Performance Limits and Geometric Properties of Array Localization

TL;DR

This paper analyzes the fundamental limits of array-based localization accuracy in wireless networks, considering static and dynamic scenarios, and introduces geometric measures to evaluate network performance.

Contribution

It derives the Cramér-Rao bound for array localization, decomposes Fisher information into distance and direction components, and proposes geometric performance measures.

Findings

Localization information is a weighted sum of anchor-antenna Fisher matrices.

Doppler shift adds direction information in dynamic scenarios.

Performance measures are validated through formulas and simulations.

Abstract

Location-aware networks are of great importance and interest in both civil and military applications. This paper determines the localization accuracy of an agent, which is equipped with an antenna array and localizes itself using wireless measurements with anchor nodes, in a far-field environment. In view of the Cram\'er-Rao bound, we first derive the localization information for static scenarios and demonstrate that such information is a weighed sum of Fisher information matrices from each anchor-antenna measurement pair. Each matrix can be further decomposed into two parts: a distance part with intensity proportional to the squared baseband effective bandwidth of the transmitted signal and a direction part with intensity associated with the normalized anchor-antenna visual angle. Moreover, in dynamic scenarios, we show that the Doppler shift contributes additional direction information, with intensity determined by the agent velocity and the root mean squared time duration of the transmitted signal. In addition, two measures are proposed to evaluate the localization performance of wireless networks with different anchor-agent and array-antenna geometries, and both formulae and simulations are provided for typical anchor deployments and antenna arrays.