Frequency Estimation Algorithm Research Articles

Multi-method piecewise low-frequency identification

Inter-area frequency modes of electromechanical oscillations are decisive factors that influence the performance of electrical power systems. However, the accurate estimation of these frequencies remains a challenge due to the non-linear behavior of the response system following a disturbance and the strong coupling among the frequencies. This work describes a curve fitting and electromechanical frequency estimation algorithm, called Multi-method Piecewise Identification (MPI), based on a combination of the Matrix Pencil Method (MPM), the Prony method, and Subspace Identification (SSI), choosing the best approximation of an interval basis according to the model accuracy index (MAI) and the mean square error (MSE). The advantages and limitations of MPI were analyzed by computational analyses that were carried out with Python-based code that estimates the low frequencies for several ringdown signals, including oscillating signals from Australian and Brazilian systems that arise after large disturbances. To ensure robustness to random and noisy conditions, the method was tested with a synthetic signal with Gaussian white noise and time-variant frequencies, and compared to the methods mentioned above, the Hilbert–Huang Transform (HHT), and Eigensystem Realization Algorithm (ERA). The MPI has shown robust results and is capable of obtaining a better fitting for the signal than the other methods.

A Frequency Estimation Algorithm for High Precision Monitoring of Significant Space Targets

A Frequency Estimation Algorithm for High Precision Monitoring of Significant Space Targets

Tacho-less spur gear condition monitoring at variable speed operation using the adaptive application of variational mode extraction

Effective condition monitoring of machine components contributes to a safer working environment for operators and assists in averting critical machinery shutdowns. In real-world industrial scenarios, fault detection must remain simplified, user-friendly and robust despite speed variations. The operational demands of machinery frequently result in speed fluctuations, leading to spectral smearing, thereby compromising the efficiency of the analysis methodology. Furthermore, the intricacies of parameter initialisation often increase the complexity of the analysis methods. This study introduces a fault diagnosis algorithm that requires minimal initialisation and operates independently of tacho pulses. The algorithm proposed in the study incorporates variational mode extraction with the maxima tracking algorithm for instantaneous frequency estimation. Hankel matrix-based selective spectral fusion is proposed to mitigate the impact of frequency tracking errors caused by transient noise. The results of spectral side-band-based fault severity analysis, conducted on an in-house spur gearbox test-bed with seeded tooth chips, underscore the superior performance of the proposed algorithm when compared to contemporary non-stationary analysis methods.

Sufficient active control of uncertain low-frequency space micro-vibrations near measurement limit of acceleration sensors

High-precision payloads such as ultra-stable optical clocks for next-generation space missions are greatly sensitive to the low-frequency micro-vibrations induced by various flexible appendages equipped on the spacecraft. The frequencies of such micro-vibrations are uncertain and near the measurement limit of acceleration sensors, leading to insufficient vibration control performance of classical feedback control. To solve this problem, a hybrid control algorithm which combines PI controller and the filter-x least-mean-square (FxLMS) algorithm is proposed in the paper. In particular, a frequency estimation algorithm is designed for the active vibration control system to provide the reference signal. In the new system, the rough estimation of disturbance frequency is given by the adaptive notch filter. Then, the frequency is refined by Kalman filter and provided into the autoregressive model, which fine-tunes the estimated frequency and offers the reference signal for the hybrid PI-FxLMS algorithm. Finally, the experimental prototype of active vibration control system is developed and the proposed control algorithm is adopted. The experimental results demonstrate the effectiveness of the frequency estimation algorithm and further validate that the proposed hybrid PI-FxLMS algorithm can effectively suppress the low-frequency micro-vibrations near the measurement limit of acceleration sensors and with uncertain frequency.

A Generalized Shuffle Framework for Privacy Amplification: Strengthening Privacy Guarantees and Enhancing Utility

The shuffle model of local differential privacy is an advanced method of privacy amplification designed to enhance privacy protection with high utility. It achieves this by randomly shuffling sensitive data, making linking individual data points to specific individuals more challenging. However, most existing studies have focused on the shuffle model based on (ε0,0)-Locally Differentially Private (LDP) randomizers, with limited consideration for complex scenarios such as (ε0,δ0)-LDP or personalized LDP (PLDP). This hinders a comprehensive understanding of the shuffle model's potential and limits its application in various settings. To bridge this research gap, we propose a generalized shuffle framework that can be applied to PLDP setting. This generalization allows for a broader exploration of the privacy-utility trade-off and facilitates the design of privacy-preserving analyses in diverse contexts. We prove that the shuffled PLDP process approximately preserves μ-Gaussian Differential Privacy with μ = O(1/√n). This approach allows us to avoid the limitations and potential inaccuracies associated with inequality estimations. To strengthen the privacy guarantee, we improve the lower bound by utilizing hypothesis testing instead of relying on rough estimations like the Chernoff bound or Hoeffding's inequality. Furthermore, extensive comparative evaluations clearly show that our approach outperforms existing methods in achieving strong central privacy guarantees while preserving the utility of the global model. We have also carefully designed corresponding algorithms for average function, frequency estimation, and stochastic gradient descent.

Real-Time Detection and Localization of Line Trip Event via Relative Phase Angles

Line trip events widely exist in power systems. They can result in power outages and a huge economic loss if not promptly detected and localized. To provide a fast and precise solution, this paper presents a Complete Coverage of Voltage Measurement (CCVM)-based line trip event detection algorithm and a Relative Phase Angle (RPA)-based line trip event localization algorithm. First, frequency and relative phase angle features during a line trip event are calculated. Then, the CCVM-based algorithm is proposed from both frequency and rate of change of frequency estimation algorithm aspects. Additionally, the RPA-based algorithm is presented, and two cases are studied to demonstrate the uniqueness of the proposed algorithm. Various experiments are conducted, where the simulation results demonstrate that the proposed CCVM-based algorithm can detect a line trip event as short as 2.07 ms. In addition, the RPA-based algorithm has 1.26 times higher localization accuracy compared with the frequency magnitude-based and phase angle-based algorithms. The experiment results on the examples from two interconnected power systems in the U.S. verified the performance of the proposed algorithms in wide-area power systems.

Highly-Linearized Heterodyne Self-Mixing Vibrometer

Vibration meters based on self-mixing interferometry are generally made in baseband, without modulations, because it is very difficult to obtain a linear modulation of the wavelength by controlling the supply current. In this paper, it is shown a multi-frequency modulation strategy for a heterodyne self-mixing vibrometer, which allows us to overcome the limits of frequency estimation algorithms and can work on a diffusing target up to a few meters away.

Combined Fourier and Zero Crossing Technique for Frequency Measurement in Power Networks in the Presence of Harmonics.

A new approach to the design of a digital algorithm for network frequency estimation is proposed. The algorithm is derived using Fourier and zero crossing technique. The Fourier method is used as digital filter and zero crosing technique is applied to the cosine and sine components of the original signal which can be corrupted by higher harmonics. The algorithm showed a very high level of robustness as well as high measurement accuracy over a wide range of frequency changes and it can be used for frequncy tracking in power networks when the higher harmonics are presented in voltage or current signals. The theoretical basis and practical implementation of the technique are discribed. To demonstrate the performance of the developed algorithm, computer simulated, as well as real life data records, are processed.

Performance Evaluation of a Linear Predictor Frequency Estimator for Mobile Flat Fading Wireless Channels

A well-known frequency estimation algorithm using the linear prediction method is analyzed for flat fading wireless channels. The estimator outputs are statistically analyzed and its jitter performances are compared with the non-fading case and the Cramer-Rao bound. We provide a closed form solution for the distribution and the variance of the frequency estimates under fading conditions by making valid assumptions. We also verify the theoretical model using simulations. Analysis shows that the variance of the estimates for flat fading channels reaches a threshold point and increasing the transmit power does not necessarily improve the performances any further.

Errata for "SpaceSaving±: An Optimal Algorithm for Frequency Estimation and Frequent Items in the Bounded-Deletion Model"

This errata article points out an implicit assumption in the work of four of us published in VLDB 2022. The SpaceSaving± algorithm in bounded deletion data stream presented in the paper implicitly assumed deletions happen after all insertions. When insertions and deletions are interleaved, that algorithm may severely underestimate item's frequency. We first illustrate this phenomenon by an example and then present a modified algorithm with minor changes to allow interleaving between insertions and deletions. We also include a pointer to a full analysis of the new algorithms.

Randomized counter-based algorithms for frequency estimation over data streams in [formula omitted] space

This note studies the problem of estimating frequencies of items over data streams. We propose a simple streaming algorithm for the problem in small space complexity. Our algorithm is a counter-based algorithm with the aid of probabilistic counting. We show that our algorithm with k counters computes, with probability at least 1−δ, the estimation with relative error at most (1+ε)N/k, taking O(klog⁡log⁡Nk+klog⁡(ε−1δ−1k)+klog⁡ℓ) space in expectation, where N is the total number of items and ℓ is the number of different items.

Frequency estimation of multiple complex sinusoids using noise suppressing predictive FIR filter

The paper presents a predictive filter based frequency estimation algorithm (PF-FE) for multiple complex sinusoids corrupted by additive white Gaussian noise. The proposed frequency estimator combines the noise suppression capability of an FIR filter with a least squares approach minimizing the sum of the squared errors of a prediction filter. The FIR filter coefficients are chosen such that the sinusoidal components are predicted with minimum distortion. Computer simulation results are given to contrast the performance of the proposed PF-FE method with six other state-of-the-art frequency-estimators and the Cramer-Rao lower bound. Furthermore, the paper provides a complexity analysis of the PF-FE method and compares it with those of the conventional MUltiple SIgnal Classification algorithm and some selected state-of-the-art methods from the literature. Performance of the proposed PF-FE method is validated with effective mean square error (EMSE) plots for model orders of three and five and under different observation lengths and signal-to-noise ratio values. Finally, the paper demonstrates how EMSE varies for the proposed method when the prediction filter length is increased from 20 to 75. After extensive simulations, it is observed that when filter length is larger than half the observation length the EMSE will start to degrade.

An all-pass based internal model principle controller for galvanometer mirror steering

Galvanometer is a critical component for beam steering in additive manufacturing, profilometry, and medical imaging. In these applications, the quality of the process relies on the precision motion control of the galvanometer to either track or reject narrow-band signals. From the internal model principle, this can be accomplished by incorporating the dynamic model of the reference or disturbance signal in the feedback loop. This paper proposes an innovative internal model principle controller based on numerically robust all-pass filters. The main concept revolves around converting the controller design into a phase response design problem with all-pass filters. For the proposed approach, the targeted frequencies of the internal model can be arbitrarily placed without sacrificing the performance. Further, it produces lower-order controller and is robust against quantization effect. When combining with frequency estimation algorithm and adaptive filter, it can be readily applied to unknown and time-varying disturbance rejection. The advantages of the proposed method are demonstrated by comparing with conventional approaches through analysis, simulation, and experimentation.

Квазиправдоподобный алгоритм оценки частоты сверхширокополосного квазирадиосигнала с неизвестной длительностью

The quasi-likelihood frequency estimation algorithm of an ultra-wideband quasi-radio signal with an unknown duration, observed with white Gaussian noise, is studied. When synthesizing the frequency estimation algorithm, instead of an unknown duration, some of its expected value was used. The dependence of the variance of the frequency estimate of an ultra-wideband quasi-radio signal on the signal-to-noise ratio for various values of the duration detuning and the dependence of the frequency estimate bias on the duration detuning for various values of the narrowband parameter are obtained. It has been established that the duration detuning has a significant effect on the efficiency of frequency estimation of an ultra-wideband quasi-radio signal, while at large values of the narrowband parameter, the obtained expressions coincide with the known expressions for the variance and bias of the frequency estimate of narrowband radio signal. Recommendations on the use of the synthesized algorithm in practical applications are formulated.

전파 거리에 따른 신호의 감쇠와 분산이 고려된 순시 주파수 추정 알고리즘 및 장거리 전파용 반사파 계측법 시뮬레이터 개발

Time-Frequency domain Reflectometry(TFDR) is used for the purpose of fault detection and evaluating the integrity in cables. TFDR can diagnose live wire in nondestructive. but, the incident signal cannot aviod attenuation and dispersion according to increasing propagation distance, propagation velocity changes with propagation distance. attenuation and dispersion in long distance lead to decresing falut detection performance of cable. therefore, Developing instantaneous frequency Estimation algorithm of signal and signal restoration algorithm in order to determine tendency of propagation velocity for propagation distance, we demonstrate the performance of algorithm by implementing TFDR simulator possible long length.

Multi-sensor random sample consensus for instantaneous frequency estimation of multi-component signals

An instantaneous frequency estimation algorithm is developed for multi-component signals acquired through multiple sensors. The proposed method estimates the mixing matrix for the strongest source in the given multi-sensor recording. The information of the mixing matrix is used to extract the corresponding source through spatial filtering. The spatially filtered signal is then analyzed using adaptive directional time-frequency distribution. The instantaneous frequencies of the extracted sources are then estimated through the Random sample consensus (RANSAC) algorithm that involves the detection of peaks, fitting of the instantaneous frequency curve using Fourier series approximation, and evaluating the instantaneous frequency estimate using an objective function. Both the mixing matrix and instantaneous frequency information is used to remove the corresponding source from the mixture signal by employing time-frequency and spatial filtering. The process mentioned above is then repeated till the instantaneous frequencies of all the sources have been estimated. Once the instantaneous frequencies of all the sources have been estimated, each source's instantaneous frequency is re-estimated by removing all the other components using time-frequency and spatial filtering. Till convergence, the process is iterated. Through numerical results, it is shown that the proposed method performs better than the relevant methods in the state of the art.

Frequency estimation for underwater CW pulse by interpolation on fractional Fourier coefficients based on amplitude ratio method

Fast and accurate estimation of sinusoidal signals plays an important role in many fields like communications, radar, sonar, etc. In underwater signal processing applications, sinusoidal signals usually take the form of CW pulses in most practical applications, therefore, zero-padding and duty-cycle show their great importance to the estimation of sinusoidal signals. In this paper, a high-precision estimation algorithm of sinusoidal signal is proposed, which combines amplitude ratio algorithm and fractional Fourier coefficient interpolation algorithm. The proposed algorithm uses the adjacent spectral line ratio algorithm instead of the Fourier coefficient maximum amplitude discrete spectral line search algorithm for coarse estimation, and modifies the traditional interpolation method. The proposed algorithm improves the Fourier coefficient interpolation algorithm by combining zero-padded signals to achieve the accurate frequency estimation for zero-padded sinusoidal signal. The performance of the algorithm is also in accordance with theoretical level for zero-padded signals, which is a great improvement over the frequency estimation algorithm for non-padded signals as well as the algorithm for zero-padding signals. The theoretical results are verified by extensive computer simulations which show that the proposed algorithm can both achieve better results for zero-padding cases and maintain comparable performance with competing algorithms for the non-padded signal. Therefore, the algorithm can be better applied to practical underwater detection or communication signals.

Harmonics and intermodulation products-based fuzzy logic (HIPBFL) algorithm for vital sign frequency estimation using a UWB radar

The ultra-wide band (UWB) radar can achieve non-contact measurement of human vital sign including respiration and heartbeat. This can be applied in the fields of healthcare, security and search-rescue mission. At present, most studies adopt the relationship between harmonics and fundamental frequency to estimate the frequency of vital sign. In this work, the harmonics and intermodulation products-based fuzzy logic (HIPBFL) algorithm for vital sign frequency estimation is proposed. For the first time, to the best of our knowledge, intermodulation products information is considered to locate possible heart rates. Then a fuzzy logic system is designed to select the optimal heart rate from them. 120 s measurement experiment on human beings was carried out at the hospital. Compared with the commonly used chirp Z-transform and moving target indicator (CZT-MTI), the harmonic multiple loop detection (HMLD) and the variational mode decomposition (VMD), the proposed HIPBFL algorithm obviously improves the estimation accuracy of heart rate. This work paves a way for the investigation of non-contact vital signs monitoring via UWB radars.

Incorporating Prior Knowledge in Local Differentially Private Data Collection for Frequency Estimation

Local differential privacy (LDP) is a prevalent measure of privacy protection as it provides rigorous privacy guarantees and has been widely studied for statistical analysis, especially in frequency estimation. As a representative LDP-enabled frequency estimation algorithm, Google's <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Randomized Aggregation Privacy-Preserving Ordinal Response</i> (RAPPOR) has been put into practice. However, it achieves sub-optimal utility due to the following limitations. Firstly, the adoption of the MD5 hash function inevitably results in the hash collision. Secondly, the application of the randomized response technique leads to randomness. To improve the practical effectiveness of RAPPOR and the utility of frequency-based services, we propose an LDP-enabled frequency estimation method called PK-RAPPOR, in which we devise an effective re-encoding hash function (RE-HF) incorporating prior knowledge (PK) about the rough frequency ranking of items. RE-HF divides items into several cohorts based on the PK and generates a unique hash value set for each item. Compared with the original RAPPOR, the hash collision can be eliminated for items from different cohorts, and the effect of randomness can be decreased by the overlapping of items from the same cohorts. We validate our proposed method with theoretical analysis and demonstrate its effectiveness with experiments on both synthetic and real-world datasets.

Distributed MIMO CW Radar for Locating Multiple People and Detecting Their Vital Signs

The distributed-multiple-input multiple-output (MIMO) continuous-wave (CW) radar with low-intermediate frequency (low-IF) receiver that is proposed in this work uses uniform linear array (ULA) antennas to estimate the direction of arrival (DOA) of subjects and recover Doppler signals by the digital beamforming (DBF) technique. Without using any modulation bandwidth, the location of multiple subjects can be determined from the known antenna positions and the estimated DOAs. This work proves that the Doppler-weighted method improves the extraction of the initial phase of the baseband signal. With respect to the recovery of each subject’s vital signs, the modified-DBF is utilized to separate individual Doppler signals while nullifying interference. The frequency estimation algorithm (FEA) is used to improve the Doppler frequency and angular resolution by 50% and 44%, respectively, in the detection of two closely spaced moving metal plates. Finally, the presented system is experimentally validated by determining the locations and vital signs of people sitting side-by-side. The estimated DOA and position errors were less than 3.3° and 10 cm, respectively. With a 25 s sensing period, the errors in the measured respiration rates (RRs) and heart rates (HRs) were less than 1.2 breath/min and 3 beats/min, respectively.