Robust Nonlinear Estimation Research Articles

Interval analysis for guaranteed and robust non-linear estimation in robotics

One of the challenges of interval analysis is to explore and bridge the gap between trivial illustrative examples for which it is not really needed and actual complicated applications for which it is still powerless. Two examples of applications pertaining to this gap are presented in this paper. The first one corresponds to the forward kinematic problem for a Stewart-Gough patform, a benchmark for numerical and symbolical computations. All real solutions are isolated in a guaranteed manner. The second example is relative to the localization and tracking of a vehicle in a unavoidable presence of outliers is taken into account, which makes the method acyually applicable. None of these problems can be solved satisfactorily by the usual local numerical methods based on iterative refinements, and the advantages provided by an approach based on interval analysis are evidenced.

Support Vector Machines: A Nonlinear Modelling and Control Perspective

In recent years neural networks as multilayer perceptrons and radial basis function networks have been frequently used in a wide range of fields, including control theory, signal processing and nonlinear modelling. A promising new methodology is Support Vector Machines (SVM), which has been originally introduced by Vapnik within the area of statistical learning theory and structural risk minimization. SVM approaches to classification, nonlinear function and density estimation lead to convex optimization problems, typically quadratic programming. However, due to their non-parametric nature, the present SVM methods were basically restricted to static problems. We discuss a method of least squares support vector machines (LS-SVM), which has been extended to recurrent models and use in optimal control problems. We explain how robust nonlinear estimation and sparse approximation can be done by means of this kernel based technique. A short overview of hyperparameter tuning methods is given. SVM methods are able to learn and generalize well in large dimensional input spaces and have outperformed many existing methods on benchmark data sets. Its full potential in a dynamical systems and control context remains to be explored.

Temporal properties of the hemodynamic response in functional MRI

Today, most studies of cognitive processes using functional magnetic resonance imaging (fMRI) adopt an event-related experimental design. Highly flexible stimulation settings require new statistical models where not only the activation amount, but also the time course of the measured hemodynamic response is analyzed. It is possible to obtain statistically valid descriptions of single hemodynamic responses from a robust nonlinear estimation procedure. Focus is placed on the temporal behaviour of the hemodynamic response: relative temporal order, changes induced by modification of the experimental context, and interindividual differences. Example analyses from recent fMRI studies underline the usefulness of this approach. Hum. Brain Mapping 8:259–271, 1999. © 1999 Wiley-Liss, Inc.

Temporal properties of the hemodynamic response in functional MRI

Today, most studies of cognitive processes using functional magnetic resonance imaging (fMRI) adopt an event-related experimental design. Highly flexible stimulation settings require new statistical models where not only the activation amount, but also the time course of the measured hemodynamic response is analyzed. It is possible to obtain statistically valid descriptions of single hemodynamic responses from a robust nonlinear estimation procedure. Focus is placed on the temporal behaviour of the hemodynamic response: relative temporal order, changes induced by modification of the experimental context, and interindividual differences. Example analyses from recent fMRI studies underline the usefulness of this approach.