Modified Recursive Least Square Algorithm Research Articles

Active vibration hybrid control strategy based on multi-DOFs piezoelectric platform

With the increasing requirements for vibration isolation in multiple degrees of freedom (multi-DOFs), active control strategy is becoming more meaningful. However, the vibration isolation performance is limited by the time delay of feedback control, and cannot meet higher requirements. Therefore, this paper proposes a multi-DOFs active vibration hybrid control (AVHC) strategy based on a piezoelectric platform. The AVHC integrates the adaptive feedforward control based on the modified recursive least squares (MRLS) algorithm, and the feedback control based on the integral force feedback (IFF) algorithm. To achieve advanced response, the ground-based vibration signal is offset by the MRLS algorithm. To further reduce the coupling of multi-DOFs, the feedback and feedforward coordinates are fused through the matrix transformation, and the signals are linearly superimposed by the AVHC. The experimental results show that the AVHC can further reduce the resonance peaks of the three translational directions ( X/ Y/ Z) compared with the feedback (FB) control. The resonance peaks are reduced from 14.6 dB (FB) to 3.11 dB (AVHC), from 14.56 dB (FB) to 5.14 dB (AVHC), and from 12.44 dB (FB) to 3.78 dB (AVHC) in X/ Y/ Z directions, respectively. The attenuation rates are improved by 73.36%, 66.19%, and 63.10% in X/ Y/ Z directions, respectively.

Nonlinear Acoustic Echo Canceller to Combat Sigmoid-Type Nonlinearities Under Noisy Environment

This paper presents a nonlinear-acoustic-echo-cancellation (NAEC) technique to tackle sigmoid-type nonlinearities under noisy environment. The nonlinear echo in acoustic systems is inevitable due to the inherent nonlinear characteristics of amplifiers and/or loudspeakers, which deteriorates the quality of speech as well as audio signal reception. Here, the sigmoid-type nonlinearity is modelled by incorporating two control parameters, which determine the shaping- and clipping-parameter values of the saturation curve at a particular room temperature. These control parameters are adjusted by utilizing the variable-step-size (VSS) least-mean-square (LMS) algorithm to enhance the convergence rate and tracking capability of presented NAEC. Furthermore, the impulse response of a room (indoor channel) in the acoustic echo path is modelled as a tap-delay-line finite-impulse-response filter, whose tap-coefficients are estimated by utilizing a modified recursive-least-squares (RLS) algorithm (involving the noise statistics) at the different values of signal-to-noise-ratio (SNR), when correlated as well as uncorrelated input signals are processed. Simulation results demonstrate the efficiency and efficacy of above mentioned adaptive NAEC technique using the VSS-LMS and modified RLS algorithms in terms of the high convergence rate as well as high value of echo-return-loss-enhancement (ERLE) factor. Both the elevating value of shaping-parameter (i.e., increasing nonlinearity level) and the alleviating value of SNR adversely affect the performance of all NAECs. However, the VSS-LMS and modified RLS algorithm based presented adaptive NAEC outperforms the traditional VSS-LMS and normalized-least-mean-square (NLMS) algorithm based NAEC under similar conditions.

A Modified RLS Algorithm for ICA with Weighted Orthogonal Constraint

Independent component analysis (ICA), as an important data processing technique, is widely employed in many areas. The objective of the ICA is to recover independent components from observed signals. Several algorithms, such as equivariant adaptive separation via independence algorithm, least-mean-square (LMS)-type algorithms and recursive least-squares (RLS)-type learning rules, are proposed to solve the ICA problem. In the present paper, a modified RLS algorithm for ICA with weighted orthogonal constraint is developed to implement source separation based on the local convergence analysis of the available algorithm. Comparative experiment results demonstrate that the proposed algorithm is better than existing learning rules in the aspect of the accuracy of separation and stability.

An EMD-MRLS de-noising method for fiber optic gyro Signal

In order to reduce the influence of fiber optic gyroscope (FOG) random drift error on inertial navigation systems (INS), a novel de-noising method is proposed in this paper, which based on an improved empirical mode decomposition (EMD) and modified recursive least square (RLS). Referred to as the EMD-MRLS method, it is developed to decompose the FOG outputs into a number of intrinsic mode functions (IMFs) after which mode manipulations are divided into three parts, noise IMFs, mixed IMFs, and information IMFs by two index parameters based on mahalanobis distance (MD). A modified RLS algorithm is then employed to process the mixed IMFs, from which the refined IMFs components are reconstructed to produce the final de-noising results. Other traditional methods, such as RLS, and EMD are investigated to provide a comparison with the proposed one through both simulated signals and experimental FOG outputs. Compared with the EMD method, the results show that the error mean is reduced by 27.01%, and the horizontal position error is reduced by 106.75m, when the INS lasts for 1000s.

Self-Tuning Control Scheme Based on the Robustnessσ-Modification Approach

This paper deals with the self-tuning control problem of linear systems described by autoregressive exogenous (ARX) mathematical models in the presence of unmodelled dynamics. An explicit scheme of control is described, which we use a recursive algorithm on the basis of the robustnessσ-modification approach to estimate the parameters of the system, to solve the problem of regulation tracking of the system. This approach was designed with the assumptions that the norm of the vector of the parameters is well-known. A new quadratic criterion is proposed to develop a modified recursive least squares (M-RLS) algorithm withσ-modification. The stability condition of the proposed estimation scheme is proved using the concepts of the small gain theorem. The effectiveness and reliability of the proposed M-RLS algorithm are shown by an illustrative simulation example. The effectiveness of the described explicit self-tuning control scheme is demonstrated by simulation results of the cruise control system for a vehicle.

Nonlinear modeling and identification of the electro-hydraulic control system of an excavator arm using BONL model

Electro-hydraulic control systems are nonlinear in nature and their mathematic models have unknown parameters. Existing research of modeling and identification of the electro-hydraulic control system is mainly based on theoretical state space model, and the parameters identification is hard due to its demand on internal states measurement. Moreover, there are also some hard-to-model nonlinearities in theoretical model, which needs to be overcome. Modeling and identification of the electro-hydraulic control system of an excavator arm based on block-oriented nonlinear(BONL) models is investigated. The nonlinear state space model of the system is built first, and field tests are carried out to reveal the nonlinear characteristics of the system. Based on the physic insight into the system, three BONL models are adopted to describe the highly nonlinear system. The Hammerstein model is composed of a two-segment polynomial nonlinearity followed by a linear dynamic subsystem. The Hammerstein-Wiener(H-W) model is represented by the Hammerstein model in cascade with another single polynomial nonlinearity. A novel Pseudo-Hammerstein-Wiener(P-H-W) model is developed by replacing the single polynomial of the H-W model by a non-smooth backlash function. The key term separation principle is applied to simplify the BONL models into linear-in-parameters structures. Then, a modified recursive least square algorithm(MRLSA) with iterative estimation of internal variables is developed to identify the all the parameters simultaneously. The identification results demonstrate that the BONL models with two-segment polynomial nonlinearities are able to capture the system behavior, and the P-H-W model has the best prediction accuracy. Comparison experiments show that the velocity prediction error of the P-H-W model is reduced by 14%, 30% and 75% to the H-W model, Hammerstein model, and extended auto-regressive (ARX) model, respectively. This research is helpful in controller design, system monitoring and diagnosis.

Decouple implementation of weight decay for recursive least square

In the conventional recursive least square (RLS) algorithm for multilayer feedforward neural networks, controlling the initial error covariance matrix can limit weight magnitude. However, the weight decay effect decreases linearly as the number of learning epochs increases. Although we can modify the original RLS algorithm to maintain a constant weight decay effect, the computational and space complexities of the modified RLS algorithm are very high. This paper first presents a set of more compact RLS equations for this modified RLS algorithm. Afterwards, to reduce the computational and space complexities, we propose a decoupled version for this algorithm. The effectiveness of this decoupled algorithm is demonstrated by computer simulations.

A robust RLS detector on tracing wireless channel information

This paper studies the estimation of the fading channel in the present of the impulse noise. The impulse noise suppression function was deduced to improve the ability of suppressing the impulse noise. The analysis has proven that the modified algorithm still meets the linear equation. In addition, this paper applies the modified recursive least square (RLS) algorithm to estimate the impulse response vector in the time-varying fading channel. The simulation results show that the modified RLS algorithm is more robust against consecutive impulse noise and have better convergence ability than conventional RLS.

Online Estimation Algorithm for a Biaxial Ankle Kinematic Model With Configuration Dependent Joint Axes

The kinematics of the human ankle is commonly modeled as a biaxial hinge joint model. However, significant variations in axis orientations have been found between different individuals and also between different foot configurations. For ankle rehabilitation robots, information regarding the ankle kinematic parameters can be used to estimate the ankle and subtalar joint displacements. This can in turn be used as auxiliary variables in adaptive control schemes to allow modification of the robot stiffness and damping parameters to reduce the forces applied at stiffer foot configurations. Due to the large variations observed in the ankle kinematic parameters, an online identification algorithm is required to provide estimates of the model parameters. An online parameter estimation routine based on the recursive least-squares (RLS) algorithm was therefore developed in this research. An extension of the conventional biaxial ankle kinematic model, which allows variation in axis orientations with different foot configurations had also been developed and utilized in the estimation algorithm. Simulation results showed that use of the extended model in the online algorithm is effective in capturing the foot orientation of a biaxial ankle model with variable joint axis orientations. Experimental results had also shown that a modified RLS algorithm that penalizes a deviation of model parameters from their nominal values can be used to obtain more realistic parameter estimates while maintaining a level of estimation accuracy comparable to that of the conventional RLS routine.

Modified RLS Algorithm and Its Application to Channel Estimation for CDMA Systems

A new adaptive algorithm is proposed by introducing some modifications to the recursive least squares (RLS) algorithm. Except for the noise variance, the proposed algorithm does not require any statistics or knowledge of the desired signal, thus, it is suitable for adaptive filtering for channel estimation in code division multiple access (CDMA) systems in cases where the standard RLS approach cannot be used. A theoretical analysis demonstrates the convergence of the proposed algorithm, and simulation results for CDMA channel estimation show that the proposed algorithm outperforms existing channel estimation schemes.

Modified Recursive Least Squares algorithm to train the Hybrid Multilayered Perceptron (HMLP) network

In this paper, a new learning algorithm, called the Modified Recursive Least Square (MRLS), is introduced for the Hybrid Multilayered Perceptron (HMLP) network. Adopting the Recursive Least Square (RLS) algorithm as its basis, the MRLS algorithm differs from RLS in the way that the weight of the linear connections for the HMLP network is estimated. The convergence rate of the MRLS algorithm is further improved by varying the forgetting factor, optimizing the way the momentum and learning rate are assigned. To investigate its applicability, the MRLS algorithm is demonstrated on the HMLP network using six benchmark data sets obtained from the UCI repository. The classification performance of the HMLP network trained with the MRLS algorithm is compared with those of the HMLP network trained with the Modified Recursive Prediction Error (MRPE) algorithm and the MLP trained with the standard RLS algorithm as well as with other commonly adopted machine learning classifiers. The comparison results indicated that the proposed MRLS trained HMLP network provides significant improvement over RLS trained MLP network, MRPE trained HMLP network, and other machine learning classifiers in terms of accuracy, convergence rate and mean square error (MSE).