In an EKF, what is the key reason for linearizing around the current estimate?

• A. It uses a particle distribution to represent uncertainty.
• B. It handles nonlinear models by local linearization.
• C. It ignores measurement noise.
• D. It is identical to a linear Kalman filter.

Answer: (B)

In an EKF, the key idea is to make a nonlinear system workable by approximating it with a linear model that is valid near where the current estimate sits. This is done by taking a first-order Taylor expansion of the state transition and measurement functions and evaluating their Jacobians at the current state estimate. That local linearization lets the filter apply the familiar linear Kalman update rules to propagate the mean and covariance, capturing uncertainty while staying computationally efficient. If the system is strongly nonlinear away from the current estimate, the approximation may be less accurate, which is why the linearization is centered on the current estimate. The other statements don’t fit: EKF relies on a probabilistic model with measurement noise, not ignoring it; it isn’t just a true linear Kalman filter because the underlying model is nonlinear and only approximated linearly around the estimate; and it doesn’t use a particle distribution like a particle filter.