Performance measures for estimating vector systems

We propose a framework of performance measures for analyzing estimators of geometrical vectors that have intuitive physical interpretations, are independent of the coordinate frame and parameterization, and have no artificial singularities. We obtain finite-sample and asymptotic lower bounds on them for large classes of estimators and show how they may be used as system design criteria. We determine a simple asymptotic relationship that is applicable to both the measures and their bounds.