3D Trilateration and 3D Triangulation.

3D Trilateration and 3D Triangulation.

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Indoor localization has recently and significantly attracted the interest of the research community mainly due to the fact that Global Navigation Satellite Systems (GNSSs) typically fail in indoor environments. In the last couple of decades, there have been several works reported in the literature that attempt to tackle the indoor localization prob...

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... radio technologies such as UWB and even more millimeter-wave (mmWave) radio create opportunities for very accurately estimating the time and angle of arrival (using phased antenna arrays) [18][19][20]. There are three prevalent terminologies that describe the geometric approach to determine position, based on distance or angle of arrival measurements: triangulation, trilateration and angulation (see Figure 2). Triangulation is the estimation of a 2D or 3D location using unilateral or multilateral measurements (the position is determined from the measured lengths of three sides of a triangle). ...

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... Applications within a 6G and Internet of Things (IoT) context benefit largely from accurate and precise indoor positioning [1], [2], [3]. A clear cut optimal solution is however not yet available [4]. One of the most commonly used technologies for this purpose is Ultra Wide Band (UWB) [5]. ...
... Commonly used wireless sensors for ranging and localization include Wi-Fi, Bluetooth, and Radio Frequency Identification (RFID) [21]. They estimate the target's location by measuring signal strength or time differences [1], with meter-level accuracy. ...
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Accurate three-dimensional (3D) localization within indoor environments is crucial for enhancing item-based application services, yet current systems often struggle with localization accuracy and height estimation. This study introduces an advanced 3D localization system that integrates updated ultra-wideband (UWB) sensors and dual barometric pressure (BMP) sensors. Utilizing three fixed UWB anchors, the system employs geometric modeling and Kalman filtering for precise tag 3D spatial localization. Building on our previous research on indoor height measurement with dual BMP sensors, the proposed system demonstrates significant improvements in data processing speed and stability. Our enhancements include a new geometric localization model and an optimized Kalman filtering algorithm, which are validated by a high-precision motion capture system. The results show that the localization error is significantly reduced, with height accuracy of approximately ±0.05 m, and the Root Mean Square Error (RMSE) of the 3D localization system reaches 0.0740 m. The system offers expanded locatable space and faster data output rates, delivering reliable performance that supports advanced applications requiring detailed 3D indoor localization.
... Emerging technologies like augmented reality (AR) and various positioning-based applications are driving the need for indoor positioning technology. Applications such as mall navigation, pathfinding in large hospitals or airports, automatic guidance for unmanned cleaning and maintenance vehicles, surveillance systems, and others demand positioning systems capable of delivering high accuracy within indoor environments [1][2][3][4][5][6]. Trilateration, a well-established technique, is commonly employed in accurate positioning systems for indoor use. ...
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The increasing focus on the development of positioning techniques reflects the growing interest in applications and services based on indoor positioning. Many applications necessitate precise indoor positioning or tracking of individuals and assets, leading to rapid growth in products based on these technologies in certain market sectors. Ultrasonic systems have already proven effective in achieving the desired positioning accuracy and refresh rates. The typical signal used in ultrasonic positioning systems for estimating the range between the target and reference points is the linear chirp. Unfortunately, it can undergo shape aberration due to the effects of acoustic diffraction when the aperture exceeds a certain limit. The extent of the aberration is influenced by the shape and size of the transducer, as well as the angle at which the transducer is observed by the receiver. This aberration also affects the shape of the cross-correlation, causing it to lose its easily detectable characteristic of a single global peak, which typically corresponds to the correct lag associated with the signal's time of arrival. In such instances, cross-correlation techniques yield results with a significantly higher error than anticipated. In fact, the correct lag no longer corresponds to the peak of the cross-correlation. In this study, an alternative technique to global peak detection is proposed, leveraging the inherent symmetry observed in the shape of the aberrated cross-correlation. The numerical simulations, performed using the academic acoustic simulation software Field II, conducted using a typical ultrasonic chirp and ultrasonic emitter, compare the classical and the proposed range techniques in a standard office room. The analysis includes the effects of acoustical reflection in the room and of the acoustic noise at different levels of power. The results demonstrate that the proposed technique enables accurate range estimation even in the presence of severe cross-correlation shape aberrations and for signal-to-noise ratio levels common in office and room environments, even in presence of typical reflections. This allows the use of emitting transducers with a much larger aperture than that allowed by the classical cross-correlation technique. Consequently, it becomes possible to have greater acoustic power available, leading to improved signal-to-noise ratio (SNR).
... It is commonly used in signal processing to filter out high-frequency noise, as the main signal of interest often is in the lower frequency range. The LPF equation is expressed as a weighted sum of the previous estimate and the current observation, where the weighting factor determines the weight given to the previous estimate versus the current observation [33][34][35]. ...
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This research delves into advancing an ultra-wideband (UWB) localization system through the integration of filtering technologies (moving average (MVG), Kalman filter (KF), extended Kalman filter (EKF)) with a low-pass filter (LPF). We investigated new approaches to enhance the precision and reduce noise of the current filtering methods—MVG, KF, and EKF. Using a TurtleBot robotic platform with a camera, our research thoroughly examines the UWB system in various trajectory situations (square, circular, and free paths with 2 m, 2.2 m, and 5 m distances). Particularly in the square path trajectory with the lowest root mean square error (RMSE) values (40.22 mm on the X axis, and 78.71 mm on the Y axis), the extended Kalman filter with low-pass filter (EKF + LPF) shows notable accuracy. This filter stands out among the others. Furthermore, we find that integrated method using LPF outperforms MVG, KF, and EKF consistently, reducing the mean absolute error (MAE) to 3.39% for square paths, 4.21% for circular paths, and 6.16% for free paths. This study highlights the effectiveness of EKF + LPF for accurate indoor localization for UWB systems.
... This is important for rapidly changing indoor situations. Time-of-flight methods, such as Ultra-Wideband (UWB) and time-of-flight cameras, provide very accurate distance measurements [30]. Robust indoor localization is achieved using vision-based techniques like object identification and feature matching, which take advantage of visual signals. ...
... To get the maximum efficiency of these systems, one must understand the properties of sound transmission. There are numerous sound-based applications, ranging from innovative uses in augmented reality to navigation areas with inadequate infrastructure [30]. The ability to function without requiring a line of sight makes it beneficial for museums, warehouses, and healthcare facilities, providing benefits in complex indoor environments [16]. ...
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Due to the increasing need for accurate location-based services, Indoor Positioning Systems (IPS) have evolved rapidly. This study reviews the literature published from 2010 to 2024, employing the Preferred Reporting Items for Systematic Reviews and Meta-Analyses (PRISMA) methodology for the identification, screening, validation, and inclusion of research literature. By exploring the complexities of IPS methodologies, algorithms, technologies, and challenges, this study offers a comprehensive introduction for researchers, scholars, and specialists. Additionally, the scope of this study expands its focus to encompass mapping techniques such as crowdsourcing, Geographic Information Systems (GIS), remote sensing, LiDAR, cartography, and augmented reality (AR). The findings of this study will contribute to the increased applicability of these methods and techniques in the field of urban planning and environmental management. Contributing to the expanding pool of knowledge on indoor positioning, this work is a valuable resource for those exploring the ever-changing field of IPS. This work not only contributes to the academic but also bridges the gap between scientific discoveries and practical, real-world applications.
... Finally, UWB and mmWave technologies demonstrate the most promising results compared to other technologies reaching centimeter-level accuracy even in multipath scenarios and are relatively insensitive to interference. A more comprehensive survey of the technologies used for positioning can be found in [10]. Our focus on this paper is on mmWave. ...
... These efforts are aimed at exploring advanced technologies to meet this need. The authors of [10] offer a comprehensive survey of 3D indoor localization techniques and approaches. It delves into various modern technologies, providing insights and evaluations. ...
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The 3D nature of modern smart applications has imposed significant 3D positioning accuracy requirements, especially in indoor environments. However, a major limitation of most existing indoor localization systems is their focus on estimating positions mainly in the horizontal plane, overlooking the crucial vertical dimension. This neglect presents considerable challenges in accurately determining the 3D position of devices such as drones and individuals across multiple floors of a building let alone the cm-level accuracy that might be required in many of these applications. To tackle this issue, millimeter-wave (mmWave) positioning systems have emerged as a promising technology offering high accuracy and robustness even in complex indoor environments. This paper aims to leverage the potential of mmWave radar technology to achieve precise ranging and angling measurements presenting a comprehensive methodology for evaluating the performance of mmWave sensors in terms of measurement precision while demonstrating the 3D positioning accuracy that can be achieved. The main challenges and the respective solutions associated with the use of mmWave sensors for indoor positioning are highlighted, providing valuable insights into their potentials and suitability for practical applications.
... Nevertheless, in all cases of determining the location, the environmental conditions are significantly important [3]. They are connected with physical phenomena which differ in the case of the analysis of open space compared with the conditions inside buildings [4], [5]. ...
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The novel approach of the Low Energy Bluetooth RSSI (Received Signal Strength Indicator) examination for a personal location during the evacuation process is presented in this paper. The presented system is based on stationary locating localization nodes installed inside the facility and portable wristbands worn by people. A method based on the propagation model and preliminary determination of its characteristics is used to calculate the wristband-locator distance. The accuracy of the distance estimations is increased by assuming Gaussian model of RSSI measurements and using the estimator of RSSI mean value. A modified multilateration approach is used to estimate the person’s position in the 2D Cartesian coordinate system. The paper also includes the outcomes of experiments conducted on the proposed approach as it was applied to the prototype evacuation supervision system. The paper presents a comparison of the position estimation error for the proposed method based on the mean RSSI value estimator with the results obtained when raw RSSI values were used. Analysis and discussion of wristband position estimation error are also included.
... The rapid development of this area has already led to the emergence of a wide variety of technologies and methods, the purpose of which is to measure the distance between objects as accurately as possible and position them in space. To solve this problem, various types of signals (sound, light, radio waves) are proposed, among which the most convenient from a technical point of view are radio systems due to their omnidirectional and high penetrating ability [1,2]. In the development of advanced radio communication systems (6G, etc.), stake has been placed in radio positioning systems [3]. ...
... The performance of various radio technologies, their benefits, and their drawbacks are widely discussed in scientific periodicals. A critical review of modern technologies that can be applied to 3D positioning-such as WiFi, Bluetooth, UWB, mmWave, visible light, and sound-based technologies-their performance, and their weak and strong points, is given in [1]. The authors of [11] focused on the technologies used in the Internet-of-Things. ...
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The use of ultra-wideband (UWB) signals for local positioning is very attractive for practice, because such signals have the potential to provide centimeter precision. In this paper, we consider wireless ranging (distance measurement) and positioning, using one of the kinds of UWB signals, i.e., chaotic radio pulses, which are noise-like signals with no constant shape. The distance measurement is based on an assessment in the receiver of the power of UWB chaotic radio pulses emitted by the transmitter. A new method for estimating their power and its experimental implementation is proposed and described. Experimental layouts of the transmitter and receiver and the principles of their operation are described. To determine the main features of this method under real signal propagation conditions, full-scale indoor measurements were carried out, and statistical estimates of the accuracy were made. We present the results of experimental testing of the proposed approach for positioning the emitter relative to a system of anchors in an office space 6 × 6.5 m2 in the mode of measuring object coordinates on a line and on a plane. The mean absolute error (MAE) of distance measurement (1D) was 25 cm, and the root mean squared error (RMSE) was 39 cm. When positioning on a plane (2D), the MAE of coordinate estimation was 34 cm and the RMSE was 42 cm. The proposed distance measurement method is intended for use in wireless UWB transceivers used in wireless sensor networks.
... The proposed method is suitable for specific indoor localization scenarios. LPF+KF excels in high-noise environments and simple motions; LPF+AVG provides adaptability and robustness in various indoor environments; and LPF+EKF utilizes direct range values for accurate position estimates, as shown in the proposed algorithm [39]. ...
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This research paper investigates ultra-wideband (UWB) localization systems by focusing on the use of average filter (AVG), Kalman filter (KF), and extended Kalman filter (EKF) algorithms, as well as a novel integrated filtering method that incorporates low-pass filter (LPF) into AVG, KF, and EKF. The study aims to improve localization loss in indoor environments using a TurtleBot robot equipped with a camera to observe ground truth positions. To evaluate the effectiveness of the proposed algorithms, a comprehensive comparison of the raw and filtered data with the camera-based ground truth observations is performed. Quantitative analyses of the results, including max, min, max-min, and mean error, are performed to evaluate the localization performance of the algorithms and the integrated filtering method. The results reveal that the integrated filtering method has performed better accuracy in comparison with existing methods.
... Time of Arrival can integrate with Kalman filter and Gaussian mixture models to remove Non-Line of Sight (NLOS) signals for accurate indoor positioning [7], and this can be used for 3D indoor positioning [8]. Time Difference of Arrival [9] and Direction of Arrival [10] can provide enhanced positioning techniques, and they usually require customized sensor configurations or deployments to fulfill their design requirements. ...
... Time Difference of Arrival can enhance the accuracy of Time of Arrival by employing a data-selective approach based on its proposed closed-form least-squares solution that disregards bad measurements [9]. Time of Arrival and Time Difference of Arrival are ideal approaches for 3D indoor positioning based on their design advantages [8]. Direction of Arrival utilizes the azimuth to establish an eigenspace for removing multipath propagation interferences [10]. ...
Article
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As indoor positioning has been widely utilized for many applications of the Internet of Things, the Received Signal Strength Indication (RSSI) fingerprint has become a common approach to distance estimation because of its simple and economical design. The combination of a Gaussian filter and a Kalman filter is a common way of establishing an RSSI fingerprint. However, the distributions of RSSI values can be arbitrary distributions instead of Gaussian distributions. Thus, we propose a Fouriertransform Fuzzyc-means Kalmanfilter (FFK) based RSSI filtering mechanism to establish a stable RSSI fingerprint value for distance estimation in indoor positioning. FFK is the first RSSI filtering mechanism adopting the Fourier transform to abstract stable RSSI values from the low-frequency domain. Fuzzy C-Means (FCM) can identify the major Line of Sight (LOS) cluster by its fuzzy membership design in the arbitrary RSSI distributions, and thus FCM becomes a better choice than the Gaussian filter for capturing LOS RSSI values. The Kalman filter summarizes the fluctuating LOS RSSI values as the stable latest RSSI value for the distance estimation. Experiment results from a realistic environment show that FFK achieves better distance estimation accuracy than the Gaussian filter, the Kalman filter, and their combination, which are used by the related works.