Particle Flow Solutions Avoiding Stiff Integration

Particle flow filters are a promising approach to nonlinear Bayesian estimation. However, the only flow with an analytic solution is the so-called exact flow. Other flows, including the geodesic and Gromov flows, are often represented by stiff deterministic or stochastic differential equations that must be numerically integrated. In this paper, we derive an analytic solution for the geodesic flow and we reduce the Gromov flow to an explicit term plus simple integrals involving a single Wiener process. Given the analytic solutions, good asymptotic performance as a function of the measurement variance is demonstrated.