I didn’t know about this book, tx. It’s written by a philosopher for a popular audience, so it’s unsurprising if it leaves out technical specifics.
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My recollection when I looked into this is that Kalman filters were, in fact, part of the inspiration for the theory (I am not certain I’m remembering this right).
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The problem here is similar to that of Bayesian rationalism. On the one hand, if you think the problem Kalman filters address is the essence of cognition, then there is no real alternative to them
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Same way that if you think belief strength is the essence of rationality, there's no real alternative to probability theory (which is Cox's theorem)
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(I don't know if there's an analogously strong result in control theory—my vague recollection is that an optimality theorem hasn't been proved rigorously but it's generally taken as true. would know!)
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Not sure what you're asking. Kalman filters are a standard part of control toolkits, and they're "optimal" in the sense of being the optimal LQG solution for linear time invariant systems with gaussian noise. They rest on something called the "certainty equivalence principle"
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Thanks, yeah, I was being vague. Kalman filters are optimal for the thing they are optimal for, and then there’s various broader classes of problems for which analogous things are provably optimal (?), and you’d like a strong result for a very broad class that isn’t done…
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That is exactly correct. Under some nice conditions, a noisy signal can be used in place of a non-noisy signal and you'll still get an optimal solution. LQG is a weird but practically important special case that reduces to a simpler case.
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The general nonlinear stochastic is intractable. It's a situation similar to navier-stokes, but not as well known. If you write down the general equations, you can sort of poke at it and get some interesting results, but outside of LQG, there are very few usable results.
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This happens to be discrete. It's a minority tradition in nonlinear distributed stochastic control that starts with Hans Witsenhausen that gets into some of it. All done in discrete, the continuous version is impossibly hard so nobody tries. Still have a pile of papers on it

