The principles of the particle filter and the representative-points of random distribution are introducedThe number-theoretic method in statistics is applied to the particle filter, The corresponding rep-points algorithms, which include the generation of initial particles, the sampling of the importance density and re-sampling, is given using the MSE rep-points. Then a deterministic particle filter algorithm, with the fewest random operative and unequally weighted particles, can be built. The simulation results show that not only the algorithm is feasible, but the performance and computational efficiency can be also improved to a certain extent.