Both the particle and Kalman filters attempt to approximate the minimum mean-square error (MMSE) estimate of the time-varying parameter. In this scenario, a prior model of the time evolution of the parameter of interest is assumed before the MMSE estimation takes place. The Kalman filter is the (optimal) MMSE estimator for a linear dynamical system with Gaussian noise. For a nonlinear system with nonGaussian noise, the particle filter approximates the mean of posterior distribution at each discrete time step with a finite number of samples or particles. For these general nonlinear systems, the particle filter approaches the MMSE estimator as the number of particles approaches infinity.
Particle Filters