Which statement best describes an advantage of UKF over EKF in navigation?

• A. UKF requires explicit Jacobians like EKF.
• B. UKF better captures nonlinearity without explicit Jacobians, often improving robustness.
• C. EKF always outperforms UKF in nonlinear cases.
• D. UKF uses particle filters.

Answer: (B)

Handling nonlinear transformations in state estimation is crucial in navigation. The unscented Kalman Filter improves robustness by not relying on a linear approximation of the motion and measurement models. Instead, it propagates a carefully chosen set of sigma points through the actual nonlinear functions and then recomputes the state mean and covariance from those transformed points. This captures more of the true effect of the nonlinearity than the EKF’s first-order linearization, which can misrepresent the transformation when nonlinearities are strong. Because the UKF doesn’t require explicit Jacobians, it reduces the risk of errors from derivative calculations and often yields better accuracy in nonlinear navigation problems. The other statements don’t fit: the UKF does not rely on Jacobians, EKF isn’t guaranteed to outperform UKF in nonlinear cases, and UKF is not a particle filter.