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arXiv 1709.02040cs.ITmath.IT
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观测模型不确定的分布线性估计

On Distributed Linear Estimation With Observation Model Uncertainties

Alireza Sani, Azadeh Vosoughi

摘要:

我们考虑分布式估计的高斯源在异质带宽约束的传感器网络中,源被损坏的独立的乘性和加性观测噪声,与不完全的统计知识的乘性噪声。对于多比特量化器,我们推导出封闭形式的均方误差(MSE)的线性最小均方误差(LMMSE)估计在FC的表达式。对于无错误和错误的通信信道,我们提出了几种速率分配方法命名为最长根到叶路径,贪婪和整数松弛(i)最小化MSE给定的网络带宽约束,(ii)最小化所需的网络带宽给定的目标MSE。我们还推导出贝叶斯Cramer-Rao下界(CRLB),并比较我们提出的方法对CRLB的MSE性能。我们的研究结果证实,对于低功率乘性观测噪声和足够的网络带宽,我们提出的方法的MSE和CRLB之间的差距可以忽略不计,而其他方法,如个别速率分配和均匀的性能不令人满意。

英文摘要:

We consider distributed estimation of a Gaussian source in a heterogenous bandwidth constrained sensor network, where the source is corrupted by independent multiplicative and additive observation noises, with incomplete statistical knowledge of the multiplicative noise. For multi-bit quantizers, we derive the closed-form mean-square-error (MSE) expression for the linear minimum MSE (LMMSE) estimator at the FC. For both error-free and erroneous communication channels, we propose several rate allocation methods named as longest root to leaf path, greedy and integer relaxation to (i) minimize the MSE given a network bandwidth constraint, and (ii) minimize the required network bandwidth given a target MSE. We also derive the Bayesian Cramer-Rao lower bound (CRLB) and compare the MSE performance of our proposed methods against the CRLB. Our results corroborate that, for low power multiplicative observation noises and adequate network bandwidth, the gaps between the MSE of our proposed methods and the CRLB are negligible, while the performance of other methods like individual rate allocation and uniform is not satisfactory.

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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