Kalman filters are wonderful things and great for keeping track of where other things are in relation to yourself. But for localizing my robot I'd generally use a Particle Filter[1] instead to allow me to represent multiple hypothesis about where I am. For example if I see a doorway I know I'm going to be by one of the doorways on the corridor but I won't be able to tell which one without further observation. But if there's a source of absolute but imprecise location, like GPS, then a Kalman filter is a good choice again.
How a Kalman filter works, in pictures (2015)
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Re: How a Kalman filter works, in pictures (2015)
#22Nice pics for exam studies. But in industry Worse Is Better and Kalman Filters is ofent just the optimal way to remove noise you yourself added in your simulation. I've never seen any implementation use of Kalman filters where the covariance matrix is actually sound ... and I usually go with just lowpassfilters or moving averages.
I've used them in radar with an actual covariance matrix. I know some people use them in robotics but I've always relied on Particle Filters. And a woman I've been dating has used them in her econometrics work and I'm pretty sure she used an actual covariance matrix given the academic context.
Re: How a Kalman filter works, in pictures (2015)
#23Earlier quoted context omitted.
It's industry standard in aerospace, granted one usually uses the EKF with nonlinear dynamics so the covariance matrix is not estimated perfectly. That setup is also flexible enough to let you introduce of band measurements from the past but with the correct timestamp and correct.
It's kind of interesting that how particular fields chose to embrace certain particular methods; till I have worked with aerospace domain,I never had heard of the Kalman filter, whereas some of the newer and even more fundamental methods like wavelets and compressed sensing appear to have such low traction in Aerospace till now.
You probably know it by some other name. It is so classical its unlikely that one hasn't run into it in some form or the other. If you assume a hidden Markov model with Gaussian state transition and Gaussian output and work out the recursive update equation KF is what you will get. It might not have been call a Kalman filter. May be Weiner filter will ring a bell, under certain assumptions they become the same thing. If not Weiner filter, recursive least squares would surely ring a bell.
Re: How a Kalman filter works, in pictures (2015)
#24This is my favourite explanation of how a Kalman filter works http://htmlpreview.github.io/?https://github.com/aguaviva/Ka...
Agree. I like how it starts "if you had 2 sensors, here is how you could combine the measurements". Then goes on to say what if you only had 1 sensor, but you know the system evolves in a linear way, you can use that to make a prediction and treat it as the input from a second sensor.
That finally made me understand it better, and it's much shorter than most explanations without losing necessary details.
Also even though I took both ML and probability and statistics courses saying "it's just Bayesian inference to update the posterior" makes it more confusing for me.
Re: How a Kalman filter works, in pictures (2015)
#25This is my favourite explanation of how a Kalman filter works http://htmlpreview.github.io/?https://github.com/aguaviva/Ka...
Here’s a good HN discussion of that article: https://news.ycombinator.com/item?id=16575679 HN comments were quite informative too.
The main comment there I found made it more complicated for me. That is, saying "it's simple because it is like a bayesian thing". Sometimes raising the level of abstraction helps, but it didn't help me here because now I had to remember all the statistics stuff about bayesian inference.
Re: How a Kalman filter works, in pictures (2015)
#26Earlier quoted context omitted.
It's industry standard in aerospace, granted one usually uses the EKF with nonlinear dynamics so the covariance matrix is not estimated perfectly. That setup is also flexible enough to let you introduce of band measurements from the past but with the correct timestamp and correct.
It's kind of interesting that how particular fields chose to embrace certain particular methods; till I have worked with aerospace domain,I never had heard of the Kalman filter, whereas some of the newer and even more fundamental methods like wavelets and compressed sensing appear to have such low traction in Aerospace till now.
Kalman filters were invented for moon lander navigation in the Apollo program, so they had taken firm root especially in the days of limited data processing capability.
Re: How a Kalman filter works, in pictures (2015)
#27Hm, this is useful to know...there are a lot of conference posters and publications about using Kalman filters to interpret neural signals, particularly from Utah microarrays for the Gee-whiz brain-machine interfaces out of the BrainGate consortium. Not having an a background in EE, I was always fuzzy as to how it worked.
Re: How a Kalman filter works, in pictures (2015)
#28It looks very similar to Bayesian estimation. I wonder what is really the difference. Does any of you know, or have a link that explains it?
I wrote this [http://www.tina-vision.net/docs/memos/1996-002.pdf] many years ago which derives the Kalman filter from a state space perspective and then as chi-squared merit function. Certainly helped me as an engineer appreciate the statistical underpinnings.
Re: How a Kalman filter works, in pictures (2015)
#29Here’s a C++/Eigen example implementation of something very similar: https://github.com/google/detectorgraph/blob/master/examples...
With autogenerated block diagram and description here: https://google.github.io/detectorgraph/docs/html/robotlocali...
Re: How a Kalman filter works, in pictures (2015)
#30https://github.com/dougszumski/KalmanFilter
^ A very simple Python implementation of a Kalman Filter with Matplotlib for visualisation.