Basic questions related to Kalman filter

1. What are the types of Kalman filter?
2. When can we use Kalman filter?
3. Why Kalman filter is optimal?
4. Why use Kalman smoother?

What are the types of Kalman filter?

The chapter introduces several types of Kalman filters used for localization, which include extended Kalman filter (EKF), unscented Kalman filter (UKF), ensemble Kalman filter (EnKF), and constrained Kalman filter (CKF).

When can we use Kalman filter?

Kalman filters are used to optimally estimate the variables of interests when they can't be measured directly, but an indirect measurement is available. They are also used to find the best estimate of states by combining measurements from various sensors in the presence of noise.

Why Kalman filter is optimal?

Kalman filter is statistically optimal in a sense that it gives the minimum error covariance estimate, based on all available observation data at the present time step under the linear system.

Why use Kalman smoother?

Good reasons for Kalman smoothing are: The Kalman smoother provides very good imputations (i.e. imputed values) for missing values in your time series. The Kalman smoother provides very good estimates of the state vector in the historical period.