Frequency Estimation Of Sinusoidal Signal Research Articles

CHOOSING THE OPTIMUM FREQUENCY ESTIMATOR UNDER SYSTEM FREQUENCY DEVIATIONS IN POWER SYSTEMS

Parameter estimation in particular the frequency estimation of sinusoidal signals contaminated with noise is of great importance due to its broad applications in many fields such as communications, instrumentation, medicine and radar. In today’s power systems, frequency deviations in the nominal system frequency would cause spurious or so-called ghost frequency components in the spectrum. Those types of frequency components complicate the real-time tracking of harmonics and interharmonics present in the system. In this study, in order to minimize the side effects of system frequency deviations the performances of various frequency estimators are evaluated against varying fundamental frequency and noise conditions and the optimum estimator is chosen.

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.

Frequency Estimation of Sinusoidal Signals Using ASIQ–Rife Interpolation Method

ABSTRACTTo establish a tradeoff between complexity and performance of frequency estimation of sinusoidal signals, a novel automatic segmentation-improved Quinn–Rife method is proposed. The proposed method first utilizes a Discrete Fourier Transform (DFT) algorithm to obtain a coarse estimation, and then divides the frequency deviation into three domains with different processing schemes, which could be suitable for low-delay applications. Simulation results show that the proposed method can overcome the inherent flaws of the classic Quinn and Rife methods, and that the root mean square error closely approaches the Cramer–Rao lower bound at a low signal-to-noise ratio with different estimation ranges. Furthermore, the method does not significantly increase the computational cost under the premise of guaranteed performance, which is beneficial for engineering applications.

Frequency determination from truly sub-Nyquist samplers based on robust Chinese remainder theorem

Abstract In this paper, a truly sub-Nyquist sampling method for frequency estimation of sinusoidal signals in noise is presented. Basically speaking, sinusoidal signals are first sampled at multiple sampling rates lower than the Nyquist rate, and then a robust Chinese remainder theorem (CRT) is proposed to estimate the frequencies of interest from the aliased frequencies obtained by taking the discrete Fourier transform of the collected samples in each undersampled waveform. Compared with compressed sensing, this method can be easily implemented from the hardware point of view. This paper provides a thorough overview of the existing research results on the robust CRT during the last decade, and discusses some related open problems as well.

Frequency estimation of a sinusoidal signal with time-varying amplitude and phase

Abstract This paper is devoted to frequency estimation of a non-stationary sinusoidal signal. The amplitude is supposed to be a known function within a constant factor, the phase should be known. Example of such problem statement is sensorless angular velocity estimation for permanent magnet synchronous motors. On the first step by reparametrization, a third order linear regression model is obtained. On the next step, an estimation algorithm is constructed based on a standard gradient approach. The frequency estimate can be computed from one of the model parameters using inverse trigonometric functions. To improve estimates quality for noisy measurements we propose a new identification method, which can be tuned to attenuate the noise influence. It is shown that the frequency estimation error converges to zero exponentially fast. The described algorithm does not require measuring or calculating derivatives of the input signal. The efficiency of the proposed approach is demonstrated through the set of numerical simulations.

Frequency Estimation of Sinusoidal Signals in Multiplicative and Additive Noise

In this paper, frequency estimation of sinusoidal signals in multiplicative and additive noise is addressed. Based on the parametric localization of distributed sources and the minimax theorem, an eigenanalysis-based frequency estimator is proposed. Furthermore, we present processing and analysis for pseudofrequency estimates in the proposed method. Especially, a priori knowledge of multiplicative noise is not required as compared with the distributed signal parameter estimator (DSPE). Monte Carlo experiments are carried out to evaluate performance. Simulation results confirm that the proposed method provides better performance than the nonlinear least squares (NLS) approach and the conventional MUSIC algorithm for separating closely spaced sinusoidal signals in multiplicative and additive noise.

Frequency estimation of the weighted real tones or resolved multiple tones by iterative interpolation DFT algorithm

Accurate frequency estimation of sinusoidal signal is commonly required in a large number of engineering practice scenarios. In this paper, an iterative frequency estimation algorithm is proposed based on the interpolation of Fourier coefficients of weighted samples. This algorithm is nearly applicable for all conventional window functions. Systematic errors for various windows are presented and the performance of the proposed algorithm is investigated in the presence of white Gaussian noise. The simulation results demonstrate that errors caused by a mistaken location of the spectral line can be significantly reduced. The proposed algorithm is straightforward to implement, has high precision, good compatibility, and is robust against additive noise, all of which make it ideal for accurate frequency estimation in spectral analysis.

Frequency estimation of undersampled sinusoidal signal based on chinese remainder theorem

Frequency estimation based on the reconstruction algorithm of the Chinese remainder theorem(CRT) is one of the frontier focuses in the fields of signal processing, electromagnetism, and optics etc. Howerver, the existing studies can only realize a rough frequency estimation of complex exponential signals. Hence this paper generalizes the CRT-based frequency reconstruction from a rough frequency estimation of complex exponential signals to the accurate frequency estimation of sinusoidal signals. The procedure of the proposed estimation scheme is as follows: (1) Detect zero crossing point on the original high-frequency sinusoidal waveform so as to determine the ideal phase information; (2) implement fast Fourier transform(FFT) to each path's undersampled signal, and then use Candan estimator to correct the frequencies at the peak FFT spectral bins so that the frequency biases can be extracted to realize phase correction; (3) use the proposed classification method based on phase features to screen the corrected remainders; (4)substitute the filtered frequency remainders into the closed-form robust Chinese remainder theorem to obtain the high-accuracy frequency estimation of the original signal. Additionally, this paper also deduces the theoretic expressions of the frequency estimation variance, which is also verified through numerical simulation. And the experimental results also reflect that the proposed scheme possesses high precision and high robustness to noise.

Frequency estimation of a sinusoidal signal via a three-point interpolated DFT method with high image component interference rejection capability

This paper proposes a three-point Interpolated Discrete Fourier Transform (IpDFT) method for frequency estimation of a discrete-time sinusoidal signal. It is based on the maximum sidelobe decay (MSD) windows and is highly effective in rejecting the detrimental effect on the estimation accuracy due to the image component of the signal spectrum. This remarkable feature is achieved by using an analytical expression based on a suitable weighting of the three largest DFT spectrum samples. The proposed method provides good results when the effect of the spectral interference due to the image component dominates other estimation error sources. The accuracy of the proposed method and of other state-of-the-art methods such as the multi-point IpDFT methods and the four-parameter sine-fitting (4PSF) algorithm are compared through both computer simulations and experimental results in the case of ideal, noisy, and harmonically distorted sinusoids. A small number of acquired cycles is assumed in order to analyze situations in which the contribution from the image component interference is significant. The performed comparison shows that the proposed method outperforms the considered multi-point IpDFT methods when the Signal-to-Noise Ratio (SNR) is higher than 30 dB and the number of acquired cycles is enough small. The proposed method outperforms also the 4PSF algorithm when the frequency estimation error is dominated by harmonics rather than wideband noise.

A two-stage autocorrelation method for frequency estimation of sinusoidal signal

A two-stage autocorrelation method is proposed for frequency estimation of a complex sinusoidal signal in complex additive white Gaussian noise. In the first stage, a function about signal frequency is constructed via an autocorrelation procedure. By the Least-Square (LS) principle, the signal frequency is estimated from the function. In the second stage, the estimated error of signal frequency in the first stage is defined. Applying the Taylor series, a function about the estimated error of signal frequency is conducted from the autocorrelation function. Applying the LS estimation once more, the estimate of estimated error of frequency in the first stage is obtained. Then the fine estimate of signal frequency is obtained. Simulation results show that the performance of proposed method can approach the Cramer–Rao lower bound in the whole frequency range.

Real-time frequency estimation for sinusoidal signals with application to robust fault detection

This paper has investigated the problem of estimating unknown frequencies of a given sinusoidal signal with disturbances and noises, as well as its usages for fault detection. On the basis of a parametric linear model of the signal, a gradient estimator with leakage is adopted to identify the frequencies. The estimation mechanism is applied to fault detection, as it achieves not only the tolerance to disturbances but also the sensitivity to faults. Simulations verify the feasibility and capability of the frequency identifier for estimating frequencies and detecting faults. Copyright © 2012 John Wiley & Sons, Ltd.

A novel frequency estimation of sinusoidal signal by noise approximation

A novel frequency estimation of sinusoidal signal by noise approximation

JOINT TIME DELAY AND FREQUENCY ESTIMATION METHOD WITH SHIFT INVARIANCE PROPERTY

This paper links the joint time delay and frequency estimation problem to the data model with shift invariance characteristics. A novel method for joint time delay and frequency estimation of sinusoidal signals received at multiple separated sensors is derived. The proposed algorithm takes advantage of multi-invariance characteristic to estimate frequency and also employs single invariance property to estimate time delay. The algorithmic performance is shown to be better than both ESPRIT method and state-space realization algorithm. Simulation results illustrate performance of this algorithm.

Genetic algorithms based robust frequency estimation of sinusoidal signals with stationary errors

In this paper, we consider the fundamental problem of frequency estimation of multiple sinusoidal signals with stationary errors. We propose genetic algorithm and outlier-insensitive criterion function based technique for the frequency estimation problem. In the simulation studies and real life data analysis, it is observed that the proposed genetic algorithm based robust frequency estimators are able to resolve frequencies of the sinusoidal model with high degree of accuracy. Among the proposed methods, the genetic algorithm based least squares estimator, in the no-outlier scenario, provides efficient estimates, in the sense that their mean square errors attain the corresponding Cramér-Rao lower bounds. In the presence of outliers, the proposed robust methods perform quite well and seem to have a fairly high breakdown point with respect to level of outlier contamination. The proposed methods significantly do not depend on the initial guess values required for other iterative frequency estimation methods.

Novel joint time delay and frequency estimation method

A novel algorithm has been proposed for joint time delay and frequency estimation of sinusoidal signals received at multiple separated sensors. The joint time delay and frequency estimation problem is linked to a trilinear model. Exploiting this link, it derives a trilinear decomposition-based joint time delay and frequency method algorithm. The simulation results reveal that the algorithm performance is close to that of the Cramer–Rao lower bound, and the proposed algorithm even supports small sample sizes.

Stability analysis of periodic orbit of an adaptive notch filter for frequency estimation of a periodic signal

Online frequency estimation of a sinusoidal signal is a classical problem and has many practical applications. Recently an adaptive notch filter (ANF) with global convergence property has been developed for frequency estimation of a pure sinusoidal signal. This paper addresses a modified ANF structure that can estimate the fundamental frequency of any periodic signal including pure sinusoidal signals. To prove the stability of the modified ANF, the paper introduces a new theorem that shows for any periodic signal, there exists a locally asymptotically stable periodic orbit of this ANF by which the frequency estimation becomes feasible. This alternative stability proof is simple and uses widely known mathematical tools, and therefore alleviates the problem complexity even when the input signal is a pure sinusoidal signal. A further contribution of this paper is obtaining a necessary and sufficient condition in terms of design parameters for local asymptotical stability of the modified ANF. This condition, obtained from the numerical study of Floquet multipliers of a linear time-varying periodic system, provides a strict stability region in the modified ANF design parameters space.

Subspace-based frequency estimation of sinusoidal signals in alpha-stable noise

In the frequency estimation of sinusoidal signals observed in impulsive noise environments, techniques based on Gaussian noise assumption are unsuccessful. One possible way to find better estimates is to model the noise as an alpha-stable process and to use the fractional lower order statistics (FLOS) of the data to estimate the signal parameters. In this work, we propose a FLOS-based statistical average, the generalized covariation coefficient (GCC). The GCCs of multiple sinusoids for unity moment order in S αS noise attain the same form as the covariance expressions of multiple sinusoids in white Gaussian noise. The subspace-based frequency estimators FLOS–multiple signal classification (MUSIC) and FLOS–Bartlett are applied to the GCC matrix of the data. On the other hand, we show that the multiple sinusoids in S αS noise can also be modeled as a stable autoregressive moving average process approximated by a higher order stable autoregressive (AR) process. Using the GCCs of the data, we obtain FLOS versions of Tufts–Kumaresan (TK) and minimum norm (MN) estimators, which are based on the AR model. The simulation results show that techniques employing lower order statistics are superior to their second-order statistics (SOS)-based counterparts, especially when the noise exhibits a strong impulsive attitude. Among the estimators, FLOS–MUSIC shows a robust performance. It behaves comparably to MUSIC in non-impulsive noise environments, and both in impulsive and non-impulsive high-resolution scenarios. Furthermore, it offers a significant advantage at relatively high levels of impulsive noise contamination for distantly located sinusoidal frequencies.

Asymptotic performance of second-order algorithms

This paper re-examines the asymptotic performance analysis of second-order methods for parameter estimation in a general context. It provides a unifying framework to investigate the asymptotic performance of second-order methods under the stochastic model assumption in which both the waveforms and noise signals are possibly temporally correlated, possibly non-Gaussian, real, or complex (possibly noncircular) random processes. Thanks to a functional approach and a matrix-valued reformulated central limit theorem about the sample covariance matrix, the conditions under which the asymptotic covariance of a parameter estimator are dependent or independent of the distribution of the signal involved are specified. Finally, we demonstrate the application of our general results to direction of arrival (DOA) estimation, identification of finite impulse response models, sinusoidal frequency estimation for mixed spectra time series, and frequency estimation of sinusoidal signal with very lowpass envelope.

Adaptive frequency estimation of sinusoidal signals in colored non-Gaussian noises

This paper studies the problem of sinusoidal frequency estimation in colored non-Gaussian ARMA noises. A new adaptive approach is proposed by using the second-and third-order statistics of the measurements. Because of the simultaneous establishment of the signal and noise models, the new approach is applicable for tracking the frequencies at each time instant for stationary and nonstationary signal and/or noise cases. The effectiveness of the new approach is demonstrated by extensive computer simulations. As expected, the approach proposed in this paper outperforms the correlation-based approaches in suppressing the effects of the colored non-Gaussian ARMA noises.

Nonlinear Least-Squares Approach to Frequency Estimation and Detection for Sinusoidal Signals with Arbitrary Envelope

In this paper, we consider the problem of estimating the frequency of a sinusoidal signal whose amplitude could be either constant or time-varying. We present a nonlinear least-squares (NLS) approach when the envelope is time-varying. It is shown that the NLS criterion can be explicitly minimized with respect to the signal amplitude and envelope values, leaving out a periodogram-like function whose peak location gives the frequency estimate. This result is a significant generalization of a similar result on the NLS frequency estimation for a sinusoidal signal with constant amplitude. A statistical analysis shows that the NLS frequency estimator is asymptotically statistically efficient. The problem of detecting amplitude time variations is next addressed. A statistical test is formulated, based on the statistics of the difference between two frequency estimates. The test is computationally efficient and yields as a by-product consistent frequency estimates under either hypothesis (i.e., constant or time-varying amplitude). Numerical examples are included to show the performance both in terms of estimation and detection.