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What is the cleanest, easiest way to explain to someone the concept of "Kalman Filter"?

What does it intuitively mean? It's a concept that I have difficulty articulating - especially when explaining to someone. How would one explain it in simple English?

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We may not do justice to the topic without mathematical expressions but an attempt could be as follows. We need to introduce some concepts, and that we are dealing with time series of observations. Some of these concepts maybe be used synonymously depending on the literature but here are the definitions :

  1. Forecasting : It means we build a view of the world by a mathematical/physical model based on the historical observation to make predictions about future of the system we are modelling.
  2. Smoothing : It means we try to make historical observations as "clean" as possible, thinking of removing noise when we try to listen a person.
  3. Interpolation: We try to obtain information about missing observations using observations close by in time.
  4. Filtering/data assimilation: This is to use data to build a probabilistic view of the data via incorporating our model.

Kalman filter possibly can lead to smoothing, filtering and forecasting as a whole package. So in Kalman Filter, we incorporate data and model, usually discrete differential equations, with the probabilistic model of the data. In Kalman's case probabilistic view is normal distribution, i.e., multi-dimensional bell curve.

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  • $\begingroup$ Please feel free to add mathematical expressions as they are really needed for better understanding.... $\endgroup$ Jul 4 at 14:35
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    $\begingroup$ Conceptual intuition may be reached with these concepts. Actually, it is a pretty advanced topic mathematically. I recall it was offered as a graduate studies elective course and only touched upon in senior Control theory course in engineering mechanics. Wikipedia has a fairly good article, a good picture with some equations en.wikipedia.org/wiki/Kalman_filter#/media/… $\endgroup$ Jul 4 at 14:45
  • $\begingroup$ @Pluviophile. Not sure why you'd ask for a plain English explanation, yet simultaneously implore Mehmet to express the Kalman Filter mathematically. Very very good answer by Mehmet if you ask me. $\endgroup$
    – EB3112
    Jul 4 at 20:41

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