What is an EKF in navigation, and why is it used?

• A. Extended Kalman Filter is a nonlinear state estimator used to fuse sensor data by linearizing around the current estimate, providing optimal estimates of position, velocity, attitude, and sensor biases with uncertainties.
• B. Algebraic filter used for linear data.
• C. Kalman filter with linear models only.
• D. Particle filter.

Answer: (A)

The Extended Kalman Filter is a nonlinear state estimator used to fuse sensor data by linearizing around the current estimate, providing optimal estimates of position, velocity, attitude, and sensor biases with uncertainties.

In navigation, the motion and sensor models are inherently nonlinear. For example, how attitude (orientation) evolves and how measurements relate to the state involve rotations and nonlinear relationships. The EKF handles this by approximating these nonlinear models with a linear one at each step, using Jacobians (their derivatives) to propagate the state covariance and perform the update with new measurements. This gives a practical, real-time way to combine high-rate inertial data with other sensors (like GPS, magnetometers, or barometers) to suppress drift and tighten estimates, all while keeping a quantified uncertainty.

The EKF is particularly useful because it preserves the Gaussian, recursive estimation framework of the Kalman filter but extends it to nonlinear systems. It's not intended for purely linear data, and it sits between linear Kalman filters (which can’t handle nonlinear dynamics well) and particle filters (which are more flexible but computationally heavier).