Adaptive Step-size Algorithm Research Articles

An Adaptive Time‐Domain Kalman Filtering Approach to Acoustic Feedback Cancellation for Hearing Aids

The adaptive filtering approach has been widely used for acoustic feedback control in the hearing aids due to its excellent performance. The commonly used adaptive filtering algorithms employ a fixed step-size, which has to compromise between the initial convergence and the steady-state misalignment. Many variable stepsize adaptive algorithms have been proposed to handle this problem. In this paper, we propose a broadband Kalman filter to resolve this problem. The acoustic feedback path is modelled by a first-order Markov model, and the observation equation is constructed using more past data vector. A major issue in the hearing aids is the computational complexity. We thus present a simplified version to reduce the complexity, which bridges between the exact Kalman filter and the affine projection algorithm. The estimation of the process and measurement noise variance is discussed in detail. A two-feedback path model is adopted to improve the algorithm's lack of re-convergence. Simulation results confirm the proposed algorithm clearly outperforms the other variable step-size adaptive filtering approaches.

Adaptive step-size fast iterative shrinkage-thresholding algorithm and sparse-spike deconvolution

The standard Fast Iterative Shrinkage-Thresholding Algorithm (FISTA) adopts a search approach consisting of linear increases to determine the step size of the internal gradient. If the input of the initial step-size is not accurate, the convergence of FISTA may be restricted when the linear search scheme is applied. To overcome this problem, we tentatively reduce the step size before each iteration to then obtain the most suitable step-size using a linear search approach. To ensure the convergence of the algorithm, we introduce the step size for the previous and subsequent iterations during the calculation process. This has allowed us sparse-spike deconvolution based on an adaptive step size algorithm (ASFISTA), which to a certain extent solves the problem of the degree of convergence of the standard method. In this paper we first present the new algorithm and then we test its convergence. In order to check the effectiveness of the modified algorithm, we use both the standard FISTA method and the improved ASFISTA method to conduct sparse spike deconvolution on a theoretical model. Finally, we carry out a similar analysis aimed at the recovery of the sparse real signal.

Multidimensional Taylor network adaptive control for MIMO time‐varying uncertain nonlinear systems with noises

SummaryIn this paper, an adaptive control approach based on the multidimensional Taylor network (MTN) is proposed here for the real‐time tracking control of multiple‐input–multiple‐output (MIMO) time‐varying uncertain nonlinear systems with noises. Two MTNs are used to formulate the optimum control and adaptive filtering approaches. The feed‐forward MTN controller (MTNC) is developed to realize the precise tracking control. The closed‐loop errors between the filtered outputs and expected values are directly chosen as the MTNC's inputs. A valid initial value selection scheme for the weights of the MTNC, which can ensure the initial stability of adaptive process, is introduced. The proposed MTNC can update its weights online according to errors caused by system's uncertain factors, based on stable learning rate. The resilient backpropagation algorithm and the adaptive variable step size algorithm via linear reinforcement are utilized to update the MTNC's weights. The MTN filter (MTNF) is developed to eliminate measurement noises and other stochastic factors. The proposed adaptive MTN filtering system possesses the distinctive properties of the Lyapunov theory–based adaptive filtering system and MTN. Lyapunov function of the filtering errors between the measured values and MTNF's outputs is defined. By properly choosing the weights update law in the Lyapunov sense, the MTNF's outputs can asymptotically converge to the desired signals. The design is independent of the stochastic properties of the input disturbances. Simulation of the MTN‐based control is conducted to test the effectiveness of the presented results.

Adaptive step size algorithm to increase efficiency of proton macro Monte Carlo dose calculation

PurposeTo provide fast and accurate dose calculation in voxelized geometries for proton radiation therapy by implementing an adaptive step size algorithm in the proton macro Monte Carlo (pMMC) method.MethodsThe in-house developed local-to-global MMC method for proton dose calculation is extended with an adaptive step size algorithm for efficient proton transport through a voxelized geometry by sampling transport parameters from a pre-simulated database. Adaptive choice of an adequate slab size in dependence of material interfaces in the proton’s longitudinal and lateral vicinity is investigated. The dose calculation algorithm is validated against the non-adaptive pMMC and full MC simulation for pencil and broad beams with various energies impinging on academic phantoms as well as a head and neck patient CT.ResultsFor material interfaces perpendicular to a proton’s direction, choice of nearest neighbor slab thickness shows best trade-off between dosimetric accuracy and calculation efficiency. Adaptive reduction of chosen slab size is shown to be required for material interfaces closer than 0.5 mm in lateral direction. For the academic phantoms, dose differences of within 1% or 1 mm compared to full Geant4 MC simulation are found, while achieving an efficiency gain of up to a factor of 5.6 compared to the non-adaptive algorithm and 284 compared to Geant4. For the head and neck patient CT, dose differences are within 1% or 1 mm with an efficiency gain factor of up to 3.4 compared to the non-adaptive algorithm and 145 compared to Geant4.ConclusionAn adaptive step size algorithm for proton macro Monte Carlo was implemented and evaluated. The dose calculation provides the accuracy of full MC simulations, while achieving an efficiency gain factor of three compared to the non-adaptive algorithm and two orders of magnitude compared to full MC for a complex patient CT.

A Path-Planning Strategy for Unmanned Surface Vehicles Based on an Adaptive Hybrid Dynamic Stepsize and Target Attractive Force-RRT Algorithm

It is well known that path planning has always been an important study area for intelligent ships, especially for unmanned surface vehicles (USVs). Therefore, it is necessary to study the path-planning algorithm for USVs. As one of the basic algorithms for USV path planning, the rapidly-exploring random tree (RRT) is popular due to its simple structure, high speed and ease of modification. However, it also has some obvious drawbacks and problems. Designed to perfect defects of the basic RRT and improve the performance of USVs, an enhanced algorithm of path planning is proposed in this study, called the adaptive hybrid dynamic stepsize and target attractive force-RRT(AHDSTAF-RRT). The ability to pass through a narrow area and the forward speed in open areas of USVs are improved by adopting the AHDSTAF-RRT in comparison to the basic RRT algorithm. The improved algorithm is also applied to an actual gulf map for simulation experiments, and the experimental data is collected and organized. Simulation experiments show that the proposed AHDSTAF-RRT in this paper outperforms several existing RRT algorithms, both in terms of path length and calculating speed.

A nonlinear Wiener system identification based on improved adaptive step-size glowworm swarm optimization algorithm for three-dimensional elliptical vibration cutting

Three-dimensional elliptical vibratory cutting (3D EVC) is a precision machining technology that has been extensively used in the aerospace, military, and civil industries. However, if the best processing performance and precise control are required, system identification is the primary prerequisite. Therefore, a 3D EVC nonlinear Wiener model system identification is studied, and an improved adaptive step-size glowworm swarm optimization algorithm (IASGSO) is proposed to identify and optimize the nonlinear Wiener system model parameters. The step-size value of the IASGSO algorithm is adjusted by the distance based on the global best point, which overcomes the shortcomings of the traditional glowworm swarm optimization (GSO) algorithm that is easy to be premature and generate oscillation near the global optimal solution in the later period. The results show that the IASGSO algorithm has the advantage of effectively searching the global optimum value over the traditional GSO algorithm by using two standard test functions to test the performance of both the GSO algorithm and IASGSO algorithm. Based on the system identification experiment, the fitting rate of the proposed method can reach the accuracy of 98.46%, proving the proposed IASGSO algorithm feasibility and accuracy to a large extent. It is expected that both the proposed IASGSO algorithm and the findings in this work will not only solve the local convergence problem of traditional algorithms but also make sense for the precision machining of processing systems.

Mitigating Impulsive Noise for Wavelet-OFDM Powerline Communication

Advanced metering infrastructure (AMI) is an important application of smart grid communication technology used for the remote monitoring and control of smart meters. Broadband powerline communication (BB-PLC) systems could perhaps be used for AMI; however, impulsive noise (IN) greatly degrades performance. In addition to the fast Fourier transform (FFT)-based orthogonal frequency-division multiplexing (OFDM), IEEE 1901 specifications have defined the other physical layer called wavelet-based OFDM. Even though many existing studies have reported the IN mitigation algorithms for the FFT-based OFDM system, these approaches may not directly apply to the wavelet-OFDM-based PLC systems. In this paper, we propose a robust receiver for PLC systems based on wavelet-OFDM. The proposed receiver comprises a pre-IN mitigation block, an adaptive inverse discrete wavelet transform, and an iterative IN reconstruction block. The iterative cancellation of strong IN samples leads to a gradual improvement in the quality of the received signal. Instead of using the frequency domain approach, we reduce the inter-dependency of the channel estimation and per-subchannel equalization by using the time domain signal processing. Besides, we apply variable step-size adaptive algorithms to reduce the impact of IN during the training processes for the channel estimator and per-subchannel equalizer. In accordance with IEEE 1901 specifications, we built a simulation environment to evaluate the effectiveness of the proposed method. Simulation results demonstrated that conventional blanking devices fall short in terms of IN mitigation, and that the proposed scheme is able to achieve performance values approaching those obtained in cases without IN.

The numerical solution of space-dependent neutron kinetics equations in hexagonal-z geometry using backward differentiation formula with adaptive step size

Solving three-dimensional space-dependent neutron kinetics equations in hexagonal-z geometry is presented in this paper. The second order backward differentiation formula (BDF) is used to discretize the time derivative terms of the equations. The semi-discretized equations are the form of the fixed source problems, which can be solved by the function expansion nodal method in the hexagonal-z geometry (Cai et al., 2016). The second order accurate time integration BDF with an adaptive step size algorithm is applied. The backward Euler method and the precursor analytic integration method are also implemented and compared with each other. Some numerical tests are used to compare these methods. The numerical results show that BDF is rather more accurate than the backward Euler method and the precursor analytic integration method when the time step is same. The results also show that BDF with adaptive step size is very efficient.

Exact Expectation Evaluation and Design of Variable Step-Size Adaptive Algorithms

The choice of a fixed step size in adaptive filtering algorithms implies a conflict between the convergence rate and the steady-state performance. In order to address this tradeoff more effectively, variable step-size schemes have been proposed. The efficiency evaluation of such techniques requires comparisons of the resulting step-size values with theoretical optimum values obtained from a statistical analysis of the adaptive algorithm convergence. The analysis generally employs statistical approximations, the most critical being the assumption of independence between the input signal and the filter coefficients. In this letter, it is argued that such a comparison can be misleading because the supposedly optimal step-size sequence sometimes induces divergence in the initial phase of learning. This occurs most often when the input signal is colored and/or heavy tailed. This instability trend can be explained by a convergence analysis that does not employ the independence hypothesis. In addition, the use of this exact analysis implies an optimal step-size sequence that can be significantly different from that obtained with standard analysis methods. This approach can be used to improve the design process of variable step-size adaptive filtering algorithms.

Variable step size adaptive cuckoo search optimization algorithm for phase diversity.

The phase diversity (PD) algorithm will eventually be converted into a large-scale nonlinear numerical optimization problem, so the selection of numerical optimization algorithm will directly determine the accuracy and speed of the algorithm settlement. In this paper, we introduce the cuckoo search optimization algorithm, which has the advantages of simple model, few parameters, and easy implementation, to the phase diversity algorithm. By improving the step size control factor in the original cuckoo search algorithm, we can make it have faster optimization speed for PD. In the simulation experiments, we further proved and gave a simple explanation in theory that in the case of large-scale wavefront sensing, compared to the traditional particle swarm algorithm, this improved algorithm has higher accuracy and faster convergence speed. Finally, we set up a simple experimental system and proved the effectiveness of the improved cuckoo search algorithm for PD.

Adaptive step-size iterative algorithm for sparse signal recovery

Abstract We develop an efficient algorithm, which can adaptively infer the step-size in each iteration, to recover sparse signal from compressive measurements. This algorithm is formulated as an iteratively alternating projection strategy; the first step projects the measurements/residuals to the signal space, implemented via a Bayesian model, and the second step projects the results obtained in the first step to the l1-ball. Variational Bayesian (VB) is employed to perform the inference of the Bayesian model and Euclidean projection (EP) is utilized to impose sparsity; thus our algorithm is dubbed VB-EP. We further derive a maximum likelihood estimator (MLE) of the Bayesian model to speed up the inference with a pre-determined step size. The convergence of this MLE-EP algorithm is analyzed and compared with the iterative shrinkage/thresholding algorithm based on the restricted isometry property of the compressive sensing matrix. Simulation results verify the superior performance of the proposed algorithm.

A BDS Interference Suppression Technique Based on Linear Phase Adaptive IIR Notch Filters.

The continuous wave interferences (CWIs) and the narrow-band interferences (NBIs) have significantly impacted the acquisition, tracking and positioning accuracy of Beidou Navigation Satellite System (BDS) receivers. As an interference suppression technology with a simple structure and low hardware cost, the adaptive infinite-duration impulse response (IIR) notch filter has been widely employed in the receivers to mitigate the CWIs and the NBIs. However, the nonlinear phase characteristics introduced by the IIR notch filters into the navigation receivers, may cause the distortion of navigation signals. It also leads to amplitude and phase distortion of the correlation peak in acquisition and loop tracking, which consequently brings on positioning errors in the measurement domain. This problem, however, has been ignored by many previous papers. Meanwhile, some other researchers came up with the idea of equalizers and all-pass networks compensating the distortion, which is also highly infeasible. Therefore, we propose a new method of an adaptive linear phase IIR notch filter with low hardware cost which is composed of three parts—the complex IIR notch filters, the IIR linear phase structure, and the adaptive and variable step-size algorithms. Applying this method, interference suppression and the correlation peak distortion compensation can be achieved with a modest increase hardware cost. This paper compares the performance of the new method with other IIR filters in both CWI and NBI scene and presents the effects of its parameters on the anti-jamming performance. Simulation results show that the proposed module has better anti-jamming performance in NBI scene and can compensate for the correlation peak distortion in the meantime.

PO-0891: Enhancing efficiency of proton macro Monte Carlo dose calculation by an adaptive step size algorithm

PO-0891: Enhancing efficiency of proton macro Monte Carlo dose calculation by an adaptive step size algorithm

Highly accurate adaptive TOF determination method for ultrasonic thickness measurement

Determining the time of flight (TOF) is very critical for precise ultrasonic thickness measurement. However, the relatively low signal-to-noise ratio (SNR) of the received signals would induce significant TOF determination errors. In this paper, an adaptive time delay estimation method has been developed to improve the TOF determination’s accuracy. An improved variable step size adaptive algorithm with comprehensive step size control function is proposed. Meanwhile, a cubic spline fitting approach is also employed to alleviate the restriction of finite sampling interval. Simulation experiments under different SNR conditions were conducted for performance analysis. Simulation results manifested the performance advantage of proposed TOF determination method over existing TOF determination methods. When comparing with the conventional fixed step size, and Kwong and Aboulnasr algorithms, the steady state mean square deviation of the proposed algorithm was generally lower, which makes the proposed algorithm more suitable for TOF determination. Further, ultrasonic thickness measurement experiments were performed on aluminum alloy plates with various thicknesses. They indicated that the proposed TOF determination method was more robust even under low SNR conditions, and the ultrasonic thickness measurement accuracy could be significantly improved.

A probabilistic model for the numerical solution of initial value problems

We study connections between ordinary differential equation (ODE) solvers and probabilistic regression methods in statistics. We provide a new view of probabilistic ODE solvers as active inference agents operating on stochastic differential equation models that estimate the unknown initial value problem (IVP) solution from approximate observations of the solution derivative, as provided by the ODE dynamics. Adding to this picture, we show that several multistep methods of Nordsieck form can be recasted as Kalman filtering on q-times integrated Wiener processes. Doing so provides a family of IVP solvers that return a Gaussian posterior measure, rather than a point estimate. We show that some such methods have low computational overhead, nontrivial convergence order, and that the posterior has a calibrated concentration rate. Additionally, we suggest a step size adaptation algorithm which completes the proposed method to a practically useful implementation, which we experimentally evaluate using a representative set of standard codes in the DETEST benchmark set.

Applications of adaptive variable step-size algorithm in turbulence observation system

Applications of adaptive variable step-size algorithm in turbulence observation system

Adaptive step-size algorithm for Fourier beam-propagation method with absorbing boundary layer of auto-determined width.

Two algorithms that enhance the utility of the absorbing boundary layer are presented, mainly in the framework of the Fourier beam-propagation method. One is an automated boundary layer width selector that chooses a near-optimal boundary size based on the initial beam shape. The second algorithm adjusts the propagation step sizes based on the beam shape at the beginning of each step in order to reduce aliasing artifacts.

An adaptive stepsize algorithm for the numerical solving of initial-value problems

Abstract The present paper focuses on the efficient numerical solving of initial-value problems (IVPs) using digital computers and one-step numerical methods. We start from considering that the integration stepsize is the crucial factor in determining the number of calculations required and the amount of work involved to obtain the approximate values of the exact solution of a certain problem for a given set of points, within a prescribed computational accuracy, is proportional to the number of accomplished iterations. We perform an analysis of the local truncation error and we derive an adaptive stepsize algorithm which coupled with a certain one-step numerical method makes the use of this structure more computationally effective and insures that the estimated values of the exact solution are in agreement with an imposed accuracy. We conclude with numerical computations proving the efficiency of the proposed step selection algorithm.

Maximum Power Point Controller for Thermoelectric Generators to Support a Vehicle Power Supply

The growing mobility increases the world-wide fuel consumption. Yet the amount of fossil fuel is limited and the environmental burden is increasing dramatically as well. Many governments have enacted laws to regulate and reduce the fuel consumption as well as the CO2 emissions of combustion engines. An idea to save fuel and to reduce the environmental burden is to use thermoelectric generators (TEGs) to recover the waste heat of the exhaust gas and convert into electric energy in automotive applications. For the linking of TEGs to the vehicle is power supply, a DC-DC converter can be used. To support a widerange of TEGs with different electric parameters, the control of DC-DC converter must be robust. Further, the control should track the maximum power point (MPP) of the TEG for an efficient power recovery. This paper presents a digital cascade controller for a boost-buck converter that charges a vehicle battery and supplies the load. To model and analyze the discontinuous converter, the state-space-averaging (SSA) is used. The tracking of the MPP is realized with a gradient algorithm and an input current control. An adaptive step size algorithm reduces the conversion time of the maximum power point tracking algorithm (MPPT). Experiments verified the controller design and the efficiency of the MPPT.

Adaptive Variable Step-Size Algorithm for Acoustic Noise Cancellation by using Multiple Sub-Filters Approach

paper, a novel algorithm for cancelling noise from the speech signal in real time environment is proposed. Least Mean Square (LMS) adaptive noise cancellers are often used to recover signal corrupted by additive noise due to its simplicity in implementation. But it has limitation when the desired signal is strong, that the excess mean-square errors increase linearly with the desired signal power. This results in downgraded performance when the desired signal exhibits large power fluctuations. In the proposed algorithm we use the benefits of both variable step size (VSS) LMS algorithm and Normalized Differential LMS (NDLMS) algorithm to deal with this situation. One more addition of this algorithm is that it uses the concept of decomposing the long adaptive filter into low order multiple sub-filters to relieve the effect of slow convergence of that long adaptive filter. Finally, The proposed (P-VSSNDLMS) algorithm yields faster convergence with minimum mean square error in simulations which carried out using real speech signal with different noise power levels. KeywordsNoise canceller (ANC), mean square error (MSE), VSSNDLMS, multiple sub-filters.