/sci/ - Science & Math » Thread #13705059

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Anonymous Fri 01 Oct 16:15:55 2021 No.13705059 View Reply Original Report

Quoted By: >>13705562 >>13705579 >>13705611 >>13705827 >>13707336

What’s the point in Kalman filter if only already known dynamics can be used to model it? How could I discovered model dynamics?
Currently getting mad at this, I don’t want to stick on random walk!

Anonymous

Anonymous Fri 01 Oct 2021 17:53:15 No.13705308 Report

Quoted By:

Bumpity bump

Anonymous

Anonymous Fri 01 Oct 2021 19:41:29 No.13705562 Report

Quoted By: >>13705580 >>13705611

>>13705059
i'm studying the extended kalman filtern rn
you can also use the KF to estimate unknown parameters (if you don't know some of them)

the nonlinear filter is needed because to estimate an unknown parameter you need to put this parameter in your state vector: your model becomes nonlinear (if it wasn't already)

Anonymous

Anonymous Fri 01 Oct 2021 19:49:10 No.13705579 Report

Quoted By: >>13705817

>>13705059
not a single number to be found in there....

you mathematicians should really be paid the wage of a linguist if you think it about it, all you guys do is write letters

Anonymous

Anonymous Fri 01 Oct 2021 19:49:12 No.13705580 Report

Quoted By:

>>13705562
but idk if this was your question
the basic KF formulation (discrete observer) is obtained by minimizing the error estimate (z - C*x^)
if you just use the discrete KF you don't use the model
the model is used in the neighbouring KF

Anonymous

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Anonymous Fri 01 Oct 2021 20:05:41 No.13705611 Report

Quoted By: >>13707340

>>13705562
>>13705059
EKF in practise:
>one or more parameters of the model of your system may be unknown or uncertain
>make them ficticious state variables, and add them to the state vector
>these unknowns may or may not be constant (for instance the mass of a body is constant, while the equivalent stiffness of a gymbal isn't)
>these variables multiply the state matrix, i.e. the estimated unknowns influence the state propagation
>the point is, the KF aims at minimizing the estimation error of all the state variables, so given enough time you will have a good enough estimation of your unknown model variables
>grand finale: the KF is the solution of a convex optimum problem (quadratic cost and linearized model) so it's a stable system (an observer is a forced system)
>your variables won't shoot to infinity for Lyapunov 2nd

i hope /sci/ likes this, because i have a control exam in a few days

Anonymous

Anonymous Fri 01 Oct 2021 21:22:11 No.13705817 Report

Quoted By:

>>13705579
huuuhhhh....based?

Anonymous

Anonymous Fri 01 Oct 2021 21:26:19 No.13705827 Report

Quoted By:

>>13705059
What's your question here?
The EKF is the iterative (and thus lightweight) sequence of steps that does least squares error minimization w.r.t. assumed covariances (for both propagation and measurements, not any higher moments describing the statistics) given a model (which you linearize).

Anonymous

Anonymous Sat 02 Oct 2021 11:57:28 No.13707336 Report

Quoted By:

>>13705059
OP here. My question is that the propagation included in the state transition matrix is something you know from already existing model.
The usual Kalman filter example is about navigation tool where movement is already a well known physical models
x = x + v* dt (and so velocity etc)
Put it simple, the differential equations are well known. Without a transition matrix you can’t build anything useful unless you used something like a random walk.
It’s really hard to find a way to apply Kalman filter outside these limited examples or am I missing something?

Anonymous

Anonymous Sat 02 Oct 2021 11:58:48 No.13707340 Report

Quoted By:

>>13705611
>state matrix, i.e. the estimated unknowns influence the state propagation
How do you estimated the influence? How do you build the dynamics?

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