It is a filter and an adaptive one at that. To see it let's compare it with the simplest IIR: x(k) = h * x(k-1) + (1-h) * u(k) To use the same language as the

It is a filter and an adaptive one at that. To see it let's compare it with the simplest IIR: x(k) = h * x(k-1) + (1-h) * u(k) To use the same language as the blog post, at time k-1 our best estimate of the state is x(k-1). Here we don't know anything about the system dynamics (but if we do we can incorporate it as an FIR as well) so our projection for time k is simply x(k-1). Our measurement at time k is u(k). Based on the same criteria of combination we should combine these two sources of information with appropriate ratios controlled by h. Without an adaptive algorithm we appeal to our prior knowledge of the signal and noise statistics to fix h. Kalman filter as presented in the blog, on the other hand, can estimate the covariance of the signal to determine the best h at any time and therefore adapt to changes of the signal.