Position Time Series Research Articles

Estimating hip impact velocity and acceleration from video-captured falls using a pose estimation algorithm

Analyzing video footage of falls in older adults has emerged as an alternative to traditional lab studies. However, this approach is limited by the labor-intensive process of manually labeling body parts. To address this limitation, we aimed to validate the use of the AI-based pose estimation algorithm (OpenPose) in assessing the hip impact velocity and acceleration of video-captured falls. We analyzed 110 videos of 13 older adults (64.0 ± 5.9 years old) falling sideways in an experimental setting. By applying OpenPose to each video, we generated a time series of hip positions in the video, which were then analyzed using custom MATLAB code to calculate hip impact velocity and acceleration. These calculations were compared against ground truth measurements obtained from motion capture systems (VICON for hip impact velocity) and inertial measurement units (MC10 for hip impact acceleration). We examined the agreement between the ground truth and OpenPose measurements in terms of mean of absolute error (MAE), mean of absolute percentage error (MAPE), and bias (mean of error). Results showed that OpenPose had a good accuracy in estimating hip impact velocity with minimal bias (MAE: 0.17 ± 0.13 m/s, MAPE: 7.28 ± 5.21%; percent bias: − 1.27%). However, its estimation of hip impact acceleration (i.e., peak vertical hip acceleration at impact) showed poor accuracy (MAPE: 26.3 ± 19.4%), showing substantial underestimation in instances of high acceleration impacts (> 3.0 g). Further ANOVA analysis revealed OpenPose’s ability to discern significant differences in hip impact velocity and acceleration based on the movement response utilized during the fall (e.g., stick-like fall, tuck-and-roll, knee block). This is the first study to validate the use of a pose estimation algorithm for identifying the hip impact kinematics in video-captured falls among older adults. Future validation studies involving diverse camera settings, fall contexts, and biomechanical parameters are warranted to extend this support for using pose estimation algorithms in this field.

Modelling of GNSS station position time series using deep learning approaches

Modelling of GNSS station position time series using deep learning approaches

An efficient improved singular spectrum analysis for processing GNSS position time series with missing data

SUMMARY The improved SSA (ISSA) method is widely recognized for directly extracting signals from gappy time-series without requiring prior interpolation. However, it is rather time consuming, particularly for long time-series with large window sizes, such as Global Navigation Satellite System (GNSS) position time-series. This study proposes an efficient ISSA method that yields equivalent results to the ISSA method while significantly reducing computation time. Both methods aim to minimize the quadratic norm of principal components, while our method has fewer unknown parameters in the principal component computation than those of the ISSA method. We evaluate the performance of the proposed method using real GNSS position time-series from 27 permanent stations located in mainland China. Results show that the proposed method can effectively reduce computation time than the ISSA method and the improvement depends on the chosen window size, the time-series length and the percentage of missing data. This efficient approach can be naturally extended to principal component analysis (PCA) and multichannel SSA (MSSA) for processing multiple incomplete time-series, improving computational efficiencies compared to the modified PCA and the improved MSSA while maintaining unchanged results. We also compare the ISSA method with the modified SSA (SSAM) and the iterative SSA methods using both real and synthetic time-series data. Results indicate that the ISSA method outperforms the SSAM method, and when conducted iteratively, also surpasses the iterative SSA method.

Derivative dynamic time warping algorithm with introduced correction for varying load fault diagnosis of nuclear power system steam turbine units

The Derivative Dynamic Time Warping (DDTW) algorithm is improved to address the multi-parameters time series classification problem faced by nuclear power system steam turbine units varying load fault diagnosis. Firstly, the entire load changing process is treated as a single sample rather than multiple time-step-samples. This ensures the complete information on the load changing processes, while avoiding interference from normal data fluctuations during faults. Secondly, Time Series Position Coefficient and Time Series Length Coefficient are proposed to correct the DDTW algorithm from two perspectives: the sequences lengths and the data positions in the sequences. This solves the singularities and timeline scaling problems, thereby preventing interference introduced by data sequences' lengths differences and ''similar data appearing at different times'' problem. The nuclear power system steam turbine unit simulation model was built to obtain load changing processes data under normal and faults statuses. In the varying load fault diagnosis test based on these data, the improved DDTW algorithm achieved an accuracy of 1.38%–12.06% higher than other methods, reaching 87.50%. Finally, The Deep Convolutional Generative Adversarial Networks (DCGAN) model was used to generate data to supplement the limited samples of complete load changing processes, and the accuracy of the novel method increased to 95.51% with the increase of data used to support the comparison.

Modeling random isotropic vector fields on the sphere: theory and application to the noise in GNSS station position time series

Modeling random isotropic vector fields on the sphere: theory and application to the noise in GNSS station position time series

Estimating and Analyzing The Stability of Brazilian Gnss Stations for Tectonic Studies

The detailed study of stresses and strains is fundamental for geophysical and geodetic studies, enabling the development of plate motion models, geodynamic processes and several proposals. GNSS positioning has been used to estimate these stresses and strains. However, for the accuracy required, it is necessary a rigorous assessment of the behavior of GNSS stations and their position time series. This paper aims to analyze the influence of the different types of geodetic monuments present in the Brazilian GNSS Continuous Monitoring Network by estimating and characterizing noise in the time series and investigating variables that can affect the stability of the stations to establish criteria for using this data in tectonic and geodynamic studies. The evaluation of 119 GNSS stations throughout Brazil indicates the significant presence of random walk noise in some of these stations, detected by analyzing the magnitude of the noise and the spectral index. It was found that the stations with unstable monuments have been observed for at least eight years and are mostly in coastal areas or under the influence of large watercourses.

Gait and Balance Assessments with Augmented Reality Glasses in People with Parkinson's Disease: Concurrent Validity and Test-Retest Reliability.

State-of-the-art augmented reality (AR) glasses record their 3D pose in space, enabling measurements and analyses of clinical gait and balance tests. This study's objective was to evaluate concurrent validity and test-retest reliability for common clinical gait and balance tests in people with Parkinson's disease: Five Times Sit To Stand (FTSTS) and Timed Up and Go (TUG) tests. Position and orientation data were collected in 22 participants with Parkinson's disease using HoloLens 2 and Magic Leap 2 AR glasses, from which test completion durations and durations of distinct sub-parts (e.g., sit to stand, turning) were derived and compared to reference systems and over test repetitions. Regarding concurrent validity, for both tests, an excellent between-systems agreement was found for position and orientation time series (ICC(C,1) > 0.933) and test completion durations (ICC(A,1) > 0.984). Between-systems agreement for FTSTS (sub-)durations were all excellent (ICC(A,1) > 0.921). TUG turning sub-durations were excellent (turn 1, ICC(A,1) = 0.913) and moderate (turn 2, ICC(A,1) = 0.589). Regarding test-retest reliability, the within-system test-retest variation in test completion times and sub-durations was always much greater than the between-systems variation, implying that (sub-)durations may be derived interchangeably from AR and reference system data. In conclusion, AR data are of sufficient quality to evaluate gait and balance aspects in people with Parkinson's disease, with valid quantification of test completion durations and sub-durations of distinct FTSTS and TUG sub-parts.

An improved Gaussian process for filling the missing data in GNSS position time series considering the influence of adjacent stations

Due to various unavoidable reasons or gross error elimination, missing data inevitably exist in global navigation satellite system (GNSS) position time series, which may result in many analysis methods not being applicable. Typically, interpolating the missing data is a crucial preprocessing step before analyzing the time series. The conventional methods for filling missing data do not consider the influence of adjacent stations. In this work, an improved Gaussian process (GP) approach is developed to fill the missing data of GNSS time series, in which the time series of adjacent stations are applied to construct impact factors, together with a comparison of the conventional GP and the commonly used cubic spline methods. For the simulation experiments, the root mean square error (RMSE), mean absolute error (MAE) and correlation coefficient (R) are adopted to evaluate the performance of the improved GP. The results show that the filled missing data of the improved GP are closer to the true values than those of the conventional GP and cubic spline methods, regardless of the missing percentages ranging from 5 to 30%, with an interval of 5%. Specifically, the mean relative RMSE and MAE improvements for the improved GP with respect to the conventional GP are 21.2%, 21.3% and 8.3% and 12.7%, 16.2% and 11.01% for the North (N), East (E) and Up (U) components, respectively. In the real experiment, eight GNSS stations are analyzed using improved GP, together with conventional GP and a cubic spline. The results indicate that the first three principal components (PCs) of the improved GP can perverse 98.3%, 99.8% and 77.0% of the total variance for the N, E and U components, respectively. This value is obviously higher than those of the conventional GP and cubic spline. Therefore, we can conclude that the improved GP can better fill in the missing data in GNSS position time series than the conventional GP and cubic spline because of the impacts of adjacent stations.

Similarities and Differences Between Natural and Simulated Slow Earthquakes

AbstractWe investigate similarities and differences between natural and simulated slow earthquakes using nonlinear dynamical system tools. We use spatio‐temporal slip potency rate data derived from Global Navigation Satellite System (GNSS) position time series in the Cascadia subduction zone and numerical simulations intended to reproduce their pulse‐like behavior and scaling laws. We provide metrics to evaluate the accuracy of simulations in mimicking slow earthquake dynamics. We investigate the influence of spatio‐temporal coarsening as well as observational noise. Despite the use of many degrees of freedom, numerical simulations display a surprisingly low average dimension, akin to natural slow earthquakes. Instantaneous dynamical indices can reach large values (>10) instead, and differences persist between numerical simulations and natural observations. We propose to use the suggested metrics as an additional tool to narrow the divergence between slow earthquake observations and dynamical simulations.

Impact of the 2008 MW\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$M_W$$\\end{document} 7.9 Great Wenchuan earthquake on South China microplate motion

Tectonic plate motions drive the earthquake cycle, as they result in the slow accrual and sudden release of energy along plate boundaries. Steadiness of plate motions over the earthquake cycle is a central tenet of the plate tectonics theory and has long been a main pillar in models of earthquake genesis, or of plate-margins seismic potential inferred from slip-deficit estimates. The advent of geodesy in the geosciences and the availability of multi-year-long series of position measurements permit tracking the motions of tectonic plates from before to after the time of significant seismic events that occur along their margins. Here, we present evidence that large earthquakes are capable of modifying the motions of entire microplates. We use high precision Global Navigation Satellite System (GNSS) position time-series covering the periods 2001–2004 and 2014–2017 to demonstrate that, contrary to the tenet above, the South China microplate motion changed after the 2008 MW\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$M_W$$\\end{document} 7.9 Great Wenchuan earthquake. The GNSS data and associated uncertainties indicate a plate motion slowdown of up to 20% that is beyond the possible impact of data noise and is thus tectonically meaningful. We use quantitative models of torque balance to show that generating this kinematic change requires a force upon the South China microplate compatible with that imparted by the Great Wenchuan earthquake of 2008. The existence of a kinematic signal linked to the earthquake cycle that impacts an entire microplate might offer an additional, novel perspective to assessing the hazards of earthquake-prone tectonic regions.

Anatomy of the spatiotemporally correlated noise in GNSS station position time series

Anatomy of the spatiotemporally correlated noise in GNSS station position time series

Comparison between GPS network analysis with undifferenced and double differenced integer ambiguity resolution: A practical perspective

Global Navigation Satellite System (GNSS) network analysis benefits from precise point positioning with undifferenced (UD) or double differenced (DD) integer ambiguity resolution (IAR). Position time series with UD-IAR and a practical DD-IAR are compared for a mixture network consisting of 57 global and 82 regional stations with 4-year observations. The sparse global stations are more affected by different IAR methods than the regional stations of Crustal Movement Observation Network of China (CMONOC). The most significant differences between UD-IAR and the practical DD-IAR are observed in velocity estimations, with averages of 0.15 and 0.30 mm/yr for the horizontal and vertical components, respectively. UD-IAR can achieve smaller root mean square at 70–83 % of the daily solutions than the practical DD-IAR for global stations. Nevertheless, moderate differences of frame parameters and annual variations are introduced by different IAR methods. The IAR is also proved to be one of the potential origins for Global Positioning System (GPS) draconitic signals and white noise at high frequency.

Slow Slip Events in New Zealand: Irregular, yet Predictable?

AbstractCurrent earthquake forecasting approaches are mainly based on probabilistic assumptions, as earthquakes seem to occur randomly. Such apparent randomness can however be caused by deterministic chaos, rendering deterministic short‐term forecasts possible. Due to the short historical and instrumental record of earthquakes, chaos detection has proven challenging, but more frequently occurring slow slip events (SSE) are promising candidates to probe for determinism. Here, we characterize the SSE signatures obtained from GNSS position time series in the Hikurangi Subduction Zone (New Zealand) to investigate whether the seemingly random SSE occurrence is governed by chaotic determinism. We find evidence for deterministic chaos for stations recording shallow SSEs, suggesting that short‐term deterministic forecasting of SSEs, similar to weather forecasts, might indeed be possible over timescales of a few weeks. We anticipate that our findings could open the door for next‐generation SSE forecasting, adding new tools to existing probabilistic approaches.

Minimum-entropy velocity estimation from GPS position time series

Minimum-entropy velocity estimation from GPS position time series

Noise analysis of irregularly sampled VLBI position time series using maximum likelihood estimation

Identification of the optimal noise model for space geodetic time series is crucial for various studies in geodynamics and geodesy. However, the position time series of Very Long Baseline Interferometry (VLBI) are typically irregularly sampled. There is no clear evidence from previous studies to support that the Maximum Likelihood Estimate (MLE) method can allow for stable and reliable noise estimates for irregularly sampled data. To address this issue, we first conducted simulation studies. Results indicate that when the number of data points in the VLBI position time series reaches 300, reliable noise estimations result can be obtained using the MLE. We also found that the higher proportion of white noise a station has, the less influences the data gaps would be on noise estimations. Second, we apply the MLE to investigate the noise properties in the 32 VLBI position time series. About 12 (37.5%) stations exhibit pure white noise, and 15 (46.9%) stations display a combination of white noise and flicker noise. For these stations, the median amplitudes of white noise in the East, North, and Up components are 3.9, 4.6, and 11.9 mm, respectively. Moreover, white and flicker noise amplitudes show a latitude-dependent pattern, with stations located in the southern hemisphere and low latitudes (0-30°N) in the northern hemisphere exhibiting higher noise amplitudes. The remaining approximately 5 stations (15.6%) have the optimal noise model of power law noise with the mean spectral index of −0.32, −0.36, and −0.53 for the East, North, and Up components, respectively. Simply assuming pure white noise can significantly affect velocity uncertainty estimates when compared to using a noise model that includes colored noise. The velocity uncertainty will be underestimated by a factor of 2.9 on average. The effects of a small proportion of colored noise in VLBI data on velocity uncertainty estimation can be ignored only when the time series length exceeds 32.6 years. Additionally, the choice of different noise model can lead to a maximum difference of 0.84 mm for the annual signal of the Up component.

First feasibility demonstration of GNSS-seismology for anthropogenic earthquakes detection.

High-rate GNSS has been proven effective in characterising waveforms and co-seismic displacements due to medium-to-strong natural earthquakes. No application focused on small magnitude events like shallow anthropogenic earthquakes, where displacements and noise have the same order of magnitude. We propose a procedure based on proper signal detection and filtering of the position and velocity time series obtained from high-rate (10Hz) GNSS data processing with two intrinsically different approaches (Precise Point Positioning and variometry). We tested it on five mining tremors with magnitudes of 3.4-4.0, looking both at event detection and its kinematic characterisation. Here we show a high agreement, at the level of 1s, between GNSS and seismic solutions for the earthquake first epoch detection. Also, we show that high-rate multi-constellation (GPS + Galileo) GNSS can reliably characterise low-magnitude shallow earthquakes in terms of induced displacements and velocities, and, including their peak values, respectively, at the level of very few millimetres and 1-2cm/s, paving the way to the routine use of GNSS-seismology for monitoring human activities prone to cause small earthquakes and related potential damages.

Investigation of background noise in the GNSS position time series using spectral analysis – A case study of Nepal Himalaya

Investigation of background noise in the GNSS position time series using spectral analysis – A case study of Nepal Himalaya

Crystal–melt interfaces in Mg2SiO4 at high pressure: structural and energetics insights from first-principles simulations

The interplay between crystal–melt and grain boundary interfaces in partially melted polycrystalline aggregates controls many physical properties of mantle rocks. To understand this process at the fundamental level requires improved knowledge about the interfacial structures and energetics. Here, we report the results of first-principles molecular dynamics simulations of two grain boundaries of (0l1)/[100] type for tilt angles of 30.4° and 49.6° and the corresponding solid–liquid interfaces in Mg2SiO4 forsterite at the conditions of the upper mantle. Our analysis of the simulated position time series shows that structural distortions at the solid–liquid interfacial region are stronger than intergranular interfacial distortions. The calculated formation enthalpy of the solid–solid interfaces increases nearly linearly from 1.0 to 1.4 J/m2 for the 30.4° tilt and from 0.8 to 1.0 J/m2 for the 49.6° tilt with pressure from 0 to 16 GPa at 1500 K, being consistent with the experimental data. The solid–liquid interfacial enthalpy takes comparable values in the range 0.9 to 1.5 J/m2 over similar pressure interval. The dihedral angle of the forsterite–melt system estimated using these interfacial enthalpies takes values in the range of 67° to 146°, showing a decreasing trend with pressure. The predicted dihedral angle is found to be generally larger than the measured data for silicate systems, probably caused by compositional differences between the simulation and the measurements.

Detection of Long‐ and Short‐Term Slow Slip Events Using a Network Inversion Filter and Dense Global Navigation Satellite System Network in Shikoku, Japan

AbstractThe study of slow slip events is essential to elucidating the slip mechanisms and frictional properties of plate interfaces. We imaged the aseismic slip at the plate interface between the subducting Philippine Sea Plate and overriding Amur Plate beneath Shikoku Island, Japan, by applying a network inversion filter to the position time series obtained from Global Navigation Satellite System data spanning January 2012 to April 2022. The results show long‐term slow slip events in the Bungo Channel, central Shikoku, and the Kii Channel, which started from 2018. We also identified 39 short‐term slow slip events associated with low‐frequency tremors. The estimated moment magnitudes of the Bungo Channel, central Shikoku, and Kii Channel slow slip events were Mw7.0, Mw6.4, and Mw6.3, respectively, with a rigidity of 30 GPa. The estimated moment magnitudes of the short‐term slow slip events ranged from Mw5.7 to Mw6.4. Most of the detected short‐term slow slip events are associated with low‐frequency tremor, and many showed propagation through the spatial domain. Events with magnitudes of ≥Mw6.30 typically consist of subevents. The slip rate of short‐term slow slip events ranges from 1 to 7 mm/day, which is considerably larger than the plate convergence rate. The short‐term slow slip events are 6 to 40 days, and follow the accepted scaling law between slip event duration and total magnitude. The short‐term slow slip event zone is consistent with a three‐segment hypothesis. The short‐term slow slip event in northwest Shikoku and long‐term slow slip event in central Shikoku may be correlated.

Application of Fourier analysis to an ellipsoidal particle on a granular magnetic bath

We employ a time-series approach to examine the motion of an ellipsoidal particle resting on an agitated granular bath composed of small magnetic spheres. We characterize the dynamics of the ellipsoidal particle by measuring the autocorrelations present in the time series of position x and angle θ using Fourier spectral analysis. We consider two different sizes of the ellipsoidal particle and different values of the constant magnetic field for the thermal bath. In all cases, power spectra follow a power law, P(f)∝1/fβ with β≈2, indicating scale invariance and Brownian-like motion for the corresponding time series. However, without a constant magnetic field, the scale invariance property is valid only for high values of the oscillating magnetic field. The present system constitutes an experimental model to generate correlated random walks.