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arXiv 1507.07385cs.ITmath.ITphysics.class-phphysics.optics
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远场无线电定位精度的基本界限

Fundamental Bounds on Radio Localization Precision in the Far Field

B. J. Dil, F. Gustafsson, B. J. Hoenders

摘要:

本文从实验和理论上研究了远场接收信号强度(RSS)测量无线电定位精度的基本界限。RSS测量与功率流测量成比例,功率流测量在与辐射的相干时间相比长的周期上时间平均。我们的实验是在一个新的本地化设置使用2.4GHz的准单色辐射,这对应于12.5厘米的平均波长。我们的实验和理论表明,RSS测量是互相关的最小距离,接近衍射极限,这等于一半的平均波长的辐射。我们的实验表明,测量RSS超过一个样本每一半的平均波长的采样密度不增加本地化精度,作为根均方误差(RMSE)渐近收敛到大约一半的平均波长。这增加了衍射极限确定(1)定位精度的下限和(2)提供最佳定位精度的采样密度的证据。我们通过实验验证了Fisher信息,Cramér-Rao下限(CRLB)和不确定性之间的理论关系,其中不确定性是由相干性和散斑理论导出的衍射下界。当我们将Fisher信息与衍射相协调时,CRLB与实验结果的准确度为97- 98%。

英文摘要:

This paper experimentally and theoretically investigates the fundamental bounds on radio localization precision of far-field Received Signal Strength (RSS) measurements. RSS measurements are proportional to power-flow measurements time-averaged over periods long compared to the coherence time of the radiation. Our experiments are performed in a novel localization setup using 2.4GHz quasi-monochromatic radiation, which corresponds to a mean wavelength of 12.5cm. We experimentally and theoretically show that RSS measurements are cross-correlated over a minimum distance that approaches the diffraction limit, which equals half the mean wavelength of the radiation. Our experiments show that measuring RSS beyond a sampling density of one sample per half the mean wavelength does not increase localization precision, as the Root-Mean-Squared-Error (RMSE) converges asymptotically to roughly half the mean wavelength. This adds to the evidence that the diffraction limit determines (1) the lower bound on localization precision and (2) the sampling density that provides optimal localization precision. We experimentally validate the theoretical relations between Fisher information, Cramér-Rao Lower Bound (CRLB) and uncertainty, where uncertainty is lower bounded by diffraction as derived from coherence and speckle theory. When we reconcile Fisher Information with diffraction, the CRLB matches the experimental results with an accuracy of 97-98%.

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