#### Communications and Signal Processing Seminar

# Robust MSE Estimation: New Methods for Old Problems

The problem of estimating a set of unknown deterministic parameters x

observed through a linear transformation H and corrupted by additive

noise, i.e., y = H x + w, arises in a large variety of areas in science

and engineering. Owing to the lack of statistical information about the

parameters x, the estimated parameters are typically chosen to optimize

a criterion based on the observed signal y. For example, the celebrated

least-squares estimator is chosen to minimize the Euclidian norm of the

data error. However, in an estimation context, the objective

typically is to minimize the size of the estimation error,

rather than that of the data error. It is well known that

estimators based on minimizing a data error can lead to a large

estimation error.

In this talk, we introduce a new framework for linear estimation, that

is aimed at developing effective linear estimators which minimize

criteria that are directly related to the estimation error. In

developing this framework, we exploit recent results in convex

optimization theory and nonlinear programming. As we demonstrate, this

framework leads to new, powerful, estimation methods that can

significantly outperform existing estimators such as least-squares and

Tikhonov regularization.

http://www.ee.technion.ac.il/Sites/People/YoninaEldar/