I have 2 signals coming up for my system:
X1 = s + n1
X2 = s + n2
where s - is the useful signal, n1,n2- different noise
So I have the set of 2 equations with 3 variables. MathCad told me that it couldn't be solved. But when I open this signals I see inside of them something in common (the s part). So is it possible to find out this part?
There is no way to find exact value of signal s. you can estimate this signal if you knew statistical behavior of n1 and n2. for example, probability distribution of n1 and n2 or frequency bands of these noises.
In addition to what Hossein said, you can vectorize the problem, i.e.,
[x1 x2]T=[1 1]T*s+[n1 n2]T. Then maximum likelihood or least squares estimation may be used.
Using a Kalman filter with a known model you can find 's' from a single equation. You can check this paper for reference
A. Routray, A. K. Pradhan, and K. P. Rao, “A Novel Kalman Filter for Frequency Estimation of Distorted Signals in Power Systems,” IEEE Trans. Instrum. Meas., vol. 51, no. 3, pp. 469–479, Jun. 2002.
This depends on how do you want to characterize the signal s;
for each case there is an appropriate way; you can check :
- filtering operation
-source separation tools
- spectrum analysis methods and so;
See. Idea! You can get a rough decision.
Exempl: n1=5; n2=2; s=10; x1=s+n1; x2=s+n2;
p=[1 1 0; 1 0 1; 2 1 1; 0 1 -1; 0 -1 1] => inv(p'p) singular
p=[1 1 0.001; 1 0.001 1; 2 1 1; 0.001 1 -1; 0 -1 1] => inv(p'p) nonsingular !!!
C={p'*p); G=inv(C)
Y=[x1; x2; x1+x2; x1-x2; x2-x1]
B=p'*Y
A=G*B
A=[ 8.9989 5.9981 3.0011] Bingo!!! [10 5 2]
1 Recommendation
2nd Feb, 2016
Ihor Shelevytsky
Kryvyi Rih Economic Institut Kyiv National Economic University, Кryvyi Rih, Ukraine
If there is a priori information value s=0 or s=1 or s=-1 ....
Then two equations and two unknown values. From choosing the best options.
7th Jul, 2016
Daniil Smirnov
ITMO University
Dear Peter Husar,
I'm thinking of calculation this S value by calculating of entropy. like BSP (blind signal separation) method
Can you help by adding an answer?
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