Multilateration utilizes geometric principles to determine the position of devices via the intersection of multiple spheres. This method requires the measurement of the time difference of arrival (TDOA) or distance from devices to at least three known reference points or anchor nodes. These anchor nodes provide the fundamental basis for computational algorithms that triangulate an accurate position. Multilateration improves upon this process by including additional reference points, enhancing the system’s precision ^[1].

The weighted centroid approach is another technique employed in indoor localization systems. This method leverages the physics center of mass concept to determine device location. By using known anchor nodes with respective distances or received signal strengths as weights, it is possible to calculate a centroid that estimates the target device’s location. This technique can be particularly advantageous when dealing with limited access to anchor nodes or when measurements must be taken quickly ^[2].

Grid-based RSS is a different approach in indoor localization systems that seeks to maximize accuracy by comparing RSS from multiple devices or nodes in a network, enhancing the resilience of a wireless network ^[3]. This method uses RSSI data to estimate the distance between devices and nodes within a network, considering potential variables that can impact signal transmissions, such as physical obstructions and environmental factors ^[4].

2. Comparisons between Indoor Positioning Techniques

Various articles provide comparisons between indoor positioning techniques. Liu et al. ^[5] investigated indoor location algorithms such as angulation, scene analysis, and proximity. Their research also delves into performance metrics, including accuracy, precision, complexity, robustness, scalability, and cost. Technological solutions like GPS, RFID, WLAN, Bluetooth, UWB, and cellular are considered. In their extensive analysis of wireless indoor localization techniques, the authors in ^[6] examined various methodologies from a device-oriented standpoint. The researcheuthors drew comparisons between device-dependent and device-independent systems, considering factors such as accuracy, cost, scalability, and energy efficiency. He and Chan ^[7] examined Wi-Fi fingerprinting technology, focusing on two key aspects: sophisticated positioning methods and effective implementation strategies. The study analyzed different techniques using spatial and temporal signal patterns, considering factors like indoor location accessibility, additional data for position estimation, constraints, and reported average precision. Hassan et al. ^[8] studied indoor positioning utilizing visible LED light technology. They analyzed various systems, including Wi-Fi, Bluetooth Low Energy, and GSM, focusing on accuracy, robustness, complexity, cost, and infrastructure reusability. Latif et al. ^[9] assessed the efficacy of multiple localization methods as well. Gu et al. ^[10] also compared indoor localization methods, focusing on wireless personal networks. Their extensive study examined a wide range of options, including both commercial and research-oriented solutions, based on security and privacy, cost, performance, resilience, complexity, user preferences, commercial availability, and limitations. Their findings were consistent with those of prior research ^[11], emphasizing that each solution employs a certain sort of technology, has its own design, and performs best in specific situations. A comprehensive overview of current smartphone-based indoor localization techniques was provided by Tiglao et al. ^[12]. A classification scheme is presented to categorize the techniques, and it was concluded that each method has its own strengths and weaknesses. It was noted that fingerprinting techniques excel when the training phase is executed well, while path loss prediction techniques offer high accuracy in specific environments. Depending on user requirements, a suitable approach is chosen. The researcheuthors envision a seamless indoor localization system with cm-level resolution, low-power consumption, and minimal latency. A low-cost and real-time indoor positioning approach that combines iBeacons and Pedestrian Dead Reckoning (PDR) was proposed by Liu et al. ^[13]. The Bluetooth Low Energy (BLE)-based iBeacon technology achieved a positioning accuracy with a Root Mean Square Error (RMSE) of 2.75 m through the fusion of Trilateration and fingerprinting methods. The rpapesearchr introduces a PDR method that incorporates filtering on heading orientation and presents a fusion approach of iBeacon and PDR to address positional jumps and drifting errors. Improved trajectory accuracy and reduced influence of initial position errors and orientation noises were demonstrated in real-time tracking experiments. Conte et al. ^[14] demonstrated the utilization of BLE for addressing occupancy detection by introducing a modified iBeacon protocol tailored to the issue. Their system, BLUESENTINEL, presents a straightforward and scalable solution for occupancy detection, leveraging users’ existing smartphones and strategically positioned beacons. Their experiments showed that even with just one beacon per room, accurate results can be achieved, which contrasts with other methods that require a higher number of antennas. The inherent power efficiency of the BLE protocol further supports the feasibility of their approach. Despite its simplicity, BLUESENTINEL achieves accuracy comparable to other advanced methods. A non-intrusive BLE-based method was proposed for zone-level occupant localization without the need for a dedicated mobile application ^[15]. This approach involves utilizing a network of BLE beacons to collect RSSI values from nearby devices. These values are then processed into RSSI tuples and utilized by supervised and semi-supervised machine learning models to determine the positions of occupants at the zone level. The supervised ensemble model showed higher accuracy and f1-score, while the semi-supervised clustering model achieved reasonable performance with minimal training data and time. Through a case study conducted in office spaces, the feasibility of this approach was demonstrated, leading to the identification of occupancy profiles that provide valuable insights into occupant behaviors. Implementation of this proposed method offers facility managers valuable occupancy insights for effective building management. Andò et al. ^[16] presented an overview of indoor localization systems, focusing on solutions tailored to the Ambient Assisted Living framework. The rpapesearchr introduces the RESIMA system as a case study, which combines wireless Ultrasound sensors for user positioning and an environmental map to enable User–environment interaction functionalities. The system aims to support end-users in navigating indoor environments safely and efficiently. By utilizing the Multi-Trilateration Algorithm (MTA), the RESIMA system demonstrated its suitability for the addressed application field. The researchtudy ^[17] extensively assessed deployment problems in wireless sensor networks (WSNs). In smart cities, where sensor nodes are distributed and must remain active to gather and transmit data, achieving optimal node deployment was crucial. Existing work in the field was reviewed, and coverage schemes were categorized into different techniques. The rpapesearchr highlights the research efforts to minimize power consumption by reducing the number of deployed nodes. A comprehensive comparison of these techniques is provided, considering their respective advantages and drawbacks. A comprehensive overview of indoor localization techniques and wireless technologies is presented by Obeidat et al. ^[18]. Various localization system technologies, including satellite-based navigation, inertial navigation systems, magnetic-based navigation, sound-based technologies, optical-based technologies, and RF-based technologies, are covered in the survey. Different localization detection techniques, such as proximity-based techniques, scene analysis, triangulation, and dead reckoning, are also explored. Additionally, the most commonly used localization algorithms and methods are introduced, such as angle of arrival (AOA), time of arrival (TOA), and received signal strength (RSS). Localization method selection depends on several factors, including cost, available resources, the type of environment, and the desired accuracy level. Ultimately, the most powerful technique is determined by its ability to provide high accuracy with minimal computational requirements. Sadowski et al. ^[19] conducted an extensive investigation comparing the efficacy of Trilateration, K-Nearest Neighbor (KNN), and Naive Bayes techniques. Their study encompassed the utilization of three prevalent IoT wireless technologies: Zigbee, Bluetooth Low Energy (BLE), and Wi-Fi. Experiments were based on three real-world datasets corresponding to three rooms with different levels of interference. The findings revealed that KNN with a parameter value of k = 4 emerged as the most accurate and precise localization method, with Naive Bayes following closely. The key contributions of this rpapesearchr can be outlined as follows:

• Investigation of indoor localization techniques, such as the Centroid algorithm, Trilateration, and Grid-Based RSS method. Analyzing their performance behavior under various wireless technologies, as well as varying levels of path loss and setting dimension.
• Rigorous and comprehensive simulations were conducted under various experimental scenarios. Each method’s performance was thoroughly evaluated based on criteria such as efficiency, precision, and adaptability across diverse technology environments.
• Detailed analysis of influence factors like noise levels, technology types (Wi-Fi, ZigBee, BLE), and tag node density and layout on the performance of each localization technique.
• Execution using Google Colab’s cloud-based GPU platform for optimized calibration procedures while providing insights into the selection of appropriate indoor localization techniques.

3. Discussion

The results from the three experiments provide valuable insights into the performance and accuracy of different localization techniques for WSNs using RSSI. We have observed that the localization techniques, namely Multilateration, Grid-based RSS, and Centroid Algorithm, have varied performance under different conditions and scenarios. In Experiment 1, Grid-based RSS exhibited the highest localization accuracy among all three techniques evaluated, irrespective of the number of tag nodes. This outcome suggests that Grid-based RSS is more robust and less sensitive to changes in the number of tag nodes involved in the experiment. On the other hand, multilateration showed slightly lower accuracy than Grid-based RSS but still outperformed the Centroid Algorithm. The poor performance of the latter is attributed to its reliance on geometric mean calculations for estimating positions with irregular or sparse node distributions. Experiment 2 reinforced the outcomes obtained from Experiment 1, confirming that multilateration provides accurate estimates for more than half of the tag nodes tested. Furthermore, it demonstrates that all three methods exhibit insensitivity toward fluctuations in the number of tag nodes involved. In analyzing the results of this experiment, it is obvious that the various localization techniques performed differently under different circumstances. Grid-based RSS demonstrated the highest accuracy in localizing tag nodes. However, this method has some limitations, such as its sensitivity to noise and higher standard deviation due to its reliance on theoretical RSSI. Increasing the number of theoretical RSSI’s could improve the localization accuracy. The weighted Centroid Algorithm displayed lower accuracy compared to Grid-based RSS and Multilateration, but was found to be more robust to noise with fewer fluctuations in the localization results. The algorithm was notably effective in localizing diagonally placed tag nodes. It is interesting to observe that its mean error increased as the number of tag nodes on the edges of the simulation space increased. Multilateration showed similar mean errors across increasing dimensions, suggesting that it is not position-biased and does not discriminate based on a tag node’s position. It is less sensitive to noise compared to Grid-based RSS but not as robust as the Weighted Centroid Algorithm regarding varying noise levels. Experiment 3, using a real-world dataset and three different wireless technologies (Wi-Fi, Bluetooth, and ZigBee), revealed that the Weighted Centroid algorithm consistently produced the highest localization accuracy across all three technologies. While Grid-based RSS exhibits superior localization accuracy under certain conditions, the Weighted Centroid Algorithm provides more consistent results across various circumstances and technologies. Multilateration offers an unbiased performance without reliance on a tag node’s position. Therefore, it is essential to consider these characteristics when selecting an appropriate localization algorithm for specific applications. Noise and shadow effect simulations in our experiments served to incorporate realistic conditions to better understand how these factors can influence localization performance. Despite these added complexities, the tested algorithms maintained stable accuracies and efficiencies through different iterations. Despite theour study offering valuable perspectives on implementing localization techniques in WSNs concerning their accuracies, it is crucial to consider various parameters such as environmental conditions, deployment scenarios, and specific application requirements for choosing an optimal localization method best suited to a particular problem context. ItWe is anticipated that theour findings will also apply to three-dimensional (3D) scenarios for the following rationale.

(1)

Weighted centroid exhibits position bias:

• If the localization accuracy of boundary nodes is higher than that of diagonal nodes in 3D, it implies that the weighted centroid is biased towards the position of the nodes.
• If both edge nodes and diagonal nodes have the same accuracy, and the z-coordinate of diagonal nodes has higher error than edge nodes, while the xy-coordinate of diagonal nodes has less error than edge nodes, it also suggests that the weighted centroid is biased towards the position of the nodes.
• If diagonal nodes have higher accuracy than edge nodes, it means that the weighted centroid localizes diagonal tag nodes more accurately than edge nodes. Consequently, this finding confirms the position bias of the weighted centroid in 3D.

Therefore, it is reasonable to assume that the weighted centroid is position-biased in 3D as well.

(2)

Weighted centroid is more robust to noise compared to the other two techniques:

The weighted centroid algorithm uses only RSSI information to localize tag nodes. Unlike multilateration, the weighted centroid algorithm does not need to calculate any distance value using the RSSI formula. It only utilizes the RSSI information as should bwn in the formula provided in Section 3.2.2. We should noted that the anchor nodes record RSSI measurements based on the RSSI formula, which applies to both 2D and 3D scenarios. Therefore, this finding is also applicable to 3D environments.

(3)

Grid-based RSS is highly sensitive to noise and theoretical RSSI:

As demonstrated in experiment 2 in Section 5.2.2, the error of the grid-based RSS method increases at a higher rate compared to the other two techniques as the noise level increases from 1 to 5. Similar to the 2D case, the accuracy of the grid-based RSS in 3D heavily depends on the RSSI measurements. If the 3D environment has fluctuating noise levels, the grid-based RSS method will still yield higher localization errors (compared to the other techniques) due to its reliance on theoretical RSSI. Therefore, this finding is scalable to 3D scenarios.

(4)

Trilateration performs best in the BLE technology:

In 3D scenarios, multilateration requires a minimum of four anchors for accurate localization. The addition of another anchor will further minimize the MSE for all three technologies (BLE, WIFI, and ZIGBEE). Additionally, the multilateration algorithm utilizes RSSI values for position estimation. Even in 3D, the anchors record RSSI values in a similar manner as in 2D scenarios. This process also incorporates some noise or shadow effect represented by numerical values specific to each technology (BLE, WIFI, and ZIGBEE). Furthermore, trilateration is a geometric method that can be extended to three dimensions. Therefore, it is reasonable to assume that trilateration would also perform well in BLE applications in 3D.

4. Conclusions

Based on the simulations and analysis conducted in this research, it wastudy, we provided that the strengths and weaknesses of the three localization techniques—Grid-based RSS, Multilateration, and Centroid Algorithm. Grid-based RSS demonstrated the highest localization accuracy but is sensitive to noise, and theoretical RSS and might not be ideal in scenarios with high fluctuations. Multilateration offered unbiased performance and was less sensitive to noise; however, it did not consistently outperform the other two techniques. The Weighted Centroid Algorithm showed impressive consistency across various conditions and technologies while maintaining reasonable localization accuracy. Thus, it is vital to consider each technique’s specific characteristics and potential applications when choosing a suitable localization algorithm for one’s needs. One interesting finding from Experiment 3 was the superior performance of the Weighted Centroid Algorithm across all three wireless technologies. While it produced lower accuracy results compared to Grid-based RSS and multilateration in certain cases, its consistency across various conditions and technologies renders it a reliable choice for real-world scenarios. As wireless technologies continue to evolve rapidly, experiments such as these play an essential role in understanding which localization algorithms may be best suited for diverse applications and environments. Furthermore, these results encourage continuous research into refining and developing new techniques to improve localization accuracy and efficiently cater to diverse use cases in both indoor and outdoor settings. In future work, we pewill explore performance enhancement through parallelization will be explored, noise-reducing correction techniques, and comparisons to Ultra-Wideband (UWB)-based localization systems for improved accuracy and effectiveness in indoor localization methods.