Novel LMS adaptive filtering algorithm with variable step size

By analyzing algorithms available for variable step size least mean square(LMS)adaptive filter,a new modified LMS adaptive filtering algorithm with variable step size is proposed,along with performance analysis based on different parameters.Compared with the existing algorithms through the simulation,the proposed algorithm has faster convergence speed and smaller steady state error.

Study of Variable Step Size LMS Adaptive Algorithm Based on Variable Region

This paper puts forward a new variable step size LMS adaptive algorithm based on variable region. The step size p（k） in the algorithm varies with the variation of the region of deviation e （k） to ensure the optimization of the three performance objectives including initial convergent speed, trace ability of the time-varying system and steady disregulation. The paper demonstrates the convergence of the algorithm accompanied by random noise,

Joint receiving mechanism based on blind equalization with variable step size for M-QAM modulation

The problem of inter symbol interference（ ISI） in wireless communication systems caused by multipath propagation when using high order modulation like M-Q AMis solved. Since the wireless receiver doesn＇t require a training sequence,a blind equalization channel is implemented in the receiver to increase the throughput of the system. To improve the performances of both the blind equalizer and the system,a joint receiving mechanismincluding variable step size（ VSS） modified constant modulus algorithms（ MC-MA） and modified decision directed modulus algorithms（ MD DMA） is proposed to ameliorate the convergence speed and mean square error（ MSE） performance and combat the phase error when using high order QAM modulation. The VSS scheme is based on the selection of step size according to the distance between the output of the equalizer and the desired output in the constellation plane. Analysis and simulations showthat the performance of the proposed VSS-MCMA-MD DMA mechanismis better than that of algorithms with a fixed step size. In addition,the MCMA-MDDMA with VSS can performthe phase recovery by itself.

Design of digital calibration based on variable step size of sub-binary SAR ADC

Addressing the impact of capacitor mismatch on the conversion accuracy of successive approximation register analog-to-digital converter(SAR ADC),a 12-bit 1 MS/s sub-binary SAR ADC designed using variable step size digital calibration was proposed.The least mean square(LMS)calibration algorithm was employed with a ramp signal used as the calibration input.Weight errors,extracted under injected disturbances,underwent iterative training to optimize weight values.To address the trade-off between conversion accuracy and speed caused by a fixed step size,a novel variable step size algorithm tailored for SAR ADC calibration was proposed.The core circuit and layout of the SAR ADC were implemented using the Taiwan Semiconductor Manufacturing Company(TSMC)0.35μm complementary metal-oxide-semiconductor(CMOS)commercial process.Simulation of the SAR ADC calibration algorithm was conducted using Simulink,demonstrating quick convergence and meeting conversion accuracy requirements compared to fixed step size simulation.The results indicated that the convergence speed of the LMS digital calibration algorithm with variable step size was approximately eight times faster than that with a fixed step size,also yielding a lower mean square error(MSE).After calibration,the simulation results for the SAR ADC exhibited an effective number of bit(ENOB)of 11.79 bit and a signal-to-noise and distortion ratio(SNDR)of 72.72 dB,signifying a notable enhancement in the SAR ADC performance.

Improved finite difference method for pressure distribution of aerostatic bearing

An improved finite difference method （FDM）is described to solve existing problems such as low efficiency and poor convergence performance in the traditional method adopted to derive the pressure distribution of aerostatic bearings. A detailed theoretical analysis of the pressure distribution of the orifice-compensated aerostatic journal bearing is presented. The nonlinear dimensionless Reynolds equation of the aerostatic journal bearing is solved by the finite difference method. Based on the principle of flow equilibrium, a new iterative algorithm named the variable step size successive approximation method is presented to adjust the pressure at the orifice in the iterative process and enhance the efficiency and convergence performance of the algorithm. A general program is developed to analyze the pressure distribution of the aerostatic journal bearing by Matlab tool. The results show that the improved finite difference method is highly effective, reliable, stable, and convergent. Even when very thin gas film thicknesses （less than 2 Win）are considered, the improved calculation method still yields a result and converges fast.

Motion Planning Method for Obstacle Avoidance of 6-DOF Manipulator Based on Improved A* Algorithm

The conventional A* algorithm may suffer from the infinite loop and a large number of search data in the process of motion planning for manipulator. To solve the problem,an improved A* algorithm is proposed in this paper by the means of selecting middle points and applying variable step segments searching during the searching process. In addition,a new method is proposed for collision detection in the workspace. In this paper,the MOTOMAN MH6 manipulator with 6-DOF is applied for motion plan. The algorithm is based on the basis of the simplification for the manipulator and obstacles by cylinder enveloping. Based on the analysis of collision detection,the free space can be achieved which makes it possible for the entire body to avoid collisions with obstacles. Compared with the Conventional A*,the improved algorithm deals with less searching points and performs more efficiently. The simulation developed in VC + + with OpenGL and the actual system experiments prove effectiveness and feasibility of this improved method.

Improved adaptive filter and its application in acoustic emission signals

In order to de-noise and filter the acoustic emission(AE) signal, the adaptive filtering technology is applied to AE signal processing in view of the special attenuation characteristics of burst AE signal. According to the contradiction between the convergence speed and steady-state error of the traditional least mean square(LMS) adaptive filter, an improved LMS adaptive filtering algorithm with variable iteration step is proposed on the basis of the existing algorithms. Based on the Sigmoid function, an expression with three parameters is constructed by function translation and symmetric transformation.As for the error mutation, e(k) and e(k-1) are combined to control the change of the iteration step. The selection and adjustment process of each parameter is described in detail, and the MSE is used to evaluate the performance. The simulation results show that the proposed algorithm significantly increases the convergence speed, reduces the steady-state error, and improves the performance of the adaptive filter. The improved algorithm is applied to the AE signal processing, and the experimental signal is demodulated by an empirical mode decomposition(EMD) envelope to obtain the upper and lower envelopes. Then, the expected function related to the AE signal is established. Finally, the improved algorithm is substituted into the adaptive filter to filter the AE signal. A good result is achieved, which proves the feasibility of adaptive filtering technology in AE signal processing.

An Efficient Reference Free Adaptive Learning Process for Speech Enhancement Applications

In issues like hearing impairment,speech therapy and hearing aids play a major role in reducing the impairment.Removal of noise signals from speech signals is a key task in hearing aids as well as in speech therapy.During the transmission of speech signals,several noise components contaminate the actual speech components.This paper addresses a new adaptive speech enhancement(ASE)method based on a modified version of singular spectrum analysis(MSSA).The MSSA generates a reference signal for ASE and makes the ASE is free from feeding reference component.The MSSA adopts three key steps for generating the reference from the contaminated speech only.These are decomposition,grouping and reconstruction.The generated reference is taken as a reference for variable size adaptive learning algorithms.In this work two categories of adaptive learning algorithms are used.They are step variable adaptive learning(SVAL)algorithm and time variable step size adaptive learning(TVAL).Further,sign regressor function is applied to adaptive learning algorithms to reduce the computational complexity of the proposed adaptive learning algorithms.The performance measures of the proposed schemes are calculated in terms of signal to noise ratio improvement(SNRI),excess mean square error(EMSE)and misadjustment(MSD).For cockpit noise these measures are found to be 29.2850,-27.6060 and 0.0758 dB respectively during the experiments using SVAL algorithm.By considering the reduced number of multiplications the sign regressor version of SVAL based ASE method is found to better then the counter parts.

Simultaneous inversion of velocity distribution and interface positions

This paper deals with the simultaneous inversion of velocity distribution and interface positions in a laterally heterogeneous medium using seismic travel time data. Due to the application of variable step length and linear interpolation techniques (for both theoretical travel times and the partial derivative matrix), the computing speed is increased greatly. As compared with other domestic computing programs of this kind, it is five times or more faster than others. Besides reflected waves, the transmitted waves can also be used to form the partial derivative matrix of travel times with respect to interface positions. So this method can make full use of the information about interface positions contained in various transmitted waves and speed up the convergence rate. Digital tests and processing results of real data indicate the feasibility and effectiveness of the method and its program.

High Order Block Method for Third Order ODEs

Many initial value problems are difficult to be solved using ordinary,explicit step-by-step methods because most of these problems are considered stiff.Certain implicit methods,however,are capable of solving stiff ordinary differential equations(ODEs)usually found in most applied problems.This study aims to develop a new numerical method,namely the high order variable step variable order block backward differentiation formula(VSVOHOBBDF)for the main purpose of approximating the solutions of third order ODEs.The computational work of the VSVO-HOBBDF method was carried out using the strategy of varying the step size and order in a single code.The order of the proposed method was then discussed in detail.The advancement of this strategy is intended to enhance the efficiency of the proposed method to approximate solutions effectively.In order to confirm the efficiency of the VSVO-HOBBDF method over the two ODE solvers in MATLAB,particularly ode15s and ode23s,a numerical experiment was conducted on a set of stiff problems.The numerical results prove that for this particular set of problem,the use of the proposed method is more efficient than the comparable methods.VSVO-HOBBDF method is thus recommended as a reliable alternative solver for the third order ODEs.

Modeling of seasonal soil cold storage using natural cold energy

To reduce energy consumption on summer air conditioning,a novel seasonal soil cold storage mode using natural energy is presented and two-dimensional transient heat transfer model of U-tube is developed. The three processes of cold storage in winter,shut-down in transition season and cold extraction in summer are simulated by using sensitive heat capacity method with variable time step. The changing of U-tube outlet water temperature in different periods,daily cold storage and cold extraction are estimated. The temperature field of the U-tube and soil around the tube is investigated. Simulations show that seasonal soil cold storage using natural cold energy is feasible in the north to Changchun,which provides theoretical support for seasonal soil cold storage application.

Maximum Power Tracking for PVs with Improved Tracking Accuracy at Irradiance Transients

PV （photovoltaic） systems need MPPT （maximum power point tracking） techniques to hamess maximum power from PV arrays. P＆O （perturb ＆ observe）, and incremental conductance methods are two basic MPPT algorithms applied to PV systems with fixed and variable step sizes. However, the existing variable step MPPT method exhibits complications which occur in the algorithm due to sudden, large irradiance changes which result in dips in power extraction. This paper proposes a modification to the existing variable step MPPT method to avoid such complications and hence improve the tracking accuracy under irradiance transients. The proposed technique is experimentally verified under sudden irradiance disturbances using a solar array. The results are compared with the existing variable step method. The superiority of the proposed technique is demonstrated through a laboratory prototype.

Dynamic Simulation of Distribution Networks Using Multi-stage Discontinuous Galerkin Method

Dynamic simulation plays a fundamental role in security evaluation of distribution networks(DNs).However,the strong stiffness and non-linearity of distributed generation(DG)models in DNs bring about burdensome computation and noteworthy instability on traditional methods which hampers the rapid response of simulation tool.Thus,a novel L-stable approximate analytical method with high accuracy is proposed to handle these problems.The method referred to as multistage discontinuous Galerkin method(MDGM),first derives approximate analytical solutions(AASs)of state variables which are explicit symbolic expressions concerning system states.Then,in each time window,it substitutes values for symbolic variables and trajectories of state variables are obtained subsequently.This paper applies MDGM to DG models to derive AASs.Local-truncation-error-based variable step size strategy is also developed to further improve simulation efficiency.In addition,this paper establishes detailed MDGM-based dynamic simulation procedure.From case studies on a numerical problem,a modified 33-bus system and a practical large-scale DN,it can be seen that proposed method demonstrates fast and dependable performance compared with the traditional trapezoidal method.

A nonparametric variable step-size subband adaptive filtering algorithm for acoustic echo cancellation

Acoustic echo cancellation is often applied in communication and video call system to reduce unnecessary echoes generated between speakers and microphones.In these systems,the speech input signal of the adaptive filter is often colored and unstable,which decays the convergence rate of the adaptive filter if the NLMS algorithm is used.In this paper,an improved nonparametric variable step-size subband(NPVSS-NSAF)algorithm is proposed to address the problem.The variable step-size is derived by minimizing the sum of the square Euclidean norm of the difference between the optimal weight vectors to be updated and the past estimated weight vectors.Then the parameters are eliminated by using the power of subband signal noise equal to the power of subband posteriori error.The performance of the proposed algorithm is simulated in the aspects of misalignment and return loss enhancement.Experiment results show a fast convergence rate and low misalignment of the proposed algorithm in system identification.

Variable-step-size second-order-derivative multistep method for solving first-order ordinary differential equations in system simulation

According to the relationship between truncation error and step size of two implicit second-order-derivative multistep formulas based on Hermite interpolation polynomial,a variable-order and variable-step-size numerical method for solving differential equations is designed.The stability properties of the formulas are discussed and the stability regions are analyzed.The deduced methods are applied to a simulation problem.The results show that the numerical method can satisfy calculation accuracy,reduce the number of calculation steps and accelerate calculation speed.

GRID-INDEPENDENT CONSTRUCTION OF MULTISTEP METHODS

A new polynomial formulation of variable step size linear multistep methods is pre- sented, where each k-step method is characterized by a fixed set of k - 1 or k parameters. This construction includes all methods of maximal order （p = k for stiff, and p = k ＋ 1 for nonstiff problems）. Supporting time step adaptivity by construction, the new formulation is not based on extending classical fixed step size methods; instead classical methods are obtained as fixed step size restrictions within a unified framework. The methods are imple- mented in MATLAB, with local error estimation and a wide range of step size controllers. This provides a platform for investigating and comparing different multistep method in realistic operational conditions. Computational experiments show that the new multi- step method construction and implementation compares favorably to existing software, although variable order has not yet been included.