Abstract: Within geostatistics research, effective estimation of
the variogram points has been examined, particularly in developing
robust alternatives. The parametric fit of these variogram points which
eventually defines the kriging weights, however, has not received
the same attention from a robust perspective. This paper proposes
the use of the non-linear Wilcoxon norm over weighted non-linear
least squares as a robust variogram fitting alternative. First, we
introduce the concept of variogram estimation and fitting. Then, as
an alternative to non-linear weighted least squares, we discuss the
non-linear Wilcoxon estimator. Next, the robustness properties of the
non-linear Wilcoxon are demonstrated using a contaminated spatial
data set. Finally, under simulated conditions, increasing levels of
contaminated spatial processes have their variograms points estimated
and fit. In the fitting of these variogram points, both non-linear
Weighted Least Squares and non-linear Wilcoxon fits are examined
for efficiency. At all levels of contamination (including 0%), using
a robust estimation and robust fitting procedure, the non-weighted
Wilcoxon outperforms weighted Least Squares.
Abstract: This paper describes a new method for affine parameter
estimation between image sequences. Usually, the parameter
estimation techniques can be done by least squares in a quadratic
way. However, this technique can be sensitive to the presence
of outliers. Therefore, parameter estimation techniques for various
image processing applications are robust enough to withstand the
influence of outliers. Progressively, some robust estimation functions
demanding non-quadratic and perhaps non-convex potentials adopted
from statistics literature have been used for solving these. Addressing
the optimization of the error function in a factual framework for
finding a global optimal solution, the minimization can begin with
the convex estimator at the coarser level and gradually introduce nonconvexity
i.e., from soft to hard redescending non-convex estimators
when the iteration reaches finer level of multiresolution pyramid.
Comparison has been made to find the performance of the results
of proposed method with the results found individually using two
different estimators.
Abstract: This paper addresses parameter and state estimation problem in the presence of the perturbation of observer gain bounded input disturbances for the Lipschitz systems that are linear in unknown parameters and nonlinear in states. A new nonlinear adaptive resilient observer is designed, and its stability conditions based on Lyapunov technique are derived. The gain for this observer is derived systematically using linear matrix inequality approach. A numerical example is provided in which the nonlinear terms depend on unmeasured states. The simulation results are presented to show the effectiveness of the proposed method.