Second-order extended particle filter with exponential family observation model

Particle filter is the most widely used Bayesian sequential state estimation method for nonlinear dynamic systems. When importance sampling is adopted, it is still a challenge to select an appropriate importance function for sampling to avoid particle degeneracy. This paper suggests a novel particle filter, called second-order extended particle filter, which uses conditional normal distribution to approximate the theoretical optimal importance function in sequential state estimation. The approximation is fulfilled through taking logarithm to the optimal importance function and implementing second-order Taylor expansion. This method is suitable for exponential family observation models, which have numerous applications in state estimation research field.