Particle Filtering on Riemannian Manifolds. Application to Covariance Matrices Tracking

摘要

17.1 Introduction Given a dynamical system characterized by a state-space model, the objective of the online Bayesian filtering is the estimation of the posterior marginal probability of the hidden state given all the observations collected until the current time. The nonlinear and/or the non Gaussian aspect of the prior transition distributions and the observation model leads to intractable integrals when evaluating the marginals. Therefore, one has to resort to approximate Monte Carlo schemes. Particle filtering [1] is such an approximate Monte Carlo method estimating, recursively in time, the marginal posterior distribution of the continuous hidden state of the system. The particle filter provides a point mass approximation of these distributions by drawing particles according to a proposal distribution and then weighting the particles in order to fit the target distribution.