Figure 7.

Normalized distributions of D_MAP, $D_{\text{MSD}}^{\left(2\right)}$, and $D_{\text{MSD}}^{\left(3\right)}$ estimates obtained from 10⁵ trajectories with a confinement level u = 0.05 and a noise with standard deviation σ = 0.15 a.u. The trajectories were generated with a diffusivity $\tilde{D}=1$ a.u., L = 1 a.u., Δt = 0.05 a.u., and N = 100 steps. For such a level of confinement, realistic experimental parameter values would be D = 0.05 μm².s⁻¹, L = 100 nm, and Δt = 10 ms. The precision on the position would then be σ = 15 nm. This noise level corresponds to a relative uncertainty of 50% on the position of the particle with respect to the mean one-dimensional displacement $\sqrt{2D\Delta t}$. (MAP estimator, solid green line; $D_{\text{MSD}}^{\left(2\right)}$, dashed blue; and $D_{\text{MSD}}^{\left(3\right)}$, dashed purple.) A vertical line is positioned at the mean value of the distribution with the corresponding color. The distributions of $D_{\text{MSD}}^{\left(2\right)}$ and $D_{\text{MSD}}^{\left(3\right)}$ are shifted toward higher values of the diffusivity under the effect of noise.