Amplitude Modulated Continuous Wave imaging lidar systems use the time-of-flight principle to determine the range to objects in a scene. Typical systems use modulated illumination of a scene and a modulated sensor or image intensifier. By changing the relative phase of the two modulation signals it is possible to measure the phase shift induced in the illumination signal, thus the range to the scene. In practical systems, the resultant correlation waveform contains harmonics that typically result in a non-linear range response. Nevertheless, these harmonics can be used to improve range precision. We model a waveform continuously variable in phase and intensity as a linear interpolation. By approximating the problem as a Maximum Likelihood problem, an analytic solution for the problem is derived that enables an entire range image to be processed in a few seconds. A substantial improvement in overall RMS error and precision over the standard Fourier phase analysis approach results.