Estimation with maximum error requirements

We consider the problem of estimating a deterministic parameter vector x from observations y = Hx + w, where H is known and w is additive noise. We seek an estimator whose estimation error is within given limits, for as wide a range of conditions as possible. The error limit is a design choice, and is generally lower than the error provided by the well-known least-squares (LS) estimator. We develop estimators guaranteeing the required error for as large a parameter set as possible, and for as large a noise level as possible. We discuss methods for finding these estimators, and demonstrate that in many cases, the proposed estimators outperform the LS estimator.