How does the EKF differ from the UKF in navigation applications?

• A. UKF uses the unscented transform; EKF uses linearization.
• B. EKF uses first-order linearization; UKF uses the unscented transform.
• C. EKF and UKF are identical in how they handle nonlinearity.
• D. EKF uses second-order Taylor expansion; UKF uses stochastic sampling.

Answer: (B)

In navigation applications, the main idea being tested is how nonlinear models are handled in state estimation. The EKF relies on a first-order linearization of the nonlinear process and measurement models around the current state estimate, obtained via Jacobians. This makes the filter behave as if the system were linear on that local neighborhood, but it can introduce errors when the true state is far from the estimate or when the nonlinearities are strong.

The UKF takes a different route: it uses the unscented transform. It selects a small set of sigma points that represent the state distribution, propagates all of them through the actual nonlinear functions, and then recomputes the mean and covariance from the transformed points. This approach captures nonlinear effects more accurately without needing explicit Jacobians. In practice, that often yields better estimates for nonlinear sensing and motion models common in navigation, at the cost of more computations.

So the best description is that the EKF uses first-order linearization, while the UKF uses the unscented transform. The other phrasing either oversimplifies or mischaracterizes how the UKF operates (namely, that it relies on stochastic sampling or that EKF uses higher-order expansions).