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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 ?

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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.

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  • $\begingroup$ I have a linear model, with clean dynamics. Is it necessary to resort to an EKF ? $\endgroup$
    – sid
    Commented Nov 5, 2015 at 22:33
  • $\begingroup$ Not at all. All I meant was that errors for other reasons are catered for in the EKF by increasing the noise variances. There's nothing stopping you from using the same technique to cater for unmodeled dynamics in a linear system. $\endgroup$
    – Peter K. ♦
    Commented Nov 6, 2015 at 13:02

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