Analytic Framework for Landmark Location Uncertainty

Abstract

In this chapter themathematical tools for analyzing landmark location uncertainty are developed. Two cases are considered. In Section 3.1 tools for calculating the Cramér–Rao lower bound are developed, and in Section 3.2 tools are developed for analyzing practical estimators. The two cases are quite different. The Cramér–Rao lower bound assumes an unbiased estimator, and so the uncertainty is entirely dependent on the covariance component, determined by (∂J/∂ ^pP^∗ _o ) . Practical estimators have bias that is dependent on the true landmark location, ^pP^∗ _o . Interesting challenges arise when performing the integration required, because the bias and covariance can change so rapidly with ^pP^∗ _o .