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i am working recently on a project in which i want to implement a Kalman filter as being an observer, and i couple this observer with a state feedback controller that produces control actions necessary to control a mobile robot.

The problem is that the governing equations for the mobile robot's motion contain errors, and this will affect the control actions produced, and at the same time the miss modelling error covariance matrix is hard to get as well as the measurement error covariance matrix. I though about using some arbitrary values for these matrices and go on with the filtration process, but i thought that it would be much better if there is anything like a kalman filter formulation that has the ability to estimate closer values for system parameters so better control actions can be obtained.

Thank you in advance.

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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.

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