ABSTRACT
The sequential Monte Carlo methods (SMCM) can be used for sequential estimation of states of nonlinear dynamic systems. These SMCMs are a kind of recursive Bayesian filter–based Monte Carlo simulation approach. The state space is partitioned in as many parts, in which the particles are filled according to some assumed probability measure. The idea in the auxiliary particle filter is to augment the existing good particles in a sense that the predictive likelihoods are large for the good particles. In an algorithm called progressive correction for particle filters, the correction step is split into several sub-correction steps associated with a decreasing sequence of variance matrices for the measurement noise. The idea of data augmentation is derived from the missing data problem. It is referred to as a scheme of augmenting the measured data and making the probabilistic inference easier. The algorithmic and numerical robustness are important aspects for the discrete time filtering.
