Extracting common signal from 4 sets of observations I am working on a signal processing assignment where I need to find out one common time domain signal from 4 observation. The math is like this:

\begin{array}{lcl} y_1(t) &amp; = &amp; a_1(t)*x(t) + b_1(t) \\
                   y_2(t)&amp; = &amp;  a_1(t)*x(t) + b_1(t) \\
                   . &amp; &amp; \\ 
                   . &amp; &amp; \\
                   y_n(t) &amp; = &amp; a_n(t)*x(t) + b_n(t)\end{array}

where:

$n$ is up to 4 in my case, and $x(t)$ is my signal of interest which I want to extract from observed signals $y_n(t)$. 

What is the general direction I should take in doing background study for this kind of application?

Thanks,
K
Because you have a set of linear equations, why don't you set up a linear system (for each data point) and solve the system (using SVD for example) to obtain the solution?

Write in the the matrix form such as $Y=\beta X$ where $\beta$ are known and $X$ is unknown.