Receiver Positions Research Articles

Detection of ionospheric disturbances with a sparse GNSS network in simulated near-real time Mw 7.8 and Mw 7.5 Kahramanmaraş earthquake sequence

On February 6, 2023 the Kahramanmaraş Earthquake Sequence caused significant ground shaking and catastrophic losses across south-central Türkiye and northwest Syria. These seismic events produced ionospheric perturbations detectable in Global Navigation Satellite System (GNSS) total electron content (TEC) measurements. This work aims to develop and incorporate a near-real-time (NRT) ionospheric disturbance detection method into JPL’s GUARDIAN system. Our method uses a Long Short-Term Memory (LSTM) neural network to detect anomalous ionospheric behavior, such as co-seismic ionospheric disturbances among others. Our method detected an anomalous signature after the second Mw 7.5 earthquake at 10:24:48 UTC (13:24 local time) but did not alert after the first Mw 7.8 earthquake at 01:17:34 UTC (04:17 local time), which had a visible disturbance of smaller amplitude likely due to lower ionization levels at night and potentially the multi-source mechanism of the slip.Plain Language Summary Seismic activity, including the destructive Kahramanmaraş Earthquake Sequence on February 6, 2023 in the Republic of Türkiye, result in vertical ground displacement that cause atmospheric waves. These waves propagate upwards to the outer atmosphere, disturbing the ionospheric electron content. This disturbance impacts the signals broadcast by positioning satellites (such as GPS) and received by ground-based receivers. If the receiver position is known, the impact to these signals can be used to measure the electron density disturbance caused by these seismically-induced atmospheric waves. Such studies usually rely on being aware of the event a priori. Using deep learning neural networks, we instead aim to detect anomalous signals automatically. We propose to utilise this method to detect seismically-induced disturbances over a large geographical area. The detection method proposed in this paper successfully detected an anomalous event in the ionosphere approximately ten minutes after the second earthquake in the Kahramanmaraş Earthquake Sequence.

Topography‐dependent eikonal solver in tilted transverse isotropic media with anelliptical factorization

AbstractIncorporating anisotropy and complex topography is necessary to perform traveltime tomography in complex land environments while being a computational challenge when traveltimes are computed with finite‐difference eikonal solvers. Previous studies have taken this challenge by computing traveltimes in transverse isotropic media involving complex topography with a finite‐difference eikonal equation solver on a curvilinear grid. In this approach, the source singularity, which is a major issue in eikonal solvers, is managed with the elliptical multiplicative factorization method, where the total traveltime field is decomposed into an elliptical base traveltime map, which has a known analytical expression and an unknown perturbation field. However, the group velocity curve can deviate significantly from an ellipse in anellipitically anisotropic media. In this case, the elliptical base traveltime field differs significantly from the anelliptical counterpart, leading to potentially suboptimal traveltime solutions, even though it helps to mitigate the detrimental effects of the source singularity. To overcome this issue, we develop a more accurate topography‐dependent eikonal solver in transverse isotropic media that relies on anelliptical factorization. To achieve this, we first define the coordinate transform from the Cartesian to the curvilinear coordinate system, which provides the necessary framework to implement the topography‐dependent transverse isotropic finite‐difference eikonal solver with arbitrary source and receiver positioning. Then, we develop a semi‐analytical method for the computation of the topography‐dependent anelliptical base traveltime field. Finally, we efficiently solve the resulting quadratic elliptical equation using the fast sweeping method and a quartic anelliptical source term through fixed‐point iteration. We assess the computational efficiency, stability and accuracy of the new eikonal solver against the solver based on elliptical factorization using several transverse isotropic numerical examples. We conclude that this new solver provides a versatile and accurate forward engine for traveltime tomography in complex geological environments such as foothills and thrust belts. It can also be used in marine environments involving complex bathymetry when tomography is applied to redatumed data on the sea bottom.

SHM System for Composite Material Based on Lamb Waves and Using Machine Learning on Hardware.

There is extensive use of nondestructive test (NDT) inspections on aircraft, and many techniques nowadays exist to inspect failures and cracks in their structures. Moreover, NDT inspections are part of a more general structural health monitoring (SHM) system, where cutting-edge technologies are needed as powerful resources to achieve high performance. The high-performance aspects of SHM systems are response time, power consumption, and usability, which are difficult to achieve because of the system's complexity. Then, it is even more challenging to develop a real-time low-power SHM system. Today, the ideal process is for structural health information extraction to be completed on the flight; however, the defects and damage are quantitatively made offline and on the ground, and sometimes, the respective procedure test is applied later on the ground, after the flight. For this reason, the present paper introduces an FPGA-based intelligent SHM system that processes Lamb wave signals using piezoelectric sensors to detect, classify, and locate damage in composite structures. The system employs machine learning (ML), specifically support vector machines (SVM), to classify damage while addressing outlier challenges with the Mahalanobis distance during the classification phase. To process the complex Lamb wave signals, the system incorporates well-known signal processing (DSP) techniques, including power spectrum density (PSD), wavelet transform, and Principal Component Analysis (PCA), for noise reduction, feature extraction, and data compression. These techniques enable the system to handle material anisotropy and mitigate the effects of edge reflections and mode conversions. Damage is quantitatively evaluated with classification accuracies of 96.25% for internal defects and 97.5% for external defects, with localization achieved by associating receiver positions with damage occurrence. This robust system is validated through experiments and demonstrates its potential for real-time applications in aerospace composite structures, addressing challenges related to material complexity, outliers, and scalable hardware implementation for larger sensor networks.

Performance Improvement by FRFT-OFDM for Visible Light Communication and Positioning Systems

In indoor visible light communication (VLC) and visible light positioning (VLP) systems, the performance of conventional orthogonal frequency-division multiplexing (OFDM) schemes is often compromised due to the nonlinear characteristics and limited modulation bandwidth of light-emitting diodes, the multipath effect in enclosed indoor environments, and the relative positions of transmitters and receivers. This paper proposes an OFDM scheme based on the fractional Fourier transform (FRFT) to address these issues, demonstrating promising results when applied to indoor VLC and VLP systems. The FRFT, a generalization of the conventional Fourier transform (FT) in the fractional domain, captures information in both the time and frequency domains, offering greater flexibility than the FT. In this paper, we first introduce the computation method of the reality-preserving FRFT for an intensity modulation/direct detection VLC system and integrate it with OFDM to optimize system performance. By adopting FRFT-OFDM under the optimal fractional order, we enhance both the bit error ratio (BER) performance and positioning accuracy. Simulation results reveal that the FRFT-OFDM scheme with an optimized fractional order significantly improves the BER and positioning accuracy compared to the FT-OFDM scheme across most receiver positions within the indoor observation plane. For communication, the FRFT-OFDM scheme achieves over 6 dB Eb/N0 gain compared to the FT-OFDM scheme at a BER of 3×10−4 when the receiver is positioned at most locations in the room. For positioning, the FRFT-OFDM scheme enhances positioning accuracy by more than 1 cm relative to the FT-OFDM scheme at most locations in the room. Notably, both systems maintain the same computational complexity and spectral efficiency.

Selected Aspects of Positioning with the GNSS Galileo

The quality of Galileo system services is affected by the accuracy of distance determination from the user’s application to the individual satellite. The goal of our research was to find out what influence the accuracy of distance determination between the user’s application of the Galileo system and the cooperating satellites of the Galileo system has on the ability to determine the location of the user’s application. A solution based on Groebner’s algebraic approaches was used to determine the receiver user’s position. When creating distance measurement error models between the Galileo system user’s receiver and cooperating satellites, we assumed that the values of those errors considered all factors that affected the accuracy of those distance measurements. To evaluate the algorithms, we used a statistical set of 500 simulation results to determine the positioning of the user’s application of the Galileo system. If the distances between the user’s application and the individual satellite were measured accurately, then the user’s application coordinate errors had values between 1.86 × 10−9 m and −1.8 × 10−8 m. These errors should be equal to zero. The positioning error was caused by a numerical error in the calculation due to the software used. If the errors of distance determination from the user’s application to the individual satellite varied from −0.05 m to 0.09 m, then the error in determining the positioning of the user’s application of the Galileo system was from 0.0 m to 1.2 m. If the distances of the user’s receiver to the satellites were measured with errors greater than 0.09 m, the errors in determining its position were much larger. The simulation results confirmed the known fact that the satellites’ geometry influences the accuracy of determining the location of the user’s application. In the following research, we will solve the problem of how to reduce the sensitivity of the mentioned algorithms when determining the position of the satellite navigation system receiver due to errors in determining the distance from the user’s application to the individual satellite.

Effective deployment strategies for optimizing area coverage in multistatic sonar detection based on Cassini oval approximation and a virtual force algorithm

Multistatic sonar is regarded as a highly promising method for detecting quiet submarines over long distances. This technique exhibits high positioning accuracy, flexible configurations, easy concealment, and robust resistance to interference. However, the sources are more expensive than receivers and performance of multistatic sonar depends strongly on the relative positions of the sources and receivers. In this work, we study the problem of optimal deployment of receivers for one source and multiple receivers type multistatic sonar to achieve maximum area coverage. The area coverage of multistatic sonar is a multi-objective optimization problem (MOOP) balancing maximum coverage against minimal cost. To simplify the MOOP, the area enclosed by a Cassini oval is approximated to two circles and the normalized area difference is analyzed. Then the required number of receivers within a rectangular area of interest (AOI) is calculated based on full coverage theory. So the MOOP is simplified into a single-objective problem focused on achieving maximal coverage with a specific number of receiver nodes. An enhanced virtual force algorithm named Delaunay triangulation hole repair virtual force algorithm (DTHRVFA) is introduced to optimize the deployment positions of receivers as a heterogeneous nodes deployment problem. Simulation results show significant improvement in coverage compared with various methods of heterogeneous nodes deployment. The proposed method effectively addresses area coverage problems associated with the deployment of one source and multiple receivers type multistatic sonar receivers.

A Receiver Position Estimation Method Based on LSTM for Multi-Transmitter Single-Receiver Wireless Power Transfer Systems

The multi-transmitter single-receiver wireless power transfer (MTSR-WPT) system has good tolerance for coil misalignment because the magnetic fields generated by multiple transmitters can be shaped to adapt to position changes in the receiver coil. In order to achieve magnetic field shaping of the MTSR-WPT system and increase power transfer efficiency, accurately estimating the position of the receiver coil is a key issue that needs to be addressed. In this article, a receiver position estimation method based on long short-term memory (LSTM) is proposed, which utilizes a data-driven approach to establish a neural network model. By learning the relationship between the measured time-series voltage data of the transmitter coils and the position of the receiver coil, the proposed model can achieve accurate position estimation of the receiver. Compared with previous works, the proposed method does not require communication between the transmitter and receiver, which is conducive to simplifying the system structure and reducing costs. In addition, the proposed LSTM-based method requires less derivation of complex formulas and the internal mechanism analysis of the system. Finally, a MTSR-WPT prototype is built to verify the proposed method. The experimental results show that the proposed LSTM-based method can achieve high-accuracy position estimation of the receiver. When the receiver moves within a range of 160 mm × 160 mm, the average error between the estimated receiver coil position using the proposed method and the actual receiver coil position is less than 2.40 mm.

Visible light communication in aircraft cabins: challenges and opportunities in power, coverage, and handover management

Abstract Visible light communication (VLC) presents a compelling solution for enhancing in-flight connectivity within commercial aircraft cabins. This study investigates the power distribution, coverage area, and handover performance of VLC systems inside aircraft based on line-of-sight (LoS) and first reflection signal. Results indicate that received power levels at different receiver positions are significantly affected with varying half-power semi-angles. Analysis of first reflection signal power distribution reveals maximum reflected power is achieved at semi-angle equal to 45°. Simulated coverage areas demonstrate the importance of half-power semi-angle size in determining signal confinement and separability. Handover simulations highlight the dynamic nature of passenger mobility and its impact on handover frequency, with smaller semi-angles resulting in higher handover counts. While directional transmission offers benefits such as interference mitigation and spatial reuse, it also introduces challenges related to handover frequency and coverage area. These findings underscore the need for careful optimization of VLC system designs and handover algorithms to ensure seamless connectivity and optimal performance in diverse aircraft environments.

Three diverse motives for information sharing

Knowledge is distributed over many individuals. Thus, humans are tasked with informing one another for the betterment of all. But as information can alter people’s action, affect and cognition in both positive and negative ways, deciding whether to share information can be a particularly difficult problem. Here, we examine how people integrate potentially conflicting consequences of knowledge, to decide whether to inform others. We show that participants (Exp1: N = 114, Pre-registered replication: N = 102) use their own information-seeking preferences to solve complex information-sharing decisions. In particular, when deciding whether to inform others, participants consider the usefulness of information in directing action, its valence and the receiver’s uncertainty level, and integrate these assessments into a calculation of the value of information that explains information sharing decisions. A cluster analysis revealed that participants were clustered into groups based on the different weights they assign to these three factors. Within individuals, the relative influence of each of these factors was stable across information-seeking and information-sharing decisions. These results suggest that people put themselves in a receiver position to determine whether to inform others and can help predict when people will share information.

A Python-Based Indoor Channel Model with Multi-Wavelength Propagation for Color Shift Keying

Color shift keying is a modulation scheme for visible light communication that uses fixtures with three or more narrow-spectral light-emitting diodes to transmit data while fulfilling the primary function of illumination. When this modulation is used indoors, the reflectivity of the walls strongly affects the inter-channel interference and illumination quality. In this paper, we present an indoor channel model that takes into account multi-wavelength propagation. This model is available as an open-source Python package. The model calculates the inter-channel interference, illuminance, correlated color temperature, and color rendering index at the receiver position. The Python package includes a module for estimating the symbol error rate. To validate the model, we computed the received power at each color photodetector for four different indoor scenarios. The model demonstrated a color rendering index of less than 15 when using IEEE-based color shift keying and non-uniform illumination on a horizontal plane. The simulation determined the required luminous flux to achieve a symbol error rate of less than 10−5 when the photodetector is at the center of the indoor space and vertically below the light source. To maintain a symbol error rate less than 10−5, the luminous flux increases when the photodetector is displaced in a diagonal direction from the center of the plane.

IRS aided visible light positioning with a single LED transmitter

We propose a visible light positioning (VLP) system with a single light emitting diode (LED) transmitter and an intelligent reflecting surface (IRS) for estimating the position of a receiver equipped with a single photo-detector. By performing a number of transmissions from the LED transmitter and optimizing the orientation vectors of the IRS elements for each transmission, position information is extracted by the receiver based on power measurements of the signals reflecting from the IRS. The theoretical limit and the maximum likelihood (ML) estimator are presented for the proposed setting. In addition, an algorithm, named IRS focusing, is proposed for determining the orientations of the IRS elements during the localization process. The effectiveness of the proposed localization approach is demonstrated through simulations. Furthermore, extensions are provided to apply the proposed approach in the presence of partial prior information about the receiver position and when the IRS is located at the LED transmitter.

Validation measurement of vehicle pass-by models for dynamic urban environments

Simulation and auralization of urban traffic noise can help city planners and residents to improve existing urban areas or plan new attractive living spaces while enabling discussions about shared auditory experiences, regardless of expertise. Evaluating street noise in the context of urban areas requires careful consideration of their urban surroundings, such as landscapes, buildings, and other structures. Obtaining measurements to validate simulations may be difficult given the variety and complexity of sounds within an urban setting. Recreating the real urban scenario on a test track, e.g., including building facades and exact source and receiver positions, helps validate simulations but also poses challenges due to varying road surfaces, weather conditions, and disturbances such as industrial or fly-over sounds. This research represents a method of bringing a measurement set-up consisting of source (e.g., vehicle), receiver (e.g., pedestrian), and surfaces (e.g., walls) to the more controlled environment of a hemi-anechoic chamber. The method is intended for the validation of previous vehicle pass-by measurements by utilizing sine sweeps with walls parked at varying distances. These environments aim to deliver more insight into the relevance of diffracted sound for configuration of urban sound simulation models.

Receiver Position Detection System of Wireless Electric Vehicle Charger Based on Novel Active Beacon Structure

Receiver Position Detection System of Wireless Electric Vehicle Charger Based on Novel Active Beacon Structure

Design optimization of a new cavity receiver for a parabolic trough solar collector

The most important parameter affecting the optical efficiency, the upper limit for an overall efficiency of parabolic trough solar collector (PTC), is the net absorbed heat rate by receiver on which solar beam radiation is concentrated. The objective of this study is to propose and optimize a new cavity receiver used in PTC for increasing optical efficiency. Three different geometries (triangle, rectangle and polygon), aperture widths, heights and positions of cavity receiver are taken as optimization parameters. A design of experiments (DoE) approach is used to evaluate the effects of these parameters on the absorbed radiation heat rate by receiver at the same time. SolTrace is used to investigate the effects of these parameters by optical analysis. The results indicate that the optimum cavity geometry is polygonal, and the cavity depth and aperture both are equal to 0.05 m. Moreover, it is found that the most effective parameter is the position of the cavity receiver, and the optimum position is at the focal line of the parabolic concentrator. The highest absorbed radiation rate by the cavity receiver and the optical efficiency of the PTC are equal to 3241.99 W and 81.05 % respectively for the optimum cavity receiver design.

Employing a two stage process with resampling, decision rules, and fine acquisition to optimize the acquisition stage of GNSS receiver performance

The optimal design of Global Navigation Satellite System (GNSS) software receivers should enable the accurate estimation of the receiver's position, velocity, and time under various environmental conditions. The software receivers consist of three sections: acquisition, tracking, and navigation. This paper specifically centers on the acquisition sections of the Global Positioning System (GPS), Global Navigation Satellite System (GLONASS), BeiDou, and Galileo satellite navigation systems. The acquisition stage necessitates the prompt and precise transmission of the satellite list within the receiver's view, along with Doppler frequency estimation and phase code offset, to facilitate a seamless transition to the tracking stage with the utmost speed and accuracy. Conventional acquisition demonstrates commendable speed, but lacks accuracy, especially in environments with a low Carrier-to-Noise Ratio (CNR). Contrastingly, precise acquisition methods will impede the speed of the acquisition stage. In this paper, a novel acquisition method is proposed. By integrating concepts like resampling, two-stage acquisition, and fine-acquisition, this method enables the attainment of higher accuracy without compromising speed. The results demonstrate that the proposed method enhances accuracy by 7.275% compared to conventional methods and boosts speed by 76.97% compared to methods focused on accuracy improvement.

Physics-constrained adaptive kernel interpolation for region-to-region acoustic transfer function: a Bayesian approach

A kernel interpolation method for the acoustic transfer function (ATF) between regions constrained by the physics of sound while being adaptive to the data is proposed. Most ATF interpolation methods aim to model the ATF for fixed source by using techniques that fit the estimation to the measurements while not taking the physics of the problem into consideration. We aim to interpolate the ATF for a region-to-region estimation, meaning we account for variation of both source and receiver positions. By using a very general formulation for the reproducing kernel function, we have created a kernel function that considers both directed and residual fields as two separate kernel functions. The directed field kernel considers a sparse selection of reflective field components with large amplitudes and is formulated as a combination of directional kernels. The residual field is composed of the remaining densely distributed components with lower amplitudes. Its kernel weight is represented by a universal approximator, a neural network, in order to learn patterns from the data freely. These kernel parameters are learned using Bayesian inference both under the assumption of Gaussian priors and by using a Markov chain Monte Carlo simulation method to perform inference in a more directed manner. We compare all established kernel formulations with each other in numerical simulations, showing that the proposed kernel model is capable of properly representing the complexities of the ATF.

Performance Evaluation of Non-Lambertian SLIPT for 6G Visible Light Communication Systems

Visible light communication (VLC) has emerged as one promising candidate technique to improve the throughput performance in future sixth-generation (6G) mobile communication networks. Due to the limited battery capacity of VLC systems, light energy harvesting has been proposed and incorporated for achieving the simultaneous lightwave information and power transfer (SLIPT) function and for improving the overall energy efficiency. Nevertheless, almost all reported works are limited to SLIPT scenarios adopting a basic and well-discussed Lambertian optical transmitter, which definitely cannot characterize the potential and essential scenarios employing distinctive non-Lambertian optical transmitters with various spatial beam characteristics. For addressing this issue, in this work, SLIPT based on a distinct non-Lambertian optical beam configuration is investigated, and for further enhancing the harvested energy and the achievable data rate, the relevant flexible optical beam configuration method is presented as well. The numerical results show that, for a typical receiver position, compared with about 1.14 mJ harvested energy and a 31.2 Mbps achievable data rate of the baseline Lambertian configuration, a harvested energy gain of up to 1.55 mJ and an achievable data rate gain of 21.1 Mbps can be achieved by the non-Lambertian SLIPT scheme explored here.

Modeling regional occupancy of fishes using acoustic telemetry: a model comparison framework applied to lake trout

Acoustic telemetry is a common tool used in fisheries management to estimate fish space use (i.e., occupancy) from a local habitat scale to entire systems. Numerous analytical models have been developed to estimate different aspects of fish movement from telemetry datasets, yet evaluations of model performance and comparisons among models are limited. Here, we develop a framework to evaluate model estimates of regional occupancy in large and fragmented systems using an acoustic receiver array in Lake Champlain. We simulated the tracks of 100 acoustically tagged fish using a random walk function and created detection events based on receiver positions and distance-based detection probability. Regional occupancy for the simulated data was estimated by six movement models that ranged in analytical complexity, and results were compared to the true distributions for each simulated track to evaluate model error. The six movement models included: (1) a basic residency index using detections alone; (2) a residency index using last-observation-carried-forward; (3) a centers of activity model; (4) linear and non-linear interpolations (i.e., least-cost paths); and (5 and 6) two dynamic Brownian bridge movement models generated using separate packages in R. We developed a model selection process to compare model performance and select the optimal analysis based on simulation error. This process showed significant differences in model performance among the six movement models based on model error. Overall, the model generating least-cost paths using linear and non-linear interpolations consistently provided the most accurate regional occupancy estimates. Based on these simulation results, we applied this model to a case study that evaluated patterns in the regional distribution of stocked lake trout (Salvelinus namaycush) in Lake Champlain, which demonstrated distinct regional occupancy of two stocked lake trout groups. These results demonstrate potential for large variability in interpretation of acoustic telemetry data for describing regional fish distribution dependent on the analytical method used.

Correlation of Player and Imaging Characteristics With Severity and Missed Time in National Football League Professional Athletes With Hamstring Strain Injury: A Retrospective Review

Background: Hamstring strain injuries (HSIs) are prevalent in US National Football League (NFL) players, but there is a paucity of information regarding imaging characteristics, injury severity, and player factors associated with time missed and risk of recurrent injury. Purpose: To describe player, football activity, clinical, and imaging characteristics of NFL players with HSIs, as well as determine player characteristics, clinical examination results, and magnetic resonance imaging (MRI) findings associated with injury occurrence, severity, and missed time. Study Design: Cross-sectional study; Level of evidence, 3. Methods: A retrospective cohort of NFL players with acute HSI (n = 180) during the 2018-2019 season was identified. Injury data were collected prospectively through a league-wide electronic health record system. Three musculoskeletal radiologists graded MRI muscle injury parameters using the British Athletics Muscle Injury Classification (BAMIC) system. Player, football, clinical, and imaging characteristics were correlated with HSI incidence and severity and with missed time from sport. Results: Of the 1098 HSIs identified during the 2018-2019 season, 416 (37.9%) were randomly sampled, and 180 (43.3%) had diagnostic imaging available. Game activity, preseason period, and wide receiver and defensive secondary positions disproportionately contributed to HSI. The biceps femoris was the most commonly injured muscle (n = 132, 73.3%), followed by the semimembranosus (n = 24, 13.3%) and semitendinosus (n = 17, 9.4%) muscles. The most common injury site was the distal third of the biceps femoris and semitendinosus muscles (n = 60, 45.5% and n = 10, 58.8%, respectively) and central part of the semimembranosus muscle (n = 17, 70.8%). Nearly half of the injuries (n = 83, 46.1%) were BAMIC grade 2; 25.6% (n = 46), grade 3; and 17.8% (n = 32), grade 4. MRI showed sciatic nerve abnormality in 30.6% (n = 55) of all HSIs and 81.3% (n = 26) of complete tendon injuries. BAMIC grade correlated with both median days and games missed. Combined biceps femoris and semitendinosus injuries resulted in the highest median days missed (27 days). Conclusion: Among NFL players with acute HSIs, the most common injury was a moderate-severity injury of the distal biceps femoris. BAMIC grade was associated with missed time.

A study of the spatial non-uniformity of reverberation time at low frequencies

This paper presents a study of the spatial non-uniformity of low-frequency reverberation time estimates. Using measured and simulated data, it is demonstrated that the reverberation times estimated from band-limited impulse responses vary as a function of space at low frequencies. The origin of this spatial dependency is investigated using a one-dimensional finite element model. It is shown that the Q-factor and reverberation time at the resonant frequency of a particular mode are spatially dependent and that the spatial dependency is related to the mode shapes. The ranges of the reverberation time estimates as a function of third-octave frequency bands in simulated and measured rooms are presented. An additional finding is that modal damping constants (obtained via eigenvalue analysis) quantify the decay of uncoupled modes but not necessarily the reverberation time. These observations have implications for measurements and simulations of reverberation time at low frequencies. When measuring a spatially averaged reverberation time, the choice of source and receiver positions is important. A guideline is proposed that defines a set of preferred measurement positions based on the mode shapes, from which estimates of the spatially averaged reverberation time can be obtained.