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Exploring Positive Noise in Estimation Theory
IEEE Transactions on Signal Processing ( IF 4.6 ) Pub Date : 2020-01-01 , DOI: 10.1109/tsp.2020.2999204
Kamiar Radnosrati , Gustaf Hendeby , Fredrik Gustafsson

Estimation of the mean of a stochastic variable observed in noise with positive support is considered. It is well known from the literature that order statistics gives one order of magnitude lower estimation variance compared to the best linear unbiased estimator (BLUE). We provide a systematic survey of some common distributions with positive support, and provide derivations of minimum variance unbiased estimators (MVUE) based on order statistics, including BLUE for comparison. The estimators are derived with or without knowledge of the hyperparameters of the underlying noise distribution. Though the uniform, exponential and Rayleigh distributions, respectively, we consider are standard in literature, the problem of estimating the location parameter with additive noise from these distribution seems less studied, and we have not found any explicit expressions for BLUE and MVUE for these cases. In addition to additive noise with positive support, we also consider the mixture of uniform and normal noise distribution for which an order statistics-based unbiased estimator is derived. Finally, an iterative global navigation satellite system (GNSS) localization algorithm with uncertain pseudorange measurements is proposed which relies on the derived estimators for receiver clock bias estimation. Simulation data for GNSS time estimation and experimental GNSS data for joint clock bias and position estimation are used to evaluate the performance of the proposed methods.

中文翻译:

探索估计理论中的正噪声

考虑在具有正支持的噪声中观察到的随机变量的平均值的估计。从文献中众所周知,与最佳线性无偏估计量 (BLUE) 相比,阶次统计给出的估计方差低一个数量级。我们提供了一些具有正支持的常见分布的系统调查,并提供了基于订单统计的最小方差无偏估计量 (MVUE) 的推导,包括用于比较的 BLUE。估计量是在了解或不了解基础噪声分布的超参数的情况下得出的。尽管我们分别考虑均匀分布、指数分布和瑞利分布是文献中的标准分布,但从这些分布中估计带有加性噪声的位置参数的问题似乎研究较少,对于这些情况,我们还没有找到 BLUE 和 MVUE 的任何显式表达式。除了具有正支持的加性噪声​​外,我们还考虑了均匀噪声分布和正态噪声分布的混合,由此导出了基于阶次统计的无偏估计量。最后,提出了一种具有不确定伪距测量值的迭代全球导航卫星系统 (GNSS) 定位算法,该算法依赖于导出的估计器进行接收机时钟偏差估计。用于 GNSS 时间估计的模拟数据和用于联合时钟偏差和位置估计的实验 GNSS 数据用于评估所提出方法的性能。我们还考虑了均匀噪声分布和正态噪声分布的混合,由此推导出了基于阶次统计的无偏估计量。最后,提出了一种具有不确定伪距测量值的迭代全球导航卫星系统 (GNSS) 定位算法,该算法依赖于导出的估计器进行接收机时钟偏差估计。用于 GNSS 时间估计的模拟数据和用于联合时钟偏差和位置估计的实验 GNSS 数据用于评估所提出方法的性能。我们还考虑了均匀噪声分布和正态噪声分布的混合,由此推导出了基于阶次统计的无偏估计量。最后,提出了一种具有不确定伪距测量值的迭代全球导航卫星系统 (GNSS) 定位算法,该算法依赖于导出的估计器进行接收机时钟偏差估计。用于 GNSS 时间估计的模拟数据和用于联合时钟偏差和位置估计的实验 GNSS 数据用于评估所提出方法的性能。
更新日期:2020-01-01
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