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
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Michael Stevens Systems Engineering

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