# Understanding the Kalman Filter

When I first encountered Kalman Filter technique, I was overwhelmed by the ton of approaches taken by various authors to explain it. It can be explained from an engineering vocabulary but I wanted to understand it from a stats point of view . One typically reads either the Frequentist approach( where Gaussian multivariate normal distribution is used to derive all the formulae) or the Bayesian approach where the usual prior-posterior stuff is used to derive Kalman Filter. Irrespective of whatever approach one comes across, unless one derives the Kalman Filter using pen and paper, it is tough to understand what’s going on.

In the bewildering literature on this technique, I think this paper by R.J.Meinhold and N.D.Singpurwalla is probably the best introduction to KF from a statistician’s point of view. The basic set of equations are introduced and the recursive estimation procedure is derived. The paper ends with two examples of local level model. All these “under the hood” details are explained in just 5 pages. Amazing feat, given that the authors do not resort to hand waving through out the exposition.