Kwasniok Frank
College of Engineering, Mathematics and Physical Sciences, University of Exeter, Exeter, United Kingdom.
Phys Rev E Stat Nonlin Soft Matter Phys. 2012 Sep;86(3 Pt 2):036214. doi: 10.1103/PhysRevE.86.036214. Epub 2012 Sep 26.
A method is proposed for determining dynamical and observational noise parameters in state and parameter identification from time series using Kalman filters. The noise covariances are estimated in a secondary optimization by maximizing the predictive likelihood of the data. The approach is based on internal consistency; for the correct noise parameters, the uncertainty projected by the Kalman filter matches the actual predictive uncertainty. The method is able to disentangle dynamical and observational noise. The algorithm is demonstrated for the linear, extended, and unscented Kalman filters using an Ornstein-Uhlenbeck process, the noise-driven Lorenz system, and van der Pol oscillator as well as a paleoclimatic ice-core record as examples. The approach is also applicable to the ensemble Kalman filter and can be readily extended to non-Gaussian estimation frameworks such as Gaussian-sum filters and particle filters.
提出了一种使用卡尔曼滤波器从时间序列中进行状态和参数识别时确定动态噪声和观测噪声参数的方法。通过最大化数据的预测似然性，在二次优化中估计噪声协方差。该方法基于内部一致性；对于正确的噪声参数，卡尔曼滤波器预测的不确定性与实际预测不确定性相匹配。该方法能够区分动态噪声和观测噪声。使用奥恩斯坦-乌伦贝克过程、噪声驱动的洛伦兹系统、范德波尔振荡器以及古气候冰芯记录作为示例，对线性卡尔曼滤波器、扩展卡尔曼滤波器和无迹卡尔曼滤波器演示了该算法。该方法也适用于集合卡尔曼滤波器，并且可以很容易地扩展到非高斯估计框架，如高斯和滤波器和粒子滤波器。
