Kalman

Hi,

I have just started off with Kalman implementation. My aim is to
estimate state vectors from the obseravtions (Z).

I have doubt regarding estimation of process noise variance matrix,
Quoting the state update eqtn

Xhat = XPred + K_G ( Z - H * Xpred )

Where K_G is the Kalman Gain

This eq follows the input model :

X_n = Phi * X_n-1  +  W_n

1) Am I right stating, the co-variance matrix Q = E[ W_n  * W_n
Trnspose] should follow the last term (P) of the prediction eq  if my
guess of Q was right. (i.e)

P =E[  (  K_G ( Z - H * Xpred )   )  *    (K_G ( Z - H * Xpred
)Trnspose  )]


2) If tht is true, can I update my Q value as a function of  P.

3) Can I use the same tactic to update my measurement noise variance
matrix from the estimate of 

( Z - H * Xpred) value.

"hurry" <hurrynarain@gmail.com> wrote in message
news:1164370322.076073.36470@f16g2000cwb.googlegroups.com...
> Hi,
>
> I have just started off with Kalman implementation. My aim is to
> estimate state vectors from the obseravtions (Z).
>
> I have doubt regarding estimation of process noise variance matrix,
> Quoting the state update eqtn
>
> Xhat = XPred + K_G ( Z - H * Xpred )
>
> Where K_G is the Kalman Gain
>
> This eq follows the input model :
>
> X_n = Phi * X_n-1  +  W_n
>
> 1) Am I right stating, the co-variance matrix Q = E[ W_n  * W_n
> Trnspose] should follow the last term (P) of the prediction eq  if my
> guess of Q was right. (i.e)
>
> P =E[  (  K_G ( Z - H * Xpred )   )  *    (K_G ( Z - H * Xpred
> )Trnspose  )]
>
>
> 2) If tht is true, can I update my Q value as a function of  P.
>
> 3) Can I use the same tactic to update my measurement noise variance
> matrix from the estimate of
>
> ( Z - H * Xpred) value.
>

You normally need to know what Q and R are apriori or make a good guess.

Tam



-- 
Posted via a free Usenet account from http://www.teranews.com

If instead of Q if we misjudge it as Q1 then is there suggestion for
that.

What I expected was, if this were true.

> > 1) Am I right stating, the co-variance matrix Q = E[ W_n  * W_n
> > Trnspose] should follow the last term (P) of the prediction eq (i.e)
> >
> > P =E[  (  K_G ( Z - H * Xpred )   )  *    (K_G ( Z - H * Xpred
> > )Trnspose  )]
> >   if my guess of Q was right.

then I can re-estimate the Q value.

Please suggest if the theory is inconsistent.

bye,
Hurry.



Heid the baw - goal!! wrote:
> "hurry" <hurrynarain@gmail.com> wrote in message
> news:1164370322.076073.36470@f16g2000cwb.googlegroups.com...
> > Hi,
> >
> > I have just started off with Kalman implementation. My aim is to
> > estimate state vectors from the obseravtions (Z).
> >
> > I have doubt regarding estimation of process noise variance matrix,
> > Quoting the state update eqtn
> >
> > Xhat = XPred + K_G ( Z - H * Xpred )
> >
> > Where K_G is the Kalman Gain
> >
> > This eq follows the input model :
> >
> > X_n = Phi * X_n-1  +  W_n
> >
> > 1) Am I right stating, the co-variance matrix Q = E[ W_n  * W_n
> > Trnspose] should follow the last term (P) of the prediction eq  if my
> > guess of Q was right. (i.e)
> >
> > P =E[  (  K_G ( Z - H * Xpred )   )  *    (K_G ( Z - H * Xpred
> > )Trnspose  )]
> >
> >
> > 2) If tht is true, can I update my Q value as a function of  P.
> >
> > 3) Can I use the same tactic to update my measurement noise variance
> > matrix from the estimate of
> >
> > ( Z - H * Xpred) value.
> >
>
> You normally need to know what Q and R are apriori or make a good guess.
>
> Tam
>
>
> 
> -- 
> Posted via a free Usenet account from http://www.teranews.com