  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.
