This is my first contribution to this forum
I have some problems to get regression to this equation:
my goal is to estimate the different a,b ans c knowing u and y.
What I know are u and y vectors over time. It would not be difficult to compute the different integrals.
My fist trial was to wright the linear system:
Like that, the problem seems to be ill posed, in fact the estimation of a, b and c do not converge (the algorithm is unstable). I tried Tikhonov regularization, improved the stability for some parameters but not for all:
I choosed Q and P ad-hoc.
I think the illness is due to:
- the choice of A and b: why should I wright u= and not = or y= or somethink else?
- The fact that in A there are some signals that are not independent:some signals are the integrals of others.
How can I regularize this ill problem? or how to wright it as a well posed problem? How to consider the integral relationship? rigorously.