Non-gaussian estimation and observer-based feedback using the Gaussian Mixture Kalman and Extended Kalman Filters
Non-gaussian estimation and observer-based feedback using the Gaussian Mixture Kalman and Extended Kalman Filters
复制标题
使用高斯混合卡尔曼和扩展卡尔曼滤波器的非高斯估计和基于观察者的反馈
DOI：
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发表时间：
2017
期刊：
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通讯作者：
D. Paley
中科院分区：
文献类型：
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作者：
Debdipta Goswami;D. Paley
本文考虑了线性和非线性环境下的非高斯估计和基于非高斯的反馈问题。非高斯过程噪声统计的非线性系统的估计对于大气和海洋采样的应用是重要的。然而，非高斯滤波在很大程度上是特定于问题的，并且大多是次优的。本文采用高斯混合模型（GMM）来描述先验非高斯分布，并应用卡尔曼滤波器更新来估计具有不确定性的状态。在线性和非线性情况下的误差的有界性分析证明在各种假设下，并由此产生的估计用于反馈控制。为了在非线性设置中应用GMM，我们利用卡尔曼滤波器的一个常见扩展：扩展卡尔曼滤波器（EKF）。数值模拟的理论结果说明。
This paper considers the problem of non-Gaussian estimation and observer-based feedback in linear and nonlinear settings. Estimation in nonlinear systems with non-Gaussian process noise statistics is important for applications in atmospheric and oceanic sampling. Non-Gaussian filtering is, however, largely problem specific and mostly sub-optimal. This manuscript uses a Gaussian Mixture Model (GMM) to characterize the prior non-Gaussian distribution, and applies the Kalman filter update to estimate the state with uncertainty. The boundedness of error in both linear and nonlinear cases is analytically justified under various assumptions, and the resulting estimate is used for feedback control. To apply GMM in nonlinear settings, we utilize a common extension of the Kalman filter: the Extended Kalman Filter (EKF). The theoretical results are illustrated by numerical simulations.