Accurate Phase Estimation Research Articles

Iterative phase-shifting algorithm immune to random phase shifts and tilts

An iterative phase-shifting algorithm based on the least-squares principle is developed to overcome the random piston and tilt wavefront errors generated from the phase shifter. The algorithm iteratively calculates the phase distribution and the phase-shifting map to minimize the sum of squared errors in the interferograms. The performance of the algorithm is evaluated via computer simulations and validated by the Fizeau interferometer measurements. The results show that the proposed algorithm has a fast convergence rate and satisfactory phase-estimation accuracy, improving the measurement precision of the phase-shifting interferometers with significant phase-shifter errors.

Some Sampling Properties of Common Phase Estimators

The instantaneous phase of neural rhythms is important to many neuroscience-related studies. In this letter, we show that the statistical sampling properties of three instantaneous phase estimators commonly employed to analyze neuroscience data share common features, allowing an analytical investigation into their behavior. These three phase estimators-the Hilbert, complex Morlet, and discrete Fourier transform-are each shown to maximize the likelihood of the data, assuming the observation of different neural signals. This connection, explored with the use of a geometric argument, is used to describe the bias and variance properties of each of the phase estimators, their temporal dependence, and the effect of model misspecification. This analysis suggests how prior knowledge about a rhythmic signal can be used to improve the accuracy of phase estimates.

Performance analysis of code-aided iterative carrier phase recovery in turbo receivers

Code-aided (CA) iterative carrier phase synchroniser can greatly improve the accuracy of phase estimation in turbo receivers. However, because of the iteration involved between phase recovery and decoding, most existing studies depend on extensive simulations rather than on theoretical analysis to evaluate the performance improvement of phase recovery by exploiting the coding constraints. In this study, the authors propose analytical methods to fill this void. The first step is to approximate the cross-talks caused by phase offset as Gaussian noise at low signal-to-noise ratios. Then, a semi-analytical method is proposed to express the distribution of extrinsic information from channel decoder as a function of phase offset. Building on this model, both the open-loop and closed-loop performances of CA iterative phase synchronisers are derived in closed-form. The analytical results explicitly reveal how extrinsic information contributes to the performance of carrier phase estimation. Monte Carlo simulation results corroborate that the proposed methods are able to accurately characterise the performance of CA iterative carrier phase recovery for systems with different channel codes.

Optimal Heisenberg-style bounds for the average performance of arbitrary phase estimates

The ultimate bound to the accuracy of phase estimates is often assumed to be given by the Heisenberg limit. Recent work seemed to indicate that this bound can be violated, yielding measurements with much higher accuracy than was previously expected. The Heisenberg limit can be restored as a rigorous bound to the accuracy provided one considers the accuracy averaged over the possible values of the unknown phase, as we have recently shown [Phys. Rev. A 85, 041802(R) (2012)]. Here we present an expanded proof of this result together with a number of additional results, including the proof of a previously conjectured stronger bound in the asymptotic limit. Other measures of the accuracy are examined, as well as other restrictions on the generator of the phase shifts. We provide expanded numerical results for the minimum error and asymptotic expansions. The significance of the results claiming violation of the Heisenberg limit is assessed, followed by a detailed discussion of the limitations of the Cramer-Rao bound.

An advanced algorithm for deformation estimation in non-urban areas

This paper presents an advanced differential SAR interferometry stacking algorithm for high resolution deformation monitoring in non-urban areas with a focus on distributed scatterers (DSs). Techniques such as the Small Baseline Subset Algorithm (SBAS) have been proposed for processing DSs. SBAS makes use of small baseline differential interferogram subsets. Singular value decomposition (SVD), i.e. L2 norm minimization is applied to link independent subsets separated by large baselines. However, the interferograms used in SBAS are multilooked using a rectangular window to reduce phase noise caused for instance by temporal decorrelation, resulting in a loss of resolution and the superposition of topography and deformation signals from different objects. Moreover, these have to be individually phase unwrapped and this can be especially difficult in natural terrains. An improved deformation estimation technique is presented here which exploits high resolution SAR data and is suitable for rural areas. The implemented method makes use of small baseline differential interferograms and incorporates an object adaptive spatial phase filtering and residual topography removal for an accurate phase and coherence estimation, while preserving the high resolution provided by modern satellites. This is followed by retrieval of deformation via the SBAS approach, wherein, the phase inversion is performed using an L1 norm minimization which is more robust to the typical phase unwrapping errors encountered in non-urban areas. Meter resolution TerraSAR-X data of an underground gas storage reservoir in Germany is used for demonstrating the effectiveness of this newly developed technique in rural areas.

Full-field stress analysis by holographic phase-stepping implementation of the photoelastic-coating method

In this paper, we describe a system for polariscopic and holographic phase-shifting implementation of the photoelastic-coating method for a full-field stress analysis. The easiest way to build the combined system is to employ a laser light source. However, coherent illumination introduces a signal-dependent speckle noise which worsens the accurate phase estimation and unwrapping. To answer the question of how it affects the phase retrieval of isochromatics, isoclinics and isopachics, we modeled in the present paper the phase-shifting photoelastic measurement in the presence of speckle noise through the calculation of the complex amplitudes in a Mach–Zender interferometer combined with a circular polariscope and made denoising of simulated and experimental fringe patterns. The latter were recorded at pure tensile load for PhotoStress®-coated samples with a mechanical stress concentrator.

The Poisson Distribution Is Applied to Improve the Estimation of Individual Cell and Micropopulation Lag Phases

Many articles dealing with individual cell lag phase determination assume that growth, when observed, comes from one cell. This assumption is not in agreement with the Poisson distribution, which uses the probability of growth in a sample to predict how many samples contain one, two, or some other number of cells. This article analyses and compares different approaches to improve the accuracy of lag phase estimation of individual cells and micropopulations. It argues that if the highest initial load, as predicted by the Poisson distribution, is assigned to the sample with the shortest lag phase, the second highest to the sample with the second shortest lag phase and so on, the resulting lag phase distributions would be more accurate. This study also proposes the use of a robust test, permutation test, to compare lag phase distributions obtained in different situations.

SNR-Aided Accurate Phase Estimation in 1-Bit Software-Defined Receiver

This work investigates the high-accuracy phase discriminator in 1-bit software-defined receiver (SDR) for three signal-to-noise ratio (SNR) ranges: low SNR, high SNR and moderate SNR. Unlike traditional approaches, our approach first distinguishes which SNR range an application falls into, and this SNR information is then utilized to select a proper phase discriminator to achieve high accuracy. For low-SNR applications, traditional arctangent phase discriminator (APD) is adopted and the analysis of asymptotic performance is derived. For high-SNR applications, the noise-balanced digital phase discriminator (NB-DPD) is adopted to improve accuracy [1]. Between them, for moderate-SNR applications, a novel SNR-aided phase discriminator (SNRaPD) is proposed. The analytical and simulation results verify the superiority of the proposed approach for applications in different SNR ranges. The determination of moderate SNR range is critical and discussed finally.

The use of phase in complex spectrum subtraction for robust speech recognition

Abstract In this paper we propose a new method for utilising phase information by complementing it with traditional magnitude-only spectral subtraction speech enhancement through complex spectrum subtraction (CSS). The proposed approach has the following advantages over traditional magnitude-only spectral subtraction: (a) it introduces complementary information to the enhancement algorithm; (b) it reduces the total number of algorithmic parameters; and (c) is designed for improving clean speech magnitude spectra and is therefore suitable for both automatic speech recognition (ASR) and speech perception applications. Oracle-based ASR experiments verify this approach, showing an average of 20% relative word accuracy improvements when accurate estimates of the phase spectrum are available. Based on sinusoidal analysis and assuming stationarity between observations (which is shown to be better approximated as the frame rate is increased), this paper also proposes a novel method for acquiring the phase information called Phase Estimation via Delay Projection (PEDEP). Further oracle ASR experiments validate the potential for the proposed PEDEP technique in ideal conditions. Realistic implementation of CSS with PEDEP shows performance comparable to state of the art spectral subtraction techniques in a range of 15–20 dB signal-to-noise ratio environments. These results clearly demonstrate the potential for using phase spectra in spectral subtractive enhancement applications, and at the same time highlight the need for deriving more accurate phase estimates in a wider range of noise conditions.

Investigation to realize a computationally efficient implementation of the high-order instantaneous-moments-based fringe analysis method

Recently, a high-order instantaneous moments (HIM)-operator-based method was proposed for accurate phase estimation in digital holographic interferometry. The method relies on piece-wise polynomial approximation of phase and subsequent evaluation of the polynomial coefficients from the HIM operator using single-tone frequency estimation. The work presents a comparative analysis of the performance of different single-tone frequency estimation techniques, like Fourier transform followed by optimization, estimation of signal parameters by rotational invariance technique (ESPRIT), multiple signal classification (MUSIC), and iterative frequency estimation by interpolation on Fourier coefficients (IFEIF) in HIM-operator-based methods for phase estimation. Simulation and experimental results demonstrate the potential of the IFEIF technique with respect to computational efficiency and estimation accuracy.

Bayesian phase tracking for multiple pulse signals

The problem of estimating the frequencies and phases of two superimposed pulse-like, repetitive signals is considered. A method of solving this problem based on Bayesian (i.e., sequential Monte-Carlo or particle) filtering is presented. The particular problem motivating the technique is estimation of the rate of maternal and foetal heartbeats, although the technique is applicable to other domains. Aspects of the problem leading to the solution are discussed, and the performance of the proposed technique is presented on both simulated signals and real heart signals. The resulting frequency estimator has very similar functionality to a phase-locked loop, and so the performance measure used is the time to lose phase lock. The estimator is also analysed in terms of the posterior Cramér–Rao bound on the phase estimation accuracy.

Improved high-order ambiguity-function method for the estimation of phase from interferometric fringes

Interferometers often encode the information on the measurand in the phase of a fringe pattern, which is usually recorded by an imaging device. Accuracy of measurements carried out by interferometric techniques is thus strongly dependent on the accuracy with which the underlying phase distribution of these fringe patterns is estimated. Fringe analysis methods, which have been developed to accomplish this task, are in general characterized by their performance in terms of both accuracy of phase estimation and associated computational complexity. We propose an improved high-order ambiguity-function-based fringe-analysis method that is demonstrated to provide an accurate and direct estimation of the unwrapped phase distribution in a highly computationally efficient manner. Presented simulation and experimental results in digital holographic interferometry depict the potential utility of the proposed method.

Piecewise polynomial phase approximation approach for the analysis of reconstructed interference fields in digital holographic interferometry

This paper proposes a new approach for the analysis of reconstructed interference fields in digital holographic interferometry. In the proposed approach the interference phase to be estimated is conceived as a piecewise polynomial signal; consequently, each segment of the reconstructed interference field is modeled as a polynomial phase signal (PPS) with constant or slowly varying amplitude. The unwrapped phase distribution is then directly computed using the maximum likelihood estimation. Salient features of the proposed approach are: it provides accurate phase estimation from a single record of the interference field; it avoids cumbersome and error-prone filtering and 2D unwrapping procedures; and it paves the way to adapt well-established PPS analysis tools available in signal processing literature for the phase estimation in holographic interferometry.

永久磁石同期モータセンサレス駆動のための高次応速帯域フィルタ形位相推定法

This paper proposes a new rotor phase estimation method for sensorless drive of permanent-magnet synchronous motors (PMSMs), which uses motor-driving stator voltage and current information for estimation. The proposed estimation method utilizes two high order low-pass filters that can change their bandwidth according to speed estimate. The high order filters have a potential to attenuate sufficiently harmonics contaminating the stator voltage and current and to produce almost-pure-sinusoidal rotor flux estimate consisting of fundamental component only. Such a sinusoidal rotor flux estimate allows high accurate estimation of rotor phase even at very low speed. In order to separate the fundamental component of the rotor flux estimate from its harmonics with no phase lag/lead in variable-speed environments, the proposed low-pass filters have a function to change its bandwidth adaptively to rotor speed. The sensorless drive system using the proposed phase estimation method can show such high performance that 1) it can startup PMSMs from standstill under the rated load; 2) it can drive PMSMs stably even at very low speed such as 1/60 of the rated speed under the rated motoring/regenerating load; 3) it can drive PMSMs accompanied with a load of over 50 times large inertia. The proposed estimation method is simple and easily installed into sensorless drive systems. This paper presents the new estimation method in detail and show how it is installed into the drive systems by using a concrete example. The usefulness of the method and the performance of the drive system are examined and confirmed through extensive experiments.

Harmonic pulsed excitation and motion detection of a vibrating reflective target

Elasticity imaging is an emerging medical imaging modality. Methods involving acoustic radiation force excitation and pulse-echo ultrasound motion detection have been investigated to assess the mechanical response of tissue. In this work new methods for dynamic radiation force excitation and motion detection are presented. The theory and model for harmonic motion detection of a vibrating reflective target are presented. The model incorporates processing of radio frequency data acquired using pulse-echo ultrasound to measure harmonic motion with amplitudes ranging from 100 to 10,000 nm. A numerical study was performed to assess the effects of different parameters on the accuracy and precision of displacement amplitude and phase estimation and showed how estimation errors could be minimized. Harmonic pulsed excitation is introduced as a multifrequency radiation force excitation method that utilizes ultrasound tonebursts repeated at a rate f(r). The radiation force, consisting of frequency components at multiples of f(r), is generated using 3.0 MHz ultrasound, and motion detection is performed simultaneously with 9.0 MHz pulse-echo ultrasound. A parameterized experimental analysis showed that displacement can be measured with small errors for motion with amplitudes as low as 100 nm. The parameterized numerical and experimental analyses provide insight into how to optimize acquisition parameters to minimize measurement errors.

Analysis of misequalization in a narrowband active noise equalizer system

This paper presents the misequalization phenomenon in a narrowband active noise equalizer (ANE) system. The origin and characteristics of such phenomenon are investigated. Analysis shows that the estimation error of secondary path transfer function introduces this undesired phenomenon. Relationship between the estimation error and misequalization is also examined. It can be concluded that, for different gain factor values, importance of phase and amplitude estimation accuracy is different. Simulations based on both theoretical calculation and experiments are conducted to support the analysis.

Effect of Coarse Surface Layer on Bed-Load Transport

Existing bed-load transport formulas may overestimate the transport rate in mountain rivers by two orders of magnitude or more. Recently published field data sets provide an opportunity to take a fresh look at the bed-load transport relationship and it is hypothesized that the overestimate is due to a failure to account for the effect of a coarse surface layer of bed material inhibiting the release of fine subsurface material. Bed-load transport is determined as gs=aρ(q−qc) where q=water discharge per unit width; qc=critical value for initiation of bed material movement; ρ=water density; and a=coefficient. The gs∕q relationship is typically piecewise linear, characterized by two transport phases with, respectively, low and high rates of change. Twenty-one flume and 25 field data sets were used to quantify the relationship for Phase 2. The flume data confirm the dependence of a on S1.5, where S=channel slope, in agreement with earlier studies. The field data additionally show that a varies inversely with the degree of bed armoring, given by the ratio of surface to subsurface bed material size. The finding is consistent with the hypothesis and suggests the need to account for the bed material supply limitation in the bed-load transport formula. However, the available data are not entirely sufficient to rule out an alternative dependency, or codependency, on flow resistance. The critical conditions for initiation of Phase 2 transport are also quantified as a function of bed material size and channel slope. The resulting set of equations allows a more accurate estimation of Phase 2 bed-load transport rates. However, the equations are empirical and should be restricted for use within the range of conditions used in their development, to determine mean rather than instantaneous transport rates and to determine bulk transport rates, not transport by size fraction.

Speckle interferometry for measurement of continuous deformations

Improvements of a method for measurement of continuous displacements and deformations with digital phase shifting speckle pattern interferometry are presented. The method is based on an algorithm that, with the knowledge of the initial phase, only needs one image at a time to evaluate continuos phase changes due to object deformations. In the improved method, the initial random phase of the speckle pattern is evaluated using a number of phase-shifted images before the deformation under study. This is used for increasing the accuracy of the initial phase estimation and reducing influences from image noise and other measurement disturbances. The phase-shifted speckle patterns are used as references for comparison with the speckle patterns of the deformed object, thereby increasing the reliability and accuracy of the phase estimations of the deformed patterns. The technique can be used for measuring deformations such as transients and other dynamic events, heat expansion as well as other phenomena where it is difficult to accomplish phase shifting during deformation.

Iterative multiuser detection with integrated channel estimation for coded DS-CDMA

A practically interesting approach for iterative channel estimation, multiuser detection, and single-user decoding based on maximum a posteriori symbol-by-symbol estimation for direct sequence/code-division multiple-access (DS-CDMA) is proposed. The receiver relies on the output of a bank of matched filters for each user and each path, and combines interference cancellation with iterated soft-decision feedback to improve channel estimation accuracy and data symbol reliability in course of a few iterations. We show that in this way, near single-user channel phase and amplitude estimation accuracy is achieved for frequency-selective fading channels, even in highly loaded systems, and illustrate that reliable data symbol estimation can be performed.

Error sources and algorithms for white-light fringe estimation at low light levels.

We address the problem of highly accurate phase estimation at low light levels, as required by the Space Interferometry Mission (SIM). The most stringent SIM requirement in this regard is that the average phase error over a 30-s integration time correspond to a path-length error of approximately 30 pm. Most conventional phase-estimation algorithms exhibit significant enough bias at the signal levels at which the SIM will be operating so that some correction is necessary. Several algorithms are analyzed, and methods of compensating for their bias are developed. Another source of error in phase estimation occurs because the phase is not constant over the integration period. Errors that are due to spacecraft motion, the motion of compensating optical elements, and modulation errors are analyzed and simulated. A Kalman smoothing approach for compensating for these errors is introduced.