What is the difference between kalman filter and extended kalman filter? I am working SLAM based problems in robotics and I want to know whether I can use Kalman filter instead of the Extended kalman filter that is predominantly used ?
If not, what is the difference?
 A: The Kalman filter (KF) is a method based on recursive Bayesian filtering
where the noise in your system is assumed Gaussian. The Extended Kalman Filter (EKF) is an extension of the classic Kalman Filter for non-linear systems where non-linearity are approximated using the first or second order derivative. As an example, if the states in your system are characterized by multimodal distribution you should use EKF instead of KF.
A: Both of them are state estimators, both of them involve the following steps:

*

*predict the state ahead ( this is the so-called prior)

*predict the covariance ahead

*compute Kalman gain

*update estimates with means (this is the filtering step)

*update error covariance

the KF or linear Kalman filter is the optimal estimator when the estimations and/or the measurements present white noise, no other linear filter can do better than the Kalman filter.
When the system is non-linear the steps are identical for the simulation of the EKF but the main difference is that in step 2  and step 3 we use linearization at the previous step and at the prior respectively, only for those two steps the other steps remain identical for both methods KF and EFK.
