Re: [Bayes++] Bayes++ w/EKF and a non-linear equation: How to model?

[Michael S. <ma...@mi...>]

On Monday, 11. December 2006 17:24, Michael Simon wrote:
> Hello, everyone.
>
> I am attempting to use the Covariance_filter as an EKF for a non-linear
> model. However, I do not understand which type of model class to use,
> and how to specify the data for the models, even after looking at the
> Bayesian Filtering overview. I'm pretty sure I need to use a
> linrz_predict_model (or something like that) but beyond that...

'Linrz_predict_model' is definately what you want. 

> The main problem is that the elements of the f function I want to use
> for the model are exponential. It's non-linear, with noise, but no
> control (it's essentially 'the object I'm trying to predict is walking
> around randomly, but within the laws of physics') How do you specify
> that?

No-control is fine. Control inputs just make the implementation more complex!
I don't understand how you model can be 'exponential' when the physics are of 
something moving around at random. Or do you mean that you have exponentially 
correlated noise in you model?

> I've been looking at the Welch and Bishop introduction and trying 
> to compare back to Bayes++, but with no avail. I'm fairly sure I could
> use the libraries if my model was linear, but I don't quite see how to
> put the non-linearity in there.

I not sure of where you are stubling. Would it be possible to post the 
equations that model your system?

The Covariance_filter implements the EKF in a fairly standard form. It should 
be usable for any non-linear problem that can be solved by an EKF.
You need to turn the maths of you model into 3 things:
	f(x) : This should be easy once you have discrete time state equation of the 
system!
	Fx : Is the Jacobian of f(x)
	GqG' : This is often written as the symmetric matrix Q and is the covariance 
of the addative noise in you discrete state equations. Generally it is 
possible (an physically more meaningful) to write this a coupling matrix G 
and an noise variance q. If this is not possible then you can numerically 
obtain G and q from Q with the following:

        // Equivalent de-correlated form as GqG'
	Float rcond = Bayesian_filter_matrix::UdUfactor (Qtemp, Q);
	rclimit.check_PSD(rcond, "decorrelating Q not PSD");
	Bayesian_filter_matrix::UdUseperate (G, q, Qtemp);

Hope this helps you in the right direction,
	Michael

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