the weight of each voxe for that particuar ink. Estimating the image vector b c given y c is an i-posed inverse probem and a reguarized east-squares estimator is given by [8] z i (k) = Πy c (k), Π = ( A T A + γc 1) 1 A T, where γ is a reguarization parameter which can be tuned to emphasize either the prior on the image covariance or the measurement. The eements of covariance matrix C are cacuated using an exponentia spatia decay [8] (6) {C} m,n = e pm pn /δ, (7) where δ is the correation distance, and m and n denote the voxe indexes. Aternative reguarization methods are possibe [9] and improved inear estimators can be deveoped when better noise modes are avaiabe [1]. From the estimated image z i (k) R N 1, a person can be ocaized by finding voxe n with highest intensity z t (k) = [x n y n ] T, where n = arg max z i (k). (8) In this paper, we ony consider ocaizing a singe person. Mutipe target tracking is not within the scope of this paper, and the readers are referred to [3], [31] and the references therein for further detais. However, we wish to point out that ARTI enhances the accuracy of the images and it woud aso increase the performance of RTI systems that are capabe of ocaizing more than one person. C. Motivation In reated iterature, the mean-removed RSS measurements are commony modeed using an exponentia mode [17] g,c (k; θ,c ) = E[r,c (k)] g,c (k; θ,c ) φ,c e (k)/λ,c, (9) where θ,c = [ φ,c λ,c ] are parameters of the mode for which φ,c defines the magnitude and direction of RSS change when the person is on the ink ine and λ,c is a parameter that contros the decay rate with respect to excess path ength (k). As an exampe, r,c and g,c for two different channes of the same ink are iustrated as a function of time in Fig. a and as a function of in Fig. b. For channe 17, φ =.16 and λ =.68 whereas for channe, φ = 8.17 and λ =.35. Since the mode parameters differ between inks and channes, using fixed vaues for them imits the achievabe accuracy of RF tomography systems. To overcome this imitation, we deveop an onine estimator for φ,c in this paper and update the weigthing in Eq. () correspondingy. Moreover, batch-training is used to fine-tune the estimates of φ,c and λ,c which can then be used in the future. A. Linear State Space Modes IV. METHODOLOGY To define the probem of tracking, consider evoution of the state sequence given by x k = Fx k 1 + q k 1, (1) where x k is state of the system at time step k, F the transition matrix describing dynamics of the system and q k 1 N (, Q k 1 ) the process noise. The objective of tracking it to recursivey estimate x k from measurements z k = Hx k + v k, (11) where H is the measurement mode matrix and v k N (, V k ) the measurement noise. In this paper, we track both the state of the voxes and target. The voxe state is composed of voxe intensity and its derivative. The target state is composed of the person s ocation and veocity. Such systems can be modeed using a

5 5 Agorithm 1: ARTI agorithm for k = 1 : K At time instant k z i k = Πy k, where y k = w c [ r c(k) µ c ] Form meas. and compute image using (6) [x i k, Pi k ] = kamanfiter(xi k 1, Pi k 1, zi k ) Estimate image state with (17) and (18) z t k = [xn yn ] T, where n = arg max H i x i k Estimate position from fitered image [x t k, Pt k ] = kamanfiter(xt k 1, Pt k 1, zt k ) Estimate target state with (17) and (18) if z t k Ht F t x t k 1 < Tn and [ẋt k ẏk t ] > Ts Condition meas. residua and speed on threshods [φ c, µ c, w c] = estimator(φ c, µ c, [x t k yk t ]T ) Update reference RSS and weight used in (1) and () end end Agorithm : [φ c, µ c, w c] = estimator(φ c, µ c, p k ) for = 1:L = p tx p k + p rx p k p tx For ink p rx Compute excess path ength if λ, φ,c = αφ,c + (1 α)( r,c (k) µ,c ), end Person is cose to ink ine, update φ,c if > λ, µ,c = αµ,c + (1 α) r,c (k), end Person is far away from ink ine, update µ,c w,c = sgn{φ,c } end denotes eement-wise vector product, the Eucidean norm, ( ) T the transpose and sgn{ } the sign function discrete white noise acceeration (DWNA) mode where the first derivative of the system is perturbed with a zero-mean white acceeration sequence. The transition matrix, process noise and measurement mode of a singe dimension DWNA mode are [3, Ch. 6] [ ] [ 1 dt 1 ] [ ] F = Q = 3 dt3 1 T dt 1 1 H = (1) 1 dt dt where dt is the samping interva. The image state can be expressed as [ x i x i = 1 x i... x i N ẋ i 1 ẋ i... ẋ i N ], (13) where x i j denotes intensity and ẋi j intensity change rate of voxe j. The transition matrix, measurement mode, and noise processes of the imaging system are F i = F, Q i = q i Q, H i = H, V i = v i. (1) Respectivey, the target state can be expressed as x t = [x t ẋ t y t ẏ t ] T, (15) where x t and y t denote position and ẋ t and ẏ t veocity of the target in the Cartesian coordinate system. The transition matrix, measurement mode, and noise processes of the target system are [ ] [ ] F F t Q = Q F t = q t Q [ ] H H t 1 = 1 H B. Kaman Fiter V t = [ ] v t v t. (16) In case F and H are inear, time-invariant and the noise sequences q k 1 and v k Gaussian, the Kaman fiter yieds the optima soution to the tracking probem in the east squares sense. The recursion of the fiter can be divided into the prediction stage [3, Ch. 5.] x k = Fx k 1 P k = FP k 1F T + Q. (17) Thereafter, the state and covariance are updated when measurement z k becomes avaiabe using the foowing recursion S k = HP k HT + V K k = P k HT S 1 k x k = x k + K k(z k Hx k ) P k = P k K ks k K T k. (18) The equations to compute covariance P k and Kaman gain K k are independent of the measurements impying that the sequence coud be cacuated beforehand and that they converge to a constant, i.e., P k P and K k K. Thus, the N voxes can share the same covariance matrix whie having independent states. This aows us to compute the prediction and update stages using matrix mutipies and additions, and the inversion in Eq. (18) is cacuated ony once. This reduces the computationa overhead notaby with respect to a soution with N independent fiters running in parae. In the experiments, the image fiter is initiaized using the first created image and the change rate is set to zero, i.e., x i 1 = [ z i 1 N 1] T. The covariance is initiaized as P i 1 = I, where I is a unit matrix. Correspondingy, the target state is initiaized using the position estimate of the first image given by Eq. (8) and veocity is set to zero, i.e., x t 1 = [ x j y j ] T with covariance P t 1 = I. C. Onine Estimator It is we known that the steady-state channe characteristics change in time if the surrounding environment is atered [1], [7], [5]. In ong-term depoyments and in domestic environments this is inevitabe as doors and windows can be opened or cosed, daiy commodities are consumed and moved, and furniture might be reocated or repaced [3], [], [1]. Under such conditions, it is mandatory to estimate the reference RSS µ,c onine. We have aso identified that if φ,c used in Eq (9) is known for each channe and ink, it significanty improves the system performance. Since the mode defined in Eq. (3) ony requires knowedge about size of the sensitivity region, we do not need to know the exact

6 6 vaue of φ,c, it is sufficient to know the expected direction of RSS change when the person obstructs the ink ine. Thus, we estimate φ,c onine and set the weight used in Eq. () as w,c sgn{φ,c }, where sgn{ } denotes the sign function. The pseudocode of ARTI is presented in Agorithm 1 and the onine estimator for µ,c and φ,c in Agorithm. The ogic to update µ,c and φ,c is straightforward. First, we compute the measurement residua z t k Ht F t x t k 1 and ony update the parameters if the current position measurement is inine with the kinematic mode estimate. Sma residua vaues indicate that the state estimate can be trusted. Second, the parameters are updated ony when the target is moving. If the person is stationary, the current ocation estimate can be inaccurate which woud ead to incorrect estimates of µ,c and φ,c. In this case, the future ocation estimates woud aso contain this error. If the two conditions hod, µ,c is updated when the person is far away from the ink ine ( > λ). Otherwise, φ,c is updated to capture the expected direction of RSS change when the person is near the ink ine ( λ). In the experiments, the reference RSS is initiaized using µ,c () = 1 T +1 k= T r,c(k), where r,c (k) are gathered during an initia training period when the monitored area is vacant. In Section VI-D, we discuss the scenario where µ,c is initiaized without a training period. The weight used in Eq. () is initiaized as w,c () = sgn{φ } and φ = 1e 3. The initia vaue of φ is seected negative because it is more ikey that attenuation is measured when the person obstructs the ink ine (see Section V-B and Tabe III) and a vaue cose to zero is used so that the estimate changes its sign rapidy if φ,c >. D. Smoothing Fiters Sometimes, it is of interest to estimate states of the system for each time instant k conditioned on a the measurements up to time step K, where K > k. This probem can be soved with Bayesian smoothing, which in genera, improves the state estimates and decreases the covariance. One Bayesian smoother is the discrete-time Kaman smoother, aso known as the Rauch-Tung-Striebe smoother (RTSS) and it can be used for computing smoothed estimates of the mode given in Eq. (1). The smoothed state estimate x k and covariance P k can be cacuated with the foowing recursion [33, Ch. 8] P k+1 = FP kf T + Q G k = P k F T (P k+1 ) 1 x k = x k + G k ( x k+1 Fx k ) P k = P k + G k ( P k+1 P k+1 )GT k, (19) where x k and P k are the Kaman fiter estimates for the mean and covariance, and G k is the smoother gain at time step k. The difference between the Kaman fiter and RTSS is that the recursion in the fiter moves forward whereas in the smoother backwards. In the smoother, recursion starts from the ast time step K with initia estimates x K = x K and P K = P K. Another possibiity for smoothing is to use a two fiter based smoother (TFS) in which a Kaman fiter is used in the forward recursion and an information fiter is used in the backward recursion [3]. The prediction step of the information fiter is given by K b k = M b ( k+1 M b k+1 + Q 1) 1 m k = ( FT I K b k) m b k+1 M k = ( () FT I K b k) M b k+1 F, where I is the identity matrix. The information vector m b k and information matrix M b k are updated using m b k = m k + HT R 1 z k M b k = M k + HT R 1 H. (1) The smoothed state estimate x k and covariance P k is a combination of the forward and backward fiter outputs G k = P k M ( k I + Pk M ) 1 k P k = ( (P k ) 1 M ) 1 () k x k = (I G k ) x k + P k m k, where x k and P k are the Kaman fiter estimates for the mean and covariance and m k and M k are the predicted information vector and information matrix. As in RTSS, recursion starts from the ast time step K with initia estimates x K = x K and P K = P K. In this paper, three different agorithms for smoothing the state estimates are considered and they are presented in the foowing. The agorithms output smoothed estimates of the target state x t k and covariance P t k. 1) RTSS-target (RTSS-T): The state estimates of the tracked target are smoothed using RTSS. The state space modes are given in Eqs. (15) and (16) and the state estimate and covariance used in Eq. (19) are x k = x t k and P k = P t k. ) RTSS-image and target (RTSS-IT): The estimated images are smoothed using RTSS. The state space modes are given in Eqs. (13) and (1) and the state estimate and covariance used in Eq. (19) are x k = x i k and P k = P i k. After smoothing the images, new position estimates are cacuated from the smoothed images and a Kaman fiter is used to track the target state x t k and covariance Pt k. Thereafter, the target state and covariance are smoothed with RTSS as in the previous agorithm to obtain x t k and P t k. 3) TFS-image and target (TFS-IT): The agorithm is the same as presented in Agorithm 1 with three differences. First, the recursion runs backward in time starting from time sampe K. Second, the image Kaman fiter is repaced by the information fiter given in Eqs. () and (1) and by the TFS given in Eq. (). The initia estimates of the information fiter are m b K = N and M b K = [3]. Third, the target Kaman fiter uses the position estimates cacuated from the smoothed images. At the end of the recursion, the state estimates of the tracked target are smoothed using RTSS to obtain x t k and P t k. This agorithm differs notaby from the other two since µ,c and φ,c are re-estimated in the backward recursion. E. Training Training parameters of the exponentia mode requires the mean-removed RSS measurements r,c (k) and excess path

7 7 (a) Open environment (Ex. 1) (b) Apartment depoyment (Ex. and 3) (c) Through-wa scenario (Ex. ) Fig. 3: The three experiment environments. Experimenta ayout of the apartment and through-wa environments are iustrated in Fig. 9 TABLE II: Experimenta Parameters J(θ,c ) = K X [r,c (k) g,c (k; θ,c )], () k=1 where g,c (k; θ,c ) is the exponentia mode defined in Eq. (9). In this paper, we use a Neder-Mead simpex agorithm [35] to find the minimum of J(θ,c ). The trained parameters are used when re-initiaizing the system. In other words, φ,c is used as the initia estimate in the onine estimator, i.e., φ = φ,c and w,c () = sgn{φ }. On the other hand, λ is substituted with λ,c in Eq. (3) to update the weighting for each ink, channe and voxe. Thereafter, Π is cacuated using Eq. (6) and the projection matrix becomes unique for each frequency channe. As an exampe, r,c and g,c with the trained mode parameters is iustrated in Fig.. For channe 17, φ,c =.16 and λ,c =.68 and these vaues are used for this channe and ink when re-initiaizing the system. V. E XPERIMENTS In this section, the experimenta setting and conducted tests are introduced. Thereafter, empirica findings how mode parameters φ and λ differ between inks and environments is presented. At the end of the section, the presented system is numericay evauated using simuations. A. Experiment Description The used wireess sensors are Texas Instruments CC531 USB donges, operating at the maximum transmit power (+.5 dbm) [36]. The IEEE standard [37] specifies 16 channes (c [11,..., 6]) within the. GHz ISM band and they are 5 MHz apart, having a MHz bandwidth. The sensors communicate in TDMA fashion on mutipe frequency ESTIMATOR FILTERS rx tx rx (k) = kptx (3) pk k + kp pk k kp p k. Given r,c (k) and (k), parameters θ,c = φ,c λ,c of the exponentia mode can be estimated by minimizing the cost function RTI ength (k) of the person with respect to ink. Using the smoothed target state estimates x tk, (k) with respect to ocation of the person pk = Ht x tk is cacuated as Parameter p γ δ λ α Tr Tv qi vi qt vt Vaue Description Voxe width [m] Reguarization parameter Correation distance [m] Excess path ength [m] Smoothing factor of EWMA Residua threshod [m] Veocity threshod [m/s] Process noise of image fiter [db/s ] Meas. noise of image fiter [db] Process noise of target fiter [m/s ] Meas. noise of target fiter [m] channes as expained in Section III-A. In each packet, the sensors incude their ID and the most recent RSS measurements of the packets received from other sensors of the network. If a packet is dropped, the next sensor in the schedue transmits after a backoff time, thus increasing the network s toerance to packet drops. The communication protoco is expained in further detai in []. In experiment 1, shown in Fig. 3a, 3 sensors are depoyed on the perimeter of an open area (7 m ). The sensors are paced on podiums at a height of one meter. The sensors are programmed to communicate on channes 11, 17,, and 6 so as to cover the entire span of avaiabe frequencies. During the test, a person waks at constant speed aong a rectanguar path and the trajectory is covered twice. Markers are paced inside the monitored area for the test person to foow, whie a metronome is used to set a predefined waking pace. In this way, each coected RSS measurement can be associated to the true ocation of the person. In experiments and 3, shown in Fig. 3b, 33 sensors are depoyed in a singe-foor, singe-bedroom apartment (58 m ). Most of the sensors are attached on the was of the apartment, whie a few of them are paced esewhere, e.g., on the edge of a marbe counter in the kitchen or on the side of the refrigerator. The antennas of the sensors are detached from the was by a few centimeters to enhance the ocaization accuracy [3]. In experiment, the sensors are programmed to communicate on channes 15,, 5, and 6 in order to avoid the interference generated by severa coexisting Wi-Fi

8 8 1 1 Open env. Cumuative probabiity Apartment Through-wa Open env. Cumuative probabiity Apartment Through-wa φ (a) CDF of φ λ (b) CDF of λ Fig. : Empirica CDFs of φ and λ in the three environments iustrated with markers and dashed ines. In the figures, fitted modes are iustrated with soid coor ines. networks found in the neighboring apartments, which woud increase the foor noise eve [38]. In experiment 3, the sensors are programmed to communicate on a 16 frequency channes. In both experiments, a person is either standing sti at a predefined ocation or waks from one ocation to another with constant speed. The trajectory is covered once. Experiment differs from the other experiments since it is a through-wa experiment as shown in Fig. 3c. In the experiment, 33 sensors are depoyed around a ounge room, outside the was of the room, covering an area of 86 m. The sensors are set on podiums at a height of one meter and they are programmed to communicate on a 16 frequency channes. In the experiment, a person waks aong a predefined path at constant speed. The path is covered six times. On average, the time interva between two consecutive transmissions is dt k = t k t k 1 =.9 ms. If S = 3 and C = as in Ex. 1, one TDMA cyce asts dt c = 3 dt k = 87 ms and one communication round dt r = dt c = 38 ms. The image and target fiters use dt = dt c. Parameters used in the experiments are given in Tabe II. B. Experimenta Findings To get an understanding how parameters φ and λ of the exponentia mode defined in Eq. (9) vary between different inks and environments, g,c (k; θ,c ) is fitted to r,c (k) using known ocation of the person. Links that were not intersected by the person during the experiment are omitted from the evauation. Thereafter, we-known probabiity distribution are fitted to the empirica distributions to find the best match. The empirica distribution of φ cosey foows a non-standardized Student s t-distribution φ T (µ φ, σ φ, ν φ ) with ocation parameter µ φ, scae parameter σ φ and shape parameter ν φ. Correspondingy, the empirica distribution of λ cosey foows a Weibu distribution λ W(a λ, b λ ) with scae parameter a λ and shape TABLE III: Distribution parameters µ φ σ φ ν φ a λ b λ Open Apartment Through-wa parameter b λ. The empirica and fitted distributions are shown in Fig. and distribution parameters are given in Tabe III. The resuts are inine with our understanding how the signa strength behaves in various environments. In open environments and when the distance between the transceivers is sma, it is expected that the RSS measurements attenuate as the person obstructs the LoS. In the open and apartment environments, µ φ is much smaer than it is in the throughwa experiment. This indicates that it is much more ikey that attenuation wi be measured in the open and apartment environments when the person is in between the transceivers. In addition, it is more ikey in these environments that the person has a arger effect on the ink and therefore, σ φ is arger. In the through-wa environment, it is ikey that a ink is not affected by the person or that the change in RSS is sma when the person is cose to the ink ine yieding a sma shape parameter σ φ. To note, the sensor distances are on average smaer in the apartment experiment ( d =.3 m) than in the open environment ( d = 6.8 m) and there are many inks that have LoS communication. Thus, it is understandabe why µ φ is smaer and σ φ is arger in the apartment environment. Size of the spatia region where the person infuences the RSS is defined by λ. In the open environment, mutipath propagation is not as severe as in the other two environments and the person mainy effects the LoS signa. Thus, λ is sma and it does not vary much between the different inks. In cuttered environments, mutipath propagation is common and the person can aso ater the RSS by affecting the mutipath

9 9 TABLE IV: Median (and 95 th percentie) ocaization errors in centimeters ONLINE SMOOTHED Ex. 1 Ex. Ex. 3 Ex. CDRTI (1.19) (56.8) 15.7 (69.83) (68.35) ARTI w/o onine est (18.9) 18.7 (6.) (68.5).59 (88.9) ARTI 19.8 (7.75) 1.3 (5.) 1.1 (7.5) 7.91 (378.9) CDRTI, RTSS-T.9 (66.13) (5.7) 1.78 (6.93) (63.7) ARTI, RTSS-T 1.33 (36.1) 8.7 (19.3) 6.96 (18.67) 66. (56.7) ARTI, RTSS-IT 1.9 (31.6) 8. (19.6) 6.81 (16.6) 7.69 (79.6) ARTI, TFS-IT 7.81 (5.6) 7.8 (17.3) 6.1 (13.18) (38.75) components impinging on the receiver antenna. This increases size of the spatia region where the person infuences the ink and therefore, λ is arger and deviates more in the apartment and through-wa environments. C. Numerica Evauation In this subsection, the presented system is numericay evauated using the same sensor positions and trajectories as in the experiments. In the simuations, the RSS measurements are generated using the exponentia mode given in Eq. (9) and the measurements are corrupted by i.i.d. Gaussian noise, i.e., η,c (k) N (, ση) where σ η =. Parameters of the exponentia mode are drawn from φ T (µ φ, σ φ, ν φ ) and λ W(a λ, b λ ) using the distribution parameters given in Tabe III and they are assumed i.i.d. for each ink and channe. Since no tempora statistica mode is known for the changes in RSS over time due to changes in the environment other than peope, the reference RSS vaue is assumed to be constant and known (µ,c = 5 db) and it is not updated by Agorithm during simuations. The presented system is evauated with respect to channe diversity RTI (CDRTI) which averages the measurements across the entire set of used channes, i.e., y (k) = 1 C C c=1 r,c(k) µ,c (k). The simuation resuts are given in Tabe IV where the median and 95 th percentie ocaization errors are reported in centimeters for the different experiments. On average, CDRTI achieves comparative accuracy as the presented system w/o onine estimation. This is understandabe, since the Kaman fiter used for enhancing the images essentiay acts as a owpass fiter, i.e., averaging the RSS measurements on the different channes (CDRTI) is equivaent to forming the images individuay for each channe and then averaging the images together. In this respect, process noise vaue of the image fiter q i can be viewed as a smoothing parameter. Using a sma vaue (q i 1) corresponds to averaging a arge number of successive images together whereas for arge vaues (q i > 1), ony the most recent images are taken into account. With onine training enabed, ARTI outperforms CDRTI in every experiment because w,c is recursivey estimated. For CDRTI, an increase in RSS is an indication that a person is not in between the transceivers which is incorrect if φ,c >. For ARTI, the same increase can be informative and indicate the person s ocation correcty if w,c sgn{φ,c }. Let us group w,c of inks that were intersected during the experiment into a coumn vector ŵ of size M 1, where M is the number of crossed inks. For these inks, we define the true weight as w, ǫw [%] 5 3 Ex.1, open Ex., apt. (C=) 1 Ex.3, apt. (C=16) Ex., through-wa Sampe [k] Fig. 5: Error of estimating w,c. where w m = sgn{φ m } and φ m T (µ φ, σ φ, ν φ ). Now, the percentage error of ŵ can be cacuated using { ɛ w = 1% M M 1 if w m ŵ m 1 m, 1 m = (5) otherwise m=1 and it is iustrated in Fig. 5 as a function of time for the different experiments. In the open and apartment experiments, the initia estimates is incorrect for approximatey 33% of the inks whereas in the through-wa experiment for 5% indicating that the through-wa environment is significanty more chaenging than the others. The figure aso reveas that higher samping rate of the channe increases the convergence rate of ŵ which is visibe by comparing ɛ w of the apartment experiments. The samping rate is four times higher in Ex. w.r.t. Ex. 3. In the experiments, the average [ number of sampes the onine] estimator has to estimate w,c is for Ex. 1 in corresponding order. Thus, using channe diversity is a tradeoff between samping rate and avaiabe information. A arge number of channes is beneficia for ocaization purposes because the probabiity increases that at east one of the channes foows the mode. However, the cost of doing so is the ower samping rate for each channe which inevitaby effects performance of the onine estimator. Accuracy of the different smoothing fiters are aso given in Tabe IV. In genera, smoothing increases the accuracy of the state estimates because the entire time horizon is taken into account. RTSS-T improves the ocaization accuracy mainy because the effect of outiers is reduced and ag induced by the target tracking Kaman fiter is compensated for. RTSS- IT decreases the error even more because the images, from which the positions are estimated, are enhanced. In addition, RTSS-IT removes ag of the image fiter which is significant

10 1 Smoothed Fitered Measured k = 91 k = 9 k = 93 k = 9 Fig. 6: The measured z i k, fitered xi k and smoothed xi k propagation fied images in Ex. 1. In the figures, the true position of the person is iustrated with a circe and the position estimate z t k using a cross if the person is moving. Removing deay of the image fiter is ceary visibe in the open and through-wa experiments where the person is continuousy in motion. TFS-IT resuts to the best accuracy. The agorithm not ony removes the ag in image and position estimates, but it aso improves the estimates of w,c and µ,c in the backward recursion yieding better measurements y k from which the images are created. This is especiay important in chaenging environments and when the experiment duration is reativey short as is the case in the through-wa experiment. It can be concuded that in idea environments (φ,c ), channe diversity, the presented image fiter and adaptive estimator do not improve the system performance significanty. The rea benefits start to be visibe as µ φ and there are inks for which φ,c >. In cuttered and chaenging environments, such as the through-wa experiment, the importance of channe diversity increases and the system performance can be significanty improved by using the presented image fiter and onine estimator. Furthermore, the state estimates can aways be improved using the presented smoothing fiters. VI. EXPERIMENTAL VALIDATION In this section, the deveopment efforts are first quantitativey evauated after which performance of the system is presented. Thereafter, mode parameters φ,c and λ,c for the different inks and channes are estimated using data from the experiments. After the mode parameters are estimated using batch-training, the system performance is reevauated. In this section, ARTI is evauated with respect to fade eve RTI (FLRTI). FLRTI weights the different channes based on their fade eve and averages the measurements across the entire set of used channes, i.e., y (k) = 1 C C c=1 ŵ,c ( r,c (k) µ,c (k)), where ŵ,c is the fade eve based weight []. In Ex. 3, q i =.1 because in these experiments the number of used channes is four times greater than in Ex. 1. Using a ower q i vaue impies that the confidence in the mode is increased and reactiveness to new measurements is decreased which is desirabe when a 16 frequency channes are used. A. Quantitative evauation The presented system comprises of three significant advancements to increase the accuracy and performance of stateof-the-art RTI systems. First, the images are fitered using a Kaman fiter. This is beneficia because now the previous state of the propagation fied x i k 1 is taken into account. In past works, it is not considered how the person atered the propagation fied at the previous time instant and vauabe information is ost. The second benefit of the image fiter is that the images can be enhanced using we known smoothing fiters. The third advantage is that the system can be designed so that the deay in x i k is significanty ower than in systems that combine the RSS measurements on different channes by weighting and averaging [], [8]. Averaging the channe measurements over the set of used channes inevitaby introduces a deay in z i k which aso effects z t k. Length of this deay is determined by parameters of the system such as transmission interva of the

11 11 Normaized voxe intensity True Measured z i j Fitered x i j Sampe [k] (a) w/o onine estimator x [m] y [m] True w/o fitering Fitered Sampe [k] (b) w/o onine estimator Normaized voxe intensity True Measured z i j Fitered x i j Sampe [k] (c) with onine estimator x [m] y [m] True w/o fitering Fitered Sampe [k] (d) with onine estimator Fig. 7: In (a), the true, measured and fitered voxe intensity vaue without estimating w,c. In (b), the resuting coordinate estimates. In (c), w,c is estimated recursivey and in (d), the resuting coordinate estimates. sensors, number of used sensors and channes, and veocity of the person. Fitering the propagation fied images is iustrated in Fig. 6. On the top row, propagation fied images z i k at four successive TDMA cyces are shown. The position estimate z t k=91 is accurate, but at the next time instant the estimate is poor because z i k=9 does not capture the person s effect to the channe correcty. The fitered propagation fied images x i k are iustrated on the midde row, and as shown, fitering improves quaity of the images eading to an enhancement in ocaization accuracy. Essentiay, the image fiter suppresses noise of the ow quaity image stream and adapts to sowy varying changes caused by the target. The second key contribution of the presented system is the recursive agorithm that is used for estimating the reference RSS vaue µ,c and expected direction of RSS change w,c. Estimating µ,c onine is crucia for maintaining the system s abiity to ocate the target in the ong run as propagation patterns of radio signas change [], [3]. Respectivey, correct estimation of w,c enabes the reconstruction of more accurate images with higher resoution. The advantage of fitering and estimating w,c onine is iustrated in Fig. 7. The normaized intensity of a singe voxe is shown in Fig. 7a. As iustrated, the measurements are very noisy resuting to extremey bad position estimates as shown in Fig. 7b. The image fiter improves estimates of the individua voxes, enhances the image quaity and reduces the positioning errors as depicted in the figures. Estimating w,c recursivey further improves the accuracy and resoution of z i k as iustrated in Fig. 7c. Together with the image fiter, this eads to a considerabe improvement in tracking accuracy as shown in Fig. 7d. It is to be noted that the measured voxe vaues are inaccurate in the beginning of the experiment k < 5 but the recursive agorithm is quicky capabe of estimating w,c correcty. Correspondingy, the coordinate estimates are inaccurate in the beginning of the experiment (approximatey the same as w/o onine earning) but aready during the second ap, the estimated trajectory cosey foows the true trajectory as iustrated in Fig. 7d. The third contribution of the paper are the presented smoothing fiters and batch-training. The smoothing fiters presented in Section IV-D can be used to enhance the state estimates even further which might be beneficia in circumstances that do not require rea-time estimates of the target state but demand as accurate estimates as possibe. One such exampe is the presented batch-training agorithm which uses the smoothed state estimates x t k and mean-removed RSS r k to estimate parameters of the system. Smoothing the images using the TF-based smoother is iustrated on the bottom row of Fig. 6. In genera, the images and position estimates are more accurate when smoothing is appied.

12 1 TABLE V: Median (and 95 th percentie) ocaization errors in centimeters ONLINE SMOOTHED TRAINED Ex. 1 Ex. Ex. 3 Ex. frti.61 (51.1) 19.9 (19.71).38 (79.5) (.9) ARTI w/o onine est (99.81) 6.76 (1.83) 3.3 (1.6) (97.9) ARTI (8.) 1.63 (57.6) (61.9) 3.67 (36.9) frti, RTSS-T 1.19 (38.51) (133.8) 19.7 (68.1) 65.3 (169.7) ARTI, RTSS-T (36.8) 13.5 (5.67) 15.9 (1.81) 3.97 (163.13) ARTI, RTSS-IT 9.66 (36.5) 1.85 (51.35) 1. (38.35) 6.8 (17.7) ARTI, TFS-IT 7.6 (9.1) 11.3 (.85) 13.9 (3.71) 19.6 (71.8) ARTI, RTSS-T 17.3 (3.5) (5.3) (37.8) 5.35 (15.33) ARTI, RTSS-IT 16. (3.63) 15.3 (9.13) 16.9 (37.5).7 (7.83) ARTI, TFS-IT (9.55) 1.67 (.) (35.8) 19.3 (65.9) ARTI-onine 16.7 (38.7) 1.67 (5.88) (3.8) (1.1) ARTI-true 13.1 (3.88) 1. (35.66) 1.9 (8.7).57 (8.75) ǫw [%] 5 3 Ex.1, open Ex., apt. (C=) 1 Ex.3, apt. (C=16) Ex., through-wa Sampe [k] B. Experimenta Resuts Fig. 8: Error of estimating w,c. The experimenta resuts are given on rows of Tabe V. On average, FLRTI achieves high accuracy in experiments 1 3. However, in Ex., there are position estimates that are very inaccurate as indicated by the high 95 th percentie vaue. Aso, the performance in the through-wa experiment is satisfactory and the positioning error is consideraby higher than in the other experiments. Comparing these resuts with the system that does not utiize the onine estimator, one can see that the achieved accuracy of FLRTI is higher. This indicates that there is information in the steady-state RSS statistics that can be used to enhance the positioning accuracy. Therefore, the obtained resuts support the deveopment efforts of earier works that expoit channe diversity and fade eve based weighting [8], [3], [], [9]. As shown on fourth row of Tabe V, ARTI outperforms FLRTI in every experiment when the onine estimator is enabed. The 95 th percentie ocaization errors of ARTI are reativey high because in the beginning of the experiments the position estimates are poor as discussed in the previous subsection. However, the accuracy of ARTI improves consideraby as more data is acquired and as the estimates of w,c improve. The accuracy of estimating w,c is iustrated in Fig. 8, where the true weight used in Eq. (5) is estimated using the batch-training agorithm and known trajectory of the person. As shown, the percentage error ɛ w decreases as more measurements are acquired improving the accuracy of the state estimates. Resuts of the different smoothing fiters are given on rows 5 8 of Tabe V and they are inine with the simuation resuts. Thus, the reader is referred to the discussion in Section V-C where the differences and benefits of the agorithms were presented. C. Training the Mode Parameters In this subsection, the smoothed state estimates obtained in the previous subsection are used as input to the batch-training agorithm presented in Section IV-E. In addition, we consider a system that does not utiize batch-training and that soey uses the recursive estimate of φ,c obtained in the previous subsection. This training scheme is denoted as ARTI-onine in Tabe V. For comparison, we aso estimate φ,c and λ,c using the person s known ocations in order to study achievabe accuracy of the system. This training scheme is denoted as ARTI-true in Tabe V. To avoid using the same data for training and vaidation, the experiments are re-conducted. The onine ocaization accuracy with the trained mode parameters are given on rows 9 13 of Tabe V and as can be seen, the accuracy of ARTI improves as a resut of training. In genera, the more accurate the position estimates used for training are, the better the ocaization accuracy is during onine operation. Of the different training schemes, parameters trained with TFS-IT resuts to the best accuracy and it neary achieves the same performance as the system that is trained with known trajectory of the person. Given the simuation and experimenta resuts, it can be concuded that the presented system achieves high accuracy in every experiment and a significant improvement over FLRTI. Exampe trajectories of ARTI, TFS-IT in Ex. 3 and Ex. are iustrated in Fig. 9. D. Discussion The computationa overhead of the image fiter and onine estimator is sma. On average, the execution time is.1 ms with FLRTI and.5 ms with ARTI in Ex. 1 using a Matab impementation and a standard aptop equipped with a.7 GHz Inte Core i7-8mq processor and 16. GB of RAM memory. Since one TDMA cyce asts 87 ms, onine operation can be easiy guaranteed. The execution time of the smoothing agorithms are 5 µs, 396 µs and 38 µs per TDMA cyce for RTSS-T, RTSS-IT and TFS-IT agorithms in corresponding order. Thus, the higher performance of TFS-IT comes with the expense of increased computationa overhead.

13 Y [m] Y [m] 6 X [m] (a) apartment (C = 16) X [m] (b) through-wa Fig. 9: Exampe trajectories of ARTI, TFS-IT. In the figures, the true trajectory is iustrated with the soid back ine, the estimated with dashed red ine and back circes indicate the sensor ocations. ǫµ [db] 3 Ex.1 1 Ex. Ex.3 Ex Sampe [k] Fig. 1: Accuracy of estimating µ,c w/o a caibration period The used training scheme shoud be seected based on requirements of the system. If it is necessary to achieve high ocaization accuracy as quicky as possibe, then batchtraining shoud be used. In this case, the simuation and experimenta resuts support using TFS-IT. On the other hand, if the depoyed system operates over an extended period of time, the benefit of batch-training diminishes. As depicted in Tabe V, ARTI-onine aready achieves comparative performance with respect to the batch-training systems, despite the fact that the conducted experiments were reativey short. Furthermore, this difference is expected to diminish even more over ong periods of time when a rich set of RSS measurements are acquired. The deveoped system is not required to have a caibration period before the person enters the monitored area. If the system is not caibrated, the first received RSS measurement is used as the reference RSS vaue. This wi resut into the situation where the state estimates are inaccurate in the beginning of the experiment. However, after the person starts to move, the person can be correcty ocaized because the reference vaues, for inks that were initiay far away from the person, are cose to the rea reference vaues. Let us denote the reference vaue at time k without the caibration period as µ w/o,c (k) and with the caibration period as µ,c(k). The root mean squared error is cacuated as ɛ µ (k) = 1 L C L C =1 c=1 ( µ,c (k) µ w/o,c (k) ) and iustrated in Fig. 1. As shown, µ w/o,c converges to µ,c as more measurements are gathered. Thus, ong-term depoyments are not required to have a caibration period if the subject is moving and the oss of accuracy is acceptabe in the beginning of the experiment. Typicay, RF tomography systems achieve high ocaization accuracy with the expense of depoying numerous sensors in the monitored area. For exampe, the sensor density in the experiments ranges from.57 sensors/m in Ex. and Ex. 3 to.38 sensors/m in Ex.. On average, resoution of the images degrades and the ocaization error increases when the sensor number is decreased as demonstrated for exampe in [3], [9]. However, with fewer sensors the samping rate for each ink respectivey increases improving the tracking accuracy and the convergence rate of the onine estimator. On the other hand, the number of used communication channes coud be increased without decreasing the samping frequency which in turn is expected to improve the ocaization accuracy. Thus, it is not a straightforward task to evauate how much the accuracy degrades when fewer sensors are used. Simuating node remova, the median tracking error is doubed when third of the sensors are randomy removed from the different experiments and in the best case, the ocaization accuracy remains the same. The resuts impy that the remaining nodes shoud be eveny distributed to assure accurate ocaization throughout the monitored area.

14 1 VII. CONCLUSIONS This paper presents ARTI, an adaptive radio tomographic imaging system. Novety of the system are in its adaptive measurement unit and in the image fiter. Onine estimation of the mode parameters enabes the system to adapt to the intrinsic nature of the different inks, channes and environment. On the other hand, the image fiter makes it possibe to take into account tempora changes of the propagation fied. The paper aso presents different smoothing fiters and batch-training is expored to estimate unknown parameters of the system. The resuts demonstrate that ARTI achieves high accuracy in three different environments, the state estimates can be enhanced using smoothing, and improved ocaization accuracy can be achieved using batch-training. To date, research on RF tomography has mainy concentrated on deriving more accurate spatia modes since they dictate the achievabe accuracy of these systems. However, we have demonstrated in this paper that high accuracy tracking can be achieved using a coarse RSS mode and by estimating its parameters onine. Generay speaking, this paper scratches the surface of onine parameter estimation and the paper is to motivate the readers toward this area of research. The used EWMA estimators are simpistic and more advanced options are avaiabe and subjects of future research. Future research shoud answer at east the foowing questions. Is it possibe to use for exampe the mode in Eq. (9) and estimate its parameters using an extended Kaman fiter or some other non-inear fiter? What about more sophisticated RSS modes, can we estimate their parameters? If the parameter estimates diverge, is it possibe to identify these occurrences and recover from them? ACKNOWLEDGMENTS This work is funded by Doctora Programme in Eectrica Engineering at Aato University. 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15 15 [8] N. Patwari, L. Brewer, Q. Tate, O. Katiokaio, and M. Bocca, Breathfinding: A wireess network that monitors and ocates breathing in a home, IEEE Journa of Seected Topics in Signa Processing, vo. 8, no. 1, pp. 3, Feb 1. [9] J. Wison, N. Patwari, and O. G. Vasquez, Reguarization methods for radio tomographic imaging, in in 9 Virginia Tech Symposium on Wireess Persona Communications, 9. [3] M. Bocca, O. Katiokaio, N. Patwari, and S. Venkatasubramanian, Mutipe target tracking with rf sensor networks, IEEE Transactions on Mobie Computing, vo. 13, no. 8, pp , Aug 1. [31] Q. Wang, H. Yigiter, R. Jäntti, and X. Huang, Locaizing mutipe objects using radio tomographic imaging technoogy, IEEE Transactions on Vehicuar Technoogy, vo. PP, no. 99, pp. 1 1, 15. [3] Y. Bar-Shaom and X.-R. Li, Estimation with Appications to Tracking and Navigation. New York, NY, USA: John Wiey & Sons, Inc., 1. [33] S. Särkkä, Bayesian Fitering and Smoothing. Cambridge University Press, 13. [3] D. Fraser and J. Potter, The optimum inear smoother as a combination of two optimum inear fiters, IEEE Transactions on Automatic Contro, vo. 1, no., pp , Aug [35] J. C. Lagarias, J. A. Reeds, M. H. Wright, and P. E. Wright, Convergence properties of the neder mead simpex method in ow dimensions, SIAM Journa on Optimization, vo. 9, no. 1, pp , [36] Texas Instruments. A USB-enabed system-on-chip soution for. GHz IEEE and ZigBee appications. [Onine]. Avaiabe: [37] IEEE standard technica specs. [Onine]. Avaiabe: http: // [38] K. Srinivasan, P. Dutta, A. Tavakoi, and P. Levis, Understanding the causes of packet deivery success and faiure in dense wireess sensor networks, in Proceedings of the th internationa conference on Embedded networked sensor systems (SenSys 6), 6, pp. 19. Nea Patwari received the B.S. (1997) and M.S. (1999) degrees from Virginia Tech, and the Ph.D. from the University of Michigan, Ann Arbor (5), a in Eectrica Engineering. He was a research engineer at Motoroa Labs, Forida, between 1999 and 1. He is an Associate Professor in the Department of Eectrica and Computer Engineering at the University of Utah. He directs the Sensing and Processing Across Networks (SPAN) Lab, which performs research at the intersection of statistica signa processing and wireess networking. Nea is aso the Director of Research at Xandem Technoogy. He has received best paper awards from the IEEE Signa Processing Magazine (9), SenseApp (1), and IPSN (1), and the 11 University of Utah Eary Career Teaching Award. Ossi Katiokaio received the B.Sc. and M.Sc. degrees in eectrica engineering from the Schoo of Eectrica Engineering, Aato University, Hesinki, Finand, both in 11. He is currenty a Ph.D. student with the department of Communications and Networking at Aato University Schoo of Eectrica Engineering where he hods an ELEC doctora schoo position as of January 1. He is the recipient of SenseApp 1 and IPSN 1 conference best paper awards. His current research interests incude RF propagation, RSS-based ocaization and tracking, signa processing and Bayesian inference. Riku Jäntti (M - SM 7) is an Associate Professor (tenured) in Communications Engineering and the head of the department of Communications and Networking at Aato University Schoo of Eectrica Engineering, Finand. He received his M.Sc (with distinction) in Eectrica Engineering in 1997 and D.Sc (with distinction) in Automation and Systems Technoogy in 1, both from Hesinki University of Technoogy (TKK). Prior to joining Aato (formery known as TKK) in August 6, he was professor pro tem at the Department of Computer Science, University of Vaasa. Prof. Jäntti is a senior member of IEEE and associate editor of IEEE Transactions on Vehicuar Technoogy. He is aso IEEE VTS Distinguished Lecturer (Cass 16). The research interests of Prof. Jäntti incude radio resource contro and optimization for machine type communications, Coud based Radio Access Networks, spectrum and coexistence management and RF Inference.