论文标题
贝尔曼过滤和平滑状态空间型号
Bellman filtering and smoothing for state-space models
论文作者
论文摘要
本文为基于贝尔曼的动态编程原理提供了一种新的过滤器，用于国家空间模型，从而在观察和/或状态转换方程中允许非线性，非高斯性和退化性。由此产生的Bellman滤波器是（迭代和扩展）Kalman滤波器的直接概括，使可伸缩性可扩展到更高的尺寸，同时保持计算便宜。它也可以扩展以实现平滑。在适当的条件下，随着时间的流逝，钟楼过滤的状态在每个时间步骤中都稳定，并且对真实状态周围的一个地区保持稳定。静态（超）参数是通过最大化过滤器成像的伪对数可能分解来估计的。在单变量仿真研究中，Bellman滤波器以基于最新的模拟技术的一小部分进行计算成本的技术。在两个经验应用中，最多涉及150个空间维度或高度退化/非线性状态动力学，Bellman Filter以准确性和速度均优于竞争方法。
This paper presents a new filter for state-space models based on Bellman's dynamic-programming principle, allowing for nonlinearity, non-Gaussianity and degeneracy in the observation and/or state-transition equations. The resulting Bellman filter is a direct generalisation of the (iterated and extended) Kalman filter, enabling scalability to higher dimensions while remaining computationally inexpensive. It can also be extended to enable smoothing. Under suitable conditions, the Bellman-filtered states are stable over time and contractive towards a region around the true state at every time step. Static (hyper)parameters are estimated by maximising a filter-implied pseudo log-likelihood decomposition. In univariate simulation studies, the Bellman filter performs on par with state-of-the-art simulation-based techniques at a fraction of the computational cost. In two empirical applications, involving up to 150 spatial dimensions or highly degenerate/nonlinear state dynamics, the Bellman filter outperforms competing methods in both accuracy and speed.
