Frequency Estimation Performance Research Articles

Augmented Complex Minimization of Error Entropy With Fiducial Points for Power System Frequency Estimation

Frequency estimation plays an important role in ensuring the stability of the power system. The augmented complex minimum error entropy (ACMEE) algorithm has achieved better performance in frequency estimation under impulsive noise environments. However, it has the problem of unknown error probability density function (PDF) in frequency tracking, the improved algorithms called the complex minimization of error entropy with fiducial points (CMEEF) and the augmented CMEEF (ACMEEF) are proposed in this paper. The ACMEEF algorithm based on widely linear modeling uses second-order statistical information to process the non-circular signal through the complex voltage signal. At the same time, it incorporates a location-sensitive cost into minimum error entropy (MEE) to automatically locate the peak of the error PDF at the origin, which can accurately estimate the grid frequency under the unbalanced system and interference of noise. The stability of the proposed algorithm and the computational complexity are analyzed. Finally, the enhanced frequency estimation performance of the proposed ACMEEF algorithm is verified through simulation results of different synthetic signals and real-world data.

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

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

Robust PLL Synchronization Unit for Grid-Feeding Converters in Micro/Weak Grids

A grid-feeding voltage source converter (GFD-VSC) requires a phase-locked loop (PLL) synchronization unit to be connected to the grid. The PLL critically affects the dynamic performance and stability of the GFD-VSC. In particular, a PLL with pre/in-loop filtering, for working under distorted/polluted conditions, possesses a narrow stability margin and deficient performance in weak grid connections and fault ride-through (FRT) transients, also poor performance in frequency estimation. To address these problems, a robust PLL with several enhanced characteristics is proposed in this article. The robust PLL with a dynamic state feedback controller is designed using an <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">${{\bm{H}}}_\infty $</tex-math></inline-formula> robust control. The feedback controller is designed to improve the dynamic stability/response of the PLL, exposed to control uncertainties and exogenous disturbances, weak-grid connection, FRT transients and to improve its performance in frequency estimation. Numerical simulations validate the effectiveness of the proposed PLL.

Time-frequency ridge estimation: An effective tool for gear and bearing fault diagnosis at time-varying speeds

For a rotary machine vibration signal collected under variable speed conditions, its time–frequency representation (TFR) contains abundant oscillatory components with time-varying amplitudes and frequencies. A single component with a sequence of peaks in the TFR is called a ridge. Accurate ridge detection from TFRs can boost rotary machine health condition assessment without rotation speed measurement. Nowadays, cost function ridge estimation and fast path optimization ridge estimation are the most widely utilized techniques. However, the unreasonable kernel function definitions and inappropriate search region selections significantly restrict the performance of instantaneous frequency estimation of target ridges. To address the deficiencies, this paper proposes a novel time–frequency ridge estimation (TFRE) method. The TFRE integrates a new cost kernel function and an adaptive search region detection principle. For the former, it comprehensively considers the trade-off between seeking peaks and ensuring the smoothness of a ridge. The latter varies the search bandwidth in real-time according to instantaneous signal signatures to effectively isolate interferences and neighboring ridges. A unique advantage of the proposed method is that it dispenses with the tuning of parameters. As a consequence, human intervention is minimized. Experimental gear and bearing vibration signals were analyzed to demonstrate the performance of the TFRE. Results indicated that the proposed TFRE is characterized by superior ridge estimation performance compared to the state-of-the-art methods.

Adaptive tracking of multisinusoidal signal for linear system with input delay and external disturbances

The problem of adaptive tracking of the output variable of a linear stationary plant behind a multiharmonic signal under conditions of control delay and external disturbances is considered. The state vector of the object is not available for direct measurements. The reference and disturbance signal parameters (amplitudes, phases, and harmonic frequencies) are a priori unknown, and a new algorithm is proposed to improve the performance of frequency estimation of a multisinusoidal signal. Examples are given that confirm the relevance of the proposed approach.

Improved Cascaded SOGI Control for Islanding-Synchronization in Photovoltaic System

This work presents an improved cascaded second-order generalized integrator (I-CSOGI) controlled photovoltaic system (PVS), which functions as an islanded system during grid interruption without energy storage. Here, a single-stage PVS structure is used, simplifying the control by automatically regulating the PV array operating point and dc-link voltage during the grid outage. The I-CDSOGI algorithm is exercised to determine the sensed voltages angle, frequency, and harmonics free positive sequence components of the sensed voltages and load currents. The advantage of the presented I-CDSOGI over the existing CDSOGI algorithm is that the gain of its frequency-locked loop is changed adaptively. It reduces the spurious change in the frequency during the sudden phase jump, which is experienced by the load voltages during synchronization. Hence, the repeated tripping of the power electronics switches, which isolates the PVS from the local grid, is reduced, and smooth synchronization is achieved. Furthermore, the cascading of two second order generalized integrator (SOGI) blocks eliminates the dc offset from the sensed signals and boosts the overall harmonics rejection capability, which enhances the angle and frequency estimation performance. A comparison is made to showcase the benefits of I-CSOGI compared with the existing SOGI-based methods in the PVS.

Time-Domain Frequency Estimation With Application to Fault Diagnosis of the Unmanned Aerial Vehicles’ Blade Damage

In this article, a novel time-domain frequency estimation approach is proposed based on the well-known subspace identification method. Differing from the fast Fourier transformation method, the nonlinear identification for frequency estimation is reformulated into the eigenvalue identification problem, which avoids the spectrum peak search. The recursive frequency estimation approach is proposed based on the updating/downdating of the Cholesky decomposition, where the extended observability matrix can be identified from a small matrix with lower computation cost. In addition, a gap metric-oriented performance indicator is proposed as a test statistic for fault detection as well as the evaluation of fault severity. The effectiveness of the proposed methods is verified for frequency estimation and fault diagnosis performance through numerical simulations and the experimental measurements from a laboratory unmanned aerial vehicle rig with partial blade damage.

An Efficient Filter Bank Structure for Adaptive Notch Filtering and Applications

Second-order IIR adaptive notch filters (ANF) andbanks (ANFB) have been extensively utilized in many applications ranging from biomedical engineering to control systems. In this paper, a new efficient ANFB is proposed that is composed of two filter banks, namely a prefilter bank with cascaded IIR notch filters and a parallel structure IIR ANFB. The second-order IIR ANFs or filter bank cells in the proposed ANFB are updated by utilizing a modified normalized gradient (ModNG) algorithm. The proposed ANFB requires the same number of cells as does a conventional parallel form ANFB. However, the filter weight initialization drawback that the conventional parallel form ANFB inherently suffers from is significantly alleviated in the proposed ANFB. Equipped with the ModNG algorithm, the proposed ANFB yields considerably improved frequency estimation performance as compared to the conventional parallel form ANFB, for a wide range of frequencies and signal-to-noise ratios (SNR). Furthermore, preliminary steady-state analysis is provided for both the proposed and conventional ANFBs, which significantly enhances our understanding of their capabilities and features. Extensive case study simulations are conducted to demonstrate the superiority of the proposed ANFB over the conventional parallel form ANFB. The proposed ANFB is also applied to real noise and vibration signals to reveal its promising analytical and practical capabilities.

An Advanced Frequency Estimation Algorithm Based on Analytic Compensation of Effects of Dominant Harmonic in Power Systems

This paper proposes an advanced frequency estimation algorithm, where the interference effect of harmonic is effectively compensated by proposing and using a new ‘harmonics interference decomposition model’. In the decomposition model, the interference effect of harmonic is represented as the sum of the two separated components, i.e., a deviation bias and an oscillatory disturbance, where the deviation bias is modeled to include only the uncoupled amplitude parameter terms and the oscillatory disturbance is modeled to exclusively include all the phase parameter coupled terms in representing a power spectral peak location. The separation and the independent compensation of the two interfering parameters significantly reduce the nonlinearity associated difficulties in deriving analytic compensation equations. Frequency estimation performance of the proposed algorithm is verified through computer simulations with diverse patterns of power system signals. The proposed algorithm’s excellent estimation accuracy and rapid convergence performance are confirmed by comparing the simulation results with those of other representative algorithms.

Anti-noise frequency estimation performance of Hanning-windowed energy centrobaric method for optical coherence velocimeter

The Optical Coherence Velocimeter (OCV) technology is a technique for high-precision displacement and vibration measurement based on the principle of spectral domain optical coherence method. The key of this technology is to realize nanometer or even sub-nanometer measurement by high precision frequency estimation method called as Hanning-window energy centrobaric method (HnWECM). This paper analyses the error transmission process of HnWECM, and proposes a calculation method based on Paserval's theorem to establishes the accuracy theory of HnWECM. It shows that the variance of the estimated frequency using HnWECM is only proportional to the signal-to-noise ratio (SNR) and very close to the Cramér-Rao Lower Bound (CRLB). The estimation performance of HnWECM is verified and compared with other frequency estimation methods by simulation and experimental results. Both the theoretical analysis and simulation results show that the HnWECM has good statistical efficiency and the best anti-noise stability. This paper reveals the reason of chosen HnWECM as the signal processing method of OCV technology and gives its accuracy theory, which will greatly promote the application of OCV technology.

A fast and precise power system frequency estimation method without iterations

The conventional power system frequency estimation methods based on the Discrete Fourier Transform (DFT) normally require iterative calculations to eliminate the errors due to spectral leakage in off-nominal frequencies. It cannot provide both fast response and good accuracy under a system disturbance. In this paper, a fast and precise frequency estimation method is presented. The theoretical analysis shows the angle difference of the positive sequence voltage is exactly linear to the frequency deviation. Based on this angle characteristic, this method is able to precisely calculate the frequency deviation from angle differences between the continuous DFT calculations without the need for any iteration. Even if there is only one single phase voltage input available, the simulated positive sequence voltages can be derived by constructing the remaining two phase-voltages utilizing an appropriate phasor shift. To effectively restrain the harmonic interferences, a two-cycle Hanning window is applied as a filter. One method to detect the phase angle jump is proposed to avoid transient frequency errors by using the 2nd order derivative of the frequency. The simulation compares the frequency estimation performance between the proposed non-iterative method and the conventional iterative method. The simulation results show the frequency response is faster and the accuracy is reliable within the range 40–70 Hz, even if there are harmonic interferences or three-phase unbalances. This proposed frequency estimation method is easy to implement, and it can be widely applied in the intelligent electronic devices within the power system.

Improved ASM-TER Training Sequence Detection and Fine Doppler Frequency Estimation Methods from a Satellite

To detect terrestrial application-specific messages (ASM-TER) signals from a satellite, a novel detection method based on the fast computation of the cross ambiguity function is proposed in this paper. The classic cross ambiguity function’s computational burden is heavy, and we transform the classic cross ambiguity function to a frequency domain version to reduce the computational complexity according to Parseval’s theorem. The computationally efficient sliding discrete Fourier transform (SDFT) is utilized to calculate the frequency spectrum of the windowed received signal, from which the Doppler frequency could be estimated coarsely. Those subbands around the Doppler frequency are selected to calculate the ambiguity function for reducing the computational complexity. Furthermore, two local sequences with half length of the training sequence are utilized to acquire a better Doppler frequency tolerance; thus, the frequency search step is increased and the computational complexity could be further reduced. Once an ASM-TER signal is detected by the proposed algorithm, a fine Doppler frequency estimation could be obtained easily from the correlation peaks of the two local sequences. Simulation results show that the proposed algorithm shares almost the same performance with the classic cross ambiguity function-based method, and the computational complexity is greatly reduced. Simulation results also show that the proposed algorithm is more resistant to cochannel interference (CCI) than the differential correlation (DC) algorithm, and the performance of fine Doppler frequency estimation is close to that of the Cramér–Rao lower bound (CRLB).

Combined Wireless Ranging and Frequency Transfer for Internode Coordination in Open-Loop Coherent Distributed Antenna Arrays

Beamforming in distributed antenna arrays requires accurate coordination of the relative phasing between the separate wireless nodes. Principally, this coordination constitutes measuring the node separations and transferring a stable frequency reference, enabling beamsteering and ensuring that the local oscillators on the separate platforms are locked. A 4.5-GHz wireless system for simultaneous high-accuracy estimation of node separation and estimation of a wirelessly transferred 10-MHz frequency reference is presented in this article. Ranging is achieved using a spectrally sparse two-tone waveform with a tone separation of 200 MHz and pulsewidth of $2~\mu \text{s}$ ; a 10-MHz frequency reference is modulated onto one of the ranging tones. The use of spectrally sparse waveforms allows simple transceiver designs compared to wideband ranging systems since the tones can be individually generated and received. The theoretical bounds for range and frequency estimation are derived for a set of common modulation formats, and experimental measurements of ranging accuracy and frequency estimation accuracy are presented, demonstrating that the proposed waveform can achieve high accuracy in both domains, with range accuracy of 3.35 mm and phase errors less than 18°, supporting coherent distributed array operations up to 5.96 GHz. The results show that the ranging estimation is effectively independent of the modulation format of the reference frequency and the frequency estimation performance is independent of the sparse waveform design for ranging. Thus, the performance of range estimation and frequency transfer may be approached independently but in the same waveform.

A carrier frequency estimation algorithm for Multi-h CPM signals

Considering the problem that Multi-h CPM signal transmission performance is excellent but carrier frequency synchronization is complex, the article proposed a multi-h CPM non-data assisted carrier frequency estimation algorithm based on maximum likelihood. Firstly, the importance of carrier frequency synchronization is explained by simulating the influence of carrier frequency offset on transmission error performance. Then, the carrier phase deviation, frequency deviation, propagation delay, modulation index error and symbol error joint likelihood function in signal transmission are given. The likelihood function is derived and the maximum likelihood carrier frequency estimation is derived in detail. Then the flow chart of the carrier frequency synchronization algorithm based on maximum likelihood is designed. Finally, the ARTM Tier2 signal is simulated by Matlab simulation. The results show that the proposed algorithm is suitable for Multi-h CPM signals and has good carrier frequency estimation performance, and is insensitive to symbol timing deviation and modulation index synchronization error.

Efficient 2-D DOA and frequency estimation for L-shaped array via RD-PM

ABSTRACTThis paper addresses the issue of joint two-dimensional direction of arrival (2-D DOA) and frequency estimation via reduced-dimensional propagator method (RD-PM) with L-shaped array. The proposed algorithm has no need for eigenvalue decomposition of the sample covariance matrix and simplifies three-dimensional global spectral search within the three-dimensional propagator method (3-D PM) to one-dimensional local search, which greatly reduces computational complexity. Furthermore, the proposed algorithm can work under both uniform and non-uniform L-shaped array and can achieve paired 2-D DOA and frequency estimates automatically. In addition, the 2-D DOA and frequency estimation performance for the proposed method is approximate 3-D PM algorithm and parallel factor (PARAFAC) method but exceeds the estimating signal parameters via rotational invariance techniques (ESPRIT) algorithm and improved PM algorithm. The detailed derivation of Cram´er-Rao bound (CRB) is provided and the simulation results demonstrate the effectiveness and superiority of the proposed approach.

An Improved $\alpha\beta$ -EPLL Based on Active Disturbance Rejection Control for Complicated Power Grid Conditions

The enhanced phase-locked loop (EPLL) adds an amplitude estimate to the conventional phase-locked loop (PLL), which solves the problem of double-frequency disturbance in the Phase-Locked Loop mathematical model at steady state. However, there are few researches on disturbance resistance design of EPLL in complicated grid environment. Therefore, periodic disturbances of different frequencies are introduced into frequency estimation and amplitude estimation of EPLL when the grid voltage has DC offset, three-phase unbalance, high-order harmonic disturbance and sub-synchronous oscillation (SSO). This will interfere with the frequency and amplitude estimation performance of the EPLL, and then affect the closed-loop control and frequency tracking of the converter. In order to improve disturbance rejection of the EPLL. Firstly, the mathematical model of the disturbance in the frequency and amplitude loop is deduced and analyzed. Then the active disturbance rejection control (ADRC) is used to improve the EPLL. Through the simulation model of MATLAB/Simulink, the parameters of the ADRC and the ESO are compared and validated. The proposed EPLL based on ADRC is verified experimentally for the tracking performance under the frequency stability or drop in complicated power grid environment.

Time-Frequency Represetation of Radar Signals Using Doppler-Lag Block Searching Wigner-Ville Distribution

Radar signals are time-varying signals where the signal parameters change over time. For these signals, Quadratic Time-Frequency Distribution (QTFD) offers advantages over classical spectrum estimation in terms of frequency and time resolution but it suffers heavily from cross-terms. In generating accurate Time-Frequency Representation (TFR), a kernel function must be able to suppress cross-terms while maintaining auto-terms energy especially in a non-cooperative environment where the parameters of the actual signal are unknown. Thus, a new signal-dependent QTFD is proposed that adaptively estimates the kernel parameters for a wide class of radar signals. The adaptive procedure, Doppler-Lag Block Searching (DLBS) kernel estimation was developed to serve this purpose. Accurate TFRs produced for all simulated radar signals with Instantaneous Frequency (IF) estimation performance are verified using Monte Carlo simulation meeting the requirements of the Cramer-Rao Lower Bound (CRLB) at SNR > 6 dB.

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.

Variable step‐size oscillator‐based adaptive notch filer algorithm using maximum correntropy criterion

A novel oscillator-based adaptive notch filter (OSC-ANF) algorithm is presented. The proposed algorithm has robustness against the impulsive noise because it is derived by using the maximum correntropy criterion (MCC). In addition, the variable step-size MCC-OSC-ANF algorithm is proposed to improve the frequency estimation performance. Experimental results show that the proposed algorithms perform better than the previous algorithm under impulsive noises.

Instantaneous Frequency Estimation for Motion Echo Signal of Projectile in Bore Based on Polynomial Chirplet Transform

Microwave interferometer is one of the devices for measuring the movement travel–varying or time-varying velocity of projectile in bore. Microwave interferometer first obtains the Doppler echo signal including the motion information of the projectile in bore, then the velocity is measured based on instantaneous frequency estimation (IFE) of the processed and transformed signal. The parametric time-frequency analysis method can make spectral energy of nonlinear frequency modulation (FM) signal concentrate at some range in the new transform domain. As the motion echo signal of projectile in bore (MSPB) is a nonlinear FM signal, it could be described by polynomial chirplet, one of polynomial FM signal modes, which is used to construct transform kernel for the signal. In this paper, Polynomial chirplet transform (PCT) method is proposed to analyze the simulation and experiment echo signals of projectile in bore. The estimation error and Renyi entropy are used to measure quantify of the time-frequency distribution. Compared with short-time Fourier transform (STFT) method and Wigner-Ville distribution (WVD) method, our results show that the PCT method has most powerful anti-interference performance and highest accuracy of instantaneous frequency estimation for the simulation signal, and lowest Renyi entropy of the instantaneous frequency estimation for the experiment signal. In general, the PCT method has powerful anti-interference performance and high time-frequency concentration and accuracy of instantaneous frequency estimation for the motion echo signal of projectile in bore.