We propose two nonlinear Kalman smoothers that rely on Student's t distributions. The T-Robust smoother finds the maximum a posteriori likelihood (MAP) solution for Gaussian process noise and Student's t observation noise, and is extremely robust against outliers, outperforming the recently proposed l1-Laplace smoother in extreme situations (e.g. 50% or more outliers). The second estimator, which we call the T-Trend smoother, is able to follow sudden changes in the process model, and is derived as a MAP solver for a model with Student's t-process noise and Gaussian observation noise. We design specialized methods to solve both problems which exploit the special structure of the Student's t-distribution, and provide a convergence theory. Both smoothers can be implemented with only minor modifications to an existing L2 smoother implementation. Numerical results for linear and nonlinear models illustrating both robust and fast tracking applications are presented.
Kalman-based Spectro-Temporal ECG Analysis using Deep Convolutional Networks for Atrial Fibrillation Detection
Aalto University（阿尔托大学）
在这篇文章中，我们提出了一种新的ECG分类框架，用于使用频谱-时间表示（即，时变频谱）和深度卷积网络。在第一步中，我们使用贝叶斯频谱时间表示的基础上估计的时变系数的傅立叶级数使用卡尔曼滤波器和平滑。接下来，我们推导出一个替代模型的基础上，随机振荡器微分方程，以加速估计的频谱时间表示在漫长的信号。最后，在对不同卷积架构进行比较评估后，我们提出了一种高效的深度卷积神经网络来对2D频谱-时间ECG数据进行分类。ECG频谱-时间数据被分为四个不同的类别：AF、非AF正常节律（正常）、非AF异常节律（其他）和噪声段（噪声）。使用PhysioNet/Computing in Cardiology（CinC）2017数据集对所提出方法的性能进行评估和评分。实验结果表明，该方法达到了80.2%的整体F1分数，这是符合最先进的算法。
