Iterative Kalman filters and system parameters estimation
Regarding the miss modeling, I am not sure how you can handle that because a good mathematical model is important inorder to get kalman filter getting to work. usually the more complex your model is, the better results you can obtain.

Regarding the process and measurement noise, that noise will not effect much of your result but even then if you want to estimate that noise covariance matrix, you can use iterative algorithms like LMS or RLS to fine tune your Noise parameters for some observations and use it further.