IMU-Based Real-Time Estimation of Gait Phase Using Multi-Resolution Neural Networks.

This work presents a real-time gait phase estimator using thigh- and shank-mounted inertial measurement units (IMUs). A multi-rate convolutional neural network (CNN) was trained to estimate gait phase for a dataset of 16 participants walking on an instrumented treadmill with speeds varying between 0.1 to 1.9 m/s, and conditions such as asymmetric walking, stop-start, and sudden speed changes. One-subject-out cross-validation was used to assess the robustness of the estimator to the gait patterns of new individuals. The proposed model had a spatial root mean square error of 5.00±1.65%, and a temporal mean absolute error of 2.78±0.97% evaluated at the heel strike. A second cross-validation was performed to show that leaving out any of the walking conditions from the training dataset did not result in significant performance degradation. A 2-sample Kolmogorov-Smirnov test showed that there was no significant increase in spatial or temporal error when testing on the abnormal walking conditions left out of the training set. The results of the two cross-validations demonstrate that the proposed model generalizes well across new participants, various walking speeds, and gait patterns, showcasing its potential for use in investigating patient populations with pathological gaits and facilitating robot-assisted walking.

Study of the Bias of the Initial Phase Estimation of a Sinewave of Known Frequency in the Presence of Phase Noise.

The estimation of the parameters of a sinusoidal signal is of paramount importance in various applications in the fields of sensors, signal processing, parameter estimation, and device characterization, among others. The presence, in the measurement system, of non-ideal phenomena such as additive noise in the signals, phase noise in the stimulus generation, jitter in the sampling system, frequency error in the experimental setup, among others, leads to increased uncertainty and bias in the estimated quantities obtained by least squares methods and those derived from them. Therefore, from a metrological point of view, it is important to be able to theoretically predict and quantify those uncertainties in order to properly design the measurement system and its parameters, such as the number of samples to acquire or the stimulus signal amplitude to use to minimize the uncertainty in the estimated values. Previous works have shown that the presence of these non-ideal phenomena leads to increased uncertainty and bias in the estimation of the sinewave amplitude. The present work complements this knowledge by focusing specifically on the effect of phase noise and sampling jitter in the bias of the initial phase estimation of a sinusoidal signal of known frequency (three­parameter sine fitting procedure). A theoretical derivation of the bias of initial phase estimation that takes into consideration the presence of phase noise in the sinewave is presented. Since a Taylor series approximation was used where only the first term was retained, it was necessary to validate the analytical derivations with numerical simulations using a Monte Carlo type of procedure. This process was applied to different conditions regarding the phase noise standard deviation, initial phase value, and number of samples. It is concluded that, in most scenarios, initial phase estimation using sine fitting is unbiased in the presence of phase noise or jitter. It is shown, however, that in cases of extremely high phase noise standard deviation and a very low number of samples, a bias occurs.

Pulse Accumulation Approach Based on Signal Phase Estimation for Doppler Wind Lidar.

Coherent Doppler wind lidar (CDWL) uses transmitted laser pulses to measure wind velocity distribution. However, the echo signal of CDWL is easily affected by atmospheric turbulence, which can decrease the signal-to-noise ratio (SNR) of lidar. To improve the SNR, this paper proposes a pulse accumulation method based on the cross-correlation function to estimate the phase of the signal. Compared with incoherent pulse accumulation, the proposed method significantly enhances the correlation between signals from different periods to obtain high SNR gains that arise from pulse accumulation. Using simulation, the study evaluates the effectiveness of this phase estimation method and its robustness against noise in algorithms which analyze Doppler frequency shifts. Furthermore, a CDWL is developed for measuring the speed of an indoor motor turntable and the outdoor atmospheric wind field. The phase estimation method yielded SNR gains of 28.18 dB and 32.03 dB for accumulation numbers of 500 and 1500, respectively. The implementation of this method in motor turntable speed measurements demonstrated a significant reduction in speed error-averaging 9.18% lower than that of incoherent accumulation lidar systems. In experiments that measure atmospheric wind fields, the linear fit curve slope between the measured wind speed and the wind speed measured via a commercial wind-measuring lidar can be reduced from 1.146 to 1.093.

Walking-Speed-Adaptive Gait Phase Estimation for Wearable Robots.

This paper introduces a Gait Phase Estimation Module (GPEM) and its real-time algorithm designed to estimate gait phases continuously and monotonically across a range of walking speeds and accelerations/decelerations. To address the challenges of real-world applications, we propose a speed-adaptive online gait phase estimation algorithm, which enables precise estimation of gait phases during both constant speed locomotion and dynamic speed changes. Experimental verification demonstrates that the proposed method offers smooth, continuous, and repetitive gait phase estimation when compared to conventional approaches such as the phase portrait method and time-based estimation. The proposed method achieved a 48% reduction in gait phase deviation compared to time-based estimation and a 48.29% reduction compared to the phase portrait method. The proposed algorithm is integrated within the GPEM, allowing for its versatile application in controlling gait assistive robots without incurring additional computational burden. The results of this study contribute to the development of robust and efficient gait phase estimation techniques for various robotic applications.

Point-Wise Phase Estimation Method in Fringe Projection Profilometry under Non-Sinusoidal Distortion.

In fringe projection profilometry, high-order harmonics information of distorted fringe will lead to errors in the phase estimation. In order to solve this problem, a point-wise phase estimation method based on a neural network (PWPE-NN) is proposed in this paper. The complex nonlinear mapping relationship between the gray values and the phase under non-sinusoidal distortion is constructed by using the simple neural network model. It establishes a novel implicit expression for phase solution without complicated measurement operations. Compared with the previous method of combining local image information, it can accurately calculate each phase value by point. The comparison results show that the traditional method is with periodic phase errors, while the proposed method can effectively eliminate phase errors caused by non-sinusoidal phase shifting.

Real-Time Tool Detection for Workflow Identification in Open Cranial Vault Remodeling.

Deep learning is a recent technology that has shown excellent capabilities for recognition and identification tasks. This study applies these techniques in open cranial vault remodeling surgeries performed to correct craniosynostosis. The objective was to automatically recognize surgical tools in real-time and estimate the surgical phase based on those predictions. For this purpose, we implemented, trained, and tested three algorithms based on previously proposed Convolutional Neural Network architectures (VGG16, MobileNetV2, and InceptionV3) and one new architecture with fewer parameters (CranioNet). A novel 3D Slicer module was specifically developed to implement these networks and recognize surgical tools in real time via video streaming. The training and test data were acquired during a surgical simulation using a 3D printed patient-based realistic phantom of an infant's head. The results showed that CranioNet presents the lowest accuracy for tool recognition (93.4%), while the highest accuracy is achieved by the MobileNetV2 model (99.6%), followed by VGG16 and InceptionV3 (98.8% and 97.2%, respectively). Regarding phase detection, InceptionV3 and VGG16 obtained the best results (94.5% and 94.4%), whereas MobileNetV2 and CranioNet presented worse values (91.1% and 89.8%). Our results prove the feasibility of applying deep learning architectures for real-time tool detection and phase estimation in craniosynostosis surgeries.

Kurtosis-Based Symbol Timing and Carrier Phase/Frequency Tracking.

Kurtosis is known to be effective at estimating signal timing and carrier phase offset when the processing is performed in a "burst mode," that is, operating on a block of received signal in an offline fashion. In this paper, kurtosis-based estimation is extended to provide tracking of timing and carrier phase, and frequency offsets. The algorithm is compared with conventional PLL-type timing/phase estimation and shown to be superior in terms of speed of convergence, with comparable variance in the matched filter output symbols.

Adaptive phase correction of diffusion-weighted images.

Phase correction (PC) is a preprocessing technique that exploits the phase of images acquired in Magnetic Resonance Imaging (MRI) to obtain real-valued images containing tissue contrast with additive Gaussian noise, as opposed to magnitude images which follow a non-Gaussian distribution, e.g. Rician. PC finds its natural application to diffusion-weighted images (DWIs) due to their inherent low signal-to-noise ratio and consequent non-Gaussianity that induces a signal overestimation bias that propagates to the calculated diffusion indices. PC effectiveness depends upon the quality of the phase estimation, which is often performed via a regularization procedure. We show that a suboptimal regularization can produce alterations of the true image contrast in the real-valued phase-corrected images. We propose adaptive phase correction (APC), a method where the phase is estimated by using MRI noise information to perform a complex-valued image regularization that accounts for the local variance of the noise. We show, on synthetic and acquired data, that APC leads to phase-corrected real-valued DWIs that present a reduced number of alterations and a reduced bias. The substantial absence of parameters for which human input is required favors a straightforward integration of APC in MRI processing pipelines.

A Hybrid SAR/ISAR Approach for Refocusing Maritime Moving Targets with the GF-3 SAR Satellite.

Due to self-motion and sea waves, moving ships are typically defocused in synthetic aperture radar (SAR) images. To focus non-cooperative targets, the inverse SAR (ISAR) technique is commonly used with motion compensation. The hybrid SAR/ISAR approach allows a long coherent processing interval (CPI), in which SAR targets are processed with ISAR processing, and exploits the advantages of both SAR and ISAR to generate well-focused images of moving targets. In this paper, based on hybrid SAR/ISAR processing, we propose an improved rank-one phase estimation method (IROPE). By using an iterative two-step convergence approach in the IROPE, the proposed method achieves accurate phase error, maintains robustness to noise and performs well in estimating various phase errors. The performance of the proposed method is analyzed by comparing it with other focusing algorithms in terms of processing simulated data and real complex image data acquired by Gaofen-3 (GF-3) in spotlight mode. The results demonstrate the effectiveness of the proposed method.

Accuracy Bounds and Measurements of a Contactless Permittivity Sensor for Gases Using Synchronized Low-Cost mm-Wave Frequency Modulated Continuous Wave Radar Transceivers.

A primary concern in a multitude of industrial processes is the precise monitoring of gaseous substances to ensure proper operating conditions. However, many traditional technologies are not suitable for operation under harsh environmental conditions. Radar-based time-of-flight permittivity measurements have been proposed as alternative but suffer from high cost and limited accuracy in highly cluttered industrial plants. This paper examines the performance limits of low-cost frequency-modulated continuous-wave (FMCW) radar sensors for permittivity measurements. First, the accuracy limits are investigated theoretically and the Cramér-Rao lower bounds for time-of-flight based permittivity and concentration measurements are derived. In addition, Monte-Carlo simulations are carried out to validate the analytical solutions. The capabilities of the measurement concept are then demonstrated with different binary gas mixtures of Helium and Carbon Dioxide in air. A low-cost time-of-flight sensor based on two synchronized fully-integrated millimeter-wave (MMW) radar transceivers is developed and evaluated. A method to compensate systematic deviations caused by the measurement setup is proposed and implemented. The theoretical discussion underlines the necessity of exploiting the information contained in the signal phase to achieve the desired accuracy. Results of various permittivity and gas concentration measurements are in good accordance to reference sensors and measurements with a commercial vector network analyzer (VNA). In conclusion, the proposed radar-based low-cost sensor solution shows promising performance for the intended use in demanding industrial applications.

The Role of Millimeter-Waves in the Distance Measurement Accuracy of an FMCW Radar Sensor.

High-accuracy, short-range distance measurement is required in a variety of industrial applications e.g., positioning of robots in a fully automated production process, level measurement of liquids in small containers. An FMCW radar sensor is suitable for this purpose, since many of these applications involve harsh environments. Due to the progress in the field of semiconductor technology, FMCW radar sensors operating in different millimeter-wave frequency bands are available today. An important question in this context, which has not been investigated so far is how does a millimeter-wave frequency band influence the sensor accuracy, when thousands of distance measurements are performed with a sensor. This topic has been dealt with for the first time in this paper. The method used for analyzing the FMCW radar signal combines a frequency- and phase-estimation algorithm. The frequency-estimation algorithm based on the fast Fourier transform and the chirp-z transform provides a coarse estimate of the target distance. Subsequently, the phase-estimation algorithm based on a cross-correlation function provides a fine estimate of the target distance. The novel aspects of this paper are as follows. First, the estimation theory concept of Cramér-Rao lower bound (CRLB) has been used to compare the accuracy of two millimeter-wave FMCW radars operating at 60 GHz and 122 GHz. In this comparison, the measurement parameters (e.g., bandwidth, signal-to-noise ratio) as well as the signal-processing algorithm used for both the radars are the same, thus ensuring an unbiased comparison of the FMCW radars, solely based on the choice of millimeter-wave frequency band. Second, the improvement in distance measurement accuracy obtained after each step of the combined frequency- and phase-estimation algorithm has been experimentally demonstrated for both the radars. A total of 5100 short-range distance measurements are made using the 60 GHz and 122 GHz FMCW radar. The measurement results are analyzed at various stages of the frequency- and phase-estimation algorithm and the measurement error is calculated using a nanometer-precision linear motor. At every stage, the mean error values measured with the 60 GHz and 122 GHz FMCW radars are compared. The final accuracy achieved using both radars is of the order of a few micrometers. The measured standard deviation values of the 60 GHz and 122 GHz FMCW radar have been compared against the CRLB. As predicted by the CRLB, this paper experimentally validates for the first time that the 122 GHz FMCW radar provides a higher repeatability of micrometer-accuracy distance measurements than the 60 GHz FMCW radar.

Performance Analysis of Global Navigation Satellite System Signal Acquisition Aided by Different Grade Inertial Navigation System under Highly Dynamic Conditions.

Under the high dynamic conditions, Global Navigation Satellite System (GNSS) signals produce great Doppler frequency shifts, which hinders the fast acquisition of signals. Inertial Navigation System (INS)-aided acquisition can improve the acquisition performance, whereas the accuracy of Doppler shift and code phase estimation are mainly determined by the INS precision. The relation between the INS accuracy and Doppler shift estimation error has been derived, while the relation between the INS accuracy and code phase estimation error has not been deduced. In this paper, in order to theoretically analyze the effects of INS errors on the performance of Doppler shift and code phase estimations, the connections between them are re-deduced. Moreover, the curves of the corresponding relations are given for the first time. Then, in order to have a better verification of the INS-aided acquisition, a high dynamic scenario is designed. Furthermore, by using the deduced mathematical relation, the effects of different grade INS on the GNSS (including Global Positioning System (GPS) and BeiDou Navigation Satellite System (BDS)) signal acquisition are analyzed. Experimental results demonstrate that the INS-aided acquisition can reduce the search range of local frequency and code phase, and achieve fast acquisition. According to the experimental results, a suitable INS can be chosen for the deeply coupled integration.

A general quantum algorithm for numerical integration.

Quantum algorithms have shown their superiority in many application fields. However, a general quantum algorithm for numerical integration, an indispensable tool for processing sophisticated science and engineering issues, is still missing. Here, we first proposed a quantum integration algorithm suitable for any continuous functions that can be approximated by polynomials. More impressively, the algorithm achieves quantum encoding of any integrable functions through polynomial approximation, then constructs a quantum oracle to mark the number of points in the integration area and finally converts the statistical results into the phase angle in the amplitude of the superposition state. The quantum algorithm introduced in this work exhibits quadratic acceleration over the classical integration algorithms by reducing computational complexity from O(N) to O(√N). Our work addresses the crucial impediments for improving the generality of quantum integration algorithm, which provides a meaningful guidance for expanding the superiority of quantum computing.

Research on Brain Networks of Human Balance Based on Phase Estimation Synchronization.

Phase synchronization serves as an effective method for analyzing the synchronization of electroencephalogram (EEG) signals among brain regions and the dynamic changes of the brain. The purpose of this paper is to study the construction of the functional brain network (FBN) based on phase synchronization, with a special focus on neural processes related to human balance regulation. This paper designed four balance paradigms of different difficulty by blocking vision or proprioception and collected 19-channel EEG signals. Firstly, the EEG sequences are segmented by sliding windows. The phase-locking value (PLV) of core node pairs serves as the phase-screening index to extract the valid data segments, which are recombined into new EEG sequences. Subsequently, the multichannel weighted phase lag index (wPLI) is calculated based on the new EEG sequences to construct the FBN. The experimental results show that due to the randomness of the time points of body balance adjustment, the degree of phase synchronization of the datasets screened by PLV is more obvious, improving the effective information expression of the subsequent EEG data segments. The FBN topological structures of the wPLI show that the connectivity of various brain regions changes structurally as the difficulty of human balance tasks increases. The frontal lobe area is the core brain region for information integration. When vision or proprioception is obstructed, the EEG synchronization level of the corresponding occipital lobe area or central area decreases. The synchronization level of the frontal lobe area increases, which strengthens the synergistic effect among the brain regions and compensates for the imbalanced response caused by the lack of sensory information. These results show the brain regional characteristics of the process of human balance regulation under different balance paradigms, providing new insights into endogenous neural mechanisms of standing balance and methods of constructing brain networks.

Pedestrian Dead Reckoning with Low-Cost Foot-Mounted IMU Sensor.

In this paper, we researched Pedestrian Dead Reckoning (PDR) with one foot-mounted IMU sensor. The issues of PDR are magnetism noise and accumulated error due to the noise included in acceleration and gyro data. Two methods are proposed in this paper. First is the gait-phase-estimation method with pitch angle for the Zero Velocity Update algorithm. Second is a method for avoiding accumulated errors by updating the roll and pitch angles with acceleration. The two experiments were conducted to examine the error of gait-phase estimation and distance estimations. The relative error of distance was about 7.40% in the case of walking straight and about 12.27% in the case of a shifting travel direction.

Spatiotemporal reconstruction method of carotid artery ultrasound from freehand sonography.

PURPOSE: 4D reconstruction based on radiation-free ultrasound can provide valuable information about the anatomy. Current 4D US technologies are either faced with limited field-of-view (FoV), technical complications, or cumbersome setups. This paper proposes a spatiotemporal US reconstruction framework to enhance its ability to provide dynamic structure information. METHODS: We propose a spatiotemporal US reconstruction framework based on freehand sonography. First, a collecting strategy is presented to acquire 2D US images in multiple spatial and temporal positions. A morphology-based phase extraction method after pose correction is presented to decouple the compounding image variations. For temporal alignment and reconstruction, a robust kernel regression model is established to reconstruct images in arbitrary phases. Finally, the spatiotemporal reconstruction is demonstrated in the form of 4D movies by integrating the US images according to the tracked poses and estimated phases. RESULTS: Quantitative and qualitative experiments were conducted on the carotid US to validate the feasibility of the proposed pipeline. The mean phase localization and heart rate estimation errors were 0.07 ± 0.04 s and 0.83 ± 3.35 bpm, respectively, compared with cardiac gating signals. The assessment of reconstruction quality showed a low RMSE (<0.06) between consecutive images. Quantitative comparisons of anatomy reconstruction from the generated US volumes and MRI showed an average surface distance of 0.39 ± 0.09 mm on the common carotid artery and 0.53 ± 0.05 mm with a landmark localization error of 0.60 ± 0.18 mm on carotid bifurcation. CONCLUSION: A novel spatiotemporal US reconstruction framework based on freehand sonography is proposed that preserves the utility nature of conventional freehand US. Evaluations on in vivo datasets indicated that our framework could achieve acceptable reconstruction performance and show potential application value in the US examination of dynamic anatomy.

Effect of Torso Kinematics on Gait Phase Estimation at Different Walking Speeds.

Human gait phase estimation has been studied in the field of robotics due to its importance for controlling wearable devices (e.g., prostheses or exoskeletons) in a synchronized manner with the user. As data-driven approaches have recently risen in the field, researchers have attempted to estimate the user gait phase using a learning-based method. Thigh and torso information have been widely utilized in estimating the human gait phase for wearable devices. Torso information, however, is known to have high variability, specifically in slow walking, and its effect on gait phase estimation has not been studied. In this study, we quantified torso variability and investigated how the torso information affects the gait phase estimation result at various walking speeds. We obtained three different trained models (i.e., general, slow, and normal-fast models) using long short-term memory (LSTM). These models were compared to identify the effect of torso information at different walking speeds. In addition, the ablation study was performed to identify the isolated effect of the torso on the gait phase estimation. As a result, when the torso segment's angular velocity was used with thigh information, the accuracy of gait phase estimation was increased, while the torso segment's angular position had no apparent effect on the accuracy. This study suggests that the torso segment's angular velocity enhances human gait phase estimation when used together with the thigh information despite its known variability.

Current developments of robotic hip exoskeleton toward sensing, decision, and actuation: A review.

The aging population is now a global challenge, and impaired walking ability is a common feature in the elderly. In addition, some occupations such as military and relief workers require extra physical help to perform tasks efficiently. Robotic hip exoskeletons can support ambulatory functions in the elderly and augment human performance in healthy people during normal walking and loaded walking by providing assistive torque. In this review, the current development of robotic hip exoskeletons is presented. In addition, the framework of actuation joints and the high-level control strategy (including the sensors and data collection, the way to recognize gait phase, the algorithms to generate the assist torque) are described. The exoskeleton prototypes proposed by researchers in recent years are organized to benefit the related fields realizing the limitations of the available robotic hip exoskeletons, therefore, this work tends to be an influential factor with a better understanding of the development and state-of-the-art technology.

Real-Time Gait Phase Estimation for Robotic Hip Exoskeleton Control During Multimodal Locomotion.

We developed and validated a gait phase estimator for real-time control of a robotic hip exoskeleton during multimodal locomotion. Gait phase describes the fraction of time passed since the previous gait event, such as heel strike, and is a promising framework for appropriately applying exoskeleton assistance during cyclic tasks. A conventional method utilizes a mechanical sensor to detect a gait event and uses the time since the last gait event to linearly interpolate the current gait phase. While this approach may work well for constant treadmill walking, it shows poor performance when translated to overground situations where the user may change walking speed and locomotion modes dynamically. To tackle these challenges, we utilized a convolutional neural network-based gait phase estimator that can adapt to different locomotion mode settings to modulate the exoskeleton assistance. Our resulting model accurately predicted the gait phase during multimodal locomotion without any additional information about the user's locomotion mode, with a gait phase estimation RMSE of 5.04 ± 0.79%, significantly outperforming the literature standard (p < 0.05). Our study highlights the promise of translating exoskeleton technology to more realistic settings where the user can naturally and seamlessly navigate through different terrain settings.

Noise-robust breathing-phase estimation on marker-free, ultra low dose X-ray projections for real-time tumor localization via surrogate structures.

PURPOSE: This paper presents a novel strategy for feature-based breathing-phase estimation on ultra low-dose X-ray projections for tumor motion control in radiation therapy. METHODS: Coarse-scaled Curvelet coefficients are identified as motion sensitive but noise-robust features for this purpose. For feature-based breathing-phase estimation, an ensemble strategy with two classifiers is used. This consensus-based estimation substantially increases tracking reliability by rejection of false positives. The algorithm is evaluated on both synthetic and measured phantom data: Monte Carlo simulated ultra low dose projections for a C-arm X-ray and on the basis of 4D-chest-CTs of eight patients on one hand side and real measurements based on a motion phantom. RESULTS: To achieve an accuracy of breathing-phase estimation of more than 95% a fluence between 20 and 400 photons per pixel (open field) is required depending on the patient. Furthermore, the algorithm is evaluated on real ultra low dose projections from an XVI R5.0 system (Elekta AB, Stockholm, Sweden) using an additional lead filter to reduce fluence. The classifiers-consensus-based-gating method estimated the correct position of the test projections in all test cases at a fluence of ∼180 photons per pixel and 92% at a fluence of ∼40 photons per pixel. The deposited dose to patient per image is in the range of nGy. CONCLUSIONS: A novel method is presented for estimation of breathing-phases for real-time tumor localization at ultra low dose both on a simulation and a phantom basis. Its accuracy is comparable to state of the art X-ray based algorithms while the released dose to patients is reduced by two to three orders of magnitude compared to conventional template-based approaches. This allows for continuous motion control during irradiation without the need of external markers.