Distance estimation using RSSI and particle filter

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Distance estimation using RSSI and particle filter Janja Svečko a,n, Marko Malajner b, Dušan Gleich b a b

Margento R&D, Gosposvetska 84, Maribor, Slovenia Faculty of Electrical Engineering and Comupter Science, University of Maribor, Slovenia

art ic l e i nf o

a b s t r a c t

Article history: Received 19 December 2013 Received in revised form 2 September 2014 Accepted 11 October 2014 This paper was recommended for publication by Dr. Q.-G. Wang

This paper presents a particle filter algorithm for distance estimation using multiple antennas on the receiver’s side and only one transmitter, where a received signal strength indicator (RSSI) of radio frequency was used. Two different placements of antennas were considered (parallel and circular). The physical layer of IEEE standard 802.15.4 was used for communication between transmitter and receiver. The distance was estimated as the hidden state of a stochastic system and therefore a particle filter was implemented. The RSSI acquisitions were used for the computation of important weights within the particle filter algorithm. The weighted particles were re-sampled in order to ensure proper distribution and density. Log-normal and ground reflection propagation models were used for the modeling of a prior distribution within a Bayesian inference. Crown Copyright & 2014 Published by Elsevier Ltd. on behalf of ISA. All rights reserved.

Keywords: Bayesian estimation Recursive estimation WSN RSSI Particle filter Multiple antennas

1. Introduction Recent progress in wireless communications and digital electronics has enabled the development of low-power, low-cost, multi-functional sensor nodes which are able to communicate with each other within Wireless Sensor Networks (WSN) [1]. These sensor nodes are randomly distributed within the WSN and in most cases the position of the node (target node) is unknown. The methods for localizing nodes within WSN are divided into four main groups [2], by considering communication parameters or network structures: Centralized or Distributed methods, Anchor-based or Anchor-free methods, Mobile or Stationary methods, and Range-based or Range-free methods. The importance of WSN is also closely related to the development of smart environments, which represent the next advance in home, industrial and transportation systems automation [3,4]. In this paper we were interested in the Range-based methods which are made up of two processes. The first process is called Ranging in which a measured value is used to estimate the distance to a reference point (anchor node). The position of the tracked object can be determined once the distance to one or more reference points is known. This process is called Range-combining and can be done explicitly or implicitly [5]. The distance at the Ranging process can be derived from the three basic properties of a radio signal: Received

n

Corresponding author. E-mail address: [email protected] (J. Svečko).

signal strength (RSS) [6], Time of flight (TOF) [7] and Angle of arrival (AOA) [8] or Direction of arrival (DOA) [9]. The RSS has several advantages compared to other methods. It can be implemented using existing wireless communication systems with minimal or no hardware changes, and it represents a physical parameter called a Receive Signal Strength Indication (RSSI) obtained by acquiring a signal strength using the physical antenna of a Radio Frequency (RF) device. The RSSI ranging methods use a signal propagation model which accurately describes the relation between the RSSI values and the distance. The challenge is to define a proper algorithm using a suitable propagation model because radio propagation is affected by fading, shadowing, and multi-path effects [9]. Many different approaches for distance estimation using RSSI within a WSN have been proposed over recent years. In [10] the authors came to the conclusion that the accuracy of distance estimation between anchor and target node is better when using of two antennas on the target node and consequently the position estimate is better. The used antennas were spaced 10 cm from each other and the average RSSI was used for further distance and positioning computation. Another approach using multiple antennas was presented in [11], where multiple antennas were placed on the target node and the transmitting antenna was selected using a round robin method. The received RSSI was used for distance estimation using different methods where all based on the log-likelihood function. It was shown that the best accuracy for distance estimation was achieved using four receiving antennas. A slightly different approach using multiple antennas is discussed in [12]. Multiple antennas were placed at the receivers' locations, called landmarks.

http://dx.doi.org/10.1016/j.isatra.2014.10.003 0019-0578/Crown Copyright & 2014 Published by Elsevier Ltd. on behalf of ISA. All rights reserved.

Please cite this article as: Svečko J, et al. Distance estimation using RSSI and particle filter. ISA Transactions (2014), http://dx.doi.org/ 10.1016/j.isatra.2014.10.003i

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Each landmark was supported by three antennas spaced within 30– 60 cm of each other. They captured the fingerprints within a real environment and then off-line localization was performed by running different localization algorithms using the collected fingerprints. They discovered that with the use of three antennas at a landmark the accuracies of the localization algorithms were better than localization using a single antenna at the receiver's side. In the contribution [13], they used multiple rotating omnidirectional antennas on a receiver device and used an angle of arrival estimation method. It was shown that with the use of four antennas placed circularly on a plate, the accuracy of the angle of arrival was better than using just one antenna. We can also see from the experimental results in [13] the RSSI dependence from the antenna radiation pattern, which is an additional problem to the multipath effects when using RSSI for localization estimation. It can be seen, from the given contributions [10–13], that the accuracies of distance and localization estimations are better when there are multiple antennas, whether on the target node or on the reference node, as compared to the use of a single antenna on the receiver or transmitter. Extensive research has also been done on estimating the localization of a target node using RSSI, by implementing various localization algorithms for improving the uses of propagation models. In contribution [14] they considered the problem of indoor localization based on RSSI and standard IEEE 802.15.4. The localization algorithm consisted of two phases where, during the first training phase, beacon packets were exchanged between the target node and anchor nodes in order to select and weigh the RSSI measurements according to their strengths. A log-normal propagation model was used for distance estimation, where the algorithm used a virtual calibration with no human intervention. During the second localization phase the final localization was done using triangulation. A similar approach to [14] is done in [15] for an indoor environment and with 802.15.4 modules. The difference between the contributions is in the localization algorithms, where [15] is similar to the fingerprinting method. During the first pre-configuration phase power decay curves are created for the whole environment in order to estimate the distance between the target node and anchor nodes. During the second localization phase the target node selects the three nearer anchor nodes by using minimum transmission power to limit the estimated location to a triangular area. In both contributions [14,15] a better accuracy is achieved with the use of the presented algorithms. Another idea for modifying the log-normal propagation model is presented in [16]. Based on the standard IEEE 802.11, they implemented a Dual Log Path Loss Model with practical parameters obtained by measurements. The parameters were classified in two groups depending on the distance between the target and the anchor node. The localization methods in [16] showed lower distance error with the presented propagation model. Other solutions, like in [17,18], take into account that RSSI-based distance estimation will have some error due to noisy RSSI readings resulting from multipath, shadowing, etc. and will achieve better accuracy with the adjusted localization algorithms, thus increasing the complexities of them. The represented contributions [14–18] have shown the importance of distance accuracy in the used localization methods and improvement in the distance estimation to lower localization error. The remainder of this paper is organized as follows. Section 2 briefly describes the radio propagation models, Section 3 represents the recursive Bayesian inference, and Section 4 covers the distance estimation using particle filter. Section 5 represents the experimental results, and Section 6 concludes the paper.

the path loss between transmitter and receiver defined as a function of frequency, distance and other conditions. The more commonly used propagation model is the log-normal model (see Appendix A.1), which is an empirical model and describes the dependence of RSSI vs. distance. The ground reflection model (see Appendix A.2) does not only consider the direct path but also takes into account the ground reflection propagation path between transmitter and receiver, and is a deterministic model. A comparison between the log-normal and ground reflection propagation models under ideal conditions is shown in Fig. 1.

3. Recursive Bayesian filter The model which describes dependence of RSSI values obtained using multiple antennas vs. distance is not generally known, therefore, the idea in this paper was to extend a particle filter, which is an extension of the Kalman filter [19]. The Kalman filter operates recursively on streams of noisy input data to produce a statistically optimal estimate of the underlying system state. The extended Kalman filter – EKF [20] is used when the state transition and observation models are not linear functions of the state. As an enhancement for resolving recursion when nonlinearities are present within the system equations, the so-called unscented Kalman filter – UKF was first presented by Julier and Uhllman [21,22]. In comparison with EKF, the UKF is less calculationally complex by avoiding the process of linearization. Those methods similar to UKF are the sequential Monte Carlo methods based on generating samples. The main difference between the methods is given in the number of used samples (Monte Carlo methods use a greater number of samples) and the used sampling method. Due to the development of technology and the increasing computational powers of computers, new methods have been developed that allow the solution of the recursive Bayesian filter by sampling, also known as Monte Carlo sampling. The given method is the so-called sequential Monte Carlo method [23], to which also belongs the particle filter [24,25], as described later in this paper. Every stochastic system can be described using a transition (1) and observation function (2), which are usually nonlinear: sk ¼ f ðsk  1 ; vk Þ

ð1Þ

yk ¼ gðsk ; wk Þ

ð2Þ

The transition function (1) defines the dependence between two states within a time sequence, where vk is the process noise. −20 GRM LNM

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Fig. 1. Comparison between ground reflection model (GRM) and log-normal model (LNM).

Please cite this article as: Svečko J, et al. Distance estimation using RSSI and particle filter. ISA Transactions (2014), http://dx.doi.org/ 10.1016/j.isatra.2014.10.003i

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The observation function (2) presents the impact of the hidden state sk on the measured outputs yk , where wk is the observation noise. It is also possible to describe a stochastic system with a probabilistic model, where the transition density pðsk jsk  1 Þ is defined by the transition function and process noise distribution pðvk Þ, whereas the likelihood pðyk jsk Þ is defined by the observation function and distribution of the observation noise pðwk Þ. The recursive Bayesian filter is used to estimate the hidden state s of a discrete-time stochastic system, on the basis of observations y. The state at time-step k is denoted by sk and the sequence of states from initial state s0 until state sk is denoted by s0:k ¼ fs0 ; s1 ; …; sk g. Every state sk provides a certain observation or measurement yk . A sequence of measurements is represented by y1:k ¼ fy1 ; y2 ; …; yk g. All information about states s0:k can be described using a posterior probability pðs0:k jy1:k Þ, which defines the probability of a sequence of states for a given observation sequence, when the Bayesian framework is considered. In most cases the entire sequence of states is not considered, and only the current state estimate sk is observed. This means that only the marginal probability pðsk jy1:k Þ at time step k is used from the Bayesian point of view. The defined marginal probability captures the entire observation's sequence, which increases the calculation complexity, therefore a recursive solution is used by using the posterior probability of the previous time step pðsk  1 jy1:k  1 Þ and the current observations yk . The given method is called the recursive Bayesian filter. The recursive Bayesian filter considers two restrictions: 1st restriction: Given the current state sk , the current observation yk is conditionally independent from all previous observations y1:k  1 . 2nd restriction: Given the state sk  1 , from the time step k  1, the current state sk is conditionally independent from all previous observations y1:k  1 . The final recursive Bayesian filter is given by: R pðyk jsk Þ pðsk jsk  1 Þpðsk  1 jy1:k  1 Þ dsk  1 ð3Þ pðsk jy1:k Þ ¼ pðyk jy1:k  1 Þ and is usually divided into two steps. Prediction step – trying to predict all possible states at the time step k from the previous state at k  1 given by: Z pðsk jy1:k  1 Þ ¼ pðsk jsk  1 Þpðsk  1 jy1:k  1 Þ dsk  1 ð4Þ Update step – using the observations yk at the time step k, attempting to predict the exact current state, given by: pðsk jy1:k Þ ¼

pðyk jsk Þpðsk jy1:k  1 Þ pðyk jy1:k  1 Þ

negligible weights. Therefore a method of resampling is used which increases the number of particles within the surroundings of those particles with importance weights and reduces the number of particles with small weights. This technique is called Sequential Importance Resampling. The implementation of a particle filter consists of three operations: 1. generating particles – sampling 2. determining particle weights – importance 3. resampling The next sections provide short overviews of the individual operations, where we handle the first two steps in one section and the resampling operation in another, respectively. 3.1. Sequential importance sampling Importance sampling enables the derivation of the forms' integrals (6), which consider all possible transitions from one state to another based on the observations: Z Iðf Þ ¼ f ðsk Þpðsk jyk Þ ds ð6Þ During importance sampling it is essential that the particles are not sampled from the original distribution pðsk jyk Þ, but from an arbitrary distribution qðsk jyk Þ, given that qðsk jyk Þ 4 0 whenever pðsk jyk Þ 4 0. This is to ensure that samples can be drawn for all states for which pðsk jyk Þ is non-zero [26]. If we rewrite the integral (6), by considering the new distribution, we obtain (7) where wðsk Þ is given by (8): Z Iðf Þ ¼ f ðsk Þwðsk Þqðsk jyk Þ ds ð7Þ

wðsk Þ ¼

pðsk jyk Þ qðsk jyk Þ

ð8Þ

With generating N independent samples fsðiÞ g according to k qðsk jyk Þ for approximating the integral Iðf Þ, we obtain (9), where wðiÞ ¼ wðsðiÞ Þ: k k I N ðf Þ ¼

1 N ∑ f ðsðiÞ Þ  wðiÞ k Ni¼1 k

ð9Þ

The sequence wðiÞ ¼ fwð1Þ ; wð2Þ ; …; wðNÞ g is called the importance k weights. Eq. (9) can be rewritten by considering the Dirac (distribution) function, given by the following equation:

ð5Þ

The given (4) and (5) steps are usually computationally infeasible, therefore, the sequential Monte Carlo integration methods are used. In this paper the Sequential Importance Resampling – SIR technique is used, also known as ‘particle filter’. It is based on the Sequential Importance Sampling – SIS technique, and belongs to the sequential Monte Carlo methods. The basic idea of particle filter is that the posterior density function is represented by weighted samples, called particles. Each particle presents the possible value of a given state over a certain time-step. The particles are theoretically sampled from analytical and non-Gaussian probabilities. In practice, importance sampling is used where the particles are not sampled from the original distribution but from a new distribution, which is also used to determine the particle weights. The new distribution is called the importance function and the weights are calculated recursively using Sequential Importance Sampling. The restriction of SIS methods is the degradation of particles, which means that one particle will be highly weighted and all other particles will have

3

I N ðf Þ ¼

1 N ∑ wðiÞ δðsk  sðiÞ Þ k Ni¼1 k

ð10Þ

The final sampling of the posterior distribution is given by (11), by considering the normalizing weights (12): N

^ k jyk Þ ¼ ∑ w ðiÞ pðs δðsk sðiÞ Þ k k

ð11Þ

i¼1

w ðiÞ ¼ k

wðiÞ k

ð12Þ

ðjÞ ∑N j ¼ 1 wk

^ k jyk Þ It can be concluded from Eq. (11), that the estimate of pðs does not only depend on the individual particles, but also on their ^ k jyk Þ can be weights. So the complete posterior distribution pðs N

; wðiÞ g . Given the previous state of the given with the set fsðiÞ k k i¼1 N

system with the set fsðiÞ ; wðiÞ g , we would like to infer about k1 k1 i ¼ 1 N

N

; wðiÞ g , where fwðiÞ g is the current state, given by fsðiÞ k k i¼1 k i¼1

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computed using the weight update step as follows: pðyk jsðiÞ ÞpðsðiÞ jsðiÞ Þ k k k1 ¼ wðiÞ k ðiÞ ðiÞ qðsk jsk  1 ; yk Þ

 wðiÞ k1

ð13Þ

The new distribution qðsðiÞ jsðiÞ ; y Þ in (13) is usually reprek k1 k sented with the prior distribution pðsðiÞ jsðiÞ Þ, so the equation can k k1 be rewritten into the following equation: ¼ pðyk jsðiÞ Þ  wðiÞ wðiÞ k k k1

ð14Þ

3.2. Resampling In order to ensure a proper distribution and density of the particles, it is necessary to proceed with resampling. In the resampling process the original number of particles is kept, but increases the number of those particles in areas with higher probability and reduces the number of particles in regions of low probability. The ‘new’ particles are generated out of particles with greater weighting (probability), where it could happen that some particles are selected several times. The resampling procedure is repeated until the degradation no longer affects the estimation. The number of effective sample size N eff that can be evaluated by the expression (15) [27] is a sufficient criterion of degradation is: N^ eff ¼

1 ðiÞ 2 ∑N i ¼ 1 ðw k Þ

ð15Þ

When the weights of all particles are equal, then the value of N^ eff equals the number of particles N, but if the N^ eff ¼ 1 this infers strong degradation. Having the effective calculated number and a predefined threshold N tr , which represents the minimal number of effective particles, the resampling is repeated until N^ eff o Ntr . The resampling procedure modifies the weighted approxima^ k jyk Þ (11) into a unlighted distribution tion of the distribution pðs (16), where nj is the number of copies of the sðjÞ particle within the k n new set fsðiÞ g: k N n 1 j n δðsk jsðiÞ Þ ¼ ∑ δðsk jsðiÞ Þ k k N i¼1 j¼1N N

^ k jyk Þ ¼ ∑ pðs

ð16Þ

n g particles Four basic algorithms exist for generating a set of fsðiÞ k [28]: systematic resampling, residual resampling, multinominal resampling, and stratified resampling. The first three algorithms were implemented into the particle filter and a comparison of efficiencies is given in the section ‘Experimental results’.

ð18Þ

If N^ eff o N tr a f ðxk Þ given by (19) is computed, where the final distance estimate is given as the mean value of the function: N

xðiÞ f ðxk Þ ¼ ∑ w ðiÞ k k

ð19Þ

i¼1

Algorithm 1. SIR – particle filter. Select type of antenna board: parallel or circular board Read RSSI values from each antenna Compute distances using LNM (21) or GRM (32) Set number of particles N Set threshold for minimal number of effective particles Ntr Set the maximum distance between transmitter–receiver D Select the resampling method: systematic, residual or multinomial resampling for time step k ¼ 0 do Generate N random particles fxðiÞ g within the maximum k distance range ½0; D end for for time step k ¼ 1 do N ðdðRSSIÞ; 1Þ

The outline of the proposed algorithm is presented in Algorithm 1. It is divided into two parts, the initial phase and the main part of the algorithm. In the first step of the initial phase the placements of antennas can be chosen (antennas placed on parallel or circular boards). During the next steps the distance is estimated, being represented by a hidden state. The posterior probability distribution pðxk jyk Þ given by (17) was used in Bayesian inference, where xk denotes the distance estimate and yk is the mean value of the distances given with the multiple RSSI values from the antennas placed on the receiver using the selected log-normal model (LNM) or ground reflection model (GRM): N

Ntr ¼ 43 N

Draw N samples from pðxðiÞ jxðiÞ Þ with Gaussian distribution k k1

4. Distance estimation using particle filter

^ k jyk Þ ¼ ∑ w ðiÞ pðx δðxk  xðiÞ Þ k k

The number of used particles (N) is predefined in the first steps of the algorithm, where we restrict ourselves to a certain maximum distance (D) between transmitter and receiver. It is assumed that this information is known in advance and also predefined during the initial phase. The prior probability distribution pðxðiÞ jxðiÞ Þ was used for the k k1 sampling step, as represented using the Gaussian probability function where μ is equal to the mean value of the distance given with selected propagation model and antenna placement at a certain point during measurements, and σ ¼1. The importance weights were estimated using Gamma distribution by considering the measurements obtained using multiple antennas, where the shape parameter is equal to the average value of the distance estimated using the selected propagation model and board type at a certain point during measurements. The scale parameter Θ is defined as an exponent function of parameters a and b, which were estimated using an exponential curve fitting function. The implemented particle filter is based on the SIR method. During the initial phase of the algorithm one of the three possible resampling methods is chosen: systematic, residual or multinominal resampling. The resampling step is iterated until N^ eff o Ntr , where the effective sample size N^ eff is calculated at each iteration and the threshold is defined within the initial phase given by the following equation [29]:

ð17Þ

i¼1

g During the time-step k ¼0, the set of independent particles fxðiÞ k is generated randomly along the whole range of possible distances.

Þ with Gamma Compute importance weights pðyk jxðiÞ k distribution ΓðdðRSSIÞ; Θða; bÞÞ Compute the normalized importance weights (12) Compute the estimate of the effective number of particles ^ eff (15) N repeat Perform resampling ðiÞ Compute importance weights pðyk jx~ k Þ with Gamma distribution Compute the normalized importance weights (12) Compute the estimate of the effective number of particles ^ N (15) eff

^ eff oNtr until N Estimate the distance as the mean value of (19) end for

Please cite this article as: Svečko J, et al. Distance estimation using RSSI and particle filter. ISA Transactions (2014), http://dx.doi.org/ 10.1016/j.isatra.2014.10.003i

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5. Experimental results Real RSSI values were measured using two different types of receivers, shown in Figs. 2 and 3. Antennas were placed on a circular board, as shown in Fig. 2 and parallel to each other, as shown Fig. 3. 12 receivers were placed on a circular plate with a diameter of 0.12 m and 8 receivers were placed parallel, separated by 0.025 m. Both configurations of the receivers were connected to a Cortex M3 NXP micro-controller using a Serial Peripheral Interface. The MRF24J40MA receivers had a micro-strip monopole antenna operating within the ISM 2.4 GHz band. In both experiments the plates with receivers were stationary and the transmitter, as shown in Fig. 4, had only one antenna with Microchip MRF24J40MA and it was mobile. The experimental results were performed on real-valued data using the physical layer of the IEEE standard 802.15.4. A carrierfrequency of 2.4 GHz was used for packet-transmitting and receiving. Whilst the transmitter was transmitting packets, the stationary receiver was reading packets on each of the antenna placed on the receiver's board, and the RSSI for each antenna was recorded. When receiving the transmitting packets, the receivers did not transmit any data. The distance between transmitter–receiver was estimated from the RSSI, without using any prior information. All the experiments were carried-out within an in-door environment with a minimal number of obstacles and in the line of sight between transmitter–receiver. The experimental results were obtained within a garage with dimensions of 50 m length, 10 m width, and 4 m height. During the experiments the transmitter and receiver were placed 1 m from the ground and the receiver was placed 1 m from the wall with a dimension of 10 m. The RSSI measurements for parallel antenna placement and circular antenna placement are shown in Figs. 5 and 6, respectively, where only four measurements of the RSSI values are

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shown in order to achieve better transparency. The RSSI values for distances between 1 and 40 m by steps of 1 m are shown in Figs. 5 and 6, respectively. The RSSI values, which correspond to antennas A1, A3, A5, and A7, are shown in Fig. 5, and Fig. 6 shows the RSSI values from antennas A1, A4, A7, and A10. It can be concluded from Fig. 6 as to which antennas are placed orthogonally to the transmitter-line (A4 and A10) and which are in the line with the transmitter, because the measurements differ by about 10 dBm between those antennas orthogonal to the transmitter and those in a line with it, which results from the RSSI dependency on multi-path propagation and the antenna radiation pattern [13]. It can also be concluded from Figs. 5 and 6 at which points of the measurements the transceiver was not in a strict line with the receiver and we can especially expose measurements at the distances of 28 m and 38 m for antennas placed on a circular board and the distances 32 m and 36 m for the parallel-placed antennas. The above-mentioned points again show the sensitivity of RSSI when interacting with the environment. The results obtained by the proposed particle filter algorithm using different re-sampling methods and different placements of the antennas are analyzed separately in Sections 5.1, 5.2.

Fig. 4. Transmitter with only one antenna.

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Fig. 5. RSSI measurements for antennas placed on parallel board (measured RSSI vs. distance).

Please cite this article as: Svečko J, et al. Distance estimation using RSSI and particle filter. ISA Transactions (2014), http://dx.doi.org/ 10.1016/j.isatra.2014.10.003i

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5.1. Data analysis for the receiver with antennas placed on a board of circular shape The estimated distances obtained using the proposed particle filter algorithm for the antenna placed on the circle board are shown in Figs. 7 and 8. The distances estimated with the particle filter using the LNM and GRM models are shown in Figs. 7 and 8, respectively. In Fig. 7 the distances were estimated using the particle filter algorithm (Algorithm 1) using the multinominal resampling method and log-normal model. The distances obtained with the particle filter were compared with the distances obtained with the log-normal model and true distances, which were represented by a linear function. Fig. 8 shows the estimated distances using the particle filter algorithm (Algorithm 1) with the multinominal re-sampling method but with the ground reflection model. The estimated distances were compared with the distance estimation using only the ground reflection model (23) at different points of measurements. In both cases the particle filter algorithm with the multinomial re-sampling method was used and achieved the best accuracy results (Figs. 9 and 10). In

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Fig. 9. Distance estimation absolute errors vs. distance using different re-sampling methods for a circular board with ground reflection model and particle filter.

Figs. 9 and 10 absolute distance estimations' errors using different types of re-sampling methods are compared for the ground reflection and log-normal model. The multinominal re-sampling method provided better results compared to the systematic or residual method. The re-sampling process had minimal impact on the accuracies of distance estimations. The ground reflection model provided better results than the log-normal model, as shown in Figs. 7 and 8. At a distance of 38 m the error for particle filter using the ground reflection model was 25.54 m and the error when only using the propagation model was 25.95 m, but at a distance of 20 m the error using the particle filter was just 0.13 m and with propagation model 2.73 m. Similar results were achieved with the particle filter and used log-normal propagation model, where at a distance of 38 m the error of particle filter was 24.93 and the error of the propagation model 27.01 m, and the best result was given at 6 m with an error of 0.09 m using the particle filter and 0.87 m when only using the propagation model. At the distances 38 m

Please cite this article as: Svečko J, et al. Distance estimation using RSSI and particle filter. ISA Transactions (2014), http://dx.doi.org/ 10.1016/j.isatra.2014.10.003i

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24

28

32

36

40

points of measurements [m]

Fig. 10. Distance estimation absolute errors vs. distance using different re-sampling methods for circular board with log-normal model and particle filter.

Fig. 12. Estimated distance using particle filter with the ground reflection model and multinomial re-sampling method vs. points of measurements compared to the estimated distance using only the ground reflection model for parallel-placed antennas.

true distance LNM model particle filter

72

12

26

multinomial systematic residual

24

64

22 re−sampling estimation error [m]

distance[m]

56 48 40 32 24 16 8

20 18 16 14 12 10 8 6 4 2

0 0

4

8

12

16

20

24

28

32

36

40

points of measurements [m] Fig. 11. Estimated distance using particle filter with the log-normal model and multinomial re-sampling method vs. points of measurements compared to the estimated distance using only the log-normal model for parallel-placed antennas.

and 16 m the measured RSSI, as shown in Fig. 6, the values had larger deviations from the mean values of RSSI, which could be a consequence of antenna radiation pattern, therefore the distance estimation obtained using particle filter had also larger errors. 5.2. Data analysis for receiver with parallel-placed antennas The log-normal model and ground reflection model were used for computing the importance weights within the particle filter algorithm. The estimated distances and true distances are shown in Figs. 11 and 12. The distances estimated using the proposed algorithm were compared with the LNM and GRM models in Figs. 11 and 12. The particle filter achieved the best results. The distances estimated using the particle filter algorithm (Algorithm 1) with the multinominal re-sampling method and the log-normal model are shown in Fig. 11 and for the ground reflection model the estimated distances are shown in Fig. 12.

0 0

2

4

6

8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 points of measurements [m]

Fig. 13. Distance estimation absolute errors vs. distance using different re-sampling methods for parallel-placed antennas with ground reflection model and particle filter.

The estimated distances using different re-sampling methods and different importance weights models (GRM and LNM) within the particle filter for parallel-placed antennas are shown in Figs. 13 and 14. The re-sampling process has a minor impact on distance accuracy but the best results were obtained using the multinomial resampling method. Although the RSSI measurements deviated (32 m and 36 m in Fig. 5) the particle filter gave superior results compared with the propagation models (LNM and GRM). At a distance of 32 m, the lognormal propagation model had an error of 32.64 m, the error of the particle filter at the same point was 8.41 m, as shown in Fig. 11 or Fig. 14. The ground reflection model provided an error of 29.48 m at a distance of 36 m and the particle filter 3.14 m, as shown in Figs. 12 and 13. The best results were achieved at a distance of 2 m and the particle filter of the log-normal model, where the error was just 0.07 m, and at a distance of 6 m with the particle filter of the ground reflection model, where the error was only 0.94 m.

Please cite this article as: Svečko J, et al. Distance estimation using RSSI and particle filter. ISA Transactions (2014), http://dx.doi.org/ 10.1016/j.isatra.2014.10.003i

J. Svečko et al. / ISA Transactions ∎ (∎∎∎∎) ∎∎∎–∎∎∎

8

24

8

multinomial systematic residual

22

true distance contribution LNM model GRM model

7

18

6

16 5

14

distance[m]

re−sampling estimation error [m]

20

12 10

4 3

8 6

2

4 1

2 0

0

2

4

6

0

8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40

0

points of measurements [m]

8 true distance contribution LNM model GRM model

6

distance[m]

5 4 3 2 1 0

0

1

2

3

4

2

3

4

5

6

points of measurements [m]

Fig. 14. Distance estimation absolute errors vs. distance using different re-sampling methods for parallel-placed antennas with log-normal model and particle filter.

7

1

5

6

points of measurements [m] Fig. 15. Comparison between circular board and the contribution.

5.3. Evaluation of the experimental results The proposed method was compared with the experimental results reported in [30]. In our previous research we found only one contribution [30], which evaluated and represented the distance estimation. In other contributions where RSSI measurements are used or multiple antennas, which we represented in the Introduction section, the focus is on localization algorithms and the distance estimation is not presented in detail. A comparison between the experimental results is shown in Figs. 15 and 16, where the proposed algorithm using parallel antennas and circularly placed antennas was compared with the results in [30]. In Figs. 15 and 16 a scatter plot is used, for a better transparency the true distance is shown as a linear function (line). In order to conduct a fair comparison, a distance range between 1 and 5 m was considered. Ref. [30] represented only 6 points of measurements, at 1 m, 2 m, 3 m, 4 m, 5 m and then there was a jump up to 8 m. In the contribution there is no explanation about the lack of data at 6 m and 7 m, so we decided to consider only the data for the first 5 points of measurements.

Fig. 16. Comparison between the parallel board and the contribution.

The estimated distances obtained using different types of antenna placements and different models using particle filter were compared with the results in [30], and are reported in Table 1. The true distances, estimated distances and the absolute values between the true distances and the estimated distances are reported in Table 1. The mean error is calculated as the average of the absolute errors. The error is also expressed as the percentage error between the true distance and the estimated distance. The mean error is then calculated as the average of the percentage errors. The differences between the proposed method and the results presented in [30] were in the distance estimation methods and within the range of the distance estimation. In [30] they used the log-normal propagation model, where they firstly measured the RSSI values at certain distances over a specific time period and with the measured data estimated parameters of the log-normal model. The points of measurements for the parameters were within the range of the actual distance estimation, which we used for comparison with our estimates and their experiment (Table 1). In the proposed particle filter algorithm, we did not make any previous measurements for estimating the parameters for the used propagation models. A difference can already be seen in the used path loss exponent factor, in the contribution it is equal to 2.6 and in our model we used value 2, which is considered to be generally the value for indoor environments with minimal obstacles. Another difference was the method of data collection (RSSI values), where in [30] all the nodes were deployed at fixed locations, from which we concluded that the data was covered at the same time for each location. In the proposed method we moved the transmitter at every point of measurements and covered the data at the particular point. All the mentioned reasons, especially the estimation of the model parameters in the contribution [30] can influence the calculated and represented distance error. The particle filter method with the LNM model and antennas placed on a circular board and a parallel-board provided meanerror values of 0.87 and 1.34 m. The GRM model for the circular and parallel boards provided error mean-values of 0.75 and 1.67 m. The method in [30] had a mean error value of 2.25 m. The proposed method with the circular board and GRM gave the best results. It was for 1.5 m more accurate than the method presented in [30]. The second best estimates were obtained with the circular board but with the log-normal propagation model. Less accurate

Please cite this article as: Svečko J, et al. Distance estimation using RSSI and particle filter. ISA Transactions (2014), http://dx.doi.org/ 10.1016/j.isatra.2014.10.003i

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Table 1 Comparison of distance estimation using the proposed method with different types of antennas placements and propagation models, with the results reported in [30]. Dist. (m)

LNM

GRM

Circle board

1 2 3 4 5 Mean error

Parallel board

Circle board

Parallel board

Contribution [30]

est: ðmÞ

err: ðmÞ

err: ð%Þ

est: ðmÞ

err: ðmÞ

err: ð%Þ

est: ðmÞ

err: ðmÞ

err: ð%Þ

est: ðmÞ

err: ðmÞ

err: ð%Þ

est: ðmÞ

err: ðmÞ

err: ð%Þ

1.94 1.80 4.18 3.08 6.14

0.94 0.20 1.78 0.92 1.14

93.5 9.9 39.2 23.0 22.9

2.14 1.80 6.04 3.21 3.46

1.14 0.20 3.04 0.79 1.54

114.1 10.0 101.3 19.7 30.9

1.74 2.20 4.45 3.00 4.63

0.74 0.20 1.45 1.00 0.37

74.3 10.0 48.2 25.0 7.4

3.32 1.76 5.45 2.87 7.21

2.32 0.24 2.45 1.13 2.21

232.1 12.2 81.6 28.3 44.2

3.03 4.29 5.10 6.62 7.23

2.03 2.29 2.10 2.62 2.23

202.5 114.3 70.0 65.0 44.5

0.88

37.7

1.34

55.2

0.75

33.0

1.67

79.7

2.25

99.3

estimates are obtained with the parallel board but the mean error was still for than 1 m more accurate than the results obtained in [30]. All the proposed methods had the smallest errors at distances of 2 m, regardless of the antennas placements and propagation models, taking into account a distance between 1 and 5 m. The main reasons for that we can find in the antenna pattern, the position of transmitter and receiver, the multi-path effects and the influences of obstacles, which were within the environment of the experiment. We must also consider that during acquisition the transmitter and receiver were not always in strict line (antennas positions). Within a range of 1–5 m the proposed method estimated distances more accurately than the method proposed in [30]. Although the method in [30] used model parameters obtained from preliminary measurements, the proposed method gave better results for 1 m, which indicated that the proposed method could be used in practice. The proposed method did not use parameter adjustments. The overall conclusion is that the proposed method provides better accuracy than the method proposed in [30]. Similar mean distance error results were obtained for the whole distance between 1 and 40 m, where the accuracies of distance estimation were better when using the circular-shaped board and the ground reflection model, followed by the circular board readings and the log-normal model. The highest mean error was achieved using the parallel board and the ground reflection model.

6. Conclusions and future work This paper proposed a method for distance estimation using real-valued RSSI values with a particle filter. The novelty of this paper is its investigation into the placements of receiving antennas, which were organized circular with a diameter 1.2 m and were distributed parallel with 0.025 m distances between each other. The goal of this paper was to estimate the hidden-state, which represents a distance using RSSI values from multiple antennas. Different combinations of particle filter, ground reflection model, log-normal model using different antennas arrangement were assessed for accuracy regarding distance estimation. The experimental results showed that the accuracy of distance estimation was better when using the proposed particle filter algorithm than with the use of only propagation models. The ground reflection propagation model using particle filter provided better distance estimation than the log-normal propagation model. The comparison between different resampling methods for the particle filter algorithm showed that the selection of the method is not critical for the accuracy of the given algorithm. A direct comparison between the methods, however, showed that

the use of the multi-nominal re-sampling method gave slightly better results than the systematic or residual methods. The best results for accuracy of distance estimation were obtained using particle filter, the circular-shaped board and the ground reflection model, followed by the method using particle filter, the circular board and the log-normal model. The highest mean error was achieved using the parallel-distributed board and ground reflection model. The proposed particle filter algorithm can be validated in several ways, because it is not limited by a prior calibration. One of the possible validations is the use of the same antennas' placements within different environments (outdoors or indoors with more obstacles). Another possibility is the use of a different number of antennas and again within different environments. The algorithm can also be used in other Range-based methods and not only using RSSI for the ranging process. In this paper we focused on RSSI because it is a low-cost solution in comparison with other localization methods. Experimental results showed that the particle filter can be used for distance estimation using RSSI.

Appendix A A.1. Log-normal model The propagation model more often used in WSN is the lognormal model or log-distance path loss model given by   d ð20Þ PLðdBÞ ¼ PLðd0 Þ þ10n log d0 where PLðdBÞ denotes the average of all possible path loss values at an arbitrary distance d, and PLðd0 Þ is the receiver power in dB at a short reference distance d0 . The parameter n is the path-loss exponent. The log-normal shadow model shows that the average received signal power decreases logarithmically with distance. The log-normal model does not take into account the different multiple paths of the transmitted signal. The path losses PLðdÞ at any value d can be modeled as a random variable with a normal distribution (in dB) with the distance-dependent mean, given by   d PLðdÞ ¼ PLðdÞ þX σ ¼ PLðd0 Þ þ 10n log þ Xσ ð21Þ d0 The resulting extended model is the log-normal shadow model (21), where X σ represents a Gaussian random variable with zero mean and standard deviations of σ [31]. The parameters (n, σ) define the statistical model and are viewed as heavily dependent on the environment. Finally the received power is given in (22) P R ðdÞ ½dB ¼ P T ½dB  PLðdÞ ½dB

ð22Þ

Please cite this article as: Svečko J, et al. Distance estimation using RSSI and particle filter. ISA Transactions (2014), http://dx.doi.org/ 10.1016/j.isatra.2014.10.003i

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A.2. Ground reflection model In the real environments the propagation path of the signal is not direct, but the signal has many reflections from the ground and obstacles, therefore, the free space propagation model is not accurate in most cases. The ground reflection (2-ray) model (Fig. 17) considers the direct path and a ground reflection propagation path between transmitter and receiver. Fig. 17 shows a scenario with an infinite, perfectly flat ground plane and no other objects obstructing the signal between the transmitter and receiver. The total received energy can then be modeled as the vector sum of the directly transmitted wave Pdirect and one ground reflected wave Pdirect, given by P R ¼ P direct þ P reflect PLF

ð23Þ

In (23) the ground reflected wave's power Preflect is multiplied by the Polarization Loss Factor – PLF, which considers the polarization difference, and consequently the loss of power. The polarization mismatch can be described with the following equation: PLF ¼ cos Θi

ð24Þ

The radio signal is never totaly reflected from the ground. Whenever a radio signal hits the junctions between different dielectric media, a portion of the energy is reflected, whilst the remaining energy is passed through the junction. The reflected portion depends upon the wave polarization, wavelength λ, incident-angle Θi and different constants of the surface (ϵr – dielectric constant, μr – magnetic permeability and σ – conductivity). The Fresnel reflection coefficients for the vertical (Γv) and horizontal (Γh) polarized signals are calculated in Eqs. (25) and (26), respectively with the assumption that both substances have equal permeability μr ¼ 1, and one dielectric is free space [32]: pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ðϵr  j60σλÞ sin Θi  ϵr  j60σλ  cos 2 Θi pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ð25Þ Γv ¼ ðϵr  j60σλÞ sin Θi þ ϵr  j60σλ  cos 2 Θi Γv ¼

pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ϵr  j60σλ  cos 2 Θ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiiffi sin Θi þ ϵr  j60σλ  cos 2 Θi sin Θi 

ð26Þ

By considering the geometry depicted in Fig. 17 the power of the direct (27) and reflected path (28) are given by   λ 2 P direct ¼ P T GT GR ð27Þ 4πD  P reflect ¼ P T GT GR

 λ 2 2 jΓj 4πR

Fig. 17. Ground reflection (2-ray) model.

ð28Þ

where qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 D ¼ ðH 2 H 1 Þ2 þ d

ð29Þ

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 R ¼ ðH 2 þ H 1 Þ2 þd

ð30Þ

Θi ¼ arctan

  H1 þ H2 d

ð31Þ

In the literature, the ground reflection (2-ray) model (32) is often used which is a simplified form of the model, where the path-loss exponent is equal to 4 and the receiver/transmitter antennas' heights (H1 and H2 ) are considered. The ground reflection model is given by P R ¼ P T GT GR

H 21 H 22 d

4

ð32Þ

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Janja Svečko graduated in 2007 from Faculty of Electrical Engineering and Computer Science in Maribor, with title “Modeling of data transmision through the speech channel of GSM system”. Since then she has been working as a researcher with the company Ultra d.o.o. within the research group Ultra advance research in Maribor, Slovenia. From 2007 to 2012 she has also been working as a junior researcher with the Laboratory for Signal Processing and Remote Control. Since 2012 she has also been working as a senior researcher with the Margento R & D.

Marko Malajner received the B.Sc. and M.Sc. degrees in electrical engineering from the University of Maribor, Maribor, Slovenia, in 2006 and 2009, respectively. His current research interests include remote controls and wireless sensor network localization.

Dušan Gleich received the B.Sc., M.Sc., and Ph.D. degrees in electrical engineering from the University of Maribor, Maribor, Slovenia, in 1997, 2000, and 2002, respectively. He is a research scientist with the Laboratory for Signal Processing and Remote Control, Faculty of Electrical Engineering and Computer Science, University of Maribor. He was a visiting scientist with German Aerospace Center, Cologne, Germany, from 2004 to 2005 and 2009. He has been an associate professor with the University of Maribor since 2010. His current research interests include image processing and data compression and extraction information from synthetic aperture radar images.

Please cite this article as: Svečko J, et al. Distance estimation using RSSI and particle filter. ISA Transactions (2014), http://dx.doi.org/ 10.1016/j.isatra.2014.10.003i