  Sequential state estimation in non-linear and non-Gaussian state spaces has a
wide range of applications in statistics and signal processing. One of the most
effective non-linear filtering approaches, particle filtering, suffers from
weight degeneracy in high-dimensional filtering scenarios. Several avenues have
been pursued to address high-dimensionality. Among these, particle flow
particle filters construct effective proposal distributions by using invertible
flow to migrate particles continuously from the prior distribution to the
posterior, and sequential Markov chain Monte Carlo (SMCMC) methods use a
Metropolis-Hastings (MH) accept-reject approach to improve filtering
performance. In this paper, we propose to combine the strengths of invertible
particle flow and SMCMC by constructing a composite Metropolis-Hastings (MH)
kernel within the SMCMC framework using invertible particle flow. In addition,
we propose a Gaussian mixture model (GMM)-based particle flow algorithm to
construct effective MH kernels for multi-modal distributions. Simulation
results show that for high-dimensional state estimation example problems the
proposed kernels significantly increase the acceptance rate with minimal
additional computational overhead and improve estimation accuracy compared with
state-of-the-art filtering algorithms.
