Robust Filtering and Estimation with Bounded Uncertainties

There are always discrepancies between design models and the actual physical systems or phenomena that they model. These discrepancies can be due to several factors including the approximation of complex models by simpler ones, the presence of unavoidable experimental errors when collecting data, or even due to unknown or unmodeled effects. Regardless of their source, such perturbations can degrade the performance of otherwise optimal designs. Examples to this effect abound in the fields of signal and image processing, digital communications, control, and others.

These possibilities have motivated over the years numerous investigations on robust design techniques that are less sensitive to such perturbations including, among others, total-least-squares methods and H_oo methods. In this talk, we provide an overview of some recent research efforts on new design strategies for models and data with bounded perturbations. In comparison to TLS and H_oo methods, the resulting design procedures perform data regularization as opposed to de-regularization. The new formulations also share some geometric properties with least-squares designs and rely on constrained game-type scenarios. The framework is broad enough to encompass applications across several disciplines, including both signal processing and control.

Examples and comparisons will be given in the context of co-channel interference cancellation, image restoration and image separation, data fusion, adaptive filtering, and Kalman filtering.