Bullet proofing Bayesian particle flow against stiffness

We derive a new theory of Bayesian particle flow that bullet proofs the algorithm against stiffness. Many researchers have attempted to apply particle flow filters, but sometimes they have gotten disappointing results owing to stiffness. Such researchers may be experts in fancy estimation algorithms, but they are rarely experts in mitigating stiffness for Itô stochastic differential equations. We solve this problem by bullet-proofing the Bayesian particle flow algorithm itself against stiffness. The new theory allows us to avoid fancy stiff ODE solvers that require large amounts of computer run time, and which are not parallelizable on GPUs. We also derive a very simple upper bound on the stiffness for our Gromov particle flow that gives us insight into the root cause of the problem. This shows that the stiffness of the flow is infinite if we do not directly measure all components of the state vector. The new theory fixes this problem completely. This paper is for normal engineers who do not have Itô calculus for breakfast.