An iterative algorithm for solving ill-conditioned linear least squares problems

A collaborative method for positioning based on GNSS inter agent range estimation

“…In this case the quality of the estimated position may be very low. In fact, it is well known that linearised set of equations are very sensitive to linear dependence of matrix rows and to small perturbation of them [14]. The hybrid PVT algorithm presented, leads indeed to a typical illconditioned set of equations and it shows high instability of the convergence of the solution.…”

“…The hybrid PVT algorithm presented, leads indeed to a typical illconditioned set of equations and it shows high instability of the convergence of the solution. An iterative algorithm proposed in [14] is adopted to enhance the convergence performance avoiding the inversion of the ill-conditioned HH product by means of a Self Adaptive Iterative Algorithm (SAIA) of Weighted Least Mean Square. For sake of completeness, the core steps of SAIA method are remarked here with a more familiar notation.…”

Combined Geometric Positioning and Performance Analysis of Multi-Resolution Optical Imageries from Satellite and Aerial Platforms Based on Weighted RFM Bundle Adjustment

“…However, in extremely ill-conditioned situations, the spectral decomposition converges slowly to obtain higher accuracy. In some cases, the convergence results deviate significantly from the true values [66]. Meanwhile, ridge parameter estimation [67,68] is a biased estimation that can suppress the morbidity of the equation by introducing an appropriate value on the main diagonal of the normal equations so that a more realistic and reliable ridge estimation solution can be achieved.…”

Novel identification algorithms for Hammerstein systems in ill-conditioned situations

“…However, if excitation is insufficient, the covariance matrix becomes very large and the singularity problem will be created. A number of studies have been performed in the field of system identification in ill-conditioned situations by using singular value decomposition (SVD) and least squares (LS) algorithms (Deng et al, 2015;Zhang et al, 1994). A Damped Least Squares (DLS) method was also obtained for parameter estimation in ill-conditioned situations (Lambert, 1987).…”