Extended Kalman Filter Training Algorithm Research Articles

Fuzzy wavelet network based on extended Kalman filter training algorithm combined with least square weight estimation: Efficient and improved chromatographic QSRR/QSPR models

Inspired by the theory of multiresolution analysis (MRA) of wavelet transforms and fuzzy concepts, a fuzzy wavelet network (FWN) is proposed for predicting the gas chromatographic retention time of phenol derivatives on fused-silica, wide-bore, and open-tubular columns with different polarities in terms of quantitative structure-retention relationship (QSRR) studies. The FWN consists of a set of fuzzy rules. Each rule corresponding to a sub-wavelet neural network (WNN) consists of single-scaling wavelets. The proposed FWN follows a two-stage efficient learning algorithm scheme, which undertakes the extended Kalman filter (EKF) training algorithm for adjusting all translation parameters, dilation parameters, and weight coefficients of the WNNs and then least square estimation for updating all the weights. 4-3-1 FWNs were developed using the descriptors selected by the multiple linear regression (MLR) models as inputs. By learning the translation parameters of the wavelets and adjusting the shape of membership functions, the model accuracy was remarkably improved. The accuracy and robustness of the generated models were illustrated using leave-one-out and leave-multiple-out cross-validations and also by Y-randomization. Sensitivity analysis by sequential zeroing of weights revealed that the molecular geometry and electronic interactions play a major role in the retention behavior of these compounds on non-polar and semi-polar columns, respectively.

Discrete-time high order neural network identifier trained with cubature Kalman filter

Abstract This paper presents a method to identify a nonlinear system, employing high order neural networks. Given an unknown discrete-time nonlinear plant subject to disturbances, a high order neural network is proposed to approximate its dynamics. To train the neural network weights, considered as new states, the cubature Kalman filter is used. A simulation example and an experimental study are included to show effectiveness of the proposed scheme. The results given by the proposed method are compared to the results produced by the extended Kalman filter training algorithm.

Control of an Industrial PA10-7CE Robot Arm Based on Decentralized Neural Backstepping Approach

This paper presents a discrete-time decentralized control strategy for trajectory tracking of a Mitsubishi PA10-7CE robot arm. A high order neural network is used to approximate a decentralized control law designed by the backstepping technique as applied to a block strict feedback form. The weights for each neural network are adapted online by extended Kalman filter training algorithm. The motion of each joint is controlled independently using only local angular position and velocity measurements. The stability analysis for closed-loop system via Lyapunov theory is included. Finally, the simulations results show the feasibility of the proposed scheme.

Dimensional Analysis of Acid Etching Effects on Vertically Grown Carbon Nanofibers Using Atomic Force Microscopy

This paper presents a discrete-time decentralized control scheme for trajectory tracking of a two degrees of freedom (DOF) robot manipulator. A high order neural network (HONN) is used to approximate a decentralized control law designed by the backstepping technique as applied to a block strict feedback form (BSFF). The weights for each neural network are adapted online by an extended Kalman filter training algorithm. The motion for each joint is controlled independently using only local angular position and velocity measurements. The stability analysis for the closed-loop system via the Lyapunov approach is included. Finally, the real-time results show the feasibility of the proposed control scheme robot manipulator.

Decentralized Neural Backstepping Control Applied to a Robot Manipulator

This paper presents a discrete-time decentralized control scheme for trajectory tracking of a two degrees of freedom (DOF) robot manipulator. A high order neural network (HONN) is used to approximate a decentralized control law designed by the backstepping technique as applied to a block strict feedback form (BSFF). The weights for each neural network are adapted online by an extended Kalman filter training algorithm. The motion for each joint is controlled independently using only local angular position and velocity measurements. The stability analysis for the closed-loop system via the Lyapunov approach is included. Finally, the real-time results show the feasibility of the proposed control scheme using a robot manipulator.

Kalman filters improve LSTM network performance in problems unsolvable by traditional recurrent nets

The long short-term memory (LSTM) network trained by gradient descent solves difficult problems which traditional recurrent neural networks in general cannot. We have recently observed that the decoupled extended Kalman filter training algorithm allows for even better performance, reducing significantly the number of training steps when compared to the original gradient descent training algorithm. In this paper we present a set of experiments which are unsolvable by classical recurrent networks but which are solved elegantly and robustly and quickly by LSTM combined with Kalman filters.

Blind identification of quadratic nonlinear models using neural networks with higher order cumulants

A novel approach to blindly estimate kernels of any discrete- and finite-extent quadratic models in higher order cumulants domain based on artificial neural networks is proposed in this paper. The input signal is assumed an unobservable independently identically, distributed random sequence which is viable for engineering practice. Because of the properties of the third-order cumulant functions, identifiability of the nonlinear model holds, even when the model output measurement is corrupted by a Gaussian random disturbance. The proposed approach enables a nonlinear relationship between model kernels and model output cumulants to be established by means of neural networks. The approximation ability of the neural network with the weights-decoupled extended Kalman filter training algorithm is then used to estimate the model parameters. Theoretical statements and simulation examples together with practical application to the train vibration signals modeling corroborate that the developed methodology is capable of providing a very promising way to identify truncated Volterra models blindly.