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arXiv 2601.06396eess.SP
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随机传感器网络中无线定位的性能分析

Performance Analysis for Wireless Localization with Random Sensor Network

The University of Melbourne(墨尔本大学)

Mengqi Ma, Aihua Xia

AI总结:

针对d维平稳各向同性随机传感器网络,提出融合RSS和AOA测量的估计器,证明在高噪声下观测联合分布与泊松点过程等价,并推导MSE和CMSE的可解析上界,建立传感器密度、观测半径和噪声方差与定位精度的标度律。

摘要:

精确的无线定位支撑着从自主系统到智能基础设施的应用。我们研究了d维平稳各向同性(平移和旋转不变)随机传感器网络中一种实用融合估计器的均方误差(MSE)和条件均方误差(CMSE),其中中央处理器结合接收信号强度(RSS)和到达角(AOA)测量来推断目标位置。我们的贡献有两方面。首先,我们建立了一个近似定理:当测量噪声足够大时,在广泛一类平稳各向同性部署下,RSS和AOA观测的联合分布在分布上与齐次泊松点过程(PPP)诱导的分布不可区分。其次,利用这一等价性,我们研究了一个基于齐次PPP的传感器网络。我们提出了一种融合估计器,其中中央处理器聚合来自一组空间分布传感器的RSS和AOA测量以推断目标位置。对于有限观测区域内的PPP部署,我们推导了MSE和CMSE的可解析上界,建立了关于传感器密度、观测半径和噪声方差的显式标度律。近似定理随后保证了这些基于PPP的界在高噪声场景下作为非泊松部署的合理代理。总体而言,结果将部署和感知参数转化为可达到的精度目标,并为下一代位置感知无线网络的设计提供了鲁棒且成本感知的指导。

英文摘要:

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.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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