> I agree that probability notation isn't the best [...] There is so much hidden context in mapping Bayes' theorem to Kalman filters that I still have to cring

> I agree that probability notation isn't the best [...] There is so much hidden context in mapping Bayes' theorem to Kalman filters that I still have to cringe. First we've got the sub-expression "p(x_k)" in the numerator, and you know that is a multivariate PDF for the state estimate, or possibly the density value of that PDF at x_k. However, we've got a very similar looking expression "p(z_k)" in the denominator, and in this case it means "an integral of the product of two PDFs". Those are wildly different substitutions for nearly the same syntax. That same confusion applies to p(x_k|z_k) and p(z_k|x_k). The first seems to indicate "the PDF of my estimate given this measurement", but the second really says something like "evaluate the PDF in the measurement space at the location which corresponds to my estimate". Essentially, p_Z(h(x_k)). If you don't already know the solution, this notation is not prescriptive for getting there.