# Deterministic method to compute “Process noise covariance matrix, Q” for a Kalman filter when parameter variations of the model is known apriori

I am implementing a Kalman filter (for a linear ODE system for now).

My model represents a physical device that has 6 "parameters", i.e. those values of the device do not evolve over time (within a time-domain simulation environment for now).

I have 100 such "slightly differing devices", i.e. whose parameter values differ from the nominal, but the distribution of all 6 of the model parameters are known apriori (Gaussian, with known mean (nominal values) and standard deviations). I think that these deviations in model parameters (from the nominal) can be treated as process noise.

I am assuming that there is no other source of process noise (i.e. no unmodeled states or other dynamics are present)

I am implementing a Kalman Filter with a single tuning parameter across all these 100 devices. Is there a deterministic way, i.e. a recipe, to compute the "Process noise covariance matrix", typically denoted as QQ in Kalman Filter literature?

I am thinking that one can somehow exploit the affine properties of Guassian distributions to arrive at the error covariance matrix, although I am a bit rusty with the math.

Partially related, but different question asked by someone else: Question about Q matrix (noise process covariance) in Kalman filter