Prediction of Time Series Empowered with a Novel SREKRLS Algorithm

For the unforced dynamical non-linear state–space model,a new Q1 and efficient square root extended kernel recursive least square estimation algorithm is developed in this article.The proposed algorithm lends itself towards the parallel implementation as in the FPGA systems.With the help of an ortho-normal triangularization method,which relies on numerically stable givens rotation,matrix inversion causes a computational burden,is reduced.Matrix computation possesses many excellent numerical properties such as singularity,symmetry,skew symmetry,and triangularity is achieved by using this algorithm.The proposed method is validated for the prediction of stationary and non-stationary Mackey–Glass Time Series,along with that a component in the x-direction of the Lorenz Times Series is also predicted to illustrate its usefulness.By the learning curves regarding mean square error(MSE)are witnessed for demonstration with prediction performance of the proposed algorithm from where it’s concluded that the proposed algorithm performs better than EKRLS.This new SREKRLS based design positively offers an innovative era towards non-linear systolic arrays,which is efficient in developing very-large-scale integration(VLSI)applications with non-linear input data.Multiple experiments are carried out to validate the reliability,effectiveness,and applicability of the proposed algorithm and with different noise levels compared to the Extended kernel recursive least-squares(EKRLS)algorithm.

Application of RLS adaptive filteringin signal de-noising

In view of the problem that noises are prone to be mixed in the signals,an adaptive signal de-noising system based on reursive least squares （RLS） algorithm is introduced.The principle of adaptive filtering and the process flow of RLS algorithm are described.Through example simulation,simulation figures of the adaptive de-noising system are obtained.By analysis and comparison,it can be proved that RLS adaptive filtering is capable of eliminating the noises and obtaining useful signals in a relatively good manner.Therefore,the validity of this method and the rationality of this system are demonstrated.

Forward/backward prediction solution for adaptive noisy FIR filtering

An important and hard problem in signal processing is the estimation of parameters in the presence of observation noise.In this paper, adaptive finite impulse response （FIR） filtering with noisy input-output data is considered and two developed bias compensation least squares （BCLS） methods are proposed.By introducing two auxiliary estimators, the forward output predictor and the backward output predictor are constructed respectively.By exploiting the statistical properties of the cross-correlation function between the least squares （LS） error and the forward/backward prediction error, the estimate of the input noise variance is obtained; the effect of the bias can thereafter be removed.Simulation results are presented to illustrate the good performances of the proposed algorithms.

An LDPC coded cooperative MIMO scheme over Rayleigh fading channels with unknown channel state information

This paper describes a coded cooperative multiple-input multiple-output(MIMO) scheme,where structured low-density parity-check(LDPC) codes belonging to a family of repeat-accumulate(RA) codes are employed.The outage probability of the scheme over Rayleigh fading channels is deduced.In an unknown channel state information(CSI) scenario,adaptive transversal filters based on a spatio-temporal recursive least squares(ST-RLS) algorithm are adopted in the destination to realize receive diversity gain.Also,a joint 'Min-Sum' iterative decoding is effectively carried out in the destination.Such a decoding algorithm agrees with the bilayer Tanner graph that can be used to fully characterize two distinct structured LDPC codes employed by the source and relay.Simulation results verify the effectiveness of the adopted filter in the coded cooperative MIMO scheme.Theoretical analysis and numerical simulations show that the LDPC coded cooperative MIMO scheme can well combine cooperation diversity,multi-receive diversity,and channel coding gains,and clearly outperforms coded noncooperation schemes under the same conditions.

Fast adaptive principal component extraction based on a generalized energy function

By introducing an arbitrary diagonal matrix, a generalized energy function (GEF) is proposed for searching for the optimum weights of a two layer linear neural network. From the GEF, we derive a recur- sive least squares (RLS) algorithm to extract in parallel multiple principal components of the input covari- ance matrix without designing an asymmetrical circuit. The local stability of the GEF algorithm at the equilibrium is analytically verified. Simulation results show that the GEF algorithm for parallel multiple principal components extraction exhibits the fast convergence and has the improved robustness resis- tance to the eigenvalue spread of the input covariance matrix as compared to the well-known lateral inhi- bition model (APEX) and least mean square error reconstruction (LMSER) algorithms.