On the Performance Limits of Map-Aware Localization

Abstract

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.

Recent Advances in Indoor Localization: A Survey on Theoretical Approaches and Applications

“…Other bounds on accuracy, such as the Bayesian Cramer Rao bounds, the WeissWeinstein bound and the extended Zik-Zakai bound can be tighter and more informative than the CRLB when the localization system is map-aware. These bounds indicate that an accuracy of 2m could be reached if a map-based priori knowledge and map-aware localization is used [16] [17]. For instance, in [17], RSS based algorithms were evaluated using trace-driven analysis and shown to benefit from the addition of more resources up to a point beyond which their performance degraded.…”

Performance Limits and Geometric Properties of Array Localization

“…Theorem 5 (Orientation-and Direction-unknown Speed-known Moving EFIM): Under Assumption 1 and 2, when the agent speed is known but both the array orientation and the moving direction are unknown, the EFIM for the position, orientation and moving direction is given by (40), shown at the bottom of this page.…”

A Performance Limit of TOA-Based Location-Aware Wireless Networks With Ranging Outliers

“…In each case, we present the corresponding approximated CRLB, the exact CRLB calculated by numerical methods, and the CRLB under the genie-aided detection assumption. In all cases J s = 12 as in [11].…”

“…Using the smoothing technique proposed in [11], we can further approximate J n1 as P M J s R 2 max and J n2 as 0, where J s is a constant. J n3 can be expressed as follows…”