The first paper linked (page 5 of http://vixra.org/pdf/1606.0328v1.pdf http://vixra.org/pdf/1606.0328v1.pdf) makes a cute connection that was new to me. It sta

The first paper linked (page 5 of http://vixra.org/pdf/1606.0328v1.pdf http://vixra.org/pdf/1606.0328v1.pdf) makes a cute connection that was new to me. It starts with the familiar formula for on-line computation of the sample mean (e.g., https://en.wikipedia.org/wiki/Algorithms_for_calculating_variance#Online_algorithm https://en.wikipedia.org/wiki/Algorithms_for_calculating_var...) -- mu_n <- mu_n-1 + (1/n) (z_n - mu_n-1) This corrects the mean "mu" based on the new observation "z_n". The paper then uses this simple expression to motivate the Kalman filter update equation, in which a new observation z_n is used to compute an innovation (or error signal) y: y = z_n - H x_n-1 The innovation is then used to update the state-estimate x, x_n = x_n-1 + K y The two updates are formally identical, with the Kalman state "x" being analogous to the running-mean "mu". I had never noticed the connection. There is a similar connection to the on-line variance.