A Lower Bound for Sequential Estimators

G. Bouleux, R. Boyer
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Abstract

A popular class of parameter estimation method is based on a sequential/iterative scheme. In this framework, each component is estimated one by one and at each iteration the underlying model is based on the estimation of a single component corrupted by a structured interference (the other components) and by an unstructured Gaussian noise. So, in the context of the bearing estimation problem, we derive the deterministic Cramer-Rao Bound, called Interfering CRB (I-CRB), associated with this model. In particular, we show that for low Interference to Noise Ratio (INR), the I-CRB reaches the CRB for a single component (without structured interference). Inversely, for high INR, the I-CRB is equal to the Prior-CRB where we assume the exact knowledge of the structured interference. In addition, we show that in the closely-spaced bearings, the I-CRB has two typical regimes depending of the INR.
序列估计量的下界
一类流行的参数估计方法是基于顺序/迭代方案。在这个框架中,每个分量被一个一个地估计,在每次迭代中,底层模型是基于被结构化干扰(其他分量)和非结构化高斯噪声破坏的单个分量的估计。因此,在方位估计问题的背景下,我们导出了与该模型相关的确定性Cramer-Rao界,称为干扰CRB (I-CRB)。特别是,我们表明,对于低干扰噪声比(INR), I-CRB达到单个组件的CRB(没有结构化干扰)。相反,对于高INR, I-CRB等于Prior-CRB,其中我们假设对结构化干扰有确切的了解。此外,我们还表明,在紧密间隔的轴承中,根据INR, I-CRB具有两种典型的状态。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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