The standard approaches to solving overdetermined linear systems Ax ≈ b construct minimal corrections to the data to make the corrected system compatible. In ordinary least squares (LS) the correction is restricted to the right hand side b, while in scaled total least squares (Scaled TLS) [10; 7] corrections to both b and A are allowed, and their relative sizes are determined by a real positive...

Least Squares Support Vector Machines (LS-SVMs) were proposed by replacing the inequality constraints inherent to L1-SVMs with equality constraints. So far this idea has only been suggested for a least squares (L2) loss. We describe how this can also be done for the sumof-slacks (L1) loss, yielding a new classifier (Least 1-Norm SVMs) which gives similar models in terms of complexity and accura...

For the lifted input–output representation of general dual-rate sampled-data systems, this paper presents a decomposition based recursive least squares (D-LS) identification algorithm using the hierarchical identification principle. Compared with the recursive least squares (RLS) algorithm, the proposed D-LS algorithmdoes not require computing the covariancematriceswith large sizes andmatrix in...

A novel least-squares (LS) scheme to estimate the channel frequency response (CFR) for orthogonal frequency division multiplexing (OFDM) over slow fading channels is presented. We take the advantage of slow fading to use repeated OFDM training blocks. This not only can facilitate the LS formulation but also improve the channel estimation performance as compared to the conventional one block LS ...

Sinusoidal model and its variants are commonly used in speech processing. In the literature, there are various methods for the estimation of the unknown parameters of sinusoidal model such as Fourier transform based on FFT algorithm and Least Squares (LS) method. Least Squares method is more accurate and actually optimum for Gaussian noise, thus, more appropriate for high-quality signal process...

We address the problem of joint Schur decomposition (JSD) of several matrices. This problem is of great importance for many signal processing applications such as sonar, biomedicine, and mobile communications. We rst present a least-squares (LS) approach for computing the JSD. The LS approach is shown to coincide with that proposed intuitively by Haardt et al, thus establishing the optimality o...

Within the context of nonlinear system identification, different variants of LS-SVM are applied to the Silver Box dataset. Starting from the dual representation of the LS-SVM, and using Nyström techniques, it is possible to compute an approximation for the nonlinear mapping to be used in the primal space. In this way, primal space based techniques as Ordinary Least Squares (OLS), Ridge Regressi...

A simple and rapid method for the determination of 137Ba isotope abundances in water samples by inductively coupled plasma-optical emission spectrometry (ICP-OES) coupled with least-squares support vector machine regression (LS-SVM) is reported. By evaluation of emission lines of barium, it was found that the emission line at 493.408 nm provides the best results for the determination...

A QR-decomposition based algorithm is presented for unbiased, equation error adaptive IIR filtering. The algorithm is based on casting the adaptive IIR filtering in a mixed Least Squares Total Least Squares (LS-TLS) framework. This formulation is shown to be equivalent to the minimization of the mean-square equation error subject to a unit norm constraint on the denominator parameter vector. An...

The ill conditioning problem of sensor registration is considered. We analyze the ill conditioning in the dense-target scenario and the dense-sensor scenario, respectively, and present a robust registration method based on the bounded variables least squares (BVLS). The proposed approach can reduce the influence of ill conditioning by means of inserting prior constraints on the desired solution...