  A key challenge when designing particle filters in high-dimensional state
spaces is the construction of a proposal distribution that is close to the
posterior distribution. Recent advances in particle flow filters provide a
promising avenue to avoid weight degeneracy; particles drawn from the prior
distribution are migrated in the state-space to the posterior distribution by
solving partial differential equations. Numerous particle flow filters have
been proposed based on different assumptions concerning the flow dynamics.
Approximations are needed in the implementation of all of these filters; as a
result the articles do not exactly match a sample drawn from the desired
posterior distribution. Past efforts to correct the discrepancies involve
expensive calculations of importance weights. In this paper, we present new
filters which incorporate deterministic particle flows into an encompassing
particle filter framework. The valuable theoretical guarantees concerning
particle filter performance still apply, but we can exploit the attractive
performance of the particle flow methods. The filters we describe involve a
computationally efficient weight update step, arising because the embedded
particle flows we design possess an invertible mapping property. We evaluate
the proposed particle flow particle filters' performance through numerical
simulations of a challenging multi-target multi-sensor tracking scenario and
complex high-dimensional filtering examples.
