Calculating correlation of slightly out of sync data
At the moment I was thinking of possible filling the NAN values with the averages of the data points above and below. For example row 2 column r_person would become $3.05$.


The problem here is that the missing data point isn't necessarily associated with a timestamp that is the average of the timestamps above and below. If it were, the procedure you suggested would be equivalent to a linear interpolation, i.e. drawing a line between the points before and after the missing timestamp, and using that line to construct a local prediction for the missing observation. Which is what you should actually do instead. 

For example in the case above, the line for the point your trying to interpolate is $\text{r_person}(ts) = 3.0 +\frac{.1}{5}(ts-23)$, so $\text{r_person}(25) = 3.04$ (I think... doing this in my head right now).