Suppose I have the following relation:
$$\phi \equiv ax \;(\mathrm{mod}\,2\pi)$$
where $a \in \mathbb{R}$ is a fixed unknown constant. The quantity $x$ is known and can be varied so that $\phi$ at different $x$ can be obtained. The $\phi$ are estimates of phase (have some confidence interval associated with them) and, as stated above, are known up to multiples of $2\pi$, so $\phi = \phi_p + n\,2\pi$ with $n \in \mathbb{Z}$, where $\phi_p$ is the principal value of $\phi$, taken either in the range $[0,2\pi)$ or $(-\pi, \pi]$. The $\phi$ are not necessarily obtained in the principal range (although they can of course be folded back as an additional step).
My question is the following: What is an efficient algorithm for unambigously estimating $a$?