Adding a measured and known random noise to the model

Dear. all,

I am going to use Stan for the regression of my noisy spectral data (time-intensity) to a simple exponential function.
The signal starts from a certain value (I_0) at t = 0 and then decay until it fades in the pure noise.

I have a good knowledge of the random noise affecting the data and I know in advance that my random noise has a normal distribution and its corresponding standard deviation. I wonder how can include it in my model so that I improve the simulation?

Here is what I have as a model.

model {
  vector[N] mu = I_0 * exp( - (tau* x) );
  y ~ normal(mu, sigma); 

Simply give sigma a prior that reflects your knowledge of the typical magnitude of this noise.