The extrapolated single propagation technique (ESPT) based particle filter is proposed. Instead of propagating all the sample state vectors using multiple numerical integrations, only one sample state vector is propagated in the ESPT. Other sample states are computed at the next epoch with an accuracy of the second-order Taylor series expansion terms. It is theoretically shown that the particle filter algorithm, which uses the ESPT for state propagation, requires up to $text90%$ reduced processing time than the conventional particle filter. Using a benchmark non-linear estimation problem the performance of the modified algorithm is compared with the particle filter. The experimental results confirm the theoretical analysis and demonstrate the effectiveness of the proposed method for non-linear state estimation. The proposed algorithm significantly reduces the processing time of the particle filter with a minor degradation in the estimation accuracy.