Inspired by Cliff Pickovers tweet and powered by my fascination about the Fourier transform, I took the time to derive and implement the Fourier series of a two dimensional piecewise linear parametric curve.

This article, treating the derivation of the particle filter, marks the last part of the nonlinear filtering series. We will derive the particle filter algorithm directly from the equations of the Bayes filter. In the end, we will have the opportunity to play around with the particle filter with our toy example.

The unscented Kalman filter describes another method for approximating the process of non-linear Bayes filtering. In this article, we will derive the corresponding equations directly from the general Bayes filter. Furthermore, we will get to know a different way to think about the unscented transform.

Observability is an important concept of classical control theory. Quite often it is motivated by abstract concepts, that are not intuitive at all. In this article, we will take a look at observability from a Bayesian perspective and will find a natural interpretation of observability.

Linear algebra is a wonderful field of mathematics with endless applications. Despite its obvious beauty, it can also be quite confusing. Especially, when it comes to subspaces, inverses and determinants. In this article, I want to present a different view on some aspects of linear algebra with the help of Gaussian distributions and Bayes theorem.

This article is the second part of the nonlinear filtering series, where we will derive the extended Kalman filter with non-additive and additive noise directly from the recursive equations of the Bayes filter.

The process of Bayes filtering requires to solve integrals, that are in general intractable. One approach to circumvent this problem is the use of grid-based filtering. In this article, we will derive this method directly from the recursive equations of the Bayes filter.

This post will start a series of articles that will treat common nonlinear filtering methods that are based on the Bayes filter. The motivation is to provide an intuitive understanding of these methods by deriving them directly from the general Bayes filter. This derivation is done in steps, that are supposed to be as atomic as possible. Furthermore, each nonlinear filtering method will be shown in action by providing an interactive example to play around with. This series will require some basic knowledge in math. Especially in linear algebra and probability theory.

This article is a brief summary of some relationships between the log-likelihood, score, Kullback-Leibler divergence and Fisher information. No explanations, just pure math.

The concept and the equations of the Kalman filter can be quite confusing at the beginning. Often the assumptions are not stated clearly and the equations are just falling from the sky. This post is an attempt to derive the equations of the Kalman filter in a systematic and hopefully understandable way using Bayesian inference. It addresses everyone, who wants to get a deeper understanding of the Kalman filter and is equipped with basic knowledge of linear algebra and probability theory.