The Unscented Kalman Filter for Machine Learning

[00:83106]机器学习的几个领域，包括分类和回归、非线性信号处理和自适应控制，都严重依赖于扩展卡尔曼滤波器（EKF）。例如，EKF在复杂控制应用所需的非线性状态估计中起着核心作用，并被用作模式识别和动态系统识别的神经网络训练中的参数估计算法。EKF在噪声时间序列的同时建模和估计（称为对偶估计）中也起着重要作用，其应用范围从语音增强到金融预测和环境建模。EKF中使用的中心近似是非线性系统动力学的线性化。虽然这样做是为了传播被估计的状态变量的均值和协方差，但EKF可能会在算法产生的估计和状态的真实统计之间引入相当大的误差。然而，该算法的计算费用比更精确的马尔可夫链蒙特卡罗（MCMC）采样方法要低得多，并且在许多情况下都能产生很好的结果。以低成本获得良好结果的好处是EKF广泛使用的主要原因。1997年，Julier和Uhlman引入了一种名为Unscented卡尔曼滤波器的新方法，通过避免系统的线性化，UKF在估计状态变量的均值和协方差方面提供了更高的准确性，从而大大提高了性能。UKF的实现不需要像EKF那样对雅可比矩阵（梯度）进行解析推导，最重要的是，在不增加计算费用的情况下实现了精度的提高。UKF的先前应用只集中在非线性控制的状态估计问题上。该项目的目标是将UKF的使用扩展到目前依赖于EKF的所有机器学习应用程序。这将需要系统地开发算法扩展和应用评估，如提案中详细介绍的那样。尽管在实现这一目标之前必须克服许多理论和实践问题。初步调查表明，UKF在这些情况下的潜在优势是显著的。显然，目前使用EKF的应用的多样性表明，拟议的研究将对各种领域产生影响

0083106WanSeveral areas of machine learning including classification and regression, nonlinear signal processing, and adaptive control, rely heavily on the extended Kalman filter (EKF). For example, the EKF plays a central role in nonlinear state estimation required by complex control applications, and is used as a parameter, estimation algorithm in neural network training for pattern recognition, and for identification of dynamic systems. The EKF also plays an important role in the simultaneous modeling and estimation (known as dual estimation) of noisy time-series, with applications ranging from speech enhancement, to financial forecasting and environmental modeling.The central approximation used in the EKF is a linearization of the nonlinear system dynamics. While this is done in order to propagate the mean and covariance of the state variables being estimated, the EKF can introduce considerable errors between the estimates produced by the algorithm and the true statistics of the state. However, the computational expense of the algorithm is considerably lower than that of more accurate Markov-Chain Monte Carlo (MCMC) sampling methods, and produces excellent results in many circumstances. The benefit of good results at low cost is primarily responsible for the widespread use of the EKF.In 1997, Julier and Uhlman introduced a new approach called the Unscented Kalman Filter By avoiding a linearization of the system, the UKF offers increased accuracy in the estimation of the mean and covariance of the state variables, resulting in a substantial performance improvement. The implementation of the UKF requires no analytic derivation of Jacobians (gradients) as in the EKF, and most importantly, the improved accuracy is achieved without an increase in computational expense.The prior application of the UKF focused only on state-estimation problems in the context of nonlinear control.The objective of this project is to extend the use of the UKF to the full breadth of machine learning applications that currently depend on the EKF. This will entail the systematic development of algorithmic extensions and application evaluations as detailed in the proposal. Although numerous theoretical and practical problems must be overcome before this goal is achieved. Preliminary investigations have shown that the potential advantages of the UKF in these contexts are significant. Clearly, the diversity of applications that currently employ the EKF suggests that the proposed research aching impact on a wide variety of fields.***