Numerically extracting the phase of a sinusoid without constant phase?

Question

I have experimental data that is proportional to $I(k) = cos(Ak + \phi(k))$, where the phase $\phi(k)$ is not constant for different values of $k$. How would I go about numerically calculating $\phi(k)$? If the phase where constant, a Fourier transform would solve my problem, but I am not sure how this would be done when the signal has a chirp. Would it be possible to fit $\phi(k)$ to coefficients from a Taylor series? Thanks!