New nonlinear iterated filter with applications to target tracking

The two most popular solutions to the nonlinear filtering problem are the Extended Kalman filter (EKF) and the Iterated Extended Kalman filter (IKF). Both are sub-optimal algorithms which employ a first-order, Taylor-series approximation to adapt the linear, Kalman filter to the nonlinear problem. While the Taylor-series approximation makes an implementation realizable, its accuracy depends heavily on the stability of the Jacobian matrix. In practice the Jacobian matrix is often numerically unstable, resulting in filter divergence and, in the case of the IKF, slowed or even non-convergence of the iterates. This paper identifies inadequacies inherent to the EKF and IKF, discusses their detrimental effect on performance, and then proposes a solution which uses the Julier et al. time update and a new iterated procedure for computing the measurement update. The resulting new iterated filter is believed to be a robust alternative to prevailing methods. Examples involving target tracking are considered.