Efficient High Degree Continuous-Time Cubature Kalman Filters

Sigma-point filters, including the Unscented Kalman Filter (UKF) and the Cubature Kalman Filter (CKF) are important modern non-linear estimation algorithms. The standard forms of these algorithms are applied to discrete-time systems, however, continuous-time forms also exist. In previous work, the author developed a runtime optimization to sigma-point filters in discrete time called the Hybrid Sigma-point Extended Kalman Filter (HESKF). Using this technique, sigma-point integration is applied to "difficult" subspaces of the dynamics, whereas "easy" subspaces are treated with Jacobian linearization, resulting in a blended filter algorithm. This present work extends the HESKF technique to a continuous-time dynamics and demonstrates the improvement in runtime with an appropriate example.