How Can I Separate Signal from Noise using corelation

Hi to All,
I am a new member of matlab, and have some questions about noise cancelation. I have 2 sequences, which names are x and y.

x= m + e ,vector length is N=730x1-------> yesterday datas
y= m' + e' ,vector length is N=730x1-------> today datas

e and e' are the thermal noise and these are uncorelated, but m and m' are the errors and these are corelated. So, I want the saparate the signal and obtain the m and m' values under cover of the corelation between two sequences.

How can I separate m and e values? Please give me some advice and instractions for this issue or Have you any advice about a method? I am a matlab user but I am just beginner degree.

Finally, corelation with 2 sequences are:
corr2(x,y)= 0.68
but I suppose that m and m' sequences corelation is over ~80%.

Thank you
Sincerely,