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:本文研究了具有线性状态动态的随机模型的状态估计,该模型在连续或离散时间内。重点是通过网格点点质量滤波器(PMF)的时间更新步骤对状态预测进行数值求解,这是 PMF 算法中计算最繁琐的部分。提出了一种新的网格操作方式,导致时间更新形式为卷积。这将 PMF 的时间复杂度从二次降低至关于网格点数的对数线性。此外,唯一转换概率值的数量大大减少,导致所需数据存储的显着减少。提出的 PMF 预测步骤在数值研究中得到验证。