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Perhaps this is a stupid question, but why is it called a _filter_? To me it just seems like a (very clever) linear projection.
by cshimmin 11y ago
Perhaps this is a stupid question, but why is it called a _filter_? To me it just seems like a (very clever) linear projection.
- robotresearcher 11y agoAs far as I know there is no deep reason, but it's traditional in the signal processing community, where a filter is a function that modifies a signal. https://en.wikipedia.org/wiki/Filter_(signal_processing) https://en.wikipedia.org/wiki/Filter_(signal_processing) Kalman trained as an electrical engineer (MIT and Columbia) so that's the lingo he was used to. There's a brief note in his Wikipedia page about having trouble publishing the technique at first. I'd like to hear the story. https://en.wikipedia.org/wiki/Rudolf_E._Kálmán https://en.wikipedia.org/wiki/Rudolf_E._Kálmán
- fspeech 11y agoIt is a filter and an adaptive one at that. To see it let's compare it with the simplest IIR: x(k) = h * x(k-1) + (1-h) * u(k) To use the same language as the blog post, at time k-1 our best estimate of the state is x(k-1). Here we don't know anything about the system dynamics (but if we do we can incorporate it as an FIR as well) so our projection for time k is simply x(k-1). Our measurement at time k is u(k). Based on the same criteria of combination we should combine these two sources of information with appropriate ratios controlled by h. Without an adaptive algorithm we appeal to our prior knowledge of the signal and noise statistics to fix h. Kalman filter as presented in the blog, on the other hand, can estimate the covariance of the signal to determine the best h at any time and therefore adapt to changes of the signal.
- ArkyBeagle 11y agoIt's a part of a "signals and systems" discipline. Operators on/in signals and systems tend to be called filters.