ArticlePublisher preview available

Frequency estimation using distributed adaptive algorithm with noisy regressor

Authors:
Sananda Kumar at KIIT University
Sananda Kumar
Upendra Kumar Sahoo at National Institute of Technology Rourkela
Upendra Kumar Sahoo
Ajit K. Sahoo
Ajit K. Sahoo
Ajit K. Sahoo
  • This person is not on ResearchGate, or hasn't claimed this research yet.
Read publisher preview
Download citation
To read the full-text of this research, you can request a copy directly from the authors.

Abstract and Figures

A smart discrete Fourier transform based modified diffusion technique is proposed in this paper that estimates the frequency in presence of regressor noise. This technique explores iterative relationship between the consecutive DFT in the form of smart DFT, and employs least mean square algorithm to measure and track the frequency. Multiple sensor nodes are employed to explore the time and space diversity following diffusion technique to improve frequency estimation. The classical diffusion algorithm is modified to address the presence of noise in regressor data. The efficacy of the modified algorithm is presented here following mathematical derivation to match both theoretical and simulation results.
Figures - available from: Multidimensional Systems and Signal Processing
This content is subject to copyright. Terms and conditions apply.
A preview of this full-text is provided by Springer Nature.
Learn more
Content available from Multidimensional Systems and Signal Processing
This content is subject to copyright. Terms and conditions apply.
Multidimensional Systems and Signal Processing (2022) 33:1185–1201
https://doi.org/10.1007/s11045-022-00837-9
Frequency estimation using distributed adaptive algorithm
with noisy regressor
Sananda Kumar1·Upendra K. Sahoo2·Ajit K. Sahoo2
Received: 22 January 2022 / Revised: 10 June 2022 / Accepted: 16 June 2022 /
Published online: 8 July 2022
© The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2022
Abstract
A smart discrete Fourier transform based modified diffusion technique is proposed in this
paper that estimates the frequency in presence of regressor noise. This technique explores
iterative relationship between the consecutive DFT in the form of smart DFT, and employs
least mean square algorithm to measure and track the frequency. Multiple sensor nodes are
employed to explore the time and space diversity following diffusion technique to improve
frequency estimation. The classical diffusion algorithm is modified to address the presence
of noise in regressor data. The efficacy of the modified algorithm is presented here following
mathematical derivation to match both theoretical and simulation results.
Keywords LMS ·DFT ·ATC diffusion ·Noisy regressor
1 Introduction
System frequency is a key property of voltage and current that is used by many applications
for monitoring, protection and control purpose. Accurate frequency estimation is very essen-
tial, as maintaining a nominal frequency is prerequisite for managing stability and normal
operation of any device. Assuming any power system signal to be pure form of sinusoid sig-
nal, the time between two zero cross over points is referred to as the time period of the signal
(Begovic et al. 1993). However the signals in practical never appear in its pure form rather
they contain noise and distortion. To overcome such problems in estimation of frequency,
lot of algorithms have been introduced like notch filtering method (Mojiri et al. 2007;Li
and Wang 2015), phase locked loop (Karimi et al. 2004; Karimi-Ghartemani et al. 2010),
BSananda Kumar
sananda.kumarfet@kiit.ac.in
Upendra K. Sahoo
sahooupen@nitrkl.ac.in
Ajit K. Sahoo
ajitsahoo@nitrkl.ac.in
1School of Electronics, KIIT DU, Bhubaneswar, Odisha 751024, India
2Electronics Department, National Institute of Technology, Rourkela, Odisha 769008, India
123
Content courtesy of Springer Nature, terms of use apply. Rights reserved.
Frequency-Domain Prony Method for Autoregressive Model Identification and Sinusoidal Parameter Estimation
Article
Full-text available
  • Jun 2020
In this study, the weighted integral method for identifying differential equation models is extended to a discrete-time system with a difference equation (DE) model and a finite-length sampled data sequence, and obtain a frequency-domain algorithm for short-time signal analysis and frequency estimation. The derivation consists of three steps. 1) Provide the DE (autoregressive model) with unknown coefficients, which is satisfied in a finite observation interval. 2) Discrete Fourier transform (DFT) the DE to obtain algebraic equations (AEs) among the Fourier coefficients. Two mathematical techniques are introduced to maintain the circulant nature of time shifts. 3) Simultaneously solve a sufficient number of AEs with least squares criterion to obtain unknowns exactly when the driving term is absent, or to obtain unknowns that minimize the driving power when it is present. The methods developed enable a decomposed processing of identification and estimation in the frequency domain. Thus, they will be suitable for maximizing statistical efficiency (smallness of estimation error variance), reducing the computational cost, and use in a resolution-enhanced time-frequency analysis of real-world signals. The performance of the proposed methods are compared with those of several DFT-based methods and Cramer-Rao lower bound. Also, the interference effect and its reduction in frequency-decomposed processing are examined.
View
Accurate Frequency Estimator of Sinusoid Based on Interpolation of FFT and DTFT
Article
Full-text available
  • Mar 2020
An accurate frequency estimator of complex sinusoid in additive white noise is proposed. It is based on interpolation of Fast Fourier Transform (FFT) and Discrete-Time Fourier Transform (DTFT). Zero-padding is firstly performed before the FFT of the sinusoid sampled data, and the coarse estimate is obtained by searching the discrete frequency index of the maximum FFT spectrum line. Then the fine estimate is obtained by employing the maximum FFT spectrum line and two DTFT sample values located on the left and right side of the maximum spectrum line. The correlation coefficients between the Fourier Transform of the noises on two arbitrarily spaced spectrum lines are derived, and the MSE calculation formula is derived in additive white noise background based on the correlation coefficients. Simulations results demonstrate that the proposed algorithm has lower MSE than the competing algorithms, and its signal-to-noise ratio (SNR) threshold is lower compared with Candan algorithm, AM algorithm and Djukanovic algorithms.
View
Diffusion LMS Strategies in Sensor Networks with Noisy Input Data
Article
Full-text available
  • Sep 2014
We investigate the performance of distributed least-mean square (LMS) algorithms for parameter estimation over sensor networks where the regression data of each node are corrupted by white measurement noise. Under this condition, we show that the estimates produced by distributed LMS algorithms will be biased if the regression noise is excluded from consideration. We propose a bias-elimination technique and develop a novel class of diffusion LMS algorithms that can mitigate the effect of regression noise and obtain an unbiased estimate of the unknown parameter vector over the network. In our development, we first assume that the variances of the regression noises are known a-priori. Later, we relax this assumption by estimating these variances in real-time. We analyze the stability and convergence of the proposed algorithms and derive closed-form expressions to characterize their mean-square error performance in transient and steady-state regimes. We further provide computer experiment results that illustrate the efficiency of the proposed algorithms and support the analytical findings.
View
View
A sliding-window DFT based algorithm for parameter estimation of multi-frequency signal
Article
  • Nov 2019
A sliding-window DFT (SWDFT) based two-step algorithm is proposed for parameter estimation of multi-frequency signal with high accuracy. In the first step, the SWDFT sequence in frequency-domain varied with time instant is obtained by performing the SWDFT on the input signal, where the coarse frequency is estimated. It has been proved that the SWDFT of a multi-frequency signal possesses the same linear relationship as the original time-domain signal and the signal-to-noise ratio (SNR) of each frequency component is enhanced by the SWDFT. In the second step, the parameters are estimated with high accuracy by a linear prediction from the SWDFT sequence, where the complex-valued least squares (CLS) framework is used. Computer simulation and practical measurement results show that the proposed algorithm can estimate parameters of a multi-frequency signal distorted by noise with high accuracy.
View
Fast and Efficient Sinusoidal Frequency Estimation by Using the DFT Coefficients
Article
  • Dec 2018
Fast and accurate frequency estimation of a complex sinusoidal plays an important role in many applications including communications, radar, and sonar. This paper presents two methods for the frequency estimation of a complex sinusoidal in noisy environments. The proposed methods interpolate on shifted DFT coefficients to acquire the frequency estimates iteratively. The first method interpolates on the q-shifted DFT coefficients of the signal, whose optimum iteration number is found to be a logarithmic function of the signal length. Furthermore, we also show that by appropriately selecting the value of the shift q, the proposed method becomes asymptotically efficient. In the second method, we use hybrid half-shifted and q-shifted DFT interpolators together, which converges in only two iterations. It is shown that both of the estimators are asymptotically unbiased with their mean square errors performing on the Cráamer- Rao lower bound. Theoretical results are validated by extensive computer simulations.
View
Distributed Frequency Estimation Over Sensor Network
Article
  • Jul 2015
Frequency estimation is a common problem in a variety of applications. In recent years, adaptive notch filtering methods have been widely adopted for solving frequency estimation problems. For frequency estimation performed by a single node, the sampling time may not be long enough, the sampling rate may not be high enough, and the noise effect may be serious. In such situations, most existing algorithms for frequency estimation can not produce accurate enough results. Here, we propose using wireless sensor networks for sampling data distributedly, and using distributed notch filtering method for dealing with this problem. In particular, we propose two distributed algorithms over sensor network, a least mean square-based distributed notch filtering (dNF) algorithm and a total least square-based dNF algorithm. The communication cost of the new proposed algorithms is low, as each node exchanges only with its neighbors the estimates other than the original data. The proposed algorithms are applied to both synthetic and real examples. Simulation results demonstrate the effectiveness of the new proposed algorithms.
View
A Complex Least Squares Enhanced Smart DFT Technique for Power System Frequency Estimation
Article
  • Jan 2015
A complex-valued least squares (CLS) framework is proposed in order to enhance the accuracy of the smart discrete Fourier transform (SDFT) algorithms [1], [2] for power system frequency estimation in the presence of both noise and harmonic pollution. It is first established that the underlying time series relationship among the consecutive DFT fundamental components employed by the original SDFT algorithms does not hold when noises or unexpected higher order harmonics are present, resulting in suboptimal estimation performances. To eliminate these adverse effects on the frequency estimation, the degree of the relationship breakdown is next quantified via a model mismatch error vector. The complex-valued least squares (CLS) technique is then employed to minimise the mean square model deviation when the SDFT voltage modelling is suboptimal. The proposed CLS-enhanced SDFT (CLS-SDFT) methods are shown to be more accurate than the original ones in heavily noisy and harmonic distorted environments, typical scenarios in on-line frequency estimation. The benefits of the SDFT framework are verified by simulations for various power system conditions, as well as for real-world measurements.
View
Frequency Estimation of Distorted and Noisy Signals in Power Systems by FFT-Based Approach
Article
  • Mar 2014
This paper focuses on the accurate frequency estimation of power signals corrupted by a stationary white noise. The noneven item interpolation FFT based on the triangular self-convolution window is described. A simple analytical expression for the variance of noise contribution on the frequency estimation is derived, which shows the variances of frequency estimation are proportional to the energy of the adopted window. Based on the proposed method, the noise level of the measurement channel can be estimated, and optimal parameters (e.g., sampling frequency and window length) of the interpolation FFT algorithm that minimize the variances of frequency estimation can thus be determined. The application in a power quality analyzer verified the usefulness of the proposed method.
View
Adaptive Frequency Estimation in Smart Grid Applications: Exploiting Noncircularity and Widely Linear Adaptive Estimators
Article
  • Sep 2012
Accurate estimation of system frequency in real time is a prerequisite for the future smart grid, where the generation, loading, and topology will all be dynamically updated. In this article, we introduce a unified framework for the estimation of instantaneous frequency in both balanced and unbalanced conditions in a three-phase system, thus consolidating the existing approaches and providing next-generation solutions capable of joint adaptive frequency estimation and system fault identification. This is achieved by employing recent developments in the statistics of complex variables (augmented statistics) and the associated widely linear models, allowing us to benefit from a rigorous account of varying degrees of noncircularity corresponding to different sources of frequency variations. The advantages of such an approach are illustrated for both balanced and unbalanced conditions, including voltage sags, harmonics and supply-demand mismatch, all major obstacles for accurate frequency estimation in the smart grid.
View