Herein, inspired by the unscented particle filter (UPF), an improved particle filter (PF) using an unscented information filter based on M-estimate (UIF-BM) to approximate the importance density function (IDF) is designed. The filtering method is proposed to obtain an accurate state estimation for a non-linear discrete time dynamical system with non-Gaussian system noises and observation noises contaminated by some Gaussian impulsive noises. The PF framework is used as a common method to handle non-Gaussian system noises. In order to obtain a precise IDF, UIF based on M-estimate is used for heavy-tailed observation noises. Meanwhile, instead of the robust Gaussian filter, the robust IF can avoid the numerical problem that zero weight functions cannot be incorporated into the framework. The simulation results indicate the estimation accuracy and efficiency of the proposed filter. Compared with the UIF-BM, PF, and UPF, the superiority of the proposed filter against the non-ideal system and observation noises is obvious.