## 1. Introduction

RFID localization of assets, robots and people has significant benefits for logistics, security and operations management. For example, GE Healthcare uses the AgileTrac platform [1] to track the physical location of each asset, via various real‐time location system (RTLS) techniques. In RFID localization, many kinds of radio measurements can be used: time of arrival (TOA), time difference of arrival (TDOA), angle of arrival (AOA) and received signal strength (RSS) [2]. While RSS is low‐cost and available in almost all standard wireless devices, most RSS‐based localization methods make the assumption that the transmitters have isotropic gain patterns. 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]. Previous studies have focused on characterizing the effects of a human body’s location and orientation on RSS measurements [4–7]. 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.

Real‐world directional gain patterns are problematic for RSS‐based localization algorithms. In RSS‐based algorithms, a model relating RSS and path length is assumed [8] or estimated from training measurements [9]. When the RFID antenna gain pattern is no longer isotropic, the distances estimated from the log‐distance model [10] will not be the same even if the RFID transmitter is in the middle of two receivers. Model‐based localization algorithms will infer that the transmitter is closer to the receiver that measured larger RSS and will thus produce estimates that are biased towards directions of high gain in the gain pattern [3].

To deal with the non‐isotropic antenna gain pattern and improve model‐based RFID localization algorithm, we need to build a model for the directionality of a transmitter RFID badge when it is worn by a person or attached to an object. We present measurements and models for a transmitter badge worn by a person. However, RFID tags attached to large objects will also experience non‐isotropic gain patterns, and thus extensions to other types of tagged objects are feasible. As presented in the study of Zhao et al. [3], the variation of RSS was modeled as a function of people's orientation (i.e., facing direction). The study also proposed (1) a first‐order model to capture most of the variation in the gain pattern as a function of people's orientation, (2) a method to estimate people's orientation and directionality from ordinary RSS measurements, and (3) an algorithm to estimate the position, orientation and gain pattern of the RFID badge called alternating gain and position estimation (AGAPE) algorithm. We apply the AGAPE algorithm together with a 2D maximum likelihood estimation (MLE) algorithm [8] and 4D MLE algorithm [3] to three sets of experiments performed at different environments: outdoor, indoor and through‐wall. Experimental results show different levels of improvement from including the first‐order gain pattern model at those different environments.

It is not obvious that a non‐isotropic gain pattern can benefit RFID localization because additional model parameters must be estimated together with the RFID locations. 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. The Bayesian Cramer‐Rao bound (Bayesian CRB) was derived in Ref. [3] for joint estimation of orientation and position, while the CRB for position estimation was derived in Ref. [8] with an isotropic gain pattern assumption. 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.

In summary, in this book chapter, we present the latest research progress in the effort to include RFID antenna gain pattern in model‐based RSS localization algorithms. We show that real‐world non‐isotropic gain pattern of RFID badge is not a problem to be ignored, but a means to improve localization accuracy. We present measurements, models, estimation algorithms and estimation lower bounds for RSS‐based localization in wireless sensor networks. Experimental results from three sets of experiments show that position estimates are improved with the inclusion of orientation estimates from the first‐order gain pattern model and the RSS measurements.

## 2. Models

Statistical models based on real‐world measurements are important for model‐based RSS localization algorithms. In this section, a measurement‐based model is presented for the gain pattern of a transmitter badge worn by a person. 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].

The log‐distance model [10] is a general model for the power *from the transmitter badge*

where

Naive model‐based localization algorithms use

### 2.1. Measurements

The recent study in Ref. [3] quantifies the effect of the orientation of a human body on the RSS measurements using datasets from several experiment campaigns. In their experimental study, two Crossbow TelosB nodes [13] operating at 2.4 GHz were used with one node (node 1) placed on a stand and the other one (node 2) hung in the middle of a person's chest. The person wearing node 2 turned 45° every 20 s, with the distance between these two nodes kept the same. Meanwhile, the RSS at node 1 was recorded on a computer. Node 2 transmitted about 20 times per second, thus about 400 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 1.5 to 5.0 m. Therefore, a total of 25,600 measurements were recorded.

Experimental results from two different experiments are shown in **Figure 1(a)**. The minimum RSS of Experiment 1 (red) and Experiment 2 (blue) are 145° and 180°, respectively, whereas the maximum RSS are 315°and 0°, respectively. **Figure 1(b)** shows the mean gain pattern, which is averaged across all experiments, and indicates that if the person's orientation is 180°, i.e., the human body blocks the line‐of‐sight (LOS) path between nodes 1 and 2, the gain pattern is close to the minimum. In contrast, if the person's orientation is 0°, i.e., facing the node1, then the gain pattern is about 20 dB higher as compared with its lowest point [the red curve in **Figure 1(b)**]. The average gain pattern in **Figure 1(b)** closely resembles a cosine function (black curve) with period 360° and amplitude 10 dB. 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].

### 2.2. Gain pattern model

Based on the results of the measurements described above, a model for the gain pattern is proposed as a cosine function with period 360°:

where

As explained in Ref. [3], the model of Eq. (2) represents the two most important characteristics observed in the measurements. 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. In a wireless sensor network with several anchor nodes, a person with a badge stands halfway between node *j* and node *k* so that the distance between the badge and these two nodes are the same, as shown in **Figure 2**. 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. (2) is a first‐order model for any periodic function. The measurements for this particular set of data showed a single order captures the vast majority of the angular variation. Any function with period

where

## 3. Localization algorithms

### 3.1. Problem statement

This chapter focuses on 2D position estimation using RSS measurements. For a wireless sensor network which has *N* anchor nodes and one badge, the position estimation corresponds to the estimation of the coordinates of a badge:

If we only use the log‐distance model in Ref. [10] to estimate distances between the badge and anchor nodes, our unknown model parameter

However, if the gain pattern model is included, two parameters in the gain pattern model must be estimated from Eq. (2). So, we include these two parameters as nuisance parameters, and the unknown parameter vector

where

### 3.2. 4D MLE algorithm

To estimate both the badge position and the gain pattern, a baseline algorithm ‐ 4D maximum likelihood estimation (MLE) algorithm is introduced here as the counterpart of the 2D MLE algorithm [8] with an isotropic antenna gain pattern assumption.

As discussed in Section 2, the received dBm power

As mentioned in Ref. [3], grid search method was used for finding the MLE solution. For instance, in the isotropic gain pattern case, the TICC2431 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. In addition, the high computation cost of a multi‐dimensional gird search also prevents it from real‐time applications. To better estimate the position and the gain pattern in real‐time, we use signal processing techniques and first‐order approximation to develop a different algorithm.

### 3.3. Gain pattern estimator

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

When measuring the gain pattern at discrete values of

where

The mean gain

Then, the gain pattern from an

The first‐order model including only the

By comparing Eqs. (8) and (2) in Section 2.2, we find the two model parameters

Thus to estimate the gain pattern, we only need to calculate the DFT term

where

Note, we need only

### 3.4. Alternating gain and position estimator

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. [3] to efficiently estimate both the position and orientation of a person in a wireless sensor network.

As described in Ref. [3], the algorithm includes (1) the initial estimation of the position of the badge using isotropic gain assumption, (2) calculation of the gain pattern parameters using the first‐order sinusoidal model, (3) re‐estimation of the badge position using the RSS‐distance model with the estimated gain pattern. The algorithm iterates until a misfit function is minimized. Note that the proposed AGAPE algorithm is a kind of alternating minimization method [16]. **Figure 3** shows the flowchart of the AGAPE algorithm. 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 output of the position estimation step is referred to as

For the orientation estimation step, given an estimated position, we calculate the gain pattern

where

## 4. Estimator lower bounds

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. [3]. The Bayesian CRB is used because the prior knowledge of the gain directionality

### 4.1. Bayesian CRB

To derive the Bayesian CRB, we assume that the orientation of the badge

The gain pattern model expressed in Eq. (2) can be rewritten as:

where

The Bayesian CRB is also called the Van Trees bound or the MSE bound [17], it is given by:

where

### 4.2. Comparison with CRB

For an estimator with deterministic parameters, a CRB is often used. With an isotropic gain pattern assumption, a CRB for position estimation using RSS is derived in Ref. [8]. When the gain pattern term in the RSS‐distance model approaches zero, that is,

With the additional parameters in the gain pattern model, the Bayesian CRB not only depends on radio channel parameters, but also depends on gain pattern parameter **Figure 4**. For very small *e.g.*, **Figure 4(a)**, which is identical to the CRB derived in Ref. [8]. For **Figure 4(b)**. 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. The average RMSE bound for *e.g.*,

## 5. Experiments and results

### 5.1. Experiment description

We present experimental datasets from three experiment campaigns in this book chapter. These experiments were performed at outdoor, indoor and through‐wall scenarios, which cover a variety of multipath effects and environmental noise conditions.

*Experiment 1*: The first experiment was performed in a 6.4 m by 6.4 m area outside the Merrill Engineering Building of the University of Utah. The area is surrounded by 28 TelosB nodes [13] deployed at known locations on stands at 1 m height, near trees and 3 m away from the building wall. A person worn a TelosB node in the middle of his chest and walked around a marked path at a constant speed of about 0.5 m/s. This outdoor experiment dataset was first reported in Ref. [3], and details can be found there.*Experiment 2*: The second experiment was an indoor experiment performed inside the Warnock Engineering Building of the University of Utah. A 6.1 m by 6.1 m area was surrounded by 20 TelosB nodes with an interdistance of 0.91 m between each two anchor nodes. A person wearing a TelosB node walked clockwise twice around a 2.7 m by 2.7 m square, as shown as the purple line in**Figure 9**. 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.*Experiment 3*: The third experiment was a through‐wall experiment, in which 34 TelosB nodes were deployed outside the living room of a residential house, as shown in**Figure 5(b)**. A person wearing a transmitter walked four times around a 3.6 m by 3.6 m square in the living room. The experiment was performed in a dynamic environment, where wind caused tree branches and leaves to sway. This experiment dataset is first reported in Ref. [19].

### 5.2. Experiment test bed and procedure

All three experiments use the same radio hardware, network protocol and follow the same procedure. TelosB nodes were used as network anchor nodes and also mobile node. In all experiments, anchor nodes were deployed at fixed locations, and one mobile node (transmitter badge) was worn by a person in the middle of their chest. All TelosB nodes were programmed with TinyOS program Spin [21] SPAN Lab. Spin protocol, and a base station connected to a laptop was used to collect RSS measurements received by all the anchor nodes.

Before people started walking in the area, a calibration was performed with no people in the experimental area. Since the locations of the anchor nodes are known, we use the measured RSS and the link length to estimate the

### 5.3. Experimental results

A unique feature of modeling RFID antenna gain pattern is that it enables estimating the orientation of the person, in addition to the person's location. We show the orientation estimation results from the AGAPE algorithm using data from Experiment 1, which was first reported in Ref. [3]. The estimated orientations are shown in **Figure 6**, together with the actual walking directions. The orientation estimates generally agree well with the actual orientations. As mentioned in Ref. [3], “the deviations from the actual orientations are generally less than 30°. However, sometimes when the person is turning, the bias is larger than 30°. This may be due to the fact that the algorithm uses RSS measurements from 28 anchor nodes to estimate the person’s orientations, and at the turning points, RSS measurements may be a mix of those recorded before, after and during turning.” The median error from the AGAPE algorithm is about 10°, and more than 90% errors are below 30°. The 4D MLE algorithm can also estimate orientation, but it takes much more computing time. As mentioned in Ref. [3], the 4D MLE implementation uses “10 times more than the AGAPE algorithm in the Python implementation, and the estimates are not more accurate than those from AGAPE.” In addition to the orientation of the badge, another model parameter

For the performance of position estimation, the CDF of the position estimation error from Experiment 1 is shown in **Figure 7**. We see that the median estimation error is about 0.61 m, and the 90th percentile estimation error is 1.22 m. However, the 2D MLE method has a median error of 2.60 m, which is about 4.3 times larger than that from AGAPE. From the comparison of the CDFs, we see that significant improvement is made if we include the orientation estimate in the localization.

In Experiment 1, a wireless sensor network with 28 anchor nodes is used to locate a badge in a 6.4 m by 6.4 m square area. However, not so many anchor nodes may be available in some applications. The following tests are performed using RSS measurements from a fraction of all anchor nodes to investigate the effect of node number on the localization accuracy.

As mentioned in Ref. [3], “in the first test—Test 1, we use RSS measurements from different numbers of equally spaced anchor nodes to locate the badge. For example, we first choose the RSS measurements from four anchor nodes at each corner of the square area. As expected, the localization is not very accurate, the RMSE of the position estimate is 3.36 m, and the RMSE of the orientation estimate is 40°. Next, we use the RSS measurements from those anchor nodes whose ID numbers are multiples of 1, 2, 3 and 4 (since the anchor nodes are placed in a numerically increasing order around the experimental area, these anchor nodes are equally spaced). The RMSEs of the position and orientation estimates are shown as dots in **Figure 8(a)** and **(b)**, respectively. We see that as the node number increases, the RMSEs of position and orientation estimates both decrease. When the node number increases to fourteen, the RMSE of the position estimate decreases to 1.30 m, and the RMSE of the orientation estimate decreases to 18°. Further increase in anchor nodes will continue to decrease the RMSEs, however, there are diminishing returns.”

“In practical scenarios, anchor nodes may not be equally spaced. Thus, in Test 2, we use RSS measurements from randomly chosen anchor nodes. For example, we randomly choose four anchor nodes and run AGAPE using the RSS measurements from these nodes. We repeat the above procedure 100 times, and each time calculate the RMSEs of the position and orientation estimates. Similarly, we randomly choose seven, ten, fourteen and twenty anchor nodes. The average RMSEs are shown as squares, and the RMSE standard deviations are shown as error bars in **Figure 8**. From **Figure 8(b)**, we see that the average orientation RMSEs in Test 2 are all larger than the RMSEs in Test 1. For position RMSEs shown in **Figure 8(a)**, the average RMSEs in Test 2 are generally larger than the RMSEs in Test 1, except for the extreme case when the number of anchor nodes is four. Thus, the AGAPE algorithm generally performs better if the anchor nodes are equally spaced. However, the AGAPE algorithm is not very sensitive to the effect of anchor nodes being non‐equally spaced. In fact, the differences between the position RMSEs in Test 1 and the average position RMSEs in Test 2 are always less than 0.4 m. Finally, we compare the performance of the naive MLE 2D method with the AGAPE algorithm using randomly chosen nodes. As shown in **Figure 8(a)**, the MLE 2D method is not very sensitive to the number of anchor nodes. However, the average position RMSEs from the MLE 2D method are always larger than those from the AGAPE algorithm for different numbers of anchor nodes.”

For Experiment 1, we see that the AGAPE algorithm can estimate both the orientation and location of a person wearing an RFID badge with good accuracy for an outdoor environment. However, its performance degrades at the indoor and through‐wall experiments, i.e., in Experiments 2 and 3. The position estimates from AGAPE and 2D MLE at a particular time in Experiment 2 are shown in **Figure 9**, together with the likelihood function of MLE. We see the MLE location estimate is biased towards the walking direction of the person, as it does not include the human body effect on the transmitter gain pattern in its model. We also see that the AGAPE algorithm is able to estimate both position and orientation of the person, and the position estimate is closer to the actual location than the 2D MLE estimate. However, AGAPE is not as accurate as in the outdoor experiments, because the modeling error in the first‐order gain pattern model increases at an indoor environment due to multipath effects.

For the through‐wall experiment Experiment 3, we see that due to the attenuation of walls, the path‐loss model parameter

We compare the root mean squared error (RMSE) of the position estimates for the above three sets of experiments. The RMSEs from the AGAPE, 2D MLE and 4D MLE algorithms are listed in **Table 1**. We see that for Experiment 1, the RMSE from the AGAPE algorithm is 0.87 m, which is similar to the 4D MLE algorithm. However, the MLE 4D algorithm uses grid search method and is not a real‐time algorithm due to its computational complexity. The RMSE from the 2D MLE algorithm is 2.64 m. So for Experiment 1, the RMSE from AGAPE is reduced by 67.2% compared to the 2D MLE algorithm. For Experiment 2, the 2D MLE has an RMSE of 1.86 m, while the RMSEs from 4D MLE and the AGAPE are 1.65 and 1.69 m, with 11% and 9% improvement, respectively. Finally, for Experiment 3, AGAPE does not have much improvement compared to MLE. Both MLE and AGAPE have RMSEs of about 2 m.

From the above comparison, we see that the 4D MLE and AGAPE algorithms are significantly more accurate than the 2D MLE algorithm for outdoor environments. The 4D MLE takes much more time than the AGAPE algorithm, but both algorithms can estimate the position and orientation of a person wearing an RFID badge in front of her chest. The benefit from the modeled directional gain pattern reduces at indoor and through‐wall environments, since the first‐order gain pattern model becomes much noisier due to the increased multipath effects. The AGAPE and 4D MLE algorithms may suffer from the ambiguity problem, that is, they may converge to a wrong position with a wrong orientation estimate. This ambiguity problem is observed when a person wearing an RFID badge presents in close proximity to walls. This problem may be resolved using orientation estimates from inertial measurement unit (IMU). However, RF device‐free localization [19, 20] may provide a simple way to solve the ambiguity issue without adding more sensing modalities.

## 6. Conclusion

In this book chapter, we present measurements and models of active RFID antenna gain pattern due to the human body effect. We find that a wireless sensor network‐based RFID localization system can actually benefit from the non‐isotropic gain pattern due to the attenuation and reflection of the human body. We present three estimation methods of RFID localization using received signal strength (RSS) measurements from a wireless sensor network: 2D maximum likelihood estimator (MLE), 4D maximum likelihood estimator (MLE) and alternating gain and position estimator (AGAPE). The 4D MLE and AGAPE algorithms can both estimate user orientation in addition to position, with the first‐order gain pattern model and the assumption that the user is wearing the RFID badge in front of her chest. However, the AGAPE algorithm significantly outperforms the 4D MLE algorithm in computational time using discrete Fourier transform (DFT) and first‐order approximation. We also derive theoretical estimation lower bound for joint orientation and position estimation problem. The Bayesian Cramer‐Rao bound (CRB) shows that the lower bound on the variance of a position estimator decreases with the inclusion of a gain pattern model to the RSS log‐distance model. Finally, we present three sets of experiments performed at outdoor, indoor and through‐wall environments. The experimental results show that the 4D MLE and AGAPE algorithms outperform the 2D MLE algorithm in localization accuracy in all datasets.