Performance Analysis for Wireless Localization with Random Sensor Network

TL;DR

This work tackles wireless target localization in d-dimensional sensor networks by fusing RSS and AOA measurements and analyzing performance under stochastic geometry models. It proves a convergence result: in high propagation-noise regimes, the observable RSS+AOA data from any stationary isotropic deployment with SRD behaves like a PPP with the same intensity, enabling a tractable finite-region PPP model. Within the finite Poisson framework, it derives explicit CMSE and MSE bounds that scale as $1/n$ and $1/(\\\lambda V_d(\\mathcal{R}))$, respectively, providing explicit design guidance on sensor count, density, and observation radius. Simulation studies across PPP, repulsive (MHP/DPP), and clustered (MCP) deployments validate the bounds and illustrate the robustness of the PPP proxy in realistic noisy environments. The results offer a robust, cost-aware benchmark for next-generation location-aware wireless networks and motivate extensions to inhomogeneous and spatially correlated propagation settings.

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.

Figures (8)

• Figure 1: Illustration of the modeling intuition. Panels (a)–(c) show a moving target (red cross) and the nearby sensors used for localization (those inside the red circle). Panels (d)–(f) present the corresponding zoomed-in views, highlighting the local sensor configuration around the target. As the target moves, the set of nearby sensors changes and appears as a random point pattern.
• Figure 2: AOA in the two-dimensional noiseless system.
• Figure 3: Estimated target location provided by individual sensors in the two-dimensional noisy system.
• Figure 4: Logistic-type variance function $\mathcal{E}(r)$ for AOA noise (in radians).
• Figure 5: CMSE (a) and MSE (b) with their theoretical bounds for PPP network versus number of sensors $n$ and sensor density $\lambda$ for $\mathcal{R} = 30$ km.

Theorems & Definitions (11)

• Theorem 1
• proof
• Remark 2
• Remark 3
• Lemma 4
• proof
• Theorem 5
• proof
• proof : Proof of Theorem \ref{['convergence_thm']}
• proof : Proof of Lemma \ref{['lemma: unbiasedEstimator']}