Estimating variables from noisy nonlinear equations

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I'm trying to solve for two scalar variables from a set of non-linear equations of the form:

$a_i\cos(x)+b_i\sin(x)=y$

Where $x,y$ are the variables, and $a_i,b_i$ with $i=1..n$ are noisy measurements. Obviously, if one ignores the noise, 2 equations are enough.

What approach can be used to minimize the effect of the noise using all the equations?