Emitter theory was a competing theory for the special theory of relativity, explaining the results of the Michelson-Morley experiment. Emitter theory keeps part of the principle of relativity but postulates the speed of light is c only relative to its source, instead of the invariance postulate. Thus, emitter theory combines electrodynamics and mechanics with a simple Newtonian theory which has no paradoxes in it.
The base of the theory is Maxwell's equations, which imply that light (and other electromagnetic waves) is a wave of the electromagnetic field. So it can directly be concluded that those waves are propagating relative to this field, which is at rest relative to the charge and the magnitude of the speed is c. Further, if the observer is moving, say at speed v towards this charge, then the speed of the light relative to observer is c+v.
In the 1960s, it became practical to test this theory. Particles called neutral pions were accelerated to near the speed of light in a particle accelerator, and the speed of the photons emitted by decay of those particles was measured. The speed was found to be exactly the same as that of light emitted by the decay of stationary particles.