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This is great! Back in the '90s, I played with Kalman filters for a predictive navigation system. I had a couple of textbooks, but it was a bear to make sense of the math. Really wish I'd had this back then!

Nav applications are the ones you see most often; it would be interesting to see an example from a completely different domain.

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There are plenty of applications in system control, when you want to estimate a variable within a system (sometimes, it's just too hard or expensive to set a sensor).

I've been close to applications that estimate the state-of-health and state-of-charge of lithium-ion batteries. I myself worked in volatility estimation of financial returns using Particle Filter (very similar principle, but usable with non-additive and/or non-Gaussian noise).

Here's some work on applications in Failure Prognosis: http://icsl.gatech.edu/aa/images/e/ed/Pfafdfp.pdf

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