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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 by sidr »

superjan wrote: post #7

It 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?

As all the other replies have mentioned, it is the same thing if you assume linear dynamics and Gaussian noise in the KF. Besides non-linearity and non-Gaussianity, there are a few other extensions that make super useful - one is that you can add an external obervable/controllable control signal. Thinking of this as an "independent" variable that you can observe or manipulate to get your desired observed value of y. This will take you into the realm of control systems engineering. Also, it's trivial (computationally) to let the dynamics be a changing function of time (i.e. instead of the fixed matrix A, let it be A(t)) - this allows you to model some pretty sophisticated dynamical systems.

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

#32

Post by nerpderp83 »

Symmetry wrote: post #21

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…

Couldn't you fuse this extra fact into a kalman filter?

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

#34

Post by Symmetry »

nerpderp83 wrote: post #32
Symmetry wrote: post #21

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…

Couldn't you fuse this extra fact into a kalman filter?

If you mean your GPS readings then yes you can and should. If you mean having multiple predictions of where you are then no, you would have to either run multiple Kalman filters explicitly or change things so much that it's no longer a Kalman filter.

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

#35

Post by vanderZwan »

rdtsc wrote: post #24
xchip wrote: post #4

This 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 th…

> "it's just Bayesian inference to update the posterior" makes it more confusing for me.

I do not know the jargon, but perhaps that is because this sentence does not give you any context for what "the posterior" is referring to?

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