Accurate Phase Estimation Research Articles

Comparison of Phase Estimation Methods for Quantitative Susceptibility Mapping Using a Rotating-Tube Phantom.

Quantitative Susceptibility Mapping (QSM) is an MRI tool with the potential to reveal pathological changes from magnetic susceptibility measurements. Before phase data can be used to recover susceptibility (Δχ), the QSM process begins with two steps: data acquisition and phase estimation. We assess the performance of these steps, when applied without user intervention, on several variations of a phantom imaging task. We used a rotating-tube phantom with five tubes ranging from Δχ=0.05 ppm to Δχ=0.336 ppm. MRI data was acquired at nine angles of rotation for four different pulse sequences. The images were processed by 10 phase estimation algorithms including Laplacian, region-growing, branch-cut, temporal unwrapping, and maximum-likelihood methods, resulting in approximately 90 different combinations of data acquisition and phase estimation methods. We analyzed errors between measured and expected phases using the probability mass function and Cumulative Distribution Function. Repeatable acquisition and estimation methods were identified based on the probability of relative phase errors. For single-echo GRE and segmented EPI sequences, a region-growing method was most reliable with Pr (relative error <0.1) = 0.95 and 0.90, respectively. For multiecho sequences, a maximum-likelihood method was most reliable with Pr (relative error <0.1) = 0.97. The most repeatable multiecho methods outperformed the most repeatable single-echo methods. We found a wide range of repeatability and reproducibility for off-the-shelf MRI acquisition and phase estimation approaches, and this variability may prevent the techniques from being widely integrated in clinical workflows. The error was dominated in many cases by spatially discontinuous phase unwrapping errors. Any postprocessing applied on erroneous phase estimates, such as QSM's background field removal and dipole inversion, would suffer from error propagation. Our paradigm identifies methods that yield consistent and accurate phase estimates that would ultimately yield consistent and accurate Δχ estimates.

Fault diagnosis of a planetary gearbox by D norm-based time synchronous averaging (DTSA) with roughly estimated phase information under an encoder-less operating condition

Minimum entropy deconvolution (MED) filter is widely used to extract fault-related impulse features from noisy vibration signals for fault diagnosis of a gearbox. However, the MED process is vulnerable to abrupt environmental and operational noise, as disturbance components can be extracted instead of fault-related features. To mitigate this issue, time-synchronous averaging (TSA) can be employed to reduce the remaining noise of the MED-filtered signal further. However, TSA requires accurately resampled vibration signals with the aid of an additional encoder system, which could be unavailable in the actual field. Although a typical phase estimation method can be employed, the phase estimation accuracy cannot be precise enough for TSA. In addition, TSA cannot fundamentally recover the fault-related features if the conventional MED filter is undesirably optimized to extract a single dominant impulse feature while eliminating fault-related features. To overcome these challenges, this paper proposes the novel use of D norms for TSA (DTSA). It was found in this paper that D norms, which encapsulate results from multiple MED filters, are amplified at every fault position with margins equal to the length of the MED filter, enabling Dnorm-based TSA (DTSA) by alleviating the slight phase error from vibration signals under an encoder-less condition. In addition, D norms contain all of the fault-related features from the measured signal and thus prevent undesirable eliminations of fault-related features as opposed to the conventional MED process. It was found in this paper that case studies involving an analytic simulation and a 2-kW planetary gearbox testbed indicate that the proposed method outperforms the conventional MED process under a slightly varying speed condition even without an encoder.

Partial Fourier reconstruction of complex MR images using complex-valued convolutional neural networks.

To provide a complex-valued deep learning approach for partial Fourier (PF) reconstruction of complex MR images. Conventional PF reconstruction methods, such as projection onto convex sets (POCS), uses low-resolution image phase information from the central symmetrically sampled k-space for image reconstruction. However, this smooth phase constraint undermines the phase estimation accuracy in presence of rapid local phase variations, causing image artifacts and limiting the extent of PF reconstruction. Using both magnitude and phase characteristics in big complex image datasets, we propose a complex-valued deep learning approach with an unrolled network architecture for PF reconstruction that iteratively reconstructs PF sampled data and enforces data consistency. We evaluate our approach for reconstructing both spin-echo and gradient-echo data. The proposed method outperformed the iterative POCS PF reconstruction method. It produced better artifact suppression and recovery of both image magnitude and phase details in presence of local phase changes. No noise amplification was observed even for highly PF reconstruction. Moreover, the network trained on axial brain data could reconstruct sagittal and coronal brain and knee data. This method could be extended to 2D PF reconstruction and joint multi-slice PF reconstruction. Our proposed method can effectively reconstruct MR data even at low PF fractions, yielding high-fidelity magnitude and phase images. It presents a valuable alternative to conventional PF reconstruction, especially for phase-sensitive 2D or 3D MRI applications.

Design of Sparse Multiband Signal for Precise Positioning With Joint Low-Complexity Time Delay and Carrier Phase Estimation

This paper presents a methodology to design a sparse multiband ranging signal with a large virtual bandwidth, from which time delay and carrier phase are estimated by a low complexity multivariate maximum likelihood (ML) method. In the estimation model for a multipath channel, not all reflected paths are considered, and time delay and carrier phase are estimated in a step-wise manner to further reduce the computational load. By introducing a measure of dependence and a measure of bias for a multipath reflection, we analyse the bias, precision and accuracy of time delay and carrier phase estimation. Since these two indicators are determined by the signal spectrum pattern, they are used to formulate an optimization for signal design. By solving the optimization problem, only a few bands from the available signal spectrum are selected for ranging. Consequently, the designed signal only occupies a small amount of signal spectrum but has a large virtual bandwidth and can thereby still offer a high ranging precision with only a small bias, based on the low-complexity simplified ML method. Numerical and laboratory experiments are carried out to evaluate the ranging performance of the proposed estimation method based on sparsely selected signal bands. Relative positioning, in which we only measure a change in position, based on either the time delay estimates or the carrier phase estimates, is presented as a proof-of-concept for precise positioning. The results show that positioning based on only 7 out of 16 signal bands, sparsely placed in the available spectrum, achieves a decimeter level accuracy when using time delay estimates, and a millimeter level accuracy when using carrier phase estimates. Compared with the case of using all available bands, and without largely decreasing the positioning performance, the computational complexity when using the sparse multiband signal can be reduced by about 80%.

An improved Quasi-Type-1 PLL based on paralleled filtering stage

In three-phase grid synchronization applications, the performance of traditional phase-locked loops will decrease under non-ideal grid voltage conditions. In order to solve the above problem, moving average filters (MAF) has been widely studied and utilized in PLLs in recently published papers with the expense of slower transient speed. This paper proposes a paralleled filtering stage to improve the dynamic performance of PLL. The suggested filter with smaller time delay is based on MAF and delay signal cancellation (DSC) operator, which is integrated in quasi-type-1 structure based PLL (QT1-PLL). Compared with differential MAF-PLL (DMAF-PLL) and QT1-PLL, the proposed filter can obtain a faster transient response without degrading phase estimation accuracy. The experimental results demonstrate that the proposed method can provide satisfactory performance.

Control of transformerless T-type DVR using multiple delayed signal cancellation PLL under unbalanced and distorted grid condition

In the near future, the power system network may experience severe voltage distortions due to association of renewable energy sources (RES), and the large penetration of power electronic based loads into the microgrid. To protect sensitive loads from these distorted and unbalanced grid conditions, the commonly used dynamic voltage restorer (DVR) requires effective control algorithms. The effective control algorithm comprises a controller, and accurate estimation of grid phase angle/frequency, and magnitude, thereby the reference DVR voltage is accurately estimated. The synchronous reference frame based phased locked loop (SRF-PLL) is commonly used for phase angle estimation. However, during unbalanced, distorted, and dc-offset conditions, the performance of SRF-PLL is unsatisfactory. To improve its performance, it is cascaded with prefilters such as dual second order generalized integrator (DSOGI), cascaded delayed signal cancellation (CDSC), and multiple delayed signal cancellation (MDSC). Among these prefilters, MDSC has superior performance under all grid conditions with less delay time and memory requirement. In addition to an effective control algorithm, the DVR system requires high power density converters. The power density of the system is increased using transformerless T-type converter. In this paper, the effectiveness of MDSC-PLL for the transformerless T-type converter based DVR is evaluated in MATLAB/Simulink for various grid conditions such as voltage sag/swell, unbalance voltage sag/swell, harmonics, and dc-offset.

Machine learning aided carrier recovery in continuous-variable quantum key distribution

The secret key rate of a continuous-variable quantum key distribution (CV-QKD) system is limited by excess noise. A key issue typical to all modern CV-QKD systems implemented with a reference or pilot signal and an independent local oscillator is controlling the excess noise generated from the frequency and phase noise accrued by the transmitter and receiver. Therefore accurate phase estimation and compensation, so-called carrier recovery, is a critical subsystem of CV-QKD. Here, we explore the implementation of a machine learning framework based on Bayesian inference, namely an unscented Kalman filter (UKF), for estimation of phase noise and compare it to a standard reference method and a previously demonstrated machine learning method. Experimental results obtained over a 20-km fibre-optic link indicate that the UKF can ensure very low excess noise even at low pilot powers. The measurements exhibited low variance and high stability in excess noise over a wide range of pilot signal to noise ratios. This may enable CV-QKD systems with low hardware implementation complexity which can seamlessly work on diverse transmission lines.

Coherent compensation and high‐resolution technology of multi‐band inverse synthetic aperture radar fusion imaging

Multi-band inverse synthetic aperture radar (ISAR) fusion imaging technology can effectively improve the range resolution without incurring high hardware cost. The coherent phase between sub-bands is a prerequisite to achieve multi-band ISAR fusion imaging. Here, a joint approach of coherent compensation and high-resolution imaging is proposed to compensate the incoherent phase and obtain high-resolution ISAR fusion images. First, an incoherent phase estimation model based on sparse representation is established, and the phase estimation accuracy is improved by a modified coherent dictionary in case of off-grid. Then, a multi-band ISAR fusion imaging model based on sparse representation is established. The complex Gaussian scale mixture priors and the complex Gaussian priors are imposed on the scatterers and noise, respectively. The solution is derived in the complex domain based on the variational Bayesian expectation maximization framework. The proposed method can not only achieve better incoherent phase compensation in the case of off-grid, but also obtain high-quality ISAR fusion images under low signal-to-noise ratio and low bandwidth sampling ratio. Experimental results verify the effectiveness and robustness of the proposed method based on both numerical simulations and real data.

Continuous Gait Phase Estimation Using LSTM for Robotic Transfemoral Prosthesis Across Walking Speeds.

User gait phase estimation plays a key role for the seamless control of the lower-limb robotic assistive devices (e.g., exoskeletons or prostheses) during ambulation. To achieve this, several studies have attempted to estimate the gait phase using a thigh or shank angle. However, their estimation resulted in some deviation from the actual walking and varied across the walking speeds. In this study, we investigated the different setups using for the machine learning approach to obtain more accurate and consistent gait phase estimation for the robotic transfemoral prosthesis over different walking speeds. Considering the transfemoral prosthetic application, we proposed two different sensor setups: i) the angular positions and velocities of both thigh and torso (S1) and ii) the angular positions and velocities of both thigh and torso, and heel force data (S2). The proposed setups and method are experimentally evaluated with three healthy young subjects at four different walking speeds: 0.5, 1.0, 1.5, and 2.0 m/s. Both results showed robust and accurate gait phase estimation with respect to the ground truth (loss value of S1: 4.54e-03 Vs. S2: 4.70e-03). S1 had the advantage of a simple equipment setup using only two IMUs, while S2 had the advantage of estimating more accurate heel-strikes than S1 by using additional heel force data. The choice between the two sensor setups can depend on the researchers' preference in consideration of the device setup or the focus of the interest.

PhaseDCN: A Phase-Enhanced Dual-Path Dilated Convolutional Network for Single-Channel Speech Enhancement

Recent deep neural network (DNN) based single-channel speech enhancement methods have achieved remarkable results in the time-frequency (TF) magnitude domain. To further improve the quality and intelligibility of enhanced speech, the attention to phase enhancement is also increasing. In this paper, we propose a novel dilated convolutional network (DCN) model to simultaneously enhance the magnitude and phase of noisy speech. Unlike the direct complex spectral mapping methods, we take the complex spectrum of the signal as the main target and the ideal ratio mask (IRM) as the auxiliary target in a multi-target learning framework to achieve their complementary advantages. Firstly, a feature extraction module is introduced to achieve the fusion of local and long-term features. Two different targets are learned separately, but share the common feature extraction module, which is helpful to extract more general and suitable features. During the joint learning, the intermediate estimation of the IRM target in the auxiliary path, contributing as the attention gating factors, helps to distinguish the speech or non-speech components of the complex-valued signals in the main path. To leverage more fine-grained long-term contextual information, we introduce a multi-scale dilated convolution approach for feature encoding. Moreover, the proposed model is a causal system, which can fully meet the low latency requirements of real-time speech products. Experimental results show that, compared with other advanced systems, the proposed model not only has better speech denoising performance and phase estimation accuracy, but also generalizes better in the speaker, noise, and channel mismatch cases.

A Two-Step Stochastic Hybrid Estimation for GNSS Carrier Phase Tracking in Urban Environments

This article presents a two-step stochastic hybrid estimation (TS-SHE) algorithm for robust and accurate carrier phase tracking of global navigation satellite system (GNSS) signals in urban environments with significant power degradation and fluctuation. The proposed algorithm adaptively combines a bank of parallel Kalman filters (KFs) with different dynamic state models to cope with the nonstationarity of GNSS signals. Different from conventional approaches, including the phase lock loop (PLL), the KF, and the interacting multiple-model (IMM) method, which strongly rely on the a priori fixed signal model to ensure good tracking performance, we develop a novel stochastic filter transition strategy utilizing the information from reliable signal condition evaluation to overcome the performance degradation caused by the model mismatch in urban environments. Therein, for the first time, we use the prior information of signal fading conditions for more accurate combined weighting of all component filters. Specifically, to obtain the prior information, GNSS data are sequentially buffered and analyzed in the first step. Then, in the second step, optimized filter weights are generated, and the overall combined carrier phase is estimated. We analyze the theoretical performance of the new algorithm and show the effects of different design parameters on the performance. The primary advantages of the proposed algorithm include: 1) the ability to rapidly recover carrier phase observation when blocked signals are reacquired and 2) high accuracy in carrier phase estimation of GNSS signals corrupted by strong multipath fading. Simulation and real data experiment results show the enhanced robustness and improved accuracy of the proposed TS-SHE algorithm compared with conventional carrier phase tracking methods.

Parameter estimation and signal detection algorithm based on adaptive capture in non-cooperative communication

Aiming at the problem that the frequency offset in the non-cooperative communication system causes the received signal spectrum to shift, which exceeds the passband of the matched filter and affects the subsequent demodulation, a parameter estimation and signal detection algorithm based on adaptive capture is proposed by this paper, which is more convenient for hardware implementation and consumes less resources. The algorithm is divided into three parts. Firstly, use the correlation value between the signal and the preamble sequence as the basis for frequency capture. Secondly, the frequency is accurately estimated based on the interpolation algorithm. Finally, the phase-locked loop structure is used to track the frequency according to the characteristics of the frequency gradually changing and the signal frequency offset is eliminated in the Digital Down Converter stage. It provides necessary conditions for accurate signal detection and phase estimation. The simulation results show that the algorithm has high estimation accuracy, wide esti-mation range and low complexity. It can also achieve better estimation accuracy and detection performance under low signal-to-noise ratio.

Accurate determination of random pattern phase in structured illumination microscopy with low modulation depth

The initial phase of structured illumination is an important parameter in structured illumination microscopy (SIM). Its estimation accuracy directly affects the reconstruction quality of SIM super-resolution images. However, when the modulation of the system is less than 0.02, the current phase estimation algorithm will cause an estimation error above 0.2 rad. An algorithm based on multi-image correlation processing in frequency domain (MCF) is proposed to solve this problem. Simulation and experimental results show that the MCF algorithm greatly improves both the initial phase estimation accuracy and the reconstruction quality of super-resolution images for low modulation SIM systems with a random phase shift. This means that the MCF algorithm can extend the scope of the SIM technology, especially for low modulation systems or systems lacking precise phase-shifting components.

Repeat-Pass Interferometric Speckle

The Gaussian speckle model for homogeneously distributed targets is commonly assumed to apply in repeat-pass radar interferometric analyses, for instance, in deformation estimation. This is despite widespread evidence from snapshot intensity observations indicating deviations from Gaussianity, as many natural land surfaces are intrinsically heterogeneous. The concern is that neglecting heterogeneity will deteriorate the phase estimates and induce underestimation of the uncertainty. Here, we introduce and theoretically characterize compound models that extend the Gaussian speckle model for repeat-pass stacks by representing heterogeneity in intensity and phase. In two L-band repeat-pass data sets, we find pervasive deviations from Gaussianity. Our estimates suggest that the heterogeneity in intensity is largely due to time-invariant, rather than dynamic, texture. Deviations from Gaussianity associated with phase heterogeneity are generally less pronounced. One notable exception with large estimated phase heterogeneity occurs over a permafrost wetland, where degrading ice wedges induce subsidence that is variable on the resolution scale. For deformation analyses, accounting for heterogeneity has, on average, a moderate impact on the phase estimates and the estimated phase uncertainty, which increases by 10% on average. However, in intrinsically heterogeneous areas, such as the permafrost wetland, the accuracy of the phase estimate can realistically improve by up to 20%, and the predicted phase uncertainty increases by 30%. The improvements in phase estimation accuracy and in the quality of the uncertainty estimates when accounting for heterogeneous speckle can, on occasion, make a notable difference for subtle or small-scale deformation.

Fault signature enhancement and skidding evaluation of rolling bearing based on estimating the phase of the impulse envelope signal

Rolling bearing skidding can seriously affect the service life and aggravate the performance degradation process of rolling bearings. Once skidding occurs under variable speed and load, the movement of rolling elements relative to the inner and outer rings is no longer strictly pure rolling. As a result, the speed of rolling bearing cage becomes more complex. In this case, fault signature extraction tends to be more difficult, especially under the condition of variable speed. Although order tracking can solve the problem induced by variable speed to a certain extent, order deviation and vagueness question in envelope order spectra caused by skidding still needs to be further explored. In view of this, an order tracking method based on accurate estimation of impulse envelope phase is proposed. This method can restore the non-periodic impulses caused by skidding to the periodic ones so as to enhance the fault signatures. Besides, the method is capable of evaluating the severity of skidding of rolling bearings by calculating skidding rate, which will be useful for evaluation of bearing performance degradation. Finally, the proposed method is validated by simulation signal and real data of faulty rolling bearings. The results show that the proposed method is efficient to enhance the fault signature and evaluate the skidding rate simultaneously.

Sampling frequency offset compensation in non-Hermitian symmetric optical OFDM

Non-Hermitian symmetric optical orthogonal frequency-division multiplexing (NHS-OFDM) can make the best use of fast Fourier transform (FFT) functions. Hence, hardware implementation of NHS-OFDM has a low complexity when maintaining the same bandwidth granularity. And the similar peak-to-average power ratio (PAPR) and bit error rate (BER) performances can be obtained in comparison with the conventional Hermitian symmetric optical orthogonal frequency-division multiplexing (HS-OFDM). However, the sampling clock frequency offset (SFO) between digital-to-analog converters (DAC) and analog-to-digital converters (ADC) always exists in asynchronous HS/NHS-OFDM systems. It will degrade BER performance seriously without compensation. In this paper, the mechanism of SFO in NHS-OFDM is analyzed and discussed. The inter-symbol differential detection (ISDD) with residual phase compensation (RPC) is applied for SFO compensation (SFOC) in the NHS-OFDM system. Moreover, enhanced residual phase estimation (ERPE) is also proposed to improve the tracking speed and accuracy of residual phase estimation. The optimal FFT size for NHS-OFDM is first identified in both additive white Gaussian noise (AWGN) channel and a 20-km standard single-mode fiber (SSMF) link. The BER performance of the ISDD with RPC/enhanced RPC (ERPC) enabled HS/NHS-OFDM is investigated by means of both numerical simulation and offline experiments. With the help of the ISDD with RPC/ERPC methods, the SFO can be compensated. Also, a slight improvement in BER performance can be achieved with the ERPC method compared to the RPC method. And the BER performance penalties can be ignored in the presence of SFO up to 200 ppm.

Quantum Enhanced Optical Phase Estimation With a Squeezed Thermal State

Quantum phase-estimation protocols can provide a measuring method of phase shift with precision superior to the standard quantum limit (SQL) due to the application of a nonclassical state of light. A squeezed vacuum state, whose variance in one quadrature is lower than the corresponding SQL, has been pointed out as a sensitive resource for quantum phase estimation and the estimation accuracy is directly influenced by the properties of the squeezed state. Here we analyze in detail the influence of the purity and squeezing level of the squeezed state on the accuracy of quantum phase estimation. The maximum precision that can be achieved for a squeezed thermal state is evaluated, and the experimental results are in agreement with the theoretical analyses. It is also found that the width of the phase-estimation interval $\mathrm{\ensuremath{\Delta}}\ensuremath{\theta}$ beyond SQL is correlated with the purity of the squeezed state.

A Stable Adaptive Gradient Descent Harmonic-Disturbance Rejection for Improving Phase-Tracking Accuracy

This paper proposes a stable adaptive gradient descent for harmonic-disturbance rejection as a tool for grid-power signal processing, magnetic rotary encoders, and permanent-magnet synchronous motors. The method can be widely applied to increase the accuracy of phase or position estimation in various systems in which harmonic disturbances exist. The proposed technique is based on learning the harmonic amplitudes by means of gradient descent on the feedback phase error. To compensate for the disadvantages of existing gradient-descent methods, the derivative expansion is fully developed with system transfer function integration for stable weighting update. In addition, an adaptive learning rate is also proposed based on discrete Lyapunov standard to achieve stability, and theoretical analysis is discussed. The performance of the method is evaluated by numerical simulation in MATLAB with various scenarios, and by the experiment with the rotary magnetic encoders. The results show that the proposed method achieves stability and high performance in harmonic rejection.

Error Compensation Algorithm for SRF-PLL in Three-Phase Grid-Connected Converters

This paper proposes an error compensation algorithm based on synchronous reference frame phase-locked loop for accurate phase estimation of the distorted three-phase voltages including asymmetrical phase voltages, harmonics, and dc offset. These errors cause undesirable periodic ripples with grid frequency in the traditional PLL and significantly degrade the overall performance of the grid-connected converters. In this paper, the effects of the errors are comprehensively analyzed in the stationary and synchronous reference frames. In particular, the errors are estimated and compensated by controlling the $\alpha $ -axis and $\beta $ -axis components in a PLL to be balanced. The proposed compensation algorithm can be implemented by some integral operations followed by simple Integral-controllers. The performance and robustness of proposed compensation technique are investigated under distorted grid conditions. The proposed technique is numerically and experimentally verified using Matlab/Simulink and Dspace1202 control board platform.

Three-Phase PLL for Grid-Connected Power Converters Under Both Amplitude and Phase Unbalanced Conditions

This paper proposes a technique for accurate phase estimation of distorted three-phase grid voltages including unbalanced amplitudes and/or phase angles. An adaptive cascaded delayed signal cancellation (CDSC) strategy is used for the generation of the amplitude balanced three-phase voltages. The CDSC strategy also eliminates both odd and even harmonics from the input voltage. An algorithm is also reported for removing the phase angle deviations from the three-phase voltages including unbalanced phase angles. Finally, a phase-locked loop (PLL) is applied to estimate the phase angle of the reference phase voltage. It requires only one PLL to estimate three phase angles of the thee-phase voltages, respectively, suffering from the unbalanced amplitudes and phase angles. It is also immune to harmonic distortions at changeable frequency environment. When compared to the CDSC-PLL and dqCDSC-PLL techniques reported in the technical literature, it can provide improved phase estimation under amplitude and phase unbalanced condition. Simulated and experimental results of the technique are acquired from the MATLAB/Simulink and dSPACE1104 control board platform, respectively, for a number of case studies observed in the grid voltage.