Regression between two noisy timeseries

Hello,

I'm currently searching for an appropriate method to solve this problem:

I have two timeseries which are simultaneously sampled and measure the same signal (in fact they are the real and imaginary part of the same timeseries) with additive noise.

The ratio between signal parts (the signal's phase angle) is known to be constant or (slowly) linear with time.
The noise is known to be independent between both timeseries and identically distributed. From plots I can see that positive and negative excursions occur equally often and medium values are more frequent than extreme values. So I assume a normal distribution for the noise.

My goal is to use this information to separate signal from noise.

Thanks in advance.

Regards   Matthias Burghardt
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