Why might you prefer an UKF for navigation in highly nonlinear scenarios?

• A. UKF always runs faster than EKF.
• B. UKF uses linearized Jacobians.
• C. UKF cannot handle nonlinearity.
• D. UKF uses sigma points to capture nonlinearities without requiring Jacobians.

Answer: (D)

When navigation problems involve strong nonlinear behavior, you want an estimate that can accurately reflect how uncertainty changes as it passes through those nonlinear dynamics. The Unscented Kalman Filter does this by using a set of sigma points that represent the current state distribution. Each sigma point is propagated through the actual nonlinear process and measurement models, and then these transformed points are recombined to form the predicted mean and covariance. This captures nonlinear effects more accurately than a single linear approximation, which is what the EKF uses. Importantly, UKF achieves this without requiring Jacobians, which can be difficult to compute or error-prone for highly nonlinear systems. The result is improved accuracy in highly nonlinear scenarios, making UKF a preferred choice. While it's true that you evaluate multiple points and it may not always be faster than an EKF, the key advantage is the better handling of nonlinear transformations without relying on Jacobians.