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This article presents a novel phasor domain approach to determine the location of faults in non-homogeneous transmission lines. Best implementation requires synchronized voltage and current phasor measurements at all terminals of the transmission line. The overall non-homogeneous transmission line model with fault is established by systematically combining the generalized compact models of all homogeneous line sections. The location of the fault is introduced as an additional state of the overall model. The derivation procedure of the model is without further assumptions, resulting in full consideration of three phase line asymmetry as well as distributed parameters of non-homogeneous transmission lines. Afterwards, the location of the fault is identified using the state estimation algorithm. Extensive numerical experiments in a two-terminal and a multi-terminal non-homogeneous transmission line demonstrate that the method has higher accuracy than existing fault location methods, independent of fault types, locations and impedances. [ABSTRACT FROM AUTHOR]