A) Brief overview of the principle of passive RFID systems

RFID technology allows data storage in small electronic transponder circuits (tags) that are particularly portable. The communication between a passive RFID tag and an interrogator (reader) is realized by RF waves. Figure 1 presents the block diagram of an RFID system.

Fig. 1. Block diagram of an RFID reader and a RF tag.

The tag, which is generally attached to a person or an object, consists of an antenna and an associated integrated circuit (chip). In passive tags there is no internal power supply, and then the chip obtains power for its operations as transponder from the RF signal transmitted by the reader. The communication consists of a query sent from the reader, to which the tag respond by sending back its data by switching its input impedance between two states, and thus modulating the backscattered signal with information.

B) Backscatter Link Budget and the RSSI method

Figure 2 shows the functional principle of the RFID communication detailing on the backscattering link budget. For clarity and without loss of generality, the transmitting and receiving antennas of the reader are presented separately, even if the monostatic configuration is currently used in commercial readers.

Fig. 2. Illustration of the RFID backscatter link.

In free space, the ratio p of the received power P _r to the transmitted power P _t depends on the distance d [m] between the tag and the reader. From the radar range equation defined in [Reference Balanis16], p is given by:

(1)$$p\left(d \right)= e_t e_r \left(1 - \left\vert \Gamma_{t} \right\vert ^2 \right)\left(1 - \left\vert \Gamma_{r} \right\vert ^2 \right)\sigma \displaystyle{{D_t \left(\theta _t \comma \; \phi _t \right)D_r \left(\theta _r \comma \; \phi _r \right)} \over {4\pi }} \left(\displaystyle{\lambda \over {4\pi d^2 }} \right)^2 \left\vert \hat \rho _w \cdot \hat \rho _r \right\vert ^2\comma \;$$

where e is the dielectric conduction loss, Γ is the reflection coefficient, σ [m²] is the radar cross section (RCS) or echo area, D(θ, ϕ) is the directivity in the direction (θ, ϕ), λ [m] is the wavelength (λ = c/f, c speed of light, f frequency), ${\hat \rho }_{r}$ is the polarization unit vector of the receiving antenna, and ${\hat \rho}_{w}$ is the polarization unit vector of the scattered waves. The indices «t» and «r» refer to the transmission and the reception conditions, respectively.

Assuming ideal conditions (i.e., impedance matching conditions in transmission and reception and polarization matching of the transmitting and receiving antennas) and the antenna gains G _t and G _r, Equation (1) can be rewritten as:

(2)$$p\left(d \right)= \sigma \displaystyle{{G_t G_r } \over {4\pi }} \left(\displaystyle{\lambda \over {4\pi d^2 }} \right)^2.$$

Therefore, the distance d can be easily deduced from Equations (1) or (2) if all other parameters are known. This approach is the principle of the RSSI method. Unfortunately in real conditions, the direct application of this method is limited and can lead to very inexact distances. Indeed, the ideal conditions are generally not verified and several parameters are unknown a priori. Firstly, the RCS σ value is very difficult to estimate: it depends on many parameters such as the chip sensitivity, the impedance matching between the tag antenna and the chip, the incident power on the tag which causes change in the input impedance of the chip, the polarization matching (which depends on the orientation between reader and tag), the modulation depth and the tagged object properties [Reference Nikitin and Rao17–Reference Colin, Moretto, Abou Chakra and Ripoll19]. Furthermore, the propagation conditions can vary with changes in the environment.

In fact, the distance d to be estimated is written as the product between the constant α which is assumed known or measured and an unknown variable γ such as:

(3)$$d = \underbrace{\underbrace{\left(\displaystyle{\lambda \over {4\pi }} \right)^{1/2} \left(\displaystyle{{G_t G_r } \over {4\pi }} \right)^{1/4}} _{\matrix{term\; constant\cr assumed\; known}} \underbrace{\left(\displaystyle{1 \over {p\left(d \right)}} \right)^{1/4} }_{\matrix{ measured \cr variable}}}_\alpha \times \underbrace{\underbrace{\chi \left(\sigma \right)^{1/4}}_{\matrix{unknown \cr variable}}}_\gamma = \alpha \times \gamma\comma \;$$

where the coefficient χ takes into account the non-ideal conditions.

Consequently, although the gain of the reader antenna and the measured powers can be considered known with a good exactness, it is not enough to achieve an accurate estimation of the distance d between the tag and the reader.

C) Proposed approach for improving the localization of the tag

The indetermination in the estimation of the distance d between tag and reader can be solved by directly considering the overall problematic: the trilateration, i.e., achieve the localization of the tag by measuring three different distances d _i, i = 1, …, 3 between the tag and three differently positioned readers. For the two-dimensional case, the trilateration consists of finding the intersection of the three circles defined by the position of the readers (center of circles) and the associated distances d _i (radius of circles). Therefore, considering that this intersection exists and is unique, the problem can be resolved, even if, the estimated distances d _i are wrong. It should be understood that the estimated distances only inform about the weight of the distance (i.e., a relative distance) and not about the absolute distance (i.e., the real distance). The distance deduced from Equation (3) is only an indicator composed of two parameters α and γ. The resolution of the problem relies on the following idea: find the three most probable radii leading to a unique intersection using scale factors (SFs) which represent the unknown variables related to the environment and the RFID system. Figure 3 illustrates the principle of the proposed approach. The readers are located on square points and the true position of the tag is a grey circle. From the estimated distances (which can be calculated from (3)), a direct trilateration detects the tag on the black circle. By applying the technique just described, now the position of the tag now corresponds to the position defined by the black star. The estimation of the tag position is consequently improved.

Fig. 3. Illustration of the modified trilateration.

The algorithm of the proposed method is illustrated in Fig. 4. The corresponding radius for each one of the three readers is estimated from the measured power received at each reader using the Friis equation. The area of the intersection of the three associated circles is calculated. If the area is not small enough, by considering that the intersection should be a point, then the radii are modified by the SF, and so on until the found area is small enough. When the algorithm stops, the distance between readers and tag and the position of the tag are known.

Fig. 4. Schematic representation of the algorithm.

Now, it should be noted that if the SFs are assumed constant (e.g., if we consider d as the unique unknown parameter) and by varying, linearly and simultaneously, each SF until we find an intersection point, the true distances d _i can be found; and then, the estimated position is correct. In this case, the correction of the estimated distances due to the SF is given by:

(4)$${d}_{i} = {d}_{i} \times SF\comma \; \quad i = 1\comma \; \, 2\comma \; \, 3\comma \;$$

where SF is a value slightly less than 1 because with the assumption that the initial radii are over-estimated, the SFs gradually decrease their values. Otherwise, other SFs could also be envisaged. The SFs can be differentiated with a weighting coefficient depending on the estimated distances. For example, a possible solution could be:

(5)$$d_{i} = d_{i} \times SF_{i}\comma \; \quad i = 1\comma \; \, 2\comma \; \, 3\comma \;$$

with

(6)$$SF_{i} = {SF} \times \left(\displaystyle{{d_{i}} \over {\sum_{{j} = 1}^{3} d_{j}/3}} \right)\comma \; \quad i = 1\comma \; \, 2\comma \; \, 3.$$

In this case, therefore the SFs take into account the relative estimated distances. The next section details the method and demonstrates the proposed concept from simulation and experimental results.

A) Validation by simulations

The objective of this section is to verify the feasibility of the proposed concept and to evaluate its performance. The parameters of the simulation are the following: three RFID readers are placed in the three corners of a square room as illustrated in Fig. 5 (filled circles); the operating frequency is 915 MHz; the power of interrogation signal (output of the readers) is 800 mW; Transmitting (TX) and Receiving (RX) antennas gain are assumed equal to 0 dBi for the simulations. Firstly, Fig. 5(a) illustrates the case where the unknown parameters, defined through the variable γ as in (3), are assumed constant. The dashed lines correspond to the estimated distances for each link reader-tag. The deduced tag position from trilateration is represented by the small circle. The solid lines represent the reference (with real distances and real tag position). After processing and using a SF varying in the same way for each link, i.e. defined by (4), the distances and the tag position are achieved. The estimation is as accurate as expected. In the following, the estimated position evaluated only using a classic trilateration is so-called direct estimated position, and the estimated position achieved after the application of the proposed method is so-called estimated position after processing. Figure 5(b) gives an example of the general case with the unknown parameter γ randomly modeled by a white Gaussian noise and centered on their previous constant value. The chosen SF is variable: it depends on the estimated distances and is adaptive as defined in (5). The estimated position after processing (dash-dot lines) is much better than the direct estimated position (dashed lines). The simulation confirms the improvement of the accuracy in the tag localization by using the proposed concept. To quantify the achieved qualitative results, Fig. 6 shows the error encountered when calculating the position of the tag compared with its real position by calculating the mean Euclidean distance in terms of the deduced root mean square (RMS) error. This error represents the accuracy on the tag location estimation in function of the variance, i.e. the power, of the white Gaussian noise added to the unknown parameters. For each variance of noise, 100 simulations are realized and the corresponding error is calculated. Figure 6 shows the mean error for each variance and illustrates the performance of the location algorithm. These simulations clearly highlight the performance of the proposed approach, both in terms of accuracy and robustness.

Fig. 5. Illustration of the principle of the location method: (a) validation of the proposed method with estimated position when the errors are assumed constant; (b) example of position estimation when the errors are different.

Fig. 6. RMS error in function of noise variance between 0 and 5.

B) Experimental validation

Finally, the proposed method is applied in a real context where the channels always present a direct path (i.e., propagation line-of-sight (LOS)) but they are more complex with the presence of multipath due to the environment. The measurement was realized in a room of 30 square meters with some furniture (Fig. 7(a)). For ease of implementation but without loss of physical meaning, the measurement setup is the following: one of the three commercial tags presented in Table 1 is positioned in a fixed manner as illustrated in Fig. 7(b); the reader (Alien ALR-9780) successively takes the 12 indicated positions; for each case the transmitted power is constant, the measured received power is presented in Table 2.

Fig. 7. Experimental configuration: (a) photo of the setup configuration; (b) functional scheme of the setup configuration.

Table 1. Tested UHF RFID tags.

Table 2. Measured received powers for different positions of the reader and for the considered tags.

At once, several remarks have to be emphasized. One reader was displaced by 12 different positions in order to offer multiple combinations and to accomplish the scheme with three readers. In order to evaluate the proposed concept, this approach is correct: being fixed to the tag and considering several configurations of the three readers, the positioning distribution is satisfied for the proposed method. Among the 220 possible combinations of three readers, only the combinations where two or three readers are not aligned are taken into account, i.e. 108 combinations. Indeed, the associations of aligned readers ({1, 2, 3}; {4, 5, 6}; {7, 8, 9}; {10, 11, 12}) were not considered because these configurations are not adequate in order to realize a trilateration; and assuming that the readers are positioned at the corners of a room, the tag cannot be aligned with two readers. It should also be noted that in practice, three readers are sufficient, even if, more readers could provide diversity and improve the accuracy of localization. Moreover, the different values of the received power for the three considered tags, even when they occupy the same position, highlight the strong influence of the specific characteristics of each tag. Furthermore, these received powers present different values which are unexpected for symmetrical positions, mainly due to the non-ideal propagation in the channel. These last two remarks reveal the type of difficulties met when the RSSI method is directly applied. It should be noted that for all the experimental experiences, in order to prove the proposed concept, the SF is simply assumed identical and linear for the three radii. Figure 8 illustrates the positioning distribution when the three readers are located in the positions {1, 5, 12} and using the tag T1.

Fig. 8. Example of the localization method by considering the three readers in the positions {1, 5, 12}.

The estimated tag position after processing is clearly better than before processing. In this specific practical case, the proposed concept seems validated. The use of a SF in order to determine the position of the tag leads to a better location estimation. In order to quantify the method more precisely, Table 3 shows several results for the 108 considered combinations of the readers and the three tags. The parameter “best estimation” compares the errors in terms of RMS error found by the direct estimation and the estimation after processing, respectively. The estimation with the smallest error wins. When the “best estimation” is realized, the second parameter “correct estimation” evaluates if this estimation is correct or not; a correct estimation is arbitrarily defined as estimation with an error less than 0.25 m. For example, consider the tag T1: 88% of the reader combinations achieve a better estimation by using the processing (and 12% are better with a direct estimation); and among these best estimations, 69% verify the criterion “correct estimation”. These results show the strong improvement provided by the proposed concept.

Table 3. Comparison and performance of the location operation achieved from direct estimation and after processing.

Figure 9 shows the histogram of the error considering the direct estimation and the post-processed estimation for the tag T1. For example, the error is zero for two configurations with direct estimation versus three with post-processed estimation; the error is equal to 0.1 m for 13 configurations with direct estimation versus 39 with post-processed estimation; etc. This graph also demonstrates the interest of the proposed processing. The estimations are better, and at the same time, the variance of error is smaller. Otherwise, numerous cases also show that certain configurations are more relevant. In particular, the pseudo-alignments, such as for example {2, 4, 7} or {3, 5, 8} can provide worst results, and therefore, these should be avoided. Consequently, a configuration with the three readers located in three corners of a room will be more appropriate than, for example, a configuration with the three readers aligned on a wall.

Fig. 9. Histogram of the error considering the direct estimation and the post-processed estimation for the tag T1.