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Simo Saarka has more recent work on continuous-discrete time systems (as you referenced) that might be interesting to contrast against - there, using Gaussian cubature that provides a nice alternative deterministic approximation method. This might be useful for additional discussion and future work. In addition I also now wondered if it is possible to derive an algorithm directly using the variational Gaussian approach. This would be more appealing from the point of having a well defined objective function with which to optimise, potentially fewer numerical issues and interpretation directly in terms of the marginal likelihood. I do look forward to reading the final version of the paper.