Can I model process noise as a known "error" in my dynamics while designing a Kalman Filter? Consider I am modelling the dynamics of a robot and using a Kalman filter to obtain estimates of some state. I have certain terms in my equation which correspond to data not accessible to this robot ( states of other robots etc).  

1) Is it fair to model these as process noise by assuming these terms to evolve based on some random process and act "Gaussian like" ? This also raises another important question:
2) Why does the Kalman Filter require us to have a positive definite covariance associated with the process noise. How do I interpret this in the real world when I am writing down process noise as some unmodeled physical terms ?
The Extended Kalman filter (EKF) effectively does that: Unmodelled nonlinearities are taken account of by assuming higher process or measurement noise, depending on where the nonlinearity appears.