On the Performance Limits of Map-Aware Localization

TL;DR

This paper derives new theoretical bounds on localization accuracy by incorporating environmental map information, revealing how map features and signal conditions influence achievable precision.

Contribution

It introduces novel bounds for map-aware localization, linking accuracy to map characteristics and identifying conditions where detailed maps are unnecessary.

Findings

Map-aware bounds relate accuracy to map shape and size.

Maps significantly improve localization under low SNR and certain geometries.

Refined maps often do not enhance accuracy beyond basic environmental features.

Abstract

Establishing bounds on the accuracy achievable by localization techniques represents a fundamental technical issue. Bounds on localization accuracy have been derived for cases in which the position of an agent is estimated on the basis of a set of observations and, possibly, of some a priori information related to them (e.g., information about anchor positions and properties of the communication channel). In this manuscript new bounds are derived under the assumption that the localization system is map-aware, i.e., it can benefit not only from the availability of observations, but also from the a priori knowledge provided by the map of the environment where it operates. Our results show that: a) map-aware estimation accuracy can be related to some features of the map (e.g., its shape and area) even though, in general, the relation is complicated; b) maps are really useful in the presence of some combination of low signal-to-noise ratios and specific geometrical features of the map (e.g., the size of obstructions); c) in most cases, there is no need of refined maps since additional details do not improve estimation accuracy.