Design and Implementation of an Indoor Localization System Based on RSSI in IEEE 802.11ax

Abstract

This article describes the design, implementation, and evaluation of an indoor localization system based on Received Signal Strength Indicator (RSSI) measurements in wireless sensor networks. While the majority of the literature uses the IEEE 802.15 standard for this type of system, all of the measurements in this study were performed using a test bench operating under the IEEE 802.11ax standard in the 2.4 GHz band. RSSI is widely used due to its simplicity and availability; however, its accuracy is limited by signal attenuation, electromagnetic interference, and environmental variability. To mitigate these limitations, the present work proposes the implementation of advanced techniques, including weighted averages and positioning algorithms such as Min–Max, Maximum Likelihood, and trilateration, aiming to achieve an accuracy of 2 m in controlled conditions. The design also included a specialized test bench to calculate the coordinates and estimate the location of unknown nodes using anchor node positioning. This approach combines the simplicity of RSSI with optimized algorithms, providing a robust and practical solution for indoor localization. The results validate the system’s effectiveness and highlight its potential for future applications in real-world environments, opening new possibilities for optimizing wireless sensor networks and addressing the current challenges in localization systems.

1. Introduction

Device localization is a fundamental technology in applications such as environmental monitoring, logistics, navigation, and wireless sensor networks. The ability to determine positions in real time enables a wide range of functionalities, from asset tracking in warehouses to indoor navigation [1]. However, the limitations of the Global Positioning System (GPS), such as signal attenuation in enclosed environments and interference in dense urban areas, highlight the need for complementary solutions [2]. Among these alternatives, the Received Signal Strength Indicator (RSSI) has emerged as a widely used technique in wireless sensor networks due to its simplicity and low cost [3]. This technique is based on the relationship between the signal strength and the distance to the receiver, using propagation models such as free space and log-normal path loss to adjust the measurements. The free-space model offers several advantages, including a simple and straightforward formula, which facilitates quick calculations. It serves as the foundation for other propagation models and provides accurate results under ideal conditions, such as satellite links. Additionally, it is independent of external factors like obstacles or weather conditions. However, it also has significant limitations. For instance, it does not accurately represent real-world environments, as it ignores obstacles and reflections. It requires a clear line of sight, and the signal attenuation increases exponentially with distance. On the other hand, the log-normal path loss model has the advantage of accounting for scattering, reflections, and diffraction, making it more realistic. It is applicable in urban, rural, and indoor environments, fits empirical data better, and allows for modeling signal fluctuations through random variability. Nevertheless, it also has drawbacks, such as greater mathematical complexity, the need for experimental data for calibration, and the potential to overestimate path loss in open environments. Although environmental factors such as physical obstacles and interference can affect its accuracy, RSSI remains a viable option, especially when combined with advanced localization algorithms [4,5]. The system proposed in this work employs anchor nodes integrating ESP32 microcontrollers [6] and NEO-6M [7] GPS modules to obtain precise geographic coordinates and the Oppo Reno 11 phone [8] as a wireless sensor. Based on these coordinates and RSSI measurements, the distances between unknown nodes and anchor nodes are calculated using path loss models adapted to the environment [9,10,11,12]. These distances are processed using algorithms such as trilateration, Maximum Likelihood Estimation (MLE), and the Min–Max method, which have been extensively validated in the literature [13]. Trilateration determines the location of an unknown node by finding the intersection of circles defined by the distances to three anchor nodes [14], while the Min–Max method employs a geometric approach based on the intersection of the square areas around the anchor nodes [15,16]. On the other hand, the Maximum Likelihood algorithm minimizes the mean squared error between the estimated and actual distances, achieving a greater accuracy in complex environments [17]. Recent studies have shown that RSSI-based systems can achieve accuracies of up to two meters under controlled conditions [18]. However, interference, multipath propagation, and signal variability remain significant challenges [19]. Advanced techniques such as Kalman filtering, channel diversity, and machine learning have been explored to improve the robustness and accuracy against these issues [20,21,22]. These solutions have diverse applications, ranging from smart factories to optimizing the logistics flows in warehouses. In the context of the Internet of Things (IoT), RSSI-based systems enable the creation of flexible and scalable sensor networks, adaptable to various scenarios and operational requirements [23,24,25]. Additionally, their low cost and simplicity make them accessible for a wide range of applications. This work presents the design and implementation of an indoor localization system using RSSI measurements in wireless sensor networks under the IEEE 802.11ax standard [26] (2.4 GHz). The main contribution of this work is the implementation of an RSSI-based localization system [27,28] combined with GPS, distinguished by its practical and accessible approach. Unlike other more theoretical or costly proposals, this system utilizes low-cost hardware, such as the ESP32 microcontroller and the NEO-6M GPS module, making it an economical and scalable alternative. As algorithms and propagation models continue to evolve, these technologies have the potential to significantly optimize operations in industrial and urban environments. The integration of GPS and RSSI into this solution offers an innovative and efficient method for real-time localization, with high applicability in real-world scenarios and a reduced cost compared to that of other approaches. The objectives of this work include the application of accessible hardware and the IEEE 802.11ax standard to facilitate its implementation in environments such as warehouse logistics and industrial automation. We cover the design and implementation of a reproducible test environment that ensures controlled evaluation conditions; the comparison of several localization algorithms, such as trilateration, Maximum Likelihood Estimation (MLE), and the Min–Max method, to identify the most accurate approach in indoor environments; and the conduction of detailed experimental validation to assess the system’s performance under both controlled and operational conditions, ensuring the reliability of the obtained results. These objectives aim to address the challenges associated with signal variability and environmental factors while providing a cost-effective and scalable solution for real-time localization in various applications. The proposed methodology combines RSSI with positioning algorithms like trilateration, Min–Max, and Maximum Likelihood Estimation (MLE) to improve the accuracy. ESP32 microcontrollers and NEO-6M GPS modules determine the anchor node coordinates for position estimation. RSSI measurements were analyzed under varying conditions, with MLE achieving the highest accuracy, outperforming trilateration and Min–Max. Challenges include the sensitivity of the RSSI to interference and model calibration. Enhancing the system’s robustness through algorithm fusion, Kalman filtering, and machine learning is discussed. The results suggest a cost-effective and scalable solution for IoT applications in industrial and logistics environments.

2. Materials and Methods

The free-space propagation model is used to predict the signal power when there is a clear line of sight between the transmitter and the receiver. Satellite communication systems and microwave links can be modeled as free-space propagation. The power received in free space by a receiving antenna, separated from the transmitter by a given distance d, is given by the Friis equation:

$$P_r\left(d\right)={\displaystyle \frac{P_t{G}_t{G}_r{\lambda }^2}{{\left(4\pi \right)}^2{d}^{2}L}}$$

(1)

where $P_r\left(d\right)$ represents the received power between the transmitter and the receiver, $P_t$ is the transmitted power, $G_t$ denotes the gain of the transmitting antenna, $G_r$ is the gain of the receiving antenna, $\lambda$ corresponds to the wavelength in meters, d is the separation distance between the transmitter and the receiver in meters, and L accounts for system losses unrelated to propagation. The path loss (PL), which represents the attenuation of the signal as a positive magnitude expressed in dB, is defined as follows:

$$PL=10log\left({\displaystyle \frac{P_t}{P_r}}\right)=-10log\left({\displaystyle \frac{G_t{G}_r{\lambda }^2}{{\left(4\pi \right)}^2{d}^2}}\right)$$

(2)

When the antenna gains are excluded (assumed to be unity), the equation is simplified into

$$PL=10log\left({\displaystyle \frac{P_t}{P_r}}\right)=-10log\left({\displaystyle \frac{{\lambda }^2}{{\left(4\pi \right)}^2{d}^2}}\right)$$

(3)

The Friis equation shows that the received power decreases with the square of the distance, implying a 20 dB drop per decade. When the received power at a reference distance $d_0$ is known, the received power at a greater distance is calculated using

$$P_r\left(d\right)=P_r\left(d_0\right)+20log\left({\displaystyle \frac{d_0}{d}}\right)$$

(4)

Large-scale propagation in indoor environments can be modeled using the log-normal shadowing loss model. This empirical model expresses the losses as a function of the distance between the transmitter and the receiver according to the following equation:

$$PL\left(d\right)=PL\left(d_0\right)+10nlog\left({\displaystyle \frac{d}{d_0}}\right)+X_{\sigma }$$

(5)

where n is the path loss exponent, which depends on the type of environment; $PL\left(d_0\right)$ represents the path loss at a reference distance $d_0$, calculated using the free-space propagation model; d is the distance between the transmitter and the receiver; $d_0$ is the reference distance; and $X_{\sigma }$ is a random variable expressed in dB that represents the typical deviation with a standard deviation of $\sigma$ dB. The RSSI (Received Signal Strength Indicator) describes the relationship between the distance to the transmitter and the signal power received at the receiver. In this case, the transmitter is the unknown node, and the receiver is the anchor node. This relationship is determined using the Friis equation, in Equation (1). Since the received power is measured in watts, it must be converted into dBm, which is the common unit for RSSI. The conversion is carried out using the formula

$$P_{\mathrm{dBm}}=10·{log}_{10}\left(\left[P_{\mathrm{W}}\right]·{10}^3\right)$$

(6)

where $P_{\mathrm{dBm}}$ is the power in decibel-milliwatts (dBm), $P_{\mathrm{W}}$ is the power in watts (W), and ${10}^3$ is the conversion factor from watts to milliwatts ($1,\mathrm{W}=1000,\mathrm{mW}$). The relationship between distance and RSSI, considering a reference distance of 1 m, is given by

$$\mathrm{RSSI}=-\left(10·n·{log}_{10}\left(d\right)-A\right)$$

(7)

Solving for the distance from Equation (7), d can be calculated as

$$d={10}^{{\displaystyle \frac{A-\mathrm{RSSI}}{10·n}}}$$

(8)

where A is the RSSI value measured at a reference distance (typically 1 m), which is a constant for the specific setup; RSSI is the current received signal strength in dBm at an unknown distance; and n is the path loss exponent, which characterizes the rate at which the signal attenuates as it propagates through the medium. It varies based on the environment (free space, urban space, indoor settings). Here, d represents the separation between the transmitter (unknown node) and the receiver (anchor nodes), which is fundamental for the localization methods being used. The IEEE 802.15 standards [29] include the following: low power consumption for battery-operated devices; short-range communication (from a few meters to tens of meters); scalability with support for topologies such as star, mesh, and tree topologies; interoperability to ensure compatibility between devices from different manufacturers; and security, with mechanisms like encryption and authentication. Additionally, these standards operate in different frequency bands (such as 2.4 GHz, 900 MHz, 868 MHz, and millimeter waves), offer variable data rates (from a few kbps to several Gbps), and are designed for specific applications like Wireless Personal Area Networks (WPANs), home automation, medical monitoring, industrial networks, and visible light communication. The flexibility and adaptability to various environments and needs are standout features of the IEEE 802.15 family. The IEEE 802.11ax standard, or Wi-Fi 6, offers several advantages, such as a higher network capacity, improved spectral efficiency, and the ability to handle more devices simultaneously through technologies like OFDMA and MU-MIMO. This makes it ideal for high-density environments. It also improves the performance in congested networks and optimizes the battery life with the Target Wake Time (TWT) feature. However, it has some drawbacks, such as the need for compatible equipment, which can lead to additional costs. Furthermore, its benefits are limited to devices supporting this standard, and it remains susceptible to interference, especially in the 2.4 GHz band. Various localization techniques based on anchor nodes or reference points are used. These methods are essential in wireless communication networks, where precise localization is crucial for calculating distances and characterizing signal propagation. One of the most common approaches is trilateration [30]. This method requires knowing the positions of three anchor nodes, $(X_1,Y_1)$, $(X_2,Y_2)$, and $(X_3,Y_3)$, as well as the distances from the anchor nodes to the unknown node, $d_1$, $d_2$, and $d_3$, respectively. The equation for a circle centered at $(X_i,Y_i)$ with the radius $d_i$ is

$${(x-X_i)}^2+{(y-Y_i)}^2=d_i^2$$

(9)

Expanding the polynomials for each circle,

$$\begin{array}{cc}\hfill (x^2-2x{X}_1+X_1^2)+(y^2-2y{Y}_1+Y_1^2)& =d_1^2\hfill \end{array}$$

(10)

$$\begin{array}{cc}\hfill (x^2-2x{X}_2+X_2^2)+(y^2-2y{Y}_2+Y_2^2)& =d_2^2\hfill \end{array}$$

(11)

$$\begin{array}{cc}\hfill (x^2-2x{X}_3+X_3^2)+(y^2-2y{Y}_3+Y_3^2)& =d_3^2\hfill \end{array}$$

(12)

Subtracting the equations to eliminate the quadratic terms $x^2$ and $y^2$, we obtain a system of two linear equations. This system can be written in matrix form as

$$\left[\begin{array}{cc}A& B\\ D& E\end{array}\right]\left[\begin{array}{c}x\\ y\end{array}\right]=\left[\begin{array}{c}C\\ F\end{array}\right]$$

(13)

To solve the system, we compute the inverse of the coefficient matrix H:

$$H=\left[\begin{array}{cc}A& B\\ D& E\end{array}\right]$$

(14)

The inverse of H is given by

$$H^{-1}={\displaystyle \frac{1}{\left|H\right|}}\left[\begin{array}{cc}E& -B\\ -D& A\end{array}\right]$$

(15)

where the determinant of H is

$$\left|H\right|=AE-BD$$

(16)

Substituting into the general formula for the unknowns x and y

$$\begin{array}{cc}\hfill x& ={\displaystyle \frac{EC-BF}{AE-BD}}\hfill \end{array}$$

(17)

$$\begin{array}{cc}\hfill y& ={\displaystyle \frac{-DC+AF}{AE-BD}}\hfill \end{array}$$

(18)

Another commonly used localization method is the Min–Max algorithm, a simple and widely used geometric method due to its ease of implementation. The distance $d_i$ from each anchor node to the unknown node is calculated, and a square is drawn centered at the position of each anchor node, with sides of a length $2·d_i$. Then, the intersection of the generated squares is determined to find a common area where the unknown node is located at the center of the resulting quadrilateral. Mathematically, the algorithm determines the maximum and minimum values to define a square with the coordinates

$$(\max (x_i-d_i),\max (y_i-d_i))$$

(19)

and

$$(\min (x_i+d_i),\min (y_i+d_i))$$

(20)

The central point of this square corresponds to the estimated position of the unknown node. Lastly, another localization method is the Maximum Likelihood Estimation (MLE) method, which analyzes the measurements obtained from the reference nodes to estimate the position of an unknown node. Its main objective is to minimize the mean squared error (MSE) between the measured and actual distances, which may be affected by noise. To begin, the distance $d_i$ from each anchor node is calculated from the RSSI values. Then, an error $e_i$ is defined as the difference between the measured distance and the actual distance between the unknown node and each anchor node as follows:

$$e_i(x_0,y_0)=d_i-\left({(x_i-x_0)}^2+{(y_i-y_0)}^2\right)$$

(21)

where $b=(x_0,y_0)$ is the position of the unknown node, and $(x_i,y_i)$ is the position of the i-th anchor node. This method estimates the position of the unknown node by minimizing $e_i$. The position estimate $(x_0,y_0)$ of the unknown node is obtained by solving a system of equations. The estimate, calculated using the MMSE estimation, is the solution to the linear system

$$y=Xb$$

(22)

where

$$X=\left[\begin{array}{cc}2(x_k-x_1)& 2(y_k-y_1)\\ ⋮& ⋮\\ 2(x_k-x_{k-1})& 2(y_k-y_{k-1})\end{array}\right]$$

(23)

and

$$y=\left[\begin{array}{c}-x_1^2-y_1^2+d_1^2-(-x_k^2-y_k^2+d_k^2)\\ ⋮\\ -x_{k-1}^2-y_{k-1}^2+d_{k-1}^2-(-x_k^2-y_k^2+d_k^2)\end{array}\right]$$

(24)

Once these values are obtained, the estimated position of the unknown node can be calculated using the formula

$$b={\left(X^{T}X\right)}^{-1}{X}^{T}y,$$

(25)

This method works well when a sufficient number of measurements is available, but if only three reference nodes are present, the results may not be accurate.

3. Results

A detailed evaluation of the data obtained during measurements of the Received Signal Strength Intensity (RSSI) under varying distance and time conditions is presented. This analysis is divided into several sections, beginning with the correlation between the signal strength and distance. As expected, the results indicate that as the distance increases, the signal strength decreases. Next, the variability in the measurements is analyzed, taking into account the fluctuations observed across different days and times. This analysis helps identify potential factors affecting the accuracy of the distance estimations. Subsequently, the application of a mathematical path loss model based on linear regression is presented, describing how the signal attenuates with increasing distance. Finally, the results of the distance estimations and localization tests are examined, comparing the obtained positions with the actual locations to evaluate the effectiveness of the localization methods employed, such as trilateration. The RSSI parameters were measured using the Physics Toolbox app on an Oppo Reno 11 device with the IEEE 802.11ax standard in the 2.4 GHz band at distances of 2, 4, 5, 6, 7 and 11 m. The receiver (the Oppo Reno 11 device) remained stationary during the measurements at these distances. The device utilized integrated sensors, such as the Wi-Fi radio frequency receiver, to capture the received signal strength. Measurements were taken at various times over a 31-day period, ensuring the collection of a comprehensive and representative dataset. A total of 186 data points were recorded for each distance (2 m, 4 m, 5 m, 6 m, 7 m, and 11 m). This systematic approach allowed for a robust and consistent analysis of the data across both temporal and spatial dimensions. The test scenario consisted of a room measuring 5 m in length, 4 m in width, and 3 m in height. The walls were made of blocks and coated with plaster, and the room featured a window and a wooden door, elements that may slightly affect the propagation of wireless signals. Inside the room, several pieces of furniture, such as a fabric sofa, a wooden table, wooden chairs, and a wooden shelf, were present, which could influence the signal attenuation. No individuals were present except for the person responsible for taking the measurements, and no other significant sources of interference were detected. The environmental conditions included a constant temperature of 22 °C, mixed lighting (natural and artificial), and a moderate level of ambient noise. Figure 1 illustrates the measurement process, while Figure 2 shows the evolution of the RSSI over time and across different distances. The average RSSI values and their standard deviations decrease progressively with distance, showing greater variability at longer ranges, as shown in

Table 1. Mean RSSI and its standard deviation as a function of distance.

Distance (m)	Mean RSSI (dBm)	Standard Deviation
2	−36	1.6546
4	−49	2.1884
5	−50	2.2917
6	−52	2.7710
7	−54	2.9925
11	−68	3.5216

. These results demonstrate a consistent and clear trend, confirming that the RSSI values decrease as the distance between the transmitter and the receiver increases. This observation aligns with the expected inverse relationship between the signal strength and distance.

The coordinates of the anchor nodes are determined using a circuit composed of an ESP32 microcontroller and a uBlox Neo-6M GPS module, with a precision of ±2 m. This integration allows the ESP32 to receive location data from the Neo-6M module, providing precise geographical coordinates.

Table 2. Connections between the ESP32 and the Neo-6M GPS module.

Neo-6M Pin	ESP32 Pin
Vcc	3.3V
GND	GND
Tx	Rx
Rx	Tx

shows the connections between the ESP32 and the Neo-6M GPS module:

The proposed GPS circuit diagram is shown in Figure 3 below.

These analyses provide a comprehensive overview of the accuracy and reliability of the methods used in this study, highlighting the factors that may influence the quality of the measurements and distance estimations. RSSI was measured over 31 days at various distances and times using the Physics Toolbox app to analyze the relationship between the RSSI and distance. The results were compared with the RSSI vs. distance data from reference [1]; as shown in Figure 4, the average RSSI decreases with distance, while the standard deviation increases at longer ranges, indicating greater variability, as shown in

Table 3. Mean RSSI and its standard deviation as a function of distance.

Distance (m)	Mean RSSI (dBm)	Standard Deviation
2	−36	1.6546
4	−49	2.1884
5	−50	2.2917
6	−52	2.7710
7	−54	2.9925
11	−68	3.5216

. This comparison reveals that the trend curve for the RSSI–distance relationship from reference [1] closely aligns with the curve derived from our measurements, demonstrating the strong consistency between the two datasets. Additionally, RSSI measurements were taken at different times of the day, considering the distance. Figure 5 shows how the RSSI varies with distance, consistently decreasing as the distance increases. The mean and standard deviation of these measurements are presented in Table 3. To visualize the correlation between RSSI and distance, scatter plots were created and are shown in Figure 6. The average RSSI values decrease as the distance increases. The corresponding standard deviations follow a similar trend, as shown in Table 3. The analysis of the relationship between RSSI and distance shows a decreasing linear trend, indicating an inverse correlation. This implies that as the distance between the transmitter and the receiver increases, the RSSI value decreases, aligning with signal loss theories as a function of distance. This linear relationship reinforces the hypothesis of a significant negative correlation between the two variables. Similarly, the variation in the RSSI over time was analyzed, considering the daily measurements from day 1 to day 31. The average values and standard deviations for each day were calculated, and the results are presented in

Table 4. Daily RSSI means and standard deviations.

Day	RSSI Mean (dBm)	Standard Deviation (dBm)
1	−52.7778	9.9860
2	−52.2778	9.6173
3	−53.2778	10.6143
4	−52.4722	10.2497
5	−52.3889	10.2658
6	−52.5556	10.2663
7	−52.3611	10.2153
8	−52.9722	10.4156
9	−52.5000	10.3606
10	−52.6944	10.6014
11	−52.5000	9.5424
12	−52.6667	9.9971
13	−51.9167	10.0438
14	−52.7222	10.0871
15	−51.9444	10.1304
16	−52.0556	9.9109
17	−52.5556	10.2858
18	−52.3056	9.7213
19	−53.0000	10.1700
20	−51.9722	10.0242
21	−52.3889	10.1539
22	−53.2500	10.2550
23	−51.5278	9.4188
24	−51.6389	9.9919
25	−52.8333	10.4922
26	−53.3889	10.7045
27	−52.6944	10.5960
28	−52.3889	10.7099
29	−52.1667	10.3551
30	−52.6667	10.1980
31	−53.0833	10.0977

. Based on these data and as observed in Figure 7, no clear correlation was identified between the RSSI and the measurement day. This suggests that the RSSI values were not significantly influenced by the date on which the measurements were taken. This reinforces the conclusion that the primary factors affecting the variability in the RSSI are distance and signal propagation. The analysis of the relationship between measurement time and RSSI is represented in a dispersion diagram. At a distance of 2 m, the average RSSI is −33.50 dBm, with a low standard deviation of 1.65 dBm, indicating a strong and stable signal. As the distance increases, the RSSI becomes more negative, with average values of −49.57 dBm at 4 m, −52.66 dBm at 5 m, −56.51 dBm at 6 m, −58.32 dBm at 7 m, and −64.53 dBm at 11 m, with standard deviations ranging from 2.19 dBm to 3.52 dBm. On the other hand, the analysis of the measurements taken at different times (10:00 a.m., 12:00 p.m., 2:00 p.m., 5:00 p.m., 8:00 p.m., and 10:00 p.m.) shows that the average RSSI remains stable within a range of −51.67 dBm to −53.83 dBm, with no clear trend linking the time of day to signal strength. This suggests that RSSI does not vary significantly throughout the day. The average values and standard deviations of RSSI are presented in

Table 5. RSSI measurements at different distances and times.

Hour/Distance	2 m	4 m	5 m	6 m	7 m	11 m
10:00 a.m.	−33	−48	−52	−55	−61	−63
12:00 p.m.	−32	−50	−56	−56	−60	−64
02:00 p.m.	−31	−50	−55	−57	−63	−66
05:00 p.m.	−36	−50	−56	−58	−62	−64
08:00 p.m.	−35	−50	−55	−57	−60	−62
10:00 p.m.	−34	−51	−54	−58	−61	−62
Mean	−33.50	−49.83	−54.67	−56.83	−61.17	−63.50
Std. Dev.	1.64	0.98	1.63	1.17	1.17	1.52

, while Figure 8 shows a dispersion diagram for the relationship between the RSSI and measurement hours, illustrating the data distribution over time. Finally, to analyze the path loss, linear regression was performed using the RSSI data, resulting in the model shown in Figure 9. The equation obtained is

$$PL\left(d\right)=PL\left(d_0\right)+10\left(3.15379\right)log\left({\displaystyle \frac{d}{d_0}}\right)+54.11723$$

(26)

where $3.15379$ represents the path loss coefficient, and $54.11723$ is the fading factor $X_{\sigma }$. Using this coefficient and the RSSI values, the distance to the unknown node is estimated using Equation (8). This distance is then applied in trilateration, Min–Max, and Maximum Likelihood algorithms to calculate the precise localization.

The RSSI values were measured over a distance range of 1 to 11 m, and the corresponding estimated distances were calculated using these values. The estimated distances were then compared to the actual distances, and the resulting percentage error was calculated. The results, as shown in

Table 6. Real distance data, RSSI, distance calculated using RSSI, and percentage error.

Real Distance [m]	RSSI [dBm]	Calculated Distance [m]
1.00	−28	0.93
2.00	−38	1.79
3.00	−44	2.78
4.00	−47	3.72
5.00	−52	4.98
6.00	−54	5.77
7.00	−57	7.18
8.00	−59	8.31
9.00	−60	8.94
10.00	−62	10.34
11.00	−63	11.13

, demonstrate that the distance estimates based on RSSI are generally accurate, with a maximum error margin of 10.50%. This indicates that the RSSI-based distance calculation provides a reasonable approximation of the real distance, falling within an acceptable error threshold. The data provided were based on using a Neo-6M GPS module to obtain geographic coordinates for both the unknown node and the anchor nodes. These coordinates were then transformed into Cartesian coordinates to optimize the localization process.

Table 7. Localization data for unknown node (latitude, longitude, X, Y coordinates).

Latitude	Longitude	X	Y
22.107777	−100.845103	309,667.415	2,445,910.095

presents the localization data for the unknown node, detailing its geographic latitude and longitude, as well as its Cartesian coordinates (X, Y). The specific data row indicates a point with a latitude of 22.107777 and a longitude of −100.845103, which corresponds to Cartesian coordinates of 309,667.415 for X and 2,445,910.095 for Y.

3.1. Localization Data and Trilateration Method Analysis

The localization data for the anchor nodes used in the trilateration algorithm are presented in

Table 8. Localization data for anchor nodes for trilateration algorithm (latitude, longitude, X, Y coordinates).

Anchor Nodes	Latitude	Longitude	X (m)	Y (m)
Node 1	22.107776	−100.84508	309,669.41	2,445,910.071
Node 2	22.107777	−100.845054	309,672.42	2,445,910.03
Node 3	22.107705	−100.84510	309,667.31	2,445,902.12

, which include both geographical coordinates (latitude and longitude) and Cartesian coordinates (X, Y) in meters. The table lists the positions of the three anchor nodes, along with their respective locations:

• Node 1: Located at the latitude 22.107776 and the longitude −100.84508, with Cartesian coordinates of 309,669.41 m for X and 2,445,910.071 m for Y;
• Node 2: Positioned at the latitude 22.107777 and the longitude −100.845054, with Cartesian coordinates of 309,672.42 m for X and 2,445,910.03 m for Y;
• Node 3: Found at the latitude 22.107705 and the longitude −100.84510, with Cartesian coordinates of 309,667.31 m for X and 2,445,902.12 m for Y.

RSSI measurements from the anchor nodes were used to estimate the distances between the unknown node and the reference nodes using signal propagation models. These distances became key parameters for the application of the trilateration algorithm, as shown in

Table 9. RSSI of anchor nodes and estimated distance for trilateration algorithm.

Anchor Nodes	RSSI (dBm)	Estimated Distance (m)
Node 1	−39	1.93
Node 2	−54	5.77
Node 3	−61	9.91

. Figure 10 shows the area where the measurements were taken, as well as the nodes, indicating the locations of the anchor nodes relative to the transmitter for the trilateration method. Subsequently, using the previously mentioned data and the trilateration algorithm, the unknown node was located. The data for the unknown node, obtained using this method, can be observed in

Table 10. Unknown node localization data via the trilateration algorithm.

Latitude	Longitude	X (m)	Y (m)
22.10779443	−100.8451071	309,667.0153	2,445,912.03

. Analyzing Table 10, the localization data for the unknown node determined through the trilateration algorithm are presented. This table includes the geographical latitude and longitude, as well as the Cartesian coordinates (X, Y) in meters, for the unknown node:

• Latitude: 22.10779443;
• Longitude: −100.8451071;
• X (m): 309,667.0153;
• Y (m): 2,445,912.03.

Finally, the actual coordinates of the unknown node were compared with those calculated using the trilateration localization algorithm, and the resulting error, in meters, was computed and is presented in

Table 11. Errors in the coordinates and position obtained through the trilateration localization algorithm.

Algorithm	Error in X (m)	Error in Y (m)	Position Error (m)
Trilateration	0.3997	1.9350	1.9758

.

3.2. Localization Data and Min–Max Method Analysis

The localization data for the anchor nodes used in the Min–Max algorithm are presented in

Table 12. Localization data for anchor nodes for the Min–Max algorithm (latitude, longitude, X, Y coordinates).

Anchor Nodes	Latitude	Longitude	X (m)	Y (m)
Node 1	22.107776	−100.84508	309,669.41	2,445,910.071
Node 2	22.107777	−100.845054	309,672.42	2,445,910.03
Node 3	22.107705	−100.84510	309,667.31	2,445,902.12

, which include their geographical latitude and longitude, as well as their Cartesian coordinates (X, Y) in meters. The table also lists the positions of the three anchor nodes, along with their respective locations:

• Node 1: Located at the latitude 22.107776 and the longitude −100.84508, with Cartesian coordinates of 309,669.41 m for X and 2,445,910.071 m for Y;
• Node 2: Positioned at the latitude 22.107777 and the longitude −100.845054, with Cartesian coordinates of 309,672.42 m for X and 2,445,910.03 m for Y;
• Node 3: Found at the latitude 22.107705 and the longitude −100.84510, with Cartesian coordinates of 309,667.31 m for X and 2,445,902.12 m for Y.

RSSI measurements from the anchor nodes were used to estimate the distances between the unknown node and the reference nodes through signal propagation models. These distances were critical to the application of the Min–Max algorithm, as shown in

Table 13. RSSI of anchor nodes and estimated distance for Min–Max algorithm.

Anchor Nodes	RSSI (dBm)	Estimated Distance (m)
Node 1	−39	1.93
Node 2	−54	5.77
Node 3	−61	9.91

. Figure 11 shows the area where the measurements were taken, as well as the nodes, indicating the locations of the anchor nodes relative to the transmitter for the Min–Max method. Once the coordinates of the anchor nodes and the distances between these nodes and the unknown node were obtained, the coordinates of the unknown node were determined using the Min–Max localization algorithm, as detailed in

Table 14. Unknown node localization data via Min–Max algorithm.

Latitude	Longitude	X (m)	Y (m)
22.10778349	−100.8450892	309,668.849	2,445,910.797

, which displays the localization data for the unknown node, including the geographical latitude and longitude, as well as the Cartesian coordinates (X, Y) in meters, for the unknown node:

• Latitude: 22.10778349;
• Longitude: −100.8450892;
• X (m): 309,668.849;
• Y (m): 2,445,910.797.

Finally, the actual coordinates of the unknown node were compared with those calculated using the Min–Max localization algorithm, and the resulting error in meters was computed and is presented in

Table 15. Errors in the coordinates and position obtained through the Min–Max localization algorithm.

Algorithm	Error in X (m)	Error in Y (m)	Position Error (m)
Min–Max	1.4340	0.7019	1.5966

.

3.3. Localization Data and Maximum Likelihood Method Analysis

The localization data for the anchor nodes used in the Maximum Likelihood algorithm are presented in

Table 16. Localization data for anchor nodes for Maximum Likelihood algorithm (latitude, longitude, X, Y coordinates).

Anchor Nodes	Latitude	Longitude	X (m)	Y (m)
Node 1	22.107776	−100.84508	309,669.41	2,445,910.071
Node 2	22.107777	−100.845054	309,672.42	2,445,910.03
Node 3	22.107705	−100.84510	309,667.31	2,445,902.12
Node 4	22.107678	−100.845103	309,667.282	2,445,899.141
Node 5	22.107777	−100.845093	309,668.417	2,445,910.083
Node 6	22.107830	−100.845103	309,667.488	2,445,916.07

, which include their geographical latitude and longitude, as well as their Cartesian coordinates (X, Y) in meters. The table lists the six anchor nodes, along with their respective positions:

• Node 1: Located at the latitude 22.107776 and the longitude −100.84508, with Cartesian coordinates of 309,669.41 m for X and 2,445,910.071 m for Y;
• Node 2: Positioned at the latitude 22.107777 and the longitude −100.845054, with Cartesian coordinates of 309,672.42 m for X and 2,445,910.03 m for Y;
• Node 3: Found at the latitude 22.107705 and the longitude −100.84510, with Cartesian coordinates of 309,667.31 m for X and 2,445,902.12 m for Y;
• Node 4: Located at the latitude 22.107678 and the longitude −100.845103, with Cartesian coordinates of 309,667.282 m for X and 2,445,899.141 m for Y;
• Node 5: Positioned at the latitude 22.107777 and the longitude −100.845093, with Cartesian coordinates of 309,668.417 m for X and 2,445,910.083 m for Y;
• Node 6: Found at the latitude 22.107830 and the longitude −100.845103, with Cartesian coordinates of 309,667.488 m for X and 2,445,916.07 m for Y.

RSSI measurements from the anchor nodes were used to estimate the distances between the unknown node and the reference nodes using signal propagation models. These distances were crucial to the application of the Maximum Likelihood algorithm, as shown in

Table 17. RSSI of anchor nodes and estimated distance for Maximum Likelihood algorithm.

Anchor Nodes	RSSI (dBm)	Estimated Distance (m)
Node 1	−39	1.93
Node 2	−54	5.77
Node 3	−61	9.91
Node 4	−64	11.97
Node 5	−31	1.08
Node 6	−55	6.2

. Figure 12 shows the area where the measurements were taken, as well as the nodes, indicating the locations of the anchor nodes relative to that of the transmitter for the Maximum Likelihood method. Once the coordinates of the anchor nodes and the distances between these nodes and the unknown node were obtained, the coordinates of the unknown node were determined using the Maximum Likelihood localization algorithm, as detailed in

Table 18. Unknown node localization data via Maximum Likelihood algorithm.

Latitude	Longitude	X (m)	Y (m)
22.10778663	−100.8450936	309,668.4	2,445,911.15

, which presents the localization data for the unknown node, including its geographical latitude and longitude, as well as its Cartesian coordinates (X, Y) in meters:

• Latitude: 22.10778663;
• Longitude:−100.8450936;
• X (m): 309,668.4;
• Y (m): 2,445,911.15.

Finally, the actual coordinates of the unknown node were compared with those calculated using the Maximum Likelihood localization algorithm, and the resulting error in meters was computed and is presented in

Table 19. Errors in coordinates and position according to the localization algorithm.

Algorithm	Error in X (m)	Error in Y (m)	Position Error (m)
Maximum Likelihood	0.9850	1.0549	1.4433

.

4. Discussion

The results obtained in this study confirm the viability of using RSSI for indoor localization, achieving an accuracy of up to two meters under controlled conditions. These findings align with previous studies [31,32], which also demonstrated the viability of RSSI-based localization. However, as observed, the estimation of distances and unknown coordinates using RSSI in IoT networks is practical but subject to the influence of obstacles and interference, which can introduce variability into the results. Regarding the evaluated localization methods, significant differences in their performance were found. Trilateration, although efficient, was highly sensitive to interference, a limitation also highlighted in previous research [33]. In contrast, the Min–Max method showed greater tolerance to such interference but at the cost of a lower accuracy. This behavior highlights the need to strike a balance between robustness and precision in complex environments. The Maximum Likelihood method, on the other hand, proved to be the most accurate, consistent with previous studies that have emphasized its ability to estimate positions more precisely using RSSI [34]. Dynamic localization methods, such as those proposed in [35,36], suggest that these approaches could complement and improve the accuracy in more complex scenarios. Specifically, [35] proposed an RSSI-based localization system for sensor networks that could enhance the estimations in dynamic environments, while [36] explored dynamic localization in sensor networks, indicating that integrating these approaches could be an effective way to improve the accuracy and flexibility of localization systems in changing conditions. Although the results are promising, RSSI-based systems still face significant limitations due to the sensitivity of the measurements to obstacles and interference. This underscores the need to optimize both the propagation models and localization algorithms to improve the accuracy in uncontrolled environments. Combining different localization methods, such as trilateration, Min–Max, and Maximum Likelihood, could be an effective strategy to optimize the accuracy in more complex scenarios, as suggested by previous studies [37,38]. As for future research directions, it is essential to explore the combination of different localization methods to overcome the limitations inherent to each, which would allow for a more robust and accurate solution, especially in complex and dynamic environments. This approach could contribute to the development of more reliable IoT networks, with applications in areas such as logistics, environmental monitoring, and smart city management [39]. An example of this kind of advancement can be found in the article “An Improved Wi-Fi RSSI-Based Indoor Localization Approach Using Deep Randomized Neural Network” [40], which presents an enhanced methodology for indoor localization using Wi-Fi signals (RSSI). This approach combines a Deep Randomized Neural Network (RandNN) and an Improved and Adaptive Kalman Filter (IAUKF). Indoor localization is challenging due to signal fluctuations, reflections, and noise in enclosed environments. The proposed method uses the RandNN to process RSSI data and predict the location, while the IAUKF helps reduce the noise and improve the estimation accuracy by smoothing fluctuations. The results show that this approach outperforms the traditional methods, providing greater accuracy and robustness in dynamic environments. This advancement has practical applications in indoor navigation, asset tracking, and location-based services in places such as shopping malls, hospitals, or warehouses. The analysis shows that the Maximum Likelihood algorithm achieves a lower error distance when comparing the real coordinates of the unknown node to the calculated ones. This indicates greater accuracy in position estimation, making it a more suitable option for applications where precision is critical. However, the Maximum Likelihood algorithm requires more nodes to achieve this level of accuracy, which may increase the system complexity and resource usage. On the other hand, algorithms like trilateration and Min–Max, with just three nodes, provide a reasonable approximation of the real position of the unknown node. Although the error in X, Y, and the position is higher compared to that with the Maximum Likelihood algorithm, they still offer a practical and efficient solution for many localization tasks, especially in scenarios with fewer nodes or limited computational resources.

5. Conclusions

The design, construction, and implementation of an indoor localization system based on RSSI in IEEE 802.11ax was carried out in this research work, utilizing a wireless sensor network. An accuracy of approximately two meters was achieved, and the expectations were met, while the feasibility of RSSI-based localization was confirmed. However, it was noted that RSSI-based distance estimation and unknown coordinate determination were significantly influenced by obstacles and interference, and the system’s accuracy was degraded. Three main localization methods were highlighted, and distinct advantages and limitations were characterized for each. Trilateration was utilized as an efficient technique for calculating the coordinates based on known distances between nodes, and an error of 1.9758 m relative to the actual position of the unknown node was achieved. However, high sensitivity to interference and obstacles was observed, and its precision was compromised. The Min–Max method was evaluated for its resilience to such interference, and a slightly lower error of 1.5966 m was yielded. Robustness in challenging environments was demonstrated, but a slight sacrifice in its accuracy along the x-axis compared to that of trilateration was observed. The best performance was achieved by the Maximum Likelihood method, with an error of 1.4433 m relative to the actual position of the unknown node. It was identified as particularly effective in scenarios involving multiple nodes and complex environments, with the highest accuracy among the three methods offered. However, greater computational resources were required, which limited its suitability for applications where the processing power was a constraint. This method was found to be the most accurate and reliable for RSSI-based indoor localization, particularly in environments with significant interference. Optimization and comprehensive test bench evaluations were emphasized as essential to ensure a consistent performance under varying conditions.