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A Kalman filter assumes that measurement noise follows a Gaussian distribution, and it continuously updates its estimate of the covariance based on previous obs
by gpcz 13y ago
A Kalman filter assumes that measurement noise follows a Gaussian distribution, and it continuously updates its estimate of the covariance based on previous observations. Therefore, if you gave it a bunch of very similar observations (like differing by 0.1) for a long time, the covariance would get very narrow. Once the activity spikes appeared, they would not have much influence on the state estimate because the probability distribution would imply they were extremely unlikely events. This would look very similar to a low-pass filter.
Although the Kalman filter retains some aggregate data about past states in its iterated covariance estimate, it is still primarily a recurrence relation where the future state depends on the immediate present, much like a discretized low-pass filter. This is part of why I'm intrigued by the parent article's use of a Kalman filter for this application.
- tel 13y agoIt sounded a lot like the interviewer didn't have enough expertise to do much over key of "Kalman filter" as sounding vaguely big data-ey. Too bad.
- gpcz 13y agoThat may be a part of it. The problem was only described in vague terms, so there's probably a reason why a Kalman filter makes sense, but as it was described in the interview it seemed more like a regression problem to me.
- michaelmior 13y agoI don't have much knowledge of Kalman filters, but the Wikipedia article[1] claims the assumption of Gaussian error is a common misconception. A quick skim of the original paper[2] seems to confirm this. [1] http://en.wikipedia.org/wiki/Kalman_filter http://en.wikipedia.org/wiki/Kalman_filter [2] http://www.cs.unc.edu/~welch/kalman/media/pdf/Kalman1960.pdf http://www.cs.unc.edu/~welch/kalman/media/pdf/Kalman1960.pdf
- gpcz 13y agoI didn't know that -- that's very interesting! Thank you for showing me that. I learned about Kalman filters in a mobile robotics course that made explicit Gaussian assumptions early on for the primary topic (SqrtSAM), and they brought up Kalman filters in its own lecture as kind of a "this is how they used to do SLAM" lecture. Considering the large amount of overlap in the methods, such as the use of linear covariance projections, I guess I made the assumption that Kalman filters had the same Gaussian assumption.
- michaelmior 13y agoSounds like a pretty interesting course. Really I know about Kalman filters is the use case.