Sunday, 11 March 2012

Kalman Filter

Over the years, on and off, I have tried to find code or otherwise code for myself a Kalman filter but unfortunately I have never really found what I want; the best I have at the moment is an implementation that is available from the technical papers and seminars section at the MESA Software web page. However, I recently read this R-Bloggers post which inspired me to look again for code on the web, and this time I found this, which is exactly what I want; accessible Octave like code that will enable me to fully understand (I hope!) the theory behind the Kalman filter and to be able to code my own Kalman filter function. After a little tinkering with the code (mostly plotting and inputs) a typical script run produces this plot:
which is a plot of a sine wave where
  • red is the underlying price (sine wave plus noise); e.g. typical price, vwap, close etc.
  • the yellow dots are "measurement noise;" e.g. high-low range
  • cyan is the Kalman filter itself
  • green are the 2 Sigma confidence levels for the filter
  • magenta is my current "MESA" implementation
I particularly like this example script as it mirrors the approach I have taken in the past with regard to creating my "idealised" sine wave time series for development purposes. I think the screen shot speaks for itself; the Kalman filter seems uncannily accurate in filtering out the noise to get the "true" underlying signal, with almost no lag at all! I shall definitely be doing some work with this in the very near future.

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