Particle flow auxiliary particle filter

Particle flow filters have been recently developed as an alternative approach for nonlinear filtering. The particles approximating the prior are migrated using differential equations to be distributed according to the posterior. Computationally tractable exact solutions only exist for linear Gaussian models. For other scenarios, approximations are required and it is not fully understood how these approximations impact the movement of the particles and the subsequent propagation of error in the filter. An alternative approach is to use the particle flow methods to perform the importance sampling step within a particle filtering framework. Existing methods along these lines involve either intensive calculation or the construction of a transport map, which can be challenging. In this paper, we propose to use existing particle flow methods in an auxiliary particle filter. The flows are used to sample auxiliary variables; and these allow us to identify importance sampling distributions that are well-matched to the posteriors. Simulations results indicate that the auxiliary particle filters we develop have accuracy and computational complexity similar to that of the underlying particle flow filters.