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Recently developed particle flow algorithms provide an alternative toimportance sampling for drawing particles from a posterior distribution, and anumber of particle filters based on this principle have been proposed. Samplesare drawn from the prior and then moved according to some dynamics over aninterval of pseudo-time such that their final values are distributed accordingto the desired posterior. In practice, implementing a particle flow samplerrequires multiple layers of approximation, with the result that the finalsamples do not in general have the correct posterior distribution. In thispaper we consider using an approximate Gaussian flow for sampling with a classof nonlinear Gaussian models. We use the particle flow within an importancesampler, correcting for the discrepancy between the target and actual densitieswith importance weights. We present a suitable numerical integration procedurefor use with this flow and an accompanying step-size control algorithm. In afiltering context, we use the particle flow to sample from the optimalimportance density, rather than the filtering density itself, avoiding the needto make analytical or numerical approximations of the predictive density.Simulations using particle flow importance sampling within a particle filterdemonstrate significant improvement over standard approximations of the optimalimportance density, and the algorithm falls within the standard sequentialMonte Carlo framework.

Approximations of the Optimal Importance Density using Gaussian Particle Flow Importance Sampling