Rudolf Kálmán Has Died • Hacker News Board

Re: Rudolf Kálmán Has Died

#71

Post by RogerL » Thu, Jul 07, 2016, 4:25 PM UTC

lacker wrote: post #20

jmaygarden wrote: post #3

Earlier quoted context omitted.

Interesting. I don't see generic Kalman filter implementations too often. Thanks for sharing. I've always found that determining where to put outputs from disparate sensors as opposed to just filtering a single observation like the GPS output in your example is challenging. Have you tried extending this to include input from other sensors (e.g. accelerometer, gyroscope, magnetometer, etc.)?

I actually found it to be such a pain in the ass to tune, it didn't even seem that great on iPhones with plain old GPS compared to a hacky bundle of heuristics. I left the code on github because why not, and it turned out over the years people have used it for various things.

GPS already use a Kalman filter to create a filtered output. You cannot apply a second filter to the output of the first and expect better results.

Specifically, the Kalman filter depends on the data having the Markov property, and that the noise is Gaussian. The output of the filter has neither property, so you are not going to get better data. You may "smooth" the data, but all you are really doing is 1) discarding useful information, and/or 2) introducing a lag into the signal.

Re: Rudolf Kálmán Has Died

#72

Post by bmmayer1 » Thu, Jul 07, 2016, 4:25 PM UTC

dexterdog wrote: post #69

bmmayer1 wrote: post #60

> "emigrated to the United States in 1943" It's always sad hearing about great minds who fled Europe shortly before or during World War II. It's a reminder of all the great minds whom we lost in the last war, and of how destructive war is to technological and human progress.

And unfortunately how constructive it is to technological process at the same time which is one of the justifications.

Technology is gained but so much intellectual capital is destroyed. And there's no good A/B test with war to see how much technological progress would have been gained from the intellectual capital if it hadn't been destroyed.

Re: Rudolf Kálmán Has Died

#73

Post by RogerL » Thu, Jul 07, 2016, 4:32 PM UTC

abstrakraft wrote: post #58

zbuf wrote: post #41

Earlier quoted context omitted.

Are alpha-beta (or alpha) filters a subset of Kalman Filters? I ask because I don't know enough about the Kalman Filter. But it seems that the parent post could also be accurate. I imagine many implementations of the Kalman Filter take advantage of the local use case, and don't necessarily have to carry a fully generalised Kalman filter.

One of the defining characteristics of the Kalman filter is that it computes a gain (called the Kalman gain) that is a function of the state covariance and the measurement covariance. Alpha-beta filters use constants, so I'd say no, they are not a subset.

You can define alpha/beta in terms of the covariance of the Kalman filter. See my book (linked above) for the derivation (I call it a g-h filter, some literature uses alpha-beta, some g-h, they are the same thing). Eli Brookner in "Tracking and Kalman Filters Made Easy" uses a different but mathematically equivalent derivation to show the relationship.

There are at least a couple dozen of commonly used filters that can be understood as form of the alpha-beta filter. Some use constants for g/h, some vary them over time. The Kalman filter varies them on each epoch based on the covariance of the state and measurements. There are other schemes. The KF is optimal in the least squares sense when the noise is Gaussian and and the system obeys the Markov property.

Another way to look at these is to derive them from Bayes' theorem. You can derive both the alpha-beta filter and Kalman filter from Bayes' theorem. It's all the same family, just with different assumptions/knowledge about your process and measurement noise.

Re: Rudolf Kálmán Has Died

#74

Post by abstrakraft » Fri, Jul 08, 2016, 7:00 AM UTC

RogerL wrote: post #73

abstrakraft wrote: post #58

Earlier quoted context omitted.

One of the defining characteristics of the Kalman filter is that it computes a gain (called the Kalman gain) that is a function of the state covariance and the measurement covariance. Alpha-beta filters use constants, so I'd say no, they are not a subset.

You can define alpha/beta in terms of the covariance of the Kalman filter. See my book (linked above) for the derivation (I call it a g-h filter, some literature uses alpha-beta, some g-h, they are the same thing). Eli Brookner in "Tracking and Kalman Filters Made Easy" uses a different but mathematically equivalent derivation to show the relationship. There are at least a couple dozen of commonly used filters that c…

I'd agree that the alpha-beta filter is a special case of the Kalman filter (which isn't what I'd call a subset, but maybe we're just arguing semantics). All the filters you mention are certainly related, but claiming that the alpha-beta filter is a Kalman filter is either naive or obstinate.