[kqr]

I see -- we are talking about two different things!

You are working on the problem of figuring out the hidden state based on noisy observations and a transition model.

I interpreted your statement much more broadly, so I was trying to discuss the problem of computing the explicit next state based on perfect knowledge of the transition model, in which case (y_1-y)/dt is a perfectly viable approach to estimate the derivative.

(You can do better by adding higher-order terms of course, but I haven't found that to be universally useful compared to making dt smaller.)