Frequency Estimation Method Research Articles

A Novel Estimation Method of Water Surface Micro-Amplitude Wave Frequency for Cross-Media Communication

Cross-media communication underpins many vital applications, especially in underwater resource exploration and the biological population monitoring domains. Water surface micro-amplitude wave (WSAW) frequency detection is the key to cross-media communication, where the WSAW frequency can invert the underwater sound source frequency. However, extracting the WSAW frequency information encounters many challenges in a real environment, such as low precision and symbol synchronization, leading to inaccurately estimating the WSAW frequency. Thus, this paper proposed a WSAW frequency estimation method based on an improved RELAX algorithm, incorporating two improvements. First, adding a nonlinear filter to the RELAX kernel function compensates for the filtered gain and enhances the WSAW frequency precision. Second, the improved RELAX kernel function is combined with the generalized inner product method to obtain the time distribution of the non-stationary signals, which is convenient for decoding. Several simulations and experiments applying our method on a Ka-band frequency modulated continuous wave (FMCW) radar demonstrate that our algorithm attains a better performance than traditional methods, e.g., periodogram and the RELAX algorithm. Using the improved algorithm affords to extract the frequency information of the WSAW signal accurately with a short sampling duration, further improving the performance indicators of the communication system, such as communication rate.

Motion parameter estimation of AUV based on underwater acoustic Doppler frequency measured by single hydrophone

This paper describes the use of a single hydrophone to estimate the motion parameters of an autonomous underwater vehicle (AUV) from the underwater acoustic signal excited by its propulsion motor. First, the frequency range of the hydroacoustic signal radiated by the AUV motor is determined, and a detection and recognition model is designed. In the case of uniform linear motion of the AUV, the geometric relationship between the Doppler frequency shift curve of the sound source is derived and the motion model of the sound source and sound line propagation is established. An estimation algorithm for the motion parameters of multiple AUVs based on data from a single hydrophone is derived. Then, for Doppler underwater acoustic signals disturbed by independent identically distributed noise with an arbitrary probability distribution, a cumulative phase difference power amplification instantaneous frequency estimation method is proposed. This method is based on the sum of multiple logarithmic functions. Finally, the effectiveness and accuracy of the algorithm in estimating the motion parameters of multiple AUVs are verified through simulations and experiments.

A novel spectral peak estimator based on underdetermined equation

This letter develops a fast spectral peak estimation method, which is inspired by the theory of compressed sensing (CS). In this work, the measurement procedure of the CS is employed to construct an underdetermined equation, and then a low complexity spectral peak search method is established by using a priori knowledge of signal amplitude. Compared with other frequency estimation methods, the proposed method requires only 10% inner products demanded to obtain the spectral peak positions, and this method can be introduced into any existing discrete Fourier transform (DFT)-based interpolation methods. Experimental results show that the proposed method yields nearly the same accuracy as other interpolation methods, but with lower computational demands.

Automated weak signal frequency estimation method based on Duffing oscillator and particle swarm optimization

The frequency of a weak signal is used for fault diagnosis and target identification in various fields. By introducing particle swarm optimization (PSO) and spectral entropy (SE), an automated weak signal frequency estimation method based on the Duffing oscillator is proposed. The proposed method uses the differential structure to enhance the timing difference of the Duffing oscillator between the chaotic and large-scale periodic states, which is quantitatively distinguished by SE. Then, the frequency of the internal driving force is adaptively adjusted by the PSO to allow the SE to reach a minimum value where the driving frequency equals the weak signal frequency. A group of weak signals with different frequencies has been tested. The maximum relative frequency error is only 0.68%. Unlike other chaotic oscillator-based frequency estimation methods, the proposed method does not need to determine the phase state manually. A rough initial frequency search range is sufficient for automatic frequency measurement of the proposed method in this paper.

An experimental extension to the discrete Laplace method for Y-STR haplotype frequency estimation

Frequency estimation for Y-STR haplotypes is a challenging problem because limited data are available and complex dependencies exist within the data. As a result, various statistical methods have been proposed for frequency estimation. The discrete Laplace method has been recommended in some contexts by the DNA commission of the ISFG. This method is limited to haplotypes with single integer repeat alleles only at all loci. We propose a generalisation of the method that handles duplicated loci such as DYS385 and less common alleles that are not integer repeats. The extension is implemented in an experimental R package called disclapmix2.

A Simple Structure for Accurate Estimation of Single-Phase Grid Frequency Under DC Offset and Both Odd and Even Harmonics

This article proposes an enhanced frequency-locked loop method for the single-phase grid frequency estimation under dc offset and both odd and even harmonics conditions. The proposed method relies on an adaptive recursive discrete Fourier transform-based frequency error detector and an integral controller. It offers a relatively simple structure and computationally efficient method. It can provide accurate frequency estimation at steady state under grid disturbances and takes a dynamic time of around one and half cycles of the fundamental frequency. The improved performance of the proposed method is verified by comparing it with the results of several existing methods reported in the technical literature. The efficacy of the proposed method is proved using simulated and real-time experimental results.

Rapid Harmonic Detection Scheme Based on Expanded Input Observer

The existence of harmonics will cause the quality of power supply in a power system to decline and will affect the normal use of the power system. Therefore, it is important to suppress harmonics in the power system, and the first step of harmonic suppression is harmonic detection. To address this phenomenon, a fast harmonic detection method is proposed in this paper. It is based on the input observer theory to construct a state space model based on the original signal and harmonic components and estimate the state variables so as to achieve harmonic extraction. The characteristic roots are used to prove the convergence of the observer. In addition, the Second-Order Generalized Integration (SOGI) frequency estimation method is chosen to cascade with it so that harmonic detection can be accomplished with unknown frequencies. The simulation results prove that the proposed method can quickly converge and accurately extract each harmonic in the case of fluctuations in the fundamental amplitude, fundamental frequency and phase of the input signal, and the whole process can be completed in 0.02 s. The possible effects of white noise on harmonic extraction are also simulated, and the results prove that the accuracy of harmonic extraction can still be guaranteed in the presence of white noise. By using the Speedgoat real-time target machine built Rapid Control Prototype (RCP) as a testbed, experiments with similar simulation conditions were performed. The results show that the method has fast and accurate harmonic detection performance.

An estimation method of Unmanned Aerial Vehicle rotor spin frequency based on laser micro-Doppler effect

Accurately estimating the rotor spin frequency of Unmanned Aerial Vehicles (UAVs) is of great significance for UAV detection and identification. However, the existing estimation methods are difficult to accurately estimate the spin frequency in different frequency bands. In this paper, for the laser radar UAV rotor target echo model, a method of estimating the rotor spin frequency of UAV based on a multiple linear regression algorithm is proposed for the first time, which is weight the two existing estimation methods through multiple linear regression algorithm can more accurately estimate the rotor spin frequency of UAV. Experimental results show that the relative error of the estimation method can be reduced from 5.98% and 9.80% to 1.07% after multiple linear regression algorithm processing, which confirms the accuracy of the proposed method, and provides a new method for the micro-Doppler feature extraction of the UAV.

A new frequency estimation method for a real-valued waveform with multiple sub-Nyquist channels based on the ESPRIT algorithm

Real-valued waveform frequency measurement problems are often encountered in signal processing and they can be solved by designing a linear system. However, they require the sampling frequency to reach twice the maximum of the measured frequency, that is, to meet the Nyquist condition, which in many cases cannot be satisfied considering the hardware limitation. Therefore, how to design a nonlinear method to reconstruct the signal frequency is of great significance. To solve the frequency estimation problem for a real-valued waveform with sub-Nyquist channels, we propose a frequency estimator based on multiple sub-Nyquist channels. Our algorithm mainly consists of the following parts: 1) Calculate the folded frequencies which are lying on the first Nyquist region for each channel based on ESPRIT. 2) Reconstruct the signal frequency by a search method according to the set of folded frequencies. Finally, the simulation results verify the good performance of our proposed algorithm.

A robust method for instantaneous frequency estimation via inverse spectral decomposition

Instantaneous frequency is an important seismic attribute, which can indicate thin beds and lithofacies boundaries. However, instantaneous frequency attribute is susceptible to noise when it is obtained by the traditional Hilbert transform (HT) method. We propose a robust method for instantaneous frequency estimation. The method first obtains the time-frequency distribution of the seismic signal by inverse spectral decomposition (ISD) and then calculates the analytic signal through the window HT transform. Inverse spectral decomposition achieves high-resolution time-frequency distribution by adding sparse constraint to the corresponding inverse problem, and therefore the noise can be suppressed. The algorithm we choose to solve the mix ℓ2 − ℓ1 problem is the fast iterative shrinkage-thresholding algorithm (FISTA). Compared with the traditional iterative least squares (IRLS) algorithm, FISTA can achieve a better computational efficiency. We perform the method on a quadratic frequency modulation (QFM) signal, a synthetic data based on a wedge model and field data sets to demonstrate its performance, compared with the HT method and the time-frequency adaptive filtering method.

A Modal Frequency Estimation Method of Non-Stationary Signal under Mass Time-Varying Condition Based on EMD Algorithm

A method to estimate modal frequency based on empirical mode decomposition (EMD) and ensemble empirical mode decomposition (EEMD) is proposed. This method can decrease the difficulties in identifying modal frequency of combine harvesters. First, we used 16 acceleration sensors installed at different test points to collect vibration signals of a corn combine harvester under operating conditions (mass time-varying conditions). Second, we calculated mean value, variance and root mean square (RMS) value of the vibration signals, and analyzed its stationarity of vibration signals. Third, the main frequencies of the 16 points were extracted using the EMD and EEMD methods. Finally, we considered modal frequencies identified by the SSI algorithm as standard, and calculated the fitting degrees of the EMD and EEMD methods. The results show that in different time periods (0~60 s and 60~120 s), the maximum differences of the mean value, variance and RMS value of signals were 0.8633, 171.1629 and 11.3767, and the vibration signal under the operating condition of field harvesting can be regarded as a typical non-stationary random vibration signal. The EMD method had more modal aliasing than EEMD, and when we obtained the fitting equations of EMD, EEMD and SSI methods, the value of the Euler distance between the EMD fitting equation and the SSI fitting equation was 446.7883, while that for EEMD and SSI was 417.2845. The vibration frequencies calculated by the EEMD method is closer to the modal frequencies identified by SSI algorithm. The proposed method provides a reference for modal frequency identification and vibration control in a complex working environment.

Two-Step Frequency Estimation of GNSS Signal in High-Dynamic Environment

To improve frequency accuracy which is affected by two parameters in high-dynamic acquisition, we propose a two-step frequency estimation method based on the mean frequency (MF) model for high-dynamic parameters estimation. The first step is based on the discrete chirp-Fourier transform (DCFT) for coarse MF estimation, where the MF accuracy and frequency search step are derived. In the second step, the maximum likelihood estimation process (MLEP) is adopted for fine MF estimation. Compared with state-of-art methods, it is verified that the two-step method can improve the detection probability in coarse MF estimation and improve the MF accuracy with low computational burdens under conditions with a moderate signal-to-noise ratio (SNR).

A Software Digital Lock-In Amplifier Method with Automatic Frequency Estimation for Low SNR Multi-Frequency Signal

In the fault diagnosis field, the fault feature signal is weak and contaminated by the noise. The lock-in amplifier is a useful tool for weak signal detection. Aiming to the amplitude error of the lock-in amplifier caused by frequency deviation between the measured signal and the reference signal, a DFT-based automatic signal frequency estimation method is studied to improve the frequency accuracy of the reference signal. Based on this frequency estimation method, a software digital lock-in amplifier method is proposed to detect the multiple frequencies signals. This proposed method can automatically measure the frequency value of the measured signal without prior frequency information. Then, the reference signals are generated through this frequency value to make the digital lock-in amplifier estimate the amplitude of the measured signal. Moreover, an iterative structure is used to implement the multiple frequencies signal measurement. The frequencies and amplitudes measurement accuracies are tested. Under different SNR conditions, the frequency relative error is less than 0.1%. In addition, the amplitude relative error with different signal frequencies is less than 1.7% when the SNR is −1 dB. This proposed software digital lock-in amplifier method has a higher signal frequency tracking ability and amplitude measurement accuracy.

A novel instantaneous frequency estimation method for operational time-varying systems using short-time multivariate variational mode decomposition

Operational modal identification of time-varying systems plays a crucial role in assessing the health condition and controlling the dynamic properties of engineering structures. However, only the response is measurable, making it challenging. Based on the variational mode decomposition (VMD) theory, this paper presents a short-time multivariate or multi-channel VMD (STMVMD) method for instantaneous frequency (IF) identification of time-varying structures in the case of output-only measurements. The idea of short-time windows overcomes the shortcoming of many VMD-based methods that employ the narrowband assumption of intrinsic mode functions (IMFs) and cannot decompose non-stationary signals involving closely-spaced wideband IMFs. After obtaining the multivariate IMFs by STMVMD, an average scheme is employed to estimate IFs, reducing the noise sensitivity of Hilbert Transform. Moreover, by tracking the center frequencies of STMVMD at different moments, another more noise-robust IF estimation method is also presented. A series of numerical and experimental examples illustrate the advantages of the proposal.

Application of two spectrum refinement methods in frequency estimation

Considering the limitation of FFT frequency estimation method in resolution, this paper briefly introduces the complex modulation ZOOM-FFT and Chirp-Z transform spectrum zooming methods. The simulation results show that the ZOOM-FFT method has better anti spectrum leakage and interference effect. Furthermore, the two methods are applied to the frequency estimation of underwater high-speed maneuvering target, and it is found that Chirp-Z transform method can obtain smoother and stable frequency history, and has more flexible frequency resolution.

A new DFT-based frequency estimation algorithm for protection devices under normal and fault conditions

Frequency is one of the essential parameters for monitoring, control, and protection in power systems. Some protection devices use frequency for deciding under various conditions of the power system. Therefore, it is important to estimate frequency rigorously and fast. In this paper, a DFT- based algorithm is introduced for frequency estimation in the presence of harmonics and decaying DC. Initially, According to the condition of the power system, the type of input signal (current or voltage) is determined. The current and voltage signals are the input to the proposed algorithm under fault and normal conditions, respectively. Based on the type of the input signal, the frequency estimation method (FEM) is selected and used. 2 FEMs are proposed to estimate the frequency based on solving a cubic equation. For both FEMs, an optimization-based filter is designed and applied to mitigate harmonics. The proposed algorithm is validated under various static and dynamic tests in MATLAB. The results show that the proposed algorithm is accurate and fast with a low computational burden.

Noniterative method for frequency estimation based on interpolated DFT with low-order harmonics elimination

The paper describes a new interpolated discrete Fourier transform (IpDFT) method for the frequency estimation of the real sine wave distorted by harmonics. The method complements recent work on the direct-formula IpDFT methods by expanding the model of the signal included in the interpolation. Spectral superposition for a total of four frequency components is accounted for in a one-step formula. Alongside the positive and negative components of the fundamental frequency, the influence from the closest low-order real harmonic is eliminated. By using the generalized maximum sidelobe decay (GMSD) window family, the interference from more distant harmonics and interharmonics is suppressed. This approach allows us to perform the measurement with a shortened data record compared to previous methods and improves accuracy in the case that a second-order harmonic is present in the signal. The study provides a five-point analytical, one-step formula that is verified by simulations and experiments in terms of accuracy and complexity. The experimental results are presented featuring straightforward C implementation on the system with an affordable microcontroller.

Blind frequency estimation of pseudo-code phase and linear frequency modulation composited fuze by Duffing oscillator

In order to blind estimate pseudo-code (PN) code phase modulation and linear frequency modulation composited fuzecarrier frequency. By improving the traditional Duffing oscillator detection model of strong reference signal, an approximate carrier frequency blind estimation method by small-scale periodic Duffing oscillator is proposed in this paper. In this method, the internal dynamic frequency is used to approximate the changes of the output time domain and phase diagram of the chaotic system during the frequency to be measured. Then calculate the different frequency to blind estimate the carrier frequency of the signal. This method widens the range of frequency detection and can realize blind frequency estimation with less prior knowledge. The parameter estimation effect of the approximate carrier frequency estimation method based on small cycle Duffing oscillator under different signal to noise ration (SNR) is simulated and analyzed in this paper. The results show that this method has better parameter estimation performance than the traditional composited fuze frequency estimation method, especially in the environment of low SNR.

Instantaneous Frequency Estimation Method for the Vibration Signal of Rotating Machinery Based on STFTSC Algorithm

In this paper, an instantaneous frequency identification method known as STFTSC is developed by combining short-time Fourier transformation and the seam carving (SC) algorithm (widely used in image processing). In this method, the STFT is applied to analyze the time-frequency energy distribution of a vibration signal under variable-speed conditions. Subsequently, the energy gradient is calculated through the Sobel operator based on the time-frequency energy distribution. The energy gradient distribution contains multiple ridges, which are corresponding instantaneous frequencies of different orders. Finally, the targeted ridge extraction is transformed into an optimization problem, and the dynamic programming algorithm (DP) is used to search the targeted ridge with the minimum energy gradient to estimate the instantaneous frequency. The effectiveness of the proposed method is validated by a simulation experiment, moreover, a rotating machinery fault simulation test bench is employed to validate the method, which is then compared with polynomial chirplet transformation (PCT) and analyzed during the test process. The results show that the STFTSC instantaneous frequency estimation algorithm has a higher extraction accuracy and better application value in engineering problems than the PCT.

A Method for Accurate Estimation of Instantaneous Frequency Considering Aliasing of Oscillation Components

A Method for Accurate Estimation of Instantaneous Frequency Considering Aliasing of Oscillation Components