# 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?

## 2 Answers

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.

• There is no "Kalman Filter". There is a "Linear Kalman Filter". There are also continuous and discrete Kalman filters. I would suggest that the state update and the covariance update are linear functions for the Linear Kalman filter. For non-linear systems approximations to the state covariance update are a (huge) pain, and approximations like the EKF (by taking a derivative, and treating the system as linear around it) are required - though they dispense with the "optimality" of the Linear system. Aug 26, 2015 at 18:36
• There are different type of Kalman filters, it depend what system you are working on. Here the question is: what is the difference between "normal" and extended.
– lcit
Aug 26, 2015 at 18:44
• Normal needs context. Weiner filter? continuous? discrete? linear? The only context is "extended" as the "alternative hypothesis". Extended is a near-but-not optimal approach to turn non-linear to linear-ish, so perhaps normal means linear? I don't know. Aug 27, 2015 at 0:34

Both of them are state estimators, both of them involve the following steps:

1. predict the state ahead ( this is the so-called prior)
2. predict the covariance ahead
3. compute Kalman gain
4. update estimates with means (this is the filtering step)
5. 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.