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Pardon my ignorance, I'm just wondering about some context, since the Kalman filter was invented in the 60s. Are Kalman filters still highly relevant, or are they (in practice and/or in theory) obsoleted by other techniques, such as general ML?
Pardon my ignorance, I'm just wondering about some context, since the Kalman filter was invented in the 60s. Are Kalman filters still highly relevant, or are they (in practice and/or in theory) obsoleted by other techniques, such as general ML?
It's also worth noting that the Kalman filter follows the EM pattern of many ML / statistical models.
It's a little simpler to derive the least squares smoothing function http://stats.stackexchange.com/a/138342
Good work putting the colour highlighting on the formulae. It does make them easier to follow for someone who is not a complete wizard with algebra. Without this little formatting touch I would find the article to be mostly a sea of symbols that I would likely skim over and still not properly understand.
Pardon my ignorance, I'm just wondering about some context, since the Kalman filter was invented in the 60s. Are Kalman filters still highly relevant, or are they (in practice and/or in theory) obsoleted by other techniques, such as general ML?
Yes, they are a staple of modern robotics and other fields. If the Kalman filter assumptions about the system hold (linear model, Gaussian noise), the Kalman filter is an optimal filter and you can't do better. There are also more complicated variants like the extended Kalman filter and the unscented Kalman that can do better when the assumptions of the Kalman filter are not accurate. It's also worth noting that the…
Pardon my ignorance, I'm just wondering about some context, since the Kalman filter was invented in the 60s. Are Kalman filters still highly relevant, or are they (in practice and/or in theory) obsoleted by other techniques, such as general ML?
Yes, they are a staple of modern robotics and other fields. If the Kalman filter assumptions about the system hold (linear model, Gaussian noise), the Kalman filter is an optimal filter and you can't do better. There are also more complicated variants like the extended Kalman filter and the unscented Kalman that can do better when the assumptions of the Kalman filter are not accurate. It's also worth noting that the…
Pardon my ignorance, I'm just wondering about some context, since the Kalman filter was invented in the 60s. Are Kalman filters still highly relevant, or are they (in practice and/or in theory) obsoleted by other techniques, such as general ML?
Beyond what the other replies are saying, the general pattern is also highly applicable. You can keep O(1) memory, update it on every new piece of unreliable data, and continually have a better understanding of what the truth is. Consider standard deviation. You can calculate the standard deviation of a stream of numbers without storing all of them, or knowing where the stream will end. 'The standard deviation so far…
Yes, you are right, but this is both a good example, and a bad example, because my old Casio calculator could do that too :)
Pardon my ignorance, I'm just wondering about some context, since the Kalman filter was invented in the 60s. Are Kalman filters still highly relevant, or are they (in practice and/or in theory) obsoleted by other techniques, such as general ML?
In those scenarios, once computational power allows, I think other approaches such as particle filters which can handle arbitrary distributions(e.g., multimodal) will start taking over. But we're not there yet(?).
[1]https://en.wikipedia.org/wiki/Kalman_filter#Optimality_and_p...
Earlier quoted context omitted.
Yes, they are a staple of modern robotics and other fields. If the Kalman filter assumptions about the system hold (linear model, Gaussian noise), the Kalman filter is an optimal filter and you can't do better. There are also more complicated variants like the extended Kalman filter and the unscented Kalman that can do better when the assumptions of the Kalman filter are not accurate. It's also worth noting that the…
In practical robotics, how often do the assumptions hold? Is it really usually true that the variables have only a linear relationship?