Ensemble Kalman Filter with Bayesian Recursive Update

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.