Several numerical methods for the solution of large linear ill-posed problems combine Tikhonov regularization with an iterative method based on partial Lanczos bidiagonalization of the operator. This paper discusses the determination of the regularization parameter and the dimension of the Krylov subspace for this kind of methods. A method that requires a Krylov subspace of minimal dimension is...

The L-curve is often applied to determine a suitable value of the regularization parameter when solving ill-conditioned linear systems of equations with a right-hand side contaminated by errors of unknown norm. The location of the vertex of the L-curve typically yields a suitable value of the regularization parameter. However, the computation of the L-curve and of its curvature is quite costly ...

Regularization is a standard statistical technique to deal with ill-conditioned parameter estimation problems. We discuss in this contribution what possibilities and advantages regularization ooers in system identiication. In the rst place regularization reduces the variance error of a model, but at the same time it introduces a bias. The familiar trade-oo between bias and variance error for th...

Nowadays, navigation is an unavoidable fact in military and civil aerial transportations. The Global Positioning System (GPS) is commonly used for computing the orientation or attitude of a moving platform. The relative positions of the GPS antennas are computed using the GPS code and/or phase measurements. To achieve a precise attitude determination, Carrier phase observations of GPS requiring...