Variable Step-size LMS Algorithm Research Articles

Adaptive Satellite Navigation Anti-Interference Algorithm Based on Inverse Cosine Function

Contrasting the dilemma that the traditional time-domain least mean square (LMS) algorithm in the existing satellite navigation receiver anti-interference system cannot satisfy the convergence time is short and maintain a low level of steady-state error at the same time, an inverse cosine variable step size LMS algorithm (ICVS-LMS) is proposed. To begin with, the LMS algorithm, with a fixed step size focuses on its effectiveness in attenuating and suppressing interference signals, is analyzed, and then the proposed ICVS-LMS algorithm is analyzed. In conclusion, both the ICVS-LMS algorithm and the traditional algorithm are simulated and compared in terms of their effectiveness in suppressing interference in satellite navigation signals. The experimental results demonstrate that the improved algorithm significantly reduces convergence time while maintaining a small steady-state error. The improved algorithm demonstrates high robustness and an obvious suppression effect on interference signals. The anti-interference performance is 8.41–12.22% higher than that of the proposed algorithm.

An incremental noise constrained LMS algorithm

While a lot of research has focused on diffusion-based algorithms for distributed estimation over adaptive networks, incremental algorithms have not been studied to that extent. Here we present an incremental scheme-based distributed least mean square algorithm that uses the variance of the additive noise as a constraint. The proposed algorithm is derived and then its theoretical performance analysis is presented. Simulation results for different scenarios are then presented and it is shown that the simulation results corroborate very well the theoretical findings. More importantly, our algorithm outperforms, a recently proposed algorithm, the variable step-size incremental-based LMS (VSSILMS) algorithm.

Robust DOA Estimation Using VSS-LMS With Low-Rank Matrix Approximation

Direction-of-arrival (DOA) estimation performance of adaptive filtering-based methods, <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">e.g.</i> , least mean square (LMS), degrades significantly in adverse conditions ( <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i.e.,</i> at low signal-to-noise ratio (SNR), small number of antenna array elements and snapshots, and in presence of two closely spaced signal sources). Moreover, these estimation methods require many regulating parameters to efficiently update the step size, which are very difficult to tune manually in practical scenarios. Although the subspace decomposition-based methods, <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">e.g</i> ., multiple signal classification (MUSIC), provide somewhat better performance in adverse conditions, they are based on the statistical properties of the signal such as spatial covariance matrix (SCM) and its eigenvalue decomposition (EVD), resulting in high computational complexity. In this paper, a robust DOA estimation method is proposed based on a variable step size LMS algorithm with low rank matrix approximation (LRMA), where the received signal de-noising problem is formulated first as a LRMA problem directly using the received signal observations instead of the SCM, and then the variable step size is calculated from the predicted instantaneous error and the estimated powers of reference and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">de-noised</i> signals. The output spatial spectrum is determined by the reciprocal of the antenna array pattern, and the high peaks in the output spatial spectrum give the received signals estimated directions. The proposed method updates the step size efficiently without choosing any regulating parameter, and achieves improved performance even in adverse conditions due to the de-noising feature of LRMA with low computational complexity. Further, we also conduct the convergence and stability analyses of the proposed iterative estimation method with the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">de-noised</i> signal. Numerical results demonstrate that the proposed method outperforms state-of-the-art methods especially those, which yielded based on adaptive filtering.

Control Study for Compensating Rotor Vibration of Four-DOF Six-Pole Hybrid Magnetic Bearings Based on Variable Step Size LMS Algorithm

In order to solve the problem that the unbalance vibration caused by rotor mass eccentricity of the four-degree-of-freedom (four-DOF) six-pole hybrid magnetic bearings (HMBs), a feed-forward compensation control strategy based on variable step size least-mean-square (LMS) adaptive filter is proposed. First, the structure, operation principle and mathematical model of the four-DOF six-pole HMBs are introduced, the motion law of rotor vibration is analyzed, and the dynamic equation is derived. Second, the variable step size LMS adaptive filter is improved by using the Versoria function. The step size of LMS algorithm is adjusted adaptively by using Versoria function model and Takagi–Sugeno (TS) fuzzy inference machine. The LMS adaptive filter can generate a signal with the same frequency, amplitude, and phase as the rotating speed to offset the vibration signal, so as to realize the vibration compensation control of the four-DOF six-pole HMB rotor. Finally, the simulations and experiments not only prove the effectiveness of this method but also show that the method has good compensation accuracy. The result shows that the Versoria function used in variable step size LMS adaptive filter for vibration compensation is better than the traditional variable step size filtering algorithm based on Sigmoid function.

Zero-Drift Error Compensation Method for Electronic Balance Based on Adaptive Filter With Autostep LMS

This article presents a new approach of compensating the zero-drift error of electronic balance based on automatic step adjustment and least mean square method (Autostep-LMS), and the detailed algorithm of Autostep-LMS is given. Unlike the classical variable step-size LMS algorithms, such as Aboulnasr-LMS algorithm, Versoria-function-LMS algorithm, and Gradient-LMS algorithm, the step control parameters of Autostep-LMS algorithm are automatically adjusted, which is helpful to reduce the complexity of how to adjust these algorithm parameters. By comparing with these classical variable step-size LMS algorithms, the simulation results show that the Autostep-LMS algorithm has faster convergence speed and smaller steady-state error. This Autostep-LMS algorithm is applied to the electronic balance, which range is 200 g and the resolution is 1 mg, and the experimental results show that the zero-drift error, repeatability error, and nonlinear error of the electronic balance are all less than 5 mg, which is superior to the recommendation of the class II electronic balance.

Music Genre Classification Algorithm Based on Multihead Attention Mechanism

Retrieving music information is indispensable and divided into multiple genres. Music genres can be attributed to set categories, which are the indispensable functions of intelligent music recommendation systems. To improve the effect of music genre classification and model construction, combined with the music genre classification algorithm, this paper combines the multihead attention mechanism to study the music genre classification algorithm model, and it analyzes the key technology of music beamforming. Moreover, this paper has made a detailed description and derivation of the array antenna model, the principle of music beamforming, and the performance evaluation criteria of music adaptive beamforming. In the second half, the nonblind classical LMS algorithm, RLS algorithm, and variable step size LMS algorithm of adaptive beamforming are studied in detail. A music genre classification algorithm model based on the multihead attention mechanism is constructed. It can be seen from the experimental research that the music genre classification algorithm based on the multihead attention mechanism proposed in this paper has obvious advantages compared with the traditional algorithm, and it has a certain role in music genre classification.

Adaptive Filter based on Absolute Average Error Adaptive Algorithm for Modeling System

Adaptive identification of the bandpass finite impulse response (FIR) filtering system is proposed through this paper using variable step-size least mean square (VSS-LMS) algorithm called absolute average error-based adjusted step-size LMS as an adapted algorithm. This algorithm used to design an adaptive FIR filter by calculating the absolute averaged value for the recently assessed error with the previous one. Then, the step size has been attuned accordingly with consideration of the slick transition of the step size from bigger to smaller to score an achievement through high convergence rate and low steady-state misadjustment over the other algorithms used for the same purpose. The simulation results through the computer demonstrate remarkable performance compared to the traditional algorithm of LMS and another VSS-LMS algorithm (normalized LMS) which used in this paper for the designed filter. The powerful of the filter has been served in the identification system, bandpass filter has been chosen to be identified in the proposed adaptive system identification. It reports conceivable enhancements in the modeling system concerning the time of convergence, which is well-defined as a fast and steady-state adjustment defined with a low level. The designed filter identified the indefinite system with less than 10 samples; meanwhile, other algorithms were taking more than 20 samples for identification. Alongside the fine behavior of preserving the tradeoff between miss adjustment and the capability of tracking, the fewer calculations and computations regarding the algorithm requirement make the applied real-time striking.

Improved Variable Step Size Least Mean Square Algorithm for Pipeline Noise

In this study, we employ the active noise control (ANC) method to eliminate the low-frequency part of the noise generated by the rotation of the axial fan in heating, ventilation, and air-conditioning (HVAC) pipelines. Because the traditional variable step size least mean square (VSS-LMS) algorithm has poor tracking performance, we propose a variable step size filtered-X least mean square (FXLMS) algorithm based on the arctangent function to improve the adaptive filtering method of the convergence speed and noise cancellation effect. The step size of the proposed algorithm can be adjusted according to the error. When the error signal is significant, a larger step can be obtained, and when the error is small, the step size smoothness of the algorithm can be optimized. Compared with the traditional VSS-LMS algorithm, the convergence speed of the proposed algorithm is increased by 29%, the noise reduction effect is enhanced by 19%, and the mean square error (MSE) is reduced by 23% (0.0084). In addition, we developed a hardware experimental platform based on noise characteristics. In the noise reduction test using a GB/T 5836.2-06 standard PVC pipeline, the system reduced the noise by 12–17 dB.

A Variable Step-Size Leaky LMS Algorithm

The leaky LMS algorithm has been extensively studied because of its control of parameter drift. This unexpected parameter drift is linked to the inadequacy of excitation in the input sequence. And generally leaky LMS algorithms use fixed step size to force the performance of compromise between the fast convergence rate and small steady-state misalignment. In this paper, variable step-size (VSS) leaky LMS algorithm is proposed. And the variable step-size method combines the time average estimation of the error and the time average estimation of the normalized quantity. Variable step-size method proposed incorporating with leaky LMS algorithm can effectively eliminate noise interference and make the early convergence, and final small misalignments are obtained together. Simulation results demonstrate that the proposed algorithm has better performance than the existing variable step-size algorithms in the unexcited environment. Furthermore, the proposed algorithm is comparable in performance to other variable step-size algorithms under the adequacy of excitation.

Sound source localization based on improved adaptive beamforming

In adaptive systems, the least mean square error (LMS) adaptive algorithm is widely used. The variable step size LMS algorithm (SVSLMS) based on the Sigmoid function has greatly improved the convergence speed, and the normalized LMS algorithm is stable Sexual performance has certain advantages. Therefore, improvement is made on this basis, the SVSLMS algorithm is normalized, and the iteration speed is increased by changing the iteration factor, and the stability of the algorithm is also improved. This paper uses MATLAB simulation tools to verify the superiority of the new algorithm. Finally, the improved algorithm is applied to beamforming to estimate the azimuth of arrival of the simulated sound source signal at the partial discharge point of the submarine power cable.

Adaptive nonlinear ANC system based on time-domain signal reconstruction technology

When the primary reference signal obtained by the existing Active noise control (ANC) system is not accurate, the control effect of interior noise will be reduced or even fail. Considering the fault-tolerate and robustness of the system, the study proposes an adaptive nonlinear ANC system for interior noise, which contains noise signal decomposition, multi-network reconstruction model and Variable step-size LMS (VSS-LMS) algorithm. The noise signal decomposition method is used to address the non-stationary of the interior noise; Based on the signal components, the multi-network model for the noise signal reconstruction of passenger ear-sides is designed, which is pre-trained by a restricted Boltzmann machine for improved reconstruction accuracy and realize the adaptive extraction of signal features; And then based on the reconstruction signal components, the controller weights of corresponding components are adaptively updated by the VSS-LMS algorithm to control the passenger ear-sides noise. The effectiveness of the proposed adaptive nonlinear ANC system is validated using noise signal sources collected from a vehicle. Compared with the different ANC systems, the proposed system is superior in terms of fault-tolerant and robustness, which can guarantee stable work of the interior noise control.

Adaptive Processing for EM Telemetry Signal Recovery: Field Data from Sichuan Province

This paper deals with the study of multi-channel adaptive noise cancellation with a focus on its application in electromagnetic (EM) telemetry. We presented new variable step-size least mean square (LMS) techniques: regularized variable step-size LMS and regularized sigmoid variable size LMS, for electromagnetic telemetry data processing. Considering the complexity and spatial distribution of environmental noise, algorithms with multiple reference signals were used to retrieve transmitted EM signals. The feasibility of the regularized variable step size LMS algorithms with numerical simulation was analyzed and presented. The adaptive processing techniques were applied in the recovery of frequency and binary phase shift key modulated signal. The proposed multi-channel adaptive technique achieves fast convergence speed, low mean squared error and is shown to have good convergence characteristics compared to conventional methods. In addition to attaining good results from the multi-channel adaptive filter and performing the signal analysis in real-time, we implemented combined fast effective impulse noise removal techniques. The combination of median and mean filters was effective in removing a wide range of impulsive noises without distorting any other data points. Further, electromagnetic telemetry data were acquired during a drilling operation in Sichuan province, China, for real field application. Data processing workflow was designed for EM telemetry data processing based on the noise characteristics, simulation results and expected result for demodulation. To establish a comprehensive overview, a performance comparison of the acquisition array system is also provided. Conclusively, the introduced multichannel adaptive noise canceling techniques are very effective in recovering transmitted EM telemetry signals.

A novel sign variable step size LMS (SiVSS-LMS) algorithm for adaptive beamforming

Beamforming algorithms are designed for generating main beams in the direction of interest and place nulls in the direction of interferences. Adaptive beamforming can be achieved by various optimization criteria. The criteria for an efficient design of algorithm is the speed of convergence, deeper null placement, better signal to noise ratio, and robustness. Motivated by the reduction in the computational complexity a new adaptive beamforming algorithm based on variable step size is proposed in this paper called sign variable step size LMS algorithm. The proposed algorithm is applied to the uniform linear array antenna. Simulation results show that it gives a better null placement in the direction of interference and the signal to noise ratio is improved upon the existing algorithms with less computational complexity.

Investigation of Blind Multi-User Detection Technology

Blind multi-user detection algorithm is an effective method to overcome multi-access interference and influence of near-far effect. This paper briefly describes commonly used algorithms of blind multi-user detection technology, introduces the application of the least mean square algorithm (LMS) and compares the performance with other algorithms. Aiming at the shortcomings of the LMS algorithm, the variable step size LMS algorithm and the relatively low complexity LMK algorithm based on the change of the input signal vector are studied.

Fast and Robust Variable-Step-Size LMS Algorithm for Adaptive Beamforming

Conventional least-mean-square (LMS) algorithm is one of the most popular algorithms, which is widely used for adaptive beamforming. But the performance of the LMS algorithm degrades significantly because the constant step size is not suitable for varying signal-to-noise ratio (SNR) scenarios. Although numerous variable-step-size LMS (VSS-LMS) algorithms were proposed to improve the performance of the LMS algorithm; however, most of these VSS-LMS algorithms are either computationally complex or not reliable in practical scenarios since they depend on many parameters that are not easy to tune manually. In this letter, a fast and robust VSS-LMS algorithm is proposed for adaptive beamforming. The VSS is obtained based on normalized sigmoid function, where the sigmoid function is calculated by using the mean of instantaneous error first and then normalized by the squared cumulative sum of instantaneous error and estimated signal power. The proposed algorithm can update the step size adaptively without tuning any parameter and outperform state-of-the-art algorithms with low computational complexity. The simulation results show better performance of the proposed algorithm.

Framework for Automated Earthquake Event Detection Based on Denoising by Adaptive Filter

Automated detection of the P-wave arrival for real-time earthquake-early-warning-system employing conventional short-time-average/long-time-average (STA/LTA) algorithm is prone to suffer from erroneous detection due to high background noise. This paper introduces an enhanced variable step-size least mean square (EVSSLMS) algorithm for considerably improving the P-wave detection. The proposed event detection scheme employs the EVSSLMS algorithm for de-noising the seismic data followed by conventional STA/LTA algorithm to detect arrival of the P-wave. The EVSSLMS algorithm outperforms the existing trigonometric least mean square (TLMS), variable step-size LMS (VSSLMS), least mean logarithmic square (LMLS) and variable α-LMLS algorithms in terms of convergence speed and steady-state error and achieves a significant enhancement in detection accuracy by 42%, 33%, 25% and 23% at low signal-to-noise ratio (SNR) as compared to the existing TLMS, VSSLMS, LMLS, and variable-α LMLS algorithms, respectively. Moreover, a high-speed and low-complexity very-large-scale-integrated (VLSI) architecture has been implemented on both field-programmable-gate array (FPGA) and application-specific-integrated circuit (ASIC) platforms for realtime applications. Comparison of architectural performance of the proposed scheme with that of architecture designed to realize variable-α LMLS algorithm exhibits 36% less slice-delay-product whereas, its ASIC implementation exhibits 7.27% less areadelay-product, 9.31% less energy-per-sample with 5.2% more maximum achievable frequency.

Adaptive Active Vehicle Interior Noise Control Algorithm Based on Nonlinear Signal Reconstruction

In this study, to reduce secondary sound source pollution in the reference signal of active noise control (ANC), a novel ANC algorithm, based on signal reconstruction, is proposed for vehicle interior noise. This algorithm combines the processes of ear-sides noise reconstruction and ANC. First, to reduce non-stationarity and nonlinearity, multi-source noise signals outside the vehicle are decomposed into a finite number of intrinsic mode function (IMF) components by empirical mode decomposition (EMD). Second, the IMFs are reconstructed by the energy-extreme division method into three components: high-frequency, intermediate-frequency and low-frequency. The radial basis function neural network (RBFNN) parameters are adjusted by the proportions of the components. Model training is performed to obtain the high-precision EMD–RBFNN reconstruction model (EMD–NNRM). The reconstructed noise signal is used as the reference signal of the variable step-size least mean square (VSS-LMS) algorithm, to control the passenger ear-sides noise. The effectiveness of the EMD–NNRM is validated using four noise signals from the outside of a vehicle. The interior noise of a high-speed vehicle is processed by the proposed algorithm and the traditional VSS-LMS algorithm for comparison. The reconstruction results show that the mean absolute error is improved by 77.64% compared with the back propagation neural network reconstruction model. Reconstructed passenger ear-sides noise can be utilized for ANC. The active control results suggest that the proposed algorithm can not only effectively suppress the interior noise but can also avoid pollution from secondary sound sources.

A variable step-size diffusion LMS algorithm with a quotient form

A new variable step-size strategy for the least mean square (LMS) algorithm is presented for distributed estimation in adaptive networks using the diffusion scheme. This approach utilizes the ratio of filtered and windowed versions of the squared instantaneous error for iteratively updating the step-size. The result is that the dependence of the update on the power of the error is reduced. The performance of the algorithm improves even though it is at the cost of added computational complexity. However, the increase in computational complexity can be minimized by careful manipulation of the update equation, resulting in an excellent performance-complexity trade-off. Complete theoretical analysis is presented for the proposed algorithm including stability, transient and steady-state analyses. Extensive experimental analysis is then done to show the performance of the proposed algorithm under various scenarios.

A High-Speed Master-Slave ADALINE for Accurate Power System Harmonic and Inter-Harmonic Estimation

This paper presents a unique two-fold adaptive linear neural network (ADALINE) for fast and accurate measurement of fundamental, harmonics, sub-harmonics, inter-harmonics and decaying DC components of a distorted current signal with additive noise. The preceding parallel approach is termed as Master-Slave ADALINE (MS ADALINE). The Slave-ADALINE adopts least mean square (LMS) algorithm with a fixed and large step-size for weight vector adjustment. During the training interval or transients, this filter performs a significant role. On the other hand, the Master-ADALINE uses a variable step-size LMS algorithm for achieving a small steady-state error. At the end of each iteration, the local averages of the squared errors of both the ADALINE's are calculated and weights of the Master-ADALINE are updated accordingly. The amplitudes and phases of desired frequency components can be worked out from Master-ADALINE's weights. The proposed architecture improves the convergence speed by establishing an independent control action between the steady-state error and the speed of convergence. The simulation results of this method under various operating situations are analyzed and compared with single fold ADALINE structure that obeys dynamic step-size LMS (DSSLMS) adaptation rule. Eventually, a scaled laboratory prototype has been developed for the validation of the proposed technique in real-time utilization. This innovative research finding makes the power system smart and precise.

Design of digital signal processor based adaptive beamformer using hybrid residual least mean square algorithm for improved performance

This paper proposes a novel hybrid residual least mean square (HRLMS) algorithm for adaptive filtering followed by an antenna beamformer using 16-element linear array. The hybridization process involves a switching between the residual-LMS (RLMS) and the conventional-LMS (CLMS) algorithms after the eighth iteration, if the square errors for four consecutive iterations are less than a threshold. The novelty of HRLMS lies in estimating best step size factor through residuals for speedy convergence followed by the CLMS switching for minimum steady state error (SSE). The novelty also includes in realizing a real-time antenna beamformer with significant sidelobe level (SLL) reduction and improved interference nulling by integration of HRLMS and space selective digital filter (SSDF). The adaptive filter and smart beamformer, based on HRLMS and HRLMS-SSDF have been implemented on TMS320VC5416 digital signal processor. The comparative performance evaluation of HRLMS has been done for convergence speed, SSE, interference nulling and SLL reduction with the existing variable step size LMS (VSSLMS) algorithms. The iteration count for convergence has been reduced by about 50% with paltry additional computational burden over the other VSSLMS algorithms. The HRLMS-SSDF provide attenuations of about 76, 33, and >50 dB, respectively for interfering signals, first SLL and higher order SLLs of beamformer.