and Ie = u.y (u is a vector). Then Ve is the coordinate of y where I acts, whereas Vm is the coordinate of x where Ie acts. We then look for F, G, a, b, c, u to optimize prediction of Ve. This looks like a Kalman filter, so we could possibly use EM algorithm to find the parameters.
The question is whether the problem is ill-posed. For example, it seems that part of the electrode could well be merged with the neuron. Perhaps we want to add constraints, such as sparsity. Or something about response time (eigenvalues of G are small?).
Similar to AEC, we could use a Kalman-like model for electrode compensation. The idea is we have two coupled systems:
and Ie = u.y (u is a vector). Then Ve is the coordinate of y where I acts, whereas Vm is the coordinate of x where Ie acts. We then look for F, G, a, b, c, u to optimize prediction of Ve. This looks like a Kalman filter, so we could possibly use EM algorithm to find the parameters.
The question is whether the problem is ill-posed. For example, it seems that part of the electrode could well be merged with the neuron. Perhaps we want to add constraints, such as sparsity. Or something about response time (eigenvalues of G are small?).