Accurate Frequency Estimation Research Articles

A high precision signal processing method for laser Doppler velocimeter

Fast Fourier transform (FFT) is commonly adopted as the signal processing method of laser Doppler velocimeter (LDV) system to get Doppler frequency which is the key factor of the calculation of object velocity. However, precision of FFT is restricted by phenomena caused by asynchronous sampling, such as spectral interference, fence effect and spectrum leakage. Aiming at enhancing the precision of LDV signal processing, an algorithm based on the association of spectral refinement and interpolation is put forward. Zoom-FFT was utilized to refine the local range of Doppler frequency estimated by FFT. The refined spectrum was further corrected by Rife-Vincent (Ⅲ) window interpolation and got the accurate estimate of Doppler frequency. Cubic spline fitting was applied to calculate the interpolation coefficient of Rife-Vincent (Ⅲ) window without solving a quintic equation in the computing procedure of interpolation. For experimental signals, the minimum relative error of proposed method is 0.02%. And for simulated signals, the minimum relative error reaches only 0.0013%. The proposed method has capability to significantly improve the precision of signal processing and is applicable for a LDV system.

Efficient and Accurate Frequency Estimator under Low SNR by Phase Unwrapping

In the case of low signal-to-noise ratio, for the frequency estimation of single-frequency sinusoidal signals with additive white Gaussian noise, the phase unwrapping estimator usually performs poorly. In this paper, an efficient and accurate method is proposed to address this problem. Different from other methods, based on fast Fourier transform, the sampled signals are estimated with the variances approaching the Cramer-Rao bound, followed with the maximum likelihood estimation of the frequency. Experimental results reveal that our estimator has a better performance than other phase unwrapping estimators. Compared with the state-of-the-art method, our estimator has the same accuracy and lower computational complexity. Besides, our estimator does not have the estimation bias.

Robust frequency estimation of unbalanced power system using a phase angle error based least mean kurtosis algorithm

In this paper, an augmented (widely linear) complex Least Mean Kurtosis (WL-LMK) algorithm that uses the negated kurtosis of the phase angle error instead of the conventional magnitude error is proposed for robust frequency estimation of three-phase power systems. The motivation of the proposed method is based on two underlying facts. First, it is primarily the phase rather than the amplitude that conveys useful information in frequency estimation. Second, the negated kurtosis based cost function is computationally efficient and most celebrated in applications where the noise contamination degrades the performance of the classical adaptive filtering algorithms. To further achieve robust frequency estimation for both balanced and unbalanced conditions, the proposed method makes use of the full second-order information within the complex-valued system voltage through the Clarke’s αβ transformation and the concept of augmented complex statistics and widely linear modelling. The estimation performance of the proposed method is evaluated for several critical cases that often arise in power system. Simulation results of both synthetic cases and experimental studies show that the proposed method achieves more accurate frequency estimates than its developed widely linear counterparts in the literature.

Time-Frequency demodulation analysis via Vold-Kalman filter for wind turbine planetary gearbox fault diagnosis under nonstationary speeds

Abstract Wind turbine planetary gearbox fault diagnosis under nonstationary speeds is a challenging topic, because of the high complexity and strong time variability of vibration signals. In order to resolve time-varying gear fault features, a quality time-frequency analysis method is in demand. Time-frequency representations based on Hilbert transform and analytic signal approach have fine time-frequency resolution, and are free from both outer (cross-term) and inner (auto-term) interferences, thus providing an effective approach to nonstationary signal analysis. However, they rely on accurate instantaneous frequency estimation, and thereby are subject to mono-component constraint. To address this issue, Vold-Kalman filter is exploited to construct time-frequency representation, by virtue of its capability to decompose the multi-component vibration signal of rotating machinery into constituent mono-component harmonic waves. Even so, intricate time-varying sidebands inherent with raw planetary gearbox vibration signals in joint time-frequency domain are still a hurdle, because they do not link to gear fault frequency directly. To solve this problem, the proposed time-frequency analysis method is further extended to generate time-varying amplitude and frequency demodulated spectra, inspired by the fact that gear fault frequency is manifested straight by the amplitude and frequency modulating frequencies. The proposed method is illustrated by numerical simulation, and is further validated using lab experimental signals of a wind turbine planetary gearbox. Both the localized and distributed faults on gears are successfully diagnosed under nonstationary speeds.

A spectrum matching method for accurate frequency estimation of real sinusoids.

It is well-known that incoherent sampling is detrimental for frequency estimation of a real sinusoid, and the estimation errors get worse when the signal lengths are very short. In this paper, a spectrum matching based frequency estimator is proposed as well as evaluated against other four two-step methods developed to suppress the effect of incoherent sampling. The spectral interference introduced by incoherent sampling is eliminated via a spectrum matching process including modulation and spectral analysis. A further error correction based on Fourier transform is conducted to generate the fine frequency estimate. Simulation results are carried out to show that the proposed method can closely approach the Cramér-Rao lower bound without any error floor, and it can outperform the other four methods particularly for short signal lengths.

Extraction and Filter Algorithm of Roll Angular Rate for High Spinning Projectiles

The accurate measurement of roll angular rate for high spinning projectile has long been a challenging problem. Aiming to obtain the accurate roll angular rate of high spinning projectile, a novel extraction and filter algorithm, BSCZT-KF, is proposed in this paper. Firstly, a compound angular motion model of high spinning projectile is established. According to the model, we translate the roll angular rate measurement problem into a frequency estimation problem. Then the improved CZT algorithm, BSCZT, was employed to realize an accurate estimation of the narrowband signal frequency. Combined with the peak detection method, the BSCZT-KF algorithm is presented to further enhance the frequency estimation accuracy and the real-time performance. Finally, two sets of actual flight tests were conducted to verify the effectiveness and accuracy of the algorithm. The test results show that the average error of estimated roll angular rate is about 0.095% of the maximum of roll angular rate. Compared with the existing methods, the BSCZT-KF has the highest frequency estimation accuracy for narrowband signal.

Predicting Cell Populations in Single Cell Mass Cytometry Data.

Mass cytometry by time‐of‐flight (CyTOF) is a valuable technology for high‐dimensional analysis at the single cell level. Identification of different cell populations is an important task during the data analysis. Many clustering tools can perform this task, which is essential to identify “new” cell populations in explorative experiments. However, relying on clustering is laborious since it often involves manual annotation, which significantly limits the reproducibility of identifying cell‐populations across different samples. The latter is particularly important in studies comparing different conditions, for example in cohort studies. Learning cell populations from an annotated set of cells solves these problems. However, currently available methods for automatic cell population identification are either complex, dependent on prior biological knowledge about the populations during the learning process, or can only identify canonical cell populations. We propose to use a linear discriminant analysis (LDA) classifier to automatically identify cell populations in CyTOF data. LDA outperforms two state‐of‐the‐art algorithms on four benchmark datasets. Compared to more complex classifiers, LDA has substantial advantages with respect to the interpretable performance, reproducibility, and scalability to larger datasets with deeper annotations. We apply LDA to a dataset of ~3.5 million cells representing 57 cell populations in the Human Mucosal Immune System. LDA has high performance on abundant cell populations as well as the majority of rare cell populations, and provides accurate estimates of cell population frequencies. Further incorporating a rejection option, based on the estimated posterior probabilities, allows LDA to identify previously unknown (new) cell populations that were not encountered during training. Altogether, reproducible prediction of cell population compositions using LDA opens up possibilities to analyze large cohort studies based on CyTOF data. © 2019 The Authors. Cytometry Part A published by Wiley Periodicals, Inc. on behalf of International Society for Advancement of Cytometry.

Distributed-mass payload dynamics and control of dual cranes undergoing planar motions

Abstract Unwanted oscillations caused by the operator-commanded motions lower the capable operating speeds and degrade the safety of dual cranes moving distributed-mass payloads. Mounting numbers of works have been devoted to the dynamics and control of dual cranes. However, few studies have been dedicated to the accurate estimation of natural frequency, which is a critical factor for controlling the dual cranes. This paper develops a new method to predict the natural frequency of dual planar cranes with different cable lengths. Furthermore, a modified extra-insensitive (MEI) input shaper is proposed to suppress the oscillations of the payload swing and pitch in the dual cranes. The MEI shaper has good robustness to large changes in the frequency, and has good performance in the jerk limitation. Simulated and experimental investigations are performed on small-scale dual cranes transporting a slender beam to validate the system dynamic behavior and the effectiveness of the MEI shaper.

Fast and Efficient Sinusoidal Frequency Estimation by Using the DFT Coefficients

Fast and accurate frequency estimation of a complex sinusoidal plays an important role in many applications, including communications, radar, and sonar. This paper presents two methods for the frequency estimation of a complex sinusoidal in noisy environments. The proposed methods interpolate on shifted DFT coefficients to acquire the frequency estimates iteratively. The first method interpolates on the $q$ -shifted DFT coefficients of the signal, whose optimum iteration number is found to be a logarithmic function of the signal length. Furthermore, we also show that by appropriately selecting the value of the shift $q$ , the proposed method becomes asymptotically efficient. In the second method, we use hybrid half-shifted and $q$ -shifted DFT interpolators together, which converges in only two iterations. It is shown that both of the estimators are asymptotically unbiased with their mean square errors performing on the Cramer–Rao lower bound. Theoretical results are validated by extensive computer simulations.

Frequency estimation and tracking by two-layered iterative DFT with re-sampling in non-steady states of power system

Frequency deviation off the nominal one is incurred by sudden changes of frequency and could introduce harmonics and inter-harmonics in the power system, which influences the accuracy of frequency estimation with method of discrete Fourier transform (DFT). A two-layered iterative DFT (TLI-DFT) with re-sampling was presented to measure the frequency in non-steady states. A simple frequency estimation method named exponential sampling is amended to calculate the initial sampling frequency in the inner-layered process of the DFT iteration. In reality, frequencies of two consecutive cycles are always interrelated with each other, so an idea of frequency tracking by outer-layered DFT between cycles is adopted. TLI-DFT can track the frequency in non-steady state in different scenarios, e.g., sudden and random frequency change, signal modulated by a cosine signal, and contaminated by decaying direct current offsets. Mean squared error of measured frequency, rate of change of frequency, and total vector error at different transient conditions indicate that the proposed algorithm is valid and more accurate than the traditional one in the non-steady states of a power system.

An Improved Synchronization Scheme for Non-Integer Multiple Spread Spectrum

Non-integer multiple spread spectrum systems are gradually being widely used in civil and military communications due to their superior communication security and signal privacy. For the difficulties in the capture of pseudo-codes in the non-integer multiple DSSS-DQPSK system under the large Doppler shift, a fourth power PMF-FFT (4th-Power-PMF-FFT) scheme is proposed. The system is optimized by zero-padding and batch FFT algorithms to eliminate scallop loss, improve carrier frequency estimation accuracy, and reduce hardware resource consumption The simulation results proved the effectiveness of the method.

How gravitational softening affects galaxy stability – I. Linear mode analysis of disc galaxies

Linear perturbation is used to investigate the effect of gravitational softening on the retrieved two-armed spiral eigenmodes of razor-thin stellar discs. We explore four softening kernels with different degrees of gravity bias, and with/without compact support (compact in the sense that they yield exactly Newtonian forces outside the softening kernel). These kernels are applied to two disc galaxy models with well-known unsoftened unstable modes. We illustrate quantitatively the importance of a vanishing linear gravity bias to yield accurate frequency estimates of the unstable modes. As such, Plummer softening, while very popular amongst simulators, performs poorly in our tests. The best results, with excellent agreement between the softened and unsoftened mode properties, are obtained with softening kernels that have a reduced gravity bias, obtained by compensating for the sub-Newtonian forces at small interparticle distances with slightly super-Newtonian forces at radii near the softening length. We present examples of such kernels that, moreover, are analytically simple and computationally cheap. Finally, these results light the way to the construction of softening methods with even smaller gravity bias, although at the price of increasingly complex kernels.

A new theoretical calculation of the equilibrium constant and temperature for the carbon isotope exchange reaction between CH4 and CO2

The equilibrium isotope fractionations among COH gases in a variety of geological settings are commonly used as isotope geothermometers to evaluate the temperatures of geothermal fluids at depth, subsurface fluid-rock interactions, volcanic-hydrothermal systems and natural gas pools. However, due to limited experimental data and sophisticated theoretical calculations, applications of these geothermometers have been restricted. This study uses the carbon isotope exchange reaction between CH4 and CO2 as a case study to develop theoretical methods that can improve accuracies in calculating harmonic vibrational frequencies for CH4 and CO2, the equilibrium constants and temperatures for the carbon isotope exchange reaction between CH4 and CO2. Results suggest that the Bigeleisen-Mayer equation is sufficient to calculate the equilibrium constants and temperatures associated with the isotope exchange reaction between CH4 and CO2 with an accurate estimation of molecular harmonic vibrational frequencies. Calculations of the harmonic frequencies of CH4 and CO2 are achieved using the B3LYP density functional method with the 6-311+G(d) basis set, and the calculated harmonic frequencies are highly consistent with experimental values. The frequency correction factor is taken as 1.022 which puts the calculated fractionation factors in good agreement with experimental values. The calculated equilibrium constants are comparable to experimental data and a theoretical data set. They are highly consistent. In order to improve the accuracy and efficiency of solving for equilibrium temperatures using the Bigeleisen-Mayer equation, symbol operation and iterative algorithm in the MatLab software have been applied to compute the temperatures instead of using limited theoretical data sets or empirical fit equations. Our calculated results suggest that this algorithm can rapidly and conveniently yield relatively precise equilibrium temperatures. This algorithm can thus provide an important tool to evaluate whether the carbon isotope exchange reaction for CH4 and CO2 has attained equilibrium and estimate the formation temperature of CH4 and CO2 in high temperature geothermal systems.

Influence of the noise on DFT-based sine-wave frequency and amplitude estimators

This paper analyses the effect of wide-band noise on the accuracy of generic sine-wave frequency and amplitude estimators based on Discrete Fourier Transform (DFT) samples located closely to the spectrum peak. A cosine window is adopted to reduce the influence on the estimated parameters of spectral leakage from the negative frequency component. Closed-form expressions for the estimator variances are derived. Moreover, the variance of a frequency estimator expressed as a ratio of generic linear functions of DFT sample modules is specifically investigated. It is also shown that the same frequency estimation accuracy can be achieved when complex-valued DFT samples are considered. The derived expressions are verified on a specific sine-wave frequency estimator and a related amplitude estimator, using both simulation and experimental results.

Prior Rough Estimation and Trigonometric Decomposition Method for Frequency Estimation of Sine Wave Distorted by Noise

Frequency estimation of sine wave distorted by noise plays an important role in modern power systems. The widely used windowed interpolation fast Fourier transform (WIFFT) can only reduce, but not completely remove, the estimation errors at the cost of an increment in the computation burden of frequency estimation. This paper proposes a frequency estimator by using the prior rough frequency estimation and trigonometric decomposition under white Gaussian noises. Firstly, a prior rough frequency is estimated by the three spectral lines WIFFT based on the Hanning window. Then, a parallel iteration of trigonometric decomposition is applied for the accurate frequency estimation. The gradient-descent method is used in the parallel iteration procedure, which can effectively restrain the interferences from harmonics and noise. Simulation and experiments results show that the proposed method can achieve accurate frequency estimation within one cycle.

Efficient and Accurate Detection and Frequency Estimation of Multiple Sinusoids

The method for detection of complex sinusoids in additive white Gaussian noise and estimation of their frequencies is proposed. It contains two stages: 1) sinusoid detection (model order estimation) and coarse frequency estimation, and 2) fine frequency estimation. The proposed method operates in the frequency domain, i.e., it uses the discrete Fourier transform (DFT) as the main tool. Sinusoid detection is performed so that a fixed probability of false alarm is provided (Neymann–Pearson criterion). For both coarse and fine frequency estimations, the three-point periodogram maximization approach is used. Simulations are carried out for variable signal-to-noise ratio, variable frequency displacement between the sinusoids and variable offset from the frequency grid. The proposed method meets the Cramer-Rao lower bound in frequency estimation and practically does not depend on the frequency displacement except for very small displacement values. In terms of model order estimation accuracy, it outperforms the state-of-the-art approaches. The most expensive operation in the method is the calculation of the DFT. Therefore, in terms of calculation complexity, the proposed method is on par with the most efficient algorithms for multiple frequency estimations.

A Narrowband Anti-Jamming Acquisition Algorithm Based on All-Phase Processing for BOC Signals

The accuracy transmission of a binary offset carrier (BOC) signal is always affected by narrowband interference (NBI), and a novel anti-jamming acquisition algorithm based on all-phase processing finite impulse response (apFIR) and partially matched filter-all phase fast Fourier transform (PMF-apFFT) is proposed in this paper. First, an apFIR filter with precise settings for arbitrary notch points was constructed, and then the PMF-apFFT method was adopted to achieve the acquisition of the contaminated BOC signals. Simulation and analysis show that the proposed algorithm can effectively suppress NBI and simultaneously complete correct pseudo-random (PN) phase search and accurate Doppler frequency estimation, and it shows superior performance in mean square error (MSE) and detection probability.

Application of Multi-Resonator Notch Frequency Control for Tracking the Frequency in Low Inertia Microgrids Under Distorted Grid Conditions

Frequency variations are much faster and more significant in microgrids with low-inertia inverters and other control devices for distributed generation. Accordingly, it is imperative to utilize a concise frequency estimation method for analyzing the transient behavior of microgrids. This paper proposes a robust algorithm which is based on multi-resonator and adaptive notch filter and is referred to as the multi-resonant notch frequency control for improving the frequency estimation of perturbed power system. In general, power system distortions such as harmonics, inter-harmonics, and faults may affect the accuracy of frequency estimation. In contrast to conventional methods for frequency estimator, the proposed method is less sensitive to distortions and unbalanced power system conditions. The proposed method uses the information in all three-phase signals which is proved to be more robust against signal variations than single-phase methods. Simulation results demonstrate the accuracy and the speed of the proposed method for frequency estimation in both grid-connected and islanded mode of low inertia microgrids under grid faults.

Accurate Frequency Estimation of a Real Sinusoid by Three New Interpolators

Interpolators are widely employed in the frequency estimation of sinusoidal signals. However, for a real-valued sinusoidal signal, the existing interpolators do not consider the negative frequency component, which leads to a frequency estimation error floor. To solve this problem and further improve the estimation accuracy, three new interpolators are proposed in this paper. These three new interpolators consist of two initial interpolators and one fine interpolator. In the proposed algorithm, the initial interpolators consider both the positive and negative frequency components and are utilized first to eliminate this error floor and obtain an initial frequency estimate. Then, the fine interpolator for the frequency estimation of a complex sinusoid is exploited to improve the accuracy of the initial frequency estimate. The theoretical analysis demonstrates that the frequency estimation mean square error of the proposed algorithm is almost equal to the Cramer-Rao lower bound. Compared with the existing time-domain analysis algorithms, the proposed algorithm has better estimation performance, especially in the case of a low signal-to-noise ratio. Compared with the existing frequency-domain analysis algorithms, the proposed algorithm has lower computational complexity and a wider valid estimation range.

A Fine Frequency Estimation Algorithm Based on Fast Orthogonal Search (FOS) for Base Station Positioning Receivers

Base station signals have been widely studied as a promising navigation and positioning signal. The time and code division-orthogonal frequency division multiplexing (TC-OFDM) signal is a novel communication and navigation fusion signal that can simultaneously implement communication and positioning services. The TC-OFDM signal multiplexes the pseudorandom noise (PRN) code, called positioning code, and the Chinese mobile multimedia broadcasting (CMMB) signal in the same frequency band. For positioning in the TC-OFDM receiver, it is necessary to acquire and track the PRN code phase and the carrier frequency. The tracking performance is directly influenced by the accuracy of the signal acquisition, especially the acquired carrier frequency accuracy. This paper focuses on the fine frequency acquisition of TC-OFDM receivers and proposes a novel fine frequency estimation algorithm, which uses a non-linear modelling method, called fast orthogonal search (FOS), to improve the frequency acquisition accuracy of TC-OFDM receivers. With this algorithm, the PRN code is first stripped off in coarse code phase. Then, the candidate functions at each of the interest frequencies are generated, which consist of pairs of sine and cosine terms. Finally, the FOS algorithm is used to detect the carrier frequency. Simulation and experimental results show that, compared with the current carrier frequency estimation algorithms, the proposed algorithm effectively improves carrier frequency estimation accuracy and then reduces the time to the first fix.