The Burnished Flow Filter is a particle flow filter constructed from the Kalman filter measurement update equations. The derivation for this filter begins by assuming the classic Kalman Filter measurement update equations are the solution to a stochastic differential equation. By using these well known equations, the derivation of this filter follows naturally to an engineer with a Kalman filtering background. The work presented here shows the derivation, and application of this filter on both linear and nonlinear problems. The Burnished Flow Filter is benchmarked against the widely used Gromov Flow Filter, revealing similar performance in linear problems and demonstrating superior consistency in the nonlinear scenarios under study. Additionally, the Burnished Flow Filter exhibits a smoother flow compared to the Gromov Flow Filter, as evidenced by a smaller state update during the first substep of the measurement update.

The incorporation of nonlinear measurement information plays an important role in Bayesian state estimation for real-word systems. While many methods exist for propagating states through continuous-time nonlinear dynamics, a complementary continuous solution for discrete-time nonlinear measurements has so far remained elusive. Building on intuition from our previous work, the Bayesian Recursive Update Filter, we formulate the nonlinear measurement update as an ordinary differential equation (ODE). This formulation naturally extends to particle flow. We define two particle flows: the first is a deterministic flow based on the ODE solution, and the second is stochastic; the numerical integration contains a diffusion term. The proposed particle flows demonstrate excellent performance on a system with deterministic dynamics and a highly accurate nonlinear measurement, a setting known to be challenging for particle filters.

Nonlinear measurement models pose a challenge to linear filters. The ensemble Kalman filter (EnKF) is a popular choice despite its tendency to diverge in systems with highly accurate, highly nonlinear measurements. In this work, we present the Bayesian Recursive Update EnKF (BRUEnKF): a novel EnKF that employs the Bayesian Recursive Update Filter (BRUF) measurement update. The BRUF divides the the extended Kalman filter (EKF) update into an integer number of steps, allowing for the recomputation of the measurement Jacobian at regular intervals. We adapt the BRUF update for an ensemble filter, taking advantage of the EnKF’s numerical covariance computation at each update step. The BRUEnKF is shown to outperform the EnKF for systems with range measurements.