I’m implementing a Kalman Filter Estimator and I’d like to define my process noise matrix in continuous time. The following equation is out of Grewal and Andrews:

where Q(t) is the continuous time process noise, Qk is discrete time (which the filter needs) and Phi is the state transition matrix.

A couple of ideas I’ve had are:

- do a coarse Euler integration, but I can’t find a method that will allow me to just predict the Kalman Estimator to a future time without an observation?
- add additional equations to the numerical propagator, but that isn’t an option for the numericalpropagatorbuilder?

Is there a way that I can implement one of these methods, or is there an alternative that I can use?