Theoretical Accuracy Limit

Abstract

We derive here a theoretical accuracy limit of the geometric estimation problem in the general mathematical framework described in Chaps. 14 and 15. It is given in the form of a bound, called the KCR (Kanatani-Cramer-Rao) lower bound, on the covariance matrix of the solution $\varvec{\theta }$. The resulting form indicates that all iterative algebraic and geometric methods achieve this bound up to higher-order terms in $\sigma$, meaning that these are all optimal with respect to covariance. As in Chaps. 14 and 15, we treat $\varvec{\theta }$ and $\varvec{\xi }_{\alpha }$ as nD vectors for generality.