bayesclasses-general

[Bayes++] Covariance matrix Q

[Nicola B. <nb...@es...>]

Hi,
I'm using a "Linear_predict_model" (but this is related also to other 
models...) for implementing an EKF and there's something I cannot understand. 
In the "bayesFlt.hpp" is reported that the vector "q" is the covariance of 
the state noise w(k)... but isn't such a covariance a symmetric matrix 
(normally called "Q")? So, if I wanna represent my covariance Q, how should I 
do?
Hope to get some feedback soon.
Cheers
Nicola

-- 
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Nicola Bellotto
University of Essex
Department of Computer Science
Wivenhoe Park
Colchester CO4 3SQ
United Kingdom

Room: 1N1.2.8
Tel. +44 (0)1206 874094
E-Mail: nb...@es...
URL: http://privatewww.essex.ac.uk/~nbello
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Re: [Bayes++] Covariance matrix Q

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

On Dienstag 13 September 2005 16:04, Nicola Bellotto wrote:
> Hi,
> I'm using a "Linear_predict_model" (but this is related also to other
> models...) for implementing an EKF and there's something I cannot
> understand. In the "bayesFlt.hpp" is reported that the vector "q" is the
> covariance of the state noise w(k)... but isn't such a covariance a
> symmetric matrix (normally called "Q")? So, if I wanna represent my
> covariance Q, how should I do?
> Hope to get some feedback soon.

G and q together represent the process (predict) noise. q is the noise=20
variance (a vector) and G is the noise coupling.
In this case the process model is=20
=A0=A0=A0=A0=A0=A0=A0=A0x(k+1) =3D f(x(k)) + G.q(k)
where q(k) in Gaussian white noise with variance q

This leads to a Kalman filter covariance update for the linear case
=A0=A0=A0=A0=A0=A0=A0=A0X(k+1) =3D F.X(k).F' + G.q.G'
This is equivalent to
=A0=A0=A0=A0=A0=A0=A0=A0X(k+1) =3D F.X(k).F' + Q
where Q =3D G.q.G'

The are a couple of reasons for expressing the process noise in this way.
a) For factorised filters (such as the UD_scheme) it is in the perfect form
b) The same noise is often additive to more then one element of the state. =
In=20
this case the size of q is less then x and G provides a physically easily=20
interpreted of how the elements of q effect x.

I hope this helps. I always ask. What are you using Bayes++ for?

Michael
=2D-=20
___________________________________
Michael Stevens Systems Engineering

34128 Kassel, Germany
Phone/Fax: +49 561 5218038

Navigation Systems, Estimation  and
                 Bayesian Filtering
    http://bayesclasses.sf.net
___________________________________

Re: [Bayes++] Covariance matrix Q

[Nicola B. <nb...@es...>]

On Wednesday 14 Sep 2005 10:07, Michael Stevens wrote:
> I hope this helps. I always ask. What are you using Bayes++ for?

Thanks for the answer. I thought it was like that indeed, but I wasn't 
completely sure.
I'm using Bayes++ for tracking people with a PTZ camera and a SICK laser 
mounted on a mobile robot (PeopleBot). I want to try different approaches of 
data fusion, starting from an EKF and then others filters, without having to 
rewrite the whole code every time. Bayes++ seems to be a good solution :)

May I give just a couple of suggestions:
- a link to this mailing-list on the main page of the website would increase 
the number of users;
- the same effect would have an improvement of the documentation. As I wrote 
in a previous email, I noticed the sources are rich of useful comments which 
unfortunately are not included in the doxygen documentation. Of course, I'm 
available if some help is needed, and so are probably other users.

Regards,

Nicola

-- 
------------------------------------------
Nicola Bellotto
University of Essex
Department of Computer Science
Wivenhoe Park
Colchester CO4 3SQ
United Kingdom

Room: 1N1.2.8
Tel. +44 (0)1206 874094
E-Mail: nb...@es...
URL: http://privatewww.essex.ac.uk/~nbello
------------------------------------------