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How a Kalman filter works, in pictures (2015)

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Re: How a Kalman filter works, in pictures (2015)

#31
post #18
post #4

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?

Kalman filters are never going to completely go away since they are optimal[1] under certain assumptions. But these assumptions are often not met so you have to start approximating (with EKF or UKF). 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] ht…

I agree both EKF and UKF are what you'll find in real world applications (because computing Jacobians is a pain!). I find the work of Jeffery Uhlmann both incredibly useful and hilarious (in that the "Unscented Kalman Filter" came from a stick of deodorant on a co-workers desk).

http://ethw.org/First-Hand:The_Unscented_Transform

Re: How a Kalman filter works, in pictures (2015)

#32
post #10
post #4

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…

Exactly, the UKF and EKF filters are very highly optimized for memory size and computation while dealing with noisy measurements non-linear and difficult to compute functions. They certainly don't require normally distributed errors.

That makes them applicable to a wide range of embedded applications. As generalized ML tools, I'm pretty doubtful unless you wanted to create something in hardware as a large set of coupled noisy state-spaces.

http://ethw.org/First-Hand:The_Unscented_Transform

Re: How a Kalman filter works, in pictures (2015)

#33
post #12
post #4

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…

KF has absolutely nothing to do with EM; no latent variables, no Jensen, no surrogate... nada.

Please stop saying that.

Re: How a Kalman filter works, in pictures (2015)

#34
post #12

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…

KF has absolutely nothing to do with EM; no latent variables, no Jensen, no surrogate... nada. Please stop saying that.

Can a KF be implemented in or explained as a RNN?
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