Performance bounds for estimating vector systems

We propose a unified framework fur the analysis of estimators of geometrica l vector quantities and vector systems through a collection of performance measures. Unlike standard performance indicators, these measures have intui tive geometrical and physical interpretations, are independent of the coord inate reference frame, and are applicable to arbitrary parameterizations of the unknown vector or system of vectors. For each measure, we derive both finite sample and asymptotic lower bounds that hold for large classes of es timators and serve as benchmarks for the assessment of estimation algorithm s, Like the performance measures themselves, these bounds are independent o f the reference coordinate frame, and we discuss their use as system design criteria.