A Diffraction Based Modified Exponential Model for Device-Free Localization with RSS Measurements Nanyong Jiang1 , Kaide Huang1 , Yao Guo1 , Guoli Wang1,2 , and Xuemei Guo1,
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1 School of Information Science and Technology Sun Yat-Sen University, Guangzhou 510006, China SYSU-CMU Shunde International Joint Research Institute, Foshan 5280000, China
[email protected]
Abstract. Radio frequency (RF) based Device-free localization and tracking (DFLT) monitors the change in received signal strength (RSS) measurements to locate the targets without carrying any electronic devices in the sensing area covered by a RF sensor network. This paper presents a new modified exponential model to accurately describe the relationship between the RSS measurements and the target state, which can effectively predict the variation of RSS when the target is present on line-of-sight (LOS) path or non-line-of-sight (NLOS) path. Based on the diffraction theory, we first show that the RSS attenuation caused by target mainly depends on two factors: the target-nodes distance and the target-link distance, which can be exploited to depict the change of RSS on LOS and NLOS, respectively. By taking into account these two factors, we then develop our model, and validate it with single link experiments. We finally explore the use of the proposed model with particle filter for DFLT, and demonstrate that our model can improve the DFLT performance by conducting actual experiments. Keywords: Device-free localization, received signal strength, radio frequency sensor networks, diffraction theory, particle filter.
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Introduction
Device-free localization and tracking (DFLT) [1] is an emerging technology that enables locating the target without carrying any devices or tags. Lots of sensor technologies, such as ultrasonic sensor, infrared camera and light sensor, can be used for the purposes of DFLT. Recently, there have been a growing interest in DFLT with using the received signal strength (RSS) measurements of radio
This work was supported by the National Science Foundation of P. R. China under Grant No. 61375080, and by the SYSU-CMU Shunde International Joint Research Institute Free Application Project under Grant No. 20130201. Corresponding author.
X. Zhang et al. (Eds.): ICIRA 2014, Part II, LNAI 8918, pp. 342–353, 2014. c Springer International Publishing Switzerland 2014
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frequency (RF) [2]. The basic idea is to monitor the changes in RSS when a target moves across or near the link that connects two sensor nodes. Actually, the presence of a moving target may diffract, reflect, or scatter the RF waves when an intrusion happens [3]. Taking advantage of this feature, the position of the target can be inferred from the RSS measurements. As opposed to the traditional sensor technologies, RF waves can transmit through walls [4], in dark or smoke-filled environments, and protect the privacy at the same time. Thus the DF system has various applications including building security and alarm systems, military and police operations, fire and disaster rescue, and so on. Several approaches have been proposed for the purpose of RSS based DFLT. One is radio tomographic imaging (RTI) [5], in which the attenuation or motion images are inferred firstly and then the target location is estimated from the images. While such a method can efficiently capture the visual shadowing images of the sensing area, it may introduce additional measurement noise in the twostep process. Another approach is based on RSS models. Exponential model [6], magnitude model [7] and ER model [8] have been presented to describe the target-induced RSS change on radio links and exploit the location information directly. However, the RSS-based models mentioned above only focus on the relationship between the target-link distance and the RSS measurements, while the changes of RSS in case that the target stands at different positions on line-ofsight (LOS) are ignored. Recently, a stochastic model based on diffraction theory [9] is proposed, which takes into account the impact of target cross-section on LOS. However, this model can not provide an effective process for the area outside the LOS. Hence, it is necessary to find a more advanced measurement model to characterize an explicit relationship between the RSS changes and the target locations. In this paper, we focus on the RSS attenuation both on LOS and non-lineof-sight (NLOS). Based on the diffraction theory, we first model human body and analyze how human body contributes to the attenuation. The theoretical analysis highlights the RSS attenuation caused by target mainly depends on two factors: the target-nodes distance and the target-link distance. These two distance factors can be used to depict the changes of RSS on LOS and NLOS paths, respectively. Inspired by this, we propose a new modified exponential model which considers both of these two factors. A single link experiment is conducted to validate the effectiveness of this theoretic model both on LOS and NLOS paths. We then exploit our model with a particle filter for the purpose of target localization and tracking. Finally, we demonstrate that the proposed modified exponential model outperforms the existing models by means of target tracking experiments in outdoor environments. The paper is organized as follows. In Section 2, we briefly formulate the modelbased DFLT problem. In Section 3, we present the new modified exponential model and conduct a single link experiment to show its validity. The experimental studies in the context of target localization and tracking are conducted to demonstrate the effective of the proposed model in Section 4.
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Problem Statement
DFLT system is based on a RF sensor network consisting of N sensor nodes and M = N (N −1) unidirectional communication links which spread over the sensing area. In each sampling interval, the N nodes broadcast packets to the neighboring nodes by using a simple token ring protocol. The RSS measurements of these M links will change when a DF person moves into the sensing area since the person can diffract, scatter,and reflect the RF signals. Therefore, the position of DF people can be estimated from the temporal variations of RSS measurements. ¯ ∈ RM×1 denotes the average background RSS measurements in the case Let γ of missing target. And γk ∈ RM×1 denotes the instantaneous RSS measurements at time k when the DF target exists in the sensing area. The presence of the target typically causes variation of RSS measurements, which is defined as zk ¯ − γk zk = γ
(1)
If we can find a mathematical model which depicts the relationship between the change in RSS and the motion state of the target xk , the predicted value yk ∈ RM×1 can be obtained. Then the error between the measurement value zk and the predicted value yk is given by ek = zk − yk
(2)
The more accurate the mathematical model is, the less noise will be introduced. While the predicted value agrees well with the measurement value, ek could be assumed to be zero-mean Gaussian, that is, ek ∼ N (0, σω2 I). Most of the RSS-based models (e.g., exponential model [6]) assume people to be a point without considering the impact of human body on LOS. The diffraction model [9] focuses on the attenuation caused by human cross-section on LOS, but the changes of RSS outside the LOS are ignored. It is inevitable to introduce unpredictable noise ek for the models mentioned above. Therefore, our goal is to propose a novel RSS-based model to reduce the noise level. we first model human body in the spatial area (i.e., an ellipsoid area that centered around the LOS) and analyze the impact of human body using the diffraction theory. The theoretical analysis demonstrates that the RSS measurements change when the target stands at different positions on LOS. By combing it with the attenuation outside the LOS which can be depicted as an exponential decay, we propose a new modified exponential model. This new model aims at depicting the changes of RSS both on LOS and NLOS accurately, thus improving DF localization and tracking performance effectively.
3 3.1
Modified Exponential Model Theoretical Modeling
Consider a single link and a DF person standing on LOS path as shown in Fig. 1. The target is approximated by a conducting cylinder [10], with radius r and
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height 2h. The ellipse centered around the LOS path denotes the spatial impact area, which has been widely used [3], [5]. The distance between the transmitting and the receiving nodes is d, and dtx (xk ), drx (xk ) are the distances between the target and the two nodes respectively.
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In this paper, we assume that the RSS attenuation is mainly caused by the diffraction. As shown in Fig. 1, when the target obstructs the LOS path, the radio waves diffract around the target as the RF propagation is obstructed, thus leading to diffraction loss. For simplicity, the human body is assumed to be a knife-edge object. Following the study of diffraction in [11], [12], the RF energy loss can be calculated based on Fresnel-Kirchhoff method. Let Ef denotes the free space field at the receiver when the target is not present, and E(xk ) denotes the field when the target stands at xk on the LOS path. Then their ratio is the electric field loss, which can be written as: B A E(xk ) 1 π 2 π 2 = 2 − j y z exp {−j( )}dy exp {−j( )}dz (3) Ef 2 2 2 −A −B
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where A, B are the Fresnel-Kirchhoff diffraction parameters given by 2d A=r λc dtx (xk )drx (xk )
(4)
B=h
2d λc dtx (xk )drx (xk )
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where λc denotes the wavelength of carrier frequency. Assuming that h r and dtx (xk ), drx (xk ) h, r, λc , the electric field loss can be approximated as follows √ E(xk ) 2 (6) Ef ≈ πA The RSS attenuation in decibel is defined as the squared electric field, |Ef /E(xk )|2 . Thus the variation of RSS on LOS yLOS can be expressed as: yLOS (xk ) ≈
π 2 r2 d λc dtx (xk )drx (xk )
(7)
From (7) we can conclude that the attenuation is determined by the distance between the target and the two nodes when the target obstructs the LOS path. The closer people gets to the transmitter/receiver, the more attenuation happens. Let β(xk ) denotes the target-node distance given by β(xk ) =
dtx (xk )drx (xk ) d
(8)
The RSS attenuation yLOS can be simply expressed as: yLOS (xk ) ≈
π 2 r2 λc β(xk )
(9)
It has been observed that, when the LOS path is vacant from the target but the spatial impact area is partially obstructed, there still exists significant attenuation which could not be ignored. Previous works have shown that the loss can be calculated by a piecewise function [13]. However, it is too complicated for a DFLT system to use this method directly. For simplicity, the exponential model is adopted to depict the attenuation on NLOS path, given by yNLOS (xk ) = ψ exp(−
λ(xk ) ) σ
(10)
where ψ is attenuation parameter, and λ(xk ) is the target-link distance function of the certain propagation link, which describes the relationship between target state xk and the LOS path. The value λ(xk ) is defined as λ(xk ) = dtx (xk ) + drx (xk ) − d
(11)
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Combining the cases of LOS and NLOS paths, we can conclude that the changes of RSS mainly depend on two factors. One is the target-link distance λ(xk ) and the other is the target-node distance β(xk ). Therefore, we propose a new model based on diffraction which can be written as: λ(xk ) ϕ exp(− ) (12) y(xk ) = β(xk ) σ Where ϕ and σ are attenuation parameters which can be identified by least square algorithm. The new model depicts the relationship between the changes of RSS and the target state both on LOS and NLOS paths. 3.2
Experimental Validation
Y coordinate(m)
We assess the validity of the proposed model using single link measurements. Two radio nodes are set separated by 6m, which use the IEEE.802.15.4 standard for communication. As shown in Fig. 2, the single people stands at different points along the LOS path with intervals of x = 0.5m, and the target stays 10s at each point. Then the person walks through the link along three different paths orthogonal to the LOS path at a low speed. We choose the RSS measurements collected in path 1 to show the attenuation on NLOS path.
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In Fig. 3, the RSS attenuation increases as the target moves close to the transmitter or receiver along the LOS path, and the minimum attenuation is observed in the middle of the link. The new model represented by red solid line fits the measurements well, which shows the attenuation caused by the target
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on LOS path mainly depends on the target-node distance β(xk ). As shown in Fig. 4, the RSS attenuation decreases dramatically when the person moves away from the LOS. It is reasonable to describes this change as an exponential decay in the proposed model. Therefore, our modified exponential model is validated to be effective both on LOS and NLOS path.
4 4.1
DFLT with Our Model Localization and Tracking Algorithm
Our task is to localize and track DF people from RSS measurements. Sequential Important Re-sampling (SIR) particle filter [14] is adopted to provide the
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position estimation. The kernel of this method is utilizing some random sample to express the posterior probability density of system variable, and the optimal approximate numerical solution of the system model can be obtained. This property is fit for our system. The target motion can be regarded as a firstorder Markov process p(xk |xk−1 , xk−2 , ..., x0 ) = p(xk |xk−1 ). It indicates that the current motion state is determined by the last motion state. Here we simply use the autoregressive gaussian (ARG) model to describe the process of target movement. That is xk+1 = xk + σv v (13) where σv is a constant and v ∼ N (0, I). The state xk is hidden into the RSS measurements zk , we use particle filter to track the posterior distribution P (xk |zk ). The pseudo-code of SIR particle filter is specified as Algorithm 1.
Algorithm 1. SIR particle filter N
N
p p Initialization: {xi0 }i=1 uniformly distributed, {ω0i }i=1 for k=1 to T do for i=1 to Np do predict step: xik ∼ f (xik |xik−1 ) weight update: ωki ∝ p(ek |xik ), ek = zk − yk ωi normalization: ω ¯ ki = Npk , i = 1, 2, . . . , N ; i i=1 ωk Np i ωk−1 xik estimation step: x ˆk ≈ i=1 1 resample step: {ωki , xik } → { , xi } Np k end for end for
4.2
Experimental Setup
As shown in Fig. 5, we build a RF sensor network with 24 radio nodes along the perimeter of a 6m×6m square area to calibrate and validate the parametric model. There is 1m interval between two adjacent nodes, and the height of each node is 1m. The radio nodes are MIB520CB made by Crossbow, which use the 2.4GHz IEEE.802.15.4 standard for communication. A base station is utilized to transmit data or command between the RF sensor and computer. In addition, a simple toking ring protocol is used to collect the RSS data of all possible radio links. RSS data of all links are gathered when a single person stands at a certain point or walks along a predefined path. These samples are then used to identify the parameters and validate the the new model using least square algorithm. In this paper, we set the parameter ϕ = 13.82 and σ = 0.023 for the experimental scene. We perform the single target localization and tracking experiments using the proposed model, exponential model and diffraction model.
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Fig. 5. Experimental platform is built in an open environment at Sun Yat-Sen University. 24 RF sensor nodes are deployed on the boundaries of a 6m×6m sensing area.
Table 1. The Localization error using different models Model Mean error (m) Max error (m) Diffraction model 0.29m 0.85m Exponential model 0.21m 0.78m Modified Exponential model 0.12m 0.25m
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7 True Trajectory Estimated Trajectory
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4.3
Localization and Tracking Results
To evaluate the effectiveness of the proposed model, 36 groups of single target localization are tested using different models. Here, the particle filter is used for localization, and each estimated position was taken after 50 iterations with 100 particles, and the average result of three model are listed in Table 1. It can be seen that the new model enhances the accuracy of estimation compared with the other two models. We choose 15 groups of localization results to demonstrate the localization performance using the new modified exponential model, as shown in Fig. 6.
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For the tracking issue, we use the ARG model to predict the motion state with the parameter σv = 0.5. Fig. 7 shows the tracking performance using the proposed model. The cumulative error distribution for tracking using different models is shown in Fig. 8, which illustrates the proposed modified model outperforms the diffraction model and the exponential model in tracking performance.
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Conclusions
We present a new modified exponential model to describe the RSS attenuation caused by people in outdoor environments. The diffraction theory is introduced to analyze how human body contributes to the RSS attenuation in this paper. The theoretical analysis highlights that the RSS attenuation mainly depends on the target-node distance and target-link distance. The proposed model, which combines these two factors, can perform well in handling the changes of RSS both on LOS and NLOS paths. Experiment results show that the modified exponential model achieves high estimation accuracy using SIR particle filter. In future, we will develop the model for multiple targets and apply it in cluttered indoor environments.
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