the 2 transformers are the sensor, by moving a core you change both inductance.
Orange signal is a phase detector, it indicate if it's on one side or the other
(0 => in phase,
1 => 180 degrees phaae shift).
Blue is a peak detector with reset, it indicate position of the core
(more amplitude = more displacement from center).
The sine wave is part of the detector.
A LVDT is a kind of linear displacement sensor, it as 3 coils and a moving core, the center coil generate a magnetic field and the 2 others coils act as the secondary. they are connected in opposite so only the difference between them appear at output. Wikipedia explain it relatively well.
