Deriving a Kalman Filter Equation for a Linear Gaussian Filtering Model with Non Zero Mean Noise
Since the model is linear taking care of known mean is pretty simple.
Measurement
Since the &quot;Bias&quot; of the measurement is known all you need is to define $ \hat{y}_{k} = {y}_{k} - {m}_{r} $. Then use it as you'd use a measurement with no bias.
Model
The model is used in the prediction step. What you should do is use the regular prediction step and add to it $ {m}_{q} $ after the prediction.
All other steps only include the covariance matrices and are the same.