How to add a Gaussian noise signal with zero-mean in a given data set?

Question

I have a real-time velocity measurement data set in a excel (.xlsx) file. I want to add the Gaussian noise signal with zero mean in this real-time data to create three set of pseudo measurements. Could you please tell me how to do this in the excel sheet?

Answer 1

You can use the following formula to produce the white noise for one cell.

= 0.5*NORM.S.INV(RAND())

Where:

• 0.5 : can change to any non-zero number. It will control the range of the data.
• NORM.S.INV(RAND()) : produces a random number from -inf to inf, with mean zero and standard deviation 1

you can create a column for noise with this equation, and then just add the data.

If you want to be thorough you can

• copy and paste as values, so that the data does not change in every iteration.
• And also perform autocorrelation (on the noise column) to verify that the data indeed are GWN (autocorrelation for non-zero shifts/timelags is zero)