Let's say I have 10 noisy sensors measuring temperature vs time, and I want to fit a linear trend which is common across all 10 sensors. How do I do this? (I believe I shouldn't average the sensors' values at each time step and then fit a trend to the resulting average, since that doesn't seem to be the same thing, but let me know if it is). Here is an example of the data I want to fit,
%% Make some fake noisy measurements
timeStep = 1:100; % Time step
for iSensor = 1:10 % Loop through sensors
% Dimensions of Temperature: nSensors x nTime
Temperature(iSensor,:) = (5 + rand(1,1))*timeStep + ...% Add noise to the true slope of 5
(rand(1, length(timeStep))-0.5)*100 + 7; % Add noise to the true offset of 7
endfigure;plot(timeStep, Temperature); xlabel('Time'); ylabel('Temperature'); title('Noisy Temperature');
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