Extended Kalman filter gain

1. What is Kalman filter gain?
2. What does an Extended Kalman Filter do?
3. Why is Extended Kalman Filter not optimal?

What is Kalman filter gain?

The Kalman-gain is the weight given to the measurements and current-state estimate, and can be "tuned" to achieve a particular performance. With a high gain, the filter places more weight on the most recent measurements, and thus conforms to them more responsively.

What does an Extended Kalman Filter do?

The Extended Kalman Filter (EKF) handles nonlinear process and measurement models by resorting to linearization for the propagation of error covariance matrix and Kalman gain computation.

Why is Extended Kalman Filter not optimal?

EKF is not optimal (mostly)

This happens because the EKF approximates state transitions and measurements using linear Taylor expansions, making the goodness of the approximation dependant on the degree of nonlinearity of the functions being approximated and on the uncertainty of its Gaussian belief [2][5].