Non-linear observer design

Hello,

I have the task to design an observer for a strongly non-linear system (MIMO) for a research project. Unfortunately, I only find very overcomplicated approaches on the internet that I do not fully understand.

I do have matlab code with ~10 classes for the different parts of the system, but was only able to install the additional states which should be observed in the corresponding classes. The system consists of a magnetic projectile, a permanent magnet and an open-loop controller. The aim is to estimate the vertical position and speed of the projectile.

This is to be determined by the induced voltage in a measuring coil, which is determined by the movement and position of the projectile.

Are there any resources that can give step by step instructions? Which design principle (Tau's observer, error linearization, extended kalman filter) is the most promising to implement?

Code can be shared if asked.

Thanks!