# Kalman filter and ekf main difference in elaborate way

I am studying about various filtering techniques for Robot pose esitimation. I came to know two very well known filter technique Kalman Filter and Extended Kalman Filter. To know about this two technique I read Probalistic Robotics books.

Kalman Filter is a technique for filtering and prediction in linear system.

Extended Kalman Filter is a technique for filtering and prediction of non-linear system.

This two definitions are not very clear to me. So I googled the term linear and non-linear system

Linear System- A linear system is a mathematical model of a system based on the use of a linear operator.

Non-Linear System: In mathematics and physical sciences, a non-linear system is a system in which the change of the output is not proportional to the change of the input.

Now both definitions are very fishy for me. They are the well structured definition but not very efficient for mobile robot.

Can any one guide me about linear and nonlinear system from scratch or from naive level. I want to know this term in concept of Mobile Robotics and Kalman filter and extended Kalman filter. Any practical example is most welcome.

• what do you mean by 'Now both definitions are very fishy for me' ? And what do you mean by 'not very efficient for mobile robot' ? Linear system can be describe by linear functions (i.e. using operands like + - * ...) while non-linear system cannot but can be described with nonlinear function (e.g. trigonometric function, exponential, ...) – N. Staub Jun 18 '18 at 17:06
• Kalman filter is a linear system whereas extended kalman filter is a non linear system what does that mean? What is called linear system ?what is called non linear system?How could I related this two terms linear and non linear with Kalman filter and ekf? – user20203 Jun 18 '18 at 19:05
• You are mixing notions. Linear and non-linear systems relate to the mathematics used to describe the system, as you pointed in your question and as I gave some examples. Then Kalman filter is a technique which is fit to linear systems because it uses properties of linear systems, unfortunately those property do not hold for nonlinear system hence a second technique called extend Kalman filter which follows the same basic idea but dealing with the additional complexity of non-linear systems. – N. Staub Jun 19 '18 at 5:18
• I really advise you to get familiar with basic mathematic tools for robotics before starting to tackle non linear filtering – N. Staub Jun 19 '18 at 5:19
• Basically, a linear system is a system which can be modeled by a set of linear equations (for instance, a mass-spring-damper system in one dimension). As soon as the system equations get nonlinear (for instance when you start considering friction in the above-mentioned system), you can't use the linear algebra formalism anymore, and everything gets more complex. I second the comment above, you really should get familiar with basic math and robotics concepts before delving into non-linear filtering methods ! – Ben Jun 19 '18 at 14:47