Search results for "Total least squares"
showing 8 items of 8 documents
Algorithms for rational discrete least squares approximation
1975
In this paper an algorithm for the computation of a locally optimal polefree solution to the discrete rational least squares problem under a mild regularity condition is presented. It is based on an adaptation of projection methods [8], [12], [13], [14], [18], [19] to the modified Gaus-Newton method [4], [10]. A special device makes possible the direct handling of the infinitely many linear constraints present in this problem.
Algorithms for Rational Discrete Least Squares Approximation Part I: Unconstrained Optimization
1976
In this paper a modification of L. Wittmeyer’s method ([1], [14]) for rational discrete least squares approximation is given which corrects for its failure to converge to a non-optimal point in general. The modification makes necessary very little additional computing effort only. It is analysed thoroughly with respect to its conditions for convergence and its numerical properties. A suitable implementation is shown to be benign in the sense of F. L. Bauer [2]. The algorithm has proven successful even in adverse situations.
Quantile regression via iterative least squares computations
2012
We present an estimating framework for quantile regression where the usual L 1-norm objective function is replaced by its smooth parametric approximation. An exact path-following algorithm is derived, leading to the well-known ‘basic’ solutions interpolating exactly a number of observations equal to the number of parameters being estimated. We discuss briefly possible practical implications of the proposed approach, such as early stopping for large data sets, confidence intervals, and additional topics for future research.
A generalization of the orthogonal regression technique for life cycle inventory
2012
Life cycle assessment (LCA) is a method used to quantify the environmental impacts of a product, process, or service across its whole life cycle. One of the problems occurring when the system at hand involves processes delivering more than one valuable output is the apportionment of resource consumption and environmental burdens in the correct proportion amongst the products. The mathematical formulation of the problem is represented by the solution of an over-determined system of linear equations. The paper describes the application of an iterative algorithm for the implementation of least square regression to solve this over-determined system directly in its rectangular form. The applied …
Descriptor-type Kalman Filter and TLS EXIN Speed Estimate for Sensorless Control of a Linear Induction Motor.
2014
This paper proposes a speed observer for linear induction motors (LIMs), which is composed of two parts: 1) a linear Kalman filter (KF) for the online estimation of the inductor currents and induced part flux linkage components; and 2) a speed estimator based on the total least squares (TLS) EXIN neuron. The TLS estimator receives as inputs the state variables, estimated by the KF, and provides as output the LIM linear speed, which is fed back to the KF and the control system. The KF is based on the classic space-vector model of the rotating induction machine. The end effects of the LIMs have been considered an uncertainty treated by the KF. The TLS EXIN neuron has been used to compute, in …
TOWARD A SOLUTION OF ALLOCATION IN LIFE CYCLE INVENTORIES: THE USE OF LEAST SQUARES TECHNIQUES
2010
Purpose: The matrix method for the solution of the so-called inventory problem in LCA generally determines the inventory vector related to a specific system of processes by solving a system of linear equations. The paper proposes a new approach to deal with systems characterized by a rectangular (and thus non-invertible) coefficients matrix. The approach, based on the application of regression techniques, allows solving the system without using computational expedients such as the allocation procedure. Methods: The regression techniques used in the paper are (besides the ordinary least squares, OLS) total least squares (TLS) and data least squares (DLS). In this paper, the authors present t…
Neural Sensorless Control of Linear Induction Motors by a Full-Order Luenberger Observer Considering the End Effects
2012
This paper proposes a neural based full-order Luenberger adaptive speed observer for sensorless linear induction motor (LIM) drives, where the linear speed is estimated with the total least squares (TLS) EXIN neuron. A novel state space-vector representation of the LIM has been deduced, taking into consideration its dynamic end effects. The state equations of the LIM have been rearranged into a matrix form to be solved, in terms of the LIM linear speed, by any least squares technique. The TLS EXIN neuron has been used to compute online, in recursive form, the machine linear speed. A new gain matrix choice of the Luenberger observer, specifically taking into consideration the LIM dynamic end…
Sensorless induction machine drive for fly-wheel generation unit based on a TLS-based non-linear observer
2016
This paper proposes a sensorless technique for an induction machine Flywheel Energy Storage System (FESS) based on a non-linear observer integrated with a total least-squares speed estimator taking into consideration the IM (Induction Machine) saturation effects. The nonlinear observer is based on an original formulation of the dynamic model of the IM including the magnetic saturation, rearranged in a space-state form, after assuming as state variables the stator current and the rotor magnetizing current space-vectors in the stator reference frame. The choice of the observer gain has been made by the use of Lyapunov's method. The speed signal needed by the non-linear observer for the flux e…