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.
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