I'm an experienced Control Engineer, with huge experience in robust linear control and estimation.
Your work will be done with efficient, commented and well-written Matlab code.
You can check my curriculum on LinkedIn.
P.S
The system you are trying to model is highly non-linear. Are you sure you want to predict it with a linear model? Maybe you want use a smarter method as neural network? I'm sure the RMS (Root mean square) error of the prediction will be lower than a simple kalman-filter.
Regards.
Luca Arzilli