Kalman Filtering: Gain Determination help

Hi Dave,

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.

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

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.

Dear Tang

What is the system and what is the model?

Kieran