Adaptive Notch Filter Research Articles

A Novel Adaptive Frequency Estimation Algorithm Based on Interpolation FFT and Improved Adaptive Notch Filter

Abstract The convergence rate and the continuous tracking precision are two main problems of the existing adaptive notch filter (ANF) for frequency tracking. To solve the problems, the frequency is detected by interpolation FFT at first, which aims to overcome the convergence rate of the ANF. Then, referring to the idea of negative feedback, an evaluation factor is designed to monitor the ANF parameters and realize continuously high frequency tracking accuracy. According to the principle, a novel adaptive frequency estimation algorithm based on interpolation FFT and improved ANF is put forward. Its basic idea, specific measures and implementation steps are described in detail. The proposed algorithm obtains a fast estimation of the signal frequency, higher accuracy and better universality qualities. Simulation results verified the superiority and validity of the proposed algorithm when compared with original algorithms.

An Adaptive Notch Gain Using an Inverse Notch Filter and a Linear Prediction Filter

SUMMARYThis paper proposes an adaptive notch filter that automatically adjusts the notch frequency and notch gain, where they are the null frequency and the depth of the null, respectively. The proposed notch filter consists of an inverse notch filter and a linear prediction filter, and gives an appropriate filter gain which can eliminate a sinusoidal noise and extract only a wide‐band signal even if they share the same frequency. We compare the capability of the proposed notch filter with traditional methods. Simulation results show that the proposed system improves the SNR in comparison to the conventional methods.

Correct Formulation of Gradient Characteristics for Adaptive Notch Filters Based on Monotonically Increasing Gradient Algorithm

Correct Formulation of Gradient Characteristics for Adaptive Notch Filters Based on Monotonically Increasing Gradient Algorithm

Resonant frequency estimation for adaptive notch filters in industrial servo systems

This paper proposes a new algorithm for estimating the resonant frequency of adaptive notch filters used in servo systems. Notch filters and adaptive notch filters are widely used in commercial servo systems for suppressing a resonance which is a major obstacle in improving their performance. However, the conventional frequency estimation algorithm gives a dynamic behavior that is proportional to the difference between the square of the estimated frequency and the square of the actual frequency. This can cause the estimation dynamics to be too slow for low-frequency resonances, if both low- and high-frequency resonances are present and if the estimator gain is designed for a high frequency. This paper develops a new algorithm to give a dynamic behavior that is proportional to the difference in the estimated frequency and actual frequency. This allows selecting the estimation parameters independent from the value of resonant frequencies. The developed algorithm is implemented to a production servo controller and applied to a production printed-circuit-board inspection system. The experimental results show that the developed algorithm is much more effective in suppressing the resonances of both low- and high-frequencies, compared to the pervious algorithm. Furthermore, the ability to suppress vibration allows increasing the feedback gain, which in turn allows improving the tack time performance from 190ms to 100ms. All experiments reported in this paper were performed in an actual industrial environment using a production system, and the developed algorithms are applied to the production system.

Performance Comparison of a Second-order adaptive IIR Notch Filter based on Plain Gradient Algorithm

This paper presents performance analysis of a second-order adaptive IIR notch filter with constrained poles and zeros in direct form II structure that is adapted by algorithms of indirect and direct frequency estimations based on plain gradient. In this work, the steady-state bias properties and stability bounds of both algorithms are derived in closed form. The simulated processes are performed in order to verify the analytical results. Furthermore, these results of the proposed filter are also compared with those results of the direct form I adaptive IIR notch filter under the same parameters. It has been revealed that the direct form II structure has given the steady-state performance over the direct form I structure.

368 - Circadian Rhythm Estimator Using Adaptive Notch Filter and Its Application to Locomotor Activity of Drosophila Melanogaster

The traditional method of circadian rhythm estimation is based on a double actogram that provides phase estimation on a daily basis, but not continuously and also fails to effectively filter noise. Our goal is to develop a circadian rhythm estimator that accurately and continuously estimates circadian phase while filtering noise. The estimator is a modified Adaptive Notch Filter (ANF), which is commonly used in signal processing. Drosophila Activity Monitor boxes house Drosophila fruit flies previously entrained to the same phase and contain sensors that measure the activity of flies. The actogram and ANF convert the raw data to a phase response curve (PRC), which describes the relationship between a stimuli (light) and circadian rhythm phase shift. White noise-corrupted data was also introduced to determine filtering effects. The PRC obtained from the actogram and ANF methods were nearly identical and also matched with literature values. With noise-corrupted data, the ANF PRC had an average error of 0.57 hours while the actogram PRC’s average error was 1.84 hours. The modified ANF is shown to be a valid and accurate method of modeling circadian rhythm continuously. The ANF was also able to successfully reject noise and the error against noise was very small compared to that of the actogram. Continuous circadian phase estimation allows more complex study of human circadian rhythm and further opens the possibility of personalized circadian rhythm estimation and light therapy.

Analysis of frequency estimation MSE for all-pass-based adaptive IIR notch filters with normalized lattice structure

This paper theoretically analyzes the Mean Square Error (MSE) on the steady-state frequency estimation realized by the all-pass-based adaptive notch filtering algorithms with the normalized lattice structure. The adaptive algorithms to be considered are the Simplified Lattice Algorithm (SLA) proposed by Regalia and the Affine Combination Lattice Algorithm (ACLA) proposed by the authors. For these two algorithms, we derive the frequency estimation MSE in closed-form. The derivation is based on construction of a linear time-invariant model for generation of frequency estimation error, and division of this model into two submodels of which output signals are statistically uncorrelated to each other. This strategy leads to more accurate theoretical MSE expressions than the direct use of the existing analysis methods. Simulation results demonstrate that our theoretical MSE expressions are in very good agreement with the simulated MSE values.

Forward Velocity Extraction From UAV Raw SAR Data Based on Adaptive Notch Filtering

Forward velocity extraction is a very important process for obtaining a high-quality unmanned aerial vehicle (UAV) synthetic aperture radar (SAR) image. Because of the constraints of low flying altitude and small platform size, the flight path of the UAV is easily disturbed by the atmospheric turbulence. The complex motion error of the UAV's flight path makes the forward velocity difficult to be extracted from raw SAR data. To address this problem, an adaptive notch filtering (ANF)-based approach for forward velocity extraction is proposed. Based on the kinetic characteristics of the UAV, the variation of Doppler centroid frequency is analyzed and exploited to remove most components of the cross-track acceleration in the low-frequency range. Then, by regarding the forward velocity component as a narrow-band component, ANF processing is employed to extract it from the estimated Doppler rate. Comparing with the methods reported in the literature, the ANF method can achieve higher accuracy and efficiency due to its excellent notching performance and strong suppression for narrow-band signals. Promising results from raw data experiments are presented to demonstrate the validity and superiority of the proposed method.

Hybrid Fluid-borne Noise Control in Fluid-filled Pipelines

This article reports on an initial investigation of a hybrid fluid-borne noise control system in hydraulic pipelines. The hybrid system is built by integrating an active feedforward noise controller with passive tuned flexible hoses. The active attenuator is designed to cancel the dominant harmonic pressure pulsations in the fluid line, while the passive hose is tuned to attenuate the residual high frequency pulsations. The active attenuator can effectively decrease the fluid-borne noise by superimposing a secondary anti-phase control signal. Adaptive notch filters with the filtered-X least mean square algorithm were applied for the controller and a frequency-domain least mean square filter was used for the secondary path on-line identification. The transmission line model was used to model the pipeline, and a time-domain hose model which includes coupling of longitudinal wall and fluid waves was used to model the flexible hose. Simulation results show that very good noise cancellation was achieved using the proposed approach, which has several advantages over existing fluid-borne noise control systems, being effective for a wide range of frequencies without impairing the system dynamic response much. While the flexible hoses may be less effective than purpose-built passive silencers, they can form an inexpensive and practical solution in combination with active control.

A Multifunctional Grid-Tied Solar Energy Conversion System With ANF-Based Control Approach

This paper presents a two stage three-phase grid-interfaced solar photovoltaic (SPV) energy conversion system with an adaptive notch filter (ANF)-based control algorithm. The proposed SPV system is a multifunction grid-interfaced SPV energy conversion system, which along with the conversion of dc-power from SPV to ac mains is capable of reactive power compensation, harmonics currents elimination, and load balancing in a three-phase ac distribution system. Compared with multiple devices with different functionalities, a multifunction grid-interfaced SPV energy conversion system is capable of saving substantially capital investment, space, and maintenance cost on behalf of multifunctional features. The ANF successfully extracts a single sinusoid of a possibly nonstationary nature from harmonics corrupted load currents at point of common coupling. The control algorithm is adaptive with respect to the fundamental frequency of the system as compared with other methods, and provides instantaneous values of the fundamental signals. Simulation and experimental results verify the validity of the presented algorithm and confirms its desirable transient and steady state performances. The total harmonics distortion of grid currents is found well under IEEE-519 standard, even under nonlinear loads.

Loop analysis of adaptive notch filters

Adaptive notch filters have been the focus of intense research for more than three decades. Low computational requirements and good performance make them attractive for tracking frequency modulated signals. Despite the extensive literature on adaptive notch filters, algorithm extensions and new models for describing the dynamics of the notch frequency continue to be proposed. In this study, the equivalence between adaptive notch filters using a plain gradient (PG) algorithm and frequency lock loops (FLLs) with exponential filtering is established. FLL theory is then used to analyse the noise performance and signal tracking capabilities of adaptive notch filters. A linear model describing the dynamics of the filter adaptation process is derived and the concepts of loop and Doppler bandwidths are introduced. Criteria based on the loop and Doppler bandwidths are suggested to set the PG adaptation step. Finally, algorithm extensions based on the FLL theory are proposed. Theoretical results are supported by Monte Carlo simulations which show the validity of the analysis performed.

Adaptive suppression method for DC‐link voltage offset in three‐phase four‐switch inverter‐fed PMSM drives

The DC-link voltage offset in three-phase four-switch (TPFS) inverter-fed permanent magnet synchronous motor (PMSM) drives deteriorates the linear modulation range severely, restricting the performance and adjustable speed range of the PMSM. An adaptive control method is proposed in this Letter to suppress the DC-link voltage offset in TPFS inverter-fed PMSM drives. By investigating the effects of four basic voltage vectors on the voltage offset, the proper compensating vectors, whose duration times are obtained by the closed-loop control, are added in each control period. Moreover, an adaptive notch filter is proposed to extract the offset component, providing excellent dynamic and steady performances even at extremely low rotor speed. Experimental results demonstrate the superiority of the proposed adaptive suppression method compared with previous methods.

From adaptive control to variable structure systems – seeking harmony

From adaptive control to variable structure systems – seeking harmony

A gradient-adaptive lattice-based complex adaptive notch filter

This paper presents a new complex adaptive notch filter to estimate and track the frequency of a complex sinusoidal signal. The gradient-adaptive lattice structure instead of the traditional gradient one is adopted to accelerate the convergence rate. It is proved that the proposed algorithm results in unbiased estimations by using the ordinary differential equation approach. The closed-form expressions for the steady-state mean square error and the upper bound of step size are also derived. Simulations are conducted to validate the theoretical analysis and demonstrate that the proposed method generates considerably better convergence rates and tracking properties than existing methods, particularly in low signal-to-noise ratio environments.

Results of instrumental observations of tidal wave propagation in the atmosphere

This paper presents the results of processing and analysis of acoustic waves in the surface layer of the atmosphere, registered at the Mikhnevo Geophysical Observatory, Institute of Geosphere Dynamics, Russian Academy of Sciences (IGD RAS). Using the autoregression model of digital series, the spectrum of acoustic oscillations was evaluated and the tidal waves in the envelopes of acoustic oscillations were distinguished. The tidal components with similar periods were separated using the method of extraction of harmonic components by using adaptive notch filters. The observed features of the spectrum of acoustic oscillations open up new opportunities for instrumental control over meteorological conditions and the establishment of general regularities controlling the regimes of energy-exchange processes in the Earth’s atmosphere.

CW interference mitigation in GNSS receiver based on frequency-locked loop

Global navigation satellite system (GNSS) receivers are highly susceptible to continuous wave (CW) interference because the received signals are extremely weak. Current interference mitigation techniques mainly use a notch filter or transform domain. This paper proposes a computationally effective algorithm based on a frequency-locked loop (FLL) to mitigate interference in GNSS receivers. The performance of the algorithm is validated through an analysis of the characteristics of the interference reduction filter and interference estimation precision. A Monte Carlo simulation is used to compare the proposed algorithm with various previous algorithms: the adaptive IIR notch filter, adaptive linear-phase FIR filter, and N-sigma DFT algorithm. The simulation results show that the proposed algorithm exhibits excellent interference estimation precision and superior anti-jamming performance compared with the conventional algorithms.

A self-optimization mechanism for generalized adaptive notch smoother

Tracking of nonstationary narrowband signals is often accomplished using algorithms called adaptive notch filters (ANFs). Generalized adaptive notch smoothers (GANSs) extend the concepts of adaptive notch filtering in two directions. Firstly, they are designed to estimate coefficients of nonstationary quasi-periodic systems, rather than signals. Secondly, they employ noncausal processing, which greatly improves their accuracy and can be applied whenever additional delay can be tolerated. The paper develops a novel performance assessment mechanism for GANS. It allows one to evaluate tracking accuracy of the smoother without prior knowledge of the true values of the system's frequency or coefficients. The extension can be employed to build a parallel bank of filters, which automatically chooses the one which is best matched to unknown and possibly time-varying tracking conditions.

Frequency estimation of sinusoids from nonuniform samples

Sinusoid signals with multiple frequencies appear in various systems and their frequencies may carry some important features. Frequency estimation from their discrete samples is one of the fundamental problems and many frequency estimators have been proposed for uniform sampling setting. In this paper, frequency estimators based on adaptive notch filtering are proposed for nonuniform sampling setting. We observe that some dynamic systems associated with adaptive notch filters can be solved in nonuniformly sampled time steps with high accuracy. This leads us to propose a digital adaptive notch filtering method to estimate frequency of a sinusoidal signal with single frequency from its nonuniform samples. The proposed method exhibits convergent and robust frequency estimation in the presence of random sampling noises, and its variance is comparable to the Cramer–Rao lower bound in the presence of additive white noise. The above method designed for single frequency estimation could track abrupt single frequency change of an input signal, but it is not applicable directly for multiple frequency estimation. Our simulations show that the proposed estimators have robust performance for sinusoidal signals with multiple distinct frequencies, and they can be used to separate two very close frequencies of an input signal in a highly noisy sampling environment.

Comparison of different filtering strategies to reduce noise in strain measurement with digital image correlation

The main limitation of digital image correlation is the remarkable noise affecting the digital image correlation–computed strain distributions. Neither manufacturers of digital image correlation systems nor the literature provide guidelines for optimal filtering of digital image correlation strain distributions. However, filtering is also associated with loss of information (smoothing of the strain gradients). We systematically explored different filtering strategies to reduce noise while minimizing the loss of information in the digital image correlation–computed strain distributions. The first filtering strategy was directly applied to the acquired images that were then fed to the digital image correlation software. Median adaptive low-pass filters and notch filters were used to eliminate noise: both strategies increased (rather than reducing) the noise in the digital image correlation–computed strain distributions. The second strategy explored was a Gaussian low-pass filtering of the strain distributions. When the optimal cutoff frequency was selected, the noise was remarkably reduced (by 70%) without excessive loss of information. At the same time, when non-optimal cutoff frequencies were used, the residual noise and/or loss of information seriously compromised the results. Finally, image combination techniques were applied both to the input images and to the strain distributions. This strategy was extremely time-consuming but not very effective (noise reduction <10%). In conclusion, the only truly effective noise reduction strategy, if measurements are carried out using commercial closed software, consists in filtering the strain distribution.

Correlation theory-based signal processing method for CMF signals

Signal processing precision of Coriolis mass flowmeter (CMF) signals affects measurement accuracy of Coriolis mass flowmeters directly. To improve the measurement accuracy of CMFs, a correlation theory-based signal processing method for CMF signals is proposed, which is comprised of the correlation theory-based frequency estimation method and phase difference estimation method. Theoretical analysis shows that the proposed method eliminates the effect of non-integral period sampling signals on frequency and phase difference estimation. The results of simulations and field experiments demonstrate that the proposed method improves the anti-interference performance of frequency and phase difference estimation and has better estimation performance than the adaptive notch filter, discrete Fourier transform and autocorrelation methods in terms of frequency estimation and the data extension-based correlation, Hilbert transform, quadrature delay estimator and discrete Fourier transform methods in terms of phase difference estimation, which contributes to improving the measurement accuracy of Coriolis mass flowmeters.