Performance Analysis for Wireless Localization with Random Sensor Network

TL;DR

This paper analyzes the performance of a fusion-based wireless localization method in random sensor networks, deriving bounds on estimation errors and establishing an approximation for complex deployments using Poisson point processes.

Contribution

It introduces an approximation theorem for sensor observations under noise and derives analytical error bounds for Poisson-based sensor networks, guiding network design.

Findings

Derived explicit scaling laws for MSE and CMSE with respect to sensor density and noise.

Established the approximation of complex sensor deployments by homogeneous Poisson point processes under high noise.

Provided practical bounds and insights for designing accurate wireless localization systems.

Abstract

Accurate wireless localization underpins applications from autonomous systems to smart infrastructure. We study the mean-squared error (MSE) and conditional MSE (CMSE) of a practical fusion-based estimator in d-dimensional, stationary isotropic (translation- and rotation-invariant) random sensor networks, where a central processor combines received-signal-strength (RSS) and angle-of-arrival (AOA) measurements to infer a target's position. Our contributions are twofold. First, we establish an approximation theorem: when measurement noise is sufficiently large, the joint law of RSS and AOA observations under a broad class of stationary isotropic deployments is, in distribution, indistinguishable from that induced by a homogeneous Poisson point process (PPP). Second, leveraging this equivalence, we investigate a homogeneous PPP-based sensor network. We propose a fusion-based estimator in which a central processor aggregates RSS and AOA measurements from a set of spatially distributed sensors to infer the target position. For this PPP deployment within a finite observation region, we derive tractable analytical upper bounds for both the MSE and CMSE, establishing explicit scaling laws with respect to sensor density, observation radius, and noise variance. The approximation theorem then certifies these PPP-based bounds as reasonable proxies for non-Poisson deployments in noisy regimes. Overall, the results translate deployment and sensing parameters into achievable accuracy targets and provide robust, cost-aware guidance for the design of next-generation location-aware wireless networks.