right objective for optimizing PSD matrix

Question

In an estimation problem, I get that in order to make the system as sensitive as possible to the estimation parameters, I need to maximize $\Delta\theta^T(s(x)s(x)^T)\Delta\theta$, for every possible $\Delta\theta$, where my control variables are x (which change the signal $s$ and this way make the system more sensitive). This is not a convex optimization problem (the relationship between $x$ and $s(x)$ is pretty complex). What would be a good optimization target in this kind of problem? I was thinking about just summing all the values of the matrix $s(x)s(x)^T$, but I didn't find a proper justification for that and it also doesn't work too well. Does anyone have any suggestions as to what might be a good approach to try here? Thanks!