I am new to learning kalman filter. I could get the gist of system. For example tracking an object in 2D $x-y$ space, you predict the next location using a series of linear equation based on the Newtonian equation of motion. Then you take a measurement , convert our prediction to the same unit as measurement compute the residue and select the estimated state part way between predicted and measurement values. However they also told that these are only good for linear systems, but fails when dealing with non linear systems.
Clarification needed
I would like to know the difference between linear system and non linear system. Is it analogous to a car going in straight line vs car taking a sudden sharp turn? As equation required to represent both trajectory are linear vs non linear?
If my assumption is correct, then we can use the necessary process noise to account for same right? So why do we have a special class Kalman filters the focus on non linear systems?
Please forgive me if the question is dumb, Please explain to me like a 5 year old !
Thank You
A drawing of why Kalman Filter is an issue in nonlinear systems
It is quite an old question but I still think this answer will help many. The picture that I made above explains it quite well. We know that the most significant assumption before we apply KF is that the system noise and the process noise are Gaussian. When applying KF to a linear system, the assumption remains at the output. It is scaled most likely, but still holds its Gaussian character. However, if your system is not linear, the preassumed Gaussian noise is distorted at the output. Depending on "how much nonlinear" is your system, that assumption breaks even worse such that KF estimation means nothing.