Replace NaN's in timeseries with longterm median for specific dates

I have a multiyear timeseries with an hourly timestep that contains NaN's. I want to replace the NaN's with the median value for the specific hour, day and month calculated over all years. In the example below, I want to take the calculated median value in G and insert it into any matching hour with missing data in X. I have played around with ismember and vaious timetable options, but am stuck. Help appreciated!

% date range
t1 = datetime(2015,1,1,1,0,0);
t2 = datetime(2020,12,31,23,0,0);
t = (t1 : hours(1) : t2)';
%make up some data with random NaN's
X = rand(size(t));
idx = randsample(size(X,1),size(X,1)/3) ;
X(idx,:) = NaN;
%convert to timetable
T = timetable(t,X);
T.Month = month(T.t,'monthofyear');
T.Day = day(T.t,'dayofmonth');
T.Time = timeofday(T.t);
%calculate the median value of each hour in a year 
G = groupsummary(T,{'Month','Day','Time'},'median','X');

%Where there are NaN's in X, insert the median value from G at the matching
%Month, Day and Time in each year

Answer 1

[Luca Ferro]

Try to see if this helps, it's conceptually the same thing but with the mean

https://ch.mathworks.com/matlabcentral/answers/1894760-how-to-write-a-code-that-takes-the-mean-of-values-of-same-dates-of-other-years-and-replaces-the-miss?s_tid=srchtitle

[Elin Jacobs]

This works perfectly, thanks so much!