Stiffness Mitigation in Stochastic Particle Flow Filters

The linear convex log-homotopy has been used in the derivation of particle flow filters. One natural question is whether it beneficial to consider other forms homotopy. We revisit this by considering a general form for which we derive filters, validate distribution flows, and obtain conditions stability flows. then formulate problem stiffness mitigation as an optimal control minimizing condition number Hessian matrix posterior density function. homotopy can be efficiently obtained solving 1-D second-order two-point boundary value problem. Compared with traditional analysis based approaches improving numbers, approach explicitly exploits special structure stochastic differential equations effectiveness proposed demonstrated numerical examples.