However, even when the antenna of a transmitter badge is considered as isotropic, people or objects can affect the RFID badge's radiation, due to the fact that they are absorbing power, altering the antenna impedance and thus distorting the antenna gain pattern [ 3 ]. In this book chapter, we present models and methods to handle, and in fact benefit from, the removal of the unrealistic isotropic gain pattern assumption. We present measurements and models for a transmitter badge worn by a person. As presented in the study of Zhao et al. In addition to experimental results, we provide theoretical results that show that the existence of a directional gain pattern can actually reduce position error for localization algorithms.
Comparison between the Bayesian CRB [ 3 ] and the CRB [ 8 ] shows that joint estimation of orientation and position may outperform result in lower mean squared error estimation of position alone in the isotropic case. A transmitter in close proximity to a human body is strongly affected by human tissue, which absorbs power and distorts the gain pattern of the transmitter [ 11 , 12 ].
Assuming known anchor node coordinates, these two model parameters can be estimated via linear regression, as in Ref. The recent study in Ref. In their experimental study, two Crossbow TelosB nodes [ 13 ] operating at 2. Meanwhile, the RSS at node 1 was recorded on a computer. Node 2 transmitted about 20 times per second, thus about RSS measurements were recorded for each of the eight different orientations made by the person. The described experiments were performed by five people in the student building as well as an empty parking lot at University of Utah.
Eight experiments were performed with various distances between the two nodes from 1. Therefore, a total of 25, measurements were recorded. It is worth to note that the variation in RSS as a function of orientation due to the presence of a person is similar to other experimental studies [ 7 , 14 ]. As explained in Ref. First, regardless of path length or person wearing the badge, the gain is higher in the direction the person is facing and lower in the opposite direction.
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Given that the person is facing node k , the mean RSS value of node k would be greater than that of node j. Second, Eq. The measurements for this particular set of data showed a single order captures the vast majority of the angular variation. Note that the model of Eq.
This chapter focuses on 2D position estimation using RSS measurements. Note that one badge is used to simplify notation in the chapter.
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However, extension to multiple badges is possible. However, if the gain pattern model is included, two parameters in the gain pattern model must be estimated from Eq. As mentioned in Ref.
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For instance, in the isotropic gain pattern case, the TICC used a 2D grid search method to find the 2D coordinate. However, when the dimension of the estimation parameter vector increases, the computation time of a grid search increases exponentially. Before we propose the algorithm to jointly estimate the position and the gain pattern, we first introduce a gain pattern estimator, assuming we know the badge position z t.
The gain pattern estimator was first proposed in Ref. Because n p and P 0 are determined by linear regression, they tend to make the model error zero mean. Then, the gain pattern from an M order model can be estimated as:. By comparing Eqs. Thus to estimate the gain pattern, we only need to calculate the DFT term G 1. Thus, we estimate G k as:. This calculation of G 1 requires only N complex multiplies and adds, where N is the number of RSS measurements received for a badge.
This low complexity is important to minimize the computational complexity of the localization algorithm.
In the gain pattern estimation, the badge position is assumed known. But in a localization algorithm, the badge position needs to be estimated. For joint position and gain pattern estimation, an alternating gain and position estimation AGAPE algorithm has been developed in Ref.
As described in Ref. The algorithm iterates until a misfit function is minimized. For the first step, given that the gain pattern is isotropic, the naive MLE method is used to estimate the badge position. The MLE solution can be derived from a conjugate gradient algorithm. However, a 2D grid search method was used to avoid the local minima problem here, in the position estimation step. Note that the 2D MLE grid search can be accomplished quickly in hardware. The steps of position and orientation estimation repeat until the following misfit function is minimized:.
One might think that the lower bound of the variance of an estimator will increase due to the introduction of an additional unknown gain pattern model. In this section, the Bayesian CRB [ 17 ] is derived by including the gain pattern model parameters as nuisance parameters, as derived in Ref. The Bayesian CRB is used because the prior knowledge of the gain directionality G 1 is available a priori. In this book chapter, we show that the CRB derived in Ref. We also show that the lower bound on the variance of a position estimator is decreased by the introduction of a gain pattern model.
The gain pattern model expressed in Eq. Thus, their distributions are close to Gaussian, by a central limit argument. This assumption is equivalent to a Rayleigh distribution [ 18 ] assumption for G 1 , which matches the prior knowledge of G 1 : 1 G 1 must have a nonnegative value; 2 G 1 is unlikely to be exactly zero and also unlikely to have very large values, since the gain pattern is related to human size. Note that the prior information only contains information of the gain pattern, no prior information about the badge position is included.
For an estimator with deterministic parameters, a CRB is often used. We show this next. Once these model parameters are calculated, the Bayesian CRB can be calculated for an L m by L m square area with four anchor nodes located at four corners. To obtain a lower bound for the overall area, we introduce the average RMSE bound , which is defined as the average value of the square root of the Bayesian CRB bounds over the area.
Lower bounds. We present experimental datasets from three experiment campaigns in this book chapter. Experiment 1 : The first experiment was performed in a 6. A person worn a TelosB node in the middle of his chest and walked around a marked path at a constant speed of about 0. This outdoor experiment dataset was first reported in Ref.
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Experiment 2 : The second experiment was an indoor experiment performed inside the Warnock Engineering Building of the University of Utah. A person wearing a TelosB node walked clockwise twice around a 2. The experiment was performed in the building lounge area, during which students occasionally walked outside the peripheral area of the sensor network. This experiment is first reported in this book chapter.
A person wearing a transmitter walked four times around a 3. The experiment was performed in a dynamic environment, where wind caused tree branches and leaves to sway. T i is denoted as a tag and its authentication center is C B. At time t , a reader R i wants to interact with the tag T i. Here, we also introduce the time window mechanism. Fig 6 shows the example of time window mechanism in VIP scheme. In time window t k , the authentication center of reader R j records the number of interaction behavior of R i , and uses them to compute the global trust value of reader R i as follows: 9 where:.
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Fig 7 expresses the details of VIP scheme. The proposed method can track the authorization use of reader by checking the interaction proof. The method avoids the impact of reader distribution and limited communication distance between readers and tags. The trust computing process of VIP scheme is summarized as four steps: 1 The authentication center pre-authorizes reader R i to interact with the tag T i ; 2 The interaction feedback record at time t is saved in the tags; 3 At the time of next interaction, the tag T i interacts with the reader R j.
The interaction feedback record at time t is added into the data packet and transmitted to the authentication center of reader R j ; 4 If the feedback score is 0, the authentication center of R j will send the abnormal event report to authentication center of R i and administration center, respectively.
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The number of authentication centers is few, and their status is stable in a multi-domain RFID system. Therefore, a centralized trust evaluation scheme is proposed to evaluate the trustworthiness of authentication centers. An administration center is in charge of managing the trust of authentication center based on the abnormal event reports of readers of its own domain.
The authentication center needs to collect the abnormal events of readers of its own domain periodically, and sends the abnormal event reports to administration center. The administration center receives the abnormal event reports and computes the trust of authentication center, as shown in Fig 8.
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Let A and B denote two different domains. C A and C B denote their authentication center, respectively. A tag T i belongs to the domain A. R i sends the authorization request to C A. If R i and T i is in the same domain A , C A computes the trust of R i as follows: 10 where is intra-domain trust, which can be obtained with Eq 9 or Eq 8.