This paper presents a new nonlinear filtering algorithm that is shown to outperform state-of-the-art particle filters with resampling. Starting from the Itˆo stochastic differential equation, the proposed algorithm harnesses Karhunen- Lo'eve expansion to derive an approximate non-autonomous dynamical system, for which transfer operator based density computation can be performed in exact arithmetic. It is proved that the algorithm is asymptotically consistent in mean-square sense. Numerical results demonstrate that explicitly accounting prior dynamics entail significant performance improvement for nonlinear non-Gaussian estimation problems with infrequent measurement updates, as compared to the performance of particle filters.