Please don't mix up TDOA and goniometers...
Well, modern goniometers are some sort of time difference based, but with receiving antennas located within a half wavelength space, so there is no doubt that the antennas receive the same period of the wave. With such a short time difference, the hyperbola arm is practically a straight line, thus giving a bearing. A goniometer can give the direction of an unmodulated wave.
On the other way, real TDOA systems are based on receivers located many wavelengths away from each other. Even if they know perfectly their locations on earth, they cannot locate a pure carrier, because periods are not numbered. They need to detect the phase of some modulation with frequencies low enough to allow some time difference to be measured with some confidence.
Then there is a much more tricky problem when the waves are not received along the earth surface, but reflected by the ionosphere : the heigth of the reflecting point is not the same for each receiver in the system. Maybe in the middle of the day or in the middle of the night, with at least 3 receivers perfectly spaced around the unknown transmitter the system begins to give something next to perfect location.
I would like any further discussion to distinguish between those 3 cases defined above. Thanks.