Last week’s post about the Kalman filter focused on the derivation of the algorithm. Today I will continue with the extended Kalman filter (EKF) that can deal also with nonlinearities. According to Wikipedia the EKF has been considered the de facto standard in the theory of nonlinear state estimation, navigation systems and GPS. Kalman filter I had the following dynamic linear model for the Kalman filter last week: \[\begin{aligned} x_{t+1} & = A x_t + w_t,\quad w_t \sim N(0,Q)\\\\\\ y_t &=G x_t + \nu_t, \quad \nu_t \sim N(0,R)\\\\\\ x_1 & \sim N(\hat{x}_0, \Sigma_0) \end{aligned} \]With \(x_t\) describing the state space evolution, \(y_t\) the observations, \(A, Q, G, R, \Sigma_0\) matrices of appropriate dimensions, \(w_t\) the evolution error and \(\nu_t\) the observation error.

At the last Cologne R user meeting Holger Zien gave a great introduction to dynamic linear models (dlm). One special case of a dlm is the Kalman filter, which I will discuss in this post in more detail. I kind of used it earlier when I measured the temperature with my Arduino at home.
Over the last week I came across the wonderful quantitative economic modelling site quant-econ.net, designed and written by Thomas J.

Last week’s Cologne R user group meeting was the best attended so far, and it was a remarkable event - I believe not a single line of R code was shown. Still, it was an R user group meeting with two excellent talks, and you will understand shortly why not much R code needed to be displayed. Introduction to Julia for R Users Download slides Hans Werner Borchers joined us from Mannheim to give an introduction to Julia for R users.

The next Cologne R user group meeting is scheduled for this Friday, 12 December 2014.
We have an exciting agenda with two talks on Julia and Dynamic Linear Models: Introduction to Julia for R Users Hans Werner Borchers
Julia is a high-performance dynamic programming language for scientific computing, with a syntax that is familiar to users of other technical computing environments (Matlab, Python, R, etc.). It provides a sophisticated compiler, high performance with numerical accuracy, and extensive mathematical function libraries.

© Markus Gesmann CC BY-NC-SA 3.0 · Powered by the Academic theme for Hugo.