(1) University of Glasgow, Kelvin Building, Glasgow G12 8QQ, Scotland.
A method to determine the parameters of the proper time resolution model for $B \rightarrow h^+ h^{' -}$ channels at LHCb is described. The method uses only information which will be available from data. The resolution model is an important input to the fit which extracts the CKM angle $\gamma$ from the channels $B_d \rightarrow \pi^+ \pi^-$ and $B_s \rightarrow K^+ K^-$. It is found that with one nominal year of LHCb data, non-trivial constraints can be found for both the parameters of the resolution model, and the background to signal ratios.