The Structured Total Least Squares (STLS) problem is an extension of the Total Least Squares (TLS) problem for solving an overdetermined system of equations Ax ≈ b. The Dynamic Total Least Squares (DTLS) problem is a special case of STLS problem. In this paper, we illustrate the TLS singular value problem by defining some vectors from a new viewpoint. And we also derive the DTLS nonlinear singu...

A solution to the singularity problem of a non–redundant robot is proposed by reformulating the inverse kinematic problem as a constraint optimization problem. The main idea is to allow a cartesian error in a certain subspace in the vicinity of a singuarity and to minimize this error subject to operational constraints such as maximum motor speeds. As a result, in every sampling instant a series...

These algorithms are, however, not designed to perform least-squares minimization under hard constraints. This short report outlines two very simple approaches to doing this to solve problems such as the one depicted by Fig. 1. The first relies on standard Lagrange multipliers [Boyd and Vandenberghe, 2004]. The second is inspired by inverse kinematics techniques [Baerlocher and Boulic, 2004] an...

This paper is focused on the application of inverse problem methodology for solving some problems that have emerged in space science. The inverse model is an implicit technique: a constrained non-linear optimization problem, in which the forward problem is iteratively solved for successive approximations of the unknown parameters. Iteration proceeds until an objective-function, representing the...

A new adaptive neural network controller for robots is presented. The controller is based on direct adaptive techniques. Unlike many neural network controllers in the literature, inverse dynamical model evaluation is not required. A numerically robust, computationally efficient processing scheme for neural network weight estimation is described, namely, the inverse QR decomposition (INVQR). The...

The least-squares linear inverse estimation problem for random fields is studied in a fractional generalized framework. First, the second-order regularity properties of the random fields involved in this problem are analysed in terms of the fractional Sobolev norms. Second, the incorporation of prior information in the form of a fractional stochastic model, with covariance operator bicontinuous...

Given a full rank matrix X with more columns than rows, consider the task of estimating the pseudo inverse X based on the pseudo inverse of a sampled subset of columns (of size at least the number of rows). We show that this is possible if the subset of columns is chosen proportional to the squared volume spanned by the rows of the chosen submatrix (ie, volume sampling). The resulting estimator...

Consider a regression model with infinitely many parameters and time series errors. We are interested in choosing weights for averaging across generalized least squares (GLS) estimators obtained from a set of approximating models. However, GLS estimators, depending on the unknown inverse covariance matrix of the errors, are usually infeasible. We therefore construct feasible generalized least s...

Because frequency load identification method will confront with the ill-posed problem of finding the inverse of coefficient matrix and it can only identify one load source, a new uncorrelated multi-source load identification algorithm based on linear regression and least-squares of generalized matrix inverse is proposed. According to response signals of multi-spot, this new algorithm can identi...

Absmct-In this work, we investigate an adaptive multigrid background (BG). A least squares solution is formulated for approach to improve the computational efficiency and the wanthe 2D inverse problem and a conjugate gradient method is titatiVe of Dm mconstNction. The idea employed at the relaxation stage of the multigrid solver, The is based on locally refined grid structure for region of inte...