Cubature Kalman smoothers

The cubature Kalman filter (CKF) is a relatively new addition to derivative-free approximate Bayesian filters built under the Gaussian assumption. This paper extends the CKF theory to address nonlinear smoothing problems; the resulting state estimator is named the fixed-interval cubature Kalman smoother (FI-CKS). Moreover, the FI-CKS is reformulated to propagate the square-root error covariances. Although algebraically equivalent to the FI-CKS, the square-root variant ensures reliable implementation when committed to embedded systems with fixed precision or when the inference problem itself is ill-conditioned. Finally, to validate the formulation, the square-root FI-CKS is applied to track a ballistic target on reentry.