A Note on Particle Flow Methods for Solving Bayesian Updates

This note revisits the theoretical foundation of the Daum–Huang particle filter concepts for solving Bayesian updating problems. We reexamine the defining necessary and sufficient condition, in the form of an operator equation, for a flow to generate a particular homotopy between the
a priori
and the
a posteriori
probability density functions. We show that two well-known flows indeed satisfy this sufficient condition in the linear-Gaussian case, restating some of the significant results in a recent series of papers coauthored by Fred Daum with our alternative proof, which we hope will provide a useful perspective for future flow-based filter developments.