What is the primary purpose of the Extended Kalman Filter in navigation applications?

• A. It linearizes nonlinear process and measurement models around the current estimate to propagate state and covariance and fuse sensor data for position, velocity, and attitude.
• B. It uses the unscented transform to handle nonlinearity without Jacobians.
• C. It performs exact nonlinear propagation without any approximation.
• D. It estimates only velocity and ignores attitude.

Answer: (A)

The Extended Kalman Filter handles nonlinear navigation models by linearizing them around the current estimate, then using that linear approximation to propagate the state and its uncertainty while fusing sensor data. In practice, you treat the motion and sensor equations as nonlinear, approximate them with first-order Taylor expansions, and compute the Jacobians with respect to the state. These Jacobians tell you how small changes in the state affect the predicted next state and the expected measurements, allowing you to update your estimate with new observations and to maintain a covariance that reflects uncertainty. This approach lets you estimate a full navigation state—position, velocity, and attitude (and sometimes biases)—from multiple sensors in a computationally manageable way. The other options describe different filtering approaches or unrealistic claims (like exact nonlinear propagation or ignoring attitude), which is why they don’t fit the Extended Kalman Filter’s purpose.