Accurate Phase Estimation Research Articles

Dynamic time warping based instantaneous frequency estimation for rotating machineries under non-stationary operating conditions

Abstract For tacho-less order tracking, it is crucial to achieve an accurate estimation of instantaneous phase and frequency under non-stationary conditions for fault diagnosis of mechanical systems. Therefore, an instantaneous frequency estimation method based on dynamic time warping for rotating machinery was proposed. Firstly, a mono-component signal is obtained by variational mode decomposition of multi-harmonic vibration signal generated in practical engineering. Then, a stationary reference signal is constructed by the mean frequency of the vibration signal, which is obtained by the signal spectrum. Aligning the vibration signal with the reference signal to obtain the rough phase estimation and warping path. Finally, a polynomial model is constructed to calculate the analytic expression of the smooth warping path to obtain the instantaneous frequency result. The simulation and experiment present that the dynamic time warping-based method can estimate the instantaneous frequency of the signal under non-stationary conditions. Compared with the classical Hilbert transform method, the proposed dynamic time-warping algorithm has stronger noise resistance.

Quantum-enhanced joint estimation of phase and phase diffusion

Accurate phase estimation in the presence of unknown phase diffusive noise is a crucial yet challenging task in noisy quantum metrology. This problem is particularly interesting due to the detrimental impact of the associated noise. Here, we investigate the joint estimation of phase and phase diffusion using generalized Holland–Burnett states, known for their experimental accessibility. These states provide performance close to the optimal state in single-parameter phase estimation, even in the presence of photon losses. We adopt a twofold approach by analyzing the joint information extraction through the double homodyne measurement and the joint information availability across all probe states. Through our analysis, we find that the highest sensitivities are obtained by using states created by directing all input photons into one port of a balanced beam splitter. Furthermore, we infer that good levels of sensitivity persist even in the presence of moderate photon losses, illustrating the remarkable resilience of our probe states under lossy conditions.

Inversion of Boreal Forest Height Using the CRITIC Weighted Least Squares Three-Stage Temporal Decorrelation Iterative Algorithm

The inversion of forest height using the RVoG (Random Volume over Ground) model is susceptible to overestimation or underestimation due to three error sources, propagating inaccuracies to the estimated forest height. Furthermore, variations in the height and density of the scenario could impact how well the RVoG three-stage inversion performs. This work utilizes the L-band single-baseline full polarization interferometric dataset as its basis. It optimally applies the CRITIC (Criteria Importance Through Intercriteria Correlation) method to the first stage of a three-stage process. This approach aims to overcome the issues mentioned above and enhance the accuracy of forest parameter estimation. A CRITIC weighted least squares temporal decoherence iterative algorithm is also proposed for the characteristics of the spaceborne data, in combination with the temporal decoherence algorithm of previous research. The proposed approach is tested and applied to both simulated and actual data. The optimization approach is first assessed using four simulated datasets that simulate coniferous forests with different densities and heights. The preliminary findings suggest that optimizing the complex coherence fitting process through the weighted least squares method enhances the accuracy of ground phase estimation and, consequently, improves the accuracy of the three-stage approach for inverting forest height. The ground phase estimation results for low forest height consistently remained within 0.02 rad, with a root mean square error (RMSE) below 0.05 rad, and no saturation occurred with increasing forest density. The enhanced algorithm outperforms the traditional technique in terms of accuracy in ground phase estimation. Subsequently, the optimized approach is applied to ALOS-2 spaceborne data, proving more successful than the conventional algorithm in reducing the RMSE of forest height. The findings illustrate the method’s superior inversion performance, obtaining an accuracy exceeding 80% in both the test and validation sets. The validation set’s RMSE is approximately 2.5 m, and the mean absolute error (MAE) is within 2 m. Moreover, it is observed that to counteract the uncertainty in temporal decoherence induced by climate change, a larger temporal baseline necessitates a larger random motion compensation term and phase offset term.

Quantum-enhanced optical phase tracking via squeezed state

Quantum-enhanced optical phase tracking is a quantum optical technique for tracking and measuring optical phases with high accuracy. It has important applications in laser interferometry, spectral analysis, and optical measurements. In this study, we propose a quantum-enhanced optical phase tracking protocol based on squeezed state optical fields. By using a continuous solid-state laser source with a central wavelength of 1064 nm, combing second harmonic generation, optical parametric oscillator, and PDH (Pound-Drever-Hall) locking technology, we prepare an initial squeezed state with a squeezing level of (8.0±0.2) dB. Through signal modulation technique and demodulation technique, we control the phase of the squeezed state optical field, thereby realizing the quantum-enhanced tracking of optical phases within the range of 0－2π. Compared with classical protocols, this protocol can suppress the noise fluctuations of phase tracking to at least 6.27 dB below the shot noise limit, improving the phase tracking accuracy by more than 76.4%. Because of the high requirements for phase measurement accuracy in applications such as angle estimation, phased array radar, and phased array sonar, this protocol is expected to improve the phase estimation accuracy beyond the shot noise limit. It provides compressed light sources for relevant fields, laying a theoretical and experimental foundation for higher-precision spatial positioning and quantum ranging techniques. The probe is made of amino acids arranged in a linear chain and joined together by peptide bonds between the carboxyl and amino groups of adjacent amino acid residues. The sequence of amino acids in a protein is determined by a gene and encoded in the genetic code. This can happen either before the protein is used in the cell, or as part of control mechanism.

A - 175 EEG Phase Can be Predicted with Similar Accuracy across Cognitive States after Accounting for Power and SNR.

Electroencephalogram (EEG) phase can capture neural oscillation dynamics. Accordingly, EEG phase is a potential target for neurofeedback and brain-computer interfaces (BCIs). However, rigorous tests of the generalizability of real-time EEG phase are needed, requiring accurate phase estimates. We examined how cognitive states affect EEG phase prediction accuracy in the parieto-occipital alpha band. We identified datasets through public repositories. After preprocessing, we used the Educated Temporal Prediction Algorithm (ETP) to predict future peaks. We compared these predictions to the original signal, and defined accuracy from 0 to 100%. Our independent variable was cognitive state (eyes-open rest, eyes-closed rest, task), dependent variable was accuracy, and covariates were EEG instantaneous power and signal-to-noise ratio (SNR). We used a linear mixed-effects model, with random effects for dataset and individual. Across the 11 datasets, we had 543 participants and 1,641,074 predictions. There were no significant accuracy differences among the conditions (p < 1e-5), with a baseline accuracy of 59.07%. Power had an effect on accuracy, with a unit increase leading to a 13.1% increase in accuracy (p < 1e-5). SNR had an effect on accuracy, with an effect size of 0.46% (p < 1e-5), with a significant negative interaction with power with an effect size of -0.51% (p < 1e-5). Our results indicated that we could predict EEG phase accurately across cognitive conditions and datasets, with higher accuracy for high instantaneous band-power and SNR. Accordingly, real-time EEG phase experiments, closed-loop technologies, and BCIs should minimize external unwanted noise while targeting periods of high power, as opposed to manipulating experimental and cognitive conditions.

State-space modeling approach for fringe pattern demodulation.

A spatial carrier fringe demodulation technique is proposed based on a state-space modeling approach for phase estimation. The fringe background intensity, carrier frequency, and phase quadrature components are considered to be the elements of the state vector, which are estimated simultaneously. The state estimation is performed using the extended Kalman filter. The simulation and experimental results are provided to demonstrate the performance comparison of the proposed method with popular and state-of-the-art methods in terms of noise robustness and phase estimation accuracy.

Adaptive PI + VPI Harmonic Current Compensation Strategy under Weak Grid Conditions

With the increase of the penetration rate of renewable energy power generation in the power system, the power grid gradually tends to be weak. Under the scenario of nonlinear load connecting to weak power grid, the grid-side voltage will produce unbalance, distortion and frequency deviation due to the influence of large internal impedance, insufficient inertia, three-phase current unbalance and harmonics of weak power grid. The operation of active power filters (APF) under above conditions can lead to significant degradation in harmonic compensation performance. An adaptive proportional integral (PI) + vector PI (VPI) harmonic compensation strategy for a three-phase APF is proposed for use in complex conditions of weak grid. The strategy consists of an adaptive notch filter based synchronous phase-locked loop (ANF-PLL) and an adaptive PI + VPI current control method. In this strategy, a series of adaptive lattice notch filters are introduced to improve the accuracy of grid phase and frequency estimation under the condition of voltage unbalance, distortion and a large range of frequency deviation. Then the phase and frequency information are used in the Park transformation of harmonic detection and current compensation control and the update of PI + VPI current control law parameters. A VPI current tracking controller with adaptive resonant frequency is constructed, which can improve the gain of the resonant frequency point and ensure that the APF can maintain the best compensation performance under the above weak grid conditions. Finally, the simulation and experimental results indicate that the ANF-PLL shows a better phase and frequency estimation performance under complex conditions of weak grid than the conventional and notch filter based methods, and the harmonic compensation strategy presented in this paper achieves a significant performance improvement under complex conditions of weak grid compared with Fixed VPI/SRF-PLL strategy and adaptive VPI/NF-PLL strategy.

Phase-shifting interferometry based on dynamic mode decomposition.

A phase retrieval algorithm in phase-shifting interferometry is presented based on dynamic mode decomposition (DMD). The complex-valued spatial mode obtained from the DMD of phase-shifted interferograms allows the derivation of the phase estimate. At the same time, the oscillation frequency associated with the spatial mode provides the phase step estimate. The performance of the proposed method is compared to methods based on least squares and principle component analysis. The simulation and experimental results demonstrate the improvement in the phase estimation accuracy and noise robustness offered by the proposed method and thus substantiate its practical applicability.

Synchronization and Control of a Single-Phase Grid-Tied Inverter under Harmonic Distortion

Grid-connected inverters in renewable energy systems must provide high-quality power to the grid according to regulatory standards such as the IEEE 1547. To provide high-quality current control when the inverter is connected to a distorted grid, the frequency and phase information of the fundamental harmonic of the grid should be accurately obtained. This paper examines controller design for a single-phase inverter when there is distortion in the grid voltage. The control structure is designed to enhance the quality of the injected current into the grid. To this end, a frequency-locked loop (FLL) sinusoidal tracking controller which is able to reject the grid harmonics is proposed. Thus, the contribution of this paper is a new frequency-locked loop structure with adaptive notch filters that can provide accurate estimation of grid phase and frequency and improve the performance of single-phase inverters working under harmonic distortion. We also present an explanation of how the proposed adaptive nonlinear scheme can be discretized for digital implementation on a microcontroller. Experimental and simulation results are presented to demonstrate the performance of the proposed controller in eliminating distortion and enhancing the quality of the produced power.

Real-Time Gait Phase Estimation Based on Neural Network and Assistance Strategy Based on Simulated Muscle Dynamics for an Ankle Exosuit

Soft exosuits have been demonstrated to possess the potential to reduce metabolism and muscle fatigue in human locomotion. How to maximize the user’s metabolic benefit and reduction of muscle fatigue are the primary objectives of assistance patterns optimization. For the exosuit controller, accurate gait phase estimation and appropriate assistance force profile are crucial factors. To gain an accurate real-time gait phase estimation, a neural network algorithm based on multi-modal information fusion was developed. The eigenvector of which was composed of Euler angles and gyroscope data of four Inertial Measurement units fixed on thigh and calf, and gait period estimated by force sensing resistor installed on foot insoles. The mean squared error of the model is below 3 ms and the regression coefficient R exceeds 0.999 when walking at a speed of 1.5 m/s. For the assistance force profile, which was designed based on the characteristics of soleus muscle dynamics. Wherein the biomechanics of walking were derived from simulation with OpenSim software. Compared with wearing an exosuit without assistance and with assistance, the metabolic demand was reduced by an average of 7.5%, and the average peak value and RMS of calf muscles involved in palntarflexion were decreased to different degrees. Our research illustrates the feasibility of neural network-based real-time gait phase estimation and assistance strategy design obtained by simulating muscle dynamics in the OpenSim software.

Two-step phase shifting algorithm based on cost function minimization

A computationally efficient phase shift estimation algorithm is proposed for two-step phase-shifting interferometry based on a cost function minimization technique. The proposed method can accurately estimate the phase shift over a wide range resulting in reliable phase estimation. Due to the analytical solution offered by the proposed method, its computational efficiency is found to be higher than the existing state-of-art methods. While the performance of some methods is user-defined parameter-dependent, the proposed method is non-parametric and user-independent. The accuracy of phase shift and subsequent phase estimation using the proposed algorithm is found to be maximum around phase shift of π/2rad which further decreases for the phase shift values closer to 0rad and πrad. The experimental results demonstrate the practical applicability of the proposed method.

Camera Calibration Based on Phase Estimation

We propose a novel camera calibration method based on phase estimation of a periodic grid pattern that is more accurate and robust to image blur, noise, and uneven illumination. Instead of intensity-based geometric feature detection from the calibration image, we extract the phase information to acquire 3-D-to-2-D point correspondence. The calibration procedure includes three steps: 1) estimate the tilt angles of input images based on a pyramid geometry model and remap the images to a canonical fronto-parallel plane to correct perspective distortion; 2) use a highly accurate phase estimation method to localize control points; and 3) apply an iterative refinement method to compute the camera parameters until convergence. Using the perspective correction and phase estimation method together help increase the accuracy of control point localization and consequently of camera calibration. Synthetic as well as real images from high accuracy patterns etched on ceramic plates and low accuracy patterns printed on article show that the proposed method outperforms the most widely-used methods, in terms of accuracy and robustness.

Desynchronizing the sleep---wake cycle from circadian timing to assess their separate contributions to physiology and behaviour and to estimate intrinsic circadian period.

Circadian clocks drive cyclic variations in many aspects of physiology, but some daily variations are evoked by periodic changes in the environment or sleep-wake state and associated behaviors, such as changes in posture, light levels, fasting or eating, rest or activity and social interactions; thus, it is often important to quantify the relative contributions of these factors. Yet, circadian rhythms and these evoked effects cannot be separated under typical 24-h day conditions, because circadian phase and the length of time awake or asleep co-vary. Nathaniel Kleitman's forced desynchrony (FD) protocol was designed to assess endogenous circadian rhythmicity and to separate circadian from evoked components of daily rhythms in multiple parameters. Under FD protocol conditions, light intensity is kept low to minimize its impact on the circadian pacemaker, and participants have sleep-wake state and associated behaviors scheduled to an imposed non-24-h cycle. The period of this imposed cycle, Τ, is chosen so that the circadian pacemaker cannot entrain to it and therefore continues to oscillate at its intrinsic period (τ, ~24.15 h), ensuring circadian components are separated from evoked components of daily rhythms. Here we provide detailed instructions and troubleshooting techniques on how to design, implement and analyze the data from an FD protocol. We provide two procedures: one with general guidance for designing an FD study and another with more precise instructions for replicating one of our previous FD studies. We discuss estimating circadian parameters and quantifying the separate contributions of circadian rhythmicity and the sleep-wake cycle, including statistical analysis procedures and an R package for conducting the non-orthogonal spectral analysis method that enables an accurate estimation of period, amplitude and phase.

Influence of multiphoton events on the quantum enhanced phase estimation.

Quantum metrology can approach measurement precision of Heisenberg Limit using an ideal quantum source, which has attracted a great interest in fundamental physical studies. However, the quantum metrology precision is impressionable to the system noise in experiments. In this paper, we analyze the influence of multiphoton events on the phase estimation precision when using a nondeterministic single photon source. Our results show there are an extra bias and quantum enhanced region restriction due to multiphoton events, which declines the quantum phase estimation precision. A limitation of multiphoton probability is obtained for quantum enhanced phase estimation accuracy under different experimental model. Our results provide beneficial suggestions for improving quantum metrology precision in future experiments.

Security Energy Efficiency Analysis of Analog Collaborative Beamforming With Stochastic Virtual Antenna Array of UAV Swarm

To extend the transmission range governed by limited transmit power, collaborative beamforming (CB) can be employed with a virtual antenna array (VAA) constructed by an unmanned aerial vehicle (UAV) swarm. CB techniques combined with physical layer security (PLS) algorithms are known to better secure transmissions of sensitive information in the presence of eavesdropping attacks, compared to co-located antenna-based schemes. In particular, analog collaborative beamforming (ACB) with random VAA topologies, which is suitable for UAV networks due to its lower signaling/channel estimation overhead compared to the digital CB, can provide a significantly higher secrecy rate by creating noise-like signals at eavesdroppers. However, the increase in energy consumption to improve secrecy rate had been ignored in the existing ACB-based PLS schemes, which is of paramount importance considering the limited onboard energy of UAVs. Thus, motivated by such limitation, in this paper, we examine the security energy efficiency of the ACB-based PLS technique, where a group of UAVs (or VAA elements) randomly change their locations in a distributed manner to randomize the array factor of the VAA, i.e., a stochastic VAA. The proposed stochastic VAA outperforms the existing static VAA in terms of secrecy energy efficiency as verified by analytic and numerical results. Further, the impact of phase errors of the proposed scheme is also presented, which indicates the significance of the accurate phase estimation.

Accurate Real-time Phase Estimation for Normal and Asymmetric Gait.

An accurate real-time gait phase estimator for normal and asymmetric gait is developed by training and testing a time-delay neural network on gait data collected from six participants during treadmill walking. The trained model can generate smooth and highly accurate predictions of the gait phase with a root mean square error of less than 3.48% and 4.31% in normal and asymmetric gait, respectively. The coefficient of determination between the estimated and target phase is greater than 99% for all subjects with both normal and asymmetric gait. The proposed gait estimator also exhibits precise heel-strike event detection with an RMSE of 2.56% and 3.70% in normal and asymmetric gait, respectively. A spatial impedance controller is then employed and tested based on the estimated gait phase of a new participant. Obtained results confirm that the controller provided assistance in coordination with the user's motion both in normal and asymmetric gait conditions. The estimated gait phase is compared in the case of walking without and with the exoskeleton in passive and active modes, indicating persistent accuracy of the gait phase estimator regardless of the walking conditions.

Predictive Locomotion Mode Recognition and Accurate Gait Phase Estimation for Hip Exoskeleton on Various Terrains

In recent years, lower-limb exoskeletons have been applied to assist people with weak mobility in daily life, which requires enhanced adaptability to complex environments. To achieve a smooth transition between different assistive strategies and provide proper assistance at the desired timing during locomotion on various terrains, two significant issues should be addressed: the delay of locomotion mode recognition (LMR) and the accuracy of gait phase estimation (GPE), which are yet critical challenges for exoskeleton controls. To tackle these challenges, a high-level exoskeleton control, including a depth sensor-based LMR method and an adaptive oscillator-based GPE approach, is developed in this study for terrain-adaptive assistive walking. An experimental study was conducted to evaluate the effectiveness and usability of the proposed control in a real-world scenario. Experimental results suggested that the depth sensor-based LMR method can detect the locomotion mode change 0.5 step ahead of the assistive strategy switch of the leading leg, while the average environment classification accuracy across five subjects was higher than 98 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\%$</tex-math></inline-formula> . The accuracy is comparable with the state-of-the-art LMR methods, but its predictive capability is beyond existing LMR methods applied in lower-limb exoskeletons. Moreover, the adaptive oscillator-based GPE approach accurately estimated the user’s gait phase during locomotion on various terrains, with a root-mean-square (RMS) gait phase reset error of only <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\pm$</tex-math></inline-formula> 0.27 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\%$</tex-math></inline-formula> , outperforming the literature standard.

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.

Low-Complexity Sampling Frequency Offset Estimation and Compensation Scheme for OFDM-Based UWOC System

In this paper, a simple sampling frequency offset (SFO) estimation and compensation scheme based on two phase-conjugated pilots is proposed and experimentally demonstrated in an OFDM-based underwater wireless optical communication (UWOC) system. The phase shift is obtained by simple multiplication for phase-conjugated pilots, and the results are averaged to perform more accurate phase estimation. The experimental results show that the estimation offset is limited within ±3 ppm when the SFO ranges from −1000 ppm to +1000 ppm over a 1 m tap water channel. Moreover, with the help of the proposed scheme, up to ±300 ppm SFO can be well-compensated with error vector magnitude (EVM) penalties below 1 dB after 1 m underwater transmission. In addition, the results demonstrate that, compared with the ideal case without SFO, our proposed SFO compensation scheme can provide nearly negligible bit error rate (BER) penalties in saltwater with the highly scattering property.

Enhanced nonlinear quantum metrology with weakly coupled solitons in the presence of particle losses

The estimation of physical parameters with Heisenberg sensitivity and beyond is one of the crucial problems for current quantum metrology. However, unavoidable lossy effect is commonly believed to be the main obstacle when applying fragile quantum states. To utilize the lossy quantum metrology, we offer an interferometric procedure for phase parameters estimation at the Heisenberg (up to 1/N) and super-Heisenberg (up to 1/N^3) scaling levels in the framework of the linear and nonlinear metrology approaches, respectively. The heart of our setup is the novel soliton Josephson Junction (SJJ) system providing the formation of the quantum probe, i.e, the entangled Fock (N00N-like) state, beyond the superfluid-Mott insulator quantum phase transition point. We illustrate that such states are close to the optimal ones even with moderate losses. The enhancement of phase estimation accuracy remains feasible both for the linear and nonlinear metrologies with the SJJs, and allows further improvement for the current experiments performed with atomic condensate solitons with a mesoscopic number of particles.