Particle filtering algorithm

Particle filter is emerging as a new hotspot of research in scientific fields in the past several years. We first show the background information of particle filters. Thereafter, the principle of the particle filter under m -order Markovian assumption is analyzed, accompanying the derivatives of the posterior density function and the weight updating formula. Meanwhile, the analysis of the drawbacks of the standard particle filter and corresponding solutions are given. And a critical survey of importance sampling density selection is shown in the following section. We also give a detailed analysis of resampling method and the sample impoverishment problem induced by resampling. We reviewed the development of adaptive particle filters following the advances of convergence analysis. The following section reviews the advances of particle filters in different application areas. Finally, the future directions are pointed out.