  Recently, there has been a surge of interest in incorporating neural networks
into particle filters, e.g. differentiable particle filters, to perform joint
sequential state estimation and model learning for non-linear non-Gaussian
state-space models in complex environments. Existing differentiable particle
filters are mostly constructed with vanilla neural networks that do not allow
density estimation. As a result, they are either restricted to a bootstrap
particle filtering framework or employ predefined distribution families (e.g.
Gaussian distributions), limiting their performance in more complex real-world
scenarios. In this paper we present a differentiable particle filtering
framework that uses (conditional) normalising flows to build its dynamic model,
proposal distribution, and measurement model. This not only enables valid
probability densities but also allows the proposed method to adaptively learn
these modules in a flexible way, without being restricted to predefined
distribution families. We derive the theoretical properties of the proposed
filters and evaluate the proposed normalising flow-based differentiable
particle filters' performance through a series of numerical experiments.
