The Kalman Filter is one of the more useful tools in data science, but while there are a lot of well-written descriptions of the Bayesian tracking technique available online and in technical books/articles, for some reason it’s hard to find a simple derivation of the Kalman Filter from first principles.
In this short note, I show how 1-dimensional Kalman Filter comes about from the properties of Bayes Rule, Fourier transform, and Gaussian distributions.
A Derivation of the Kalman Filter
The generalisation of the proof to multi-dimensional Kalman Filter can be done in a similar way.
Mental Models 4 Life 