At first glimpse, time averaging seems unlikely to help with CCV, when correlation times for protein levels can be longer than cell division times, reaching 48 hours in human cells [@sigal2006variability]. However, since gradient sensing bias from CCV depends on the locations of strong- and weak-signaling cells within the cluster, time averaging can be successful if it is over a time long enough for the cluster to re-arrange. This is true even if, as we initially assume, CCV biases $\Delta^i$ are time-independent. We expect gradient sensing error with time averaging, ${\ensuremath{\sigma_{\mathbf{g},T}}}^2$, will decrease by a factor of $T/\tau_r$ from ${\ensuremath{\sigma_{\mathbf{g},0}}}^2$, where $\tau_r$ is a correlation time related to cell positions ([Fig. ]{}\[fig:timeaverage\]). Is this true, and how should we define $\tau_r$?

Our earlier results suggest that CCV dominates the gradient sensing error. Ligand-receptor noise will also be even less relevant in the presence of time averaging, as the receptor relaxation time (seconds to minutes [@wang2007quantifying]) is much faster than that for cluster re-arrangement (tens of minutes or longer). We therefore completely neglect ligand-receptor binding fluctuations, allowing an analytical solution for the MLE estimator ${\ensuremath{\hat{{ {\mathbf g}}}}\xspace}$ ([*Methods*]{}, Appendix \[app:mle\]).

![. a) Schematic drawing of how cell-cell rearrangement can change bias 