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力学的随机模型的状态估计问题，重点关注基于网格点的点质量滤波器（PMF）中时间更新步骤的数值解——这是PMF算法中计算量最大的部分。提出一种新颖的网格操作方法，将时间更新转化为卷积形式，从而将PMF的时间复杂度从网格点数的二次阶降至对数-线性阶。此外，该方法大幅减少了唯一转移概率值的数量，显著降低了数据存储需求。通过数值研究验证了所提PMF预测步骤的有效性。