Kalman Filtering: Gain Determination help

[Snip]

Have you initialized P properly? You must give it some initial estimate of
the variance of the process. The determination of R and Q is not so
important. The Kalman filter is very robust and you use R and Q for tuning,
so even when R and Q are wrong it should work.

HTH

Robert

Er, they're singular. :-)

Try:

eps = 0.01;

Q = [eps 0   0
     0   eps 0
     0   0   100];

R = [559.5 0   0
     0     eps 0
     0     0   eps];

and see what you get.

Ciao,

Peter K.

Peter K. wrote:


Is singularity of Q and R really a problem? Since they describe the
covariance of the state and the measurement it seems perfectly valid to
have zero main diagonals.

According to the theory, Q and R have only to be positive semidefinite,
which is the case here.

Maybe the system Dave is trying to estimate is not observable?

Regards

Robert

Peter K. wrote:

That was exactly the problem.  There were some other modifications
(i.e. corrections) I made to the code, but that was reason it was
giving me that error initially.  The results I get are excellent.
Thanks to all who provided insight.

On a side note, I'm wondering if I can compensate for non-vertical
flights (say it launches at a 25deg angle)...?  For non-vertical
flights, the accelerometer measurement will be higher than the actual
y-axis acceleration.  The exact equation is A_vertical = A_measured *
cos(angle), although I'm treating cos(angle) as a changing scalar.  I'm
toying with the idea of trying to estimate this scaler.

I was hoping to use the ratio of the change in velocity (i.e. the
change in velocity between time step k-1 to k) with the direct
accelerometer measurement.  The pressure sensor input will keep the
estimated velocity lower than the integrated acceleration.  So, could
this ratio be used as a 'virtual' sensor?  I believe my new 'A' matrix
becomes:

    A=[1               dt              X(4)*.5*dt^2    0
         0               1               X(4)*dt           0
         0               0               X(4)*1            0
         0               0               0                   1];

where:

X=[position
    velocity
    acceleration
    vertical_scalar];

And my scaler measurement (i.e. virtual sensor) is

s_meas(i)=(X(i,2)-X(i-1,2))/(a_meas(i-1)*dt);

I guess this is getting into Extended Kalman Filters?  Anyways, is it
possible for this method of estimating the non-vertical scalar work?

Thanks in advance for any insight!
Dave

I am doing some work using Kalman filter. The result is not right.
There is some steady-state error. Is this because of the accuracy of
the mathematical model? Thanks. Have a good day.

What is the system and what is the model?


Kieran