Cubature Kalman Filters

In this paper, we present a new nonlinear filter for high-dimensional state estimation, which we have named the cubature Kalman filter (CKF). The heart of the CKF is a spherical-radial cubature rule, which makes it possible to numerically compute multivariate moment integrals encountered in the nonlinear Bayesian filter. Specifically, we derive a third-degree spherical-radial cubature rule that provides a set of cubature points scaling linearly with the state-vector dimension. The CKF may therefore provide a systematic solution for high-dimensional nonlinear filtering problems. The paper also includes the derivation of a square-root version of the CKF for improved numerical stability. The CKF is tested…