A novel noise reduction technique for underwater acoustic signals based on complete ensemble empirical mode decomposition with adaptive noise,minimum mean square variance criterion and least mean square adaptive filter

Underwater acoustic signal processing is one of the research hotspots in underwater acoustics.Noise reduction of underwater acoustic signals is the key to underwater acoustic signal processing.Owing to the complexity of marine environment and the particularity of underwater acoustic channel,noise reduction of underwater acoustic signals has always been a difficult challenge in the field of underwater acoustic signal processing.In order to solve the dilemma,we proposed a novel noise reduction technique for underwater acoustic signals based on complete ensemble empirical mode decomposition with adaptive noise(CEEMDAN),minimum mean square variance criterion(MMSVC) and least mean square adaptive filter(LMSAF).This noise reduction technique,named CEEMDAN-MMSVC-LMSAF,has three main advantages:(i) as an improved algorithm of empirical mode decomposition(EMD) and ensemble EMD(EEMD),CEEMDAN can better suppress mode mixing,and can avoid selecting the number of decomposition in variational mode decomposition(VMD);(ii) MMSVC can identify noisy intrinsic mode function(IMF),and can avoid selecting thresholds of different permutation entropies;(iii) for noise reduction of noisy IMFs,LMSAF overcomes the selection of deco mposition number and basis function for wavelet noise reduction.Firstly,CEEMDAN decomposes the original signal into IMFs,which can be divided into noisy IMFs and real IMFs.Then,MMSVC and LMSAF are used to detect identify noisy IMFs and remove noise components from noisy IMFs.Finally,both denoised noisy IMFs and real IMFs are reconstructed and the final denoised signal is obtained.Compared with other noise reduction techniques,the validity of CEEMDAN-MMSVC-LMSAF can be proved by the analysis of simulation signals and real underwater acoustic signals,which has the better noise reduction effect and has practical application value.CEEMDAN-MMSVC-LMSAF also provides a reliable basis for the detection,feature extraction,classification and recognition of underwater acoustic signals.

Low Complexity Minimum Mean Square Error Channel Estimation for Adaptive Coding and Modulation Systems

Performance of the Adaptive Coding and Modulation(ACM) strongly depends on the retrieved Channel State Information(CSI),which can be obtained using the channel estimation techniques relying on pilot symbol transmission.Earlier analysis of methods of pilot-aided channel estimation for ACM systems were relatively little.In this paper,we investigate the performance of CSI prediction using the Minimum Mean Square Error(MMSE)channel estimator for an ACM system.To solve the two problems of MMSE:high computational operations and oversimplified assumption,we then propose the Low-Complexity schemes(LC-MMSE and Recursion LC-MMSE(R-LC-MMSE)).Computational complexity and Mean Square Error(MSE) are presented to evaluate the efficiency of the proposed algorithm.Both analysis and numerical results show that LC-MMSE performs close to the wellknown MMSE estimator with much lower complexity and R-LC-MMSE improves the application of MMSE estimation to specific circumstances.

Mean Square Stability of the Composite Milstein Method for Nonlinear Stochastic Differential Delay Equations

In this paper, we construct a composite Milstein method for nonlinear stochastic differential delay equations. Then we analyze the mean square stability for this method and obtain the step size condition under which the composite Milstein method is mean square stable. Moreover, we get the step size condition under which the composite Milstein method is global mean square stable. A nonlinear test stochastic differential delay equation is given for numerical tests. The results of numerical tests verify the theoretical results proposed.

A Quantized Kernel Least Mean Square Scheme with Entropy-Guided Learning for Intelligent Data Analysis

Quantized kernel least mean square(QKLMS) algorithm is an effective nonlinear adaptive online learning algorithm with good performance in constraining the growth of network size through the use of quantization for input space. It can serve as a powerful tool to perform complex computing for network service and application. With the purpose of compressing the input to further improve learning performance, this article proposes a novel QKLMS with entropy-guided learning, called EQ-KLMS. Under the consecutive square entropy learning framework, the basic idea of entropy-guided learning technique is to measure the uncertainty of the input vectors used for QKLMS, and delete those data with larger uncertainty, which are insignificant or easy to cause learning errors. Then, the dataset is compressed. Consequently, by using square entropy, the learning performance of proposed EQ-KLMS is improved with high precision and low computational cost. The proposed EQ-KLMS is validated using a weather-related dataset, and the results demonstrate the desirable performance of our scheme.

A modified fractional least mean square algorithm for chaotic and nonstationary time series prediction

A method of modifying the architecture of fractional least mean square （FLMS） algorithm is presented to work with nonlinear time series prediction. Here we incorporate an adjustable gain parameter in the weight adaptation equation of the original FLMS algorithm and absorb the gamma function in the fractional step size parameter. This approach provides an interesting achievement in the performance of the filter in terms of handling the nonlinear problems with less computational burden by avoiding the evaluation of complex gamma function. We call this new algorithm as the modified fractional least mean square （MFLMS） algorithm. The predictive performance for the nonlinear Mackey glass chaotic time series is observed and evaluated using the classical LMS, FLMS, kernel LMS, and proposed MFLMS adaptive filters. The simulation results for the time series with and without noise confirm the superiority and improvement in the prediction capability of the proposed MFLMS predictor over its counterparts.

Calculation of Significant Wave Height Using the Linear Mean Square Estimation Method

Significant wave height is an important criterion in designing coastal and offshore structures.Based on the orthogonality principle, the linear mean square estimation method is applied to calculate significant wave height in this paper.Twenty-eight-year time series of wave data collected from three ocean buoys near San Francisco along the California coast are analyzed.It is proved theoretically that the computation error will be reduced by using as many measured data as possible for the calculation of significant wave height.Measured significant wave height at one buoy location is compared with the calculated value based on the data from two other adjacent buoys.The results indicate that the linear mean square estimation method can be well applied to the calculation and prediction of significant wave height in coastal regions.

Separate Least Mean Square Based Equalizer with Joint Optimization for Multi-CAP Visible Light Communication

Visible light communication(VLC) is expected to be a potential candidate of the key technologies in the sixth generation(6G) wireless communication system to support Internet of Things(IoT) applications. In this work, a separate least mean square(S-LMS) equalizer is proposed to compensate lowpass frequency response in VLC system. Joint optimization is employed to realize the proposed S-LMS equalizer with pre-part and post-part by introducing Lagrangian. For verification, the performance of VLC system based on multi-band carrier-less amplitude and phase(m-CAP) modulation with S-LMS equalizer is investigated and compared with that without equalizer,with LMS equalizer and with recursive least squares(RLS)-Volterra equalizer. Results indicate the proposed equalizer shows significant improved bit error ratio(BER) performance under the same conditions. Compared to the RLS-Volterra equalizer, SLMS equalizer achieves better performance under low data rate or high signal noise ratio(SNR) conditions with obviously lower computational complexity.

Random Crank-Nicolson Scheme for Random Heat Equation in Mean Square Sense

The goal of computational science is to develop models that predict phenomena observed in nature. However, these models are often based on parameters that are uncertain. In recent decades, main numerical methods for solving SPDEs have been used such as, finite difference and finite element schemes [1]-[5]. Also, some practical techniques like the method of lines for boundary value problems have been applied to the linear stochastic partial differential equations, and the outcomes of these approaches have been experimented numerically [7]. In [8]-[10], the author discussed mean square convergent finite difference method for solving some random partial differential equations. Random numerical techniques for both ordinary and partial random differential equations are treated in [4] [10]. As regards applications using explicit analytic solutions or numerical methods, a few results may be found in [5] [6] [11]. This article focuses on solving random heat equation by using Crank-Nicol- son technique under mean square sense and it is organized as follows. In Section 2, the mean square calculus preliminaries that will be required throughout the paper are presented. In Section 3, the Crank-Nicolson scheme for solving the random heat equation is presented. In Section 4, some case studies are showed. Short conclusions are cleared in the end section.

MEAN SQUARE DEVIATION ANALYSIS OF INTERANNUAL SST VARIABILITY IN TROPICAL PACIFIC AND INDIAN OCEAN

Using the SST data series in tropical ocean (20N ~ 20S, 50E ~ 80W) during 1951 ~ 1997 to calculate its monthly mean square deviation, the work obtains results showing that interannual SST variability of the Pacific is more significant than that of the Indian Ocean, especially near the central and eastern equatorial Pacific (165W～90W, 6N～6S), where it ranges from 2C to 4C. The interannual SST variability is obvious in November and December but small in March and April. The interannual variability of 搘arm pool?SST is not so obvious as that of the eastern equatorial Pacific. However, interannual SST variability of the Indian Ocean ranges from 1C to 2C or so, being smaller than that of the Pacific. In the Indian Ocean, interannual SST variability of the Southern Hemisphere is more obvious than that of the Northern Hemisphere. According to above characteristics of interannual SST variability, the key sectors are determined.

Finite Difference Scheme for Solving Parabolic Partial Differential Equations with Random Variable Input under Mean Square Sense

This study deal with seven points finite difference method to find the approximation solutions in the area of mean square calculus solutions for linear random parabolic partial differential equations. Several numerical examples are presented to show the ability and efficiency of this method.

Blind spectrum sensing based on the ratio of mean square to variance

Anderson-Darling （AD） sensing, characteristic function （CF） sensing and order statistic （OS） sensing are three common spectrum sensing （SS） methods based on goodness of fit （GOF） testing. However, AD and OS sensing needs the prior information of noise variance; CF and OS sensing have high computation complexity. To circumvent those difficulties, in this paper, the ratio of the mean square to variance （RM2V） of the samples, after deriving its probability density function （PDF）, is employed as a test statistic to detect the availability of the vacant spectrum in the cognitive radio （CR） system. Then a blind SS method based on RM2V is proposed, which is dubbed as RM2V sensing, and its exact theoretical threshold is obtained via the derived PDF of RM2V. The performance of RM2V sensing is evaluated by theoretical analysis and Monte Carlo simulations. Comparing with the conventional energy detection （ED）, AD, CF and OS sensing, RM2V sensing, with no need of noise variance, has advantages from the aspect of computation complexity and detection performance.

Tong-type identity and the mean square of the error term for an extended Selberg class

In 1956, Tong established an asymptotic formula for the mean square of the error term of the summatory function of the Piltz divisor function d3（n）. The aim of this paper is to generalize Tong＇s method to a class of Dirichlet series L（s） which satisfies a functional equation. Let a（n） be an arithmetical function related f t to a Dirichlet series L（s）, and let E（x） be the error term of ∑＇n≤x a（n）. In this paper, after introducing a class of Diriclet series with a general functional equation （which contains the well-known Selberg class）, we establish a Tong-type identity and a Tong-type truncated formula for the error term of the Riesz mean of the coefficients of this Dirichlet series L（s）. This kind of Tong-type truncated formula could be used to study the mean square of E（x） under a certain assumption. In other words, we reduce the mean square of E（x） to the problem of finding a suitable constant σ＊ which is related to the mean square estimate of L（s）. We shall represent some results of functions in the Selberg class of degrees 2 -4.

Power Quality Improvement for Grid-connected PV System Based on Distribution Static Compensator with Fuzzy Logic Controller and UVT/ADALINE-based Least Mean Square Controller

This paper presents a novel method of power quality enrichment in a grid-connected photovoltaic(PV) system using a distribution static compensator(DSTATCOM). The paper consists of two-step control processes. In the primary step, a fuzzy logic controller(FLC) is employed in the DC-DC converter to extract the peak power point from the PV panel, where the FLC produces a switching signal for the DC-DC converter.In the secondary step, a unit vector template(UVT)/adaptive linear neuron(ADALINE)-based least mean square(LMS) controller is adopted in the DC-AC converter, i. e., voltage source converter(VSC). The input to this VSC is the boosted DC voltage, which originates from the PV panel as a result of DC-DC conversion. The VSC shunted with the power grid is known as a DSTATCOM, which can maintain the power quality in the distribution system. The UVT controller generates reference source currents from the grid voltages and DC-link voltages.The ADALINE-based LMS controller calculates the online weight according to the previous weights by the sensed load current. The UVT/ADALINE-based LMS controller of a DSTATCOM performs several tasks such as maintaining the sinusoidal source current, achieving a unity power factor, and performing reactive power compensation. The reference current extracted from the UVT/ADALINE-based LMS controller is fed to the hysteresis current controller to obtain the desired switching signal for the VSC. A 100 k W solar PV system integrated into a three-phase four-wire distribution system through a four-leg VSC is designed in MATLAB/Simulink. The performances of the FLC and UVT/ADALINE-based LMS controllers are demonstrated under various irradiances as well as constant temperature and nonlinear loading conditions.

Robust Iteration-dependent Least Mean Square-based Distribution Static Compensator Using Optimized PI Gains

A robust iteration-dependent least mean square(RIDLMS)algorithm-based fundamental extractor is developed to estimate the fundamental components of the load current for a four-wire DSTATCOM with a nonlinear load.The averaging parameter for calculating the variable step size is iteration dependent and uses variable tuning parameters.Rather than using the current value,the previous learning rate was used in this method to achieve a more adaptive solution.This additional control factor aids in determining the exact learning rate,resulting in reliable and convergent outcomes.Its faster convergence rate and the avoidance of local minima make it advantageous.The estimation of the PI controller gains is achieved through a self-adaptive multi-population algorithm.The adaptive change in the group number will increase exploration and exploitation.The self-adaptive nature of the algorithm was used to determine the subpopulation number needed according to the fitness value.The main advantage of this self-adaptive nature is the multi-population spread throughout the search space for a better optimal solution.The estimated gains of the PI controllers are used for the DC bus and AC terminal voltage error minimization.The RIDLMS-based control with PI gains obtained using the proposed optimization algorithm showed better power quality performance.The considered RIDLMS-supported control was demonstrated experimentally using d-SPACE-1104.

Demodulation method combining virtual reference interferometry and minimum mean square error for fiber-optic Fabry–Perot sensors

We propose a cavity length demodulation method that combines virtual reference interferometry（VRI） and minimum mean square error（MMSE） algorithm for fiber-optic Fabry–Perot（F-P） sensors. In contrast to the conventional demodulating method that uses fast Fourier transform（FFT） for cavity length estimation,our method employs the VRI technique to obtain a raw cavity length, which is further refined by the MMSE algorithm. As an experimental demonstration, a fiber-optic F-P sensor based on a sapphire wafer is fabricated for temperature sensing. The VRI-MMSE method is employed to interrogate cavity lengths of the sensor under different temperatures ranging from 28°C to 1000°C. It eliminates the ＂mode jumping＂ problem in the FFT-MMSE method and obtains a precision of 4.8 nm, corresponding to a temperature resolution of 2.0°C over a range of 1000°C. The experimental results reveal that the proposed method provides a promising, high precision alternative for demodulating fiber-optic F-P sensors.

LAGRANGE STABILITY IN MEAN SQUARE OF STOCHASTIC REACTION DIFFUSION EQUATIONS

This work is devoted to the discussion of stochastic reaction diffusion equations and some new theorems on Lagrange stability in mean square of the solution are established via Lyapunov method which is nothing to be done in the past.

Evaluation of Particle Numbers via Two Root Mean Square Radii in a 2-Species Bose–Einstein Condensate

The coupled Gross–Pitaevskii equations for two-species BEC have been solved analytically under the Thomas-Fermi approximation(TFA). Based on the analytical solution, two formulae are derived to relate the particle numbers N_A and N_B with the root mean square radii of the two kinds of atoms. Only the case that both kinds of atoms have nonzero distribution at the center of an isotropic trap is considered. In this case the TFA has been found to work nicely. Thus, the two formulae are applicable and are useful for the evaluation of N_A and N_B.

An analysis of reverberation fluctuation by mean square derivation

A method for evaluating the fluctuation of the reverberation envelope is proposed and examined through simulation and real data in this paper.This method is different from the coefficient of variation which is only a function of the first and second order moment of the reverberation statistical model.By using the standard variance of the mean square derivate(MSD) of the reverberation envelope,the paper shows that the reverberation fluctuation is a function of the bandwidth of the emitted signal,and that a large value of the square variance means little fluctuation of the reverberation envelope.Theoretical studies show that the standard variance is proportional to the bandwidth of the emitted signal,so we conclude that less time width or larger bandwidth of the transmitted signal produces less fluctuation.Simulation and real active sonar data processing are used to verify this conclusion.

Asynchronous Dissipative Control and Robust Exponential Mean Square Stabilization for Uncertain Fuzzy Neutral Markov Jump Systems

This paper researches the strict dissipative control problem for uncertain fuzzy neutral Markov jump systems by Takagi-Sugeno fuzzy rules.The asynchronous phenomenon is considered between the uncertain fuzzy neutral Markov jump systems modes and asynchronous fuzzy P-D feedback controller modes,which is described by a hidden Markov model.Via using linear matrix inequalities,the desired asynchronous fuzzy P-D feedback controller is obtained,which can ensure that the closed-loop uncertain fuzzy neutral Markov jump systems satisfies robustly exponential mean square stabilization with strict dissipativity.A numerical example and a single-link robot arm are utilized to demonstrate the effectiveness of the method.

An Improved Proportionate Normalized Least Mean Square Algorithm for Sparse Impulse Response Identification

In this paper after analyzing the adaptation process of the proportionate normalized least mean square(PNLMS) algorithm, a statistical model is obtained to describe the convergence process of each adaptive filter coefcient. Inspired by this result, a modified PNLMS algorithm based on precise magnitude estimate is proposed. The simulation results indicate that in contrast to the traditional PNLMS algorithm, the proposed algorithm achieves faster convergence speed in the initial convergence state and lower misalignment in the stead stage with much less computational complexity.