How a Kalman filter works, in pictures (2015)
1–10 of 35 posts
Re: How a Kalman filter works, in pictures (2015)
#2Nice 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.
Re: How a Kalman filter works, in pictures (2015)
#3Nice 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.
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.
Re: How a Kalman filter works, in pictures (2015)
#4This is my favourite explanation of how a Kalman filter works
http://htmlpreview.github.io/?https://github.com/aguaviva/Ka...
Re: How a Kalman filter works, in pictures (2015)
#5Nice 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.
Also chiming in - I do control stuff in aerospace, Kalman Filters are the industry standard, have been so for decades, verging on low-tech now. Lots of interest in online particle filters in my little niche currently.
Re: How a Kalman filter works, in pictures (2015)
#6Needs a (2015), plus, recent discussion:
https://news.ycombinator.com/item?id=13449229 (213 points, Jan 21 2017, 32 comments)
Re: How a Kalman filter works, in pictures (2015)
#7It 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?
Re: How a Kalman filter works, in pictures (2015)
#8Nice 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.
What you're saying is definitely appropriate for finance. In general I find Kalman filters a little suspect where the underlying dynamics of the system can change over time, and when the physical process that gives rise to the dynamics isn't known.
Re: How a Kalman filter works, in pictures (2015)
#9It 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?
Yes it is a special case of Bayesian inference under the assumptions that the system is linear and that the priors and likelihoods are Gaussian.
Re: How a Kalman filter works, in pictures (2015)
#10It 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?
There is really no difference. You can frame the Kalman filter as a Bayesian posterior inference problem.
For example, for a stationary linear Gaussian model, you have a transition model of the form: z_t = Az_{t-1} + Bu_t + e where e ~ Gaussian(0,Q) and an observation model of the form: x_t = Cz_{t} + Du_t + d, where, d ~ Gaussian (0,R)
Since, z_t and x_t are both multivariate gaussians in this model, you can compute the posterior distribution on z_t's, which will also be a Gaussian. That is basically the Kalman filter.
As the writeup mentions, you might choose a non-Gaussian noise model, in which case the posterior distribution is not a Gaussian and then you employ something like a unscented Kalman filter or extended Kalman filter.