Approach For Frequency Estimation Research Articles

Systematic Control Design for Adaptive Rejection of Narrow-Band Disturbances Based on a Novel Resonant Generalized Extended State Observer

In this paper, the adaptive rejection of multiple narrow-band disturbances with time-varying frequencies is investigated. A systematic control approach based on a resonant generalized extended state observer (RGESO) is proposed. The frequency response of the RGESO is shaped into a desired form to reject the total disturbance, including the wide-band uncertainties and the narrow-band disturbances. The state-space realization of the RGESO is also provided to estimate both the states and the total disturbance. To handle the time-varying frequencies of the narrow-band disturbances, a direct frequency estimation approach based on the Levenberg–Marquardt method and an online supervision strategy is presented to improve convergence and reliability, and the estimations are then used to adapt the RGESO parameters. Parameter tuning and stability robustness analysis methods are also developed for the proposed scheme to facilitate its application. Finally, extensive simulations are conducted to demonstrate the effectiveness of our method.

A Quartic Polynomial Based Approach for Multi-Sinusoidal Frequency Estimation

A Quartic Polynomial Based Approach for Multi-Sinusoidal Frequency Estimation

Frequency Acquisition Approach in Polarization-Modulated Ranging Based on Lock-in Analysis

In this study, we propose a frequency measurement and estimation approach based on a lock-in analysis for precise frequency determination in polarization-modulated ranging signals. In this method, the modulation signal of an electro-optic modulator (EOM) is manipulated to introduce an intermediate frequency (IF) component into the detected signal. Subsequently, the detected signal is analyzed using lock-in analysis techniques to extract the necessary frequency component, and a new swept frequency waveform is generated, facilitating the frequency acquisition and distance calculation. We conducted theoretical derivations, simulations and experiments to validate the effectiveness of this method. The research findings suggest that our method can enhance the accuracy of frequency measurements by a factor of approximately ten when compared to a direct detection approach, leading to a corresponding improvement in ranging precision. Furthermore, even with larger sweep step sizes and smaller modulation frequencies, the proposed approach can achieve superior ranging results.

Low complexity subspace approach for unbiased frequency estimation of a complex single-tone

We propose a single-tone frequency estimator of a one-dimensional complex signal in complex white Gaussian noise. The estimator is based on the subspace approach and the unitary transformation. Due to its low space and time-complexity, we name the estimator as Low complexity Unitary Principal-singular-vector Utilization for Model Analysis (LUPUMA). Regardless of the observation length, LUPUMA provides a uniform estimation variance over the whole frequency range, while achieving the lowest time-complexity among subspace methods. The proposed estimator asymptotically reaches the Cramér-Rao Lower Bound. For short observations, the signal-to-noise ratio threshold of LUPUMA corresponds to the threshold of the maximum likelihood estimator. The low space and time-complexity along with the stable and state-of-the-art estimation performance for short observations make LUPUMA an ideal candidate for applications with a limited number of signal samples, limited computational power, limited memory, and for applications that require rapid processing time (low latency).

Performance Optimization in Frequency Estimation of Noisy Signals: Ds-IpDTFT Estimator.

This research presents a comprehensive study of the dichotomous search iterative parabolic discrete time Fourier transform (Ds-IpDTFT) estimator, a novel approach for fine frequency estimation in noisy exponential signals. The proposed estimator leverages a dichotomous search process before iterative interpolation estimation, which significantly reduces computational complexity while maintaining high estimation accuracy. An in-depth exploration of the relationship between the optimal parameter p and the unknown parameter δ forms the backbone of the methodology. Through extensive simulations and real-world experiments, the Ds-IpDTFT estimator exhibits superior performance relative to other established estimators, demonstrating robustness in noisy conditions and stability across varying frequencies. This efficient and accurate estimation method is a significant contribution to the field of signal processing and offers promising potential for practical applications.

A Low-Cost and Accurate Microwave Sensor System for Permittivity Characterization

A novel low-cost microwave sensor system is proposed for accurate sensing of the real relative permittivity of materials under test (MUT). The proposed solution eliminates the need for using advanced measurement devices such as the vector network analyzer (VNA) for sensor characterization. The proposed sensor system is built on a software-defined radio platform. A suitable two-stage frequency estimation approach was developed for estimating the frequency shift of the resonator sensor associated with the real relative permittivity of the MUT. First, the neighborhood of the resonance frequency is obtained utilizing a low-resolution coarse search, followed by a fine search method to accurately estimate the resonance frequency. For the fine search, we modified the AM frequency estimation algorithm and the Golden-Section search algorithm, GS method to suite the proposed sensor system. The performance of the proposed sensor system is validated through simulations and experiments. To demonstrate the feasibility of the concept, experiments were conducted by implementing the solution on a Universal Software Radio Peripheral (USRP) transceiver using a resonator sensor for detecting the binary mixture of water and methanol. The results show that the proposed sensor system achieves measurement accuracy comparable to advanced equipment such as the VNA. Thus, the proposed sensor system could be a low-cost alternative for sensor characterization purposes with accuracy comparable to standard equipment.

Advantages of a Statistical Estimation Approach for Clock Frequency Estimation of Heterogeneous and Irregular CGRAs

Estimating the maximum clock frequency of homogeneous Coarse Grained Reconfigurable Arrays/Architectures (CGRAs) with an arbitrary number of Processing Elements (PE) is difficult. Clock frequency estimation of highly heterogeneous CGRAs takes additional factors into account, thus is even more difficult. Main challenges are the heterogeneous set of operators for each Processing Element (PE) and the irregular interconnect (connecting a CGRA’s PEs). Multiple estimation approaches could be reasonable. We propose an optimized statistical estimator, which is based on our prior work. We demonstrate its superiority to state-of-the-art neural networks in terms of accuracy and robustness, especially in situations with a sparse set of training data.

A wide-area nodal frequency estimation and tracking approach

Synchronization of the nodal frequencies at a nominal frequency value throughout the network is essential for ensuring the reliable operation of the entire power system. This synchronization is achieved by maintaining a near real-time generation load balance. A large disturbance in this balance results in frequency deviations in time and space. Since significant frequency deviations can lead to load shedding, operating instability, and even blackouts, system operators use a combination of control actions to restore the system frequency very close to its nominal level. The effectiveness of these control actions, however, will depend on the accuracy with which the system-wide frequency is measured. A novel approach for directly tracking the frequency at each node of an electric power system is proposed in this paper. This approach is based on a tracking state estimation and considers two different methodologies, according to the existing time frame between estimations. Lastly, case studies are presented to evaluate the proposal's effectiveness in estimating nodal frequencies and directly observing interarea oscillations from the state estimation results.

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.

Taking Account of Seasonality in a Regional Flood Frequency Estimation Approach Based on Event Simulations

Regional flood estimation is an important issue in hydrology to anticipate and reduce the damages caused by extreme rainfall events. Approaches based on event simulation are particularly suitable to address this. As research has demonstrated the seasonality of rainfall characteristics, many flood frequency estimation approaches take into account rainfall seasonality to include seasonal fluctuations. For an event-based approach, since its hydrological model is initialized for each rainfall event, its performance is very sensitive to the initial states of the model. The seasonality of its hydrological model could thus become a decisive factor. Due to the complexity of the regionalization method, very few flood frequency estimation approaches based on event simulation have been regionalized at a large scale and do not consider the seasonality of hydrological parameters. This is the case for the SHYREG method studied in this article. Using data from HYDRO French database and SAFRAN, we discuss several adapted configurations considering the seasonality of both rainfall and hydrological parameters during its calibration and regionalization phase. Tests were carried out on 1929 catchments throughout France. Rather than calibrating a constant annual parameter for the hydrological model, we calibrated “winter” and “summer” parameters based on different observed flow quantiles (“seasonal”, “annual”, or “both”). Criteria on flood quantiles were calculated for different samplings. We also discuss the representativeness of seasonal parameters for the regionalization procedure and hydrological coherence observed from this seasonal parameterization. It seems that calibrating parameters based on seasonal flow quantiles helps reproduce annual quantiles, while the opposite is not possible. Among all the calibration configurations, calibration performed on both seasonal and annual flow quantiles makes the largest improvement compared to the initial annual parameterization method. It can correctly restitute seasonal flood quantiles for both calibration and validation catchments, with an obvious improvement in terms of estimating flood frequency in ungauged sites. It shows that the seasonality of hydrological parameters is worth considering for a regional flood estimation approach.

Sine Fourier Transform-based Frequency Estimation

This paper presents an approach for frequency estimation based on applying a sine Fourier transform and observations of particularly selected characteristic points of sidelobes. The bias of frequency estimation caused by the refusal to complement the developed algorithm by a corresponding cosine transform is eliminated by a specific selection of frequencies, for which a Fourier transform is calculated, and consecutive iteration of calculations is done for various durations of the analyzed signal. This paper also presents approaches for the recognition of a frequency interval with the exact value of frequency for a case of an analyzed signal with noise contamination.

Low-Complexity High-Resolution Frequency Estimation of Multi-Sinusoidal Signals

High-resolution frequency estimation is crucial for some applications. Accordingly, the present study proposes three high-performance computationally-efficient methods for high-resolution frequency estimators, which are designed based on a modified likelihood function. Traditional maximum likelihood based approaches for high-resolution frequency estimation are inefficient since the associated optimization problem is non-convex. Accordingly, in the first estimator proposed in this study, the amplitudes and frequencies of the multi-sinusoidal signals are estimated iteratively based on a simple linear Taylor approximation and a low-dimensional closed-form solution in every iteration. In the second estimator, the frequencies are determined directly using a primal decomposition approach and a gradient descent search method. Finally, a novel low-complexity parallel interference cancellation (PIC)-based frequency estimation approach is developed. The simulation results show that the proposed designs not only meet the Cramér-Rao lower bound (CRLB) in most cases of the conducted examples, but also possess lower computational complexity than existing state-of-the-art approaches.

Adaptive Photonic Microwave Instantaneous Frequency Estimation Using Machine Learning

Instantaneous microwave frequency estimation enables numerous essential applications in the commercial, defense, and civilian marketplace. The advancement of applications is hindered by the bottleneck in electronic-based frequency measurement systems including narrow bandwidth, high errors rate, and low dynamic range. Photonics-based frequency estimation approaches not only increase the operation frequency range and provide rapid measurement response, but also benefit from immunity to electromagnetic interference and enhancement in system adaptability. Despite the unique advantages offered by photonics-based frequency estimation approaches, it is challenging to obtain linear mapping between the unknown frequency and the measured optical characteristics due to the nonlinear response in electro-optical devices, which consequently results in degradation in measurement precision and a complex calibration relationship. Therefore, it is critical to mitigate the challenge to achieve dynamic, adaptive, and high-precision estimation of microwave frequency. To this end, this letter presents the design and demonstration of a high-precision photonic based instantaneous frequency estimation system driven by machine learning. A three-layer deep neural network is used to tackle device nonlinearity and system noise, resulting in absolute error of < 50 MHz and root mean square error of 1.1 MHz.

An Automated Approach for Electric Network Frequency Estimation in Static and Non-Static Digital Video Recordings.

Electric Network Frequency (ENF) is embedded in multimedia recordings if the recordings are captured with a device connected to power mains or placed near the power mains. It is exploited as a tool for multimedia authentication. ENF fluctuates stochastically around its nominal frequency at Hz. In indoor environments, luminance variations captured by video recordings can also be exploited for ENF estimation. However, the various textures and different levels of shadow and luminance hinder ENF estimation in static and non-static video, making it a non-trivial problem. To address this problem, a novel automated approach is proposed for ENF estimation in static and non-static digital video recordings. The proposed approach is based on the exploitation of areas with similar characteristics in each video frame. These areas, called superpixels, have a mean intensity that exceeds a specific threshold. The performance of the proposed approach is tested on various videos of real-life scenarios that resemble surveillance from security cameras. These videos are of escalating difficulty and span recordings from static ones to recordings, which exhibit continuous motion. The maximum correlation coefficient is employed to measure the accuracy of ENF estimation against the ground truth signal. Experimental results show that the proposed approach improves ENF estimation against the state-of-the-art, yielding statistically significant accuracy improvements.

An automated approach for fringe frequency estimation and removal in infrared spectroscopy and hyperspectral imaging of biological samples

In infrared spectroscopy of thin film samples, interference introduces distortions in spectra, commonly referred to as fringes. Fringes may alter absorbance peak ratios, which hampers the spectral analysis. We have previously introduced extended multiplicative signal correction (EMSC) for fringes correction. In the current article, we provide a robust open-source algorithm for fringe correction in infrared spectroscopy and propose several improvements to the Fringe EMSC model. The suggested algorithm achieves a more precise fringe frequency estimation by mean centering of the measured spectrum and applying a window function prior to the Fourier transform. It selects two frequencies from a user defined number of maxima in the Fourier domain. The improved Fringe EMSC algorithm is validated on two experimental datasets, one of them being a hyperspectral image. Techniques for separating sample spectra from background spectra in hyperspectral images, and techniques to identify spectra affected by fringes are also provided.

A novel frequency tracker for sinusoidal signal based on state dependent Riccati Equation filter

This paper presents a new approach for frequency estimation and tracking based on State Dependent Riccati Equation Filter (SDREF). The SDREF is an alternative concept to the well-known Extended Kalman Filter (EKF) to design a robust nonlinear filter, with low computational costs and better performances. The aim is to estimate and track the time-varying fundamental frequency of harmonic sinusoidal signals in general and more particularly the fundamental electric frequency. Through this study, the performance of the proposed approach is compared to the widely adopted the EKF, taking into account several aspects both theoretically and real-life applications. It has been shown that the proposed estimator performs better than the usual EKF estimator in terms of noise robustness, estimation accuracy, and tracking ability both in numerical simulations and experimental study.

High speed trains communication systems in 5G cellular networks

In this paper, a new transmitter-receiver structure for high speed train (HST) data transmission and detection in fifth generation (5G) communication systems is proposed. This structure employs a new Doppler shift frequency (DSF) estimation approach, projected in this paper, to calculate the channel taps' DSFs at the base station (BS) receiver. The estimated DSFs are used to calculate the channel taps' angle of departures (AoDs). Considering the estimated AoDs, the transmitter beamformer regulates its coefficients to suppress the non-line of sight channel taps (NLoSCTs) and a DSF compensation block is employed to alleviate the line of sight channel tap's (LoSCT's) DSF. The proposed DSF estimation approach is a two-phase scheme which obtains a coarse estimation of DSFs at the first phase and calculates DSFs more accurately at the second phase. While this two-phase DSF estimation approach is able to estimate DSFs in both multipath rich and Rician channel models, an alternative DSF estimation scheme for Rician channel models is proposed which can estimate the LoSCT's DSF with much lower computational complexity compared to the two-phase DSF estimation method. Simulation results indicate the fidelity of the proposed DSF estimation methods and the proposed transmitter-receiver structure.

Deep Learning versus Spectral Techniques for Frequency Estimation of Single Tones: Reduced Complexity for Software-Defined Radio and IoT Sensor Communications.

Despite the increasing role of machine learning in various fields, very few works considered artificial intelligence for frequency estimation (FE). This work presents comprehensive analysis of a deep-learning (DL) approach for frequency estimation of single tones. A DL network with two layers having a few nodes can estimate frequency more accurately than well-known classical techniques can. While filling the gap in the existing literature, the study is comprehensive, analyzing errors under different signal-to-noise ratios (SNRs), numbers of nodes, and numbers of input samples under missing SNR information. DL-based FE is not significantly affected by SNR bias or number of nodes. A DL-based approach can properly work using a minimal number of input nodes N at which classical methods fail. DL could use as few as two layers while having two or three nodes for each, with the complexity of O{N} compared with discrete Fourier transform (DFT)-based FE with O{Nlog2 (N)} complexity. Furthermore, less N is required for DL. Therefore, DL can significantly reduce FE complexity, memory cost, and power consumption, which is attractive for resource-limited systems such as some Internet of Things (IoT) sensor applications. Reduced complexity also opens the door for hardware-efficient implementation using short-word-length (SWL) or time-efficient software-defined radio (SDR) communications.

A Reduced Complexity Tensor Approach for Order Selection and Frequency Estimation

This paper presents a reduced complexity tensor approach for order selection and subspace-based frequency estimation. The proposed covariance tensor based order selection algorithm, termed as CT-OS, uses singular values of the covariance tensor formed from the 1D noisy observations of multiple complex sinusoids. Experimental results show that the CT-OS algorithm is capable of providing accurate order selection under short observations and is robust under medium to high signal-to-noise ratios. The proposed covariance tensor based frequency estimator, termed as CT-FE, utilizes a singular vector matrix in the higher-order singular value decomposition of the covariance tensor. Experimental results show that the CT-FE outperforms the subspace alignment and separation algorithm (SAS-Est) and a recent two-stage order and frequency estimation algorithm. Furthermore, both theoretical analysis and experimental results demonstrate reduced computational complexity and time for the proposed CT-OS against the recent covariance tensor based order estimation algorithm CTB-OE. The CT-FE algorithm is also shown to enjoy reduced computational complexity and time when compared with the frequency estimator SAS-Est.

Method Consideration of Variation Diagnosis and Design Value Calculation of Flood Sequence in Yiluo River Basin, China

The conventional approaches of the design flood calculation are based on the assumption that the hydrological time series is subject to the same distribution in the past, present, and future, i.e., the series should be consistent. However, the traditional methods may result in overdesign in the water conservancy project since the series has non-stationary variations due to climate change and human activities. Therefore, it is necessary to develop a new approach for frequency estimation of non-stationary time series of extreme values. This study used four kinds of mutation test methods (the linear trend correlation coefficient, Mann–Kendall test, sliding t-test, and Pettitt test) to identify the trend and mutation of the annual maximum flow series (1950–2006) of three hydrological stations in the Yiluo River Basin. Then we evaluated the performance of two types of design flood methods (the time series decomposition-synthesis method, the mixed distribution model) under the impacts of climate change and human activities on hydro-meteorological conditions. The results showed that (a) the design flood value obtained by the time series decomposition-synthesis method based on the series of the backward restore is larger than that obtained by the decomposition synthesis method based on the series of the forward restore; (b) when the return period is 100 years or less, the design flood value obtained by the mixed distribution model using the capacity ratio parameter estimation method is less than that obtained by the hybrid distribution model with simulated annealing parameter estimation method; and (c) both methods can overcome sequence inconsistency in design frequencies. This study provides insight into the frequency estimation of non-stationary time series of extreme values under the impacts of climate change and human activities on hydro-meteorological conditions.