摘要翻译：
本文提出了一种新的鲁棒广义最大似然型无迹卡尔曼滤波器（GM-UKF）的理论框架和方程，该滤波器能够抑制观测和新息异常值，同时滤除非高斯测量噪声。由于用相量测量单元(PMU)计算的有功和无功功率测量的误差服从长尾概率分布，传统的UKF依赖于加权最小二乘估计器，提供了强偏态状态估计。相比之下，我们的GM-UKF的状态估计和残差被证明是大致高斯的，允许sigma点可靠地逼近预测和校正的状态向量的均值和协方差矩阵。为了发展我们的GM-UKF，我们首先通过同时处理预测和观测得到一个批模式回归形式，其中使用了统计线性化方法。我们证明了这样导出的方程组与无味变换的方程组是等价的。然后，提出了一种鲁棒GM估计器，该估计器在使用投影统计量计算权值的同时使凸Huber代价函数最小化。将PS's应用于由序列相关的预测状态向量和新息向量组成的二维矩阵，以检测观测和新息离群值。这些异常值被GM估计器使用迭代重加权最小二乘算法抑制。最后，由总影响函数导出了GM-UKF状态估计的渐近误差协方差矩阵。在论文中，将给出大量的仿真结果来验证所提方法的有效性和鲁棒性。
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英文标题：
《Robust Power System Dynamic State Estimator with Non-Gaussian
  Measurement Noise: Part I--Theory》
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作者：
Junbo Zhao and Lamine Mili
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最新提交年份：
2017
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分类信息：

一级分类：Mathematics        数学
二级分类：Statistics Theory        统计理论
分类描述：Applied, computational and theoretical statistics: e.g. statistical inference, regression, time series, multivariate analysis, data analysis, Markov chain Monte Carlo, design of experiments, case studies
应用统计、计算统计和理论统计：例如统计推断、回归、时间序列、多元分析、数据分析、马尔可夫链蒙特卡罗、实验设计、案例研究
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一级分类：Computer Science        计算机科学
二级分类：Systems and Control        系统与控制
分类描述：cs.SY is an alias for eess.SY. This section includes theoretical and experimental research covering all facets of automatic control systems. The section is focused on methods of control system analysis and design using tools of modeling, simulation and optimization. Specific areas of research include nonlinear, distributed, adaptive, stochastic and robust control in addition to hybrid and discrete event systems. Application areas include automotive and aerospace control systems, network control, biological systems, multiagent and cooperative control, robotics, reinforcement learning, sensor networks, control of cyber-physical and energy-related systems, and control of computing systems.
cs.sy是eess.sy的别名。本部分包括理论和实验研究，涵盖了自动控制系统的各个方面。本节主要介绍利用建模、仿真和优化工具进行控制系统分析和设计的方法。具体研究领域包括非线性、分布式、自适应、随机和鲁棒控制，以及混合和离散事件系统。应用领域包括汽车和航空航天控制系统、网络控制、生物系统、多智能体和协作控制、机器人学、强化学习、传感器网络、信息物理和能源相关系统的控制以及计算系统的控制。
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一级分类：Electrical Engineering and Systems Science        电气工程与系统科学
二级分类：Systems and Control        系统与控制
分类描述：This section includes theoretical and experimental research covering all facets of automatic control systems. The section is focused on methods of control system analysis and design using tools of modeling, simulation and optimization. Specific areas of research include nonlinear, distributed, adaptive, stochastic and robust control in addition to hybrid and discrete event systems. Application areas include automotive and aerospace control systems, network control, biological systems, multiagent and cooperative control, robotics, reinforcement learning, sensor networks, control of cyber-physical and energy-related systems, and control of computing systems.
本部分包括理论和实验研究，涵盖了自动控制系统的各个方面。本节主要介绍利用建模、仿真和优化工具进行控制系统分析和设计的方法。具体研究领域包括非线性、分布式、自适应、随机和鲁棒控制，以及混合和离散事件系统。应用领域包括汽车和航空航天控制系统、网络控制、生物系统、多智能体和协作控制、机器人学、强化学习、传感器网络、信息物理和能源相关系统的控制以及计算系统的控制。
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一级分类：Statistics        统计学
二级分类：Statistics Theory        统计理论
分类描述：stat.TH is an alias for math.ST. Asymptotics, Bayesian Inference, Decision Theory, Estimation, Foundations, Inference, Testing.
Stat.Th是Math.St的别名。渐近，贝叶斯推论，决策理论，估计，基础，推论，检验。
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英文摘要：
  This paper develops the theoretical framework and the equations of a new robust Generalized Maximum-likelihood-type Unscented Kalman Filter (GM-UKF) that is able to suppress observation and innovation outliers while filtering out non-Gaussian measurement noise. Because the errors of the real and reactive power measurements calculated using Phasor Measurement Units (PMUs) follow long-tailed probability distributions, the conventional UKF provides strongly biased state estimates since it relies on the weighted least squares estimator. By contrast, the state estimates and residuals of our GM-UKF are proved to be roughly Gaussian, allowing the sigma points to reliably approximate the mean and the covariance matrices of the predicted and corrected state vectors. To develop our GM-UKF, we first derive a batch-mode regression form by processing the predictions and observations simultaneously, where the statistical linearization approach is used. We show that the set of equations so derived are equivalent to those of the unscented transformation. Then, a robust GM-estimator that minimizes a convex Huber cost function while using weights calculated via Projection Statistics (PS's) is proposed. The PS's are applied to a two-dimensional matrix that consists of serially correlated predicted state and innovation vectors to detect observation and innovation outliers. These outliers are suppressed by the GM-estimator using the iteratively reweighted least squares algorithm. Finally, the asymptotic error covariance matrix of the GM-UKF state estimates is derived from the total influence function. In the companion paper, extensive simulation results will be shown to verify the effectiveness and robustness of the proposed method.
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PDF链接：
https://arxiv.org/pdf/1703.0479