Stability in linear estimation

The stability with respect to model uncertainty of linear estimators of the coefficients of a linear combination of deterministic signals in noise is investigated. A class of estimators having nominal performances constrained to be close to that of the nominal linear, unbiased, minimum-variance (LUMV) estimator is specified. Two estimator stability indexes are defined, one based on a worst-case estimate mean-square error and the other on a type of signal-to-noise ratio. The estimator minimizing each index, subject to the optimality constraints, is found by reference to related LUMV estimation results. In most cases, the minimizing (or most stable) estimator is the same under the two indexes