An integration-free approach for particle flow filtering
For practitioners of nonlinear Bayesian estimation, this work provides a computationally efficient and stiffness-free alternative to numerical integration in particle flow filters, though it is limited to linear Gaussian measurements and requires extension for general nonlinear cases.
This paper develops an exact, integration-free closed-form solution for the exact Daum-Huang deterministic particle flow under vector linear Gaussian measurements, eliminating the need for numerical integration and its associated computational cost and stiffness issues. The solution is proven mathematically equivalent to the exact Kalman measurement update and can be embedded in an N-step slicing method for nonlinear models.
Log-homotopy particle flow filters realize nonlinear Bayesian estimation by continuously migrating samples from the prior to the posterior distribution. This transport is governed by a pseudo-time ordinary differential equation (ODE). A major practical challenge of these filters is the need for numerical integration, which suffers from high computational cost and susceptibility to stiffness. This paper develops an exact, integration-free closed-form solution for the exact Daum--Huang (EDH) deterministic particle flow under vector linear Gaussian measurements. By transforming the ODE into a specific eigenspace, closed-form algebraic expressions are derived for both the homogeneous state transition matrix and the inhomogeneous forcing term. We prove that this analytic solution is mathematically equivalent to the exact Kalman measurement update. Furthermore, we demonstrate how this closed-form evaluation can be embedded within an $N$-step slicing method, providing a stiffness-mitigating, integration-free particle update for highly nonlinear measurement models.