Re: [Bayes++] Covariance matrix Q
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From: Michael S. <ma...@mi...> - 2005-09-14 09:07:48
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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 ___________________________________ |