Nonlinear Kalman filtering with semi-parametric Biscay distributions

The problem of nonlinear estimation is reexamined, and a new semi-parametric representation of uncertainty called the Biscay distribution is presented. The Biscay distribution is combined with the extended Kalman filter (EKF) and a new filtering paradigm called the Biscay distribution filter (BDF) is developed. The BDF is provably optimal for linear estimation and generalizes naturally to nonlinear estimation. Further, the BDF is of the same computational order of complexity as the EKF. The BDF is compared with the EKF through an application in re-entry vehicle tracking.