This paper deals with state estimation of stochastic models with linear state dynamics, continuous or discrete in time. The emphasis is laid on a numerical solution to the state prediction by the time-update step of the grid-point-based point-mass filter (PMF), which is the most computationally demanding part of the PMF algorithm. A novel way of manipulating the grid, leading to the time-update in form of a convolution, is proposed. This reduces the PMF time complexity from quadratic to log-linear with respect to the number of grid points. Furthermore, the number of unique transition probability values is greatly reduced causing a significant reduction of the data storage needed. The proposed PMF prediction step is verified in a numerical study.

翻译：本文研究具有线性状态动态的随机模型的状态估计问题，时间域可为连续或离散。重点聚焦于基于网格点的点质量滤波器（PMF）中时间更新步骤的状态预测数值解法——这是PMF算法中计算量最大的部分。本文提出一种新颖的网格操作方式，将时间更新转化为卷积形式，使PMF的时间复杂度从关于网格点数的二次复杂度降低为对数线性复杂度。此外，该方法大幅减少了唯一转移概率值的数量，从而显著降低所需数据存储量。通过数值研究验证了所提PMF预测步骤的有效性。