Fig. 2.

Maximum likelihood estimation of diffusion coefficient from a one step prediction process.$N({\widehat{\mathbf{x}}}_{k-1}^{+},{\mathbf{P}}_{k-1}^{+})$ and $N({\widehat{\mathbf{x}}}_k^{-},{\mathbf{P}}_k^{-})$ are 2D Gaussian distributions that characterize previous step posterior estimates and current step prior estimate, respectively. The translation of the means represents the deterministic feedback kicks while the increase in uncertainty is due to diffusion. The likelihood of detecting a photon at time τ_k is proportional to the overlap integral between the prior estimate and the excitation beam profile (red Gaussian centered at y_k )